5. STEAM NOZZLES 5.1. INTRODUCTION In stea steam m turb turbin ines es,, the the overa overall ll tran transf sfor orma mati tion on of heat heat ener energy gy of steam steam into into mechani mechanical cal work work takes takes place place in two stages. stages. The available available energy of steam steam is first first converted into kinetic energy and then this kinetic energy is transformed into mechanical work. The first step is accomplished with devices called steam nozzles. A steam nozzle is a duct or passage of smoothly varying cross sectional area which converts heat energy of steam into kinetic energy. The shape of nozzle is designed such that it will perform this conversion of energy with minimum loss. When steam flows through a nozzle, expansion of steam takes place. uring this expansion, the pressure of steam decreases and also the heat content !"nthalpy#. With the expendi expenditur turee of enthal enthalpy py,, the veloci velocity ty and specif specific ic volume volume increa increase. se. Also, Also, with with the expansion of steam, there will be condensation condensa tion of steam with varying dryness fraction. The mass of steam passing through any section of nozzle remains constant. $o, the variation of pressure and the cross section of nozzle depend upon the velocity, specific volume and dryness fraction of steam. The velocity increases continuously from entrance to exit of the nozzle. The cross section of the nozzles may be circular, rectangular, elliptical or s%uare. The smallest section in the nozzle is known as throat. The nozzles are used in steam and gas turbines, &et engines, for propulsion of rocket rocket motors motors,, flow flow measur measureme ements nts,, in in&ect in&ectors ors for pum pumping ping water water,, in e&ecto e&ectors rs for removing air from condensers etc. The ma&or function of nozzles is to produce a &et of steam or gas with high velocity to drive steam or gas turbines. $o, the nozzles are located &ust before the steam or gas turbines. When the nozzles velocity gas is produced and there will be no %uestion of condensation and hence dryness fraction
When the nozzles are used with steam turbines, they perform the following functions. '. They conver convertt part of heat energy energy of steam !obtain !obtained ed from boiler# boiler# into into kinetic kinetic energy. (. In case of impulse impulse turbine turbiness !details !details of steam steam turbines turbines are are given in the chapter chapter ) steam steam turbines#, the nozzles direct the &et of high velocity steam against the blades of rotor which then convert the kinetic energy e nergy of steam into mechanical !shaft# work. In case of reaction turbines, the nozzles nozz les discharge high velocity steam on to the rotor blades. The reactive force of steam against the nozzle produces motion of rotor and work is obtained. When a fluid is decelerated in a duct or passage !velocity decreases# causing a rise in pressure during the travel along the stream, then the duct or passage is known as ) iffuser. iffusers iffusers are extensively used in centrifugal, axial flow compressors, ram&ets and combustion chambers etc., We study about steam nozzles only ) *ozzles in which the working fluid is steam. 5.2. TYPES OF STEAM NOZZLES
There are three important types of steam nozzles+ '. onve onverg rgen entt nozzi nozzie. e. (. ive iverg rgen entt nozzl nozzle. e. -. onverg onvergent ent ) dive diverg rgent ent nozzle. nozzle.
Types pes of $team *ozzles Fig.5.1: Ty If the cross section of the nozzle decreases continuously from entrance to exit then it is called /Convergent nozzle0. If the cross section of a nozzle increases continuously from entrance to exit then it is called / Divergent nozzle nozzle0. If the cross section of a nozzle decreases first upto certain length and then increases upto exit then it is called /Convergent - Divergent nozzle0. This is used mostly in various types of steam turbines. The three types of the nozzle are shown in fig.1.' 5.3. FLOW OF STEAM THROUGH NOZZLES In most of the cases, the steam enters the nozzle with low velocity compared to exit velocity, and it is generally neglected. As already mentioned, the function of a nozzle is to convert internal energy of steam into kinetic energy and this is done by expanding the steam from a high pressure23& to a low pressurep(. The flow flow of steam steam through through nozzles nozzles may be regard regarded ed as adiabat adiabatic ic expans expansion ion because in nozzles, the velocity of steam is so high that there will be no time available for heat exchange with surroundings and so heat is neither supplied nor re&ected. 4owever, work is performed by increasing the kinetic energy of steam. Also, in a nozzle, the change of potential energy is negligible and no work is done on or by the fluid. The expansion of steam in a nozzle is not a free expansion and the steam is not throttled because it has a very high velocity at the end of expansion and the pressure as well as enthalpy enthalpy decrease as expansion expansion takes place. The pressure at which steam leaves the nozzle is known as 5ack pressure. In actual practice, always some friction is produced between steam and the walls of the nozzle this friction causes resistance for the flow of steam, which is converted into heat. This heat tends to dry the steam. $o, for the design of a nozzle, the effect of friction has to be considered. There is a phenomenon known as ) super saturation that occurs in the flow of steam through nozzles. This is due to time lag in the condensation of steam during expansion. This super saturated flow affects mass and condition of the steam discharged. $o, the flow of steam through a nozzle may be regarded as either+
'. 6evers 6eversibl iblee adiabati adiabaticc or isentrop isentropic ic flow. flow. (. Adiabat Adiabatic ic flow flow modif modified ied by fric frictio tion. n. -. $uper $uper sat satur urat ated ed flo flow w. The nozzle as a system is shown in fig.1.( where plane ' is the entrance of the nozzle and plane ( is the exit of the nozzle.
Fig.5.2: A *ozzle
7ig 1.- shows the expansion on 8)9 and T)$ diagrams.
Fig.5.3: "xpansion of $team
The analysis of steam nozzles is also valid for gas nozzles !*ozzles in which the working fluid is a gas# where dryness fraction x='. $uper saturation is limited to flow of steam only and it doesn:t occur in gas nozzles. 5.4. EQUATION OF CONTINUITY ;et us consider the flow of steam through a nozzle. ;et m < =ass flow rate of steam A = ,ross sectional area at any section C < 9elocity of steam V s= $pecific volume of steam
kg/sec m( m/sec m3 /kg
According to continuity e%uation, mass flow rate at any section remains constant. $o, for steady flow of fluid, m < A.
∴
A 1 C 1 A 2 C 2 C < < V s V s 1 V s 2
mV s = A.C
< constant
7or points ',( etc., along the length of the nozzle. This e%uation is valid if steam is filled completely in every section of the nozzle To allow the expansion to take place properly, area at any section of nozzle must be such that it will accommodate steam whatever volume and velocity may prevail at that point. The mass flow is same at all sections of the nozzle. $o, area of cross section varies as (C/V s ). The manner in which C and V s vary depend upon the properties of the fluid flowing. $o, the shape or contour of the nozzle depends upon the nature of the fluid flowing. 7or a li%uid substance, V s remains almost constant with change of pressure. With decreasing pressure, the velocity of substance C increases and so the value of (C/V s ) goes on increasing. $o, the cross sectional area, > should decrease with decrease of pressure. The 7ig.1.>.!a# shows proper contour of longitudinal section of a nozzle suitable for a li%uid. This is a convergent nozzle. While both velocities ? and specific volume V s increase, the rate of increase of specific volume is less than that of velocity resulting in increasing value of (C/V x ).
Fig.5.4: @eneral 7orms of *ozzles
7ig.1.>.!b# shows proper contour for some hypothetical substance for which both velocity and specific volume increase at same rate so that their ratio C/V s remains constant at all sections. $o, the cross sectional area A should be constant at all points and the nozzle becomes a plain tube. 7ig.1.>.!c# shows a divergent nozzle suitable for a fluid for which (C/V s ) decrease with the drop of pressure. The specific volume increases at a faster rate tha velocity with the drop of pressure. $o, the cross sectional area should increase as the pressure decreases. 7ig.1.>.!d# shows widely used general form of convergent ) divergent nozzle suitable for gases and vapours. While velocity and specific volume both increases from start, velocity increases faster than specific volume first but after a certain critical point, specific volume increases more rapidly than velocity. $o, the value of (C/V s ) first increases to a maximum value and then decreases re%uiring a nozzle of convergent ) divergent form. 5.5. GENERAL FLOW ANALYSIS 7or calculating the variations of area of nozzle, it is essential to know how the expansion takes place. In what way the enthalpy and specific volume vary along the length of nozzle. It has been already mentioned that the expansion process is assumed to be adiabatic and hence for ideal frictionless case, the entropy remains constant in the nozzle.
The fig.1.1 shows the variation of velocity, specific volume and area along the length of a nozzle. It is assumed that e%ual pressure drop occurs in each unit length of the nozzle.
Fig.5.5: 9ariation of 9elocity, $pecific 9olume and Area along the length of a *ozzle
At high pressures, the specific volume increases at first slowly as pressure drops while velocity increases at a faster rate. As the expansion proceeds, the specific volume increases faster than velocity. $o, as we proceed from high pressure p' to a low pressure p( at the exit of the nozzle, the area decreases to a minimum and then increases resulting convergent divergent form of the nozzle. The point in the nozzle where area is minimum is called throat and the pressure at the throat is called ) critical pressure. At this section the mass flow per unit area is maximum. The velocity of fluid at the throat of a nozzle operating at its designed pressure ratio !when the flow rate is maximum# is e%ual to velocity of sound, and it is called ) $onic velocity. The flow upto throat is sub sonic and the flow after throat is supersonic !greater than velocity of sound#. In nozzles, accelerated flow takes place ) the velocity increases and pressure decreases with the flow of fluid. If the fluid velocity is less than the sound or sonic velocity, then the area of the nozzle must decreases i.e., the nozzle must converge which results in converging portion. As we know, the velocity increases continuously in a nozzle from inlet to exit. After throat, the fluid velocity becomes greater than sonic velocity and to accelerate flow the area must increase or thenozzle must diverge resulting in diverging portion of nozzle. The ratio of fluid velocity to local sound velocity is known as ) =ach number. The fig.1.B shows a general form of convergent ) divergent nozzle. !Also called e)lavel nozzle#
Fig.5.: onvergent C ivergent *ozzle
A convergent nozzle is used if exit pressure is e%ual to or more than the critical pressure and convergent ) divergent nozzle is used if exit pressure is less than the critical pressure. As already mentioned, the velocity of steam at inlet to a nozzle is very small compared to exit velocity. ;ow velocity implies large inlet area and most nozzles are shaped in such as way that the inlet area is large and converges rapidly to throat area. A ventruimeter which is used for flow measurement of fluids is also convergent divergent in shape. 5ut, in it, there is no continuous rise or fall of pressure. $o, it is neither a complete nozzle nor a diffuser. In its convergent portion, the pressure is decreasing, velocity is rising and this portion acts as a sub sonic nozzle. In the divergent portion, pressure is rising, velocity is falling and this portion acts as subsonic diffuser. The pressure at throat may not necessarily imply sonic velocity. The ratio of critical pressure to initial pressure is called ) critical pressure ratio (p( /p' ) - At the throat, the pressure is critical !velocity of fluid e%uals to sound velocity#, area is minimum and mass flow per unit area is maximum. With li%uids, convergent ) divergent shape is never used because the sonic velocity in li%uids is very high !About '1DD m/sec compare to about --D m/sec in air# which is out of the limit of practical velocities used. 5.. STEADY FLOW ENERGY EQUATION onsider steady flow of 'kg of steam through a nozzle. ;et 8' and 8( <8ressures at inlet and exit C ' and C 2 =9elocities at inlet and exit V s' and V s( = $pecific volumes at inlet and exit u1 and u2 = Internal energy at inlet and exit ' and E( < "levation at inlet and exit !1 "n# !2 < "nthalpy at inlet and exit < 4eat supplied if any $ % = Work done if any
7or a steady flow process !without any accumulation of the fluid between inlet and exit#, by the principle of conservation of energy "nergy at entrance or inlet < "nergy at exit. &ork #one in 'orcing 1kg o' ste"m into nozzle niti"l intern"l energ* niti"l kinetic energ* niti"l potenti"l energ* +e"t supplie# i' "n* 'rom t!e surroun#ings = &ork #one in sen#ing out 1 kg o' ste"m 'rom nozzle ,in"l intern"l energ* ,in"l kinetic energ* ,in"l potenti"l energ* &ork #one i' "n* to t!e surroun#ings.
8' v' F u'
1 2
C 21 g ' $ = 8( v2 Fu2
1 2
C 22 FgE(F %
8' v' F u'=!1 "nthalpy of steam at inlet 8( v2 Fu2 = !2 "nthalpy of steam at outlet @enerally, changes in potential energy are negligible. g '< gE( If no heat is supplied from surroundings then $ = D. If no work is done to the surroundings, then % = D. !1
1 2
C 21 = !2
1 2
C 22
This is the steady flow energy e%uation of a nozzle. In this e%uation the effect of friction is not considered.
5.!. FLOW OF STEAM THROUGH A CON"ERGENT # DI"ERGENT NOZZLE The fig.1.G shows a convergent ) divergent nozzle.
Fig.5.!: onvergent C ivergent *ozzle In the converging portion ')( !7rom inlet to throat#, there is a drop in steam pressure with a rise in its velocity. Also, there is a drop in the enthalpy of the steam. This drop of enthalpy is not utilised in doing external work but converted into kinetic energy. In the divergent portion ()- !7rom throat to exit#, there is further drop of steam pressure with a further rise in its velocity. Again, there is a drop in the enthalpy which is converted into kinetic energy. *ow, at the outlet, steam leaves the nozzles with high velocity and low pressure.
5.$. EFFECT OF FRICTION IN A NOZZLE% NOZZLE EFFICIENCY When steam flows through a nozzle, for a given pressure drop, the final velocity of steam gets reduced because of the following losses+
'. The friction between steam and walls of nozzle. (. Internal friction of steam itself. -. $hock losses. =ost of the friction in a convergent divergent nozzle occurs in the divergent portion )between throat and exit. ue to the effect of friction, the actual flow through a nozzle is not isentropic but still approximately adiabatic. The effects of friction are+ '. The enthalpy drop is reduced and hence the final velocity. (. The kinetic energy gets converted into heat due to friction and is absorbed by the steam. ue to this, the final dryness fraction of steam increases. -. $team becomes more dry due to increased dryness fraction and hence specific volume of steam increases and mass flow rate decreases. The effect of friction is shown on the h)s diagram or =other chart in fig.1.H.
Fig.5.$+ "ffect of friction in a *ozzle
8oint A represents the initial condition of steam which enters the nozzle in a dry saturated state. If the effect of friction is neglected, the expansion of steam from entrance to throat is represented by A)5 and that from throat to exit by 5). The whole expansion from A to is isentropic. The heat drop (! A ) !c ) is known as ) Isentropic heat drop or 6ankine heat drop. In actual practice, the expansion process is modified by friction. ;et point represent the final condition of steam. *ow, A5: represents the actual expansion ) Adiabatic expansion. ryness fraction at 5: is more than at . $o, the effect of friction is to improve the %uality of the steam. The heat drop (! A ) ! :# is the actual enthalpy drop during the expansion of steam when effect of friction is considered and is known as ) useful heat drop. The useful heat drop is less than the isentropic heat drop. If the steam enters the nozzle in a super heated condition, then during expansion, the friction tends to super heat the steam. The ratio of actual or useful heat drop to isentropic heat drop is known as ) oefficient of nozzle or nozzle efficiency. . ηnozzle <
= *ozzle efficiency
Actualheat drop
< isentropic heat drop AB '
<
AC
<
h A− hB' h A −hC
<
hact hisen
The efficiency of a nozzle generally varies from D.H1 to D.1. The efficiency of a nozzle depends upon the following factors+ '. (. -. >. 1. B. G. H.
=aterial of the nozzle. $ize and shape of the nozzle. 7inish of the nozzle. Angle of divergence. *ature of the fluid and its state, 7riction. 7luid velocity. Turbulence in the flow passages.
5.&. COEFFICIENT OF DISCHARGE The effect of friction on mass flow is taken into account by the term ) oefficient of discharge. It is defined as the ratio of actual mass flow rate to mass flow rate corresponding to isentropic expansion. 5.1'. "ELOCITY OF STEAM $team enters the nozzle with high pressure and low velocity and leaves the nozzle with high velocity and low pressure. The initial velocity compared to exit velocity is so small and is generally neglected. ;et C '< 9elocity of steam at entrance of nozzle m/sec. C (< 9elocity of steam at any section of nozzle m/sec !' < "nthalpy of entering steam k0/kg k0/kg !2= "nthalpy of steam at the section considered
7or unit mass flow of steam, we have the steady flow energy e%uation+
C 21
!' F
2 2
C 2 2
< !( F
C 22 2
2
=
C 1 2
!!') !(#
The gain in kinetic energy between any two sections is e%ual to loss of enthalpy. "nthalpy drop !# = (!l - !2 )
2
C 2
∴
2
2
=
C 1 2
!!d#
*eglecting the velocity of entering steam or velocity of approach
C 22 2
∴
!!d#
=
c22 = 2 !# <(DDD !#
∴ c2 =
√ 2000 hd
< >>.G( √ hd
m/sec.
In actual practice, always certain amount of friction exits between steam and the surfaces of the nozzle. This reduces the enthalpy drop by 'D)'1 percent and hence the exit velocity of steam is also reduced correspondingly. onsidering the effect of friction
√ Khd
∴ c2 < >>.G(
< *ozzle efficiency or coefficient of nozzle. 5.11. "ELOCITY COEFFICIENT In the problems of nozzles, sometimes, the term velocity coefficient is used for accounting the effects of friction. 9elocity coefficient is defined as the ratio of actual exit velocity to exit velocity when the flow is isentropic for the same pressure drop.
9elocity coefficient
<
Actualexit velocity isentropic exit velocity C B' C C
<
√
Actual heat drop isentropic heatdrop
The velocity coefficient depends upon the dimensions of the nozzle, roughness of the nozzle walls, velocity of flow, friction etc. 5.12. MASS OF STEAM DISCHARGED THROUGH A NOZZLE
The steam flowing through a nozzle approximately follows the e%uation pvn < constant.
where n = '.'-1 for saturated steam < '.-DD for superheated steam. 7or wet steam, from Eenner:s e%uations n = '.D-1 F D.' x' . Where x'< Initial dryness fraction of steam.
;et
p1 < Initial pressure of steam v1 < Initial volume of ' kg of steam p2 = 8ressure of steam at throat v2 - 9olume of steam at pressure p2 A = ross sectional area of nozzle V 2 = 9elocity of leaving steam
) /m2 ) m3 /kg ) /m2 -
m3 /kg
) m( ) m/sec.
Work done during 6ankine cycle !6ankine area# < rop in enthalpy
@ain in kinetic energy <
!*eglecting initial velocity#
@ain in kinetic energy is e%ual to enthalpy drop.
We know that
p'n v' = p( v(n
8utting the value of !v(2v&# from e%uation !(# in e%uation !'#
9olume of steam flowing 2 sec = ross sectional area of nozzle x velocity. =A.V2 9olume of ' kg of steam i.e., specific volume of steam at pressure p2 = v( m3 /kg
Then, mass of steam discharged through the nozzle per second
$ubstituting the value of v( from e%uation !-#
This e%uation gives mass of steam in kgs/sec flowing through a nozzle for a pressure drop from p'to p( 5.13. CRITICAL PRESSURE RATIO 7rom e%uation !># the rate of mass flow of steam per unit is given by+
The mass flow per unit are has maximum value at :throat: which has minimum area. The value of pressure ratio (p2 /p1 ) at throat can be calculated from e%uation !1# corresponding to maximum value of m/A. "xcept the ratio (p2 /p1 ) all other terms in this e%uation are constant. $o, m/A will be maximum when is maximum.
ifferentiating the above expression with respect to (p2 /p1 ) and e%uating to zero for a maximum discharge per unit area.
The ratio (p2 /p1 ) is known as ) ritical pressure ratio and its value depends upon the value of index n. The pressure at throat is known as ) ritical pressure and the ratio of pressure at minimum cross section i.e., throat (p2 ) to initial pressure ) pressure at entrance (p1 ) is known as Jcritical pressure ratio. The area of throat of all steam nozzles should be designed on this ratio. The following table gives approximate values of index n and corresponding values of critical pressure ratio. I(i)i*+ C,(-i)i,( , S)/*0 $uper heated or super saturated ry saturated Wet
"*+1/ ,. I(-/2
n
'.-DD '.'-1 '.''!'.D-1 F D.' x1#
C3i)i4*+ P3/5513/ R*)i,
D.1>B D.1GH D.1H( x' < Initial dryness fraction of steam
5.14. PHYSICAL E6PLANATION OF CRITICAL PRESSURE $uppose there are two vessels A and which are &oined by a diaphragm containing a convergent nozzle as shown in fig.1..
Fig.5.&: onvergent *ozzle
Fig.5.1': ritical 8ressure ;et the vessel A contains steam at pressure p' while pressure p( in vessel is varied at will. ;et the pressure p( in vessel initially is e%ual to pressure p'. Then no flow takes place. *ow, if p( is reduced gradually, the discharge through the nozzle will increase accordingly as shown in fig.1.'D. When the pressure p( approaches a :critical: value, the rate of discharge also approaches a maximum value. If p( is reduced below this critical value, rate of discharge doesn:t increase but remains constant as that at :critical pressure: and fluid expands violently to p2. The ratio of exit pressure p( to inlet pressure p' is called ) critical pressure ratio. We know that velocity of steam at any section in the nozzle is
7or maximum discharge, critical pressure ratio
The above e%uation represents the local velocity of sound in steam at pressure p2 and density K( < '2v(. $o, the velocity of steam in adiabatic and frictionless flow reaches the velocity of sound in steam at throat and this velocity is known as ) $onic velocity. When friction is present, sonic velocity in steam occurs &ust beyond throat. The critical pressure gives the velocity of steam at throat e%ual to velocity of
sound. In a convergent ) divergent nozzle, the flow in convergent portion of nozzle is sub sonic !less than the velocity of sound#, sonic at throat and in divergent portion, it is supersonic !=ore than the velocity of sound#. 7or a convergent ) divergent nozzle, the cross sectional area of throat fixes the mass flow through the nozzle for fixed inlet conditions. To increase the velocity of steam above sonic velocity !To supersonic velocity# by expanding the steam below critical pressure, divergent portion for the n ozzle is necessary. 5.15. DIAMETERS OF THROAT AND E6IT FOR MA6IMUM DISCHARGE onsider a convergent ) divergent nozzle. The fig. 1.'' shows h)s diagram for the nozzle.
Fig.5.11: !-s iagram for a onvergent)ivergent nozzle
;et
8' < Initial pressure of steam -/m. !' < "nthalpy of inlet steam ) 0/kg. p2 p-, !2 !3 < orresponding value at throat. x' = ryness and exit fraction of steam at inlet. x2 - ryness fraction of steam at throat ) m/sec V 2 = 9elocity of steam at throat v < $pecific volume of steam at throat corresponding to 2 pressure p( !7rom steam tables# Cm -2kg
x-, 9-, v-, A- < orresponding values at exit. m - =ass of steam discharged J kg The first step is to estimate the critical or throat pressure (p2 ) for the given initial conditions of steam. *ow on the =ollier chart !!) s chart#, locate points. It is a point where the initial pressure !p'# line meets the given dryness fraction ! x'# line. Through A draw a vertical line to meet critical pressure (p2 ) line at . A represents expansion of steam from inlet to throat. "xtend the line A to meet the exit pressure line !p-# at C. C represents expansion from throat to exit, i.e., expansion in divergent portion. *ow, find out the values of enthalpy and dryness fraction for points A C from the chart. onsidering the flow of steam from inlet to throat+ "nthalpy drop =!1 =!1 ) !2 9elocity of steam at throat < V 2 < >>.G √ !d =ass of steam discharged 2 sec.
!vs( specific volume of dry saturated steam#
If the nozzle is convergent, then, the nozzle terminates at throat and hence throat is the exit of the nozzle. 7or a convergent ) divergent nozzle consider the flow of steam from entrance to exit. "nthalpy drop =!e = !1-!3 9elocity of steam at exit < =ass of steam discharged
$ince mass flow rate is same
9s- < $pecific volume of dry saturated steam at pressure p-. ?nowing the value of :m:, areas of diameters of throat and exit can be determined. 5.1. LENGTH OF A NOZZLE The length of convergent portion should be very short to reduce surface friction and generally its length is about B mm. The convergence of the walls tends to stabilize the flow as shown in fig.1.'(.
Fig.5.12: ;ength of *ozzle In the divergent portion of the nozzle, on account of inertia, high velocity steam has the tendency to flow along the axis is the form of circular &et of area e%ual to throat area. If the divergence is rapid steam will not occupy the increased area provided. $o, steam may pass out through the divergent portion without drop of pressure as shown in
7ig. 1.'(!a#. $o, the divergent portion should have sufficient length so that steam has enough time to occupy the full cross sectional area thus resulting in drop of pressure and increase in kinetic energy. This re%uires gradual increase in area. In practice, the length of nozzle from throat to exit is such that the included cone angle is about 'DL as shown in 7ig. 1.'(!c#. 5.1!. SUPER SATURATED OR META STA7LE FLOW When a super heated vapour expands adiabatically or isentropically, the vapour begins to condense when saturated vapour line is reached. As expansion continues below this line into wet region, condensation proceeds gradually and steam becomes more and more wet there is always a stable mixture of steam and condensate !li%uid# at any point during expansion. This type of expansion is in thermal e%uilibrium and is shown in 7ig. 1.'- on 4-s and !-s diagrams.
Fig.5.13: "xpansion of $team under Thermal "%uilibrium
The point $ in expansion lies on saturation line and represents the point at which condensation within the vapour &ust begins. The condensation of steam occurs when steam passes through certain distance in the nozzle and after certain short interval of time. When steam flows through the nozzle, the discharge of steam through the nozzle will be slightly less than the theoretical discharge due to the effect of friction. 5ut, during the flow of wet steam through the nozzle, the measured discharge is slightly greater than the theoretical discharge even though we consider the effect of friction. *ormally, condensation starts around tiny dust particles which are always present in commercial steam plants in sufficient %uantity. When steam is free of foreign particles, condensation process is delayed and the temperature of the steam continues to fall. This is known as ) super saturation. When certain degree of super saturation is reached, the presence of dust particles has no effect on condensation and e%uilibrium between vapours and li%uid phases is attained completely and also instantaneously. In normal condensation, the random kinetic energy of the molecules falls to a level which is insufficient to overcome the attractive forces of the molecules and some of the slower moving molecules &oin together to form tiny droplets of water. A certain time interval is essential for the collection of these molecules to form droplets. In actual practice, the velocity of steam in sonic or even supersonic and the convergent portion of the nozzle is so short the molecules of steam find no sufficient time to collect and form droplets and steam doesn:t condense at the saturation temperature corresponding to the pressure but continues to expand with fall in temperature but without condensation. As a result, e%uilibiurm between li%uid and
vapour phases is delayed. The expansion takes place very rapidly and condensation can:t keep pace with expansion and lags behind. ue to this, the steam remains in an unnatural dry or super heated state. The steam in such conditions is said to be :super ) saturated: or : meta ) stable:. It is also called ) $uper cooled steam and its temperature at any pressure is less than the saturation temperature corresponding to that pressure. The flow of super saturated steam through the nozzle is called ) super saturated or meta stable or non ) e%uilibrium flow. $uper saturation means that steam doesn:t condense at the saturation temperature corresponding to the pressure as it occurs in case of e%uilibrium pressure as it occurs in case of e%uilibrium flow.In the state of :super saturation:, the steam is under cooled to a temperature less than that corresponding to its pressure hence, the density of steam increases and hence the measured discharge increases than the calculated theoretical discharge. "xperiments showed that in the absence of dust dry saturated steam when suddenly expanded, doesn:t condense until its density is about H times that of saturated vapour of the same pressure. 4!e re"sons 'or super s"tur"te# 'lo% "re5 '. The flow of steam is so rapid that it doesn:t allow time for transfer of heat. It may take about D.DD' second only for steam to travel from inlet to exit of nozzle. (. There may not be any dust particles which generally form nucleus for condensation. At a certain instant, the supersaturated steam condenses suddenly to its natural state. Thus, flow of steam through a nozzle may be regarded as either ideal adiabatic or adiabatic flow modified by friction and super saturation. The fig. 1.'> shows the super saturated flow on 4-s and !)s diagrams.
Fig.5.14: $uper $aturated 7low
8oint A: represents the position of initial super heated steam at entrance pressure p'. The line A - A represents isentropic expansion of steam in thermal e%uilibrium upto saturation line. ;ine AC represents isentropic expansion of steam in super saturated region. Mpto the point at which condensation occurs, the state of steam is not of stable e%uilibrium not unstable e%uilibrium either, since a small disturbance will cause condensation to commence. $o, steam in this condition is said to be in meta stable state. 8oint C represents the meta stable state. It is obtained by drawing a vertical line from points to Wilson line. At the steam condenses suddenly. ;ine CD represents condensation of steam at constant enthalpy. 8oint D is obtained by drawing a horizontal line through C to meet throat pressure p2 of the nozzle. ;ine D, represents isentropic expansion of steam in the divergent portion in thermal e%uilibrium. uring the partial
condensation of steam D, sufficient amount of heat is released which raises the temperature back to saturation temperature. 7ollowing relations may be used for solving problems on super saturated flow+
5.1$. EFFECTS OF SUPER SATURATION The following are the important effects that occur during super saturated flow of steam in a nozzle. '. As the condensation doesn:t take place during super saturated expansion, the temperature at which super saturation occurs will be less than the super saturation temperature corresponding to the pressure. $o, the density of super saturated steam will be more than that for e%uilibrium conditions. !@enerally H times that of ordinary saturated vapour at the corresponding pressure# This gives increase in the mass of steam discharged
(.
ue to super saturation, the entropy and specific volume increase.
-.
$uper saturation increases slightly the dryness fraction. >. 7or some pressure limits, super saturation reduces enthalpy drop slightly. As velocity is proportional to s%uare root of enthalpy drop exit velocity is also reduced slightly. When meta stable conditions exist in the nozzle =ollier chart !4)$ chart# should not be used and the expansion must be considered to follow the law pv'.- = C i.e., with index of expansion for super heated steam. The problems on super saturated flow can:t be solved by =ollier chart unless Wilson line is drawn on it. 5.1&. WILSON LINE @enerally, there is a limit upto which super saturated flow is possible. This limit of super saturation is represented by a curve known as ) Wilson line, on the =ollier diagram. Above this curve, steam is super saturated and super heated. 5eyond Wilson line, there is no super saturation. At Wilson line condensation occurs suddenly and irreversibly at constant enthalpy and then remains in stable condition. The result is to reduce heat drop slightly during expansion causing corresponding reduction in exit velocity and final dryness fraction increases slightly. The limiting condition of under cooling at which condensation begins and restores the conditions of thermal e%uilibrium is called Wilson line. @enerally, Wilson line closely follows D.B dryness fraction line. In nozzles, this limit may be within the nozzle or after the vapour leaves the nozzle. 5.2'. DEGREE OF UNDER COOLING It is the difference between super saturated steam temperature and saturation
temperature at that pressure. 6efer T)$ diagram of fig. -.'>. The temperature 4 2 is less than the normal temperature of steam at pressure p2. The state C is known as ) Mnder cooled as the temperature of steam is lesser than the saturation temperature at pressure p2. The amount of under cooling !ifference in temperatures# is known as ) egree of under cooling. egree of under cooling < 4 2 6 4 ( : There is a limit to the degree of under cooling possible and the limit to which the super saturated flow is possible is given by ) Wilson line. The region between the Wilson line and the dry saturated line is called ) $uper saturated zone. When Wilson line is reached, condensation begins at constant enthalpy and pressure remains unaltered. DEGREE OF SUPER SATURATION The ratio of pressures corresponding to temperature of super saturated steam and saturation temperature is known as ) egree of super saturation.
