1. NonNon-Is Isen entr trop opic ic flow flow : Rea Reall flo flow w 2. Shoc Shockw kwav avee & Exp Expan ansi sion on wav waves es Normal shockwave Oblique shockwave Prandtl Meyer expansion 3. Duct Duct Flow Flow with with Frict Friction ion withou withoutt Heat Heat Transf Transfer er (Fanno flow) 4. Duct Duct Flow Flow with with Heat Heat Transf Transfer er and Neglig Negligibl iblee Friction Force (Reyleigh Flow)
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1. NonNon-Is Isen entr trop opic ic flow flow : Rea Reall flo flow w 2. Shoc Shockw kwav avee & Exp Expan ansi sion on wav waves es Normal shockwave Oblique shockwave Prandtl Meyer expansion 3. Duct Duct Flow Flow with with Frict Friction ion withou withoutt Heat Heat Transf Transfer er (Fanno flow) 4. Duct Duct Flow Flow with with Heat Heat Transf Transfer er and Neglig Negligibl iblee Friction Force (Reyleigh Flow)
Non-Isentropic flow : Real flow What is Non-Isentropic Flow ? 1. Irreve Irreversi rsible ble ( there there is is viscou viscouss effect effect)) only only 2. Non Adiab Adiabatic atic ( There There is heat transfer transfer)) only 3. Comb Combin inat atio ion n of of Bot Both h
Non-Isentropic flow : Real flow What is Non-Isentropic Flow ? 1. Irreversible ( there is viscous effect) only ≠ and = 2. Non Adiabatic ( There is heat transfer) only ≠ and = 3. Combination of Both ≠ and ≠
= ln
ln
Isentropic flow Flow through Convergent Divergent Duct Flow conditions
(1)
= 1 ,
= 1 ,
∗
= 1
Is there an flow through the duct? How is about the following flow through the duct?
(2) (3) (4)
= 1 ,
= 0.95 , = 0.95 ,
= 0.9725,
= 0.85,
∗ ∗
= 0.1278,
= 0.7 5 = 0.528
∗
= 0.528
Isentropic flow Flow through Convergent Divergent Duct Mach number and Mass flow rate
6
Non-Isentropic flow Flow through Convergent Divergent Duct
Normal shock wave
pc
If the pressure at exit , pe is less than p3 and greater than pd so the normal shock wave will appear inside the divergent duct The shock wave occurs in supersonic speed The Mach number change from supersonic to subsonic The flow properties change abruptly
Non-Isentropic flow Normal Shock
ℎ = ℎ = ℎ +
Continuity equation
= =
Momentum equation
Normal shockwave : shock waves that occur in a plane / cross section normal to the direction of flow A supersonic flow across a normal shock wave becomes subsonic Total enthalpy remains constant across the shock (conservation energy principle)
Entropy
2
= ℎ +
2
=
> 0
= ( )
8
Non-Isentropic flow Prandtl Relation
Flow relation between before shock wave and after shock wave
∗
= ∗
∗
(∗ ) =
1 ∗
where M
*
M
=
1 2 ( 1) M 2
0.5
2 + ( 1) 2 ( 1)
Non-Isentropic flow Prandtl Relation
Flow relation between before shock wave and after shock wave =
∗
∗
2 + ( 1) 2 ( 1)
What is happen if M1 ∞
Non-Isentropic flow Prandtl Relation
Flow relation between before shock wave and after shock wave 2
1
Non-Isentropic flow Static Properties Relation
Properties relation between before shock wave and after shock wave
Density
=
=
( + 1) 2 + ( 1)
Pressure
What is happen if M1 ∞
=
2 ( 1) ( + 1)
Temperature
=
2 1
[2 + 1 ]
( + 1)
Non-Isentropic flow
Non-Isentropic flow Entropy
=
= ln
2 ( 1)
−/(−)
2 + ( 1)
( + 1)
=
1 ( 1)
/(−)
( + 1)
2 ( + 1)
1 +1
+
( 1)
2 + ( 1) ( + 1)
Non-Isentropic flow Entropy
1
Non-Isentropic flow Air Speed Measurement in Supersonic flight
16
Non-Isentropic flow
1. A blunt nose missile is flying at Mach 2 at standard sea level. Calculate the temperature and pressure at the nose of the missile
Non-Isentropic flow Air Speed Measurement in Supersonic flight
Pressure ratio
p02 1 M 2 p1 4 M 1 2 1 2
2 1
1
2 M ( 1) 2 1
1 18
Non-Isentropic flow
2. Air with initial stagnation conditions of 700 kPa and 530 K passes through a frictionless CD nozzle Th troat area is 5 cm2 and the exit area is 12.5 cm2. The back pressure is 350 kPa, and a normal shock wave occurs within the diverging section. determine (a) The Mach number at the exit (b) The change in stagnation pressure (c) Mach number before and after the shock (d) the nozzle area at the point of shock (e) The back pressure if the flow were isentropic throughout
Non-Isentropic flow QUIZ 3 Air with initial stagnation conditions of 700 kPa and 330 K passes through a CD nozzle at the rate of 1 kg/s. At the exit are of the nozzle the stagnation pressure is 550 kPa and the stream pressure is 550 kPa. The nozzle is insulated and there is no irreversibility except for the occurrence of a shock (a) What is the nozzle throat area ? (b) What is Mach number before and after the shock ? (c) What is the nozzle area at the point of shock and at the exit (d) What is the stream density at the exit (e) The back pressure if the flow were isentropic throughout
Critical Total Properties relations Total Temperature
Total Pressure
1 p0* 1 M 2 p0
2 ( 1) M 1
2
1
T 0 T 0*
1 M 2
1 M
2 2
2 1 M 2
Non-Isentropic flow Graph of Total Temperature at Various Mach number T 0 T 0*
1 M 2
1 M
2 2
2 1 M 2
3.0
Supersonic
2.0 h c a M 1.0
Subsonic
0.0 0.0
0.5
1.0
1.5
T0/T0*
Adding heat will increase flow velocity or Mach number in Subsonic flow and decrease flow velocity of Mach number in Supersonic flow Extracting heat (cooling of the flow) will decrease flow velocity or Mach number in Subsonic flow and increase flow velocity of Mach number in Supersonic flow
Non-Isentropic flow Graph of Total Pressure at Various Mach number
2 ( 1) M 1
2
1 * p0 1 M 2 p0
1
3
Supersonic
2
h c a M 1
Subsonic
0 0
1
2
3
p0/p0*
4
5
6
Non-Isentropic flow Graph of Static Pressure at Various Mach number
p p*
1 1 M 2
3.0
2.0 h c a M 1.0
Supersonic
Subsonic 0.0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
p/p*
For subsonic flow (M<1), adding heat will decrease pressure For supersonic flow (M>1), adding heat will increases pressure
Non-Isentropic flow Graph of Density at Various Mach number r *
r
1 2 M
1 M 2 1
3.0
Supersonic
2.0 h c a M 1.0
Subsonic
0.0 0.0
2.0
4.0
6.0
/ *
8.0
10.0
12.0
Non-Isentropic flow Graph of Static Temperature at Various Mach number T *
