Scilab Textbook Companion for Turbines, Compressors And Fans by S. M. Yahya1 Created by Ankur Garg M.TECH. Mechanical Engineering National Institute of Technology, Tiruchirappalli College Teacher Dr. M. Udayakumar Cross-Checked by Bhavani Bhavani Jalkrish May 30, 2016
1
Funded by a grant from the National Mission on Education through ICT, http://spoken-tutorial.org/NMEICT-Intro. This Textbook Companion and Scilab codes written in it can be downloaded from the ”Textbook Companion Project” section at the website http://scilab.in
Book Description Title: Turbines, Compressors And Fans Author: S. M. Yahya Publisher: Tata Mcgraw Hill Education Pvt. Ltd., New Delhi Edition: 4 Year: 2011 ISBN: 0-07-070702-2
1
Book Description Title: Turbines, Compressors And Fans Author: S. M. Yahya Publisher: Tata Mcgraw Hill Education Pvt. Ltd., New Delhi Edition: 4 Year: 2011 ISBN: 0-07-070702-2
1
Scilab numbering policy used in this document and the relation to the above book. Exa Example (Solved example) Eqn Equation (Particular equation of the above book) AP Appendix to Example(Scilab Code that is an Appednix to a particular
Example of the above book) For example, Exa 3.51 means solved example 3.51 of this book. Sec 2.3 means a scilab code whose theory is explained in Section 2.3 of the book.
2
Contents List of Scilab Codes
4
2 Thermodynamics
5
3 Gas Turbine Plants
13
4 Steam Turbine Plants
20
5 Combined Cycle Plants
27
6 Fluid dynamics
31
7 Dimensional Analysis and Performance Parameters
34
8 Flow Through Cascades
40
9 Axial Turbine Stages
47
11 Axial Compressor Stages
60
12 Centrifugal Compressor Stage
73
13 Radial Turbine Stages
81
14 Axial Fans and Propellers
87
15 Centrifugal Fans and Blowers
94
16 Wind Turbines
97
3
18 Miscellaneous Solved Problems in Turbomachines
4
99
List of Scilab Codes Exa 2.1 Exa 2.2 Exa 2.3 Exa 2.4 Exa 2.5 Exa 2.6 Exa 3.1 Exa 3.2 Exa 3.3 Exa 3.4 Exa 3.5 Exa 4.1 Exa 4.2 Exa 4.3 Exa 5.1 Exa 5.2 Exa 6.1 Exa 6.2 Exa 6.3 Exa 7.1 Exa 7.2 Exa 7.3 Exa 7.4 Exa 8.1 Exa 8.2 Exa 8.3 Exa 8.4 Exa 8.5
Calculation on a Diffuser . . . . . . . . . . . . . . . . Determining the infinitesimal stage efficiencies . . . . . Calculations on air compressor . . . . . . . . . . . . . compressor with same temperature rise . . . . . . . . Calculations on three stage gas turbine . . . . . . . . . Calculations on a Gas Turbine . . . . . . . . . . . . . Constant Pressure Gas Turbine Plant . . . . . . . . . Gas Turbine Plant with an exhaust HE . . . . . . . . ideal reheat cycle Gas Turbine Plant . . . . . . . . . . Calculations on Gas Turbine Plant . . . . . . . . . . . Calculations on Gas Turbine Plant . . . . . . . . . . Calculations on Steam Turbine Plant . . . . . . . . . Steam Turbine Plant for different reheat cycles . . . . Calculations on Steam Turbine Plant . . . . . . . . . . Calculation on combined cycle power plant . . . . . . combined gas and steam cycle power plant . . . . . . . inward flow radial turbine 32000rpm . . . . . . . . . . radially tipped Centrifugal blower 3000rpm . . . . . . Calculation on an axial flow fan . . . . . . . . . . . . . Calculation for the specific speed . . . . . . . . . . . . Calculating the discharge and specific speed . . . . . . Calculation on a small compressor . . . . . . . . . . . Calculation on design of a single stage gas turbine . . Calculation on a compressor cascade . . . . . . . . . . Calculation on a turbine blade row cascade . . . . . . Calculation on a compressor cascade . . . . . . . . . . Calculation on a blower type annular cascade tunnel . Calculation on a compressor type radial cascade tunnel 5
5 6 7 8 9 11 13 14 15 16 17 20 22 23 27 29 31 32 33 34 36 36 38 40 41 42 44 45
Exa 9.1 Exa 9.2 Exa 9.3 Exa 9.4 Exa 9.5 Exa 11.1 Exa 11.2 Exa 11.3 Exa 11.4 Exa 11.5 Exa 11.6 Exa 11.7 Exa 12.1 Exa 12.2 Exa 12.3 Exa 12.4 Exa 12.5 Exa 13.1 Exa 13.2 Exa 13.3 Exa 14.1 Exa 14.2 Exa 14.3 Exa 14.4 Exa 14.5 Exa 14.6 Exa 15.1 Exa 15.2 Exa 16.1 Exa 18.1 Exa 18.2 Exa 18.3 Exa 18.4 Exa 18.5 Exa 18.6 Exa 18.7 Exa 18.8 Exa 18.9
Calculation on multi stage turbine . . . . . . . Calculation on an axial turbine stage . . . . . . Calculation on an axial turbine stage . . . . . axial turbine stage 3000 rpm . . . . . . . . . . Calculation on a gas turbine stage . . . . . . . Calculation on an axial compressor stage . . . Calculation on an axial compressor stage . . . Calculation on an axial compressor stage . . . . Calculation on hub mean and tip sections . . . Forced Vortex axial compressor stage . . . . . General Swirl Distribution axial compressor . . flow and loading coefficients . . . . . . . . . . Calculation on a centrifugal compressor stage . Calculation on a centrifugal air compressor . . centrifugal compressor stage 17000 rpm . . . . Radially tipped blade impeller . . . . . . . . . Radially tipped blade impeller . . . . . . . . . ninety degree IFR turbine . . . . . . . . . . . . Mach Number and loss coefficient . . . . . . . . IFR turbine with Cantilever Blades . . . . . . . Axial fan stage 960 rpm . . . . . . . . . . . . . Downstream guide vanes . . . . . . . . . . . . . upstream guide vanes . . . . . . . . . . . . . . rotor and upstream guide blades . . . . . . . . DGVs and upstream guide vanes . . . . . . . . open propeller fan . . . . . . . . . . . . . . . . Centrifugal fan stage 1450 rpm . . . . . . . . . Centrifugal blower 3000 rpm . . . . . . . . . . Wind turbine output 100 kW . . . . . . . . . . Gas Turbine nozzle row . . . . . . . . . . . . . Steam Turbine nozzle . . . . . . . . . . . . . . Irreversible flow in nozzles . . . . . . . . . . . . Calculation on a Diffuser . . . . . . . . . . . . Calculation on a Draft Tube . . . . . . . . . . Calculations on a Gas Turbine . . . . . . . . . RHF of a three stage turbine . . . . . . . . . . Calculation on an air compressor . . . . . . . . Constant Pressure Gas Turbine Plant . . . . . 6
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
47 50 53 56 57 60 62 63 64 66 69 71 73 74 75 78 78 81 83 85 87 88 89 90 91 92 94 95 97 99 100 102 102 103 104 105 106 108
Exa 18.10 Exa 18.11 Exa 18.12 Exa 18.13 Exa 18.15 Exa 18.16 Exa 18.17 Exa 18.18 Exa 18.19 Exa 18.20 Exa 18.21 Exa 18.22 Exa 18.23 Exa 18.24 Exa 18.25 Exa 18.26 Exa 18.27 Exa 18.28 Exa 18.29 Exa 18.30 Exa 18.31 Exa 18.32 Exa 18.33 Exa 18.34 Exa 18.35 Exa 18.37 Exa 18.38 Exa 18.39 Exa 18.40 Exa 18.41 Exa 18.42 Exa 18.43 Exa 18.44 Exa 18.45 Exa 18.46 Exa 18.47 Exa 18.48 Exa 18.49
Calculation on combined cycle power plant . . . . Calculation on combined cycle power plant . . . . turbo prop Gas Turbine Engine . . . . . . . . . . . Turbojet Gas Turbine Engine . . . . . . . . . . . . Impulse Steam Turbine 3000 rpm . . . . . . . . . . large Centrifugal pump 1000 rpm . . . . . . . . . . three stage steam turbine . . . . . . . . . . . . . . Ljungstrom turbine 3600 rpm . . . . . . . . . . . . blower type wind tunnel . . . . . . . . . . . . . . . Calculation on an axial turbine cascade . . . . . . low reaction turbine stage . . . . . . . . . . . . . . Isentropic or Stage Terminal Velocity for Turbines axial compressor stage efficiency . . . . . . . . . . Calculation on an axial compressor cascade . . . . Calculation on two stage axial compressor . . . . . Calculation on an axial compressor cascade . . . . Isentropic Flow Centrifugal Air compressor . . . . centrifugal Air compressor . . . . . . . . . . . . . . Centrifugal compressor with vaned diffuser . . . . Inward Flow Radial Gas turbine . . . . . . . . . . Cantilever Type IFR turbine . . . . . . . . . . . . IFR turbine stage efficiency . . . . . . . . . . . . . Vertical Axis Crossflow Wind turbine . . . . . . . Counter Rotating fan . . . . . . . . . . . . . . . . Sirocco Radial fan 1440 rpm . . . . . . . . . . . . Calculation for the specific speed . . . . . . . . . . Kaplan turbine 70 rpm . . . . . . . . . . . . . . . Calculation for Pelton Wheel prototype . . . . . . Francis turbine 910 rpm . . . . . . . . . . . . . . . Calculation for the Pelton Wheel . . . . . . . . . . Calculation for Tidal Power Plant . . . . . . . . . Francis turbine 250 rpm . . . . . . . . . . . . . . . Pelton Wheel 360 rpm . . . . . . . . . . . . . . . . Kaplan turbine 120 rpm . . . . . . . . . . . . . . . Fourneyron Turbine 360 rpm . . . . . . . . . . . . Crossflow Radial Hydro turbine . . . . . . . . . . . Calculation on a Draft Tube . . . . . . . . . . . . Centrifugal pump 890 kW . . . . . . . . . . . . . . 7
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
110 112 114 115 117 119 120 121 122 124 125 127 128 128 129 131 132 134 135 137 139 140 141 142 143 144 146 147 147 148 149 150 151 153 154 155 156 157
Exa 18.50 Exa 18.51 Exa 18.52 Exa 18.53 Exa 18.54 Exa 18.55
Centrifugal pump 1500 rpm . . . . . . . . Axial pump 360 rpm . . . . . . . . . . . . NPSH for Centrifugal pump . . . . . . . . NPSH and Thoma Cavitation Coefficient Maximum Height of Hydro Turbines . . . Propeller Thrust and Power . . . . . . . .
8
. . . . . .
. . . . . .
. . . . . .
. . . . . .
. . . . . .
. . . . . .
. . . . . .
158 159 160 162 163 164
Chapter 2 Thermodynamics
Scilab code Exa 2.1 Calculation on a Diffuser
1 2 3 4 5 6 7
/ / s c i l a b Code Exa 2 . 1 C a l c u l a t i o n on a D i f f u s e r
p 1 = 8 0 0 ; / / I n i t i a l P r e s s u r e i n kPa T 1 = 5 4 0 ; / / I n i t i a l T e m p er a t u re i n K p 2 = 5 8 0 ; // F i na l P r es s u r e i n kPa gamma =1.4; // S p e c i f i c Heat R at io c p = 1 0 0 5 ; // S p e c i f i c Heat a t C o ns ta nt P r es s u r e i n J
/(kgK) R = 0 . 2 8 7 ; // U n i v e r s a l Gas C on st an t i n kJ /kgK g = 9 . 8 1 ; / / G r a v i t a t i o n a l a c c e l e r a t i o n i n m/ s ˆ 2 s g = 1 3 . 6 ; // S p e c i f i c G ra vi ty o f m er cu r y n = 0 . 9 5 ; // E f f i c i e n c y i n % A R = 4 ; // Area R at io o f D i f f u s e r d e l p = ( 3 6 7 ) * ( 1 e - 3 ) * ( g ) * ( s g ) ; // T ot al P r e s su r e L os s A cr os s t he D i f f u s e r i n kPa p r = p 1 / p 2 ; // P r e ss u r e R at io
8 9 10 11 12 13
14 15 16 17
T 2 s = T 1 / ( p r ^ ( ( gamma - 1 ) / gamma ) ) ; T2=T1-(n*(T1-T2s)); c2 = sqrt ( 2 * c p * ( T 1 - T 2 ) ) ;
9
ro2=p2/(R*T2); c3=c2/AR; m=0.5*1e-3*ro2*((c2^2)-(c3^2)); n_D=1-(delp/m); disp ( ”%” , n _ D * 1 e 2 , ” E f f i c i e n c y o f t h e p3=(p2+n_D*m)*1e-2; disp ( ”m/s” , c 2 , ” t h e v e l o c i t y o f a i r a t is”) 25 disp ( ”m/s” , c 3 , ” th e v e l o c i t y o f a i r a t is”) 26 disp ( ” b a r ” , p 3 , ” s t a t i c p r e s s u r e a t t h e is”) 18 19 20 21 22 23 24
d i f f u s er i s ”) d i f f u s er entry d i f fu s e r e xi t d i f f u s e r e x it
Scilab code Exa 2.2 Determining the infinitesimal stage efficiencies
1 / / Exa 2 . 2 D e te r mi ni ng t h e i n f i n i t e s i m a l
s ta g e
efficiencies 2 p1=1.02; / / I n i t i a l P r e s s u r e i n b a r 3 T1=300; / / I n i t i a l T e m p er a t u re i n K 4 5 6 7 8 9 10
// part (a) T 2 = 3 1 5 ; // F i n a l T em pe ra tu re i n K gamma =1.4; // S p e c i f i c Heat R at io g = 9 . 8 1 ; / / G r a v i t a t i o n a l a c c e l e r a t i o n i n m/ s ˆ 2 s g = 1 ; // S p e c i f i c G r a v i t y o f a i r d e l p = ( 1 5 0 0 ) * ( 0 . 0 0 1 ) * ( g ) * ( s g ) ; // T ot al P r e s su r e L os s A cr os s t he D i f f u s e r i n kPa
11 12 13 14 15 16
p2=p1+(0.01*delp); p r = p 2 / p 1 ; // P r e ss u r e R at io T 2 s = T 1 * ( p r ^ ( ( gamma - 1 ) / gamma ) ) ; n _ c = ( T 2 s - T 1 ) / ( T 2 - T 1 ) ; // E f f i c i e n c y i n % n _ p = ( ( gamma - 1 ) / gamma ) * ( ( log ( p 2 / p 1 ) ) / ( log ( T 2 / T 1 ) ) ) ; disp ( ”%” , n _ c * 1 0 0 , ” ( a ) E f f i c i e n c y o f t he c om pr es so r
10
is”) 17 disp ( ”%” , n _ p * 1 0 0 , ” and i n f i n i t e s i m a l s t a g e E f fi c ie n cy or p ol yt ro pi c e f f i c i e n c y o f the c o mp r e ss o r i s ” ) 18 19 / / p ar t ( b ) D et er mi ni ng t he
i n f i n i t e s i m a l s t a ge
efficiency 20 21 22 23 24 25 26
p 2 _ b = 2 . 5 ; // F i n a l p r e s s u r e i n b ar n _ b = 0 . 7 5 ; // E f f i c i e n c y p r _ b = p 2 _ b / p 1 ; // P r e s su r e R at io T 2 s _ b = T 1 * ( p r _ b ^ ( ( gamma - 1 ) / gamma ) ) ; T2_b=T1+((T2s_b-T1)/n_b); n _ p _ b = ( ( gamma - 1 ) / gamma ) * ( ( log ( p 2 _ b / p 1 ) ) / ( log ( T 2 _ b / T 1 ))); 27 disp ( ”%” , n _ p _ b * 1 0 0 , ” ( b ) i n f i n i t e s i m a l s t ag e
E f fi c ie n cy or p ol yt ro pi c e f f i c i e n c y o f the c o mp r e ss o r i s ” )
Scilab code Exa 2.3 Calculations on air compressor
1 2 3 4 5 6 7 8 9 10
/ / s c i l a b Code Exa 2 . 3 C a l c u l a t i o n on a c om pr es so r p1=1.0; / / I n i t i a l P r e s s u r e i n b a r t 1 = 4 0 ; / / I n i t i a l T e mp e ra t ur e i n d e g r e e C T 1 = t 1 + 2 7 3 ; // i n K el vi n s = 8 ; // number o f s t a g e s m = 5 0 ; // mass f l ow r a t e t hr ou gh t he c om pr es so r i n kg /s p r = 1 . 3 5 ; // e q u a l P r es s u r e R at io i n e a ch s t a ge o p r = p r ^ s ; // O v er a l l P r es s u r e R at io gamma =1.4; // S p e c i f i c Heat R at io c p = 1 . 0 0 5 ; // S p e c i f i c Heat a t C on st a nt P r es s u r e i n kJ/(kgK) 11
11 n = 0 . 8 2 ; // O v e r a l l E f f i c i e n c y 12 13 // p ar t ( a ) D e te r m in in g s t a t e o f a i r a t t h e
c om p re ss o r e x i t 14 15 16 17 18 19 20
p9=opr*p1; d e l T c = T 1 * ( o p r ^ ( (gamma - 1 ) / gamma ) - 1 ) / n ; T9=T1+delTc; disp ( ” b a r ” , p 9 , ” ( a ) E xi t P r e ss u r e i s ” ) disp ( ”K” , T 9 , ” and E x i t T em pe ra tu re i s ” )
// p ar t ( b ) D et er mi ni ng t he p o l y t r o p i c o r s m al l s t a g e efficiency
21 n _ p = ( ( gamma - 1 ) / gamma ) * ( ( log ( p 9 / p 1 ) ) / ( log ( T 9 / T 1 ) ) ) ; 22 disp ( ”%” , n _ p * 1 0 0 , ” ( b ) s m a l l s t a g e E f f i c i e n c y o r p o l y t r o p i c e f f i c i e n c y o f t he c om pr es so r i s ” ) 23 24 // p ar t ( c ) D et er mi ni ng e f f i c i e n c y o f e ac h s t a g e 25 n _ s t = ( p r ^ ( ( gamma - 1 ) / gamma ) - 1 ) / ( p r ^ ( ( ( gamma - 1 ) / gamma ) /n_p)-1); 26 disp ( ”%” , n _ s t * 1 0 0 , ” ( c ) E f f i c i e n c y o f e ac h s t a g e i s ” ) 27 28 / / p a rt ( d ) D et er mi ni ng power r e q u i r e d t o d r i v e t he
compressor 29 n _ d = 0 . 9 ; // O v e r a l l e f f i c i e n c y o f t h e d r i v e 30 P = m * c p * d e l T c / n _ d ; 31 disp ( ”MW” , P / 1 e 3 , ” ( d ) Power r e q u i r e d t o d r i v e t he c o mp r e ss o r i s ” )
Scilab code Exa 2.4 compressor with same temperature rise
1 / / Exa 2 . 4 c o mp re s so r w it h same t em p er a tu r e r i s e 2 3 p1=1.0; / / I n i t i a l P r e s s u r e i n b a r
12
4 5 6 7 8 9 10 11 12 13 14 15
t 1 = 4 0 ; / / I n i t i a l T e mp e ra t ur e i n d e g r e e C T 1 = t 1 + 2 7 3 ; // i n K el vi n s = 8 ; // number o f s t a g e s pr=1.35; o p r = p r ^ s ; // O v er a l l P r es s u r e R at io n = 0 . 8 2 ; // O v e r a l l E f f i c i e n c y p9=opr*p1; gamma =1.4; d e l T c = ( T 1 * ( o p r ^ ( ( gamma - 1 ) / gamma ) - 1 ) / n ) ; delTi=delTc/s; T9=T1+delTc; n _ p = ( ( gamma - 1 ) / gamma ) * ( ( log ( p 9 / p 1 ) ) / ( log ( T 9 / T 1 ) ) ) ;
// s ma ll s t a g e E f f i c i e n c y o r p o l y t r o p i c efficiency 16 m = 8 ; 17 T ( 1 ) = T 1 ; 18 for i = 1 : m 19 T(i+1)=T(i)+delTi; p r ( i ) = ( 1 + ( d e l T i / T ( i ) ) ) ^ ( n _ p / ( (gamma - 1 ) / gamma ) ) ; 20 21 n _ s t ( i ) = ( p r ( i ) ^ ( (gamma - 1 ) / gamma ) - 1 ) / ( p r ( i ) ^ ( ( ( gamma - 1 ) / gamma ) / n _ p ) - 1 ) ; 22 disp ( T ( i ) , ”T i s ” ) ; 23 disp ( p r ( i ) , ” p r e s s u r e r a t i o i s ” ) 24 disp ( n _ s t ( i ) ,” e f f i c i e n c y i s ” ) 25 end
Scilab code Exa 2.5 Calculations on three stage gas turbine
1 / / s c i l a b Code Exa 2 . 5 C a l c u l a t i o n on t h r e e s t a ge
g as t u r bi n e 2 3 p1=1.0; / / I n i t i a l 4 gamma =1.4;
Pressure in bar
13
5 6 7 8 9 10 11 12 13
T 1 = 1 5 0 0 ; / / I n i t i a l T e m p er a t u r e i n K s = 3 ; // number o f s t a g e s o p r = 1 1 ; // O v er a l l P r es s ur e R at io
15 16 17 18
// p ar t ( a ) D et er mi ni ng p r e s s u r e r a t i o o f e ac h s t a g e p r = o p r ^ ( 1 / s ) ; // e q u a l P r es s u r e R at io i n e a ch s t a ge disp ( p r , ” ( a ) P r e s s u r e r a t i o o f e a c h s t a g e i s ” )
// p a rt ( b ) D et er mi ni ng t he p o l y t r o p i c o r s m a ll s t a g e efficiency 14 n _ o = 0 . 8 8 ; // O v e r a l l E f f i c i e n c y
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
d e l T = T 1 * ( 1 - o p r ^ ( - ( ( gamma - 1 ) / gamma ) ) ) * n _ o ; T2=T1-delT; n _ p = ( log ( T 1 / T 2 ) ) / ( ( ( gamma - 1 ) / gamma ) *( log ( o p r ) ) ) ; disp ( ”%” , n _ p * 1 0 0 , ” ( b ) s m a l l s t a g e E f f i c i e n c y o r p o ly tr o pi c e f f i c i e n c y o f the t ur bi ne i s ” )
/ / p a r t ( c ) D e te r mi n in g mass f l o w r a t e P = 3 0 0 0 0 ; // Power o u tp ut o f t h e T ur bi ne i n kW n _ d = 0 . 9 1 ; // O v e ra l l e f f i c i e n c y o f t h e d r i v e c p = 1 . 0 0 5 ; // S p e c i f i c Heat a t C on st a nt P r es s u r e i n kJ/(kgK) m=P/(cp*delT*n_d); disp ( ” k g / s ” ,m , ” ( c ) m ass f l o w r a t e
is ”)
/ / p ar t ( d ) D et er mi ni ng e f f i c i e n c y o f e ac h s t a g e n _ s t = ( 1 - p r ^ ( n _ p * ( - ( (gamma - 1 ) / gamma ) ) ) ) / ( 1 - p r ^ ( - ( ( gamma - 1 ) / gamma ) ) ) ; disp ( ”%” , n _ s t * 1 0 0 , ” ( d ) E f f i c i e n c y o f e a c h s t a g e i s ” ) d=3; T(1)=T1; for i = 1 : d d e l T ( i ) = T ( i ) * ( 1 - p r ^ ( n _ p * ( - ( (gamma - 1 ) / gamma ) ) ) ) ; T(i+1)=T(i)-delT(i); P(i)=m*cp*delT(i); printf ( ” \n P(%d)=%f MW” , i , P ( i ) * 1 e - 3 ) end
14
Scilab code Exa 2.6 Calculations on a Gas Turbine
1 2 3 4 5 6 7 8 9
/ / s c i l a b C o d e Ex E x a 2 . 6 c a l c u l a t i o n o n a g as as t u r b i n e
funcprot ( 0 ) ; p 1 = 5 ; // / / I n l e t P r e ss ss ur e i n bar / / E xi xi t P r e s s u r e i n b a r p 2 = 1 . 2 ; // T 1 = 5 0 0 ; / / I n i t i a l T e m p er e r a t u re re i n K gamma =1.4; m = 2 0 ; // / / m a s s f l o w r a t e o f t he he g a s i n k g / s / / S p e c i f i c H e a t a t C on o n st s t a nt n t P r es es s ur e i n c p = 1 . 0 0 5 ; //
kJ/(kgK) 10 n _ T = 0 . 9 ; // // O v e r a l l E f f i c i e n c y 11 p r = p 1 / p 2 ; // / / P r e ss s s u r e R at a t io io 12 / / p a r t ( a ) T 2 s = T 1 / ( p r ^ ( ( gamma gamma - 1 ) / gamma ) ) ; T2=T1-(n_T*(T1-T2s)); n_p=( log (T1/T2))/( log (T1/T2s)); disp ( ”%” ”%” , n _ p * 1 0 0 , ” ( a ) s m a l l s t a g e E f f i c i e n c y o r p o l y t r o p i c e f f i c i e n c y o f t he h e e xp x p an a n si s i on on i s ” ) 17 P = m * c p * ( T 1 - T 2 ) ; 18 disp ( ”kW” , P , ” an and Power d e v e l o p e d i s ” ) 19 20 / / p a r t ( b ) 21 A R = 2 . 5 ; // / / A r e a R at a t io io o f D i f f u s e r 22 R = 0 . 2 8 7 ; // / / U n i v e r s a l G a s C on o n st s t an a n t i n k J /k / kg K 23 p 3 = 1 . 2 ; // / / E x i t P re r e ss ss ur e f o r d i f f u s e r i n bar 24 c 2 = 7 5 ; // / / V e l o c i t y o f g a s a t t u r b i n e e x i t i n m/ s 25 c 3 = c 2 / A R ; 26 n _ d = 0 . 7 ; // // E f f i c i e n c y o f t h e d i f f u s e r 27 r o 2 = p 2 / ( R * T 2 ) ; 28 d e l p = n _ d * ( 0 . 5 * 0 . 0 0 1 * r o 2 * ( ( c 2 ^ 2 ) - ( c 3 ^ 2 ) ) ) ; / / d e l p =p =p 3 13 14 15 16
15
−p 2 d 29 disp ( ”mm W.G. ” , d e l p * 1 0 0 0 0 0 / 9 . 8 1 , ” ( b ) s t a t i c p r e s s u r e a cr os s the d i f f u s e r i s ”) 30 31 32 33 34 35
p2d=p3-delp; prd=p1/p2d; T 2 s d = T 1 / ( p r d ^ ( ( gamma gamma - 1 ) / gamma ) ) ; T2d=T1-(n_T*(T1-T2sd)); Pd=m*cp*(T1-T2d); a n d I n c r e a s e i n t he h e p o w e r o ut u t pu pu t o f disp ( ”kW” , P d - P , ” an t he h e t u r bi bi n e i s ” )
36 37 disp ( ” Co Comment :
E r r o r i n T ex ex tb t b oo o o k , A ns n s we w e rs r s v a r y d ue ue to Rou ound nd− rs ” ) − o f f E r r o rs
16
Chapter 3 Gas Turbine Plants
Scilab code Exa 3.1 Constant Pressure Gas Turbine Plant
1 / / s c i l a b C o d e E xa xa 3 . 1 C on o n st s t an a n t P r e s su s u r e G a s T ur u r bi b i ne ne
Plant 2 3 4 5 6 7 8 9 10
M inimum T e mp m p e ra r a t ur ur e i n d e g r e e C t 1 = 5 0 ; / / Mi T 1 = t 1 + 2 7 3 ; // / / i n K el e l vi vi n Maximum T e m p e r a tu tu r e i n d e g r e e C t 3 = 9 5 0 ; / / Ma / / i n K el e l vi vi n T 3 = t 3 + 2 7 3 ; // n _ c = 0 . 8 2 ; / / C om o m pr p r es e s so so r E f f i c i e n c y b i ne ne E f f i c i e n c y n _ t = 0 . 8 7 ; / / T u r bi gamma =1.4; // / / S p e c i f i c H e a t R at a t io io / / S p e c i f i c H e a t a t C on o n st s t a nt n t P r es es s ur e i n c p = 1 . 0 0 5 ; // kJ/(kgK)
11 b e e t a = T 3 / T 1 ; 12 a l p h a = b e e t a * n _ c * n _ t ; 13 T _ o p t = sqrt ( a l p h a ) ; / / F or o r maximum p o we w e r o u t p ut ut , t h e
t em e m pe p e ra r a tu t u re r e r a t i o s i n t he h e t u r bi b i n e a n d c om o m pr p r es e s so so r 14 15 / / p ar a r t ( a ) D et e t er e r mi m i ni n i ng ng p r e s s u r e
a n d c o m p r e ss ss o r 17
r a t i o o f t he he t u r b i n e
16 p r = T _ o p t ^ ( gamma /( gamma - 1 ) ) ; 17 disp ( p r , ” ( a ) P r e s su r e R at io i s ” ) 18 19 / / p a r t ( b ) D e t er m i n in g maximum p ow er o u tp u t p e r u n i t
f lo w r a t e 20 w p _ m a x = c p * T 1 * ( ( T _ o p t - 1 ) ^ 2 ) / n _ c ; 21 disp ( ”kW/( kg/ s ) ” ,wp_max , ” ( b ) maximum p o we r o u t p u t p e r u n i t f lo w r a t e i s ” ) 22 23 // p a rt ( c ) D et er mi ni ng t he rm al e f f i c i e n c y o f t he
p l a n t f o r maximum p ow er o u t p u t 24 n_th=( T_opt -1)^2/(( beeta -1)*n_c -(T_opt -1)); 25 disp ( ”%” , n _ t h * 1 0 0 , ” ( c ) t he rm al e f f i c i e n c y o f t he p l a n t f o r maximum p ow er o u t p u t i s ” )
Scilab code Exa 3.2 Gas Turbine Plant with an exhaust HE
1 / / s c i l a b Code Exa 3 . 2 Gas T ur bi ne P la nt w it h an
e x h a u s t HE 2 T1=300; / / Minimum 3 funcprot ( 0 ) ; 4 p r = 1 0 ; // p r e s s u r e
c y c l e T em pe ra tu re i n K e l v i n r a t i o o f t h e t u r b in e and
compressor 5 T3=1500; / / Maximum c y c l e T e mp e ra t ur e i n K e l v i n 6 m = 1 0 ; // mass f l ow r a t e t hr ou gh t he t u r bi n e and c om p re ss o r i n kg / s 7 e ( 1 ) = 0 . 8 ; // t he rm al r a t i o o f t he h ea t e xc ha ng er 8 9 10 11 12
e(2)=1; n _ c = 0 . 8 2 ; / / C om pr es so r E f f i c i e n c y n _ t = 0 . 8 5 ; / / T u r bi n e E f f i c i e n c y gamma =1.4; // S p e c i f i c Heat R at io c p = 1 . 0 0 5 ; // S p e c i f i c Heat a t C on st a nt P r es s u r e i n
kJ/(kgK) 18
13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
beeta=T3/T1; T 2 s = T 1 * ( p r ^ ( ( gamma - 1 ) / gamma ) ) ; T2=T1+((T2s-T1)/n_c); T 4 s = T 3 * ( p r ^ ( - ( ( gamma - 1 ) / gamma ) ) ) ; T4=T3-((T3-T4s)*n_t);
for i = 1 : 2 T5=T2+e(i)*(T4-T2); T6=T4-(T5-T2); Q_s=cp*(T3-T5); Q_r=cp*(T6-T1);
/ / p a r t ( a ) D e te rm i ni n g p ower d e v el o p e d w_p=Q_s-Q_r; P=m*w_p; printf ( ” f o r e f f e c t i v e n e s s =%f , \n ( a ) t h e p ow er d e v e l o p e d i s %f kW” , e ( i ) , P )
28 29 / / p ar t ( b ) D et er mi ni ng t he rm al
e f f i c i e n c y o f t he
plant 30 n _ t h = 1 - ( Q _ r / Q _ s ) ; 31 disp ( ”%” , n _ t h * 1 0 0 , ” ( b ) t h er m al e f f i c i e n c y o f t he p l an t i s ” ) 32 end 33 34 / / p a r t ( c ) D e t e r m i n i n g e f f i c i e n c i e s o f t h e i d e a l
J o u l es c y c l e 35 n _ J o u l e = 1 - ( p r ^ ( (gamma - 1 ) / gamma ) / b e e t a ) ; 36 disp ( ”%” , n _ J o u l e * 1 0 0 , ” ( c ) e f f i c i e n c y o f t h e i d e a l J o u le s c y c l e w it h p e r f e c t h ea t e xc ha ng e i s ” ) 37 n _ C a r n o t = 1 - ( T 1 / T 3 ) ; 38 disp ( ”%” , n _ C a r n o t * 1 0 0 , ” and t he Ca rn ot c y c l e e f f i c i e n c y i s ”)
19
Scilab code Exa 3.3 ideal reheat cycle Gas Turbine Plant
1 / / s c i l a b Code Exa 3 . 3 i d e a l
r e h e a t c y c l e g as
turbine 2 T1=300; / / Minimum c y c l e T em pe ra tu re i n K e l v i n 3 r = 2 5 ; // p r e s s u r e r a t i o o f t he t u rb i ne and compressor 4 gamma =1.4; 5 T3=1500; / / Maximum c y c l e T e mp e ra t ur e i n K e l v i n 6 c p = 1 . 0 0 5 ; // S p e c i f i c Heat a t C on st a nt P r es s u r e i n
kJ/(kgK) 7 8 9 10 11
beeta=T3/T1; n =( gamma - 1 ) / gamma ; t=(r^n); d = 1 / sqrt ( t ) ;
12 13 14 15
// p a rt ( a ) D et er mi ni ng mass f l o w r a t e t hr ou gh t he t u r b i n e and c o mp r e ss o r c=2*beeta*[1-d]; wp_max=cp*T1*(c+1-t); m=1000/wp_max; disp ( ” k g / s ” ,m , ” ( a ) m ass f l ow r a t e t hr ou gh t he t u r b i n e and c om p re ss o r i s ” )
16 17 / / p ar t ( b ) D et er mi ni ng t he rm al
e f f i c i e n c y o f t he
plant 18 n _ t h = ( c + 1 - t ) / ( 2 * b e e t a - t - ( b e e t a /sqrt ( t ) ) ) ; 19 disp ( ”%” , n _ t h * 1 0 0 , ” ( b ) t h er m al e f f i c i e n c y o f t he p l an t i s ” )
Scilab code Exa 3.4 Calculations on Gas Turbine Plant
1 / / s c i l a b Code Exa 3 . 4 C a l c u l a t i o n s on G as T ur bi ne
P la nt f o r an i d e a l r e he a t c y c l e w i th optimum 20
2 3 4 5 6
r e he a t p r e s s u r e and p e r f e c t e xh au st T 1 = 3 0 0 ; / / Minimum c y c l e T em pe ra tu re r = 2 5 ; // p r e s s u r e r a t i o o f t he t u rb i ne compressor T 3 = 1 5 0 0 ; / / Maximum c y c l e T e mp e ra t ur e gamma =1.4; // S p e c i f i c Heat R at io c p = 1 . 0 0 5 ; // S p e c i f i c Heat a t C on st a nt kJ/(kgK)
7 8 9 10 11
beeta=T3/T1; n =( gamma - 1 ) / gamma ; t=(r^n); d = 1 / sqrt ( t ) ;
12 13 14 15
h ea t e xc ha ng e in Kelvin and in Kelvin P r es s u r e i n
// p a rt ( a ) D et er mi ni ng mass f l o w r a t e t hr ou gh t he t u r b i n e and c o mp r e ss o r c=2*beeta*[1-d]; wp_max=cp*T1*(c+1-t); m=1000/wp_max; disp ( ” k g / s ” ,m , ” mass f l o w r a t e t hr ou gh t he t u r b i n e and c o mp r e ss o r i s ” )
16 17 18 / / p ar t ( b ) D et er mi ni ng t he rm al
e f f i c i e n c y o f t he
plant 19 c = sqrt ( t ) * ( sqrt ( t ) + 1 ) / ( 2 * b e e t a ) ; 20 n _ t h = 1 - c ; 21 disp ( ”%” , n _ t h * 1 0 0 , ” t h er m a l e f f i c i e n c y is”)
o f t h e p la nt
Scilab code Exa 3.5 Calculations on Gas Turbine Plant
1 / / s c i l a b Code Exa 3 . 5 C a l c u l a t i o n s on G as T ur bi ne
Plant 2
21
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
P = 1 0 e 4 ; / / P ow er O ut pu t i n kW T 1 = 3 1 0 ; / / Minimum c y c l e T em pe ra tu re i n K e l v i n p 1 = 1 . 0 1 3 ; // C o m p r e s s o r I n l e t P r es s u r e i n b ar p r _ c = 8 ; // C om pre ss or p r e s s u r e r a t i o gamma =1.4; gamma_g=1.33; R=0.287; p 2 = p r _ c * p 1 ; // Co mp re ss or E xi t P r e ss u r e i n b ar T 3 = 1 3 5 0 ; / / Maximum c y c l e T e m p er a t u re ( T u r b i n e i n l e t
temp ) i n K e lv i n n _ c = 0 . 8 5 ; / / C om pr es so r E f f i c i e n c y p 3 = 0 . 9 8 * p 2 ; // t u r b i n e i n l e t p r e s s u r e p 4 = 1 . 0 2 ; // t u r b i n e e x i t p r e s s u r e i n b a r C V = 4 0 * 1 0 e 2 ; // C a l o r i f i c Va l u e o f f u e l i n kJ /kg ; n _ B = 0 . 9 8 ; // Co mb us ti on E f f i c i e n c y n _ m = 0 . 9 7 ; // M ec ha ni ca l e f f i c i e n c y n _ t = 0 . 9 ; // T u rb in e E f f i c i e n c y n _ G = 0 . 9 8 ; // G en er at or E f f i c i e n c y c p _ a = 1 . 0 0 5 ; // S p e c i f i c Heat o f a i r a t C o n s t a n t P r e s s u r e i n kJ / ( kgK )
/ / A i r C om p re ss or T 2 s = T 1 * ( p r _ c ^ ( ( gamma - 1 ) / gamma ) ) ; T2=T1+((T2s-T1)/n_c); w_c=cp_a*(T2-T1);
/ / Gas T u r bi n e n_g=( gamma_g -1)/ gamma_g ; c p _ g = 1 . 1 5 7 ; // S p e c i f i c Heat o f g as a t C o n s t a n t
P r e s s u r e i n kJ / ( kgK ) 30 31 32 33 34 35 36 37
pr_t=p3/p4; T 4 s = T 3 / ( p r _ t ^ ( ( g a m ma _ g - 1 ) / g a m m a _ g ) ) ; T4=T3-(n_t*(T3-T4s)); w_t=cp_g*(T3-T4); w_net=w_t-w_c; w_g=n_m*n_G*w_net;
/ / p a r t ( a ) D e t er m i n in g Gas Fl ow R at e 22
38 39 40 41 42 43 44 45 46 47 48 49
m_g=P/w_g; disp ( ” k g / s ” , m _ g , ” ( a ) Gas f l o w r a t e i s ” )
/ / p a r t ( b ) D e t er m i n in g F ue l−A ir R a ti o F_A=((cp_g*T3)-(cp_a*T2))/((CV*n_B)-(cp_g*T3)); disp ( F _ A , ” ( b ) F u el −A ir R at io i s ” )
// p a rt ( c ) A ir f l ow r a t e m_a=m_g/(1+F_A); disp ( ” k g / s ” , m _ a , ” ( c ) A ir f l o w r a t e
is ”)
/ / p ar t ( d ) D et er mi ni ng t he rm al e f f i c i e n c y o f t he plant
50 m _ f = m _ g - m _ a ; 51 n _ t h = m _ g * w _ n e t / ( m _ f * C V ) ; 52 disp ( ”%” , n _ t h * 1 0 0 , ” ( d ) t h er m al p l an t i s ” ) 53 54 // p ar t ( e ) D et er mi ni ng O v er a l l
e f f i c i e n c y o f t he
e f f i c i e n c y o f t he
plant 55 n _ o = n _ m * n _ G * n _ t h ; 56 disp ( ”%” , n _ o * 1 0 0 , ” ( e ) o v e r a l l e f f i c i e n c y o f t h e p l an t i s ” ) 57 58 // p ar t ( f ) D et er mi ni ng i d e a l J o u l e c y c l e e f f i c i e n c y 59 n _ J o u l e = 1 - ( 1 / ( p r _ c ^ ( (gamma - 1 ) / gamma ) ) ) ; 60 disp ( ”%” , n _ J o u l e * 1 0 0 , ” ( f ) e f f i c i e n c y o f t he i d e a l J ou le c y c l e i s ” )
23
Chapter 4 Steam Turbine Plants
Scilab code Exa 4.1 Calculations on Steam Turbine Plant
1 / / s c i l a b Code Exa 4 . 1 C a l c u l a t i o n s on Steam T ur bi ne
Plant 2 3 4 5 6 7
p 1 = 2 5 ; // T u rb i ne I n l e t P r es s u r e i n b a r p 2 = 0 . 0 6 5 ; // C on de ns er P r e s su r e i n b ar n _ B = 0 . 8 2 ; // B o i l e r e f f i c i e n c y delp=p1-p2; v _ w = 0 . 0 0 1 ; // S p e c i f i c Volume a t c o nd e ns e r P r e ss u r e
i n m3 / k g 8 9 h 1 = 1 6 0 . 6 ; // fro m s team t a b l e s a t p1 = 0. 06 5 b ar 10 h 2 = h 1 + ( d e l p * 1 0 0 * v _ w ) ; 11 12 / / p a r t ( a ) D e t er m i ni n g e x a c t and a p p ro x i ma t e R an ki ne
e f f i c i e n c y o f t h e p la nt 13 h 3 = 2 8 0 0 ; // from stea m t a b l e v ap ou r e n th a lp y a t 25 bar 14 h 4 = 1 9 3 0 ; // from stea m t a b l e 15 n _ r a n k i n e _ e x = ( h 3 - h 4 - ( h 2 - h 1 ) ) / ( h 3 - h 1 - ( h 2 - h 1 ) ) ;
24
16 disp ( ”%” , n _ r a n k i n e _ e x * 1 0 0 , ” ( a ) ( i ) E x ac t R a nk i ne e f f i c i e n c y i s ”) 17 18 n _ r a n k i n e _ a p p = ( h 3 - h 4 ) / ( h 3 - h 1 ) ; 19 disp ( ”%” , n _ r a n k i n e _ a p p * 1 0 0 , ” ( a ) ( i i ) A p p r o x i m a t e Ra n ki n e e f f i c i e n c y i s ” ) 20 21 / / p a r t ( b ) D e te r mi n in g t h er m al and r e l a t i v e
e f f i c i e n c i e s of the pl an t 22 n _ t = 0 . 7 8 ; / / T u r bi ne E f f i c i e n c y 23 C V = 2 6 . 3 * 1 0 e 2 ; // C a l o r i f i c V a l u e o f f u e l i n kJ /kg ; 24 n _ t h = ( n _ t * ( h 3 - h 4 ) ) / ( h 3 - h 1 ) ; 25 disp ( ”%” , n _ t h * 1 0 0 , ” ( b ) ( i ) t he rm al e f f i c i e n c y o f t he p l an t i s ” ) 26 n _ r e l = n _ t h / n _ r a n k i n e _ a p p ; 27 disp ( ”%” , n _ r e l * 1 0 0 , ” ( i i ) r e l a t i v e e f f i c i e n c y o f t he p l an t i s ” ) 28 29 // p a rt ( c ) D et er mi ni ng O v e r a ll e f f i c i e n c y o f t he
plant 30 n _ o = n _ t h * n _ B ; 31 disp ( ”%” , n _ o * 1 0 0 , ” ( c ) o v e r a l l e f f i c i e n c y o f t h e p l a n t is”) 32 33 / / p a r t ( d ) T ur bi ne and O v e r a l l h e at r a t e s 34 h r _ t = 3 6 0 0 / n _ t h ; 35 disp ( ”kJ/kWh” , h r _ t , ” ( d ) ( i ) T u r bi n e H ea t R at e i s ” ) 36 h r _ o = 3 6 0 0 / n _ o ; 37 disp ( ”kJ/kWh” , h r _ o , ” ( d ) ( i i ) o v e r a l l H ea t R at e i s ” ) 38 39 / / p a r t ( e ) S te am C o n s um p t io n p e r kWh 40 m _ s = 3 6 0 0 / ( n _ t * ( h 3 - h 4 ) ) ; 41 disp ( ”kg/kWh” , m _ s , ” ( e ) S te am C o n s um p t i on i s ” ) 42 43 / / p a r t ( f ) F u e l C o n s um p t i on p e r kWh 44 m _ f = 3 6 0 0 / ( C V * n _ o ) ; 45 disp ( ”kg/kWh” , m _ f , ” ( f ) F u e l C o ns u mp t io n i s ” )
25
Scilab code Exa 4.2 Steam Turbine Plant for different reheat cycles
1 2 / / s c i l a b Code Exa 4 . 2 Steam T ur bi ne P la nt f o r
d i f f e r e n t r eh e a t c y c l e s 3 4 p 1 = 1 6 0 ; // T u rb in e I n l e t P r es s u r e i n b ar 5 T1=500; / / T u r b in e E nt ry T em pe ra tu re i n D e gr ee
Celsius 6 7 8 9 10 11 12 13 14 15 16 17
p2=0.06;
// C on de ns er P r e ss u r e i n b ar
// fro m s team t a b l e s a t p1 = 0.0 6 bar , h 1 = 1 4 7 ; // S p e c i f i c E n th al py o f w at er i n kJ / kg h 2 = 2 5 6 7 ; // S p e c i f i c E nt ha lp y o f s team i n kJ /kg
h 3 = 3 2 9 5 ; // from stea m t a b l e h 4 = 1 9 4 7 ; // from stea m t a b l e q_n=h3-h1; n_N=(h3-h4)/(q_n); x=(h4-h1)/(h2-h1); disp ( ”%” , n _ N * 1 0 0 , ” f o r non r e he a t c y c l e p l an t e f f i c i e n c y i s ”) 18 disp ( ”kJ/kWh” ,3600/n_N , ” T u r bi n e H ea t R at e i s ” ) 19 disp (x , ” f i n a l d r y ne ss f r a c t i o n i s ” ) 20 / / f o r r eh e a t c y c l e 21 22 p ( 1 ) = 7 0 ; 23 h 5 ( 1 ) = 3 4 1 2 ; // i n kJ / kg 24 h 7 ( 1 ) = 3 0 6 5 ; // i n kJ / kg 25 h 6 ( 1 ) = 2 0 9 4 ; // i n kJ / kg 26 p ( 2 ) = 5 0 ; 27 h 5 ( 2 ) = 3 4 3 3 ; // i n kJ / kg
26
h 7 ( 2 ) = 2 9 8 1 ; // i n kJ / kg h 6 ( 2 ) = 2 1 4 4 ; // i n kJ / kg p(3)=25; h 5 ( 3 ) = 3 4 7 5 ; // i n kJ / kg h 7 ( 3 ) = 2 8 2 6 ; // i n kJ / kg h 6 ( 3 ) = 2 2 4 9 ; // i n kJ / kg for i = 1 : 3 q_r(i)=h5(i)-h7(i); a(i)=(h6(i)-h4)/(q_r(i)); n _ r ( i ) = 1 - a ( i ) ; // e xa c t Ra n ki n e e f f i c i e n c y b(i)=q_r(i)*n_r(i)/n_N; n_th(i)=(q_n+b(i))*n_N/(q_n+q_r(i)); hr_t(i)=3600/n_th(i); x(i)=(h6(i)-h1)/(h2-h1); disp ( ” b a r ” , p ( i ) , ” f o r r e h ea t p r e s s u r e ” ) disp ( ” k J ” , q _ r ( i ) , ”q R=” ) disp ( ” k J ” , h 6 ( i ) - h 4 , ”H6−H4= ” ) disp ( ”%” , n _ r ( i ) * 1 0 0 , ” Ra n ki n e e f f i c i e n c y o f t h e p l a n t is”) 46 disp ( ”%” , n _ t h ( i ) * 1 0 0 , ” t h e r m a l e f f i c i e n c y o f t h e p l an t i s ” ) 47 disp ( ”kJ/kWh” , h r _ t ( i ) , ” H ea t R at e i s ” ) 48 disp ( x ( i ) , ” f i n a l d ry ne s s f r a c t i o n i s ” ) 49 50 end 51 52 disp ( ” Comment : E r r o r i n T ex tb oo k , A ns we rs v a r y d ue to Round− o f f E r r o rs ” ) 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
Scilab code Exa 4.3 Calculations on Steam Turbine Plant
1 / / s c i l a b Code Exa 4 . 3 C a l c u l a t i o n s on Steam T ur bi ne
Plant 27
2 3 p 1 = 8 2 . 7 5 ; // T u r bi ne I n l e t P r es s u r e i n b a r 4 T1=510; / / T u r b in e E nt ry T em pe ra tu re i n D e gr ee
Celsius 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38
p c = 0 . 0 4 2 ; // C on de ns er P r e s su r e i n b ar H=3420; n_e=0.85; gamma =1.4; n_st1=0.85;
p2=22.75;
// f o r r e ge n er a ti v e c yc l e h s ( 1 ) = 1 2 1 . 4 ; // fro m s team t a b l e s and m o l l i e r c h a r t p ( 6 ) = p 2 ; // p r e s s u r e a t b l e ed p o i n t 1 H s ( 6 ) = 3 0 8 0 ; // E n th al py o f stea m a t b l ee d p o in t 1 h1s=931; h s ( 6 ) = h 1 s ; // E n th a lp y o f w at er a t b l ee d p o in t 1 H_22=H-(n_st1*(H-h1s)); p ( 5 ) = 1 0 . 6 5 ; // p r e s s u r e a t b l e ed p o i n t 2 H s ( 5 ) = 2 9 5 0 ; // E n th al py o f stea m a t b l ee d p o in t 2 h s ( 5 ) = 7 7 2 ; // E n th a lp y o f w at er a t b l ee d p o in t 2 p ( 4 ) = 4 . 3 5 ; // p r e s s u r e a t b l e e d p oi nt 3 H s ( 4 ) = 2 7 3 0 ; // E n th al py o f stea m a t b l ee d p o in t 3 h s ( 4 ) = 6 1 2 ; // E n th a lp y o f w at er a t b l ee d p o in t 3 p ( 3 ) = 1 . 2 5 ; // p r e s s u r e a t b l e e d p oi nt 4 H s ( 3 ) = 2 5 9 0 ; // E n th al py o f stea m a t b l ee d p o in t 4 h s ( 3 ) = 4 4 4 ; // E n th a lp y o f w at er a t b l ee d p o in t 4 p ( 2 ) = 0 . 6 ; // p r e s s u re a t b l e ed p o i n t 5 H s ( 2 ) = 2 5 1 0 ; // E n th al py o f stea m a t b l ee d p o in t 5 h s ( 2 ) = 3 6 0 ; // E n th a lp y o f w at er a t b l ee d p o in t 5 m=1; h_c=121.4; x=0.875;
28
39 40 41 42 43 44 45 46 47 48 49 50
disp (x , ” ( a ) t h e f i n a l s t a t e a t p oi nt C i s ” ) for i = 2 : 6 alpha(i)=(Hs(i)-hs(i-1))/(Hs(i)-hs(i)); m=m*alpha(i); end disp ( ” k g ” ,m , ” ( b ) The m ass o f s team r a i s e d p er kg o f stea m r e a c hi n g t he c o nd e ns e r i s ” )
// p ar t ( c ) t he rm al e f f i c i e n c y w it h f e ed h e at i ng
H_c=2250; h_n=hs(6); n_th=1-((H_c-h_c)/(m*(H-h_n))); hr_t=3600/n_th;
// ( c ) t he im pro vemen t i n t he rm al e f f i c i e n c y and h ea t rate
c=H-H_c; d=H-h_c; n_R=(H-H_c)/(H-h_c); hr_R=3600/n_R; deln_th=(n_th-n_R)/n_R; disp ( ”%” , d e l n _ t h * 1 0 0 , ” ( c ) t h e r e f o r e , t h e i m pr o ve me nt in e f f i c i e n cy i s ”) 57 d e l h r _ t = ( h r _ R - h r _ t ) / h r _ R ; 58 disp ( ”%” , d e l h r _ t * 1 0 0 , ” and , t h e i mp ro ve me nt i n h e at r a te i s ”) 59 60 / / p ar t ( d ) d e c r e a s e o f s team f l ow t o t he c on d e n s er 51 52 53 54 55 56
p e r kWh due t o f e e d h e a t i n g 61 62 63 64 65 66 67 68 69 70 71
q_s=m*(H-h_n); q_r=H_c-h_c; w_t=q_s-q_r; wt_m=w_t/m; sf_r=3600/wt_m; s_c=sf_r/m;
/ / w it ho ut f e ed h e at i ng
wt_f=H-H_c; m_wf=3600/wt_f; sr_c=(m_wf-s_c)/m_wf; disp ( ”%” , s r _ c * 1 0 0 , ” ( d ) t he d e c r e a s e i n stea m
29
r e a c h i n g t he c o n d e ns e r i s ” ) 72 disp ( ” comment : t h e c a l c u l a t i o n f o r t h e i mp ro ve me nt i n e f f i c i e n c y i s wrong i n t h e book . ” )
30
Chapter 5 Combined Cycle Plants
Scilab code Exa 5.1 Calculation on combined cycle power plant
1 / / s c i l a b Code Exa 5 . 1 .
C a l c u l a t i o n on co mb ined
c y c l e power p l a nt 2 3 P _ g t = 1 e 5 ; / / P ow er O ut pu t i n kW 4 m _ g = 4 0 0 ; // mass f lo w r a t e o f t he e xh au st g as i n kg /
s 5 c p _ g = 1 . 1 5 7 ; // S p e c i f i c Heat o f g as a t C o n s t a n t
P r e s s u r e i n kJ / ( kgK ) 6 x = 0 . 9 ; // d ry n e ss f r a c t i o n o f s tea m a t t h e t u rb i n e exit 7 8 / / p ar t ( a ) D et er mi ni ng c a p a c i t y o f t he b o i l e r
i n kg
o f st ea m p er ho ur 9 p 1 = 9 0 ; // st ea m P r es s u r e a t t he e nt r y o f s tea m t ur bi n e i n bar 10 / / fro m s team t a b l e s 11 t _ 6 s = 3 0 3 . 3 ; // s a t u r a t i o n t em pe ra tu re a t 90 b a r i n degree C 12 t _ 5 s = t _ 6 s ;
31
13 h _ f g = 1 3 8 0 . 8 ; // fro m s team t a b l e l i q u i d
v a p o ur
e n th a lp y a t 90 b ar 14 p p = 2 0 ; // p in ch p o i n t i n d eg re e C 15 16 17 18 19
t_6=t_6s+pp; h_5s=2744.6; h_6s=1363.8;
20 21 22 23 24 25 26 27
// Ex ha us t g a s t em p er a tu re a t g as t u r b i n e end i n d e g r e e C T 4 = t 4 + 2 7 3 ; // i n K el vi n p _ c = 0 . 1 ; // C on de ns er p r e s s u r e i n b ar t 7 = 1 7 6 ; // Ex ha us t g a s t em pe ra t ur e a t s t a c k i n degree C T 7 = t 7 + 2 7 3 ; // i n K el vi n h _ 7 s = 1 9 1 . 8 ; // S p e c i f i c E n th a lp y o f w at er i n kJ /kg
t4=592.6;
m_st=(m_g*cp_g*(t_6-t7))/(h_6s-h_7s); disp ( ” t o n n e s / h r ” , m _ s t * 3 . 6 , ” ( a ) c a p ac i t y o f t he b o i l e r i n kg o f s team p er h o u r i s ” )
28 29 / / p a rt ( b ) t em p er a tu re o f s tea m a t t u r b i n e e n tr y 30 t _ 5 = t _ 6 + ( ( m _ s t * ( h _ 5 s - h _ 6 s ) ) / ( m _ g * c p _ g ) ) ; // e n er g y
b a l a nc e f o r t he e v a p o r a to r 31 32 h _ 4 s = h _ 5 s + ( m _ g * c p _ g * ( t 4 - t _ 5 ) / m _ s t ) ; 33 t _ 4 s = 5 4 0 ; // i n d e g re e C fro m s tea m t a b l e a t p=90
bar 34 disp ( ” d e g r e e c e l s i u s ” , t _ 4 s , ” ( b ) t e m pe r a tu r e o f s te am a t t u r b in e e nt ry i s ” ) 35 36 / / p a r t ( c ) s te am t u r b i n e
p l a n t o u tp u t a nd t h e r ma l
efficiency 37 38 39 40 41 42
h_5=2350; h_6=2150; w_st_s=h_4s-h_5; w_st_g=w_st_s*(m_st/m_g); P_st=m_st*w_st_s; disp ( ”MW” , P _ s t / 1 0 e 0 2 , ” ( c ) P ower o u t pu t o f t h e s te am
32
t u r b i n e p l an t i s ” ) 43 q _ s t = h _ 4 s - h _ 7 s ; 44 n _ s t = w _ s t _ s / q _ s t ; 45 disp ( ”%” , n _ s t * 1 0 0 , ” t he rm al E f f i c i e n c y o f s taem t u r b i n e p l an t i s ” ) 46 47 / / p ar t ( d ) t he rm al e f f i c i e n c y o f t he co mb ined c y c l e
plant n _ g t = 0 . 2 6 6 6 ; / / Gas t u r b in e p l a n t E f f i c i e n c y w_gt=P_gt/m_g; q_gt=w_gt/n_gt; n_c=(w_gt+w_st_g)/q_gt; disp ( ”%” , n _ c * 1 0 0 , ” ( d ) t he rm al E f f i c i e n c y o f co mb ined c y c l e p l a nt i s ” ) 53 disp ( ” Comment : E r r o r i n T ex tb oo k , A ns we rs v a r y d ue to Round− o f f E r r o rs ” ) 48 49 50 51 52
Scilab code Exa 5.2 combined gas and steam cycle power plant
1 / / s c i l a b Code Exa 5 . 2 com bin ed g as and s tea m c y c l e
p ow er p l a n t 2 P _ g t = 1 0 e 0 3 ; / / P ow er O ut pu t i n kW 3 n _ s t = 0 . 3 2 ; // Steam t u r b i n e power p l a nt E f f i c i e n c y 4 5 6 7 8 9 10
/ / p a r t ( a ) s tea m t u r b i n e p l a n t o u tp ut n _ g t = 0 . 2 ; // Gas t u r b i n e p l an t E f f i c i e n c y
q_gt=P_gt/n_gt; q_st=(1-n_gt)*q_gt; P_st=n_st*q_st; disp ( ”MW” , P _ s t / 1 0 e 0 2 , ” ( a ) P ower o u tp ut o f t h e s te am t u r b i n e p l an t i s ” )
11 12 / / p ar t ( b ) t he rm al
e f f i c i e n c y o f t he co mb ined c y c l e 33
plant 13 n _ c = n _ g t + n _ s t - ( n _ g t * n _ s t ) ; 14 disp ( ”%” , n _ c * 1 0 0 , ” ( b ) t he rm al E f f i c i e n c y o f co mb ined c y c l e p l a nt i s ” ) 15 16 // p a rt ( c ) t he h ea t r a t e o f t he co mb ined c y c l e p l a nt 17 h r _ c = 3 6 0 0 / n _ c ; 18 disp ( ”kJ/kWh” , h r _ c , ” ( c ) H e at R at e o f t h e c om bi ne d c y cl e p la nt i s ” )
34
Chapter 6 Fluid dynamics
Scilab code Exa 6.1 inward flow radial turbine 32000rpm
1 / / s c i l a b Code Exa 6 . 1 i nw a r d f l o w r a d i a l 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
t u rb i n e
32000rpm P = 1 5 0 ; / / P ow er O ut pu t i n kW N = 3 2 e 3 ; / / S p e ed i n RPM d 1 = 2 0 / 1 0 0 ; // o u t er d ia me te r o f t he i m p e l l e r i n m d 2 = 8 / 1 0 0 ; // i n ne r d ia me te r o f t h e i m p e l l e r i n m V 1 = 3 8 7 ; // A bs ol ut e V e lo c i t y o f g as a t e nt ry i n m/ s V 2 = 1 9 3 ; // A bs ol ut e V e lo c i t y o f g as a t e x i t i n m/ s
/ / p a rt ( a ) d e te r mi n i ng mass f l o w r a t e
u1=%pi*d1*N/60; u2=d2*u1/d1; w_at=u1^2/10e2; m=P/w_at; disp ( ” k g / s ” ,m , ” ( a ) m ass f l o w r a t e i s ” )
/ / p ar t ( b ) d e t er m i n in g t he p e rc e n t a g e e ne rg y t r a n s f e r due t o t h e c h a n g e o f r a d i u s
17 n = ( ( u 1 ^ 2 - u 2 ^ 2 ) / 2 e 3 ) / w _ a t ;
35
18 disp ( ”%” , n * 1 0 0 , ” ( b ) p e r ce n t ag e e ne rg y t r a n s f e r t o t he c h a n g e o f r a di u s i s ” )
due
Scilab code Exa 6.2 radially tipped Centrifugal blower 3000rpm
1 / / s c i l a b Code Exa 6 . 2 r a d i a l l y
t ip p e d C e n t r i f u g a l
b l o w e r 3 0 0 0 rpm 2 P = 1 5 0 ; / / P ow er O ut pu t i n kW 3 N = 3 e 3 ; / / S p e ed i n RPM 4 d 2 = 4 0 / 1 0 0 ; // o u t er d ia me te r o f t he i m p e l l e r i n m 5 d 1 = 2 5 / 1 0 0 ; // i n ne r d ia me te r o f t he i m p e l l e r i n m 6 b = 8 / 1 0 0 ; // i m p e l l e r w i d t h a t e nt ry i n m 7 n _ s t = 0 . 7 ; // s t a g e e f f i c i e n c y 8 V 1 = 2 2 . 6 7 ; // A bs ol ut e V e l o c i t y a t e n t ry i n m/ s 9 r o = 1 . 2 5 ; // d e ns i t y o f a i r i n kg /m3 10 11 12 13 14 15 16 17 18 19 20 21 22 23
/ / p a rt ( a ) d e te r mi n i ng t he p r e s s u r e d e ve l op e d
u2=%pi*d2*N/60; u1=d1*u2/d2; w_ac=u2^2; delh_s=n_st*w_ac; delp=ro*delh_s; disp ( ”mm W.G. ” , d e l p / 9 . 8 1 , ” ( a ) t he p r e s s u r e d e v el o p ed i s ” )
// p a rt ( b ) d e te r mi n i ng t he power r e q u i r e d
A1=%pi*d1*b; m=ro*V1*A1; P=m*w_ac/10e2; disp ( ”kW” ,P , ” ( b ) P ower r e q u i r e d
36
is ”)
Scilab code Exa 6.3 Calculation on an axial flow fan
1 / / s c i l a b Code Exa 6 . 3 C a l c u l a t i o n on an a x i a l f lo w
fan 2 3 4 5 6 7 8 9 10
N = 1 . 4 7 e 3 ; / / S p e ed i n RPM d = 3 0 / 1 0 0 ; // Mean d ia m e te r o f t he i m p e l l e r i n m r o = 1 . 2 5 ; // d e ns i t y o f a i r i n kg /m3
// p ar t ( b ) d et er mi ni n g t h e p r e s s u r e r i s e fan
a c ro s s th e
u=%pi*d*N/60; w_c=u^2/3; delp=ro*w_c; disp ( ”mm W.G. ” , d e l p / 9 . 8 1 , ” ( b ) t he p r e s s u r e a c r o s s t h e f an i s ” )
37
ris e
Chapter 7 Dimensional Analysis and Performance Parameters
Scilab code Exa 7.1 Calculation for the specific speed
1 // s c i l a b Code Exa 7 . 1 C a l c u l a t i o n f o r t he
sp eci fic
speed 2 3 4 5 6 7 8 9 10 11 12 13 14 15
funcprot (0)
// part (a ) s p e c i f i c speed of gas tur bin e P = 2 e 3 ; / / Gas T u r bi n e P owe r O ut pu t i n kW N = 1 6 e 3 ; / / S p e ed i n RPM T 1 = 1 e 3 ; / / E n tr y T e mp er at ur e i n K e l v i n En tr y P r e s s u r e i n b a r p 1 = 5 0 ; // p 2 = 2 5 ; // E x i t P re ss u r e i n b ar c p = 1 . 1 5 e 3 ; // S p e c i f i c Heat a t C o ns ta nt P r es s u r e i n J/(kgK)
gamma_g=1.3; omega=%pi*2*N/60; r o = p 1 * 1 e 5 / ( ( ( g a m ma _ g - 1 ) / g a m m a _ g ) * c p * T 1 ) ; p re ss ur e r a t i o p r = p 2 / p 1 ; // T 2 s = T 1 * ( p r ^ ( ( g a m ma _ g - 1 ) / g a m m a _ g ) ) ; delh_s=cp*(T1-T2s);
38
16 N S = o m e g a * sqrt ( P * 1 0 e 2 / r o ) * d e l h _ s ^ ( - 5 / 4 ) 17 disp ( N S , ” ( a ) t h e s p e c i f i c s p ee ee d o f g a s t u r b i n e 18 19 / / p a r t ( b ) t h e s p e c i f i c s p ee ee d o f a c e n t r i f u g a l 20 21 22 23
24 25 26 27 28 29 30 31 32 33 34
35 36 37 38 39 40 41 42 43 44 45
is ”)
compressor p r _ b = 2 ; // / / C om o m pr p r e ss s s or or p r e s s u r e r a t i o e d i n RPM N _ b = 2 4 e 3 ; / / S p e ed m=1.5; // i n kg kg / s // S p e c i f i c H e a t o f a i r a t C o n s t a n t c p _ a = 1 . 0 0 5 e 3 ; // P r e s s u r e i n k J / ( kg kgK ) R=0.287; gamma =1.4; T 1 _ b = 3 0 0 ; / / E n tr t r y T e m pe p e ra r a tu t u re re i n K e l v i n Entry P re ss ur e i n b ar p1_b=1; // ro_b=p1_b*1e2/(R*T1_b); omega_b=%pi*2*N_b/60; Q=m/ro_b; T 2 = T 1 _ b * ( p r _ b ^ ( ( gamma gamma - 1 ) / gamma ) ) ; delh_s_b=cp_a*(T2-T1_b); N S _ b = o m e g a _ b * sqrt ( Q ) * d e l h _ s _ b ^ ( - 3 / 4 ) ; disp ( N S _ b , ” ( b ) t he he s p e c i f i c s p pee ed ed o f a c e n t r i f u g a l c o mp m p r e ss ss o r i s ” )
/ / p a r t ( c ) t h e s p e c i f i c s p e ed e d o f a n a x i a l c o m p r e s so so r / / C om o m pr p r es e s so so r p r e s s u r e r a t i o p r _ c = 1 . 4 ; // N _ c = 6 e 3 ; / / S p e ed e d i n RPM i n kg kg / s m_c=15; //
omega_c=%pi*2*N_c/60; Q_c=m_c/ro_b; T 2 _ c = T 1 _ b * ( p r _ c ^ ( (gamma ( gamma -1)/ -1)/ gamma ) ) ; delh_s_c=cp_a*(T2_c-T1_b); N S _ c = o m e g a _ c * sqrt ( Q _ c ) * d e l h _ s _ c ^ ( - 3 / 4 ) disp ( N S _ c , ” ( c ) t h e s p e c i f i c s p e e d o f a n a x i a l c o mp m p r e ss ss o r i s ” )
39
Scilab code Exa 7.2 Calculating the discharge and specific speed
1 2 / / s c i l a b C o d e Ex E x a 7 . 2 C a l c u l a t i n g t he he d i s c h a r g e o f
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
a g e o m e t r i c a l l y s i m i l a r b lo l o we w e r a n d s p e c i f i c s pe p e ed ed o f t h e f an an / / C om o m pr p r es e s so so r p r e s s u r e r a t i o p r = 2 ; // N 1 = 1 . 4 7 e 3 ; / / f a n S p ee e e d i n RP RPM e e d i n RP RPM N 2 = 0 . 3 6 e 3 ; / / b l o w e r S p ee Q 1 = 2 ; // / / d i s c h a r g e i n m3 m3 / s h = 1 0 e - 3 ; / / i n m W. G . ro_w=10e2; / / d e n s i t y o f a i r i n k g /m /m3 r o _ a = 1 . 2 5 ; // omega1=%pi*2*N1/60; g = 9 . 8 1 ; / / i n m/ m/ s 2 p=ro_w*g*h H=p/(ro_a*g); delh_s=g*H; N S = o m e g a 1 * sqrt ( Q 1 ) * d e l h _ s ^ ( - 3 / 4 ) disp ( N S , ” t h e s p e c i f i c s p e e d i s ” )
/ / f o r t he h e s a m e s p e c i f i c s pe p e ed e d o f two g e o m e t r i c a l l y s i m i la r f an s
18 a = N 1 / N 2 ; 19 Q 2 = a ^ 2 * Q 1 ; 20 disp ( ”m3/s” , Q 2 , ” a n d t h e d i s c h a r g e o f a g e o m e t r i c a l l y s i m i l a r b lo l o we we r i s ” )
Scilab code Exa 7.3 Calculation on a small compressor
40
1 / / s c i l a b C o d e Ex E x a 7 . 3 C a l c u l a t i o n o n a s m al al l 2 3 4 5 6
compressor / / C om o m pr p r e ss s s or or p r e s s u r e r a t i o p r = 1 . 6 ; // N 1 = 5 4 e 3 ; / / S p e ed e d i n RPM // e f f i c i e n c y n _ c = 0 . 8 5 ; // m_a=1.5778; // i n kg kg / s // S p e c i f i c H e a t o f a i r a t C o n s t a n t c p _ a = 1 . 0 0 9 ; // P r e s s u r e i n k J / ( kg kgK )
7 gamma =1.4; 8 / / p ar a r t ( a ) d e t er e r m i n in i n g t he h e p o w e r r e q u ir ir e d t o d r i ve
t h e c o m pr p r e s so so r 9 T01=300; / / E n tr t r y T e mp m p er e r at a t ur ur e i n K e l v i n 10 p 0 1 = 1 . 0 0 8 ; / / Entry P re ss ur e i n b ar 11 12 13 14 15
n = ( gamma gamma - 1 ) / gamma ; T2s=T01*(pr^n); delh_s=cp_a*(T2s-T01)/n_c; P=m_a*delh_s; ow e r r e q u i r e d t o d r i v e t he he disp ( ”kW” , P , ” ( a ) P ow c o mp m p r e ss ss o r i s ” )
16 17 / / p a rt r t ( b ) d e te t e r mi m i n i ng n g t he h e s pe p e e d , m a s s f l ow o w r a te te ,
p r e s s u r e r a t i o and po we r r e q u i r e d o f a g e o m e t r i c a l l y s i m i l a r c om o m pr p r es e s so so r 18 / / g e o m e t r i c a l l y s i m i l a r c om o m pr p r es e s so s o r o f 3 t im i m es e s t he he s i z e o f s m a l l c om o m pr p r es e s so s o r i s c o n s tr t r u ct ct ed 19 N 2 = N 1 / 3 ; 20 disp ( ”rpm” , N 2 , ” ( b ) ( i ) s p pee ed ed o f a g e o m e t r i c a l l y s i m i l a r c oom m pr p r es e s so so r i s ” ) 21 m 2 = 9 * m _ a ; 22 disp ( ” k g / s ” , m 2 , ” ( b ) ( i i ) m as as s f l o w r a t e o f a g e o m e t r i c a l l y s i m i l a r c oom m pr p r es e s so so r i s ” ) 23 disp ( p r , ” ( b ) ( i i i ) p r e s s u r e r a t i o o f a g e o m e t r i c a l l y s i m i l a r c oom m pr p r es e s so so r i s ” ) 24 P 2 = 9 * P ; 25 disp ( ”kW” , P 2 , ” ( b ) ( i v ) P ow ower r e q u i r e d i s ” )
41
Scilab code Exa 7.4 Calculation on design of a single stage gas turbine
1 / / s c i l a b C o d e Ex Exa 7 . 4 C a l c u l a t i o n o n a s i n g l e
s ta g e
g as as t u rb i n e 2 3 4 5 6 7 8 9 10
gamma_g=1.33; gamma =1.4 R_g=284.1; R=287; P = 1 e 3 ; / / P ow ow er er O ut u t pu p u t i n kW e d i n RPM N 1 = 3 e 3 ; / / S p e ed n _ t = 0 . 8 7 ; // // e f f i c i e n c y / / S p e c i f i c H e a t o f g as as a t C o n s t a n t c p _ g = 1 . 1 4 5 ; //
P r e s s u r e i n k J / ( kg kgK ) 11 c p _ a = 1 . 0 0 4 5 ; // // S p e c i f i c H e a t o f a i r a t C o n s t a n t P r e s s u r e i n k J / ( kg kgK ) 12 13 / / p ar a r t ( a ) ma m a s s f lo l o w r a te t e o f t h e g as a s t h r o ug u g h t he he
turbine 14 15 16 17 18 19 20 21 22 23
t r y T e mp m p er e r at a t ur ur e i n K e l v i n T 0 1 = 1 0 0 0 ; / / E n tr p01=2.5; // Entry P re ss ur e i n bar t r y T em e m pe p e r at a t ur u r e o f a i r i n K el e l vi vi n T 0 1 a = 5 0 0 ; / / E n tr p01a=2; // E n t r y P re r e ss s s u r e o f a i r i n b ar ar E x i t P re r e ss s s u r e i n b ar ar p02=1; // pr0=p01/p02; T 0 2 = T 0 1 * ( p r 0 ^ ( - ( ( g a m ma ma _ g - 1 ) / g a m m a _ g ) ) ) ; delh_s1=cp_g*(T01-T02)*n_t; m_g=P/delh_s1; m a s s f lo l o w r a t e o f t h e g as as disp ( ” k g / s ” , m _ g , ” ( a ) ma t hr h r ou o u gh g h t he he t u r b i n e i s ” )
24 25 / / p ar a r t ( b ) s pe p e e d , m a s s f l o w r at at e ,
42
p r e s s u r e r a t i o and
p ow ow e r r e q u i r e d 26 N 2 = sqrt ( 1 / 2 ) * 5 * N 1 ; 27 disp ( ”rpm” , N 2 , ” ( b ) ( i ) s p pee ed ed o f a g e o m e t r i c a l l y s i m i l a r c oom m pr p r es e s so so r i s ” ) 28 a = 0 . 2 ; // a=D2/D 2/D11 ; 29 m 2 = ( a ^ 2 ) * sqrt ( R _ g / R ) * sqrt ( T 0 1 / T 0 1 a ) * ( p 0 1 a / p 0 1 ) * m _ g ; 30 disp ( ” k g / s ” , m 2 , ” ( b ) ( i i ) m as as s f l o w r a t e o f a g e o me t r ic a l ly s i m i l a r t ur bi n e i s ”) 31 d e l h _ s 2 = 0 . 5 * d e l h _ s 1 ; 32 P 2 = m 2 * d e l h _ s 2 ; 33 disp ( ”kW” , P 2 , ” ( b ) ( i i i ) P o we we r d e v e l o p e d i s ” ) 34 p r = ( 1 - ( d e l h _ s 2 / ( c p _ a * T 0 1 a * n _ t ) ) ) ^ ( - 1 / ( (gamma ( gamma - 1 ) / gamma ) ) ; 35 disp ( p r , ” ( b ) ( i v ) p r e s s u r e r a t i o o f a g e o m e t r i c a l l y s i m i l a r t u r b in in e i s ” )
43
Chapter 8 Flow Through Cascades
Scilab code Exa 8.1 Calculation on a compressor cascade
1 / / s c i l a b C o d e Ex E x a 8 . 1 C a l c u l a t i o n o n a c om o m pr p r es e s so so r
cascade 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
/ / A bs b s ol o l ut u t e V e l o c i t y o f a i r a t e nt n t ry r y i n m/ s V 1 = 7 5 ; // a l p h a 1 = 4 8 ; // / / a i r a ng n g l e a t e n tr tr y / / a i r a ng n g le le a t e x i t a l p h a 2 = 2 5 ; // / / p i t ch c h − c ho h o rd rd r a t i o p = 1 . 1 ; // d e l p s = 1 1 ; // / / s t a g n a t i o n p r e s s u r e l o s s i n mm mm W. G . / / d e ns n s i t y o f a i r i n k g /m /m3 r o = 1 . 2 5 ; // g=9.81; a=0.5*(tand(alpha1)+tand(alpha2)); alpham=atand(a); b=0.5*ro*(V1^2); Y=delps*g/b; disp ( Y , ” t h e l o s s c o e f f i c i e n t i s ” ) c=(cosd(alpham)^3)/(cosd(alpha1)^2); C_D=p*Y*c; disp ( C _ D , ” t h e d r a g c o e f f i c i e n t i s ” ) d=2*p*(tand(alpha1)-tand(alpha2))*cosd(alpham); 44
19 20 21 22 23 24
25 26 27 28 29 30
e=C_D*tand(alpham); C_L=d-e; disp ( C _ L , ” t h e L i f t c o e f f i c i e n t i s ” ) f=(cosd(alpha1)^2)/(cosd(alpha2)^2); C_ps=1-f; disp ( C _ p s , ” t h e I d e a l p r e s s u r e r e c o v e r y c o e f f i c i e n t is”) C_pa=C_ps-Y; disp ( C _ p a , ” t h e A c t u a l p r e s s u r e r e c o v e r y c o e f f i c i e n t is”) n_D=C_pa/C_ps; disp ( n _ D , ” t h e D i f f u s e r e f f i c i e n c y i s ” ) n_dmax=1-(2*C_D/C_L); disp (n_dmax , ” t h e Maximum D i f f u s e r e f f i c i e n c y i s ” )
Scilab code Exa 8.2 Calculation on a turbine blade row cascade
1 / / s c i l a b Code Exa 8 . 2 C a l c u l a t i o n on a t u r b i n e
b l a d e row c a s c a d e 2 3 4 5 6 7 8 9 10 11 12
b la de a ng l e a t e nt ry b e t a 1 = 3 5 ; // b e t a 2 = 5 5 ; // b la de a n g l e a t e x i t i = 5 ; // i n c i d e n ce d e l t a = 2 . 5 ; // d e v i a t i o n a l p h a 1 = b e t a 1 + i ; // a i r a ng l e a t e n tr y a l p h a 2 = b e t a 2 - d e l t a ; // a i r a ng le a t e x i t t _ c = 0 . 3 ; / / maximum t h i c k n e s s −c h o r d r a t i o ( t / l ) a _ r = 2 . 5 ; // a s p e c t r a t i o
/ / p a r t ( a ) o p ti mu m p i t c h −c h or d r a t i o fro m Z w e i f e l s relation 13 C _ z = 0 . 8 ; // from Z w ei f el ’ s r e l a t i o n 14 p _ c = C _ z / ( 2 * ( c o s d ( a l p h a 2 ) ^ 2 ) * ( t a n d ( a l p h a 1 ) + t a n d (
45
alpha2))); 15 disp ( p _ c , ” ( a ) t h e optimum p i t c h −c ho rd r a t i o from Z w ei f el s r e l a t i o n i s ” ) 16 17 / / p a r t ( b ) l o s s c o e f f i c i e n t f ro m S o d e r b e r g s a nd
Ha wth or ne r e l a t i o n s 18 e p = a l p h a 1 + a l p h a 2 ; // d e f l e c t i o n a ng le Zeeta=0.075; b=(1+Zeeta)*(0.975+(0.075/a_r)) zeeta=b-1; disp ( z e e t a , ” ( b ) ( i ) t h e l o s s c o e f f i c i e n t f r o m S od er b e rg s r e l a t i o n i s ” ) 23 z _ p = 0 . 0 2 5 * ( 1 + ( ( e p / 9 0 ) ^ 2 ) ) ; / / H awth orn e ’ s r e l a t i o n 24 disp ( z _ p , ” ( b ) ( i i ) t h e l o s s c o e f f i c i e n t f r o m Ha wth or ne r e l a t i o n i s ” ) 25 z = ( 1 + ( 3 . 2 / a _ r ) ) * z _ p ; // t h e t o t a l c as ca de l o s s 19 20 21 22
coefficient 26 27 28 29 30 31 32 33 34
Y=0.5*(z+zeeta);
// pa r t ( c ) dr ag c o e f f i c i e n t alpham=atand(0.5*(tand(alpha2)-tand(alpha1))); C_D=p_c*Y*(cosd(alpham)^3)/(cosd(alpha2)^2); disp ( C _ D , ” ( c ) the drag c o e f f i c i e n t i s ” )
// pa rt (d ) L i f t c o e f f i c i e n t
C _ L = ( 2 * p _ c * ( t a n d ( a l p h a 1 ) + t a n d ( a l p h a 2 ) ) * c o s d ( a l p h a m) ) +(C_D*tand(alpham)); 35 disp ( C _ L , ” ( d ) t h e L i f t c o e f f i c i e n t i s ” )
Scilab code Exa 8.3 Calculation on a compressor cascade
1 / / s c i l a b Code Exa 8 . 3 C a l c u l a t i o n on a c om pr es so r
cascade 46
2 3 4 5 6 7 8 9
t h e t a = 2 5 ; / / Camber a n g l e g a m m a _ a = 3 0 ; // s t a g g e r a n g l e i = 5 ; // i n c i d e n ce t _ c = 0 . 0 3 1 ; / / momentum t h i c k n e s s −c h o r d r a t i o ( t / l ) p _ c = 1 ; // p i t ch −c ho rd r a t i o
/ / p a r t ( a ) c a s c a de b l a d e a n g l e s b e t a 1 = ( ( 2 * g a m m a _ a ) + t h e t a ) * 0 . 5 ; //
b l a d e a n gl e a t
entry 10 b e t a 2 = ( ( 2 * g a m m a _ a ) - t h e t a ) * 0 . 5 ; // b la de a n g l e a t
exit 11 disp ( ” ( a ) t h e r ef o r e , t he b l a de a n g l es a r e ” ) 12 disp ( ” d e g r e e ” , b e t a 1 , ” b e t a 1 = ” ) 13 disp ( ” d e g r e e ” , b e t a 2 , ” b e t a 2 = ” ) 14 15 // p a rt ( b ) t he n om in al a i r a n g l e s 16 a l p h a 1 = b e t a 1 + i ; // a i r a ng l e a t e n tr y 17 a l p h a 2 = a t a n d ( t a n d ( a l p h a 1 ) - ( 1 . 5 5 / ( 1+ ( 1 . 5 * p _ c ) ) ) ) ; //
a i r a ng l e a t e x i t 18 disp ( ” ( b ) t h e r e f o r e , t h e a i r a n g l e s a re ” ) 19 disp ( ” d e g r e e ” ,alpha1 , ” a l p h a 1 = ” ) 20 disp ( ” d e g r e e ” ,alpha2 , ” a l p h a 2 = ” ) 21 22 / / p a r t ( c ) s t a g n a t i o n p r e s s u r e l o s s c o e f f i c i e n t 23 Y = 2 * t _ c * p _ c * ( c o s d ( a l p h a 1 ) ^ 2 ) / ( c o s d ( a l p h a 2 ) ^ 3 ) ; 24 disp (Y , ” ( c ) t h e s t a g n a t i o n p r e s s u r e l o s s c o e f f i c i e n t is”) 25 26 // pa rt (d ) dr ag c o e f f i c i e n t 27 a l p h a m = a t a n d ( 0 . 5 * ( t a n d ( a l p h a 1 ) + t a n d ( a l p h a 2 ) ) ) ; 28 C _ D = p _ c * Y * ( c o s d ( a l p h a m ) ^ 3 ) / ( c o s d ( a l p h a 1 ) ^ 2 ) ; 29 disp ( C _ D , ” ( d ) t h e d r a g c o e f f i c i e n t i s ” ) 30 31 // pa rt ( e ) Li f t c o e f f i c i e n t 32 C _ L = ( 2 * p _ c * ( t a n d ( a l p h a 1 ) - t a n d ( a l p h a 2 ) ) * c o s d ( a l p h a m) ) -(C_D*tand(alpham)); 33 disp ( C _ L , ” ( e ) t h e L i f t c o e f f i c i e n t i s ” )
47
Scilab code Exa 8.4 Calculation on a blower type annular cascade tunnel
1 / / s c i l a b Code Exa 8 . 4 b lo we r t yp e a n nu l ar c a sc a de
tunnel 2 3 4 5 6
t=35; T = t + 2 7 3 ; // t e s t Te mp er at ur e i n K el vi n p = 1 . 0 2 ; // t e s t P re ss ur e i n b a r d m = 5 0 / 1 0 0 ; // mean d ia me te r o f t he i m p e l l e r b la d e i n
m 7 8 9 10
b = 1 5 / 1 0 0 ; // b la de l e n g t h i n m n _ o = 0 . 6 ; // s t a g e e f f i c i e n c y R=287; c = 1 0 0 ; // Maximum V e l o c i t y u ps t re am o f t h e c a s c a d e
in m/s 11 r o = p * 1 0 e 4 / ( R * T ) ; // d e ns i t y o f a i r i n kg /m3 12 13 / / p ar t ( a ) d e t e r m i n i n g t he t o t a l p r e s s u r e d ev el op ed
by t he b lo we r 14 15 16 17 18 19 20 21 22 23 24
d_h=0.5*ro*(c^2); loss=0.1*d_h; delp=d_h+loss; disp ( ”mm W.G. ” , d e l p / 9 . 8 1 , ” ( a ) t he p r e s s u r e d e v el o p ed i s ” )
/ / p ar t ( b ) d et e r m i n in g t he d i s c ha r g e A = % p i * d m * b ; // t he a nn ul us c r o ss − s e c t i o n a l a re a Q=c*A; disp ( ”m3/min” , Q * 6 0 , ” ( b ) t he d i s c h a r g e
is ”)
// p a rt ( c ) d e te r mi n i ng t he power r e q u i r e d t o d r i v e t h e b l ow e r 48
25 P = Q * d e l p / ( n _ o * 1 0 e 2 ) ; 26 disp ( ”kW” ,P , ” ( c ) Power r e q u i r e d t o d r i v e t he b lo we r is”)
Scilab code Exa 8.5 Calculation on a compressor type radial cascade tun-
nel 1 / / s c i l a b Code Exa 8 . 5 c om pr es so r t yp e r a d i a l
c a s ca d e t u nn e l 2 3 4 5 6 7 8 9 10 11 12
M = 0 . 7 ; // Mach Number p r = 0 . 7 2 1 ; // p r=p t /p0 From i s e n t r o p i c g as t a b l e s t _ o p t = 0 . 9 1 1 ; / / t o p t =Tt / T0 A tm os ph er ic P r es s u r e i n b ar p a = 1 . 0 1 3 ; // Ta=306; // i n K n _ c = 0 . 6 5 ; // e f f i c i e n c y R=288; gamma =1.4; alpha=30; d m = 4 5 / 1 0 0 ; // mean d ia me te r o f t he i m p e l l e r b la d e i n
m 13 b = 1 0 / 1 0 0 ; // b l a d e w i dt h i n m 14 c p _ a = 1 . 0 0 8 ; // S p e c i f i c Heat o f a i r a t C o n s t a n t
P r e s s u r e i n kJ / ( kgK ) 15 16 17 18 19 20
/ / p ar t ( a ) p r e s s u r e r a t i o o f t he c om pr es so r pr_c=1/pr; disp ( p r _ c , ” ( a ) p r e s s u r e
r a t i o o f t he c om pr es so r i s ” )
/ / p ar t ( b ) s t a g n a t io n p r e s s u r e i n t h e s e t t l i n g chamber
21 p 0 2 = p a * p r _ c ; 22 disp ( ” b a r ” , p 0 2 , ” ( b ) s t a g n a t i on
49
p r e s s u r e i n t he
s e t t l i n g chamber i s ” ) 23 24 // p a rt ( c ) t e s t
s e c t i o n c o n d i t i o n s ( s t a t i c p r e ss u r e , t e mp e r at u r e and v e l o c i t y )
25 26 27 28 29 30 31 32
33 34 35 36 37 38 39 40 41 42 43
n =( gamma - 1 ) / gamma ; T 0 2 s = T a * ( p r _ c ^ ( (gamma - 1 ) / gamma ) ) ; T02=Ta+((T02s-Ta)/n_c); T_t=t_opt*T02; p_t=pr*p02; c _ t = M * sqrt ( gamma * R * T _ t ) ; disp ( ” ( c ) t e s t s e c t i o n c o n d i t i o n s a r e g i v en by : ” ) disp ( ” b a r ” , p _ t , ” s t a t i c p r e s s u r e o f a i r i n t h e t e s t s e c t i on i s ”) disp ( ”K” , T _ t , ” s t a t i c t em pe ra tu re o f a i r i n t h e t e s t s e c t i on i s ”) disp ( ”m/s” , c _ t , ” v e l o c i t y o f a i r i n t h e t e s t s e c t i o n is”)
// p a rt ( d ) d e te r mi n i ng mass f l o w r a t e
c_r=c_t*sind(alpha); r o _ t = p _ t * 1 e 5 / ( R * T _ t ) ; // d e ns i t y o f a i r i n kg /m3 A_t=%pi*dm*b; m=ro_t*A_t*c_r; disp ( ” k g / s ” ,m , ” ( d ) mass f l ow r a t e o f c om pr es so r i s ” )
// p a rt ( e ) d e te r mi n i ng t he power r e q u i r e d t o d r i v e t he a i r c om p re ss o r
44 d e l h _ s = c p _ a * ( T 0 2 - T a ) ; 45 P = m * d e l h _ s ; 46 disp ( ”kW” ,P , ” ( e ) Power r e q u i r e d t o d r i v e t he a i r c o mp r e ss o r i s ” )
50
Chapter 9 Axial Turbine Stages
Scilab code Exa 9.1 Calculation on multi stage turbine
1 / / s c i l a b Code Exa 9 . 1 C a l c u l a t i o n on m ul ti s t a g e
turbine 2 3 4 5 6 7 8 9
d = 1 ; // mean d ia m e te r o f t he i m p e l l e r b la d e i n m T 1 = 5 0 0 ; / / I n i t i a l T em p er a tu r e i n d e g r e e C t 1 = T 1 + 2 7 3 ; // i n K el vi n I n i t i a l P r e s su r e i n b ar p 1 = 1 0 0 ; // N = 3 e 3 ; / / S p e ed i n RPM i n kg / s m = 1 0 0 ; // a l p h a 2 = 7 0 ; // e x i t a n g l e o f t h e f i r s t s t a g e n o z z l e
blades 10 11 12 13 14
// p ar t ( a ) s i n g l e s t a g e i mp ul se nsti=0.78; u=%pi*d*N/60; s i g m a = 0 . 5 * ( s i n d ( a l p h a 2 ) ) ; / / maximum u t i l i z a t i o n
factor 15 c 2 = u / s i g m a ; 16 c x = c 2 * ( c o s d ( a l p h a 2 ) ) ;
51
b e t a 2 = a t a n d ( 0 . 5 * ( t a n d ( a l p h a 2 ) ) ) ; / / b e t a 2=b e t a 3 wst=2*(u^2)*1e-3; P=m*wst; disp ( ” ( a ) f o r s i n g l e s t a g e i mp ul se ” ) disp ( ” d e g r e e ” , b e t a 2 , ” b l a d e a n g l e s a r e b et a2=b et a3= ” ) 22 disp ( ”MW” , P * 1 e - 3 , ” Power d e v e l o p e d i s ” ) 23 24 s v = 0 . 0 4 ; / / s p e c i f i c v ol um e o f s te am a f t e r e x p a n s i o n 17 18 19 20 21
i n m3/ k g 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
h = ( m * s v ) / ( c x * % p i * d ) ; // h2=h3=h disp ( ”cm” , h * 1 e 2 , ” b l ad e h e ig h t i s ” ) delhs=wst/nsti; disp ( ” f i n a l s t a t e o f t h e s tea m i s ” ) p = 8 1 . 5 ; // f ro m e n th a l p y −e n t r o py d ia g ra m T=470; disp ( ” b a r ” ,p , ”p=” ) disp ( ” d e g r e e C ” ,T , ”T=” )
/ / p a r t ( b ) Two−s t a g e C u r ti s w he el
nstc=0.65; u=%pi*d*N/60; sigma2=0.25*(sind(alpha2)); c2_2=u/sigma2; cx2=c2_2*(cosd(alpha2)); b e t a 2 _ 2 = a t a n d ( ( 3 * u ) / c x 2 ) ; / / b e t a 2=b e t a 3 alpha3=atand((2*u)/(c2_2*cosd(alpha2))); // alpha2 ’=
alpha3 beta2_s=atand((u)/cx2); // beta2 ’=beta3 ’ wI=6*(u^2)*1e-3; wII=2*(u^2)*1e-3; wst2=wI+wII; P2=m*wst2; disp ( ” ( b ) f o r Two−s t a g e C u r ti s w he el ” ) disp ( ” d e g r e e ” ,alpha3 , ” a i r a n g l e s a r e a l p h a 2 s=a l ph a 3= ”) 49 disp ( ” d e g r e e ” ,beta2_2 , ” f o r f i r s t s t a g e b l ad e a n g l e s a r e b e t a 2=b e t a 3= ” ) 42 43 44 45 46 47 48
52
50 disp ( ” d e g r e e ” ,beta2_s , ” f o r s ec on d s t a ge b l a de a n g l es a r e b e t a 2 s=b e t a 3 s = ” ) 51 52 disp ( ”MW” , P 2 * 1 e - 3 , ” Power d e v e l o p e d i s ” ) 53 54 d e l h s 2 = w s t 2 / n s t c ; 55 / / f ro m e n t ha l p y −e nt ro p y d ia gr am f o r t he e xp a ns i on 56 disp ( ” f i n a l s t a t e o f t h e s tea m i s ” ) 57 p 2 = 2 7 ; 58 T 2 = 3 6 5 ; 59 v 2 = 0 . 1 0 5 ; / / s p e c i f i c v ol um e o f s te am a f t e r
e x p a n s i o n i n m3/ k g 60 disp ( ” b a r ” , p 2 , ”p=” ) 61 disp ( ” d e g r e e C ” , T 2 , ”T=” ) 62 disp ( ”m3/kg” , v 2 , ”v=” ) 63 64 65 66 67 68 69 70 71 72 73
h2=(m*v2)/(cx2*%pi*d); disp ( ”cm” , h 2 * 1 e 2 , ” b l ad e h e i g h t i s ” )
74 75 76 77 78 79
80 81 82 83
// pa rt ( c ) Two−s t a g e R ea te au w he el
nst1=0.78; wI3=2*(u^2)*1e-3; wII3=2*(u^2)*1e-3; wst3=wI3+wII3; P3=m*wst3; disp ( ” ( c ) f o r Two−s t a g e R ea te au w he el ” ) disp ( ” d e g r e e ” , b e t a 2 , ” b l a d e a n g l e s a r e b et a2=b et a3= ” ) disp ( ”MW” , P 3 * 1 e - 3 , ” Power d e v e l o p e d i s ” ) delhs3=wst3/nst1; disp ( ” f i n a l s t a t e o f t h e s tea m i s ” ) p 3 = 6 5 ; // f ro m e n t ha l p y −e n t r o p y d ia g ra m T3=445; v 3 = 0 . 0 5 ; / / s p e c i f i c v ol um e o f s te am a f t e r e x p a n s i o n
i n m3/ k g disp ( ” b a r ” , p 3 , ”p=” ) disp ( ” d e g r e e C ” , T 3 , ”T=” ) disp ( ”m3/kg” , v 3 , ”v=” )
h3=(m*v3)/(cx*%pi*d);
53
84 disp ( ”cm” , h 3 * 1 e 2 , ” b l a de h e i g h t f o r t he s ec on d s t a g e is”) 85 86 // p ar t ( d ) s i n g l e s t a ge 50% r e a c t i o n 87 n s t r = 0 . 8 5 ; 88 s i g m a 4 = s i n d ( a l p h a 2 ) ; // maximum u t i l i z a t i o n f a c t o r 89 c 2 _ 4 = u / s i g m a 4 ; / / c 2 4 =w 3 90 c x 4 = c 2 _ 4 * ( c o s d ( a l p h a 2 ) ) ; / / a l p h a 2=b e t a 3 ; 91 b e t a 2 _ 4 = 0 ; / / b e t a 2=a l p h a 3 92 w s t 4 = ( u ^ 2 ) * 1 e - 3 ; 93 P 4 = m * w s t 4 ; 94 disp ( ” ( d ) f o r s i n g l e s t a g e 50% r e a c t i o n ” ) 95 disp ( ” d e g r e e ” ,beta2_4 , ” b l a d e a n g l e s a r e b et a2=a lp ha 3 = ”) 96 disp ( ” d e g r e e ” ,alpha2 , ” a nd b e t a 3=a l p h a 2= ” ) 97 disp ( ”MW” , P 4 * 1 e - 3 , ” Power d e v e l o p e d i s ” ) 98 d e l h s 4 = w s t 4 / n s t r ; 99 / / f ro m e n t ha l p y −e n t r o p y d i a gr a m 100 disp ( ” f i n a l s t a t e o f t h e s tea m i s ” ) 101 p 4 = 9 0 ; 102 T 4 = 4 8 5 ; 103 v 4 = 0 . 0 3 5 ; 104 disp ( ” b a r ” , p 4 , ”p=” ) 105 disp ( ” d e g r e e C ” , T 4 , ”T=” ) 106 disp ( ”m3/kg” , v 4 , ”v=” ) 107 h 4 = ( m * v 4 ) / ( c x 4 * % p i * d ) ; 108 disp ( ”cm” , h 4 * 1 e 2 , ” t h e r o to r b la de h e i g h t a t e x i t i s ” )
Scilab code Exa 9.2 Calculation on an axial turbine stage
1 / / s c i l a b Code Exa 9 . 2 C a l c u l a t i o n on a n a x i a l
t u rb i n e s t ag e 54
2 3 d h = 0 . 4 5 0 ; / / h ub d i am et er i n m 4 d t = 0 . 7 5 0 ; // t i p d ia me te r i n m 5 d = 0 . 5 * ( d t + d h ) ; // mean d i am e te r o f t he i m p e l l e r
b la de i n m 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
r=d/2; T 1 = 5 0 0 ; / / I n i t i a l T em p er a tu r e i n d e g r e e C t 1 = T 1 + 2 7 3 ; // i n K el vi n I n i t i a l P r e s su r e i n b ar p 1 = 1 0 0 ; // N = 6 e 3 ; // r o t o r S pe ed i n RPM i n kg / s m = 1 0 0 ; // a i r a n g l e a t n oz zl e e x i t a l p h a 2 m = 7 5 ; // b e t a 2 m = 4 5 ; // a i r a n gl e a t r o t o r e n t r y a i r a n g l e a t r o t or e xi t b e t a 3 m = 7 6 ; // u=%pi*d*N/60; uh=%pi*dh*N/60; ut=%pi*dt*N/60;
/ / f o r mean s e c t i o n
c 2 m = ( c o s d ( b e t a 2 m ) / s i n d ( a l p h a2 m - b e t a 2 m ) ) * u ; cx2m=c2m*cosd(alpha2m); ct2m=c2m*sind(alpha2m); ct3m=(cx2m*tand(beta3m))-u; C2=r*ct2m; C3=r*ct3m;
/ / p ar t ( a ) t h e r e l a t i v e and a b s o l u t e a i r a n g l e s disp ( ” f o r mean s e c t i o n ” ) disp ( ” ( a ) t h e r e l a t i v e and a b s o l u t e a i r a n g l e s a re ” ) disp ( ” d e g r e e ” ,beta2m , ” a i r a n g le a t r o t o r e nt r y i s beta2m= ” ) 30 disp ( ” d e g r e e ” ,beta3m , ” a i r a ng l e a t r o t o r e x i t i s beta3m= ” ) 31 disp ( ” d e g r e e ” ,alpha2m , ” a i r a ng le a t n o z z l e e x i t i s alpha2m= ” ) 32 / / p ar t ( b ) d e g r ee o f r e a c t i o n 33 c x = c x 2 m ; 34 R = c x * ( t a n d ( b e t a 3 m ) - t a n d ( b e t a 2 m ) ) * 1 0 0 / ( 2 * u ) ; 35 disp ( ”%” ,R , ” ( b ) d e g r e e o f r e a c t i o n i s ” )
55
36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52
/ / p a r t ( c ) b l a d e −to −g as s pe e d r a t i o sigma=u/c2m; disp ( s i g m a , ” ( c ) blad e −to −g as s pe ed r a t i o
/ / p a r t ( d ) s p e c i f i c w or k omega=2*%pi*N/60; w=omega*(C2+C3); disp ( ” k J / k g ” , w * 1 e - 3 , ” ( d ) s p e c i f i c w or k i s ” )
// par t ( e ) the lo ad in g c o e f f i c i e n t z=w/(u^2); disp (z , ” ( e ) t h e l o a d i n g
coefficient is ”)
/ / f o r hub s e c t i o n
53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70
i s ”)
rh=dh/2; alpha2h=atand(C2/(rh*cx)); disp ( ” f o r hub s e c t i o n ” ) disp ( ” ( a ) t h e r e l a t i v e and a b s o l u t e a i r a n g l e s a re ” ) disp ( ” d e g r e e ” ,alpha2h , ” a i r a ng le a t n o z z l e e x i t i s a l p h a 2 h= ” ) beta2h=atand(tand(alpha2h)-(uh/cx)); disp ( ” d e g r e e ” ,beta2h , ” a i r a n g le a t r o t o r e nt r y i s beta2h= ”) beta3h=atand((C3/(rh*cx))+(uh/cx)); disp ( ” d e g r e e ” ,beta3h , ” a i r a ng l e a t r o t o r e x i t i s beta3h= ”)
/ / p ar t ( b ) d e g r ee o f r e a c t i o n Rh=cx*(tand(beta3h)-tand(beta2h))*100/(2*uh); disp ( ”%” , R h , ” ( b ) d e g r ee o f r e a c t i o n i s ” )
/ / p a r t ( c ) b l a d e −to −g as s pe e d r a t i o c2h=cx/(cosd(alpha2h)); sigmah=uh/c2h; disp (sigmah , ” ( c ) blad e −to −g as s pe e d r a t i o
i s ”)
/ / p a r t ( d ) s p e c i f i c w or k wh=uh*cx*(tand(beta3h)+tand(beta2h)); disp ( ” k J / k g ” , w h * 1 e - 3 , ” ( d ) s p e c i f i c w or k i s ” )
// par t ( e ) the lo ad in g c o e f f i c i e n t zh=wh/(uh^2); disp ( z h , ” ( e ) t h e l o a d i n g
coefficient is ”)
56
71 72 73 74 75 76
// f o r t i p s e c t i o n
77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93
rt=dt/2; alpha2t=atand(C2/(rt*cx)); disp ( ” f o r t i p s e c t i o n ” ) disp ( ” ( a ) t h e r e l a t i v e and a b s o l u t e a i r a n g l e s a re ” ) disp ( ” d e g r e e ” ,alpha2t , ” a i r a ng le a t n o z z l e e x i t i s alpha2t= ”) beta2t=atand(tand(alpha2t)-(ut/cx)); disp ( ” d e g r e e ” ,beta2t , ” a i r a n g le a t r o t o r e nt r y i s beta2t= ”) beta3t=atand((C3/(rt*cx))+(ut/cx)); disp ( ” d e g r e e ” ,beta3t , ” a i r a ng l e a t r o t o r e x i t i s beta3t= ”)
/ / p ar t ( b ) d e g r ee o f r e a c t i o n Rt=cx*(tand(beta3t)-tand(beta2t))*100/(2*ut); disp ( ”%” , R t , ” ( b ) d e g r ee o f r e a c t i o n i s ” )
/ / p a r t ( c ) b l a d e −to −g as s pe e d r a t i o c2t=cx/(cosd(alpha2t)); sigmat=ut/c2t; disp (sigmat , ” ( c ) blad e −to −g as s pe e d r a t i o
i s ”)
/ / p a r t ( d ) s p e c i f i c w or k wt=ut*cx*(tand(beta3t)+tand(beta2t)); disp ( ” k J / k g ” , w t * 1 e - 3 , ” ( d ) s p e c i f i c w or k i s ” )
// par t ( e ) the lo ad in g c o e f f i c i e n t zt=wt/(ut^2); disp ( z t , ” ( e ) t h e l o a d i n g
coefficient is ”)
Scilab code Exa 9.3 Calculation on an axial turbine stage
1 / / s c i l a b Code Exa 9 . 3 C a l c u l a t i o n on a n a x i a l
t u rb i n e s t ag e 2 3 d h = 0 . 4 5 0 ; / / h ub d i am et er i n m
57
4 d t = 0 . 7 5 0 ; // t i p d ia me te r i n m 5 d = 0 . 5 * ( d t + d h ) ; // mean d i am e te r o f t he i m p e l l e r
b la de i n m 6 7 8 9 10 11 12 13 14 15 16
r=d/2; R _ m = 0 . 5 ; // d eg re e o f r e a c t i o n f o r mean s e c t i o n T 1 = 5 0 0 ; / / I n i t i a l T em p er a tu r e i n d e g r e e C t 1 = T 1 + 2 7 3 ; // i n K el vi n p 1 = 1 0 0 ; // I n i t i a l P r e s su r e i n b ar N = 6 e 3 ; // r o t o r S pe ed i n RPM m = 1 0 0 ; // i n kg / s a i r a n g l e a t n oz zl e e x i t a l p h a 2 m = 7 5 ; // a i r a n gl e a t r o t o r e n t r y b e t a _ 2 m = 0 ; // b e t a _ 3 m = 7 5 ; // a i r a n g l e a t r o t or e xi t
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38
u_m=%pi*d*N/60; uh=%pi*dh*N/60; ut=%pi*dt*N/60;
/ / a s s u m i n g r a d i a l e q u i l l i b r i u m and f r e e v o r te x f lo w i n t h e s t a ge , a x i a l v e l o c i t y i s c on st an t throughout
/ / f o r mean s e c t i o n c_xm=u_m*cotd(alpha2m); c_2m=(1/sind(alpha2m))*u_m; c_t2m=u_m; disp ( ” f o r mean s e c t i o n ” )
/ / p a r t ( c ) b l a d e −to −g as s pe e d r a t i o sigma_m=u_m/c_2m; disp (sig ma_m , ” ( c ) bl ad e −to −g as s pe e d r a t i o
i s ”)
/ / p a r t ( d ) s p e c i f i c w or k w_m=u_m*c_t2m; disp ( ” k J / k g ” , w _ m * 1 e - 3 , ” ( d ) s p e c i f i c w or k i s ” )
// par t ( e ) the lo ad in g c o e f f i c i e n t shi_m=w_m/(u_m^2); disp ( s h i _ m , ” ( e ) t h e l o a d i n g
/ / f o r hub s e c t i o n rh=dh/2; n=(sind(alpha2m)^2);
58
coefficient is ”)
c_x2h=c_xm*((r/rh)^n); c_t2h=c_t2m*((r/rh)^n); c_2h=c_2m*((r/rh)^n); disp ( ” f o r hub s e c t i o n ” ) disp ( ” ( a ) t h e r e l a t i v e a i r a n g l e s a r e ” ) beta2h=atand((c_t2h-uh)/c_x2h); disp ( ” d e g r e e ” ,beta2h , ” a i r a n g le a t r o t o r e nt r y i s beta2h= ”) 46 b e t a 3 h = a t a n d ( u h / c _ x 2 h ) ; 47 disp ( ” d e g r e e ” ,beta3h , ” a i r a ng l e a t r o t o r e x i t i s beta3h= ”) 48 / / p ar t ( b ) d e g r ee o f r e a c t i o n 49 R h = c _ x 2 h * ( t a n d ( b e t a 3 h ) - t a n d ( b e t a 2 h ) ) * 1 0 0 / ( 2 * u h ) ; 50 disp ( ”%” , R h , ” ( b ) d e g r ee o f r e a c t i o n i s ” ) 51 / / p a r t ( c ) b l a d e −to −g as s pe e d r a t i o 52 s i g m a h = u h / c _ 2 h ; 53 disp (sigmah , ” ( c ) blad e −to −g as s pe e d r a t i o i s ” ) 54 / / p a r t ( d ) s p e c i f i c w or k 55 w h = u h * c _ t 2 h ; 56 disp ( ” k J / k g ” , w h * 1 e - 3 , ” ( d ) s p e c i f i c w or k i s ” ) 57 / / p a r t ( e ) t h e l o a d i n g c o e f f i c i e n t 58 s h i _ h = w h / ( u h ^ 2 ) ; 59 disp ( s h i _ h , ” ( e ) t h e l o a d i n g c o e f f i c i e n t i s ” ) 60 61 // f o r t i p s e c t i o n 62 r t = d t / 2 ; 63 c _ x 2 t = c _ x m * ( ( r / r t ) ^ n ) ; 64 c _ t 2 t = c _ t 2 m * ( ( r / r t ) ^ n ) ; 65 c _ 2 t = c _ 2 m * ( ( r / r t ) ^ n ) ; 66 disp ( ” f o r t i p s e c t i o n ” ) 67 disp ( ” ( a ) t h e r e l a t i v e a i r a n g l e s a r e ” ) 68 b e t a 2 t = a t a n d ( ( c _ t 2 t - u t ) / c _ x 2 t ) ; 69 disp ( ” d e g r e e ” ,beta2t , ” a i r a n g le a t r o t o r e nt r y i s beta2t= ”) 70 b e t a 3 t = a t a n d ( u t / c _ x 2 t ) ; 71 disp ( ” d e g r e e ” ,beta3t , ” a i r a ng l e a t r o t o r e x i t i s beta3t= ”) 72 / / p ar t ( b ) d e g r ee o f r e a c t i o n 39 40 41 42 43 44 45
59
73 74 75 76 77 78 79 80 81 82 83
Rt=c_x2t*(tand(beta3t)-tand(beta2t))*100/(2*ut); disp ( ”%” , R t , ” ( b ) d e g r ee o f r e a c t i o n i s ” )
/ / p a r t ( c ) b l a d e −to −g as s pe e d r a t i o sigmat=ut/c_2t; disp (sigmat , ” ( c ) blad e −to −g as s pe e d r a t i o
i s ”)
/ / p a r t ( d ) s p e c i f i c w or k wt=ut*c_t2t; disp ( ” k J / k g ” , w t * 1 e - 3 , ” ( d ) s p e c i f i c w or k i s ” )
// par t ( e ) the lo ad in g c o e f f i c i e n t shi_t=wt/(ut^2); disp ( s h i _ t , ” ( e ) t h e l o a d i n g
coefficient is ”)
Scilab code Exa 9.4 axial turbine stage 3000 rpm
1 2 3 4 5 6 7 8 9 10 11 12
/ / s c i l a b Code Exa 9 . 4 a x i a l t u r b i n e s t a g e 3 0 0 0 rpm
d = 1 ; // mean d ia m e te r o f t he i m p e l l e r b la d e i n m r=d/2; N = 3 e 3 ; // r o t o r S pe ed i n RPM a _ r ( 1 ) = 1 ; // a s p e c t r a t i o a_r(2)=2; a_r(3)=3; a i r a n g l e at n oz z l e e xi t a l p h a 2 = 7 0 ; // alpha3=0; a i r a n gl e a t r o t o r e n t r y b e t a _ 2 = 5 4 ; // s i g m a = 0 . 5 * ( s i n d ( a l p h a 2 ) ) ; // b la d e t o g as s pe ed
ratio 13 14 15 16 17 18
u=%pi*d*N/60; c2=u/sigma; cx=c2*(cosd(alpha2)); b e t a _ 3 = b e t a _ 2 ; // a i r a n g l e a t r o t or e xi t phi=cx/u; e _ R = b e t a _ 2 + b e t a _ 3 ; // R o t o r d e f l e c t i o n a n g l e
60
19 z e e t a _ p _ N = 0 . 0 2 5 * ( 1 + ( ( a l p h a 2 / 9 0 ) ^ 2 ) ) ; // p r o f i l e
l o ss
c o e f f i c i e n t fo r no zz le 20 z e e t a _ p _ R = 0 . 0 2 5 * ( 1 + ( ( e _ R / 9 0 ) ^ 2 ) ) ; // p r o f i l e
l o ss
co efficient for rotor 21 for i = 1 : 3 22 disp ( a _ r ( i ) , ” when A s pe c t r a t i o =” ) 23 z e e t a _ N = ( 1 + ( 3 . 2 / a _ r ( i ) ) ) * z e e t a _ p _ N ; // t o t a l
l o ss
c o e f f i c i e n t f o r no zz le 24 z e e t a _ R = ( 1 + ( 3 . 2 / a _ r ( i ) ) ) * z e e t a _ p _ R ; // t o t a l
l o ss
co efficient for rotor 25 a = ( z e e t a _ R * ( s e c d ( b e t a _ 3 ) ^ 2 ) ) + ( z e e t a _ N * ( s e c d ( a l p h a 2) ^2)); 26 b = p h i * ( t a n d ( a l p h a 2 ) + t a n d ( b e t a _ 3 ) ) - 1 ; 27 c = ( z e e t a _ R * ( s e c d ( b e t a _ 3 ) ^ 2 ) ) + ( z e e t a _ N * ( s e c d ( a l p h a 2) ^2))+(secd(alpha3)^2); 28 n _ t t = inv ( 1 + ( 0 . 5 * ( p h i ^ 2 ) * ( a / b ) ) ) ; 29 disp ( ”%” , n _ t t * 1 e 2 , ” t o t a l −to −t o t a l e f f i c i e n c y i s ” ) 30 n _ t s = inv ( 1 + ( 0 . 5 * ( p h i ^ 2 ) * ( c / b ) ) ) ; 31 disp ( ”%” , n _ t s * 1 e 2 , ” t o t a l −to − s t a t i c e f f i c i e n c y i s ” ) 32 end
Scilab code Exa 9.5 Calculation on a gas turbine stage
1 / / s c i l a b Code Exa 9 . 5 C a l c u l a t i o n on a g as t u r b i n e
stage 2 3 4 5 6 7 8 9
R m = 0 . 5 ; // D e gr ee o f r e a c t i o n funcprot ( 0 ) ; T 1 = 1 5 0 0 ; // i n K el vi n p 1 = 1 0 ; // I n i t i a l P r e s su r e i n b ar N = 1 2 e 3 ; // r o t o r S pe ed i n RPM i n kg / s m = 7 0 ; // p r = 2 ; // P r e ss u r e R at io
61
10 n _ s t = 0 . 8 7 ; // S ta ge E f f i c i e n c y 11 a l p h a _ 2 = 6 0 ; // Fixed Blade e x i t a ng le 12 c p = 1 0 0 5 ; // S p e c i f i c Heat a t C o ns ta nt P r es s u r e i n J
/(kgK) 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
R=287; gamma =1.4; n =( gamma - 1 ) / gamma ; T3ss=T1/(pr^n); delh1_3=cp*(T1-T3ss)*n_st; delh1_2=0.5*delh1_3; c2 = sqrt ( 2 * d e l h 1 _ 2 ) ; sigma_opt=sind(alpha_2); u=sigma_opt*c2;
// pa rt ( a ) Flow c o e f f i c i e n t cx=c2*cosd(alpha_2); phi=cx/u; disp ( p h i , ” ( a ) Flow c o e f f i c i e n t
is ”)
// p a rt ( b ) mean d i am e te r o f t he s t a g e d=u*60/(%pi*N); disp ( ”m” ,d , ” ( b ) mean d i am et e r o f t he s t a g e i s ” )
/ / p a r t ( c ) p ow er d e v e l o p e d P=m*delh1_3; disp ( ”MW” , P * 1 e - 6 , ” ( c ) p ow er d e v e l o p e d
is ”)
/ / p ar t ( d ) p r e s s u r e r a t i o a c r o s s t h e f i x e d and r o t o r b la de r i n g s
delh1_3ss=delh1_3/n_st; delT1_3=delh1_3/cp; delT1_3ss=delh1_3ss/cp; s t a g e _ l o s s = d e l T 1 _ 3 ss - d e l T 1 _ 3 ; delT1_2=delh1_2/cp; delT1_2s=delT1_2+(0.5*stage_loss) pr_stator=((1-(delT1_2s/T1))^(-1/n)); disp (pr_stator , ” ( d ) p r e s s u r e r a t i o a c r o s s t h e f i x e d b la de r i n g s i s ” ) 44 p r _ r o t o r = p r / p r _ s t a t o r ; 36 37 38 39 40 41 42 43
62
45 disp (pr _rotor , ” and p r e s s u r e r a t i o a c r o s s t h e r o t o r b la de r i n g s i s ” ) 46 47 / / p a r t ( e ) h ub−t i p r a t i o o f t he r o t o r 48 p 2 = p 1 / p r _ s t a t o r ; 49 T 2 = T 1 - d e l T 1 _ 2 ; 50 r o 2 = ( p 2 * 1 e 5 ) / ( R * T 2 ) ; 51 l 2 = m / ( r o 2 * c x * % p i * d ) ; 52 p 3 = p 2 / p r _ r o t o r ; 53 T 3 = T 1 - d e l T 1 _ 3 ; 54 r o 3 = p 3 * 1 e 5 / ( R * T 3 ) ; 55 l 3 = m / ( r o 3 * c x * % p i * d ) ; 56 l = 0 . 5 * ( l 2 + l 3 ) ; 57 r m = d / 2 ; 58 r h = r m - ( l / 2 ) ; 59 r t = r m + ( l / 2 ) ; 60 disp ( r h / r t , ” ( e ) hub−t i p r a t i o o f t h e r o t o r i s ” ) 61 62 // p ar t ( f ) d e g r ee o f r e a c t i o n a t t he hub and t i p 63 R h = 1 - ( ( 1 - R m ) * ( r m ^ 2 / r h ^ 2 ) ) ; 64 R t = 1 - ( ( 1 - R h ) * ( r h ^ 2 / r t ^ 2 ) ) ; 65 disp ( ”%” , R h * 1 e 2 , ” ( f ) d e g r e e o f r e a c t i o n a t t he hub i s ”) 66 disp ( ”%” , R t * 1 e 2 , ” ( f ) d eg re e o f r e a c t i o n a t t he t i p i s ”)
63
Chapter 11 Axial Compressor Stages
Scilab code Exa 11.1 Calculation on an axial compressor stage
1 / / s c i l a b Code Exa 1 1 . 1 C a l c u l a t i o n on a n a x i a l
c o mp r e ss o r s t a g e 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
R m = 0 . 5 ; // D e gr ee o f r e a c t i o n funcprot ( 0 ) ; T 1 = 3 0 0 ; // i n K el vi n I n i t i a l P r e s s u r e i n b ar p1=1; / / gamma =1.4; N = 1 8 e 3 ; // r o t o r S pe ed i n RPM d = 3 6 / 1 0 0 ; / / Mean B la de r i n g d i am et er i n m h = 6 / 1 0 0 ; // b la de h e i g h t a t e nt ry i n m c x = 1 8 0 ; // A xi al v e l o c i t y i n m/ s a i r a n g l e a t r o t o r and s t a t o r e x i t a l p h a _ 1 = 2 5 ; // w d f = 0 . 8 8 ; / / w or k−done f a c t o r i n kg / s m = 7 0 ; // p r = 2 ; // P r e ss u r e R at io n _ s t = 0 . 8 5 ; // S ta ge E f f i c i e n c y n _ m = 0 . 9 6 7 ; // M ec ha ni ca l E f f i c i e n c y c p = 1 0 0 5 ; // S p e c i f i c Heat a t C o ns ta nt P r es s u r e i n J
64
/(kgK) 19 20 21 22 23 24 25 26 27
R=287; u=%pi*d*N/60; n =( gamma - 1 ) / gamma ;
28 29 30 31 32 33 34 35 36
phi=cx/u;
37 38 39 40 41 42 43 44 45 46 47 48 49 50
/ / p ar t ( a ) a i r a n g l e s a t r o t o r and s t a t o r e nt ry
cy1=cx*tand(alpha_1); wy1=u-cy1; beta1=atand(wy1/cx); disp ( ” d e g r e e ” , b e t a 1 , ” a i r
a n g l e s a t r o t o r and s t a t o r e n t r y a r e b e t a 1=a l p h a 2= ” )
// p ar t ( b ) mass f lo w r a te o f t h e a i r
ro1=(p1*1e5)/(R*T1); A1=%pi*d*h; m=ro1*cx*A1; disp ( ” k g / s ” ,m , ” ( b ) mass f lo w r a t e o f t h e a i r
i s ”)
/ / p a r t ( c ) D e te r mi n in g p ower r e q u i r e d t o d r i v e t h e compressor
beta2=alpha_1; w=wdf*u*cx*(tand(beta1)-tand(beta2)) P=m*w/n_m; disp ( ”kW” , P / 1 0 0 0 , ” ( c ) Power r e q u i r e d t o d r i v e t he c o mp r e ss o r i s ” )
// pa rt (d ) Load ing c o e f f i c i e n t shi=w/(u^2); disp ( s h i , ” (d ) Load ing
co efficient is ”)
// p ar t ( e ) p r e s s u r e r a t i o d ev el o p ed by t he s t a ge
delTa=w/cp; delTs=n_st*delTa; pr=((1+(delTs/T1))^(1/n)); disp ( p r , ” ( e ) p r e s s u r e r a t i o d ev el op ed by t he s t a g e ”)
51
65
is
52 53 54 55
/ / p a r t ( f ) Mach number a t t h e r o t o r e n t r y w1=cx/(cosd(beta1)); M w 1 = w 1 / sqrt ( gamma * R * T 1 ) ; disp ( M w 1 , ” ( f ) Mach number a t t h e r o t o r
entry is ”)
Scilab code Exa 11.2 Calculation on an axial compressor stage
1 / / s c i l a b Code Exa 1 1 . 2 C a l c u l a t i o n on a n a x i a l
c o mp r e ss o r s t a g e 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
T 1 = 3 1 4 ; // i n K el vi n I n i t i a l P r e s s u r e i n mm Hg p1=768; / / N = 1 8 e 3 ; // r o t o r S pe ed i n RPM d = 5 0 / 1 0 0 ; / / Mean B la de r i n g d i am et er i n m u = 1 0 0 ; // p e r i p h e r a l s pe ed i n m/ s h = 6 / 1 0 0 ; // b la de h e i g h t a t e nt ry i n m beta1=51; beta2=9; a i r a n g le a t r o t o r and s t a t o r e x i t a l p h a _ 1 = 7 ; // w d f = 0 . 9 5 ; / / w or k−done f a c t o r i n kg / s m = 2 5 ; // n _ s t = 0 . 8 8 ; // S ta ge E f f i c i e n c y n _ m = 0 . 9 2 ; // M ec ha ni ca l E f f i c i e n c y c p = 1 0 0 5 ; // S p e c i f i c Heat a t C o ns ta nt P r es s u r e i n J
/(kgK) 17 18 19 20 21 22 23 24
R=287; gamma =1.4; n =( gamma - 1 ) / gamma ;
/ / p ar t ( a ) a i r a n g l e a t s t a t o r e nt ry cx=u/(tand(alpha_1)+tand(beta1)); disp ( c x , ”cx=” ) a l p h a 2 = a t a n d ( t a n d ( a l p h a _ 1 ) + t a n d ( b e t a 1 ) - t a n d ( b e t a 2 ))
66
25 disp ( ” d e g r e e ” ,alpha2 , ” a i r a n g le a t s t a t o r e nt ry a l p h a 2 = ”) 26 27 / / p a rt ( b ) b l ad e h e i g h t a t e n tr y and hub−t i p
is
d i am et er r a t i o 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
ro1=(p1/750*1e5)/(R*T1); h1=m/(ro1*cx*%pi*d); disp ( ”cm” , h 1 * 1 e 2 , ” ( b ) b la d e h e i g h t a t e n t r y i s ” ) dh=d-h1; disp ( d h , ”dh=” ) dt=d+h1; disp ( d t , ”dt=” ) disp ( d h / d t , ” a n d h ub−t i p d ia me te r r a t i o i s ” )
// par t ( c ) st ag e Loading c o e f f i c i e n t w=wdf*u*cx*(tand(beta1)-tand(beta2)); shi=w/(u^2); disp ( s h i , ” (d ) Load ing c o e f f i c i e n t i s ” )
// p ar t ( d ) s t a g e p r e s s u r e r a t i o
delTa=w/cp; delTs=n_st*delTa; pr=((1+(delTs/T1))^(1/n)); disp ( p r , ” ( e ) p r e s s u r e r a t i o d ev el op ed by t he s t a g e ”)
47 48 / / p a r t ( e ) D e te r mi n in g p ower r e q u i r e d
to drive the
compressor 49 P = m * w / n _ m ; 50 disp ( ”kW” , P / 1 0 0 0 , ” ( e ) Power r e q u i r e d t o d r i v e t he c o mp r e ss o r i s ” )
Scilab code Exa 11.3 Calculation on an axial compressor stage
67
is
1 / / s c i l a b Code Exa 1 1 . 3 C a l c u l a t i o n on a n a x i a l
c o mp r e ss o r s t a g e 2 3 // p ar t ( c ) V e r i f i c a t i o n
o f s t a g e e f f i c i e n c y o f e xa
11.1 beta1=54.82; alpha_1=25; beta2=alpha_1; alpha_2=beta1; p h i = 0 . 5 3 ; // Flow c o e f f i c i e n t Y R = 0 . 0 9 ; / / l o s s c o e f f i c i e n t f o r t h e b l a d e r ow s n _ s t = 1 - ( ( p h i * Y R * ( s e c d ( b e t a 1 ) ^ 2 ) ) / ( t a n d ( b e t a 1 ) - t a n d( beta2))) 11 disp ( ”%” , n _ s t * 1 e 2 , ” s t ag e e f f i c i e n c y n s t =” ) 12 / / p a r t ( d ) D e t e r m i n i n g e f f i c i e n c i e s o f t h e r o t o r a nd 4 5 6 7 8 9 10
D i f f u s e r b la d e ro ws 13 n _ D = 1 - ( Y R / ( 1 - ( ( s e c d ( a l p h a _ 1 ) ^ 2 ) / ( s e c d ( a l p h a _ 2 ) ^ 2 ) )) ) 14 disp ( ”%” , n _ D * 1 0 0 , ” E f f i c i e n c y o f t h e d i f f u s e r n D= n R=” )
Scilab code Exa 11.4 Calculation on hub mean and tip sections
1 / / s c i l a b Code Exa 1 1 . 4 C a l c u l a t i o n on hub , mean and
t ip s e c ti o n s 2 3 4 5 6 7 8 9 10
d m = 5 0 / 1 0 0 ; / / Mean B la de r i n g d i am et e r i n m rm=dm/2; d h = 0 . 3 0 9 8 3 5 4 ; // from r e s u l t s o f ex a 1 1 . 2 dt=0.6901646; u m = 1 0 0 ; // p e r i p h e r a l s pe ed i n m/ s beta_1m=51; beta_2m=9; a l p h a _ 1 m = 7 ; // a i r a n g l e a t r o t o r and s t a t o r
68
e xi t
11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
alpha_2m=50.177922; omega=um/rm; rh=dh/2; rt=dt/2; uh=omega*rh; ut=omega*rt;
/ / p ar t ( a ) r o t o r b la de a i r a n g l e s
cx=73.654965; c_theta1m=cx*tand(alpha_1m); C1=rm*c_theta1m; c_theta1h=C1/rh; c_theta1t=C1/rt; c_theta2m=cx*tand(alpha_2m); C2=rm*c_theta2m; c_theta2h=C2/rh; c_theta2t=C2/rt; disp ( ” ( a ) t h e r o t o r b la de a i r a n g l e s a re ” )
/ / f o r hub s e c t i o n
alpha1h=atand(C1/(rh*cx)); alpha2h=atand(C2/(rh*cx)); disp ( ” f o r hub s e c t i o n ” ) disp ( ” d e g r e e ” ,alpha1h , ” a l p h a 1 h = ” ) disp ( ” d e g r e e ” ,alpha2h , ” a l p h a 2 h = ” ) beta1h=atand((uh/cx)-tand(alpha1h)); beta2h=atand((uh/cx)-tand(alpha2h)); disp ( ” d e g r e e ” ,beta1h , ” b e t a 1 h = ” ) disp ( ” d e g r e e ” ,beta2h , ” b e t a 2 h = ” )
// f o r t i p s e c t i o n
alpha1t=atand(C1/(rt*cx)); alpha2t=atand(C2/(rt*cx)); disp ( ” f o r t i p s e c t i o n ” ) disp ( ” d e g r e e ” ,alpha1t , ” a l p h a 1 t= ” ) disp ( ” d e g r e e ” ,alpha2t , ” a l p h a 2 t= ” ) beta1t=atand((ut/cx)-tand(alpha1t)); beta2t=atand((ut/cx)-tand(alpha2t)); disp ( ” d e g r e e ” ,beta1t , ” b e t a 1 t= ” )
69
49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78
disp ( ” d e g r e e ” ,beta2t , ” b e t a 2 t= ” )
// pa rt (b ) Flow c o e f f i c i e n t s disp ( ” (b ) Flow c o e f f i c i e n t s ar e ” )
phi_h=cx/uh; disp ( p h i _ h , ” p h i h = ” ) phi_m=cx/um; disp ( p h i _ m , ”phi m=” ) phi_t=cx/ut; disp ( p h i _ t , ” p h i t =” )
// p a rt ( c ) d e g r e es o f r e a c t i o n disp ( ” ( c ) D eg re es o f r e a c t i o n a r e ” )
Rh=cx*(tand(beta1h)+tand(beta2h))*100/(2*uh); disp ( ”%” , R h , ”Rh=” ) Rm=cx*(tand(beta_1m)+tand(beta_2m))*100/(2*um); disp ( ”%” , R m , ”Rm=” ) Rt=cx*(tand(beta1t)+tand(beta2t))*100/(2*ut); disp ( ”%” , R t , ”Rt=” )
/ / p a r t ( d ) s p e c i f i c w or k w=omega*(C2-C1); disp ( ” k J / k g ” , w * 1 e - 3 , ” ( d ) s p e c i f i c w or k i s ” )
// par t ( e ) the lo ad in g c o e f f i c i e n t s disp ( ” ( e ) t h e l o a d i n g c o e f f i c i e n t s a r e ” )
shi_h=w/(uh^2); disp ( s h i _ h , ” s h i h =” ) shi_m=w/(um^2); disp ( s h i _ m , ” s h i m = ” ) shi_t=w/(ut^2); disp ( s h i _ t , ” s h i t =” )
Scilab code Exa 11.5 Forced Vortex axial compressor stage
70
1 / / s c i l a b Code Exa 1 1 . 5 F or ce d V or te x a x i a l
c o mp r e ss o r s t a g e 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
d m = 5 0 / 1 0 0 ; / / Mean B la de r i n g d i am et e r i n m rm=dm/2; d h = 0 . 3 0 9 8 3 5 4 ; // from r e s u l t s o f ex a 1 1 . 2 dt=0.6901646; u m = 1 0 0 ; // p e r i p h e r a l s pe ed i n m/ s beta_1m=51; beta_2m=9; a i r a n g l e a t r o t o r and s t a t o r a l p h a _ 1 m = 7 ; // alpha_2m=50.177922; omega=um/rm; rh=dh/2; rt=dt/2; uh=omega*rh; ut=omega*rt;
e xi t
/ / p ar t ( a ) r o t o r b la de a i r a n g l e s
cx=73.654965; c_theta1m=cx*tand(alpha_1m); C1=c_theta1m/rm; c_theta1h=C1*rh; c_theta1t=C1*rt; K1=cx^2+(2*(C1^2)*(rm^2)); c x 1 h = sqrt ( K 1 - ( 2 * ( C 1 ^ 2 ) * ( r h ^ 2 ) ) ) ; c x 1 t = sqrt ( K 1 - ( 2 * ( C 1 ^ 2 ) * ( r t ^ 2 ) ) ) ; c_theta2m=cx*tand(alpha_2m); C2=c_theta2m/rm; c_theta2h=C2*rh; c_theta2t=C2*rt; K 2 = c x ^ 2 - ( 2 * ( C 2 - C 1 ) * o m e g a * ( r m ^ 2 ) ) + ( 2 * ( C 2 ^ 2 ) * ( r m ^ 2 ) ); c x 2 h = sqrt ( K 2 + ( 2 * ( C 2 - C 1 ) * o m e g a * ( r h ^ 2 ) ) - ( 2 * ( C 2 ^ 2 ) * ( r h ^2))); 32 c x 2 t = sqrt ( K 2 + ( 2 * ( C 2 - C 1 ) * o m e g a * ( r t ^ 2 ) ) - ( 2 * ( C 2 ^ 2 ) * ( r t ^2))); 33 disp ( ” ( a ) t h e r o t o r b la de a i r a n g l e s a re ” ) 34 / / f o r hub s e c t i o n 35 a l p h a 1 h = a t a n d ( C 1 * r h / c x 1 h ) ;
71
36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57
alpha2h=atand(C2*rh/cx2h); disp ( ” f o r hub s e c t i o n ” ) beta1h=atand((uh/cx1h)-tand(alpha1h)); beta2h=atand((uh/cx2h)-tand(alpha2h)); disp ( ” d e g r e e ” ,beta1h , ” b e t a 1 h = ” ) disp ( ” d e g r e e ” ,beta2h , ” b e t a 2 h = ” )
// f o r t i p s e c t i o n
alpha1t=atand(C1*rt/cx1t); alpha2t=atand(C2*rt/cx2t); disp ( ” f o r t i p s e c t i o n ” ) beta1t=atand((ut/cx1t)-tand(alpha1t)); beta2t=atand((ut/cx2t)-tand(alpha2t)); disp ( ” d e g r e e ” ,beta1t , ” b e t a 1 t= ” ) disp ( ” d e g r e e ” ,beta2t , ” b e t a 2 t= ” )
/ / p a r t ( b ) s p e c i f i c w or k
wh=omega*(C2-C1)*(rh^2); wm=omega*(C2-C1)*(rm^2); wt=omega*(C2-C1)*(rt^2); disp ( ” k J / k g ” , w h * 1 e - 3 , ” ( b ) s p e c i f i c w or k a t hub i s ” ) disp ( ” k J / k g ” , w m * 1 e - 3 , ” s p e c i f i c w or k a t mean s e c t i o n is”) 58 disp ( ” k J / k g ” , w t * 1 e - 3 , ” s p e c i f i c wo rk a t t i p i s ” ) 59 / / p a r t ( c ) t h e l o a d i n g c o e f f i c i e n t s 60 disp ( ” ( c ) t h e l o a d i n g c o e f f i c i e n t s a r e ” ) 61 s h i _ h = w h / ( u h ^ 2 ) ; 62 disp ( s h i _ h , ” s h i h =” ) 63 s h i _ m = w m / ( u m ^ 2 ) ; 64 disp ( s h i _ m , ” s h i m = ” ) 65 s h i _ t = w t / ( u t ^ 2 ) ; 66 disp ( s h i _ t , ” s h i t =” ) 67 68 // p a rt ( c ) d e g r e es o f r e a c t i o n 69 disp ( ” ( d ) D eg re es o f r e a c t i o n a r e ” ) 70 R h = ( ( c x 1 h ^ 2 ) * ( s e c d ( b e t a 1 h ) ^ 2 ) - ( c x 2 h ^ 2 ) * ( s e c d ( b e t a 2h ) ^2))*100/(2*wh); 71 R m = ( ( c x ^ 2 ) * ( s e c d ( b e t a _ 1 m ) ^ 2 ) - ( c x ^ 2 ) * ( s e c d ( b e t a _ 2 m )
72
72 73 74 75
^2))*100/(2*wm); R t = ( ( c x 1 t ^ 2 ) * ( s e c d ( b e t a 1 t ) ^ 2 ) - ( c x 2 t ^ 2 ) * ( s e c d ( b e t a 2t ) ^2))*100/(2*wt); disp ( ”%” , R h , ”Rh=” ) disp ( ”%” , R m , ”Rm=” ) disp ( ”%” , R t , ”Rt=” )
Scilab code Exa 11.6 General Swirl Distribution axial compressor
1 / / s c i l a b Code Exa 1 1 . 6 G en er al S w i r l D i s t r i b u t i o n
a x i a l c o mp re s so r 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
R m = 0 . 5 ; // D e gr ee o f r e a c t i o n d m = 3 6 / 1 0 0 ; / / Mean B la de r i n g d i am et e r i n m rm=dm/2; N = 1 8 e 3 ; // r o t o r S pe ed i n RPM h = 6 / 1 0 0 ; // b la de h e i g h t a t e nt ry i n m dh=dm-h; dt=dm+h; c x = 1 8 0 ; // A xi al v e l o c i t y i n m/ s a i r a n g le a t r o t o r and s t a t o r a l p h a _ 1 m = 2 5 ; // alpha_2m=54.820124; um=%pi*dm*N/60; omega=um/rm; rh=dh/2; rt=dt/2; uh=omega*rh; ut=omega*rt;
/ / p ar t ( a ) r o t o r b la de a i r a n g l e s c_theta1m=cx*tand(alpha_1m); c_theta2m=cx*tand(alpha_2m); a=0.5*(c_theta1m+c_theta2m)
73
e xi t
24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
b=rm*(c_theta2m -c_theta1m) *0.5; c_theta1h=a-(b/rh); c_theta1t=a-(b/rt); K 1 = c x ^ 2 + ( 2 * ( a ^ 2 ) * ( ( b / ( a * r m ) ) +log ( r m ) ) ) ; c x 1 h = sqrt ( K 1 - ( 2 * ( a ^ 2 ) * ( ( b / ( a * r h ) ) + log ( r h ) ) ) ) ; c x 1 t = sqrt ( K 1 - ( 2 * ( a ^ 2 ) * ( ( b / ( a * r t ) ) + log ( r t ) ) ) ) ;
c_theta2h=a+(b/rh); c_theta2t=a+(b/rt); K 2 = c x ^ 2 + ( 2 * ( a ^ 2 ) * (log ( r m ) - ( b / ( a * r m ) ) ) ) ; c x 2 h = sqrt ( K 2 - ( 2 * ( a ^ 2 ) * ( log ( r h ) - ( b / ( a * r h ) ) ) ) ) ; c x 2 t = sqrt ( K 2 - ( 2 * ( a ^ 2 ) * ( log ( r t ) - ( b / ( a * r t ) ) ) ) ) ; disp ( ” ( a ) t h e r o t o r b la de a i r a n g l e s a re ” )
/ / f o r hub s e c t i o n
alpha1h=atand(c_theta1h/cx1h); alpha2h=atand(c_theta2h/cx2h); disp ( ” f o r hub s e c t i o n ” ) beta1h=atand((uh/cx1h)-tand(alpha1h)); beta2h=atand((uh/cx2h)-tand(alpha2h)); disp ( ” d e g r e e ” ,beta1h , ” b e t a 1 h = ” ) disp ( ” d e g r e e ” ,beta2h , ” b e t a 2 h = ” )
// f o r t i p s e c t i o n
alpha1t=atand(c_theta1t/cx1t); alpha2t=atand(c_theta2t/cx2t); disp ( ” f o r t i p s e c t i o n ” ) beta1t=atand((ut/cx1t)-tand(alpha1t)); beta2t=atand((ut/cx2t)-tand(alpha2t)); disp ( ” d e g r e e ” ,beta1t , ” b e t a 1 t= ” ) disp ( ” d e g r e e ” ,beta2t , ” b e t a 2 t= ” )
/ / p a r t ( b ) s p e c i f i c w or k w=2*omega*b; disp ( ” k J / k g ” , w * 1 e - 3 , ” ( b ) s p e c i f i c w or k i s ” )
// par t ( c ) the lo ad in g c o e f f i c i e n t s disp ( ” ( c ) t h e l o a d i n g c o e f f i c i e n t s a r e ” ) shi_h=w/(uh^2);
74
62 63 64 65 66 67 68 69 70 71 72 73 74 75
disp ( s h i _ h , ” s h i h =” ) shi_m=w/(um^2); disp ( s h i _ m , ” s h i m = ” ) shi_t=w/(ut^2); disp ( s h i _ t , ” s h i t =” )
// p a rt ( c ) d e g r e es o f r e a c t i o n disp ( ” ( d ) D eg re es o f r e a c t i o n a r e ” ) R h = ( ( c x 1 h ^ 2 ) * ( s e c d ( b e t a 1 h ) ^ 2 ) - ( c x 2 h ^ 2 ) * ( s e c d ( b e t a 2h ) ^2))*100/(2*w); R t = ( ( c x 1 t ^ 2 ) * ( s e c d ( b e t a 1 t ) ^ 2 ) - ( c x 2 t ^ 2 ) * ( s e c d ( b e t a 2t ) ^2))*100/(2*w); disp ( ”%” , R h , ”Rh=” ) disp ( ”%” , R m * 1 0 0 , ”Rm=” ) disp ( ”%” , R t , ”Rt=” ) disp ( ”Comment : b oo k c o n t a i n s wrong c a l c u l a t i o n f o r Rt v a lu e ” )
Scilab code Exa 11.7 flow and loading coefficients
1 / / s c i l a b Code Exa 1 1 . 7 f l o w and l o a d i n g
coefficients 2 u = 3 3 9 . 2 9 ; / / i n m/ s 3 c x = 1 8 0 ; // A xi al v e l o c i t y i n m/ s 4 a l p h a _ 1 m = 2 5 ; // a i r a n g le a t r o t o r and s t a t o r e x i t 5 6 7 8 9 10 11 12
phi(1)=0.2; phi(2)=0.4; phi(3)=cx/u; phi(4)=0.6; phi(5)=0.8; n=5; for i = 1 : n shi(i)=1-phi(i)*(2*tand(alpha_1m));
75
13 disp ( p h i ( i ) , ”when fl ow c o e f f i c i e n t ph i=” ) disp ( s h i ( i ) , ” t h e n l o a d i n g c o e f f i c i e n t s h i =” ) 14 15 end
76
Chapter 12 Centrifugal Compressor Stage
Scilab code Exa 12.1 Calculation on a centrifugal compressor stage
1 / / s c i l a b Code Exa 1 2 . 1 C a l c u l a t i o n on a c e n t r i f u g a l
c o m pr e s so r s t a g e 2 T 0 1 = 3 3 5 ; // i n K el vi n 3 4 5 6 7 8 9 10 11
funcprot ( 0 ) ; p 0 1 = 1 . 0 2 ; // I n i t i a l P r e s su r e i n b ar d h = 0 . 1 0 ; // hub d i am e te r i n m d t = 0 . 2 5 ; // t i p d ia me te r i n m m = 5 ; // i n kg / s gamma =1.4; N = 7 . 2 e 3 ; // r o t o r S pe ed i n RPM d 1 = 0 . 5 * ( d t + d h ) ; / / Mean B la de r i n g d i a m et e r c p = 1 0 0 5 ; // S p e c i f i c Heat a t C o ns ta nt P r es s u r e i n J
/(kgK) 12 13 14 15 16 17
A=%pi*((dt^2)-(dh^2))/4; R=287;
// I t r i a l ro1=(p01*1e5)/(R*T01); cx0=m/(ro1*A); T0=T01-((cx0^2)/(2*cp));
77
18 19 20 21 22 23 24 25 26 27 28 29 30
n =( gamma - 1 ) / gamma ; p1=p01*((T0/T01)^(1/n)); ro=(p1*1e5)/(R*T0); cx=m/(ro*A);
// I I T ri al
31 32 33 34 35 36 37 38 39 40 41
cx2=123; T1=T01-((cx2^2)/(2*cp)); p2=p01*((T1/T01)^(1/n)); ro2=(p2*1e5)/(R*T1); cx1=m/(ro2*A); u1=%pi*d1*N/60; beta1=atand(cx1/u1); disp ( ” d e g r e e ” , b e t a 1 , ” a i r a n gl e a t i n du c er b l a de e n t r y b e t a 1=” ) w1=cx1/(sind(beta1)); a1 = sqrt ( gamma * R * T 1 ) ; Mw1=w1/a1; disp ( M w 1 , ” t h e R e l a t i v e Mach n umber a t i n d u c e r b l a d e e n t r y Mw1=” ) alpha1=atand(cx1/u1); disp ( ” d e g r e e ” ,alpha1 , ” a i r a n g l e a t IGVs e x i t a lp ha 1= ”) c1=cx1/(sind(alpha1)); T1_new=T01-((c1^2)/(2*cp)); a 1 _ n e w = sqrt ( gamma * R * T 1 _ n e w ) ; Mw1_new=cx1/a1_new; disp (Mw1 _new , ” t h e new v a l u e o f R e l a t i v e Mach number Mw1 new=” )
Scilab code Exa 12.2 Calculation on a centrifugal air compressor
1 / / s c i l a b Code Exa 1 2 . 2 C a l c u l a t i o n on a c e n t r i f u g a l
a i r c om p re ss o r 78
2 3 4 5 6 7 8 9 10 11
T 0 1 = 2 8 8 ; // i n K el vi n p 0 1 = 1 . 0 2 ; // I n i t i a l P r e s su r e i n b ar d h = 0 . 1 0 ; // hub d i am e te r i n m d t = 0 . 2 5 ; // t i p d ia me te r i n m i n kg / s m = 5 ; // gamma =1.4; n =( gamma - 1 ) / gamma ; N = 7 . 2 e 3 ; // r o t o r S pe ed i n RPM d 2 = 0 . 4 5 ; // I m p e l l e r d i a me te r i n m c p = 1 0 0 5 ; // S p e c i f i c Heat a t C o ns ta nt P r es s u r e i n J
/(kgK) 12 13 14 15 16
u2=%pi*d2*N/60; pr0=((1+(u2^2/(cp*T01)))^(1/n)); disp ( p r 0 , ” p r e s s u r e r a t i o d e ve lo p ed p r0=” ) w=u2^2; disp ( ”kW/( kg/ s ) ” , w * 1 e - 3 , ” Power r e q u i r e d t o d r i v e t he c o m p r e s s o r P=” )
Scilab code Exa 12.3 centrifugal compressor stage 17000 rpm
1 / / s c i l a b Code Exa 1 2 . 3 C a l c u l a t i o n on a c e n t r i f u g a l
c o m pr e s so r s t a g e 2 3 4 5 6 7 8 9 10 11 12
funcprot (0) T 0 1 = 3 0 6 ; / / E n tr y T e mp er at ur e i n K e l v i n p 0 1 = 1 . 0 5 ; // En tr y P r e s s u r e i n b a r d h = 0 . 1 2 ; // hub d i am e te r i n m d t = 0 . 2 4 ; // t i p d ia me te r i n m i n kg / s m = 8 ; // m u = 0 . 9 2 ; // s l i p f a c t o r n _ s t = 0 . 7 7 ; // s t a ge e f f i c i e n c y gamma =1.4; N = 1 7 e 3 ; // r o t o r S pe ed i n RPM
79
13 14 15 16
d _ i t = 0 . 4 8 ; // I m p e l l e r t i p d ia me te r i n m d 1 = 0 . 5 * ( d t + d h ) ; / / Mean B la de r i n g d i a m et e r rm=d1/2; c p = 1 0 0 5 ; // S p e c i f i c Heat a t C o ns ta nt P r es s u r e i n J
/(kgK) 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
47
A=%pi*((dt^2)-(dh^2))/4; R=287; n = 8 6 ; // number o f i t e r a t i o n s ro01=(p01*1e5)/(R*T01); cx(1)=m/(ro01*A); for i = 1 : n T1=T01-((cx(i)^2)/(2*cp)); p 1 = p 0 1 * ( ( T 1 / T 0 1 ) ^ ( 1 / ( (gamma - 1 ) / gamma ) ) ) ; ro1=(p1*1e5)/(R*T1); cx(i+1)=m/(ro1*A); if c x ( i + 1 ) = = c x ( i ) then disp ( ”m/s” , c x ( i + 1 ) , ”cx=” ) disp ( T 1 , ”T1” ) disp ( p 1 , ” p 1 ” ) disp ( r o 1 , ” r o 1 ” ) end end cx1=cx(i+1); u1m=%pi*d1*N/60; omega=u1m/rm; rh=dh/2; rt=dt/2; uh=omega*rh; ut=omega*rt; u2=d_it*u1m/d1; beta1h=atand(cx1/uh); beta1m=atand(cx1/u1m); beta1t=atand(cx1/ut); disp ( ” ( a ) W it ho ut IGVs ” ) disp ( ” d e g r e e ” ,beta1h , ” a i r a n gl e a t hub s e c t i o n beta1h=” ) disp ( ” d e g r e e ” ,beta1m , ” a i r a n gl e a t mean s e c t i o n beta1m=” )
80
48 disp ( ” d e g r e e ” ,beta1t , ” a i r a n g le a t t i p s e c t i o n beta1t=” ) 49 w 1 t = c x 1 / ( s i n d ( b e t a 1 t ) ) ; 50 a1 = sqrt ( gamma * R * T 1 ) ; 51 M 1 t = w 1 t / a 1 ; 52 disp ( M 1 t , ” t h e maximum Mach n um be r a t i n d u c e r b l a d e en tr y M1t=” ) 53 p r 0 = ( ( 1 + ( m u * n _ s t * ( u 2 ^ 2 ) / ( c p * T 0 1 ) ) ) ^ ( 1 / ( (gamma - 1 ) / gamma ) ) ) ; 54 disp ( p r 0 , ” t o t a l p r e s s u r e r a t i o d ev el op ed i s ” ) 55 P = m * m u * ( u 2 ^ 2 ) ; 56 disp ( ”kW” , P / 1 0 0 0 , ” Power r e q u i r e d t o d r i v e t he c o m p r e ss o r w i t h ou t IGVs i s ” ) 57 58 / / p a r t ( b ) w i th IGVs 59 a l p h a 1 h = b e t a 1 h ; 60 a l p h a 1 m = b e t a 1 m ; 61 a l p h a 1 t = b e t a 1 t ; 62 disp ( ” ( b ) W ith IGVs ” ) 63 disp ( ” d e g r e e ” ,alpha1h , ” a i r a n g l e a t hub s e c t i o n alpha1h=” ) 64 disp ( ” d e g r e e ” ,alpha1m , ” a i r a n gl e a t mean s e c t i o n alpha1m=” ) 65 disp ( ” d e g r e e ” ,alpha1t , ” a i r a ng le a t t i p s e c t i o n a l p h a 1 t = ”) 66 c 1 t = c x 1 / ( s i n d ( a l p h a 1 t ) ) ; 67 T 1 t = T 0 1 - ( ( c 1 t ^ 2 ) / ( 2 * c p ) ) ; 68 a 1 t = sqrt ( gamma * R * T 1 t ) ; 69 M w 1 t = c x 1 / a 1 t ; 70 disp ( M w 1 t , ” t h e maximum Mach n um be r a t i n d u c e r b l a d e e n t r y Mw1t=” ) 71 p r 0 _ w = ( ( 1 + ( n _ s t * ( m u * ( u 2 ^ 2 ) - ( u 1 m ^ 2 ) ) / ( c p * T 0 1 ) ) ) ^ ( 1 /( ( gamma - 1 ) / gamma ) ) ) ; 72 disp ( p r 0 _ w , ” t o t a l p r e s s u re r a t i o d ev el op ed i s ” ) 73 P _ w = m * ( m u * ( u 2 ^ 2 ) - ( u 1 m ^ 2 ) ) ; 74 disp ( ”kW” , P _ w / 1 0 0 0 , ” Power r e q u i r e d t o d r i v e t he c o mp r e ss o r i s ” ) 75 disp ( ”Comment : h e re t he s o l u t i o n i s f ou nd o ut u s i ng
81
programming , s o t h i s g i v e s s l i g h t l y s m al l v a r i a t i o n from t h a a ns we rs g i ve n i n h te book , b ut a ns we rs fro m t he p r e s e n t s o l u t i o n a r e e xa c t . ” )
Scilab code Exa 12.4 Radially tipped blade impeller
1 // s c i l a b Code E xa 1 2 . 4 . b R a d ia l l y t i p p ed b l a de
impeller 2 3 4 5 6 7 8 9 10 11 12 13
14 15
p h i 2 = 0 . 2 6 8 ; // Flow c o e f f i c i e n t T 0 1 = 2 9 3 ; // i n K el vi n I n i t i a l P r e s su r e i n b ar p 0 1 = 1 ; // d r = 2 . 6 6 7 ; / / d i a m et e r r a t i o ( d 2/ d1 ) gamma =1.4; R=287; N = 8 e 3 ; // r o t o r S pe ed i n RPM d 1 = 0 . 1 8 ; // Mean d ia me te r a t t he i m p e l l e r e n t r y i n m u1=%pi*d1*N/60; a1 = sqrt ( gamma * R * T 0 1 ) ; Mb1=u1/a1; disp ( M b 1 , ” t h e Mach n umber a t i n d u c e r b l a d e e n t r y Mb1 =” ) M2 = sqrt ( ( ( d r ^ 2 ) * ( M b 1 ^ 2 ) * ( 1 + ( p h i 2 ^ 2 ) ) ) / ( 1 + ( 0 . 5 * ( gamma -1)*(dr^2)*(Mb1^2)*(1-(phi2^2))))); disp ( M 2 , ” t h e f l o w Mach n umber a t i m p e l l e r e x i t M2=” )
Scilab code Exa 12.5 Radially tipped blade impeller
1 / / s c i l a b Code Exa 1 2 . 5 R a d ia l l y t i p p ed b l a de
impeller 82
2 // p ar t ( a ) f r e e v o r te x f lo w 3 r 3 = 0 . 2 5 ; // v o l u t e b as e c i r c l e r a d i u s i n m 4 c _ t h e t a 3 = 1 7 7 . 5 ; // t a n g e n t i a l v e l o c i t y component o f
a i r i n m/ s 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
K=r3*c_theta3; b = 0 . 1 2 ; / / w i d th i n m Q = 5 . 4 ; // d i s c h a r g e i n m3/ s n=8; disp ( ” p a r t ( a ) ” ) theta(1)=%pi/4; theta(2)=%pi/2; theta(3)=3*%pi/4; theta(4)=%pi; theta(5)=5*%pi/4; theta(6)=3*%pi/2; theta(7)=7*%pi/4; theta(8)=2*%pi; disp ( ” t h e v o l u t e r a d i i a t e i g h t a ng ul ar p o s i t i o n s a r e g i v e n b el o w : ” ) for i = 1 : n r 4 ( i ) = r 3 *exp ( t h e t a ( i ) * Q / ( 2 * % p i * K * b ) ) disp ( ” r a d i a n ” , t h e t a ( i ) , ” a t t h e t a =” ) disp ( ”cm” , r 4 ( i ) * 1 0 0 , ”r4=” ) end L=r4(8)-r3; disp ( L / ( 2 * r 3 ) ,” ( a ) th r o a t −to −d i a m et e r r a t i o ( L/ d3 )=” )
// p a rt ( b ) c o n st a n t mean v e l o c i t y o f 14 5 m/ s c m = 1 4 5 ; // c o n st a n t mean v e l o c i t y i n m/ s disp ( ” p a r t ( b ) ” ) for i = 1 : n r4b(i)=r3+(Q/(cm*b)*(theta(i)/(2*%pi))); disp ( ” r a d i a n ” , t h e t a ( i ) , ” a t t h e t a =” ) disp ( ”cm” , r 4 b ( i ) * 1 0 0 , ”r4=” ) end L_b=r4b(8)-r3; disp ( L _ b / ( 2 * r 3 ) ,” ( b ) t h r o a t −to −d i am et e r r a t i o ( L/ d3 )= ”)
83
84
Chapter 13 Radial Turbine Stages
Scilab code Exa 13.1 ninety degree IFR turbine
1 2 3 4 5 6 7 8 9 10 11 12 13
/ / s c i l a b Code Exa 1 3 . 1 n i n et y d e g re e IFR t u r b i n e t = 6 5 0 ; // i n d eg r e e C T 0 1 = t + 2 7 3 ; // i n K el vi n E x i t P r e ss u r e i n b ar p 3 = 1 ; //
gamma =1.4; s i g m a = 0 . 6 6 ; / / b la de −to −i s e n t r o p i c s pe e d r a t i o N = 1 6 e 3 ; // r o t o r S pe ed i n RPM b 2 = 5 / 1 0 0 ; // b la de h e i g h t a t e nt ry i n m a ir angle at n ozzl e e xi t a l p h a _ 2 = 2 0 ; // d _ r = 0 . 4 5 ; / / r o t o r d i am et er r a t i o ( d3 / d2 ) p 0 1 _ 3 = 3 . 5 ; // t o t a l −to − s t a t i c P r e s su r e R at io ( p 01 / p3 ) n _ N = 0 . 9 5 ; / / N oz z le E f f i c i e n c y c p = 1 0 0 5 ; // S p e c i f i c Heat a t C o ns ta nt P r es s u r e i n J
/(kgK) 14 15 16 17 18
R=287; n =( gamma - 1 ) / gamma ;
// p ar t ( a ) t he r o t o r d i a me te r c _ 0 = sqrt ( 2 * c p * T 0 1 * ( 1 - ( p 0 1 _ 3 ^ ( - n ) ) ) )
85
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
u_2=sigma*c_0; d2=60*u_2/(%pi*N); disp ( ”cm” , d 2 * 1 e 2 , ” ( a ) t he r o t o r d i am e te r i s ” )
/ / p ar t ( b ) a i r a n g l e a t r o t o r b la de e x i t
d3=d2*d_r; c_r2=u_2*tand(alpha_2); u3=%pi*d3*N/60; beta3=atand(c_r2/u3); disp ( ” d e g r e e ” , b e t a 3 , ” ( b ) a i r a ng le a t r o t o r b la de e x i t b e t a 3=” )
/ / p a r t ( c ) mass f l o w r a t e
T03=T01-((u_2^2)/cp); T3=T03-((c_r2^2)/(2*cp)); T2=T3+((0.5*(u_2^2))/cp); c2=u_2/(cosd(alpha_2)); p01_2=(1-(((0.5*(c2^2))/(cp*n_N))/T01))^(-1/n); p01=p3*p01_3; p2=p01/p01_2; ro2=(p2*1e5)/(R*T2); m=ro2*c_r2*%pi*d2*b2; disp ( ” k g / s ” ,m , ” ( c ) mass f l o w r a t e i s ” )
/ / p ar t ( d ) hub and t i p d i am e t e r s a t t he r o t o r e x i t
ro3=(p3*1e5)/(R*T3); b3=m/(ro3*c_r2*%pi*d3); dh=d3-b3; disp ( ”cm” , d h * 1 e 2 , ” ( d ) hub d ia me te r a t t he r o t o r e x i t is”) 47 d t = d 3 + b 3 ; 48 disp ( ”cm” , d t * 1 e 2 , ” ( d ) t i p d ia me te r a t t he r o t o r e x i t is”) 49 50 / / p a r t ( e ) D e t er m i n in g t h e p ow er d e v e l o p e d 51 P = m * ( u _ 2 ^ 2 ) ; 52 disp ( ”kW” , P / 1 0 0 0 , ” ( e ) P o we r d e v e l o p e d i s ” ) 53
86
54 / / p a r t ( f ) t h e t o t a l −to − s t a t i c
E f fi c ie n cy o f the
stage 55 n _ t s = ( u _ 2 ^ 2 ) / ( c p * T 0 1 * ( 1 - ( ( p 3 / p 0 1 ) ^ n ) ) ) ; 56 disp ( ”%” , n _ t s * 1 e 2 , ” ( f ) t h e t o t a l −to − s t a t i c o f the s ta ge i s ” )
E f f i ci e n c y
Scilab code Exa 13.2 Mach Number and loss coefficient
1 / / s c i l a b Code Exa 1 3 . 2 Mach Number and l o s s
coefficient 2 t = 6 5 0 ; // i n d eg r e e C 3 T 0 1 = t + 2 7 3 ; // i n K el vi n 4 p 3 = 1 ; // E x i t P r e ss u r e i n b ar 5 6 7 8 9 10 11 12 13
gamma =1.4; s i g m a = 0 . 6 6 ; / / b la de −to −i s e n t r o p i c s pe e d r a t i o N = 1 6 e 3 ; // r o t o r S pe ed i n RPM b 2 = 5 / 1 0 0 ; // b la de h e i g h t a t e nt ry i n m a ir angle at n ozzl e e xi t a l p h a _ 2 = 2 0 ; // d _ r = 0 . 4 5 ; / / r o t o r d i am et er r a t i o ( d3 / d2 ) p 0 1 _ 3 = 3 . 5 ; // t o t a l −to − s t a t i c P r e s su r e R at io ( p 01 / p3 ) n _ N = 0 . 9 5 ; / / N oz z le E f f i c i e n c y c p = 1 0 0 5 ; // S p e c i f i c Heat a t C o ns ta nt P r es s u r e i n J
/(kgK) 14 15 16 17 18 19 20 21
R=287; n =( gamma - 1 ) / gamma ; c _ 0 = sqrt ( 2 * c p * T 0 1 * ( 1 - ( p 0 1 _ 3 ^ ( - n ) ) ) ) u_2=sigma*c_0; M b 0 = u _ 2 / sqrt ( gamma * R * T 0 1 ) ;
/ / p a r t ( a ) Mach number a t n o z z l e e x i t
M 2 = M b 0 / ( c o s d ( a l p h a _ 2 ) *sqrt ( 1 - ( 0 . 5 * ( gamma - 1 ) * ( M b 0 ^ 2 ) *(secd(alpha_2)^2)))); 22 disp ( M 2 , ” ( a ) t h e f l o w Mach number a t n o z z l e e x i t M2=”
87
) 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52
/ / p a r t ( b ) r o t o r e x i t R e l a t i v e Mach number
d2=60*u_2/(%pi*N); d3=d2*d_r; c_r2=u_2*tand(alpha_2); u3=%pi*d3*N/60; beta3=atand(c_r2/u3); w3=u3/(cosd(beta3)); T03=T01-((u_2^2)/cp); T3=T03-((c_r2^2)/(2*cp)); a3 = sqrt ( gamma * R * T 3 ) ; M3_rel=w3/a3; disp (M3_rel , ” ( b ) t h e R e l a t i v e Mach number a t r o t o r e x i t i s ”)
// part ( c ) Nozzl e enth alpy l o s s
coefficient
T2=T3+((0.5*(u_2^2))/cp); c2=u_2/(cosd(alpha_2)); T 2 s = T 01 - ( ( 0 . 5 * ( c 2 ^ 2 ) ) / ( c p * n _ N ) ) ; c2=u_2/(cosd(alpha_2)); zeeta_N=cp*(T2-T2s)/(0.5*(c2^2)); disp (zee ta_N , ” ( c ) t h e N o z zl e e n t ha l p y l o s s co ef f i c i e n t is ”)
// part (d) ro to r enthalpy lo s s c o e f f i c i e n t
p01_2=(1-(((0.5*(c2^2))/(cp*n_N))/T01))^(-1/n); p01=p3*p01_3; p2=p01/p01_2; T3s=T2/((p2/p3)^n); zeeta_R=cp*(T3-T3s)/(0.5*(w3^2)); disp (zee ta_R , ” ( d ) t h e r o t o r e n t h a l p y l o s s c o e f f i c i e n t is”) 53 disp ( ” c om me nt : N o z z l e e n t h a l p y l o s s c o e f f i c i e n t
v a l ue i s n o t c o r r e c t l y c a l c u l a t e d i n t h e t e x tb oo k . t h e a b o ve v al u e i s c o r r e c t . ” )
88
Scilab code Exa 13.3 IFR turbine with Cantilever Blades
1 / / s c i l a b Code Exa 1 3 . 3 IFR t u r b i n e w it h C a n t i l e v e r
Blades 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21 22
23 24 25 26
p h i = 0 . 4 ; // fl ow c o e f f i c i e n t funcprot ( 0 ) ; P = 1 0 0 ; / / Power d e v e l o p e d i n kW n _ t t = 0 . 9 ; // t o t a l −to −t o t a l E f f i c i e n c y N = 1 2 e 3 ; // r o t o r S pe ed i n RPM m = 1 ; // i n kg / s T 0 1 = 4 0 0 ; // i n K el vi n gamma =1.4; d _ r = 0 . 8 ; // r o t o r d i am e te r r a t i o ( d3 / d2 ) u2 = sqrt ( P * 1 0 0 0 / ( 2 * m ) ) ; d2=60*u2/(%pi*N); disp ( ”cm” , d 2 * 1 e 2 , ” t he r o t o r d ia m e te r a t e nt r y i s ” ) d3=d2*d_r; disp ( ”cm” , d 3 * 1 e 2 , ” t he r o t o r d ia me te r a t e x i t i s ” ) beta2=atand(phi); disp ( ” d e g r e e ” , b e t a 2 , ” a i r a ng l e a t r o t o r e n tr y i s beta2=” ) d3=d2*d_r; u3=%pi*d3*N/60; c_r2=u2*phi; beta3=atand(c_r2/u3); disp ( ” d e g r e e ” , b e t a 3 , ” a i r a ng le a t r o t o r e x i t i s beta3=” ) cp=1005; n =( gamma - 1 ) / gamma ; alpha_2=atand(c_r2/(2*u2)); disp ( ” d e g r e e ” ,alpha_2 , ” a i r a ng le a t n o z z l e e x i t i s a l p h a 2 = ”)
89
27 p 0 1 _ 0 3 = ( 1 - ( ( 2 * ( u 2 ^ 2 ) ) / ( n _ t t * c p * T 0 1 ) ) ) ^ ( - 1 / n ) ; 28 disp (p01_03 , ” s t a g n a t i o n p r e s s u r e r a t i o a c r o s s t h e s t ag e i s ”)
90
Chapter 14 Axial Fans and Propellers
Scilab code Exa 14.1 Axial fan stage 960 rpm
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
/ / s c i l a b Code Exa 1 4 . 1 A xi al f an s t a ge 9 60 rpm b e t a 3 = 1 0 ; // r o t o r b la de a i r a ng le a t e x i t i n d eg re e d h = 0 . 3 ; // hub d i am et e r i n m d t = 0 . 6 ; // t i p d ia me te r i n m N = 9 6 0 ; // r o t o r S pe ed i n RPM P = 1 ; / / Power r e q u i r e d i n kW p h i = 0 . 2 4 5 ; // fl o w c o e f f i c i e n t T 1 = 3 1 6 ; // i n K el vi n p1=1.02; // I n i t i a l Pres sure in bar
R=287; A=%pi*((dt^2)-(dh^2))/4; d=0.5*(dt+dh); u=%pi*d*N/60; cx=phi*u; Q=cx*A; ro=(p1*1e5)/(R*T1); delp0_st=ro*(u^2)*(1-(phi*(tand(beta3)))); disp ( ”mm W.G. ” , d e l p 0 _ s t / 9 . 8 1 , ” s t a g e p r e s s u r e r i s e ”)
91
is
19 I P = Q * d e l p 0 _ s t / 1 0 0 0 ; // i d e a l power r e q u i r e d t o d r i v e
t he f an i n kW 20 n _ o = I P / P ; 21 disp ( ”%” , n _ o * 1 e 2 , ” t h e o v e r a l l E f f i c i e n c y o f t h e f a n is”) 22 b e t a 2 = a t a n d ( u / c x ) ; 23 disp ( ” d e g r e e ” , b e t a 2 , ” t h e b la de a i r a ng l e a t t h e e n t r y b e t a 2=” ) 24 d e l p _ s t = 0 . 5 * r o * ( u ^ 2 ) * ( 1 - ( p h i ^ 2 * ( t a n d ( b e t a 3 ) ^ 2 ) ) ) ; 25 D O R = d e l p _ s t / d e l p 0 _ s t ; 26 disp ( ”%” , D O R * 1 e 2 , ” t he d eg re e o f r e a c t i o n i s ” ) 27 o m e g a = 2 * % p i * N / 6 0 ; 28 g H = d e l p 0 _ s t / r o ; 29 N S = o m e g a * sqrt ( Q ) / ( g H ^ ( 3 / 4 ) ) ; 30 disp ( N S , ” t h e d i m e n s i o n l e s s s p e c i f i c s p ee d i s ” )
Scilab code Exa 14.2 Downstream guide vanes
1 2 3 4 5 6 7 8 9 10 11 12 13
/ / s c i l a b Code E xa 1 4 . 2 Downstream g u i d e v a ne s
b e t a 3 = 1 0 ; // r o t o r b la de a i r a ng le a t e x i t i n d eg re e d h = 0 . 3 ; // hub d i am et e r i n m d t = 0 . 6 ; // t i p d ia me te r i n m N = 9 6 0 ; // r o t o r S pe ed i n RPM p h i = 0 . 2 4 5 ; // fl o w c o e f f i c i e n t d=0.5*(dt+dh); u=%pi*d*N/60; cx=phi*u; cy3=u-(cx*tand(beta3)); alpha3=atand(cy3/cx); disp ( ” t h e r o t o r b l ad e a i r a ng le s , o v e r a l l e f f i c i e n c y
, f l o w r at e , power r e q u i r e d and d e g r e e o f r e a c t i o n a re t he same a s c a l c u l a t e d i n Ex 1 4 1 ” ) 92
14 disp ( ” d e g r e e ” ,alpha3 , ” t he g ui de va ne a i r t h e e n t r y a l p h a 3=” )
a ng le a t
Scilab code Exa 14.3 upstream guide vanes
1 / / s c i l a b Code Exa 1 4 . 3 u ps tr ea m g u id e v an es 2 b e t a 2 = 8 6 ; // r o t o r b l a d e a i r a n gl e a t i n l e t i n 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
degree d h = 0 . 3 ; // hub d i am et e r i n m d t = 0 . 6 ; // t i p d ia me te r i n m N = 9 6 0 ; // r o t o r S pe ed i n RPM p h i = 0 . 2 4 5 ; // fl o w c o e f f i c i e n t T 1 = 3 1 6 ; // i n K el vi n p1=1.02; // I n i t i a l Pres sure in bar R=287; n _ o = 0 . 6 4 7 ; // o v e r a l l E f f i c i e n c y o f t h e d r i v e A=%pi*((dt^2)-(dh^2))/4; d=0.5*(dt+dh); u=%pi*d*N/60; cx=phi*u; Q=cx*A; ro=(p1*1e5)/(R*T1);
// p ar t ( i ) s t a t i c stage
p r e s s u re r i s e i n t he r o t o r and
19 d e l h 0 _ s t = ( u ^ 2 ) * ( ( p h i * ( t a n d ( b e t a 2 ) ) ) - 1 ) ; 20 d e l p 0 _ s t = r o * d e l h 0 _ s t ; 21 disp ( ”mm W.G. ” , d e l p 0 _ s t / 9 . 8 1 , ” ( i ) s t a t i c p r e s s u r e r i s e i n t h e s t a ge i s ” ) 22 b e t a 3 = a t a n d ( u / c x ) ; 23 w 2 = c x / ( c o s d ( b e t a 2 ) ) ; 24 w 3 = c x / ( c o s d ( b e t a 3 ) ) ; 25 d e l p _ r = 0 . 5 * r o * ( ( w 2 ^ 2 ) - ( w 3 ^ 2 ) ) ;
93
26 disp ( ”mm W.G. ” , d e l p _ r / 9 . 8 1 , ” and t he s t a t i c p r e s s u re r i s e in the r ot or i s ”) 27 28 / / p a r t ( i i ) t h e s t a g e p r e s s u r e c o e f f i c i e n t a nd
d eg re e o f r e a c t i o n 29 30 31 32 33 34
shi=2*((phi*(tand(beta2)))-1); disp ( s h i , ” ( i i ) s t a g e p r e s s u r e c o e f f i c i e n t i s ” ) DOR=0.5*((phi*(tand(beta2)))+1); disp ( ”%” , D O R * 1 e 2 , ” and t he d eg r e e o f r e a c t i o n i s ” )
// p ar t ( i i i ) t he b la de a i r a n g l e a t t h e r o t o r e x i t and t he a i r a n gl e a t t he UGV e x i t 35 disp ( ” d e g r e e ” , b e t a 3 , ” ( i i i ) t he b l ad e a i r a n g l e a t t he r o t o r e x i t b et a3=” ) 36 c y 2 = ( c x * t a n d ( b e t a 2 ) ) - u ; 37 a l p h a 2 = a t a n d ( c y 2 / c x ) ; 38 disp ( ” d e g r e e ” ,alpha2 , ” and t he a i r a n g le a t t he UGV e x i t a l p h a 2=” ) 39 40 // p a rt ( i v ) Power r e q u i r e d t o d r i v e t he f an 41 m = r o * Q ; 42 P = m * d e l h 0 _ s t / n _ o ; 43 disp ( ”kW” , P / 1 0 0 0 , ” ( i v ) Power r e q u i r e d t o d r i v e t he f an i s ” )
Scilab code Exa 14.4 rotor and upstream guide blades
1 / / s c i l a b Code Exa 1 4 . 4 r o t o r and u ps tr ea m g u id e
blades 2 b e t a 2 = 3 0 ; // r o t o r b l a d e a i r a n gl e a t
inlet in
degree 3 b e t a 3 = 1 0 ; // r o t o r b la de a i r a ng le a t e x i t i n d eg re e 4 d h = 0 . 3 ; // hub d i am et e r i n m
94
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
23 24 25 26 27
d t = 0 . 6 ; // t i p d ia me te r i n m N = 9 6 0 ; // r o t o r S pe ed i n RPM p h i = 0 . 2 4 5 ; // fl o w c o e f f i c i e n t T 1 = 3 1 6 ; // i n K el vi n p1=1.02; // I n i t i a l Pres sure in bar R=287; n _ d = 0 . 8 8 ; // E f f i c i e n c y o f t h e d r i v e n _ f = 0 . 8 ; // E f f i c i e n c y o f t h e f a n A=%pi*((dt^2)-(dh^2))/4; d=0.5*(dt+dh); u=%pi*d*N/60; cx=phi*u; Q=cx*A; ro=(p1*1e5)/(R*T1); delh0_st=(u^2)*phi*(tand(beta2)-tand(beta3)); n_o=n_f*n_d; delp0_st=n_f*ro*delh0_st; disp ( ”mm W.G. ” , d e l p 0 _ s t / 9 . 8 1 , ” s t a t i c p r e s s u r e r i s e i n the s ta ge i s ”) shi=2*phi*(tand(beta2)-tand(beta3)); disp ( s h i , ” s t a g e p r e s s u r e c o e f f i c i e n t i s ” ) m=ro*Q; P=m*delh0_st/n_d; disp ( ”kW” , P / 1 0 0 0 , ” Power r e q u i r e d t o d r i v e t he f an i s ”)
Scilab code Exa 14.5 DGVs and upstream guide vanes
1 / / s c i l a b Code E xa 1 4 . 5 DGVs and u p st re a m g u i d e
vanes 2 b e t a 2 = 8 6 ; // r o t o r b l a d e a i r a n gl e a t
inlet in
degree 3 b e t a 3 = 1 0 ; // r o t o r b la de a i r a ng le a t e x i t i n d eg re e
95
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
22 23 24 25 26
d h = 0 . 3 ; // hub d i am et e r i n m d t = 0 . 6 ; // t i p d ia me te r i n m N = 9 6 0 ; // r o t o r S pe ed i n RPM p h i = 0 . 2 4 5 ; // fl o w c o e f f i c i e n t T 1 = 3 1 6 ; // i n K el vi n p1=1.02; // I n i t i a l Pres sure in bar R=287; n _ d = 0 . 8 ; // E f f i c i e n c y o f t h e d r i v e n _ f = 0 . 8 5 ; // E f f i c i e n c y o f t h e f a n A=%pi*((dt^2)-(dh^2))/4; d=0.5*(dt+dh); u=%pi*d*N/60; cx=phi*u; Q=cx*A; ro=(p1*1e5)/(R*T1); delh0_st=2*(u^2)*((phi*(tand(beta2)))-1); delp0_st=n_f*ro*delh0_st; disp ( ”mm W.G. ” , d e l p 0 _ s t / 9 . 8 1 , ” s t a t i c p r e s s u r e r i s e i n the s ta ge i s ”) shi=4*((phi*(tand(beta2)))-1); disp ( s h i , ” s t a g e p r e s s u r e c o e f f i c i e n t i s ” ) m=ro*Q; P=m*delh0_st/n_d; disp ( ”kW” , P / 1 0 0 0 , ” P ow er o f t h e e l e c t r i c m o to r i s ” )
Scilab code Exa 14.6 open propeller fan
1 2 3 4 5 6
/ / s c i l a b Code Exa 1 4 . 6 open p r o p e l l e r f an c _ u = 5 ; // u ps tr ea m v e l o c i t y i n m/ s c _ s = 2 5 ; // d own st re am v e l o c i t y i n m/ s t = 3 7 ; // i n d eg re e C T = t + 2 7 3 ; // i n K el vi n d=0.5;
96
p=1.02; / / I n i t i a l P r e s s u r e i n b a r R=287; n _ o = 0 . 4 ; // o v e r a l l E f f i c i e n c y o f t h e f a n A=%pi*(d^2)/4; c=0.5*(c_u+c_s); Q=c*A; ro=(p*1e5)/(R*T); m=ro*c*A; disp ( ” k g / s ” ,m , ” ( a ) f l o w r a t e t h r o ug h t he f an i s ” ) delh_0=0.5*((c_s^2)-(c_u^2)); delp_0=ro*delh_0; disp ( ”mm W.G. ” , d e l p _ 0 / 9 . 8 1 , ” ( b ) s t a t i c p r e s s u re r i s e i n the s ta ge i s ”) 19 P = m * d e l h _ 0 / n _ o ; 20 disp ( ”kW” , P / 1 0 0 0 , ” ( c ) Power r e q u i r e d t o d r i v e t he f an is”) 7 8 9 10 11 12 13 14 15 16 17 18
97
Chapter 15 Centrifugal Fans and Blowers
Scilab code Exa 15.1 Centrifugal fan stage 1450 rpm
1 / / s c i l a b Code Exa 1 5 . 1
C e n t r i f u g a l f an s t a g e 1 4 5 0
rpm 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
d 1 = 0 . 1 8 ; // i n n e r d ia me te r o f t he i m p e l l e r i n m d 2 = 0 . 2 ; // o u t er d ia me te r o f t h e i m p e l l e r i n m N = 1 4 5 0 ; / / r o t o r S pe ed i n RPM c 1 = 2 1 ; // A bs ol ut e v e l o c i t y a t e n t ry i n m/ s w 1 = 2 0 ; // r e l a t i v e v e l o c i t y a t e nt r y i n m/ s c 2 = 2 5 ; // A bs ol ut e v e l o c i t y a t e x i t i n m/ s w 2 = 1 7 ; // r e l a t i v e v e l o c i t y a t e x i t i n m/ s m = 0 . 5 ; // f lo w r a t e i n kg / s n _ m = 0 . 7 8 ; // o v e r a l l E f f i c i e n c y o f t h e motor r o = 1 . 2 5 ; // d e ns i t y o f a i r i n kg /m3
u1=%pi*d1*N/60; u2=%pi*d2*N/60; d e l p _ r = 0 . 5 * r o * ( ( w 1 ^ 2 ) - ( w 2 ^ 2 ) ) + ( 0 . 5 * r o * ( ( u 2 ^ 2 ) - ( u 1 ^2 ) )); 17 d e l p 0 _ s t = 0 . 5 * r o * ( ( ( w 1 ^ 2 ) - ( w 2 ^ 2 ) ) + ( ( u 2 ^ 2 ) - ( u 1 ^ 2 ) ) + ((
98
18 19 20 21 22 23
c2^2)-(c1^2))); disp ( ”mm W.G. ” , d e l p 0 _ s t / 9 . 8 1 , ” ( a ) s t a g e p r e s s u r e r i s e is”) DOR=delp_r/delp0_st; disp ( D O R , ” ( b ) t he d e g r e e o f r e a c t i o n i s ” ) w_st=delp0_st/ro; P=m*w_st/n_m; disp ( ”W” ,P , ” ( c ) t h e m ot or Power r e q u i r e d t o d r i v e t h e f an i s ” )
Scilab code Exa 15.2 Centrifugal blower 3000 rpm
1 / / s c i l a b Code Exa 1 5 . 2 C e n t r i f u g a l b lo we r 3 00 0 rpm 2 3 b e t a 2 = 9 0 ; // r o t o r b l a d e a i r a n gl e a t i n l e t i n
degree 4 N = 3 e 3 ; // r o t o r S pe ed i n RPM 5 T1=310; // i n K el vi n 6 p1=0.98; // I n i t i a l Pres sure in bar 7 8 9 10 11 12 13 14 15
R=287; n _ d = 0 . 8 8 ; // E f f i c i e n c y o f t h e d r i v e n _ f = 0 . 8 2 ; // E f f i c i e n c y o f t h e f a n Q = 2 0 0 / 6 0 ; // d i s c h a r g e i n m3/ s h = 1 0 0 0 ; / / mm c ol um n o f w a t e r delp0=h*9.81; P i = Q * d e l p 0 / 1 0 0 0 ; // i d e a l power P=Pi/(n_d*n_f); disp ( ”kW” ,P , ” ( a ) P ower r e q u i r e d by t h e e l e c t r i c m ot or is”)
16 17 / / p a rt ( b ) i m p e l l e r d i am et e r 18 r o = ( p 1 * 1 e 5 ) / ( R * T 1 ) ; 19 u2 = sqrt ( d e l p 0 / ( r o * n _ f ) ) ;
99
20 21 22 23 24 25 26 27 28 29 30 31 32
d2=u2*60/(%pi*N); disp ( ”cm” , d 2 * 1 e 2 , ” ( b ) t he i m p e l l e r
d i am et er i s ” )
// p a rt ( c ) i n n e r d i am et er o f t he b l ad e r i n g c_r2=0.2*u2; c_i=0.4*u2; d1 = sqrt ( Q * 4 / ( % p i * c _ i ) ) ; disp ( ”cm” , d 1 * 1 e 2 , ” ( c ) t he i n n e r d i am e te r o f t he b l ad e r i ng i s ”)
// p ar t ( d ) a i r a n g l e a t t h e e nt ry u1=u2*d1/d2; beta1=atand(c_r2/u1); disp ( ” d e g r e e ” , b e t a 1 , ” ( d ) t h e a i r a n g l e a t t h e e nt ry beta1=” )
33 34 // p a rt ( e ) i m p e l l e r w id th s a t e n tr y and e x i t 35 b 1 = Q / ( c _ r 2 * % p i * d 1 ) ; 36 disp ( ”cm” , b 1 * 1 e 2 , ” ( e ) t he i m p e l l e r wi dt h a t e n tr y i s ” ) 37 b 2 = b 1 * d 1 / d 2 ; 38 disp ( ”cm” , b 2 * 1 e 2 , ” and t he i m p e l l e r w i d t h a t e x i t i s ” ) 39 40 / / p a r t ( f ) number o f i m p e l l e r b l a d e s 41 z = 8 . 5 * s i n d ( b e t a 2 ) / ( 1 - ( d 1 / d 2 ) ) ; 42 disp (z , ” ( f ) t he number o f i m p e l l e r b l a d e s i s ” ) 43 44 / / p a r t ( g ) t h e s p e c i f i c s p e e d 45 g H = u 2 ^ 2 ; 46 o m e g a = 2 * % p i * N / 6 0 ; 47 N S = o m e g a * sqrt ( Q ) / ( g H ^ ( 3 / 4 ) ) ; 48 disp ( N S , ” ( g ) t h e d i m e n s i o n l e s s s p e c i f i c s p ee d i s ” )
100
Chapter 16 Wind Turbines
Scilab code Exa 16.1 Wind turbine output 100 kW
1 2 3 4 5 6 7 8 9
/ / s c i l a b Code E xa 1 6 . 1 Wind t u r b i n e o ut p ut 1 00 kW
c _ u = 4 8 * 5 / 1 8 ; // wind u ps tr ea m v e l o c i t y i n m/ s n = 0 . 9 5 ; // o v e r a l l E f f i c i e n c y o f t h e d r i v e P = 1 0 0 ; // a e r o g e n e r a t o r p ower o u tp u t i n kW n _ m = 0 . 9 ; // m ec ha ni ca l E f f i c i e n c y o f t he d r i v e n _ a = 0 . 7 ; // a er od yn am ic E f f i c i e n c y r o = 1 . 1 2 5 ; // d e n s i ty o f a i r i n kg /m3 c p _ m a x = 0 . 5 9 3 ; / / p o we r c o e f f i c i e n t f o r t h e w i n d m i l l (
Pi/Pu) 10 11 12 13 14
/ / p ar t ( a ) p r o p e l l e r d i a me te r o f t he w in d m i l l A=2*P*1e3/(ro*(c_u^3)*n*n_m*n_a*cp_max); d = sqrt ( 4 * A / % p i ) ; disp ( ”m” ,d , ” ( a ) t he p r o p e l l e r d ia me te r o f t he w i nd m il l i s ” )
15 16 / / p a r t ( b ) 17 disp ( ” ( b ) c o r r e s p o n d i n g
t o maximum p ow er ” ) 101
18 c = 2 * c _ u / 3 ; 19 disp ( ”m/s” ,c , ” t he wind v e l o c i t y t hr ou gh t he p r o p el l e r d i sc i s ”) 20 d e l p 1 _ a = 5 * r o * ( c ^ 2 ) / 8 ; 21 disp ( ”mm W.G. ” , d e l p 1 _ a / 9 . 8 1 , ” t he g au g e p r e s s u r e b e f o r e t he d i s c i s ” ) 22 d e l p 2 _ a = - 3 * r o * ( c ^ 2 ) / 8 ; 23 disp ( ”mm W.G. ” , d e l p 2 _ a / 9 . 8 1 , ” t he g au g e p r e s s u r e a f t e r the d i sc i s ”) 24 F x = ( d e l p 1 _a - d e l p 2 _ a ) * A ; 25 disp ( ”kN” , F x * 1 e - 3 , ” and t he a x i a l t h r u s t i s ” )
102
just
just
Chapter 18 Miscellaneous Solved Problems in Turbomachines
Scilab code Exa 18.1 Gas Turbine nozzle row
1 2 3 4 5 6 7
/ / s c i l a b Code Exa 1 8 . 1 Gas T ur bi ne n o z z l e row
T 1 = 6 0 0 ; // E nt ry Te mp er at ur e o f t he g as i n K el vi n p 1 = 1 0 ; // I n l e t P re ss u r e i n b a r gamma_g=1.3; d e l T = 3 2 ; / / T em pe ra tu re d ro p o f t h e g a s ( T1−T2 ) i n K c p _ g = 1 . 2 3 * 1 e 3 ; // S p e c i f i c Heat o f g as a t C o n s t a n t
P r e s s u r e i n kJ / ( kgK ) 8 p r 1 _ 2 = 1 . 3 ; / / p r e s s u r e r a t i o ( p1 / p2 ) 9 10 11 12 13 14 15 16
T 2 s = T 1 / ( p r 1 _ 2 ^ ( ( g a m ma _ g - 1 ) / g a m m a _ g ) ) ; delTs=T1-T2s;
/ / p ar t ( a ) n o zz l e e f f i c i e n c y n_N=delT/delTs; disp ( ”%” , n _ N * 1 0 0 , ” ( a ) n o z zl e e f f i c i e n c y
// part (b) 103
is ”)
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
disp ( ” ( b ) ( i ) f o r i d e a l f l o w : ” ) p2=p1/pr1_2; h_01=cp_g*T1; h2s=cp_g*T2s; c _ 2 s = sqrt ( ( h _ 0 1 - h 2 s ) / 0 . 5 ) ; disp ( ”m/s” , c _ 2 s , ” t h e n o z z l e e x i t v e l o c i t y i s ” ) R_g=cp_g*((gamma_g -1)/gamma_g); M _ 2 s = c _ 2 s / ( sqrt ( g a m m a _ g * R _ g * T 2 s ) ) ; disp ( M _ 2 s , ” a nd t h e Mach n um ber i s ” ) disp ( ” ( b ) ( i i ) f o r a c t u a l f l o w : ” ) T2=T1-delT; a2 = sqrt ( g a m m a _ g * R _ g * T 2 ) ; c _ 2 = sqrt ( ( c p _ g * d e l T ) / 0 . 5 ) ; disp ( ”m/s” , c _ 2 , ” t h e n o z z l e e x i t v e l o c i t y i s ” ) M2=c_2/a2; disp ( M 2 , ” a nd t h e Mach n um be r i s ” )
// p ar t ( c ) s t a g n a t i o n p r e s s u r e l o s s nozzle
a c r o s s t he
35 p 0 1 = p 1 ; 36 p 0 2 = p 2 / 0 . 7 9 ; // fro m i s e n t r o p i c
g as t a b l e s p2 / p02 = 0 . 7 9 a t gamma = 1 . 3 a nd M2 = 0 . 6 1 3
37 d e l p 0 = p 0 1 - p 0 2 ; 38 disp ( ” b a r ” , d e l p 0 , ” ( c ) t he s t a g n a t i o n p r e s s u r e l o s s a c ro s s th e n o zz l e i s ”) 39 40 // p ar t ( d ) n o zz l e e f f i c i e n c y b a s ed on s t a g n a t i o n
p r es s ur e l o s s 41 d e l p = p 1 - p 2 ; 42 n _ N _ a = 1 - ( d e l p 0 / d e l p ) ; 43 disp ( ”%” , n _ N _ a * 1 0 0 , ” ( d ) t h e n o z z l e e f f i c i e n c y on s t a g n a t i o n p r e s s u r e l o s s i s ” )
104
based
Scilab code Exa 18.2 Steam Turbine nozzle
1 2 3 4 5 6 7 8 9 10 11 12 13
/ / s c i l a b Code Exa 1 8 . 2 Steam T ur bi ne n o z z l e
t 1 = 5 5 0 ; / / E n tr y T e mp er at ur e i n K e l v i n p 1 = 1 7 0 ; // I n l e t P re s s u r e i n b a r p 2 = 1 2 0 . 7 ; // E xi t P r es s u r e i n b ar d = 1 ; / / Mean B la de r i n g d i am et er i n m a l p h a _ 2 = 7 0 ; // n o zz l e a n g l e i n d eg re e g a m m a _ g = 1 . 3 ; // f o r s u pe r he a te d stea m R = 0 . 5 * 1 e 3 ; // i n J /kgK m = 2 8 0 ; // i n kg / s
/ / p ar t ( a ) e x i t v e l o c i t y c2 o f s tea m h 1 = 3 4 4 0 ; // from s u pe r he a te d stea m t a b l e s a t p1 and t1 14 h 2 = 3 3 5 0 ; // a t p2 15 t 2 = 5 0 3 ; // a t p2 i n d eg re e C 16 v _ s 2 = 0 . 0 2 6 8 ; // S p e c i f i c Volume a t p2 i n m3/ kg 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
c _ 2 = sqrt ( ( h 1 - h 2 ) * 1 e 3 / 0 . 5 ) ; disp ( ”m/s” , c _ 2 , ” ( a ) t h e n o z z l e e x i t v e l o c i t y
is ”)
// part (b) T2=t2+273; a2 = sqrt ( g a m m a _ g * R * T 2 ) ; M2=c_2/a2; disp ( M 2 , ” ( b ) a nd t h e e x i t Mach number i s ” )
// par t ( c ) cx=c_2*cosd(alpha_2); h=m*v_s2/(%pi*cx*d); disp ( ”cm” , h * 1 e 2 , ” ( c ) n o z z l e b l a de h e ig h t a t e x i t
is ”)
T 2 s = 0 . 8 7 * ( t 1 + 2 7 3 ) ; // T2s /T1 =0 .8 7 f ro m g a s t a b l e s p 2 s = 0 . 5 4 6 * p 1 ; // p 2s / p1 = 0. 54 6 fro m g as t a b l e s v s _ s = 0 . 0 3 1 ; // fro m s tea m t a b l e s a _ s = sqrt ( g a m m a _ g * R * T 2 s ) ; disp ( ”m/s” , a _ s , ” t he c o rr e s p o n d i n g n o z z l e e x i t
105
velocity is ”) 36 c x _ s = a _ s * c o s d ( a l p h a _ 2 ) ; 37 m _ m a x = c x _ s * % p i * d * h / ( v s _ s ) ; 38 disp ( ” k g / s ” , m _ m a x , ” t h e maximum p o s s i b l e m as s f l o w r a te i s ”)
Scilab code Exa 18.3 Irreversible flow in nozzles
1 2 3 4 5 6
/ / s c i l a b Code Exa 1 8 . 3 I r r e v e r s i b l e p r = 0 . 8 4 3 ; / / p r=p / p 0 n _ n = 0 . 9 5 ; // n o z z l e e f f i c i e n c y
f l ow i n n o z z l e s
gamma =1.4; M s = 0 . 5 ; // f ro m g a s t a b l e s f o r gammma and p r v a l u e Ma = sqrt ((2/( gamma - 1) ) * ( n _ n / ( 1 - n _ n + ( 2 / ( ( gamma - 1 ) * ( M s ^2)))))); 7 disp ( M a , ” a c t u a l v a l u e o f t h e Mach number i s ” )
Scilab code Exa 18.4 Calculation on a Diffuser
1 2 3 4 5 6 7 8 9 10
// s c i l a b Code Exa 1 8 . 4 C a l c u l a t i o n on a D i f f u s e r
p e = 3 5 ; / / I n i t i a l P r e s s u r e i n mm W. G . p a = 1 . 0 1 3 5 ; // a mb i e n t p r e s s u r e i n b a r c 1 = 1 0 0 ; // e nt ry v e l o c i t y i n m/ s C_pa=0.602; // act ual pr es su re reco very c o e f f i c i e n t r o = 1 . 2 5 ; // d e n s i t y i n kg /m3 g = 9 . 8 1 ; / / G r a v i t a t i o n a l a c c e l e r a t i o n i n m/ s ˆ 2 A r = 1 . 8 5 ; // Area R at io o f D i f f u s e r
106
11 / / p a r t ( a ) 12 C _ p s = 1 - ( 1 / ( A r ^ 2 ) ) ; 13 disp ( C _ p s , ” ( a ) i d e a l v al ue o f t h e p r e s s u re r e c o v e r y co ef f i c i e n t is ”) 14 15 / / p a r t ( b ) 16 n _ D = C _ p a / C _ p s ; 17 disp ( ”%” , n _ D * 1 e 2 , ” ( b ) E f f i c i e n c y o f t h e d i f f u s e r i s ” ) 18 19 / / p a r t ( c ) 20 p 1 = p a + ( p e * g * 1 e - 5 ) ; 21 p 0 1 = p 1 + ( 0 . 5 * r o * ( c 1 ^ 2 ) * 1 e - 5 ) ; 22 d e l p _ 0 = ( C _ p s - C _ p a ) * ( 0 . 5 * r o * ( c 1 ^ 2 ) * 1 e - 5 ) ; 23 disp ( ”mm W.G. ” , d e l p _ 0 * 1 e 5 / g , ” ( c ) t h e s t a g n a t i o n p re ss ur e l o s s a cr os s the d i f f u s er i s ” ) 24 25 / / p a r t ( d ) 26 p 0 2 = p 0 1 - d e l p _ 0 ; 27 c 2 = c 1 / A r ; 28 p 2 = p 0 2 - ( 0 . 5 * r o * ( c 2 ^ 2 ) * 1 e - 5 ) ; 29 disp ( ”mm W.G. ” , ( p 2 - p a ) * 1 e 5 / g , ” ( d ) t he g au ge p r e s s u r e at the d i f f u s er e xi t i s ” )
Scilab code Exa 18.5 Calculation on a Draft Tube
1 2 3 4 5 6 7
// s c i l a b Code Exa 1 8 . 5 C a l c u l a t i o n on a D ra ft Tube
c 2 = 6 . 2 5 ; // e x i t v e l o c i t y i n m/ s r o = 1 e 3 ; // d e n s i t y i n kg /m3 g = 9 . 8 1 ; / / G r a v i t a t i o n a l a c c e l e r a t i o n i n m/ s ˆ 2 A R = 1 . 6 ; // Area R at io o f D i f f u s e r Q = 1 0 0 ; // d i s c h a r g e i n m3/ s
107
8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
n _ D = 0 . 8 2 ; // E f f i c i e n c y
o f t he D ra ft Tube
// part (a)
c1=c2*AR; A1=Q/c1; disp ( ”m2” , A 1 , ” ( a ) a r e a o f c r os s −s e c t i o n a t e nt ry i s ” ) A2=A1*AR; disp ( ”m2” , A 2 , ” and t he a r e a o f c r os s −s e c t i o n a t e x i t is”)
// part (b) delHi=((c1^2)-(c2^2))/(2*g); delH_a=delHi*n_D; disp ( ”m” ,delH_a , ” ( b ) a c t u a l head g a in e d by t he D ra f t Tube i s ” )
// par t ( c ) m=ro*Q; delP_a=m*g*delH_a; disp ( ”MW” , d e l P _ a * 1 e - 6 , ” ( c ) t h e a d d i t i o n a l po we r g e n er a t ed i s ” )
26 27 / / p a r t ( d ) 28 L o s s = d e l H i - d e l H _ a ; 29 disp ( ”m” , L o s s , ” ( d ) t h e l o s s th e d r a ft tube i s ”)
o f head due t o l o s s e s i n
Scilab code Exa 18.6 Calculations on a Gas Turbine
1 / / s c i l a b Code Exa 1 8 . 6
C a l c u l a t i o n s on a G as
Turbine 2 3 m = 4 7 2 ; // f lo w r a t e o f h o t g a s e s i n k g / s
108
4 5 6 7 8 9 10
T 0 1 = 1 3 3 5 ; // T ur bi ne i n l e t temp i n K el v in p 0 1 = 1 0 ; // T u rb in e I n l e t P r es s u r e i n b ar c 2 = 1 5 0 ; // e x i t v e l o c i t y i n m/ s p r 0 = 1 0 ; // T u rb in e p r e s s u r e r a t i o gamma_g=1.67; T 2 = 5 6 0 ; // T em p e r a tu r e o f g a s e s a t e x i t i n K el vi n c p _ g = 1 . 1 5 7 ; // S p e c i f i c Heat o f g as a t C o n s t a n t
P r e s s u r e i n kJ / ( kgK ) 11 12 13 14 15 16 17 18 19 20 21 22
/ / p ar t ( a ) D e te r m in in g t o t a l t o t o t a l e f f i c i e n c y T02=T2+(0.5*(c2^2)/(cp_g*1e3)); T 0 2 s = T 0 1 / ( p r 0 ^ ( ( g a m ma _ g - 1 ) / g a m m a _ g ) ) ; n_tt=(T01-T02)/(T01-T02s); disp ( ”%” , n _ t t * 1 0 0 , ” ( a ) t o t a l t o t o t a l e f f i c i e n c y
/ / p ar t ( b ) D e te r mi ni ng t o t a l t o s t a t i c T 2 s = T 0 2s - ( 0 . 5 * ( c 2 ^ 2 ) / ( c p _ g * 1 e 3 ) ) ; n_ts=(T01-T02)/(T01-T2s); disp ( ”%” , n _ t s * 1 0 0 , ” ( b ) t o t a l t o s t a t i c )
is ”)
effic ienc y
e f f i c i e n cy i s ”
23 24 // p ar t ( c ) D et er mi ni ng t he p o l y t r o p i c e f f i c i e n c y 25 n _ p = ( ( g a m m a _ g ) / ( g a m ma _ g - 1 ) ) * ( (log ( T 0 1 / T 0 2 ) ) / ( log ( p r 0 ))); 26 disp ( ”%” , n _ p * 1 0 0 , ” ( c ) p o l y t r o p i c e f f i c i e n c y i s ” ) 27 28 / / p a r t ( d ) D e te r mi n in g p ower d e v el o p e d by t h e
turbine 29 P = m * c p _ g * ( T 0 1 - T 0 2 ) ; 30 disp ( ”MW” , P / 1 e 3 , ” ( d ) Power d e v el o p e d b y t h e t u r b i n e is”)
109
Scilab code Exa 18.7 RHF of a three stage turbine
1 2 3 4 5 6 7 8 9 10 11 12
/ / s c i l a b Code Exa 1 8 . 7 RHF o f a t h r e e s t a g e t u r b i n e
p1=1.0; / / I n i t i a l P r e s s u r e i n b a r gamma =1.4; T 1 = 1 5 0 0 ; / / I n i t i a l T e m p er a t u r e i n K s = 3 ; // number o f s t a g e s o p r = 1 1 ; // O v er a l l P r es s ur e R at io p r = o p r ^ ( 1 / s ) ; // e q u a l P r es s u r e R at io i n e a ch s t a ge n _ T = 0 . 8 8 ; // O v e r a l l E f f i c i e n c y d e l T a = T 1 * ( 1 - o p r ^ ( - ( (gamma - 1 ) / gamma ) ) ) * n _ T ; T2=T1-delTa; n _ p = ( log ( T 1 / T 2 ) ) / ( ( ( gamma - 1 ) / gamma ) *( log ( o p r ) ) ) ; //
p o l y t r o p i c o r s ma ll s t a g e e f f i c i e n c y 13 c p = 1 . 0 0 5 ; // S p e c i f i c Heat a t C on st a nt P r es s u r e i n kJ/(kgK) 14 n _ s t = ( 1 - p r ^ ( n _ p * ( - ( (gamma - 1 ) / gamma ) ) ) ) / ( 1 - p r ^ ( - ( ( gamma - 1 ) / gamma ) ) ) ; // s t a ge e f f i c i e n c y 15 T ( 1 ) = T 1 ; 16 for i = 1 : 3 17 d e l T ( i ) = T ( i ) * ( 1 - p r ^ ( n _ p * ( - ( (gamma - 1 ) / gamma ) ) ) ) ; 18 delw_s(i)=delT(i)*cp/n_st; T(i+1)=T(i)-delT(i); 19 20 end 21 w _ a = c p * d e l T a ; 22 w _ s = w _ a / n _ T ; 23 R H F = ( d e l w _ s ( 1 ) + d e l w _ s ( 2 ) + d e l w _ s ( 3 ) ) / w _ s ; 24 disp ( R H F , ” t he r e h e a t f a c t o r i s ” )
Scilab code Exa 18.8 Calculation on an air compressor
1 / / s c i l a b Code Exa 1 8 . 8 C a l c u l a t i o n on a n a i r
110
compressor 2 3 4 5 6 7
funcprot (0) p1=1.0; / / I n i t i a l P r e s s u r e i n b a r T 1 = 3 0 5 ; / / I n i t i a l T em p er a tu r e i n d e g r e e K k = 1 6 ; // number o f s t a g e s m = 4 0 0 ; // mass f l ow r a t e t hr ou gh t he c om p re ss o r i n
kg/s 8 p _ r c = 1 0 ; // o v e r a l l P r e s s u r e R a ti o 9 gamma =1.4; // S p e c i f i c Heat R at io 10 c p = 1 . 0 0 5 ; // S p e c i f i c Heat a t C on st a nt P r es s u r e i n
kJ/(kgK) 11 n _ p = 0 . 8 8 ; // p o l y t r o p i c e f f i c i e n c y 12 13 14 15 16 17 18 19 20 21
// p a rt ( a ) D et er mi ni ng s t a g e P r e s su r e R at io pr=p_rc^(1/k); disp ( p r , ” ( a ) s t a g e P r e ss u r e R at io
is ”)
/ / p ar t ( b ) D et er mi ni ng t he s t a g e e f f i c i e n c y
T 2 s = T 1 * ( p r ^ ( ( gamma - 1 ) / gamma ) ) ; T 2 = T 1 * ( p r ^ ( ( gamma - 1 ) / ( gamma * n _ p ) ) ) ; n_st=(T2s-T1)/(T2-T1); disp ( ”%” , n _ s t * 1 0 0 , ” ( b ) s t a g e E f f i c i e n c y o f t he c o mp r e ss o r i s ” )
22 23 / / p a r t ( c ) D e te r mi n in g p ower r e q u i r e d
for the f i r s t
stage 24 P 1 = m * c p * ( T 2 - T 1 ) ; 25 disp ( ”MW” , P 1 / 1 e 3 , ” ( c ) P ower r e q u i r e d f o r t h e f i r s t s t ag e i s ”) 26 27 / / p a r t ( d ) O v e r a l l C om pr es so r E f f i c i e n c y 28 T 1 7 = T 1 * exp ((( gamma - 1 ) / ( gamma * n _ p ) ) * ( log ( p _ r c ) ) ) ; //
k+1=17; 29 T 1 7 s = T 1 * ( p _ r c ^ ( (gamma - 1 ) / gamma ) ) ; 30 n _ C = ( T 1 7 s - T 1 ) / ( T 1 7 - T 1 ) ; 31 disp ( ”%” , n _ C * 1 0 0 , ” ( d ) O v e r a ll Co mp re ss or E f f i c i e n c y is”)
111
32 33 / / p a r t ( e ) D e te r mi n in g p ower r e q u i r e d
to drive the
compressor 34 P = m * c p * ( T 1 7 - T 1 ) ; 35 disp ( ”MW” , P / 1 e 3 , ” ( e ) Power r e q u i r e d t o d r i v e t he c o mp r e ss o r i s ” )
Scilab code Exa 18.9 Constant Pressure Gas Turbine Plant
1 / / s c i l a b Code Exa 1 8 . 9 C on st an t P r e ss u r e Gas
T u rb i ne P l a n t 2 3 T 1 = 2 9 8 ; / / M inimum T e m p er a t u re i n K e l v i n 4 b e e t a = 4 . 5 ; / / Maximum t o Minimum T e m p e r a t u r e r a t i o (
T max/T min) 5 m = 1 1 5 ; // mass f l o w r a t e t hr ou gh t he t u r b i n e and c om p re ss o r i n kg / s 6 n _ C = 0 . 7 9 ; / / C om pr es so r E f f i c i e n c y 7 n _ T = 0 . 8 3 ; / / T u r bi ne E f f i c i e n c y 8 gamma_g=1.33; 9 R=0.287; 10 c p = ( g a m m a _ g / ( g a m ma _ g - 1 ) ) * R ; // S p e c i f i c Heat a t
C on st an t P r e s s u r e i n kJ / ( kgK ) 11 a l p h a = b e e t a * n _ C * n _ T ; 12 t _ o p t = sqrt ( a l p h a ) ; / / F or maximum p o we r o u t p ut , t h e
t em pe ra tu re r a t i o s i n t he t u r bi n e and c om pr es so r 13 14 / / p a rt ( a ) D et er mi ni ng optimum p r e s s u r e
r a t i o o f t he
plant 15 r = t _ o p t ^ ( g a m m a _ g / ( g a m m a _g - 1 ) ) ; 16 disp (r , ” ( a ) optimum p r e s s u r e r a t i o 17 18 / / p a r t ( b ) Ca rn ot ’ s e f f i c i e n c y
112
o f t he p l an t i s ” )
19 n _ C a r n o t = 1 - ( 1 / b e e t a ) ; 20 disp ( ”%” , n _ C a r n o t * 1 0 0 , ” ( b ) Ca r n o t e f f i c i e n c y o f t he p l an t i s ” ) 21 22 // p a rt ( c ) D et er mi ni ng J ou le ’ s c y c l e e f f i c i e n c y 23 n _ J o u l e = 1 - ( 1 / t _ o p t ) ; 24 disp ( ”%” , n _ J o u l e * 1 0 0 , ” ( c ) e f f i c i e n c y o f t he J o u l e c y cl e i s ”) 25 26 / / p ar t ( d ) D et er mi ni ng t he rm al e f f i c i e n c y o f t he
p l a n t f o r maximum p ow er o u t p u t 27 n_th=( t_opt -1)^2/(( beeta -1)*n_C -(t_opt -1)); 28 disp ( ”%” , n _ t h * 1 0 0 , ” ( d ) t he r ma l e f f i c i e n c y o f t h e p l a n t f o r maximum p ow er o u t p u t i s ” ) 29 30 / / p a r t ( e ) D e t e r m i n i n g p ow er o u t p u t 31 w p _ m a x = c p * T 1 * ( ( t _ o p t - 1 ) ^ 2 ) / n _ C ; // maximum work
output 32 P _ m a x = m * w p _ m a x ; 33 disp ( ”MW” , P _ m a x / 1 e 3 , ” ( e ) Po wer o u t p u t i s ” ) 34 35 / / p a r t ( f ) D e t er m i n in g p ow er g e n e r a t e d by t h e
t u r b i n e r e q u i r e d t o d r i v e t he c om pr es so r 36 T 3 = b e e t a * T 1 ; / / Maximum T e m p e r a t ur e i n d e g r e e K 37 38 39 40
T 4 s = T 3 * ( r ^ ( - ( ( g a m ma _ g - 1 ) / g a m m a _ g ) ) ) ; T4=T3-((T3-T4s)*n_T); P_T=m*cp*(T3-T4); disp ( ”MW” , P _ T / 1 e 3 , ” ( f ) P ower g e n e r a t e d by t h e t u rb i n e i s ”)
41 42 / / p a r t ( g ) D e te rm i ni n g p ower a b so r be d by t h e
compressor 43 44 45 46
T2s=T1*(r^((gamma_g -1)/gamma_g)); T2=T1+((T2s-T1)/n_C); P_C=m*cp*(T2-T1); disp ( ”MW” , P _ C / 1 e 3 , ” ( g ) Power a b so r be d by t h e c o mp r e ss o r i s ” )
47
113
48 / / p a r t ( h ) h e a t s u p p l i e d i n t h e c o mb u st i on c ha mb er 49 Q s = m * c p * ( T 3 - T 2 ) ; 50 disp ( ”MW” , Q s / 1 e 3 , ” ( h ) h ea t s u p p l i e d i n t he c om bu st io n c ha m be r i s ” )
Scilab code Exa 18.10 Calculation on combined cycle power plant
1 / / s c i l a b Code Exa 1 8 . 10 C a l c u l a t i o n on com bin ed
c y c l e power p l a nt 2 3 P _ g t = 2 5 . 8 4 5 ; // Power Output o f g as t u r b i n e p l a nt i n
MW 4 P _ s t = 2 1 ; // Power Output o f s team t u r b i n e p l a nt i n
MW 5 m _ g t = 1 1 5 ; // mass f lo w r a te o f t h e e x ha us t g as i n kg
/s 6 7 8 9
n _ T = 0 . 8 6 ; / / T u r bi ne E f f i c i e n c y gamma_g=1.33; R=0.287; c p = ( g a m m a _ g / ( g a m ma _ g - 1 ) ) * R ; // S p e c i f i c Heat a t
10 11 12 13
C on st an t P r e s s u r e i n kJ / ( kgK ) T 3 = 1 3 4 1 ; / / Maximum T em p er at ur e i n g a s t u r b i n e i n d e g r e e K f ro m Ex1 8 . 9 p 1 = 8 4 ; // st ea m P r es s u r e a t t he e nt r y o f s tea m t ur bi n e i n bar / / fro m s team t a b l e s t _ 6 s = 2 9 8 . 4 ; // s a t u r a t i o n t em pe ra tu re a t 84 b a r i n degree C
14 t _ 5 s = t _ 6 s ; 15 h _ 6 s = 1 3 3 6 . 1 ; // fro m s team t a b l e l i q u i d
v a p o ur
e n th a lp y a t 84 b ar 16 t 6 = 5 3 5 ; // stea m t e m pe ra t ur e a t t he e n tr y o f s tea m t u r b i n e i n d eg r e e C 114
17 18 19 20 21 22 23 24 25
T 6 = t 6 + 2 7 3 ; // i n K el vi n h _ 4 s = 3 4 6 0 ; // from m o l l i e r d ia gr am a t t =535 d e g re e C h_7=2050; p _ c = 0 . 0 7 ; // C on de ns er p r e s s u r e i n b ar r = 8 . 8 5 0 2 4 6 4 ; / / optimum p r e s s u r e r a t i o f ro m Ex18 . 9 T 4 = 8 7 5 . 9 2 9 7 4 ; / / f ro m E x 1 8 . 9 t 4 = T 4 - 2 7 3 ; // i n d eg re e C h _ 7 s = 1 6 3 . 4 ; // S p e c i f i c E n th a lp y o f w at er i n kJ /kg m _ s t = P _ s t * 1 e 3 / ( ( h _ 4 s - h _ 7 ) * n _ T ) ; // mass f lo w r a t e o f
t he stea m i n kg / s 26 27 / / p a r t ( a ) E xh au st g a s t e mp e r at u r e a t s t a c k 28 t _ 7 = t 4 - ( ( m _ s t * ( h _ 4 s - h _ 7 s ) ) / ( m _ g t * c p ) ) ; // e n er g y
b a l a nc e f o r t he e co n o m i s e r e n t ry ( 7 ’ ) t o t he s u p e r h ea t e r e x i t ( 4 ’ ) 29 disp ( ” d e g r e e c e l s i u s ” , t _ 7 , ” ( a ) E xh au st g a s t em p er a tu r e a t s t a c k i s ” ) 30 31 / / p a rt ( b ) mass o f s team p er kg o f g as 32 disp ( ” k g ” , m _ s t / m _ g t , ” ( b ) mass o f stea m p er kg o f g as is”) 33 34 / / p a r t ( c ) P i n c h P o i n t ( PP ) 35 t _ 6 = t _ 7 + ( ( m _ s t * ( h _ 6 s - h _ 7 s ) ) / ( m _ g t * c p ) ) ; // e n er g y
b a l a nc e f o r t he e co n o m i s e r 36 37 38 39 40 41 42
PP=t_6-t_6s; disp ( ” d e g r e e c e l s i u s ” , P P , ” ( c ) P i n c h P o i n t ( PP ) i s ” )
// p ar t ( d ) t he rm al e f f i c i e n c y o f stea m t u r bi n e p l an t delh4s_7ss=(h_4s-h_7)*n_T; n_st=delh4s_7ss/(h_4s-h_7s); disp ( ”%” , n _ s t * 1 0 0 , ” ( d ) t he rm al E f f i c i e n c y t u r b i n e p l an t i s ” )
43 44 // p a rt ( e ) t he rm al
o f stea m
e f f i c i e n c y o f t he co mb ined c y c l e
plant 45 n _ B = 0 . 9 7 8 ; / / A ss um in g C om bu st io n ch am be r E f f i c i e n c y 46 Q s = 1 0 2 . 7 2 5 5 4 ; // h ea t s u p p li e d i n t he c o mb us ti on
115
c ha mb er f ro m Ex 1 8 . 9 47 Q s s = Q s / n _ B ; // power s u p p l i e d t o t he comb ined c y c l e 48 n _ g s t = ( P _ g t + P _ s t ) / Q s s ; 49 disp ( ”%” , n _ g s t * 1 0 0 , ” ( e ) t he rm al
Effi cien cy of co mb in ed g a s and s te am p ower p l a n t i s ” )
50 51 // p a rt ( f ) t he d r yn e ss
f r a c t i o n o f stea m a t t he
t u r b i n e e x ha u s t 52 x = 0 . 8 7 5 ; // from M o l l i e r d ia gr am a t p =0. 07 b ar 53 disp (x , ” ( f ) t he d r y n es s f r a c t i o n o f s tea m a t t he t u r b i n e e xh a us t i s ” )
Scilab code Exa 18.11 Calculation on combined cycle power plant
1 / / s c i l a b Code Exa 1 8 . 11 C a l c u l a t i o n on com bin ed
c y c l e power p l a nt 2 3 P _ g t = 2 5 . 8 4 5 ; // Power Output o f g as t u r b i n e p l a nt i n
MW 4 P _ s t = 2 1 ; // Power Output o f s team t u r b i n e p l a nt i n
MW 5 m _ g t = 1 1 5 ; // mass f lo w r a te o f t h e e x ha us t g as i n kg
/s 6 7 8 9
n _ T = 0 . 8 6 ; / / T u r bi ne E f f i c i e n c y gamma_g=1.33; R=0.287; c p = ( g a m m a _ g / ( g a m ma _ g - 1 ) ) * R ; // S p e c i f i c Heat a t
C on st an t P r e s s u r e i n kJ / ( kgK ) 10 T 3 = 1 3 4 1 ; / / Maximum T em p er at ur e i n g a s t u r b i n e i n d e g r e e K f ro m Ex1 8 . 9 11 p 1 = 8 4 ; // st ea m P r es s u r e a t t he e nt r y o f s tea m t ur bi n e i n bar 12 / / fro m s team t a b l e s 116
13 t _ 6 s = 2 9 8 . 4 ; // s a t u r a t i o n t em pe ra tu re a t 84 b a r i n
degree C 14 h _ 6 s = 1 3 3 6 . 1 ; // fro m s team t a b l e l i q u i d
v a p o ur
e n th a lp y a t 84 b ar 15 p p ( 1 ) = 2 0 ; // p in ch p o i n t i n d eg r e e C 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
pp(2)=28.2; pp(3)=35;
for i = 1 : 3 printf ( ” \ n f o r PP=%d d e g r e e C\n ” , p p ( i ) ) t_6=t_6s+pp(i); h _ 4 s = 3 4 6 0 ; // from m o l l i e r d ia gr am a t t =535 d e g re e C h_7=2050; p _ c = 0 . 0 7 ; // C on de ns er p r e s s u r e i n b ar T 4 = 8 7 5 . 9 2 9 7 4 ; / / f ro m E x 1 8 . 9 t 4 = T 4 - 2 7 3 ; // i n d eg re e C h _ 7 s = 1 6 3 . 4 ; // S p e c i f i c E n th a lp y o f w at er i n kJ /kg
// p a rt ( a ) st ea m f l o w p er kg o f g as m _ s t _ g t = c p * ( t 4 - t _ 6 ) / ( h _ 4 s - h _ 6 s ) ; // s tea m f l ow p er kg o f g a s 31 disp ( ” k g ” ,m_st_g t , ” ( a ) stea m f l o w p er kg o f g as i s ” ) 32 33 / / p a r t ( b ) E xh au st g a s t e mp e r at u r e a t s t a c k 34 t _ 7 = t _ 6 - ( ( m _ s t _ g t * ( h _ 6 s - h _ 7 s ) ) / ( c p ) ) ; // e n er g y
b a l a nc e f o r t he e co n o m i s e r e n t ry ( 7 ’ ) t o t he s u p e r h ea t e r e x i t ( 4 ’ ) 35 disp ( ” d e g r e e c e l s i u s ” , t _ 7 , ” ( b ) E x ha u st g a s t em p er a tu r e a t s t a c k i s ” ) 36 37 38 39 40
/ / p a r t ( c ) s te am t u r b i n e p l a n t o u tp u t h_7ss=2247; P_st=m_st_gt*m_gt*(h_4s-h_7ss); disp ( ”MW” , P _ s t / 1 e 3 , ” ( c ) P ower o u t pu t o f t h e s te am t u r b i n e p l an t i s ” )
41 42 // p ar t ( d ) t he rm al e f f i c i e n c y 43 d e l h 4 s _ 7 s s = ( h _ 4 s - h _ 7 ) * n _ T ;
117
o f stea m t u r bi n e p l an t
44 n _ s t = d e l h 4 s _ 7 s s / ( h _ 4 s - h _ 7 s ) ; 45 disp ( ”%” , n _ s t * 1 0 0 , ” ( d ) t he rm al E f f i c i e n c y o f stea m t u r b i n e p l an t i s ” ) 46 47 // p a rt ( e ) t he rm al e f f i c i e n c y o f t he co mb ined c y c l e
plant 48 n _ B = 0 . 9 7 8 ; / / A ss um in g C om bu st io n ch am be r E f f i c i e n c y 49 Q s = 1 0 2 . 7 2 5 5 4 ; // h ea t s u p p li e d i n t he c o mb us ti on
c ha mb er f ro m Ex 1 8 . 9 50 Q s s = Q s / n _ B ; // power s u p p l i e d t o t he comb ined c y c l e 51 n _ g s t = ( P _ g t + ( P _ s t * 1 e - 3 ) ) / Q s s ; 52 disp ( ”%” , n _ g s t * 1 0 0 , ” ( e ) t he rm al
Effi cien cy of co mb in ed g a s and s te am p ower p l a n t i s ” )
53 end 54 55 disp ( ” Comment :
E r r o r i n T ex tb oo k , A ns we rs v a r y d ue to Round− o f f E r r o rs ” )
Scilab code Exa 18.12 turbo prop Gas Turbine Engine
1 // s c i l a b Code E xa 1 8 . 12 t ur bo p ro p Gas T ur bi ne
Engine 2 3 4 5 6 7 8 9
T i = 2 6 8 . 6 5 ; // i n K el vi n n _ C = 0 . 8 ; // C om pr es so r E f f i c i e n c y c 1 = 8 5 ; // e nt ry v e l o c i t y i n m/ s m = 5 0 ; // mass f lo w r a t e o f a i r i n kg / s R=287; gamma =1.4; // S p e c i f i c Heat R at io c p = 1 . 0 0 5 ; // S p e c i f i c Heat a t C on st a nt P r es s u r e i n
kJ/(kgK) 10 u = 5 0 0 / 3 . 6 ; // s pe e d o f a t ur b o p ro p a i r c r a f t i n m/ s 11 d e l T = 2 2 5 ; // t em p er a tu re r i s e t hr ou gh t he c om p re ss o r 118
(T02−T01 ) i n K 12 p i = . 7 0 1 ; / / I n i t i a l P r e s s u r e i n b a r 13 n _ D = 0 . 8 8 ; // i n l e t d i f f u s e r e f f i c i e n c y 14 a _ i = sqrt ( gamma * R * T i ) ; 15 M i = u / a _ i ; 16 T o i _ i = 1 / 0 . 9 6 5 ; / / ( To i /Ti ) fro m i s e n t r o p i c
f l ow g as
t a b l e s a t Mi and gamma v a l u e s 17 18 19 20 21
T01=Ti*Toi_i; T1=T01 -(0.5*(c1^2)/(cp*1e3));
// part ( a ) T 1 s _ i = 1 + n _ D * ( ( T 1 / T i ) - 1 ) ; // ( T1s / Ti ) i s e n t r o p i c
t em pe ra tu re r a t i o t hr ou gh t he d i f f u s e r 22 p 1 _ i = T 1 s _ i ^ ( gamma /( gamma - 1 ) ) ; / / ( p 1s / p i ) i s e n t r o p i c p r es s ur e r a t i o 23 p 1 = p 1 _ i * p i ; 24 d e l p _ D = p 1 - p i ; 25 disp ( ” b a r ” ,delp_D , ” ( a ) i s e n t r o p i c p r e s s u re r i s e t h r o ug h t he d i f f u s e r i s ” ) 26 27 // p ar t ( b ) c om pr es so r p r e s s u r e r a t i o 28 T 0 2 s = T 0 1 + ( d e l T * n _ C ) ; 29 r _ o c = ( T 0 2 s / T 0 1 ) ^ ( gamma /( gamma - 1 ) ) ; / / c o m p r e s s o r
p r e s s u r e r a t i o ( p 02 / p01 ) 30 disp ( r _ o c , ” ( b ) c om pr es so r p r e s s u r e r a t i o i s ” ) 31 32 / / p a r t ( c ) 33 P = m * c p * d e l T ; 34 disp ( ”MW” , P * 1 e - 3 , ” ( c ) po we r r e q u i r e d c o mp r e ss o r i s ” )
to drive the
Scilab code Exa 18.13 Turbojet Gas Turbine Engine
119
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
/ / s c i l a b Code Exa 1 8 . 1 3 T u rb o je t Gas T ur bi ne E ng in e
17 18 19 20 21 22 23
T 1 = 2 2 3 . 1 5 ; // i n K el vi n n _ C = 0 . 7 5 ; / / C om pr es so r E f f i c i e n c y c 1 = 8 5 ; // e nt ry v e l o c i t y i n m/ s m = 5 0 ; // mass f lo w r a t e o f a i r i n kg / s R=287; n _ B = 0 . 9 8 ; // C om bu st io n ch am be r E f f i c i e n c y Q f = 4 3 * 1 e 3 ; // C a l o r i f i c V a l u e o f f u e l i n kJ /kg ; T 0 3 = 1 2 2 0 ; // T u rb in e i n l e t s t a g n a t i o n temp i n
Kelvin n _ T = 0 . 8 ; // T u rb in e E f f i c i e n c y gamma =1.4; // S p e c i f i c Heat R at io n _ m = 0 . 9 8 ; // M e ch an ic al e f f i c i e n c y s i g m a = 0 . 5 ; / / f l i g h t t o j e t s p ee d r a t i o ( u / c e ) n _ N = 0 . 9 8 ; // e xh au st n o zz l e e f f i c i e n c y c p = 1 . 0 0 5 ; // S p e c i f i c Heat a t C on st a nt P r es s u r e i n kJ/(kgK) u = 8 8 6 / 3 . 6 ; // f l i g h t s pe ed o f a t ur bo p ro p a i r c r a f t in m/s d e l T = 2 0 0 ; // t em p er a tu re r i s e t hr ou gh t he c om p re ss o r (T02−T01 ) i n K pi=.701; / / I n i t i a l P r e s s u r e i n b a r n _ D = 0 . 8 8 ; // i n l e t d i f f u s e r e f f i c i e n c y
a1 = sqrt ( gamma * R * T 1 ) ; M 1 = u / a 1 ; // Mach n umber a t t h e c o m pr e ss o r i n l e t T 1 _ 0 1 = 0 . 8 8 1 ; / / ( T1/ T01 ) fr om i s e n t r o p i c f l ow g as
t a b l e s a t M1 a nd gamma v a l u e s 24 25 26 27 28 29
T01=T1/T1_01; T1=T01 -(0.5*(c1^2)/(cp*1e3));
// p ar t ( a ) c om pr es so r p r e s s u r e r a t i o T02s=T01+(delT*n_C); r _ o c = ( T 0 2 s / T 0 1 ) ^ ( gamma /( gamma - 1 ) ) ; / / c o m p r e s s o r
p r e s s u r e r a t i o ( p 02 / p01 ) 30 disp ( r _ o c , ” ( a ) c om pr es so r p r e s s u r e r a t i o i s ” ) 31 32 / / p a r t ( b )
120
33 T 0 2 = T 0 1 + d e l T ; 34 f = ( ( c p * T 0 3 ) - ( c p * T 0 2 ) ) / ( ( Q f * n _ B ) - ( c p * T 0 3 ) ) ; // f =(ma/
mf ) ; e n e r g y b a l a n c e i n t h e c o mb u st i o n ch am be r 35 disp ( 1 / f , ” ( b ) A i r−F ue l R at io i s ” ) 36 37 38 39 40
// p a rt ( c ) t u r b i n e p r e s s u r e r a t i o / / t u r b i n e p ow er i n p u t P T=n m ∗ (ma+mf ) ∗ cp ∗ (T03−T01) / / p ow er i n p u t t o t h e c o m p r e ss o r P C=ma∗ cp ∗ (T02−T01) T 0 4 s = T 0 3 - ( d e l T / ( n _ m * n _ T * ( 1 + f ) ) ) ; // f ro m e n er g y b a l a n c e P T=P C 41 r _ o t = ( T 0 3 / T 0 4 s ) ^ ( gamma /( gamma - 1 ) ) ; / / t u r b i n e p r e s s u r e r a t i o ( p 03 / p04 ) 42 disp ( r _ o t , ” ( c ) t u r bi n e p r e s s u r e r a t i o i s ” ) 43 44 // p a rt ( d ) e xh a us t n o z z l e p r e s s u r e r a t i o 45 c e = u / s i g m a ; // j e t v e l o c i t y a t t h e e x i t o f t h e
e xh a us t n o z z l e 46 47 48 49
T04=T03-(delT/(n_m*(1+f))); Te=T04 -(0.5*(ce^2)/(cp*1e3)); Tes=T04-((T04-Te)/n_N); r _ N = ( T 0 4 / T e s ) ^ ( gamma /( gamma - 1 ) ) ; / / e x h a u st n o z z l e
p r e s s u r e r a t i o ( p 04 / pe ) 50 disp ( r _ N , ” ( d ) e xh au st n o z zl e p r e s s u r e r a t i o
is ”)
51 ae = sqrt ( gamma * R * T e ) ; 52 M e = c e / a e ; // Mach number 53 disp ( M e , ” a nd t h e Mach Number i s ” )
Scilab code Exa 18.15 Impulse Steam Turbine 3000 rpm
1 // sci lab
c od e E xa 1 8 . 15 I mp ul se Steam T ur bi ne 3 00 0
rpm 2 3 P = 5 0 0 ; / / P ow er O ut pu t i n kW
121
4 u = 1 0 0 ; // p e r i p h e r a l s pe e d o f t he r o t o r b l a d es i n m/
s 5 c y 2 = 2 0 0 ; // w h i r l component o f t he a b s o l u t e v e l o c i t y 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
a t e nt r y o f t h e r o t o r c y 3 = 0 ; // w h i r l component o f t he a b s o l u t e v e l o c i t y at e xi t o f the r ot or a l p h a 2 = 6 5 ; // n o z z l e a n g le a t e x i t n _ s t = 0 . 6 9 ; // i s e n t r o p i c s ta g e e f f i c i e n c y p 2 = 8 ; / / stea m p r e s s u r e a t t he e x i t o f t he f i r s t s ta g e i n bar t 2 = 2 0 0 ; // s team t em pe ra tu re a t t he e x i t o f t he f i r s t s t a g e i n d e gr e e C N = 3 e 3 ; // r o t o r S pe ed i n RPM / / p a r t ( a ) Mean d i a me t er o f t h e s t a g e
d=u*60/(%pi*N); disp ( ”m” ,d , ” ( a ) Mean d i am et er o f t he s t a g e i s ” )
/ / p a rt ( b ) mass f l ow r a t e o f t he stea m w _ s t = 2 * ( u ^ 2 ) * 1 e - 3 ; // s p e c i f i c work m=P/w_st; disp ( ” k g / s ” ,m , ” ( b ) mass f l o w r a t e o f t he s tea m i s ” )
/ / p a r t ( c ) i s e n t r o p i c e n t ha l p y d ro p delh_s=w_st/n_st; disp ( ” k J / k g ” ,delh_s , ” ( c ) i s e n t r o p i c e n th a lp y d ro p i s ” )
// p a rt ( d ) r o t o r b l ad e a n g l e s cx=cy2/(tand(alpha2)); beta3=atand(u/cx); disp ( ” d e g r e e ” , b e t a 3 , ” ( d ) t he r o t o r b la d e a n g l es a r e beta2=beta3=” )
30 31 // p a rt ( e ) b l ad e h e i g h t a t t he n o z z l e e x i t 32 v _ s 2 = 0 . 2 6 0 8 ; / / fro m s team t a b l e s a t p2=8 ba r and t 2
=200 d e g r e e C 33 Q = m * v _ s 2 ;
122
34 h = Q / ( c x * % p i * d ) ; 35 disp ( ”m” ,h , ” ( e ) b l a de h e ig h t a t t he n o z z l e
exit is ”)
Scilab code Exa 18.16 large Centrifugal pump 1000 rpm
1 / / s c i l a b Code Exa 1 8 . 16
l a r g e C e n t r i f u g a l pump 1 00 0
rpm 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
N = 1 e 3 ; // r o t o r S pe ed i n RPM H = 4 5 ; // h e i g h t i n m ro=1e3; g = 9 . 8 1 ; / / G r a v i t a t i o n a l a c c e l e r a t i o n i n m/ s ˆ 2 n _ o = 0 . 7 5 ; // o v e r a l l E f f i c i e n c y o f t h e d r i v e d r = 2 ; / / d i a me t er r a t i o ( d 2 /d1 ) p h i = 0 . 3 5 ; // fl ow c o e f f i c i e n t ( cr 2 /u2 ) Q = 2 . 5 ; // d i s c h a r g e i n m3/ s
/ / p a r t ( a ) P ower r e q u i r e d t o d r i v e t h e pump P=(ro*Q*g*H)/(n_o); disp ( ”kW” , P * 1 e - 3 , ” ( a ) P ower r e q u i r e d t o d r i v e t he pump i s ” )
/ / p ar t ( b ) i m p e l l e r d i am e te r s a t e n t ry and e x i t
21 22
u2 = sqrt ( g * H ) ; w_p=u2^2; d2=u2*60/(%pi*N); disp ( ”cm” , d 2 * 1 e 2 , ” ( b ) t he i m p e l l e r d ia me te r a t e x i t is”) d1=d2/2; disp ( ”cm” , d 1 * 1 e 2 , ” and t he i m p e l l e r d ia m e te r a t e nt r y is”)
23 24 / / p a r t ( c ) i m p e l l e r
w i dt h 123
25 26 27 28 29 30 31 32 33
c_r2=phi*u2; b=Q/(c_r2*%pi*d2); disp ( ”cm” , b * 1 e 2 , ” ( c ) t h e i m p e l l e r
w id th i s ” )
// p ar t ( d ) i m p e l l e r b la d e a n gl e a t t he e n t ry
c_r1=Q/(b*%pi*d1); u1=u2/dr; beta1=atand(c_r1/u1); disp ( ” d e g r e e ” , b e t a 1 , ” ( d ) t he i m p e l l e r b l a de a n gl e a t t h e e n t r y b e t a 1=” )
Scilab code Exa 18.17 three stage steam turbine
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
/ / s c i l a b Code Exa 1 8 .1 7 t h r e e s t a ge stea m t u r bi n e
t 1 = 2 5 0 ; / / I n i t i a l T em p er a tu r e i n d e g r e e C n _ T = 0 . 7 5 ; // o v e r a l l E f f i c i e n c y o f t h e t u r b i n e p1=10; // I n i t i a l Pres sure in bar n _ m = 0 . 9 8 ; // M ec ha ni ca l E f f i c i e n c y m=5; N = 1 e 3 ; // r o t o r S pe ed i n RPM H = 4 5 ; // h e i g h t i n m ro=1e3; g = 9 . 8 1 ; / / G r a v i t a t i o n a l a c c e l e r a t i o n i n m/ s ˆ 2 Q = 2 . 5 ; // d i s c h a r g e i n m3/ s
P=(ro*Q*g*H)/(n_T); delh_T=P/(m*n_m*1e3); delh_st=delh_T/3; delh1_4ss=delh_T/n_T;
/ / p a r t ( a ) s te am c o n d i t i o n s h 1 = 2 9 4 0 ; // from M o l l i e r d ia gr am 124
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
disp ( ” ( a ) stea m c o n d i t i o n s a t t he t u r bi n e e x i t a r e : ” ) h_4ss=h1-delh1_4ss; p 4 = 1 . 2 ; // i n b a r disp ( ” b a r ” , p 4 , ” p r e s s u r e : ” ) h4=2640; x4=0.98; t 4 = 1 0 4 . 8 ; // i n d eg r e e C disp ( ” d e g r e e C ” , t 4 , ” t e m p e r a t u r e : ” ) disp ( x 4 , ” t he d ry n e ss f r a c t i o n i s : ” )
// p ar t ( b ) s t a g e E f f i c i e n c i e s
h2=h1-delh_st; p2=5; h3=h2-delh_st; p3=2.5; h4=h3-delh_st; h2s=2795; h3s=2705; h4s=2605; n_st1=delh_st/(h1-h2s); n_st2=delh_st/(h2-h3s); n_st3=delh_st/(h3-h4s); disp ( ”%” , n _ s t 1 * 1 0 0 , ” ( b ) E f f i c i e n c y o f t he f i r s t s t ag e i s ”) 44 disp ( ”%” , n _ s t 2 * 1 0 0 , ” E f f i c i e n c y o f t he s ec on d s t a g e is”) 45 disp ( ”%” , n _ s t 3 * 1 0 0 , ” E f f i c i e n c y o f t he t h i r d s t a g e is”)
Scilab code Exa 18.18 Ljungstrom turbine 3600 rpm
1 // s c i l a b Code E xa 1 8 . 18 L ju ng st ro m t u r b i n e 3 60 0 rpm 2
125
3 4 5 6 7 8 9 10 11 12 13 14 15 16
d 1 = 0 . 9 2 ; // i n n e r d ia me te r o f t he i m p e l l e r i n m d 2 = 1 ; // o u t er d ia me te r o f t he i m p e l l e r i n m N = 3 . 6 e 3 ; // r o t o r S pe ed i n RPM a p l h a _ 1 = 2 0 ; // b la de e x i t a n g l e i n d eg re e p 2 = 0 . 1 ; / / e x i t P r es s u r e o f stea m i n b a r x 2 = 0 . 8 8 ; // d ry ne ss f r a c t i o n a t e x i t n _ s t = 0 . 8 3 ; // s t a g e E f f i c i e n c y u1=%pi*d1*N/60; u2=%pi*d2*N/60;
/ / p a r t ( a ) p o we r d e v e l o p e d sigma=cosd(aplha_1)/2; w_st=u1^2+u2^2; disp ( ”kW/( kg/ s ) ” , w _ s t * 1 e - 3 , ” ( a ) p ow er d e v e l o p e d p e r u n i t f lo w r a t e i s ” )
17 18 // p a rt ( b ) i s e n t r o p i c e n th a lp y dr op 19 d e l h _ s = w _ s t / n _ s t ; 20 disp ( ” k J / k g ” , d e l h _ s * 1 e - 3 , ” ( b ) i s e n t r o p i c e nt h a l p y d ro p i s ” ) 21 22 / / p a r t ( c ) s tea m c o n d i t i o n s a t e n t r y 23 disp ( ” ( c ) s te am c o n d i t i o n s a t e n t r y a r e : ” ) 24 p 1 = 0 . 1 8 ; // i n b a r 25 disp ( ” b a r ” , p 1 , ” p r e s s u r e : ” ) 26 x 1 = 0 . 9 ; 27 disp ( x 1 , ” t he d ry n e ss f r a c t i o n i s : ” )
Scilab code Exa 18.19 blower type wind tunnel
1 / / s c i l a b Code Exa 1 8 . 19 b lo we r t yp e wind t u nn e l 2 3 T 0 1 = 3 1 0 ; // i n K el vi n
126
4 5 6 7 8 9 10 11 12 13
I n i t i a l P r e ss u r e i n b ar p 0 1 = 1 . 0 1 3 ; // n _ n = 0 . 9 6 ; // n o z z l e e f f i c i e n c y n _ c = 0 . 7 8 ; / / c om pr es so r e f f i c i e n c y Ma(1)=0.5; Ma(2)=0.9; p i ( 1 ) = 0 . 8 3 7 ; // f ro m i s e n t r o p i c f lo w g as t a b l e s pi(2)=0.575; gamma =1.4; // S p e c i f i c Heat R at io R=287; c p = 1 . 0 0 5 ; // S p e c i f i c Heat a t C on st a nt P r es s u r e i n kJ/(kgK)
14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
for i = 1 : 2 printf ( ” when Ma=%f ” , M a ( i ) )
// part ( a ) M s = ( ( n _ n / ( M a ( i ) ^ 2 ) ) - ( ( (gamma - 1 ) / 2 ) * ( 1 - n _ n ) ) ) ^ ( - 1 / 2 ) ; disp ( M s , ” ( a ) Mach n umber f o r i s e n t r o p i c f l ow i s ” )
// part (b) p0e=1; p_r0(i)=p0e/pi(i); disp ( p _ r 0 ( i ) ,” ( b ) p r e s s u r e r a t i o o f t he c o mp re ss or i s ”)
// par t ( c )
d e l T 0 e _ 0 i = ( ( p _ r 0 ( i ) ^ ( (gamma - 1 ) / gamma ) ) - 1 ) / n _ c ; T0e=T01+(T01*delT0e_0i); d e l T 0 e _ t = n _ n * ( 1 - ( p _ r 0 ( i ) ^ ( ( 1 -gamma ) / gamma ) ) ) * T 0 e ; T_t=T0e-delT0e_t; disp ( ”K” , T _ t , ” ( c ) t he t e s t s e c t i o n t em pe ra t ur e i s ” ) a _ t = sqrt ( gamma * R * T _ t ) ; c_t=Ma(i)*a_t; disp ( ”m/s” , c _ t , ” and t h e t e s t s e c t i o n v e l o c i t y i s ” )
// part (d) ro_t=p01*1e5/(R*T_t); A_t=0.17*0.15; m=ro_t*A_t*c_t;
127
40 41 42 43 44 45
disp ( ” k g / s ” ,m , ” ( d ) mass f l o w r a t e i s ” )
// par t ( e )
P(1)=m*cp*(T0e-T01); P(2)=m*cp*(T_t-T01); disp ( ”kW” , P ( i ) , ” ( e ) p ower r e q u i r e d is”) 46 end
f o r t h e c o m pr e ss o r
Scilab code Exa 18.20 Calculation on an axial turbine cascade
1 / / s c i l a b Code Exa 1 8 .2 0 C a l c u l a t i o n on a n a x i a l
t u r b i n e c a sc a de 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
b e t a 1 = 3 5 ; // b la de a ng l e a t e nt ry b e t a 2 = 5 5 ; // b la de a n g l e a t e x i t i ( 1 ) = 5 ; // i n c i d e n c e i(2)=10; i(3)=15; i(4)=20; d e l t a = 2 . 5 ; // d e v i a t i o n a l p h a 2 = b e t a 2 - d e l t a ; // a i r a ng le a t e x i t a _ r = 2 . 5 ; // a s p e c t r a t i o ( h / l )
n=4; for m = 1 : n
// part ( a ) printf ( ” \ n f o r i n c i d e n c e =%d\n” , i ( m ) ) a l p h a 1 = b e t a 1 + i ( m ) ; // a i r a ng le a t e n tr y e p = a l p h a 1 + a l p h a 2 ; // d e f l e c t i o n a ng le disp ( ” d e g r e e ” , e p , ” ( a ) f lo w d e f l e c t i o n i s ” ) p _ c = 0 . 5 0 5 ; // ( s / l )
128
22 / / p a r t ( b ) l o s s c o e f f i c i e n t f ro m H aw th or ne 23 24 z _ p = 0 . 0 2 5 * ( 1 + ( ( e p / 9 0 ) ^ 2 ) ) ; / / H awth orn e ’ s 25 disp ( z _ p , ” ( b ) t h e p r o f i l e l o s s c o e f f i c i e n t Ha wth or ne r e l a t i o n i s ” ) 26 z = ( 1 + ( 3 . 2 / a _ r ) ) * z _ p ; // t h e t o t a l c as ca de
coefficient 27 disp (z , ” and t h e t o t a l l o s s 28 29 30 31 32 33 34 35
re la t io n s re la ti on f ro m loss
c o e f f i c i e n t is ”)
Y=z;
// pa rt ( c ) dr ag and l i f t
coefficients
alpham=atand((0.5*(tand(alpha2)-tand(alpha1)))); C_D=p_c*Y*((cosd(alpham)^3)/(cosd(alpha2)^2)); disp ( C _ D , ” ( c ) the drag c o e f f i c i e n t i s ” )
C _ L = ( 2 * p _ c * ( t a n d ( a l p h a 1 ) + t a n d ( a l p h a 2 ) ) * c o s d ( a l p h a m) ) +(C_D*tand(alpham)); 36 disp ( C _ L , ” a nd t h e L i f t c o e f f i c i e n t i s ” ) 37 end
Scilab code Exa 18.21 low reaction turbine stage
1 2 3 4 5 6 7 8 9 10 11
/ / s c i l a b Code Exa 1 8 .2 1 lo w r e a c t i o n t u r bi n e s t a ge
B e t a 2 = 3 5 ; // r o t o r b la de a i r a ng le i n d eg re e a l p h a 1 = 0 ; // f i x e d b la de a i r a ng le i n d eg re e alpha2=65; beta3=52.5; I ( 1 ) = 0 ; // i n c i d e n c e a n g l e I(2)=5; I(3)=10; I(4)=15; I(5)=20;
129
12 13 14 15 16 17 18 19
a _ r = 2 . 5 ; // a s p e c t r a t i o ( h / l ) for i = 1 : 5 disp ( ” d e g r e e ” , I ( i ) , ” when i n c i d e n c e =” ) b e t a 2 ( i ) = B e t a 2 + I ( i ) ; // b et a2 v a r i e s w i t h i n c i d e n c e
// part ( a )
p h i = c o s d ( a l p h a 2 ) * c o s d ( b e t a 2 ( i ) ) / ( s i n d ( a l p ha 2 - b e t a 2 ( i ))); 20 e p = a l p h a 1 + a l p h a 2 ; // d e f l e c t i o n a ng le 21 disp ( p h i , ” ( a ) fl ow c o e f f i c i e n t i s ” ) 22 p _ c = 0 . 5 0 5 ; / / p i t c h −c h or d r a t i o ( s / l ) 23 24 // p a rt ( b ) b l ad e t o g as s pe ed r a t i o 25 s i g m a = s i n d ( a l p h a2 - b e t a 2 ( i ) ) / ( c o s d ( b e t a 2 ( i ) ) ) ; 26 disp ( s i g m a , ” ( b ) b l a de t o g as s pe ed r a t i o i s ” ) 27 z _ N = 2 . 2 8 * 0 . 0 2 5 * ( 1 + ( ( e p / 9 0 ) ^ 2 ) ) ; // Hawthorne ’ s
relation 28 29 30 31 32 33 34 35
// part ( c) degree of reac tion R=0.5*phi*(tand(beta3)-tand(beta2(i))); disp ( ”%” , R * 1 e 2 , ” ( c ) t he d e g re e o f r e a c t i o n
is ”)
/ / p a r t ( d ) t o t a l −to −t o t a l e f f i c i e n c y e _ R = b e t a 2 ( i ) + b e t a 3 ; // R o t o r d e f l e c t i o n a n g l e z e e t a _ p _ R = 0 . 0 2 5 * ( 1 + ( ( e _ R / 9 0 ) ^ 2 ) ) ; // p r o f i l e l o s s co efficient for rotor 36 z e e t a _ R = ( 1 + ( 3 . 2 / a _ r ) ) * z e e t a _ p _ R ; // t o t a l l o s s co efficient for rotor 37 38 39 40 41 42
a = ( z e e t a _ R * ( s e c d ( b e t a 3 ) ^ 2 ) ) + ( z _ N * ( s e c d ( a l p h a 2 ) ^ 2 ) ); b=phi*(tand(alpha2)+tand(beta3))-1; n _ t t = inv ( 1 + ( 0 . 5 * ( p h i ^ 2 ) * ( a / b ) ) ) ; disp ( ”%” , n _ t t * 1 e 2 , ” ( d ) t o t a l −to − t o t a l e f f i c i e n c y i s ” ) end
130
Scilab code Exa 18.22 Isentropic or Stage Terminal Velocity for Turbines
1 // s c i l a b Code Exa 1 8 .2 2 I s e n t r o p i c
o r S ta ge
T er mi na l V e l o c i t y f o r T ur bi ne s 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
T 0 1 = 1 2 7 3 ; // i n K el vi n funcprot ( 0 ) ; p 0 1 = 5 ; // I n i t i a l P r e s su r e i n b ar e x i t g a s P re ss ur e i n b a r p 0 2 = 3 . 5 ; // c p = 1 . 0 0 5 ; // S p e c i f i c Heat a t C on st a nt P r es s u r e i n
kJ/(kgK) gamma =1.4; // S p e c i f i c Heat R at io m = 2 8 ; // mass f l o w r a t e o f t he g a s i n kg / s n _ t t = 0 . 8 4 ; // s t a ge e f f i c i e n c y shi=1.7; // st ag e lo ad in g c o e f f i c i e n t
pr_0=p01/p02; d e l h 0 1 _ 0 3 s s = c p * T 0 1 * ( 1 - ( p r _ 0 ^ ( ( 1 -gamma ) / gamma ) ) ) ;
// p a rt ( a ) s t a g e t e r m in a l v e l o c i t y c0 = sqrt ( 2 * d e l h 0 1 _ 0 3 s s * 1 e 3 ) ; disp ( ”m/s” , c 0 , ” ( a ) s t a g e t e r m i n al
velocity is ”)
// p ar t ( b ) i s e n t r o p i c b la d e t o g as s pe ed r a t i o s i g m a _ s = sqrt ( 0 . 5 * n _ t t / s h i ) ; disp (sig ma_s , ” ( b ) t he i s e n t r o p i c r a t io i s ”)
b la de t o g a s s pe e d
// p a rt ( c ) p e r i p h e r a l s pe ed o f t he r o t o r u=sigma_s*c0; disp ( ”m/s” ,u , ” ( c ) p e r i p h e r a l s pe ed o f t he r o t o r i s ” )
/ / p a r t ( d ) t h e p ow er d e v e l o p e d 131
28 P = m * n _ t t * d e l h 0 1 _ 0 3 s s ; 29 disp ( ”MW” , P * 1 e - 3 , ” ( d ) t he power d e ve l op e d i s ” )
Scilab code Exa 18.23 axial compressor stage efficiency
1 / / s c i l a b Code Exa 1 8 .2 3 a x i a l
c om pr es so r s t a g e
efficiency 2 3 4 5 6 7
R = 0 . 5 ; // D eg re e o f r e a c t i o n n _ R = 0 . 8 4 9 ; // e f f i c i e n c y o f r o t o r b la de row n _ D = 0 . 8 4 9 ; // e f f i c i e n c y o f d i f f u s e r b l a d e row n_st=R*n_R+(1-R)*n_D; disp ( ”%” , n _ s t * 1 e 2 , ” t h e v al ue o f s t a g e e f f i c i e n c y )
is ”
Scilab code Exa 18.24 Calculation on an axial compressor cascade
1 / / s c i l a b Code Exa 1 8 .2 4 C a l c u l a t i o n on a n a x i a l
c o mp r e ss o r c a s c a de 2 3 4 5 6 7 8 9 10
beta1=51; beta2=9; a i r a n g le a t r o t o r and s t a t o r e x i t a l p h a _ 1 = 7 ; // u = 1 0 0 ; // t e s t s e c t i o n v e l o c i t y o f a i r i n m/ s cx=u/(tand(alpha_1)+tand(beta1)); w1=cx/cosd(beta1); a l p h a 2 = a t a n d ( t a n d ( a l p h a _ 1 ) + t a n d ( b e t a 1 ) - t a n d ( b e t a 2 )) c2=cx/cosd(alpha2);
132
11 Y _ D = 0 . 0 3 6 7 ; // l o s s
co e ff i c i e n t for
di ff us er blade
row Y _ R = 0 . 0 3 9 3 ; / / l o s s c o e f f i c i e n t f o r r o t o r b l a d e ro w z_R=Y_R*((w1/u)^2); z_D=Y_D*((c2/u)^2); phi=cx/u; n_st=1-(0.5*phi*(z_D*(secd(alpha2)^2)+z_R*(secd( beta1)^2))/(tand(beta1)-tand(beta2))); 17 disp ( ”%” , n _ s t * 1 e 2 , ” t h e v al ue o f s t a g e e f f i c i e n c y i s ” ) 12 13 14 15 16
Scilab code Exa 18.25 Calculation on two stage axial compressor
1 / / s c i l a b Code Exa 1 8 .2 5 C a l c u l a t i o n on two s t a g e
a x i a l c o mp re s so r 2 3 4 5 6 7 8 9 10 11 12 13 14 15
T 0 1 = 3 1 0 ; // i n K el vi n funcprot ( 0 ) ; gamma =1.4; p 0 1 = 1 . 0 2 ; // I n i t i a l P r e s su r e i n b ar pr_o=2; pr_o1=1.5; N = 7 . 2 e 3 ; // r o t o r S pe ed i n RPM d = 6 5 / 1 0 0 ; / / Mean B la de r i n g d i am et er i n m h = 1 0 / 1 0 0 ; // b la de h e i g h t a t e nt ry i n m n _ p = 0 . 9 ; // p o l y t r o p i c e f f i c i e n c y w d f = 0 . 8 7 ; / / w or k−done f a c t o r m = 2 5 ; // i n kg / s c p = 1 . 0 0 5 ; // S p e c i f i c Heat a t C on st a nt P r es s u r e i n
kJ/(kgK) 16 R = 2 8 7 ; 17 T 0 1 ( 1 ) = T 0 1 ; 18 // p ar t ( a ) s t a g e p r e s s u r e
ratio 133
19 p r _ o 2 = p r _ o / p r _ o 1 ; 20 disp ( p r _ o 2 , ” ( a ) p r e s s u r e r a t i o d ev el o p ed by t he 2 nd s t ag e i s ”) 21 22 // p a r t ( b ) s t a g e e f f i c i e n c y 23 n =( gamma - 1 ) / gamma ; 24 n _ s t 1 = ( ( p r _ o 1 ^ n ) - 1 ) / ( ( p r _ o 1 ^ ( n / n _ p ) ) - 1 ) ; 25 disp ( ”%” , n _ s t 1 * 1 e 2 , ” ( b ) s t a g e e f f i c i e n c y f o r t h e s ta g e 1 i s ”) 26 n _ s t 2 = ( ( p r _ o 2 ^ n ) - 1 ) / ( ( p r _ o 2 ^ ( n / n _ p ) ) - 1 ) ; 27 disp ( ”%” , n _ s t 2 * 1 e 2 , ” and s t a g e e f f i c i e n c y f o r t h e s ta g e 2 i s ”) 28 / / p a r t ( c ) p ower r e q u i r e d t o d r i v e t h e c o m pr e s so r 29 T 0 2 = T 0 1 * ( p r _ o 1 ^ ( ( gamma - 1 ) / gamma ) ) ; 30 P 1 = m * c p * ( T 0 2 - T 0 1 ) / n _ s t 1 ; 31 disp ( ”kW” , P 1 , ” ( c ) power r e q u i r e d f o r t he 1 s t s t a g e is”) 32 T 0 2 s = T 0 1 + ( T 0 1 * ( p r _ o 1 ^ ( (gamma - 1 ) / gamma ) - 1 ) / n _ s t 1 ) ; 33 P 2 = m * c p * T 0 2 s * ( p r _ o 2 ^ ( (gamma - 1 ) / gamma ) - 1 ) / n _ s t 2 ; 34 disp ( ”kW” , P 2 , ” and power r e q u ir e d f o r t he 2 nd s t a g e is”) 35 36 37 38 / / p ar t ( d ) a i r a n g l e s o f t he r o t o r s and s t a t o r s 39 A 1 = % p i * d * h ; 40 r o _ 0 1 = ( p 0 1 * 1 e 5 ) / ( R * T 0 1 ) ; 41 c x = m / ( r o _ 0 1 * A 1 ) ; 42 T1=T01-((cx^2)/(2*cp*1e3)); p 1 = p 0 1 * ( ( T 1 / T 0 1 ) ^ ( 1 / ( (gamma - 1 ) / gamma ) ) ) ; 43 44 r o 1 = ( p 1 * 1 e 5 ) / ( R * T 1 ) ; 45 c x _ n e w = m / ( r o 1 * A 1 ) ; 46 c 1 = c x _ n e w ; 47 disp ( ” f o r f i r s t s t a g e ” ) 48 u = % p i * d * N / 6 0 ; 49 b e t a 1 = a t a n d ( u / c 1 ) ; 50 disp ( ” d e g r e e ” , b e t a 1 , ” b e t a 1 = ” ) 51 w s t 1 = c p * ( T 0 2 - T 0 1 ) * 1 e 3 / n _ s t 1 ;
134
52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74
cy2=wst1/(wdf*u); alpha2=atand(cy2/cx_new); disp ( ” d e g r e e ” ,alpha2 , ” a l p h a 2 = ” ) beta2=atand((u/cx_new)-tand(alpha2)); disp ( ” d e g r e e ” , b e t a 2 , ” b e t a 2 = ” ) R=cx_new*(tand(beta1)+tand(beta2))*100/(2*u); disp ( ”%” ,R , ” d e gr ee o f r e a c t i o n f o r t he f i r s t s t a g e is”)
T01_II=T02s; disp ( ” f o r s e co n d s t a g e ” ) T 0 2 _ I I = T 0 1 _ I I * ( p r _ o 2 ^ ( (gamma - 1 ) / gamma ) ) ; wst2=cp*1e3*(T02_II -T01_II)/ n_st2; alpha1s=beta2; cy1s=cx_new*tand(alpha1s); cy2s=(cy1s)+(wst2/(wdf*u)); alpha2s=atand(cy2s/cx_new); disp ( ” d e g r e e ” ,alpha2s , ” a l p h a 2 s = ” ) beta1s=atand((u-cy1s)/cx_new); disp ( ” d e g r e e ” ,beta1s , ” b e t a 1 s = ” ) beta2s=atand((u-cy2s)/cx_new); disp ( ” d e g r e e ” ,beta2s , ” b e t a 2 s = ” ) R_II=cx_new*(tand(beta1s)+tand(beta2s))*100/(2*u); disp ( ”%” , R _ I I , ” D eg re e o f R ea ct io n f o r t he s ec on d s t ag e i s ”)
Scilab code Exa 18.26 Calculation on an axial compressor cascade
1 / / s c i l a b Code Exa 1 8 .2 4 C a l c u l a t i o n on a n a x i a l
c o mp r e ss o r c a s c a de 2 3 R = 0 . 5 9 0 6 ; // D e g re e o f r e a c t i o n 4 beta1=66;
135
5 6 7 8 9
beta2=22; alpha2=61; p _ R = 0 . 8 6 5 ; // p i tc h −c ho rd r a t i o ( s / l ) f o r r o t o r p _ S = 0 . 9 6 3 ; // p i tc h −c ho rd r a t i o ( s / l ) f o r s t a t o r a i r a ng l e a t r o t o r and s t a t o r a l p h a _ 3 = b e t a 2 ; //
exit 10 u = 1 0 0 ; // t e s t s e c t i o n v e l o c i t y o f a i r i n m/ s 11 Y _ D = 0 . 0 7 7 ; // p r o f i l e l o s s c o e f f i c i e n t f o r s t a t o r b l a d e ro w 12 Y _ R = 0 . 0 8 ; / / l o s s c o e f f i c i e n t f o r r o t o r b l a d e row 13 b e t a _ m = a t a n d ( 0 . 5 * ( t a n d ( b e t a 1 ) + t a n d ( b e t a 2 ) ) ) ; 14 C _ D _ R = p _ R * Y _ R * ( c o s d ( b e t a _ m ) ^ 3 ) / ( c o s d ( b e t a 1 ) ^ 2 ) ; 15 C _ L _ R = ( 2 * p _ R * ( t a n d ( b e t a 1 ) - t a n d ( b e t a 2 ) ) * c o s d ( b e t a _ m) ) -(C_D_R*tand(beta_m)); 16 n _ R = 1 - ( 2 * C _ D _ R / ( C _ L _ R * s i n d ( 2 * b e t a _ m ) ) ) ; 17 disp ( ”%” , n _ R * 1 e 2 , ” t he v a l ue o f r o t o r c as ca d e e f f i c i e n c y i s ”) 18 19 a l p h a m = a t a n d ( 0 . 5 * ( t a n d ( a l p h a 2 ) + t a n d ( a l p h a _ 3 ) ) ) ; 20 C _ D _ S = p _ S * Y _ D * ( c o s d ( a l p h a m ) ^ 3 ) / ( c o s d ( a l p h a 2 ) ^ 2 ) ; 21 C _ L _ S = ( 2 * p _ S * ( t a n d ( a l p h a 2 ) - t a n d ( a l p h a _ 3 ) ) * c o s d ( alpham))-(C_D_S*tand(alpham)); 22 n _ D = 1 - ( 2 * C _ D _ S / ( C _ L _ S * s i n d ( 2 * a l p h a m ) ) ) ; 23 disp ( ”%” , n _ D * 1 e 2 , ” t h e v al ue o f d i f f u s e r c a sc a de e f f i c i e n c y i s ”) 24 25 n _ s t = R * n _ R + ( 1 - R ) * n _ D ; 26 disp ( ”%” , n _ s t * 1 e 2 , ” t h e v al ue o f s t a g e e f f i c i e n c y i s ” )
Scilab code Exa 18.27 Isentropic Flow Centrifugal Air compressor
1 / / s c i l a b Code Exa 1 8 .2 7 I s e n t r o p i c Flow− c e n t r i f u g a l
136
A ir c o mp r e ss o r 2 3 T 0 1 = 3 3 5 ; // i n K el vi n 4 p 0 1 = 1 . 0 2 ; // I n i t i a l P r e s su r e i n b ar 5 b e t a 1 = 6 1 . 4 ; // a i r a n g l e a t t h e i n l e t o f
a xi al
i n d u ce r b l a d es 6 7 8 9
gamma =1.4; d 1 = 0 . 1 7 5 ; / / Mean B la de r i n g d i am et er a t e n tr y d 2 = 0 . 5 ; // i m p e l l e r d ia me te r a t e x i t c p = 1 0 0 5 ; // S p e c i f i c Heat a t C o ns ta nt P r es s u r e i n J
/(kgK) 10 A 1 = 0 . 0 4 1 2 ; // Area o f c r o s s
s e ct i on at the i m pe l le r
inlet 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
R=287;
N ( 1 ) = 5 7 0 0 ; // r o t o r S pe ed i n RPM N(2)=6200; N(3)=6700; N(4)=7200; for i = 1 : 4 printf ( ” \n f o r N=%d rpm\n\n ” , N ( i ) ) u1=%pi*d1*N(i)/60; u2=%pi*d2*N(i)/60; c1=u1*tand(beta1); T1=T01-((c1^2)/(2*cp)); p 1 = p 0 1 * ( ( T 1 / T 0 1 ) ^ ( gamma /( gamma - 1 ) ) ) ; ro1=(p1*1e5)/(R*T1); p r 0 = ( ( 1 + ( u 2 ^ 2 / ( c p * T 0 1 ) ) ) ^ (gamma /( gamma - 1 ) ) ) ; disp ( p r 0 , ” ( a ) p r e s s u re r a t i o i s ” ) m=ro1*A1*c1; disp ( ” k g / s ” ,m , ” ( b ) mass f lo w r a te o f a i r i s ” ) T 0 2 = T 0 1 * ( p r 0 ^ ( ( gamma - 1 ) / gamma ) ) ; P=m*cp*(T02-T01); disp ( ”kW” , P * 1 e - 3 , ” ( c ) Power r e q u i r e d t o d r i v e t he c o m p r e s s o r P=” ) end
137
Scilab code Exa 18.28 centrifugal Air compressor
1 2 3 4
/ / s c i l a b Code Exa 1 8 .2 8 c e n t r i f u g a l A ir c om pr es so r T 0 1 = 3 3 5 ; // i n K el vi n I n i t i a l P r e s su r e i n b ar p 0 1 = 1 . 0 2 ; // b e t a 1 = 6 1 . 4 ; // a i r a n g l e a t t h e i n l e t o f a x i a l i n d u ce r b l a d es
5 6 7 8 9
gamma =1.4; N = 7 2 0 0 ; / / r o t o r S pe ed i n RPM d 1 = 0 . 1 7 5 ; / / Mean B la de r i n g d i am et er a t e n tr y d 2 = 0 . 5 ; // i m p e l l e r d ia me te r a t e x i t c p = 1 0 0 5 ; // S p e c i f i c Heat a t C o ns ta nt P r es s u r e i n J
/(kgK) 10 A 1 = 0 . 0 4 1 2 ; // Area o f c r o s s
s e ct i on at the i m pe l le r
inlet 11 R = 2 8 7 ; 12 b 2 = A 1 / ( % p i * d 2 ) ; 13 disp ( ”cm” , b 2 * 1 e 2 , ” ( a ) w i d t h o f t he i m p e l l e r a t e x i t is”) 14 u 2 = % p i * d 2 * N / 6 0 ; 15 / / f o r N= 72 00 rpm 16 p 1 = 0 . 9 4 4 4 5 7 9 ; / / f ro m Ex18 . 2 7 17 p r = 1 . 4 2 0 6 9 8 8 ; / / p r e s s u r e r a t i o 18 m = 5 . 0 0 6 1 0 7 8 ; // mass f lo w r a t e o f a i r i n k g / s 19 T 0 2 = 3 7 0 . 3 5 3 8 1 ; 20 r o 2 = 1 . 1 ; / / t r i a l a nd e r r o r 21 c r 2 ( 1 ) = m / ( A 1 * r o 2 ) ; 22 n = 2 ; 23 for i = 1 : n c 2 ( i ) = sqrt ( c r 2 ( i ) ^ 2 + ( u 2 ^ 2 ) ) ; 24 25 T2=T02-((c2(i)^2)/(2*cp)); p02=pr*p01; 26
138
27 28 29 30 31 32 33 34 35 36
p 2 = p 0 2 * ( ( T 2 / T 0 2 ) ^ ( 1 / ( (gamma - 1 ) / gamma ) ) ) ; ro2=(p2*1e5)/(R*T2); cr2(i+1)=m/(ro2*A1); end cr=cr2(3); disp ( p 2 / p 1 , ” ( b ) t h e s t a t i c p r e s s u r e r a t i o i s ” )
// p a rt ( c ) alpha2=atand(cr/u2); disp ( ” d e g r e e ” ,alpha2 , ” ( c ) t he d i r e c t i o n
a lp ha 2 o f t he a b s o l u t e v e l o c i t y v e c t o r ( c2 ) o r t he d i f f u s e r a n g l e a t e nt ry i s ” )
Scilab code Exa 18.29 Centrifugal compressor with vaned diffuser
1 // s c i l a b Code Exa 1 8 . 29 2 3 4 5 6 7 8 9 10 11 12 13 14
C e n t r i f u g a l c om p re ss o r w it h
vaned d i f f u s e r T 0 1 = 3 1 0 ; // i n K el vi n I n i t i a l P r e ss u r e i n b ar p 0 1 = 1 . 1 0 3 ; // d h = 0 . 1 0 ; // hub d i am e te r i n m d 2 = 0 . 5 5 ; // i m p e l l e r d ia me te r i n m c 1 = 1 0 0 ; // V e l o c i t y o f a i r a t t h e e nt ry o f i nd u c er c 3 = c 1 ; // V e l o c i t y o f a i r a t d i f f u s e r e x i t s h i = 1 . 0 3 5 ; // power i n pu t f a c t o r m u = 0 . 9 ; // s l i p f a c t o r m = 7 . 5 ; // i n kg / s gamma =1.4; N = 1 5 e 3 ; // r o t o r S pe ed i n RPM disp ( ” ( a ) f o r r a d i a l l y t ip p e d b l a d e s ” ) c p = 1 0 0 5 ; // S p e c i f i c Heat a t C o ns ta nt P r es s u r e i n J
/(kgK) 15 R = 2 8 7 ; 16 n _ t t = 0 . 8 1 ; // t o t a l t o t o t a l
139
e f f ic i e n cy
17 18 19 20 21 22
23 24 25 26 27 28
29 30 31 32 33 34
35 36 37 38
T1=T01-((c1^2)/(2*cp)); p 1 = p 0 1 * ( ( T 1 / T 0 1 ) ^ ( gamma /( gamma - 1 ) ) ) ; ro1=(p1*1e5)/(R*T1); A1=m/(ro1*c1); dt = sqrt ( ( A 1 * 4 / ( % p i ) ) + ( d h ^ 2 ) ) ; disp ( ”cm” , d t * 1 e 2 , ” ( i ) t i p d ia me te r o f t he i n du c er a t e n tr y i s ” ) d 1 = 0 . 5 * ( d t + d h ) ; / / Mean B la de r i n g d i a m et e r u1=%pi*d1*N/60; w1 = sqrt ( ( u 1 ^ 2 ) + ( c 1 ^ 2 ) ) ; a1 = sqrt ( gamma * R * T 1 ) ; M1_rel=w1/a1; disp (M1_rel , ” ( i i ) t h e R e l a t i v e Mach number a t i n d u c e r b l a d e e n t r y Mw1=” ) u2=%pi*d2*N/60; w_st=shi*mu*(u2^2); T02=T01+(w_st/cp); T02s=T01+(n_tt*(T02-T01)); p r _ 0 = ( T 0 2 s / T 0 1 ) ^ ( gamma /( gamma - 1 ) ) ; disp ( p r _ 0 , ” ( i i i ) s t a g n a t i o n p r e s s u r e r a t i o d e ve l op e d is”) P=m*cp*(T02-T01); disp ( ”kW” , P * 1 e - 3 , ” ( i v ) t h e po we r r e q u i r e d i s ” ) disp ( ” ( b ) f o r vaned d i f f u s e r ” ) c _ t h e t a 2 = m u * u 2 ; / / v e l o c i t y o f w h i r l ( s w i r l component
) at the i mp el le r e xi t 39 // v a n e l e s s s pa ce b e t we en t he i m p e l l e r e x i t and t he va ned d i f f u s e r e n tr y =0 .1 ∗ i m p e l l e r r a di u s 40 // r2 s=r2 ∗ 1 . 1 ; 41 / / w i d t h o f t h e c a s i n g a f t e r t h e i m p e l l e r e x i t = 1. 4 ∗ i m p e l l e r p a ss a g e w i dt h 42 43 44 45 46 47
c_theta2s=c_theta2/(1.1*1.4); cr2=c1; cr2s=cr2/(1.1*1.4); c 2 s = sqrt ( ( c r 2 s ^ 2 ) + ( c _ t h e t a 2 s ^ 2 ) ) ; alpha2s=atand(cr2s/c_theta2s); disp ( ” d e g r e e ” ,alpha2s , ” ( i ) t he d i r e c t i o n t h e d i f f u s e r e nt ry i s a l p ha 2 s=” )
140
o f f lo w a t
T2s=T02-((c2s^2)/(2*cp)); a 2 s = sqrt ( gamma * R * T 2 s ) ; M2s=c2s/a2s; disp ( M 2 s , ” ( i i ) t h e Mach number a t t h e d i f f u s e r e n t r y is”) 52 A r = c 2 s / c 3 ; 53 d 3 _ 2 s = 1 . 1 6 ; // d3 / d 2s from l a s t t r i a l g i ve n i n t he 48 49 50 51
book 54 a l p h a 3 = a c o s d ( c o s d ( a l p h a 2 s ) / d 3 _ 2 s ) ; 55 A r _ v = d 3 _ 2 s * s i n d ( a l p h a 3 ) / ( s i n d ( a l p h a 2 s ) ) ; 56 disp ( A r _ v , ” ( i i i ) A rea r a t i o o f t he van ed d i f f u s e r i s ” ) 57 T 0 3 = T 0 2 ; 58 T 3 = T 0 3 - ( ( c 3 ^ 2 ) / ( 2 * c p ) ) ; 59 p r 3 _ 1 = ( ( ( T 3 * T 0 1 ) / ( T 1 * T 0 3 ) ) ^ (gamma /( gamma - 1 ) ) ) * p r _ 0 ; 60 disp ( p r 3 _ 1 , ” ( i v ) t h e s t a t i c p r e s s u r e r a t i o o f t he c o mp r e ss o r i s ” ) 61 disp ( ” comment : C a l c u l a t i o n s i n t h e b oo k a r e wrong i n
t he b e g in n i ng i t s e l f f o r p1 . s o t he v a l u e s s l i g h t l y d i f f e r s h e re o nl y f o r p a rt ( a ) ” )
Scilab code Exa 18.30 Inward Flow Radial Gas turbine
1 / / s c i l a b Code Exa 1 8 . 3 0 I nw ar d Flow R a d ia l Gas
turbine 2 3 T 1 = 8 7 3 ; // t he g as e n t ry t em pe ra tu re a t n o z z l e i n
Kelvin 4 p 1 = 4 ; // t h e g a s e nt ry p r e s s u re a t n o z z l e i n b a r 5 n _ T = 0 . 8 5 ; // i s e n t r o p i c e f f i c i e n c y 6 d 2 = 0 . 4 ; // r o t o r b la de r i n g d ia me te r a t e nt ry i n m 7 d 3 = 0 . 2 ; // r o t o r b la d e r i n g d ia me t e r a t e x i t i n m 8 p r _ t = 4 ; // s t a t i c P r e s s u r e R a ti o a c r o s s t he t u r b i n e ( 141
p3/p1) 9 p r _ n = 2 ; // s t a t i c P r e s s u r e R a ti o a c r o s s t he n o z z l e s ( p3/p1) 10 p h i = 0 . 3 ; / / f l o w c o e f f i c i e n t a t i m p e l l e r e n t r y 11 12 13 14
gamma =1.4; N = 1 8 e 3 ; // r o t o r S pe ed i n RPM m = 5 ; // mass f lo w r a t e o f g a s i n kg / s c p = 1 0 0 5 ; // S p e c i f i c Heat a t C o ns ta nt P r es s u r e i n J
/(kgK) 15 16 17 18 19 20 21 22 23
R=287; u2=%pi*d2*N/60; u3=%pi*d3*N/60; cr2=phi*u2;
// part (a)
T 3 s s = T 1 / ( p r _ t ^ ( (gamma - 1 ) / gamma ) ) ; T3=T1-n_T*(T1-T3ss); T 2 s = T 1 / ( p r _ n ^ ( ( gamma - 1 ) / gamma ) ) ; T 2 = T 2 s + ( 0 . 5 * ( T 3 - T 3 s s ) ) ; // h a l f o f t he l o s s e s ( T3−
T3 s s ) o cc ur i n t he n o z z l e s 24 25 26 27
28 29 30 31 32 33 34 35 36
p2=p1/pr_n; rho2=(p2*1e5)/(R*T2); b2=m/(rho2*cr2*%pi*d2); disp ( ”cm” , b 2 * 1 e 2 , ” ( a ) a x i a l wi d t h o f t h e i m p e l l e r b l a de p a s s a g e a t e n t ry i s ” ) alpha2=atand(cr2/u2); disp ( ” d e g r e e ” ,alpha2 , ” ( b ) n o z z l e e x i t a i r a n g l e i s ” ) cx3=cr2; beta3=atand(cx3/u3); disp ( ” d e g r e e ” , b e t a 3 , ” ( c ) i m p e l l e r e x i t a i r a n gl e i s ” ) c_theta3=0; c_theta2=u2; P = m * ( u 2 * c _ t he t a 2 - u 3 * c _ t h e t a 3 ) ; disp ( ”kW” , P * 1 e - 3 , ” ( d ) p ow er d e v e l o p e d i s ” )
142
Scilab code Exa 18.31 Cantilever Type IFR turbine
1 / / s c i l a b Code Exa 1 8 . 31 C a n t i l e v e r Type IFR t u r b i n e 2 3 P = 1 5 0 ; / / Power d e v e l o p e d i n kW 4 T 0 1 = 9 6 0 ; // t he g as e nt r y t em pe ra tu re a t n o z zl e i n
Kelvin 5 p 0 1 = 3 ; // t he g as e nt ry p r e s s u r e a t n o zz l e i n b a r 6 b e t a 2 = 4 5 ; // a i r a n g l e a t r o t o r b la de e nt ry ( fro m radial direction ) 7 b e t a 3 = 6 5 ; // a i r a n g l e a t r o t o r b la de e x i t ( from radial direction ) 8 d 2 = 0 . 2 ; // r o t o r b la de r i n g d ia me te r a t e nt ry i n m 9 d 3 = 0 . 1 5 ; // r o t o r b la de r i n g d i am e t e r a t e x i t i n m 10 gamma =1.4; 11 N = 3 6 e 3 ; // r o t o r S pe ed i n RPM 12 a l p h a _ 2 = 1 5 ; // a i r a n g l e a t n o z z l e e x i t ( fro m
t a n g e nt i a l d i r e c t i o n ) 13 p r 0 = 2 . 2 9 ; // t o t a l −to − s t a t i c P r e s su r e R at io ( p 01 / p3 ) 14 n _ N = 0 . 9 4 ; / / N oz z le E f f i c i e n c y 15 c p = 1 1 0 0 ; // S p e c i f i c Heat a t C o ns ta nt P r es s u r e i n J /(kgK) 16 17 18 19 20 21 22
R = c p * ( ( gamma - 1 ) / gamma ) ; u2=%pi*d2*N/60; u3=%pi*d3*N/60;
23 24 25 26 27 28 29 30
// p ar t ( a ) mass f lo w r a te o f t h e g as c r 2 _ t h e t a 2 = t a n d ( a l p h a _ 2 ) ; // c r 2 t h e t a 2 =c r 2 / c t h e t a 2 c _ t h e t a 2 = u 2 / ( 1 - c r 2 _ t h e t a 2 ) ; / / c t h e t a 2 =c r 2 ∗ tan ( al ph a2 )+u2 cr2=c_theta2*cr2_theta2; cr3=cr2; c_theta3=(cr3*tand(beta3))-u3; w_st=(u2*c_theta2)+(u3*c_theta3); m=P/(w_st*1e-3); disp ( ” k g / s ” ,m , ” ( a ) mass f lo w r a te o f t h e g as i s ” )
// p ar t ( b ) r o t o r b la d e a x i a l l e ng t h a t e n t ry 143
31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57
c2=cr2/sind(alpha_2); T 2 s = T 01 - ( ( 0 . 5 * ( c 2 ^ 2 ) ) / ( c p * n _ N ) ) ; T2=T01-((T01-T2s)*n_N); p _ r n = ( T 2 s / T 0 1 ) ^ (gamma /( gamma - 1 ) ) ; p2=p01*p_rn; rho2=(p2*1e5)/(R*T2); b2=m/(rho2*cr2*%pi*d2); disp ( ”cm” , b 2 * 1 e 2 , ” ( b ) r o t o r b la de a x i a l l e n g t h a t e n tr y i s ” )
/ / p a r t ( c ) t o t a l −to −t o t a l t u r b i n e e f f i c i e n c y T 0 3 s s = T 0 1 * ( p r 0 ^ ( ( 1 - gamma ) / gamma ) ) ; n_T=P/(m*cp*1e-3*(T01-T03ss)); disp ( ”%” , n _ T * 1 e 2 , ” ( c ) t o t a l −to −t o t a l t u rb i ne e f f i c i e n c y i s ”)
// p a rt ( d ) r o t o r b l ad e l e n g th a t e x i t p03=p01/pr0; T03=T01-(P/(m*cp*1e-3)); c3 = sqrt ( ( c r 3 ^ 2 ) + ( c _ t h e t a 3 ^ 2 ) ) ; T3=T03-((cr3^2)/(2*cp)); p 3 = p 0 3 * ( ( T 3 / T 0 3 ) ^ ( gamma /( gamma - 1 ) ) ) ; ro3=(p3*1e5)/(R*T3); b3=m/(ro3*cr3*%pi*d3); disp ( ”cm” , b 3 * 1 e 2 , ” ( d ) r o t o r b la de l e n g t h a t e x i t
// p a rt ( e ) d e g re e o f r e a c t i o n DOR=(T2-T3)/(T01-T03); disp ( ”%” , D O R * 1 e 2 , ” ( e ) d e g re e o f r e a c t i o n
is ”)
Scilab code Exa 18.32 IFR turbine stage efficiency
1 / / s c i l a b Code Exa 1 8 . 32 IFR t u r b i n e s t a g e
144
is ”)
efficiency 2 3 4 5 6 7
// part (b)
R=0.48; sigma_s=0.6; n_n=0.92; a l p h a _ 2 = 1 5 ; //
a i r a n g l e a t n o z z l e e x i t ( fro m t a n g e nt i a l d i r e c t i o n )
8 n _ s t = 2 * s i g m a _ s *sqrt ( n _ n * ( 1 - R ) ) * c o s d ( a l p h a _ 2 ) ; 9 disp ( ”%” , n _ s t * 1 0 0 , ” s t a g e e f f i c i e n c y o f t h e r a d i a l t u rb i n e i s ”)
Scilab code Exa 18.33 Vertical Axis Crossflow Wind turbine
1 / / s c i l a b Code Exa 1 8 .3 3 V e r t i c a l A xi s C r o s sf l ow
Wind t u r b i n e 2 3 4 5 6 7 8 9 10
c 1 = 2 4 / 3 . 6 ; // wind s p ee d i n m/ s c 2 = 3 0 / 3 . 6 ; // r o t o r s pe ed i n m/ s m 1 = 2 5 ; // mass f lo w r a t e o f a i r a t wind s i d e i n k g/ s a i r m ass f l ow r a t e i n kg / s m 2 = 3 1 . 2 5 ; // r o t o r d 1 = 3 ; // r o t o r o u t er d ia me te r i n m d 2 = 2 ; // r o t o r i n n e r d ia me te r i n m gamma =1.4; a i r a n g l e a t r o t o r e nt ry ( fro m a l p h a = 3 7 ; //
t a n g e nt i a l d i r e c t i o n ) 11 12 13 14 15 16 17
c(1)=c1; c(2)=c2; m(1)=m1; m(2)=m2;
for i = 1 : 2 c_theta1=c(i)*cosd(alpha);
145
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
u1=c_theta1/2; u2=u1*d2/d1; disp ( ”kmph” , c ( i ) * 3 . 6 , ” f o r s p e e d=” )
/ / p a r t ( a ) o ptimum r o t o r s p e ed N=60*u1/(%pi*d1); disp ( ”rpm” ,N , ” ( a ) o ptimum r o t o r
s p ee d i s ” )
// p a rt ( b ) b l ad e t o wind s pe ed r a t i o sigma=u1/c(i); disp ( s i g m a , ” b l ad e t o wind s pe ed r a t i o
i s ”)
// par t ( c ) hy dr au li c powers and e f f i c i e n c i e s
Ph=m(i)*((2*(u1^2))+(u2^2)); disp ( ”Watts” , P h , ” ( c ) h y d r a u l i c p ow er i s ” ) n_h=((2*(u1^2))+(u2^2))/(0.5*(c(i)^2)); disp ( ”%” , n _ h * 1 e 2 , ” and h y d r a ul i c e f f i c i e n c y end
is ”)
Scilab code Exa 18.34 Counter Rotating fan
1 2 3 4 5 6 7 8 9 10 11 12
/ / s c i l a b Code Exa 1 8 . 34 Co un te r R o ta ti n g f an
n = 0 . 8 0 9 ; // co mb ined e f f i c i e n c y o f t he f a n s p h i = 0 . 2 4 5 ; // fl o w c o e f f i c i e n t A = 0 . 2 1 2 ; / / d a t a f ro m Ex14 . 1 d = 0 . 4 5 ; / / d a ta f ro m Ex14 . 1 u = 2 2 . 6 2 ; / / d a t a f ro m Ex14 . 1 cx=phi*u; Q = 1 . 1 7 5 ; / / i n m3/ s d e l p 0 _ I = 5 5 0 . 7 5 5 ; / / d a ta f ro m Ex14 . 1 delp0_II=delp0_I; delp0=delp0_I+delp0_II;
146
13 disp ( ”mm W.G. ” , d e l p 0 / 9 . 8 1 , ” ( a ) t he o v e r a l l p r e s s u r e r i s e o b t ai ne d i s ” ) 14 I P = Q * d e l p 0 ; // p ower r e qu i r e d f o r i s e n t r o p i c f lo w i n
Watts 15 P = I P / n ; 16 disp ( ”kW” , P * 1 e - 3 , ” ( b ) t h e Power r e q u i r e d
is ”)
Scilab code Exa 18.35 Sirocco Radial fan 1440 rpm
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
/ / s c i l a b Code Exa 1 8 .3 5 S i r o c c o R ad ia l f an 1 4 4 0 rpm
d 2 = 0 . 4 ; // o u t er d ia me te r o f t h e i m p e l l e r i n m d 1 = 0 . 3 6 ; // i n n e r d ia me te r o f t he i m p e l l e r i n m b = 0 . 5 ; // a x i a l l en g t h o f t h e i m p e l l e r i n m r h o = 1 . 2 5 ; // d e n s i ty o f a i r i n kg /m3 N = 1 4 4 0 ; / / r o t o r S pe ed i n RPM P = 5 0 ; / / Power r e q u i r e d i n kW
u1=%pi*d1*N/60; u2=%pi*d2*N/60; beta1=atand(d2/d1); disp ( ” d e g r e e ” , b e t a 1 , ” ( a ) t h e b la de a i r a n g l e a t t he i m p e l l e r e n tr y b et a1=” ) beta2=90-beta1; disp ( ” d e g r e e ” , b e t a 2 , ” and t he b la de a i r a n g l e a t t h e i m p e l l e r e x i t b et a2=” ) delp0=2*rho*(u2^2); disp ( ”mm W.G. ” , d e l p 0 / 9 . 8 1 , ” ( b ) t he s t a g n a t i o n p re ss ur e r i s e a cr o ss the fan i s ” ) cr1=u1*tand(beta1); m=rho*cr1*%pi*d1*b; disp ( ” k g / s ” ,m , ” ( c ) mass f l o w r a t e o f t he a i r t hr ou gh
147
t h e f an i s ” ) 22 c _ t h e t a 1 = 0 ; // f o r z e r o i n l e t s w i r l 23 w _ s t = 2 * ( u 2 ^ 2 ) ; 24 I P = m * w _ s t / 1 0 0 0 ; // i d e a l power r e qu i r e d t o d r iv e t h e
f a n i n kW 25 n = I P / P ; 26 disp ( ”%” , n * 1 e 2 , ” ( d ) t h e E f f i c i e n c y o f t he f an
is ”)
Scilab code Exa 18.37 Calculation for the specific speed
1 // s c i l a b Code Exa 1 8 .3 7 C a l c u l a t i o n
f o r t he
s p e c i f i c sp eed 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
/ / p a r t ( 1 ) s p e c i f i c s p e ed o f A x i a l f l o w g a s t u r b i n e P 1 = 0 . 5 e 3 ; / / Gas T u r bi n e Po wer O ut pu t i n kW N 1 = 6 0 ; / / S pe ed i n RPS
omega1=%pi*2*N1; ro1=2; d e l h _ 1 = 3 0 ; // c h a ng e o f e nt ha l p y i n kJ N S _ 1 = o m e g a 1 * sqrt ( P 1 * 1 0 e 2 / r o 1 ) * ( ( d e l h _ 1 * 1 e 3 ) ^ ( - 5 / 4 ) ) ; disp ( N S _ 1 , ” 1 . t h e s p e c i f i c s p ee d o f A x i a l f l o w g a s t u rb i n e i s ”)
/ / p a r t ( 2 ) s p e c i f i c s p e e d o f IFR g a s t u r b i n e P 2 = 0 . 7 5 e 3 ; / / Gas T u r bi n e P ower O ut pu t i n kW N 2 = 3 0 0 ; / / S p ee d i n RPS
omega2=%pi*2*N2; ro2=1; d e l h _ 2 = 2 5 0 ; // c h an g e o f e nt h a l p y i n kJ N S _ 2 = o m e g a 2 * sqrt ( P 2 * 1 0 e 2 / r o 2 ) * ( ( d e l h _ 2 * 1 e 3 ) ^ ( - 5 / 4 ) ) ; disp ( N S _ 2 , ” 2 . t h e s p e c i f i c s p e ed o f IFR g a s t u r b i n e is”)
20
148
21 22 23 24 25 26 27
/ / p a r t ( 3 ) t h e s p e c i f i c s p ee d o f an a x i a l c o m pr e ss o r N _ c = 1 2 0 ; / / S pe ed i n RPS
omega_c=%pi*2*N_c; Q _ c = 2 5 ; // f l o w r a t e i n m3/ s d e l h _ 3 = 4 0 ; // c h a ng e o f e nt ha l p y i n kJ N S _ c = o m e g a _ c *sqrt ( Q _ c ) * ( ( d e l h _ 3 * 1 e 3 ) ^ ( - 3 / 4 ) ) ; disp ( N S _ c , ” 3 . t h e s p e c i f i c s p e ed o f an a x i a l c o mp r e ss o r i s ” )
28 29 / / p a r t ( 4 ) t h e s p e c i f i c
s p ee d o f a c e n t r i f u g a l
compressor 30 Q = 5 ; // f l o w r a t e i n m3/ s 31 d e l h _ 4 = 3 5 ; // c h a ng e o f e nt ha l p y i n kJ 32 N S _ 4 = o m e g a _ c *sqrt ( Q ) * ( ( d e l h _ 4 * 1 e 3 ) ^ ( - 3 / 4 ) ) ; 33 disp ( N S _ 4 , ” 4 . t h e s p e c i f i c s p ee d o f a c e n t r i f u g a l c o mp r e ss o r i s ” ) 34 35 / / p a r t ( 5 ) t h e s p e c i f i c s p ee d o f an a x i a l f a n 36 N 5 = 2 2 ; / / S pe ed i n RPS 37 o m e g a _ 5 = 2 * % p i * N 5 ; 38 Q _ 5 = 3 . 5 ; // f l o w r a t e i n m3/ s 39 r h o = 1 . 2 5 ; // d e n s i t y i n kg /m3 40 g = 9 . 8 1 ; // g r a v i t a t i o n a l a c c e l e r a t i o n i n m/ s 2 41 H 1 = 5 5 / r h o ; // hea d i n m 42 N S _ 5 = o m e g a _ 5 *sqrt ( Q _ 5 ) * ( ( g * H 1 ) ^ ( - 3 / 4 ) ) ; 43 disp ( N S _ 5 , ” 5 . t h e d i m e n s i o n l e s s s p e c i f i c s p ee d o f an a x ia l fan i s ”) 44 45 / / p a r t ( 6 ) t h e s p e c i f i c s p ee d o f a R a d ia l f a n 46 N 6 = 2 0 ; / / S pe ed i n RPS 47 o m e g a _ 6 = 2 * % p i * N 6 ; 48 Q _ 6 = 1 . 4 ; // f l o w r a t e i n m3/ s 49 50 H 2 = 5 2 / r h o ; // hea d i n m 51 N S _ 6 = o m e g a _ 6 *sqrt ( Q _ 6 ) * ( ( g * H 2 ) ^ ( - 3 / 4 ) ) ; 52 disp ( N S _ 6 , ” 6 . t h e d i m e n s i o n l e s s s p e c i f i c s p ee d o f a R ad ia l f an i s ” )
149
Scilab code Exa 18.38 Kaplan turbine 70 rpm
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
/ / s c i l a b Code Exa 1 8 . 38 Kaplan t u r b i n e 70 rpm
/ / p a r t ( a ) f l o w r a t e a nd s p e c i f i c s p e e d P = 8 e 3 ; / / Ga s P ow er O ut pu t i n kW N = 7 0 ; / / S p e ed i n RPM H = 1 0 ; // n et head i n m n _ m = 0 . 8 5 ; // e f f i c i e n c y omega=%pi*2*N/60; N S = o m e g a * sqrt ( P * 1 0 e 2 ) * ( H ^ ( - 5 / 4 ) ) / 5 4 9 . 0 1 6 ; disp ( N S , ” ( a ) t h e s p e c i f i c s p ee d o f t u r b i n e i s ” ) r h o = 1 0 0 0 ; // d e n s i t y i n kg /m3 g = 9 . 8 1 ; // g r a v i t a t i o n a l a c c e l e r a t i o n i n m/ s 2 Q=P*1e3/(n_m*rho*g*H); disp ( ”m3/s” ,Q , ” and t he f l o w r a t e i s ” )
// p a rt ( b ) d e te r mi n i ng t he s pe ed , f l o w r a t e and p ower f o r t h e mo del D p _ m = 1 2 ; // Dp m=Dp/Dm N p = N ; // Sp eed f o r p r o to t yp e H m = 3 ; // hea d o f t he model H p = H ; // hea d f o r p r o to t yp e N m = N p * D p _ m * sqrt ( H m / H p ) ; disp ( ”rpm” , N m , ” ( b ) s pe ed f o r t he model i s ” ) Dm_p=1/Dp_m; Qp=Q; Q m = ( D m _ p ^ 2 ) * sqrt ( H m / H p ) * Q p ; disp ( ”m3/s” , Q m , ” t he f lo w r a t e f o r model i s ” ) Pm=n_m*rho*g*Qm*Hm; disp ( ”kW” , P m * 1 e - 3 , ” t h e power f o r t he model i s ” )
150
Scilab code Exa 18.39 Calculation for Pelton Wheel prototype
1 / / s c i l a b Code Exa 1 8 .3 9 C a l c u l a t i o n
f o r t he P el to n
Wheel 2 3 4 5 6 7 8 9 10 11 12 13 14
N m = 1 0 2 ; / / S pee d f o r t h e m od el i n RPM H m = 3 0 ; // n et hea d f o r t he model i n m n _ m = 1 ; // Assuming e f f i c i e n c y Q m = 0 . 3 4 5 ; // d i s c h a r g e i n m3/ s r h o = 1 0 0 0 ; // d e n s i t y i n kg /m3 g = 9 . 8 1 ; // g r a v i t a t i o n a l a c c e l e r a t i o n i n m/ s 2 omega_m=%pi*2*Nm/60; Pm=n_m*rho*g*Qm*Hm; N S = o m e g a _ m * sqrt ( P m ) * ( H m ^ ( - 5 / 4 ) ) / 5 4 9 . 0 1 6 ; disp ( N S , ” t h e s p e c i f i c s p ee d o f t u r b i n e i s ” )
/ / d e te r mi n i ng t he s pe ed , f l o w r a t e and power f o r t h e p r o t o t yp e 15 H p = 1 5 0 0 ; // head f o r p r o to t yp e 16 17 18 19 20 21 22
Pp=((Hp/Hm)^(3/2))*Pm; disp ( ”MW” , P p * 1 e - 6 , ” t he power f o r t he p r o t o t y p e i s ” ) o m e g a _ p = N S * 5 4 9 . 0 1 6 * ( H p ^ ( 5 / 4 ) ) / (sqrt ( P p ) ) ; Np=omega_p*60/(2*%pi); disp ( ”rpm” , N p , ” s pe ed f o r t he p r ot o t y p e i s ” ) Qp = sqrt ( H p / H m ) * Q m ; disp ( ”m3/s” , Q p , ” t he f lo w r a t e f o r p r o to ty pe i s ” )
Scilab code Exa 18.40 Francis turbine 910 rpm
151
1 / / s c i l a b Code Exa 1 8 .4 0 C a l c u l a t i o n
f o r t he F r a n ci s
turbine 2 3 / / p a r t ( a ) d e t e r m i n i n g t h e s pe ed , 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
s p e c i f i c s p e ed and
p ower f o r t h e m ode l Q m = 0 . 1 4 8 ; // d i s c h a r g e i n m3/ s N = 9 1 0 ; / / S p e ed i n RPM H m = 2 5 ; // n et hea d i n m n = 0 . 9 ; // e f f i c i e n c y omega=%pi*2*N/60; N S = o m e g a * sqrt ( Q m ) * ( H m ^ ( - 3 / 4 ) ) * 0 . 1 8 0 4 ; disp ( N S , ” ( a ) t h e s p e c i f i c s p ee d o f t u r b i n e i s ” ) N u = N / ( sqrt ( H m ) ) ; disp ( ”rpm” , N u , ” u n i t s pe ed f o r t he model i s ” ) r h o = 1 0 0 0 ; // d e n s i t y i n kg /m3 g = 9 . 8 1 ; // g r a v i t a t i o n a l a c c e l e r a t i o n i n m/ s 2 Pm=rho*g*Qm*Hm; disp ( ”kW” , P m * 1 e - 3 , ” t h e power f o r t he model i s ” )
/ / p a r t ( b ) d e t e rm i n i n g t h e s pe ed , f l o w r a t e and p ower f o r t he p r o t ot y p e 19 H p = 2 5 0 ; // head f o r p r ot o ty p e 20 D p _ m = 6 ; // Dp m=Dp/Dm 21 22 23 24 25 26 27
Qp = sqrt ( H p / H m ) * Q m * ( D p _ m ^ 2 ) ; disp ( ”m3/s” , Q p , ” ( b ) t he f l o w r a t e f o r p r o t o t y p e i s ” ) Pp=rho*g*Qp*Hp*n; disp ( ”MW” , P p * 1 e - 6 , ” t he power f o r t he p r o t o t y p e i s ” ) o m e g a _ p = N S * ( H p ^ ( 3 / 4 ) ) / ( 0 . 1 8 0 4 *sqrt ( Q p ) ) ; Np=omega_p*60/(2*%pi); disp ( ”rpm” , N p , ” s pe ed f o r t he p r ot o t y p e i s ” )
Scilab code Exa 18.41 Calculation for the Pelton Wheel
152
1 / / s c i l a b Code Exa 1 8 .4 1 C a l c u l a t i o n
f o r t he P el to n
Wheel N S = 0 . 1 ; // s p e c i f i c sp ee d H 1 = 1 0 0 0 ; // n et hea d f o r t he model i n m Q 1 = 1 ; // d i s c h a r g e i n m3/ s o m e g a 1 = N S * ( H 1 ^ ( 3 / 4 ) ) / (sqrt ( Q 1 ) * 0 . 1 8 0 4 ) ; N1=omega1*60/(2*%pi); disp ( ”rpm” , N 1 , ” s pe e d o f t h e r o t a t i o n i s ” ) r h o = 1 0 0 0 ; // d e n s i t y i n kg /m3 g = 9 . 8 1 ; // g r a v i t a t i o n a l a c c e l e r a t i o n i n m/ s 2 P1=rho*g*Q1*H1;
2 3 4 5 6 7 8 9 10 11 12
14 15 16 17 18 19
N 2 = N 1 * sqrt ( H 2 / H 1 ) ; disp ( ”rpm” , N 2 , ” s pe ed f o r t he p r ot o t y p e i s ” ) Q2 = sqrt ( H 2 / H 1 ) * Q 1 ; disp ( ”m3/s” , Q 2 , ” t he d i s c h a r g e f o r t h e p ro to t y pe i s ” ) P2=((H2/H1)^(3/2))*P1; disp ( ”MW” , P 2 * 1 e - 6 , ” t he power f o r t he p r o t o t y p e i s ” )
/ / d e te r mi n i ng t he s pe ed , f l o w r a t e and power f o r t h e p r o t o t yp e 13 H 2 = 1 0 0 ; // head f o r p r ot o ty p e
Scilab code Exa 18.42 Calculation for Tidal Power Plant
1 / / s c i l a b Code Exa 1 8 .4 2 C a l c u l a t i o n
f o r T id al Power
Plant 2 3 T = 5 0 e 6 ; // c a pa c it y o f b a s i n i n c ub i c m et e rs o f s ea 4 5 6 7
water N = 6 0 ; / / S pe ed f o r t h e mo del i n RPM N S = 3 ; // s p e c i f i c sp ee d H = 9 . 8 ; // n et hea d f o r t he model i n m n _ o = 0 . 7 8 ; // Assuming e f f i c i e n c y 153
8 9 10 11 12 13 14 15 16 17
r h o = 1 0 0 0 ; // d e n s i t y i n kg /m3 g = 9 . 8 1 ; // g r a v i t a t i o n a l a c c e l e r a t i o n i n m/ s 2 n ( 1 ) = 5 ; // number o f t u r b i n e s n(2)=10; omega=%pi*2*N/60;
P=(NS^2)*(H^(5/2))*(549.016^2)/(omega^2); disp ( ”MW” , P * 1 e - 6 , ” ( a ) t he power f o r t he t u r b i n es Q = P / ( n _ o * r h o * g * H ) ; // d i s c h a r g e i n m3/ s disp ( ”m3/s” ,Q , ” ( b ) t h e d i s c h a r g e r a t e f o r t h e t u r b i n es i s ” ) disp ( ” ( c ) ” ) for i = 1 : 2 disp ( n ( i ) , ” when number o f t u r b i n e s a r e : ” ) t=T/(n(i)*Q*3600); disp ( ” h o u r s ” ,t , ” d u ra t io n o f o p e ra t i o n i s ” ) end
18 19 20 21 22 23
Scilab code Exa 18.43 Francis turbine 250 rpm
1 2 3 4 5 6 7 8 9 10 11 12 13
/ / s c i l a b Code Exa 1 8 . 43 F r a n ci s t u r b i n e 2 50 rpm
N S = 0 . 4 ; // s p e c i f i c sp ee d N = 2 5 0 ; / / S p e ed i n RPM H = 7 5 ; // n et head i n m b e t a 3 = 2 5 ; // e x i t a n g l e o f t he r u nn er b l a d e s n _ o = 0 . 8 1 ; // o v e r a l l e f f i c i e n c y g = 9 . 8 1 ; // g r a v i t a t i o n a l a c c e l e r a t i o n i n m/ s 2 r h o = 1 0 0 0 ; // d e n s i t y i n kg /m3
// part (a) u 2 = 0 . 6 * sqrt ( 2 * g * H ) ; c r 2 = 0 . 2 1 * sqrt ( 2 * g * H ) ; omega=%pi*2*N/60;
154
is ”)
14 Q = ( N S ^ 2 ) * ( H ^ ( 3 / 2 ) ) / ( ( 0 . 1 8 0 4 ^ 2 ) * ( o m e g a ^ 2 ) ) ; 15 disp ( ”m3/s” ,Q , ” ( a ) t he d i s c h a r g e r a t e f o r t h e t u r b in e is”) 16 / / p a r t ( b ) 17 d 2 = u 2 * 6 0 / ( % p i * N ) ; 18 disp ( ”m” , d 2 , ” ( b ) o u t er d i am et er o f t he r un ne r b l ad e r i ng i s ”) 19 c r 3 = c r 2 ; 20 c x 3 = c r 3 ; 21 // Eu le r work , w ET=u2 ∗ c t h e t a 2 22 c _ t h e t a 2 = ( ( g * H ) - ( 0 .5 * ( c x 3 ^ 2 ) ) ) / u 2 ; 23 u 3 = c x 3 / ( t a n d ( b e t a 3 ) ) ; 24 d 3 = u 3 * 6 0 / ( % p i * N ) ; 25 disp ( ”m” , d 3 , ” and i n n er d ia m e te r o f t he r un ne r b la d e r i ng i s ”) 26 / / p a r t ( c ) 27 a l p h a 2 = a t a n d ( c r 2 / c _ t h e t a 2 ) ; 28 disp ( ” d e g r e e ” ,alpha2 , ” ( c ) t he i n l e t g u id e v an e e x i t a n gl e i s ” ) 29 b e t a 2 = a t a n d ( c r 2 / ( c _ t he t a 2 - u 2 ) ) ; 30 disp ( ” d e g r e e ” , b e t a 2 , ” and i n l e t a n g l e o f t he r un ne r b l a d e s i s b et a2= ” ) 31 / / p a r t ( d ) 32 n _ h = ( u 2 * c _ t h e t a 2 ) / ( g * H ) ; 33 disp ( ”%” , n _ h * 1 e 2 , ” ( d ) t h e h y d r a u l i c e f f i c i e n c y i s ” ) 34 / / p a r t ( e ) 35 P = n _ o * r h o * g * Q * H ; 36 disp ( ”MW” , P * 1 e - 6 , ” ( e ) t h e o u t p u t p ow er i s ” ) 37 disp ( ” comment : t he c a l c u l a t i o n f o r c t h e ta 2 i s do ne
w ro ng ly i n t he book . h en ce t he v a l u e s o f a lp ha 2 , b e ta 2 , n h d i f f e r s f ro m t h e b oo k . ” )
Scilab code Exa 18.44 Pelton Wheel 360 rpm
155
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
/ / s c i l a b Code Exa 1 8 . 4 4 P e l to n Wheel 3 60 rpm
d = 2 ; / / mean d i a m et e r i n m N = 3 6 0 ; / / S p e ed i n RPM t h e t a = 1 5 0 ; // d e f l e c t i o n a n g l e o f w a te r j e t i n d eg r e e H = 1 4 0 ; // n et hea d f o r t he model i n m q = 4 5 0 0 0 ; / / d i s c h a r g e i n l i t r e s / min Q = q * 1 e - 3 / 6 0 ; / / i n m3/ s r h o = 1 0 0 0 ; // d e n s i t y i n kg /m3 g = 9 . 8 1 ; // g r a v i t a t i o n a l a c c e l e r a t i o n i n m/ s 2
// part (a) u=%pi*d*N/60; c2 = sqrt ( 2 * g * H ) ; sigma=u/c2; disp ( s i g m a , ” ( a ) b la de t o j e t s pe ed r a t i o
is ”)
// part (b)
w2=c2-u; w3=w2; beta2=0; beta3=180-theta; cy2=c2; cy3=u-(w3*cosd(beta3)); w_T=u*(cy2-cy3); m=rho*Q; P_T=m*w_T; disp ( ”kW” , P _ T * 1 e - 3 , ” ( b ) t h e p ower d e v el o p e d i s ” )
// par t ( c ) n=w_T/(0.5*(c2^2)); disp ( ”%” , n * 1 e 2 , ” ( c ) t he
eff ici enc y is ”)
// part (d)
n_max=0.5*(1+cosd(beta3)); disp ( ”%” , n _ m a x * 1 e 2 , ” ( d ) t h e Maximum e f f i c i e n c y P_max=m*g*H*n_max; disp ( ”kW” , P _ m a x * 1 e - 3 , ”and the Maximum power d e v el o p ed i s ” )
35 / / p a r t ( e ) 36 s i g m a _ o p t = 0 . 5 ; / / f o r Maximum e f f i c i e n c y 37 u _ o p t = s i g m a _ o p t * c 2 ;
156
is ”)
38 N _ o p t = u _ o p t * 6 0 / ( d * % p i ) ; 39 disp ( ”rpm” , N _ o p t , ” ( e ) s p pee ed e d o f t he he r o t a t i o n
c o r r e s p o n d i n g t o Ma M aximum e f f i c i e n c y 40 / / p a r t ( f )
is ”)
41 o m e g a = % p i * 2 * N / 6 0 ; 42 N S = o m e g a * sqrt ( P _ T ) * ( H ^ ( - 5 / 4 ) ) / 5 4 9 . 0 1 6 ; 43 disp ( N S , ” ( f ) t h e s p e c i f i c s p e e d o f t u r b i n e
is ” )
Scilab code Exa 18.45 Kaplan turbine 120 rpm
1 2 3 4 5 6 7 8
/ / s c i l a b C o d e Ex E x a 1 8 . 45 4 5 K a p l a n t u r b i n e 1 20 2 0 rpm
N = 1 2 0 ; / / S p e ed e d i n RPM / / n et et h ea d i n m H = 2 5 ; // Q = 1 2 0 ; // / / d i s c h a r g e i n m3 m3 / s / / r un u n ne n e r d i am a m e te te r i n m d t = 5 ; // d h _ t = 0 . 4 ; / / h u b− t i p r a t i o o f t h e r u n n e r / / i n l e t a n g l e o f t h e r un u n ne ne r b l a d e s i n b e t a 2 = 1 5 0 ; //
degree 9 n_o=0.8; / /// o v e r a l l e f f i c i e n c y 10 r h o = 1 0 0 0 ; // / / d e n s i t y i n k g /m /m3 11 g = 9 . 8 1 ; // / / g r a v i t a t i o n a l a c c e l e r a t i o n i n m/ s 2 12 / / p a r t ( a ) 13 14 15 16 17 18 19 20 21
P=n_o*rho*g*Q*H; t p u t p ow ow e r i s ” ) disp ( ”MW” , P * 1 e - 6 , ” ( a ) t h e o u tp
// part (b) omega=%pi*2*N/60; N S = o m e g a * sqrt ( P ) * ( H ^ ( - 5 / 4 ) ) / 5 4 9 . 0 1 6 ; ee d o f t u r b i n e disp ( N S , ” ( b ) t h e s p e c i f i c s p ee
is ”)
// par t ( c ) dh=dh_t*dt; / / me m e a n d i am a m e te t e r o f t he he i m p e l l e r d = 0 . 5 * ( d t + d h ) ; //
b la l a de de i n m 157
22 23 24 25 26
u=%pi*d*N/60; cx=Q*4/(%pi*(dt^2-dh^2)); cy2=u-(cx*tand(90-(180-beta2))); alpha2=atand(cx/cy2); he i n l e t disp ( ” d e g r e e ” ,alpha2 , ” ( c ) t he a n gl gl e i s ”)
g u id i d e v an an e e x i t
27 / / p a r t ( d ) 28 b e t a 3 = a t a n d ( c x / u ) ; 29 disp ( ” d e g r e e ” , b e t a 3 , ” ( d ) t he h e e x i t a n gl g l e o f t he h e r un u n ne ne r b l a d e s i s b et e t a3 a 3= ” ) 30 / / p a r t ( e ) 31 n _ h = ( u * c y 2 ) / ( g * H ) ; 32 disp ( ”%” ”%” , n _ h * 1 e 2 , ” ( e ) t he he h y d r a u l i c e f f i c i e n c y i s ” )
Scilab code Exa 18.46 Fourneyron Turbine 360 rpm
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
/ / s c i l a b C o d e E xa xa 1 8 . 4 6 F ou o u rn r n ey e y ro r o n T ur u r bi b i ne n e 3 60 6 0 rp m
/ / o u t er e r d ia i a me m e te t e r o f t he he i m p e l l e r i n m d 2 = 3 ; // d 1 = 1 . 5 ; // / / i n ne n e r d ia i a me m e te te r o f t h e i m p e l l e r i n m / / n et et h ea d i n m H = 5 0 ; // r h o = 1 0 0 0 ; // / / d e n s i t y i n k g /m /m3 / / g r a v i t a t i o n a l a c c e l e r a t i o n i n m/ s 2 g = 9 . 8 1 ; // N = 3 6 0 ; // / / r o t o r S pe p e ed e d i n RP RPM // o v e r a l l e f f i c i e n c y n _ o = 0 . 7 8 5 ; // P = 4 ; / / P ow ow er er O u tp tp u t i n MW u1=%pi*d1*N/60; u2=%pi*d2*N/60; // part (a)
Q=P*1e6/(n_o*rho*g*H); disp ( ”m3/s” , Q , ” ( a ) t he he d i s c h a r g e i s ” ) / / v e l o c i t y o f w a t e r a t e x i t i n m/ s c 2 = 9 ; //
// part (b) 158
18 19 20 21 22 23
w_ET=(g *H) -(0.5*(c2^2) ); n_h=w_ET/(g*H); ”%” , n _ h * 1 e 2 , ” ( b ) t h e h y d r a u l i c e f f i c i e n c y disp ( ”%”
is ”)
// par t ( c ) cr2=c2; b=Q/(cr2*%pi*d2); // a x i a l l en gt h o f t he i m pe l le r i n
m 24 25 26 27 28 29 30 31
disp ( ”cm” , b * 1 e 2 , ” ( c ) t h e r u nn n n e r p a s s a g e w id i d th th i s ” )
// part (d) beta2=atand(cr2/u2); l a de d e a i r a ng n g le le a t th e disp ( ” d e g r e e ” , b e t a 2 , ” ( d ) t h e b la i m p e l l e r e x i t b eett a2 a 2 =” ) c_theta1=w_ET/u1; cr1=Q/(b*%pi*d1); beta1=atand(cr1/(u1-c_theta1)); an d t he h e b la l a de de a i r a ng le a t th e disp ( ” d e g r e e ” , b e t a 1 , ” an i m p e l l e r e n tr t r y b eett a1 a 1 =” )
32 / / p a r t ( e ) 33 a l p h a 1 = a t a n d ( c r 1 / c _ t h e t a 1 ) ; 34 disp ( ” d e g r e e ” ,alpha1 , ” ( e ) t he h e g u id i d e v a ne ne e x i t is”)
angle
Scilab code Exa 18.47 Crossflow Radial Hydro turbine
1 / / s c i l a b C o d e Ex E x a 1 8 . 47 4 7 C r o ss s s f l ow o w R a di di a l Hydro
turbine 2 3 4 5 6 7 8
N = 5 0 ; / / S p e ed e d i n RPM / / n et et h ea d i n m H = 2 5 ; // Q = 1 5 0 ; // / / d i s c h a r g e i n m3 m3 / s P = 2 0 ; / / P ow o w er er O u tp t p u t i n MW r un u n ne n e r d ia i a me m e te te r i n m d1=3.5; // d r = 1 . 3 ; // / / d ia i a me m e te t e r r a t i o o f t h e r u nn n n er er
159
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
34 35 36 37
r h o = 1 0 0 0 ; // d e n s i t y i n kg /m3 g = 9 . 8 1 ; // g r a v i t a t i o n a l a c c e l e r a t i o n i n m/ s 2 u1=%pi*d1*N/60; u2=u1/dr; c_theta1=2*u1; c_theta2=u2; w_st1=(u1*c_theta1)-(u2*c_theta2); u3=u2; c_theta3=u2; c_theta4=0; w_st2=(u3*c_theta3)-(u1*c_theta4); w_st=w_st1+w_st2;
// part (a)
n_h=w_st/(g*H); disp ( ”%” , n _ h * 1 e 2 , ” ( a ) t h e h y d r a u l i c e f f i c i e n c y i s ” ) Ph=rho*Q*w_st; disp ( ”MW” , P h * 1 e - 6 , ” and t he h y d r a u l i c power i s ” ) n_o=P*1e6/(rho*Q*g*H); disp ( ”%” , n _ o * 1 e 2 , ” and t h e o v e r a l l e f f i c i e n c y i s ” )
// part (b) omega=%pi*2*N/60; N S = o m e g a * sqrt ( P * 1 e 6 ) * ( H ^ ( - 5 / 4 ) ) / 5 4 9 . 0 1 6 ; disp ( N S , ” ( b ) t h e s p e c i f i c s p ee d o f t u r b i n e
is ”)
// par t ( c ) disp ( ” ( c ) A do pt in g t h e f l o w m ode l o f t h e c r o s s f l o w w in d t u r b i n e ” ) P_h=rho*Q*((2*(u1^2))+(u2^2)); disp ( ”MW” , P _ h * 1 e - 6 , ” t h e h y d r a u l i c power i s ” ) nh=((2*(u1^2))+(u2^2))/(g*H); disp ( ”%” , n h * 1 e 2 , ” and h y dr a u l i c e f f i c i e n c y i s ” )
Scilab code Exa 18.48 Calculation on a Draft Tube
160
1 2 3 4 5 6 7 8 9 10 11 12
/ / s c i l a b Code Exa 1 8 . 48 C a l c u l a t i o n on a D r af t Tube
p a = 1 . 0 1 3 ; // a tm o s p h er ic p r e s s u r e i n b ar p 3 = 0 . 4 * p a ; // t u r b i n e e x i t p r e s s u r e i n b a r r h o = 1 e 3 ; // d e n s i t y i n kg /m3 g = 9 . 8 1 ; / / G r a v i t a t i o n a l a c c e l e r a t i o n i n m/ s ˆ 2 n _ D = 0 . 8 2 ; // E f f i c i e n c y o f t he D ra ft Tube d e l H i = 3 . 1 0 5 8 8 6 9 ; // f ro m Ex 1 8 . 5
// part (b)
Hd=delHi; H s = ( ( p a - p 3 ) * 1 e 5 / ( r h o * g ) ) - ( n _ D * H d ) ; // Hs=Z3−Z4 disp ( ”m” , H s , ” ( b ) t he s u c t i o n head ( h e i g h t o f t he t u r b i n e e x i t a bo ve t he t a i l r a c e ) i s ” ) 13 disp ( ” comment : t he c a l c u l a t i o n f o r Hs i s done
w ro ng ly i n t he book . h en ce t he v a lu e o f Hs d i f f e r s from the book . ” )
Scilab code Exa 18.49 Centrifugal pump 890 kW
1 2 3 4 5 6 7 8 9 10 11 12 13 14
/ / s c i l a b Code E xa 1 8 . 4 9 C e n t r i f u g a l pump 8 9 0 kW
H = 5 0 ; // hea d d e ve l op e d i n m P = 8 9 0 ; / / Power r e q u i r e d i n kW N S = 0 . 7 5 ; // s p e c i f i c sp ee d rho=1e3; g = 9 . 8 1 ; / / G r a v i t a t i o n a l a c c e l e r a t i o n i n m/ s ˆ 2 n _ h = 0 . 9 1 ; // h y d r a u l i c e f f i c i e n c y f = 0 . 9 2 5 ; // b lo c k ag e f a c t o r f o r t he f lo w Q = 1 . 5 ; // d i s c h a r g e i n m3/ s o f w at er u 2 = 0 . 8 * sqrt ( 2 * g * H ) ; c r 2 = 0 . 3 * sqrt ( 2 * g * H ) ; d r = 0 . 5 ; / / d i a m et e r r a t i o ( d 1/ d2 )
// part (a) 161
15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
o m e g a = N S * ( H ^ ( 3 / 4 ) ) / ( 0 . 1 8 0 4 *sqrt ( Q ) ) ; N=omega*60/(2*%pi); disp ( ”rpm” ,N , ” ( a ) t he s pe e d o f r o t a t i o n
i s ”)
/ / p a rt ( b ) i m p e l l e r d i am et e r d2=u2*60/(%pi*N); disp ( ”m” , d 2 , ” ( b ) t he i m p e l l e r
d i am et er i s ” )
// p a rt ( c ) c_theta2=g*H/(u2*n_h); beta2=atand(cr2/(u2-c_theta2)); disp ( ” d e g r e e ” , b e t a 2 , ” ( c ) t he b l a d e a i r a n gl e a t t he i m p e l l e r e x i t b et a2=” ) u1=u2*dr; cr1=cr2; beta1=atand(cr1/u1); disp ( ” d e g r e e ” , b e t a 1 , ” and t he b la de a i r a n g l e a t t h e i m p e l l e r e n tr y b et a1=” )
// pa rt (d ) b2=Q/(cr2*%pi*d2*f); disp ( ”m” , b 2 , ” ( d ) t he i m p e l l e r wi dt h a t e x i t
is ”)
//part ( e ) ov era ll Eff ici enc y n_o=rho*Q*H*g/(P*1e3); disp ( ”%” , n _ o * 1 e 2 , ” ( e ) o v e r a l l
effic ienc y is ”)
Scilab code Exa 18.50 Centrifugal pump 1500 rpm
1 2 3 4 5 6 7 8
/ / s c i l a b Code Exa 1 8 . 5 0 C e n t r i f u g a l pump 1 5 00 rpm
N = 1 5 0 0 ; / / r o t o r S pe ed i n RPM H = 5 . 2 ; / / head i n m b = 2 / 1 0 0 ; / / wi dt h i n m d 1 = 2 . 5 / 1 0 0 ; // e nt ry d ia me te r o f t h e b la de r i ng i n m d 2 = 0 . 1 ; // e x i t d i am et e r o f t h e b la de r i n g i n m rho=1e3;
162
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
g = 9 . 8 1 ; / / G r a v i t a t i o n a l a c c e l e r a t i o n i n m/ s ˆ 2 n _ o = 0 . 7 5 ; // o v e r a l l E f f i c i e n c y o f t h e d r i v e u2=%pi*d2*N/60; u1=u2*d1/d2;
// p ar t ( a ) i m p e l l e r b la d e a n gl e a t t he e n t ry
c_r2=0.4*u2; c_r1=c_r2*d2/d1; beta1=atand(c_r1/u1); disp ( ” d e g r e e ” , b e t a 1 , ” ( a ) t h e i m p e l l e r b la de a n g l e a t t h e e n t r y b e t a 1=” )
//part (b) dischar ge Q=c_r1*%pi*d1*b; disp ( ” l i t r e s / s e c ” , Q * 1 e 3 , ” ( b ) t he d i s c h a r g e
is ”)
/ / p a r t ( c ) P ow er r e q u i r e d P=(rho*Q*g*H)/(n_o); disp ( ”kW” , P * 1 e - 3 , ” ( a ) P ower r e q u i r e d t o d r i v e t he pump i s ” )
// part (d) omega=%pi*2*N/60; N S = ( H ^ ( - 3 / 4 ) ) * 0 . 1 8 0 4 * ( o m e g a ) *sqrt ( Q ) ; disp ( N S , ” ( d ) t h e s p e c i f i c s p e e d i s ” )
Scilab code Exa 18.51 Axial pump 360 rpm
1 2 3 4 5
/ / s c i l a b Code E xa 1 8 . 5 1 A x i a l pump 3 60 rpm N = 3 6 0 ; // r o t o r S pe ed i n RPM d h = 0 . 3 0 ; // hub d ia me te r o f t h e i m p e l l e r i n m b e t a 2 = 4 8 ; // e x i t a n g l e o f t he r un ne r b l a d es ( fro m
th e t a n g en t i a l d i r e c t i o n ) 6 c x = 5 ; // a x i a l v e l o c i t y o f w a t e r t h ro u gh t h e i m p e l l e r i n m/ s 7 n _ h = 0 . 8 7 ; // h y d r a u l i c e f f i c i e n c y 163
8 9 10 11 12 13 14 15 16
n _ o = 0 . 8 3 ; // o v e r a l l E f f i c i e n c y Q = 2 . 5 ; // d i s c h a r g e i n m3/ s rho=1e3; g = 9 . 8 1 ; / / G r a v i t a t i o n a l a c c e l e r a t i o n i n m/ s ˆ 2
// part ( a ) dt = sqrt ( ( 4 * Q / ( c x * % p i ) ) + ( d h ^ 2 ) ) ; disp ( ”m” , d t , ” ( a ) t he i m p e l l e r t i p d ia m e te r i s ” )
// p ar t ( b ) i m p e l l e r b la d e a n gl e a t t he e n t ry d = 0 . 5 * ( d t + d h ) ; // mean d i am e te r o f t he i m p e l l e r b la de i n m
17 u = % p i * d * N / 6 0 ; 18 b e t a 1 = a t a n d ( c x / u ) ; 19 disp ( ” d e g r e e ” , b e t a 1 , ” ( b ) t he i m p e l l e r b l a de a n gl e a t t h e e n t r y b e t a 1=” ) 20 / / p a r t ( c ) 21 c y 2 = u - ( c x / t a n d ( b e t a 2 ) ) ; 22 H = n _ h * u * c y 2 / g ; 23 disp ( ”m” ,H , ” ( c ) t h e h ea d d e v e l o p e d i s ” ) 24 / / p a r t ( d ) P owe r r e q u i r e d 25 P = ( r h o * Q * g * H ) / ( n _ o ) ; 26 disp ( ”kW” , P * 1 e - 3 , ” ( d ) Power r e q u i r e d t o d r i v e t he pump i s ” ) 27 / / p a r t ( e ) 28 o m e g a = % p i * 2 * N / 6 0 ; 29 N S = ( H ^ ( - 3 / 4 ) ) * 0 . 1 8 0 4 * ( o m e g a ) *sqrt ( Q ) ; 30 disp ( N S , ” ( e ) t h e s p e c i f i c s p e e d i s ” )
Scilab code Exa 18.52 NPSH for Centrifugal pump
1 / / s c i l a b Code E xa 1 8 . 5 2 NPSH f o r C e n t r i f u g a l pump 2 3 H = 3 0 ; // hea d d e ve l op e d i n m 4 d s = 0 . 1 5 ; // s u c t i o n p ip e d ia me te r i n m
164
5 f = 0 . 0 0 5 ; // C o e f f i c i e n t
o f f r i c t i o n f o r t he s u c t i o n
pipe 6 p a = 1 . 0 1 3 ; // a tm o s p h er ic p r e s s u r e i n b ar 7 A s = % p i / 4 * ( d s ^ 2 ) ; / / C ro s s− s e c t i o n a l Area o f t h e 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38
s u c t i o n p i p e i n m2 r h o = 1 e 3 ; // d e n s i t y o f w at er i n kg /m3 g = 9 . 8 1 ; / / G r a v i t a t i o n a l a c c e l e r a t i o n i n m/ s ˆ 2 t = 3 0 ; // t em pe ra tu re o f w at er i n d e g r ee C p v = 0 . 0 4 2 4 ; // v a p o u r p r e s s u r e o f w a te r a t t v al u e
Hv=pv*1e5/(rho*g); Z ( 1 ) = 0 ; // a l t i t u d e i n m Z(2)=2500; p ( 1 ) = p a ; // a t a l t i t u d e Z=0 p ( 2 ) = 0 . 7 4 7 ; / / a t Z =2 50 0m Q ( 1 ) = 0 . 0 6 5 ; // d i s c h a r g e i n m3/ s o f w at er Q(2)=0.1; Q(3)=0.15; H s ( 1 ) = 3 ; // v e r t i c a l l en g t h o f t h e s u c t i o n p i pe i n m Hs(2)=5; for i = 1 : 3 disp ( ”m3/s” , Q ( i ) , ” when Q=” ) cs=Q(i)/As; for k = 1 : 2 disp ( ”m” , H s ( k ) , ”and Hs=” ) delHf=4*f*(Hs(k)/ds)*(cs^2/(2*g)); for j = 1 : 2 disp ( ”m” , Z ( j ) , ”and Z=” ) Ha=p(j)*1e5/(rho*g); H1=Ha-(Hs(k)+(cs^2/(2*g))+delHf); NPSH=H1-Hv; disp ( N P S H , ”NPSH=” ) sigma=NPSH/H; disp ( s i g m a , ” C a v i ta t i o n C o e f f i c i e n t s ig ma=” ) end end end
165
Scilab code Exa 18.53 NPSH and Thoma Cavitation Coefficient
1 / / s c i l a b Code Exa 1 8 . 5 3 NPSH a nd Thoma C a v i t a t i o n
Coefficient 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
H = 6 0 ; // hea d d e ve l op e d i n m c 1 = 8 ; // e x i t v e l o c i t y i n m/ s p a = 1 . 0 1 3 3 ; // a mb i e n t p r e s s u r e i n b a r rho=1e3; n _ d = 0 . 8 ; // E f f i c i e n c y o f t he D ra ft Tube g = 9 . 8 1 ; / / G r a v i t a t i o n a l a c c e l e r a t i o n i n m/ s ˆ 2 t a = 3 0 ; // a mb ien t t em p er a tu re o f w at er i n d e gr e e C p v = 0 . 0 4 2 4 ; // v a p o u r p r e s s u r e o f w a te r a t t v al u e Hv=pv*1e5/(rho*g);
//Q=c1 ∗A1=c2 ∗A2 A r ( 1 ) = 1 . 2 ; / / d r a f t t u be a r e a r a t i o ( A2/A1=c 1 / c 2 ) Ar(2)=1.4; Ar(3)=1.6; H s = 2 . 5 ; // v e r t i c a l
l e n g t h o f t he d r a f t t u b e b e tw e en t he t u r b i n e e x i t and t he t a i l r a ce i n m
17 H a = p a * 1 e 5 / ( r h o * g ) ; 18 for i = 1 : 3 19 H s d = ( c 1 ^ 2 ) * ( 1 - ( 1 / ( A r ( i ) ^ 2 ) ) ) / ( 2 * g ) ; // i d e a l 20
21 22
head g ai n e d by t he d r a f t t u be H d = n _ d * H s d ; // A c tu a l he ad g a i n ed by t h e d r a f t tube disp ( A r ( i ) , ” f o r A re a R a t i o Ar=” ) disp ( ”m” , H d , ” ( a ) A ct ua l head g a in e d by t he d r a f t t ub e i s ” )
H1=Ha-(Hs+Hd); 23 24 NPSH=H1-Hv; 25 disp ( N P S H , ” ( b )NPSH=” )
166
26 s i g m a = N P S H / H ; 27 disp ( s i g m a , ” a nd C a v i t a t i o n p a r a m e t e r ( Thoma Number ) sigma=” ) 28 end
Scilab code Exa 18.54 Maximum Height of Hydro Turbines
1 / / s c i l a b Code Exa 1 8 . 5 4 Maximum H e i gh t o f Hydro
Turbines 2 3 4 5 6 7 8 9 10 11
H = 5 2 ; // hea d d e ve l op e d i n m c 1 = 6 . 5 ; // e x i t v e l o c i t y i n m/ s p a = 1 . 0 1 3 3 ; // a mb i e n t p r e s s u r e i n b a r rho=1e3; n _ d = 0 . 7 5 ; // E f f i c i e n c y o f t he D ra ft Tube g = 9 . 8 1 ; / / G r a v i t a t i o n a l a c c e l e r a t i o n i n m/ s ˆ 2 t a = 2 0 ; // a mb ien t t em p er a tu re o f w at er i n d e gr e e C sigma_cr=0.1; p v = 0 . 0 2 3 ; // v a p ou r p r e s s u r e o f w at er a t t v a l u e (
f ro m t a b l e s ) 12 13 14 15 16 17 18 19 20 21 22 23
Hv=pv*1e5/(rho*g);
//Q=c1 ∗A1=c2 ∗A2 A r = 1 . 5 ; / / d r a f t t u be a r e a r a t i o ( A2/A1=c 1 / c 2 ) Z ( 1 ) = 0 ; // a l t i t u d e i n m
Z(2)=2500; Z(3)=3000; Z(4)=4000; p ( 1 ) = p a ; // a t a l t i t u d e Z=0 p ( 2 ) = 0 . 7 4 7 ; / / a t Z =2 50 0m p ( 3 ) = 0 . 7 0 1 ; // a t a l t i t u d e Z=3000m p ( 4 ) = 0 . 6 5 7 ; / / a t Z =4 00 0m H s d = ( c 1 ^ 2 ) * ( 1 - ( 1 / ( A r ^ 2 ) ) ) / ( 2 * g ) ; // i d e a l head
g a i ne d by t he d r a f t t u be 167
24
H d = n _ d * H s d ; // A c tu a l he ad g a i n ed by t h e d r a f t
tube 25 H a = p a * 1 e 5 / ( r h o * g ) ; 26 for i = 1 : 4 27 disp ( ”m” , Z ( i ) , ” For Z=” ) Ha=p(i)*1e5/(rho*g); 28 29 H1=Ha-(Hsd+Hd); H s = H a - ( ( s i g m a _ c r * H ) + H d + H v ) ; // v e r t i c a l 30
31
l en gt h o f t h e d r a f t t u b e b et w ee n t he t u rb i ne e x i t and t he t a i l r a c e i n m disp ( ”m” , H s , ” t h e maximum h e i g h t o f t h e t u r b i n e e x i t a bo ve t he t a i l r a c e i s ” )
NPSH=sigma_cr*H; 32 33 disp ( N P S H , ”NPSH=” ) 34 end
Scilab code Exa 18.55 Propeller Thrust and Power
1 2 3 4 5 6
/ / s c i l a b Code Exa 1 8 . 55 P r o p e l l e r T hr us t and Power
c _ u = 5 ; // u ps tr ea m v e l o c i t y i n m/ s c _ s = 1 0 ; // d own st re am v e l o c i t y i n m/ s r h o = 1 e 3 ; // d e n s i t y o f w at er i n kg /m3 c = 0 . 5 * ( c _ u + c _ s ) ; // v e l o c i t y o f w a te r t hr ou gh t he
p r o p e l l e r i n m/ s 7 d ( 1 ) = 0 . 5 ; // p r o p e l l e r d ia me te r i n m d(2)=1; d(3)=1.5; delh_0=0.5*((c_s^2)-(c_u^2)); delp_0=rho*delh_0; disp ( ” b a r ” , d e l p _ 0 * 1 e - 5 , ” ( b ) s t a g na t i o n p r e s s u r e a cr os s the p r o p el l e r i s ”) 13 for i = 1 : 3 8 9 10 11 12
168
ris e
