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diff --git a/Turbomachines_by_A_V_Arasu/5-AXIAL_FLOW_STEAM_AND_GAS_TURBINES.ipynb b/Turbomachines_by_A_V_Arasu/5-AXIAL_FLOW_STEAM_AND_GAS_TURBINES.ipynb new file mode 100644 index 0000000..83c71a5 --- /dev/null +++ b/Turbomachines_by_A_V_Arasu/5-AXIAL_FLOW_STEAM_AND_GAS_TURBINES.ipynb @@ -0,0 +1,906 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 5: AXIAL FLOW STEAM AND GAS TURBINES" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.10: ACTUAL_STAGE_POWER_OUTPUT.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"R=0.5//Degree of reaction\n", +"P0=2.2//Inlet pressure in bar\n", +"T0=443//Inlet temperature in K\n", +"N=2400//Rotor running speed in rpm\n", +"Dm=0.5//Rotor mean diameter in m\n", +"a1=36//Rotor inlet angle in degree\n", +"a2=19//Stator exit angle in degree\n", +"ns=0.88//Stage efficiency\n", +"m=1//Mass flow rate of steam in kg/s\n", +"\n", +"//calculations\n", +"b2=a1//Outlet angle of the rotor blade in degree\n", +"b1=a2//Inlet angle of the rotor blade in degree\n", +"U=(3.1415*Dm*N)/60//Mean blade speed in m/s\n", +"Ca=(2*U*R)/(tand(b2)-tand(b1))//Axial velocity in m/s\n", +"W=m*U*Ca*(tand(a1)+tand(a2))*10^-3//Power output in kW\n", +"dh=W/ns//Stage enthalpy drop in kJ/kg\n", +"\n", +"//output\n", +"printf('(a)Power output is %3.2f kW\n(b)Stage enthalpy drop is %3.2f kJ/kg',W,dh)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.11: ROTOR_BLADE_ANGLES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"P0=800//Inlet pressure of hot gas in kPa\n", +"T1=973//Inlet temperature of hot gas in K\n", +"P2=100//Final pressure of hot gas in kPa\n", +"a1=73//Nozzle angle in degree\n", +"m=35//Mass flow rate in kg/s\n", +"ns=0.9//Nozzle efficiency\n", +"Cp=1.005//Specific heat of gas at constant pressure in kJ/kg.K\n", +"r=1.4//Ratio of specific heats of air\n", +"\n", +"//calculations\n", +"b1=atand(tand(a1)/2)//Inlet angle of the rotor blade in degree\n", +"b2=b1//Outlet angle of the rotor blade in degree\n", +"pi=2/tand(a1)//Flow coefficient\n", +"psil=pi*(tand(b1)+tand(b2))//Blade loading coefficient\n", +"dh=ns*Cp*T1*(1-(P2/P0)^((r-1)/r))//Change in enthalpy in kJ/kg\n", +"W=m*dh*10^-3//Power developed in MW\n", +"\n", +"//output\n", +"printf('(a)Rotor blade angles\n Inlet angle of the rotor blade is %3.2f degree\n Outlet angle of the rotor blade is %3.2f degree\n(b)Flow coefficient is %3.3f\n(c)Blade loading coefficient is %3.f\n(d)Power developed is %3.1f MW',b1,b2,pi,psil,W)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.12: POWER_DEVELOPED_AND_ANGLES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"P0=100//Initial pressure of steam in bar\n", +"T0=773//Initial temperature of steam in K\n", +"D=1//Turbine diameter in m\n", +"N=3000//Speed of turbine in rpm\n", +"m=100//Mass flow rate of steam in kg/s\n", +"a1=70//Exit angle of the first stage nozzle in degree\n", +"ns1=0.78//Stage efficiency of first stage \n", +"ns2=ns1//Stage efficiency of second stage\n", +"\n", +"//calculations\n", +"U=(3.1415*D*N)/60//Mean blade speed in m/s\n", +"C1=(2*U)/sind(a1)//Velocity of steam at exit from nozzle in m/s \n", +"b11=atand(tand(a1)/2)//Inlet angle of the rotor blade in degree\n", +"b21=b11//Outlet angle of the rotor blade in degree\n", +"b12=b21//Inlet angle of the rotor blade in second stage in degree\n", +"b22=b12//Outlet angle of the rotor blade in second stage in degree\n", +"W=4*m*U^2*10^-6//Total work done in both the stages in MW\n", +"dh02=2*U^2*10^-3//Change in enthalpy in first stage of turbine in kJ/kg\n", +"dh02s=(dh02/ns1)//Change in enthalpy isentropically of turine first stage in kJ/kg\n", +"printf('The values of enthalpy and specific volume are taken from the mollier chart at inlet and exit conditions respectively')\n", +"h0=3370//Enthalpy at beginning of first stage in kJ/kg\n", +"h2=h0-dh02//Enthalpy at the end of first stage in kJ/kg\n", +"h2s=h0-dh02s//Isentropic enthalpy at the end of first stage in kJ/kg\n", +"v2=0.041//Specific volume at the end of first stage in m^3/kg\n", +"dh24=2*U^2*10^-3//Change in enthalpy in second stage of turbine in kJ/kg\n", +"dh24s=dh24/ns2//Change in enthalpy isentropically of turine second stage in kJ/kg\n", +"h4=h2-dh24//Enthalpy at beginning of second stage in kJ/kg\n", +"h4s=h2-dh24s//Isentropic enthalpy at the end of second stage in kJ/kg\n", +"v4=0.05//Specific volume at the end of second stage in m^3/kg\n", +"\n", +"Ca=C1*cosd(a1)//Axial velocity in m/s\n", +"h1r=(m*v2)/(3.1415*D*Ca)//Blade height at first stage rotor exit in m\n", +"h2r=(m*v4)/(3.1415*D*Ca)//Blade height at second stage rotor exit in m\n", +"\n", +"//output\n", +"printf('\n\n(a)rotor blade angles\n Inlet angle of the rotor blade is %3.2f degree\n Outlet angle of the rotor blade is %3.2f degree\n Inlet angle of the rotor blade in second stage is %3.2f degres\n Outlet angle of the rotor blade in second stage is %3.2f degree\n(b)Total work done or Power developed in both the stages is %3.2f MW\n(c)final state of steam\n Enthalpy at beginning of first stage is %3i kJ/kg\n Enthalpy at the end of first stage is %3.2f kJ/kg\n Isentropic enthalpy at the end of first stage is %3.2f kJ/kg\n Specific volume at the end of first stage is %3.3f m^3/kg\n Enthalpy at beginning of second stage is %3.1f kJ/kg\n Isentropic enthalpy at the end of second stage is %3.2f kJ/kg\n Specific volume at the end of second stage is %3.2f m^3/kg\n(d)blade height\n Blade height at first stage rotor exit is %3.4f m\n Blade height at second stage rotor exit is %3.4f m',b11,b21,b12,b22,W,h0,h2,h2s,v2,h4,h4s,v4,h1r,h2r)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.13: ROTOR_BLADE_ANGLES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"P0=100//Initial pressure of steam in bar\n", +"T0=773//Initial temperature of steam in K\n", +"D=1//Turbine diameter in m\n", +"N=3000//Speed of turbine in rpm\n", +"m=100//Mass flow rate of steam in kg/s\n", +"a1=70//Exit angle of the first stage nozzle in degree\n", +"ns=0.65//Stage efficiency of first stage \n", +"\n", +"//calculations\n", +"U=(3.1415*D*N)/60//Mean blade speed in m/s\n", +"C1=(4*U)/sind(a1)//Velocity of steam at exit from nozzle in m/s\n", +"Ca=C1*cosd(a1)//Axial velocity in m/s\n", +"Wx1=3*U//Inlet whirl velocity in m/s\n", +"b11=atand(Wx1/Ca)//Inlet angle of the rotor blade in degree\n", +"b21=b11//Outlet angle of the rotor blade in degree\n", +"C2=Ca//Velocity of steam at exit from stage in m/s\n", +"b22=atand(U/Ca)//Outlet angle of the rotor blade in degree\n", +"b12=b22//Inlet angle of the rotor blade in in degree\n", +"W=m*8*U^2*10^-6//Total work done or power developed in MW\n", +"printf('The values of enthalpy and specific volume are taken from the mollier chart at inlet and exit conditions respectively')\n", +"h0=3370//Enthalpy at beginning of stage in kJ/kg\n", +"dh04=(W*10^3)/m//Change in enthalpy of turbine in kJ/kg\n", +"dh04s=dh04/ns//Change in enthalpy isentropically of turine in kJ/kg\n", +"h4=h0-dh04//Enthalpy at beginning of stage in kJ/kg\n", +"h4s=h0-dh04s//Isentropic enthalpy at the end of stage in kJ/kg\n", +"v4=0.105//Specific volume at the end of stage in m^3/kg\n", +"h=(m*v4)/(3.1415*D*Ca)//Rotor blade height in m\n", +"\n", +"printf('\n\n(a)rotor blade angles\n Inlet angle of the rotor blade is %3.2f degree\n Outlet angle of the rotor blade is %3.2f degree\n Inlet angle of the rotor blade in second stage is %3.2f degres\n Outlet angle of the rotor blade in second stage is %3.2f degree\n(b)Total work done or Power developed in both the stages is %3.2f MW\n(c)final state of steam\n Enthalpy at beginning of first stage is %3i kJ/kg\n Enthalpy at beginning of stage is %3.1f kJ/kg\n Isentropic enthalpy at the end of stage is %3.2f kJ/kg\n Specific volume at the end of stage is %3.3f m^3/kg\n(d)rotor blade height is %3.4f m',b11,b21,b12,b22,W,h0,h4,h4s,v4,h)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.14: ROTOR_BLADE_ANGLE_FOR_DEGREE_OF_REACTION_50.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"a1=(90-30)//Nozzle angle in axial direction in degree\n", +"Ca=180//Axial velocity in m/s\n", +"U=280//Rotor blade speed in m/s\n", +"R=0.25//Degree of reaction\n", +"\n", +"//calculations\n", +"Cx1=Ca*tand(a1)//Velocity of whirl at inlet in m/s\n", +"b1=atand((Cx1-U)/Ca)//Blade angle at inlet in degree\n", +"b2=a1//Blade angle at exit in degree as degree of reaction is 0.5\n", +"\n", +"//output\n", +"printf('(a)Blade angle at inlet is %3i degree\n(b)Blade angle at exit is %3i degree',b1,b2)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.15: POWER_AND_BLADE_ANGLES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"R=0.5//Degree of reaction\n", +"ns=0.85//Stage efficiency\n", +"P0=800//Inlet pressure of hot gas in kPa\n", +"T0=900//Inlet temperature of hot gas in K\n", +"U=160//Blade speed in m/s\n", +"m=75//Mass flow rate of hot gas in kg/s\n", +"a1=70//Absolute air angle at first stage nozzle exit in degree\n", +"\n", +"//calculations\n", +"C1=U/sind(a1)//Velocity of steam at exit from nozzle in m/s\n", +"Ca=C1*cosd(a1)//Axial velocity of hot gas in m/s\n", +"C2=Ca//Velocity of steam at exit from stage in m/s\n", +"b1=0//Blade angle at inlet in degree as Wx1=0 \n", +"a2=b1//Stator exit angle in degree as degree of reaction is 0.5\n", +"b2=a1//Blade angle at outlet in degree as degree of reaction is 0.5\n", +"Cx2=0//Velocity of whirl at outlet in m/s\n", +"Cx1=U//Velocity of whirl at inlet in m/s\n", +"W=m*U*(Cx1+Cx2)*10^-6//Power developed in MW\n", +"Wm=W*10^3/m//Work done per unit mass flow rate in kJ/kg\n", +"dhs=Wm/ns//Isentropic enthalpy drop in kJ/kg\n", +"\n", +"//output\n", +"printf('(a)Rotor blade angles\n Absolute air angle at first stage nozzle exit is %3i degree\n Blade angle at outlet is %3i degree\n Blade angle at inlet is %3i degree\n Stator exit angle is %3i degree\n(b)Power developed is %3.2f MW\n(c)Isentropic enthalpy drop is %3.2f kJ/kg',a1,b2,b1,a2,W,dhs)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.16: DEGREE_OF_REACTION.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"b1m=46//Rotor blade angle at entry at mean section in degree\n", +"b2m=75//Rotor blade angle at exit at mean section in degree\n", +"a1m=75//Nozzle angle at exit at mean section in degree\n", +"DhDt=0.6//Hub to tip ratio\n", +"N=7500//Mean rotor speed in rpm\n", +"Dh=0.45//Hub diameter in m\n", +"\n", +"//calculations\n", +"R=0.5//Degree of reaction as a1m=b2m\n", +"a2m=b1m//Stator angle at exit at mean section in degree\n", +"Dm=(Dh+(Dh/DhDt))/2//Mean diameter of turbine at mean section in m\n", +"Um=(3.1415*DhDt*N)/60//Mean blade speed in m/s\n", +"Ca=Um/(tand(a1m)-tand(b1m))//Axial velocity in m/s\n", +"pi=Ca/Um//Flow coefficient\n", +"psil=pi*(tand(b1m)+tand(b2m))//Blade loading coefficient\n", +"a1h=atand(tand(a1m)*((Dm/2)/(Dh/2)))//Nozzle angle at inlet at root section in degree\n", +"Uh=(3.14*Dh*N)/60//Blade speed at root section in m/s\n", +"b1h=atand(tand(a1h)-(Uh/Ca))//Rotor blade angle at entry at root section in degree\n", +"a2h=atand(tand(a2m)*((Dm/2)/(Dh/2)))//Stator angle at exit at root section in degree\n", +"b2h=atand((Uh/Ca)+tand(a2h))//Rotor blade angle at exit at root section in degree\n", +"pih=Ca/Uh//Flow coefficient at root section\n", +"Rh=(pih/2)*(tand(b2h)-tand(b1h))//Degree of reaction at root section\n", +"psilh=pih*(tand(b1h)+tand(b2h))//Blade loading coefficient at root section\n", +"\n", +"//output\n", +"printf('Mean section\n (a)Degree of reaction is %3.1f\n (b)Blade loading coefficient is %3.2f\nRoot section (a)Degree of reaction is %3.2f\n (b)Blade loading coefficient is %3.2f',R,psil,Rh,psilh)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.17: GAS_VELOCITIES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"T00=973//Total head inlet temperature in K\n", +"P00=4.5//Total head inlet pressure in bar\n", +"P2=1.6//Static head outlet pressure in bar\n", +"m=20//Gas flow rate in kg/s\n", +"a1=(90-28)//Nozzle outlet angle measured perpendicular to blade velocity in degree\n", +"Dmh=10//Mean blade diameter to blade height ratio \n", +"NLC=0.1//Nozzle loss coefficient\n", +"Cp=1155.6//Specific heat of gas at a constant pressure in kJ/kg\n", +"R=289//Gas constant in J/kg\n", +"r=1.333//Ratio of specific heats of gas \n", +"\n", +"//calculations\n", +"T2ss=T00*(P2/P00)^((r-1)/r)//Isentropic temperature at outlet in mid section in K here T00=T01\n", +"T1s=T2ss//Isentropic temperature at inlet at mid section in K\n", +"C1m=(2*Cp*(T00-T1s)/1.1)^(1/2)//Velocity of steam at exit from nozzle at mid section in m/s\n", +"T1=T00-((C1m^2)/(2*Cp))//Gas temperature at mid section in K\n", +"d=(P2*10^5)/(R*T1)//Density of gas in kg/m^3\n", +"Rg=(Cp*(r-1)/r)//Gas constant of the gas in kJ/kg\n", +"Ca=C1m*cosd(a1)//Axial velocity in m/s\n", +"h=((m/(d*Ca))*(1/(Dmh*3.1415)))^(1/2)//Hub height in m\n", +"Dm=Dmh*h//Mean blade diameter in m\n", +"Dh=Dm-h//Hub diameter in m\n", +"a1h=atand(((Dm/2)/(Dh/2))*tand(a1))//Discharge angle at hub in degree\n", +"C1h=Ca/cosd(a1h)//Gas velocity at hub section in m/s\n", +"T1h=T00-((C1h^2)/(2*Cp))//Gas temperature at hub in K here T01=T00\n", +"Dt=Dm+h//Tip diameter in m\n", +"a1t=atand(((Dm/2)/(Dt/2))*tand(a1))//Gas discharge angle at tip in degree\n", +"C1t=Ca/cosd(a1t)//Gas velocity at tip in m/s\n", +"T1t=T00-((C1t^2)/(2*Cp))//Gas temperature in K here T00=T01\n", +"\n", +"//output\n", +"printf('(a)At mid section\n Gas velocity is %3.1f m/s\n Gas temperature is %3.1f K\n Gas discharge angle is %3i degree\n(b)At hub section\n Gas velocity is %3.1f m/s\n Gas temperature is %3.2f K\n Gas discharge angle is %3.2f degree\n(c)At tip section\n Gas velocity is %3.1f m/s\n Gas temperature is %3.2f K\n Gas discharge angle is %3.2f degree',C1m,T1,a1,C1h,T1h,a1h,C1t,T1t,a1t)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.18: ABSOLUTE_AND_RELATIVE_ANGLES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"a1=75//Nozzle air angle in degree\n", +"Rh=0//Degree of reaction\n", +"N=6000//Running speed of hub in rpm\n", +"Dh=0.45//Hub diameter in m\n", +"Df=0.75//Tip diameter in m\n", +"\n", +"\n", +"//calculations\n", +"Uh=(3.1415*Dh*N)/60//Hub speed in m/s\n", +"C1h=Uh/((sind(a1))/2)//Velocity of steam at exit from nozzle in hub in m/s\n", +"Cah=C1h*cosd(a1)//Axial velocity at hub in m/s\n", +"Cx1h=C1h*sind(a1)//Whirl component of velocity at inlet in hub in m/s\n", +"b1h=atand((Cx1h-Uh)/Cah)//Rotor blade angle at entry at hub section in degree\n", +"b2h=b1h//Rotor blade angle at exit at mean section in degree as zero reaction section\n", +"sopt=sind(a1)/2//Blade to gas speed ratio at hub\n", +"rm=((Dh/2)+(Df/2))/2//Mean radius in m\n", +"rmrh=(rm/(Dh/2))^((sind(a1))^2)//Ratio of inlet velocity at hub and mean for constant nozzle air angle at hub section\n", +"C1m=C1h/rmrh//Velocity of steam at exit from nozzle at mean section in m/s\n", +"Cx1m=Cx1h/rmrh//Velocity of whirl at inlet at mean section in m/s\n", +"Ca1m=Cah/rmrh//Axial velocity at mean section in m/s\n", +"Um=(3.1415*2*rm*N)/60//Mean blade speed in m/s\n", +"b1m=atand((Cx1m-Um)/Ca1m)//Rotor blade angle at entry at mean section in degree\n", +"b2m=atand(Um/Ca1m)//Rotor blade angle at exit at mean section in degree for axial exit Cx2=0\n", +"s=Um/C1m//Blade to gas ratio at mean\n", +"Rm=(Ca1m/(2*Um))*(tand(b2m)-tand(b1m))//Degree of reaction of mean section\n", +"rmrt=((rm)/(Df/2))^((sind(a1))^2)//Ratio of inlet velocity at tip and mean for constant nozzle air angle at tip section\n", +"C1t=C1m*rmrt//Velocity of steam at exit from nozzle at tip section in m/s\n", +"Cx1t=Cx1m*rmrt//Velocity of whirl at inlet at tip section in m/s\n", +"Ca1t=Ca1m*rmrt//Axial velocity at tip section in m/s\n", +"Ut=(3.1415*Df*N)/60//Mean tip speed in m/s\n", +"b1t=atand((Cx1t-Ut)/Ca1t)//Rotor blade angle at entry at tip section in degree\n", +"b2t=atand(Ut/Ca1t)//Rotor blade angle at exit at tip section in degree for axial exit Cx2=0\n", +"st=Ut/C1t//Blade to gas ratio at tip\n", +"Rf=(Ca1t/(2*Ut))*(tand(b2t)-tand(b1t))//Degree of reaction of tip section\n", +"\n", +"//output\n", +"printf('(1)Hub section\n (a)\n Absolute air angle is %3.2f degree\n Relative air angle is %3.2f degree\n (b)Blade to gas speed ratio is %3.3f\n (c)Degree of reaction is %3i\n(2)Mean section\n (a)\n Absolute air angle is %3.2f degree\n Relative air angle is %3.2f degree\n (b)Blade to gas speed ratio is %3.3f\n (c)Degree of reaction is %3.3f\n(3)Tip section\n (a)\n Absolute air angle is %3.2f degree\n Relative air angle is %3.2f degree\n (b)Blade to gas speed ratio is %3.3f\n (c)Degree of reaction is %3.3f\n',b1h,b2h,sopt,Rh,b1m,b2m,s,Rm,b1t,b2t,st,Rf)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.1: INLET_ANGLE_OF_MOVING_BLADE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"C1=500//Steam velocity in m/s\n", +"U=200//Blade speed in m/s\n", +"b2=(90-25)//Exit angle of moving blade measured in axial direction in degree\n", +"a1=(90-20)//Nozzle angle in axial direction in degree\n", +"m=5//Steam flow rate in kg/s\n", +"\n", +"printf('The scale of the velocity vector diagram is 1:50\n\nThe following values are obtained from the velocity vector diagram')\n", +"\n", +"b1=33//Moving blade inlet angle in degree\n", +"a2=56//Direction of steam at the exit in degree\n", +"C2=160//Exit velocity of the steam in m/s\n", +"Wx1=270//Inlet whirl velocity in m/s\n", +"Wx2=285//Exit whirl velocity in m/s\n", +"Ca1=175//Inlet axial velocity in m/s\n", +"Ca2=135//Exit axial velocity in m/s\n", +"\n", +"//calculations\n", +"Wm=U*(Wx1+Wx2)*10^-3//Work done per kg of steam in kW/kg\n", +"AT=m*(Ca1-Ca2)//Axial thrust in N\n", +"W=m*Wm//Power developed in kW\n", +"Ndia=((U*(Wx1+Wx2))/((C1^2)/2))//Diagram or blade efficiency \n", +"\n", +"//output\n", +"printf('\n\n(a)Moving blade inlet angle is %3i degree\n(b)\n Exit velocity of the steam is %3i m/s\n Direction of steam at the exit is %3i degree\n(c)Work done per kg of steam is %3i kW/kg\n(d)\n Axial thrust is %3i N\n Power developed is %3i kW\n(e)Diagram or blade efficiency is %3.3f',b1,C2,a2,Wm,AT,W,Ndia)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.2: AXIAL_THRUST_ON_BLADING.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"U=300//Blade speed in m/s\n", +"a=20//Nozzle angle in degree\n", +"dhs=473//Isentropic heat drop in kJ/kg\n", +"Nn=0.85//Nozzle efficiency\n", +"W2W1=0.7//Blade velocity coefficient\n", +"nM=0.9//Mechanical efficiency\n", +"\n", +"//initial calculations\n", +"dh=Nn*dhs//Useful heat drop converted into kinetic energy in kJ/kg\n", +"C1=(2*1000*dh)^(1/2)//Velocity of steam at exit from nozzle in m/s\n", +"\n", +"printf('The scale of the velocity vector diagram is 1:100\n\nThe following values are obtained from the velocity vector diagram')\n", +"\n", +"Ca1=310//Inlet axial velocity in m/s\n", +"Ca2=210//Exit axial velocity in m/s\n", +"Wx1=550//Inlet whirl velocity in m/s\n", +"Wx2=380//Exit whirl velocity in m/s\n", +"W1=620//inlet Blade velocity in m/s\n", +"\n", +"//calculations\n", +"W2=W2W1*W1//Exit bladde velocity in m/s\n", +"AT=Ca1-Ca2//Axial thrust in N/kg\n", +"Wm=U*(Wx1+Wx2)*10^-3//Work developed per kg of steam/sec in kW/(kg/s)\n", +"P=Wm*nM//Power developed per kg of steam/sec in kW/(kg/s)\n", +"m=3600/P//Steam rate per kW.hr in kg\n", +"Ndia=((U*(Wx1+Wx2))/((C1^2)/2))//Diagram or blade efficiency \n", +"MNdia=(sind(90-a))^(2)//Maximum blade efficiency under optimum conditions \n", +"Ns1=Wm/dhs//Stage efficiency\n", +"Ns2=Ndia*Nn//Stage efficiency in other method\n", +"E=(((W1^2)-(W2^2))/2)*10^-3//Energy loss in blade friction in kJ/kg\n", +"\n", +"//output\n", +"printf('\n\n(a)Axial thrust is %3i N/kg\n(b)\n Work developed per kg of steam/sec is %3i kW/(kg/s)\n Power developed per kg of steam/sec is %3.1f kW/(kg/s)\n Steam rate per kW.hr is %3.1f kg\n(c)\n Diagram or blade efficiency is %3.3f\n Maximum blade efficiency under optimum conditions is %3.3f\n Stage efficiency is %3.4f\n(d)Energy loss in blade friction is %3.3f kJ/kg',AT,Wm,P,m,Ndia,MNdia,Ns1,E)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.3: VELOCITY_OF_STEAM_AT_EXIT.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"P1=5//Input pressure of steam in bar\n", +"P2=3//Exhaust pressure of steam in bar\n", +"C0=75//Carry over velocity of steam in m/s\n", +"a1=20//Nozzle angle in degree\n", +"UC1=0.4//The direction of blade rotation and blade speed ratio\n", +"b2=20//Blade exit angle in degree\n", +"m=2.5//Steam flow rate in kg/s\n", +"W=206//Power Output of the stage in kW\n", +"Nn=0.9//Efficiency of the nozzle\n", +"\n", +"printf('Assuming isentropic expansion the enthalpy drop can be found from steam table\n\nThe following values are obtained from steam tables')\n", +" \n", +"h1=2747.5//Enthalpy at initial pressure in kJ/kg\n", +"s1=6.819//Entropy at initial pressure in kJ/kg.K\n", +"s2=s1//Entropy at final pressure in kJ/kg.K\n", +"sfp2=1.647//Entropy of fliud at final pressure in kJ/kg.K\n", +"sfgp2=5.367//Entropy of fliud-gas mixture at final pressure in kJ/kg.K\n", +"hfg=2170.1//Enthalpy of fliud-gas mixture in kJ/kg\n", +"hf=551.5//Enthalpy of fliud in kJ/kg\n", +"\n", +"printf('\n\nThe scale of the velocity vector diagram is 1:50\n\nThe following values are obtained from the velocity vector diagram')\n", +"\n", +"W1=280//Relative velocity at inlet in m/s\n", +"W2=240//Relative velocity at exit in m/s\n", +"\n", +"//calculations\n", +"x2=(s2-sfp2)/sfgp2//The percentage of wet steam \n", +"h2s=hf+(x2*hfg)//The isentropic enthalpy at the second stage in kJ/kg\n", +"dhs=h1-h2s//Isentropic heat drop in kJ/kg\n", +"C1=((2000*Nn*dhs)+(C0^2))^(1/2)//Velocity of steam at exit from nozzle in m/s\n", +"U=UC1*C1//Blade speed in m/s\n", +"Wx1Wx2=(W*10^3)/(m*U)//The sum of whirl components of velocity in m/s\n", +"Ndia=(U*Wx1Wx2)/((C1^2)/2)//Diagram efficiency \n", +"RV=W2/W1//Relative velocity ratio \n", +"E=dhs+((C0^2)/2000)//Energy supplied per kg in kJ/kg\n", +"Ns1=(U*Wx1Wx2)/(E*10^3)//Stage efficiency\n", +"Ns2=Ndia*Nn//Stage efficiency in other method\n", +"\n", +"//output\n", +"printf('\n\n(a)Velocity of steam at exit from nozzle is %3.2f m/s\n(b)Diagram efficiency is %3.4f\n(c)Relative velocity ratio is %3.3f\n(d)\n Stage efficiency in method 1 is %3.4f\n Stage efficiency in method 2 is %3.4f',C1,Ndia,RV,Ns1,Ns2)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.4: BLADE_INLET_ANGLE_FOR_EACH_ROW.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"C1=600//Velocity of steam at exit from nozzle in m/s\n", +"U=120//Blade speed in m/s\n", +"a1=16//Nozzle angle in degree\n", +"b2=18//Discharge angle for first moving ring in degree \n", +"a11=21//Discharge angle for the fixed ring in degree \n", +"b22=35//Discharge angle for the second moving ring in degree\n", +"Wr=0.9//Blade velocity coefficient\n", +"m=1//Mass flow rate in kg/s\n", +"\n", +"printf('\n\nThe scale of the velocity vector diagram is 1:50\n\nThe following values are obtained from the velocity vector diagram')\n", +"\n", +"W1=485//Relative velocity at inlet for first stage in m/s\n", +"W2=Wr*W1//Relative velocity for first stage at exit in m/s\n", +"Wx1=460//Inlet whirl velocity for first stage in m/s\n", +"Wx2=410//Exit whirl velocity for first stage in m/s\n", +"Ca1=170//Inlet axial velocity for first stage in m/s\n", +"Ca2=135//Exit axial velocity for first stage in m/s\n", +"C2=325//Exit velocity of the steam for first stage in m/s\n", +"b1=20//Blade inlet angle for first row of moving blade in degree\n", +"C11=Wr*C2//Steam velocity at inlet to second row of moving blades in m/s\n", +"W12=190//Relative velocity at inlet for second stage in m/s\n", +"W22=Wr*W12//Relative velocity at exit for second stage in m/s\n", +"Wx11=155//Inlet whirl velocity for second stage in m/s\n", +"Wx22=140//Exit whirl velocity for second stage in m/s\n", +"Ca11=110//Inlet axial velocity for second stage in m/s\n", +"Ca22=100//Exit axial velocity for second stage in m/s\n", +"b11=35//Blade inlet angle for second row of moving blade in degree\n", +"dWx1=Wx1+Wx2//Driving force for first stage in m/s\n", +"dWx11=Wx11+Wx22//Driving force for second stage in m/s\n", +"dW=(dWx1+dWx11)*1//Total driving force for unit mass flow rate in N\n", +"AT1=Ca1-Ca2//Axial thrust for first stage in m/s\n", +"AT2=Ca11-Ca22//Axial thrust for second stage in m/s\n", +"AT=(AT1+AT2)*1//Total axial thrust for unit mass flow rate in N\n", +"DP=m*U*(dWx1+dWx11)*10^-3//Diagram power in kW\n", +"DE=(U*(dWx1+dWx11))/((C1^2)/2)//Diagram efficiency\n", +"MDE=(sind(90-a1))^2//Maximum diagram efficiency\n", +"\n", +"//output\n", +"printf('\n\n(a)\n Blade inlet angle for first row of moving blade is %3.i degree\n Blade inlet angle for second row of moving blade is %3i degree\n(b)\n Driving force for first stage is %3i m/s\n Driving force for second stage is %3i m/s\n Total driving force for unit mass flow rate is %3i N\nTotal axial thrust for unit mass flow rate is %3i N\n(c)Diagram power is %3.1f kW\n(d)Diagram efficiency is %3.3f\n(e)Maximum diagram efficiency is %3.3f',b1,b11,dWx1,dWx11,dW,AT,DP,DE,MDE)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.5: ROTOR_SPEED.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"C1=100//Velocity of steam at exit from nozzle in m/s\n", +"h=0.04//Mean blade height in m\n", +"b2=20//Exit angle of moving blade in degree\n", +"CaU=3/4//Ratio of flow velocity and blade speed at mean radius\n", +"m=10000/3600//steam flow rate in kg/s\n", +"\n", +"//calculations\n", +"a1=b2//Nozzle angle in degree\n", +"Ca=C1*cosd(90-a1)//Flow velocity in m/s\n", +"U=Ca/CaU//Mean blade velocity in m/s\n", +"v=0.60553//Specific volume of steam from steam table at 3 bar with dry saturated steam in m^3/kg\n", +"A=(m*v)/Ca//Annulus area in m^2\n", +"D=A/(3.1415*h)//Mean blade diameter in m\n", +"N=(U*60)/(3.14*D)//Rotor speed in rpm\n", +"\n", +"printf('\n\nThe scale of the velocity vector diagram is 1:10\n\nThe following values are obtained from the velocity vector diagram')\n", +"\n", +"W1=59//Relative velocity at inlet for first stage in m/s\n", +"Wx1Wx2=142//Sum of whirl components of velocity in m/s\n", +"DP=m*U*Wx1Wx2*10^-3//Diagram power in kW\n", +"Wm=U*(Wx1Wx2)//Work done per kg of steam in kJ/kg\n", +"W2=C1//Relative velocity at exit for first stage in m/s\n", +"E=((C1^2)/2)+(((W2^2)-(W1^2))/2)//Energy input per kg in kJ/kg when W2=C1\n", +"Ndia=Wm/E//Diagram efficiency \n", +"RV=(W2-W1)/W1//Percentage increase in relative velocity \n", +"dH=((W2^2)-(W1^2))/2*10^-3//Enthalpy drop in the moving blades in kJ/kg\n", +"H=2*dH//Total enthalpy drop in two stages in kJ/kg\n", +"\n", +"//output\n", +"printf('\n\n(a)The rotor speed is %3i rpm\n(b)The diagram power is %3.2f kW\n(c)The diagram efficiency is %3.3f\n(d)Percentage increase in relative velocity is %3.3f\n(e)\n Enthalpy drop in the moving blades is %3.3f kJ/kg\n Total enthalpy drop in two stages is %3.3f kJ/kg',N,DP,Ndia,RV,dH,H)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.6: STEAM_FLOW_RATE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"R=0.5//Degree of reaction\n", +"P1=14//Initial pressure in bar\n", +"T1=588//Initial temperature in K\n", +"P2=0.14//Final pressure in bar\n", +"Ns=0.75//Stage efficiency \n", +"RF=1.04//Reheat factor \n", +"N=20//No. of stages\n", +"W=11770//Total power output in kW\n", +"a1=20//Exit blade angle in degree\n", +"hD=1/12//Ratio of blade height to blade mean diameter \n", +"\n", +"//calculations\n", +"hs1=3080//Isentropic enthalpy at initial condition from mollier chart in kJ/kg\n", +"hs2=2270//Isentropic enthalpy at final condition from mollier chart in kJ/kg\n", +"dhs=hs1-hs2//Isentropic enthalpy change in kJ/kg\n", +"Nt=Ns*RF//Overall efficiency\n", +"dh=Nt*dhs//Actual enthalpy drop in kJ/kg\n", +"hs=dh/N//Enthalpy drop per stage in kJ/kg\n", +"m=W/dh//Mass flow rate in kg/s\n", +"C11=1.43*1//Velocity of steam at exit from nozzle in m/s in terms of U for 0.5 degree of reaction\n", +"Wm=1*((2*C11*sind(90-a1))-1)//Work done per mass of steam in terms of U^2 in kJ/kg\n", +"U=((hs*10^3)/Wm)^(1/2)//Mean blade velocity in m/s as work done equals enthalpy drop per stage \n", +"C1=1.43*U//Velocity of steam at exit from nozzle in m/s \n", +"Ca=C1*cosd(90-a1)//Flow velocity in m/s\n", +"v=1.618//Specific volume of steam from steam table at 1.05 bar with dry saturated steam in m^3/kg\n", +"D=((m*v)/(hD*3.14*Ca))^(1/2)//Blade mean diameter in m\n", +"N=(U*60)/(3.14*D)//Rotor speed in rpm\n", +"\n", +"//output\n", +"printf('(a)Mass flow rate of steam is %3.2f kg/s\n(b)Mean blade velocity is %3.1f m/s \n(c)Blade mean diameter is %3.3f m \n(d)Rotor speed is %3i rpm',m,U,D,N)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.7: NOZZLE_EXIT_ANGLE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"rh=0.225//Blade roof radius in m\n", +"rt=0.375//Blade tip radius in m\n", +"b1m=45//Inlet angle of the rotor blade at mid height in degree\n", +"a1m=76//Outlet angle of the nozzle blade at mid height in degree\n", +"b2m=75//Outlet angle of the rotor blade at mid height in degree\n", +"N=6000//Speed of turbine in rpm\n", +"\n", +"//calculations\n", +"rm=(rh+rt)/2//Mean radius in m\n", +"Um=(2*3.14*rm*N)/60//Mean blade speed at mean radius in m/s\n", +"Ca=Um/((tand(a1m))-(tand(b1m)))//Flow velocity in m/s\n", +"Cx1m=Ca*tand(a1m)//Velocity of whirl at inlet at mid height in m/s\n", +"Cx2m=Ca*tand(b2m)-Um//Velocity of whirl at inlet at mid height in m/s\n", +"Cx1h=(Cx1m*rm)/rh//Velocity of whirl at inlet at hub height in m/s\n", +"a1h=atand(Cx1h/Ca)//Inlet angle of the nozzle blade at hub height in degree\n", +"Uh=(2*3.1415*rh*N)/60//Mean blade speed at hub in m/s\n", +"b1h=atand(tand(a1h)-(Uh/Ca))//Inlet angle of the rotor blade at hub in degree\n", +"Cx2h=Cx2m*rm/rh//Velocity of whirl at outlet at hub in m/s\n", +"b2h=atand((Uh+Cx2h)/Ca)//Outlet angle of the rotor blade at hub in degree\n", +"Cx1t=Cx1m*rm/rt//Velocity of whirl at inlet at tip in m/s\n", +"a1t=atand(Cx1t/Ca)//Inlet angle of the nozzle blade at tip height in degree\n", +"Ut=(2*3.14*rt*N)/60//Mean blade speed at tip in m/s\n", +"b1t=atand(tand(a1t)-(Ut/Ca))//Inlet angle of the rotor blade at tip in degree\n", +"Cx2t=Cx2m*rm/rt//Velocity of whirl at outlet at tip in m/s\n", +"b2t=atand((Ut+Cx2t)/Ca)//Outlet angle of the rotor blade at hub in degree\n", +"Rh=(Ca/(2*Uh))*(tand(b2h)-tand(b1h))//Degree of reaction at hub\n", +"Rt=(Ca/(2*Ut))*(tand(b2t)-tand(b1t))//Degree of reaction at tip\n", +"\n", +"//output\n", +"printf('(a)for hub\n (1)Inlet angle of the nozzle blade at hub height is %3.1f degree\n (2)Inlet angle of the rotor blade at hub is %3i degree\n (3)Outlet angle of the rotor blade at hub is %3.2f degree\n (4)Degree of reaction at hub is %3.3f\n(b)for tip\n (1)Inlet angle of the nozzle blade at tip height is %3.2f degree\n (2)Inlet angle of the rotor blade at tip is %3i degree\n (3)Outlet angle of the rotor blade at tip is %3i degree\n (4)Degree of reaction at tip is %3.3f',a1h,b1h,b2h,Rh,a1t,b1t,b2t,Rt)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.8: BLADE_ANGLES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"Ca=180//Air velocity at the exit of nozzle in m/s\n", +"a1=(90-27)//Nozzle inclination perpendicular to direction of rotation in degree\n", +"R=0.5//Degree of reaction\n", +"U=180//Blade speed in m/s\n", +"\n", +"//calculations\n", +"Cx1=Ca*tand(a1)//Inlet whirl velocity in m/s\n", +"b11=atand((Cx1-U)/Ca)//Inlet angle of the rotor blade at inlet velocity triangle in degree\n", +"pi=Ca/U//Ratio of air velocity and blade velocity \n", +"b21=atand((2*R/pi)+tand(b11))//Outlet angle of the rotor blade at inlet velocity triangle in degree\n", +"C2=Ca//Exit velocity of the steam in m/s\n", +"b22=atand(U/C2)//Outlet angle of the rotor blade at outlet velocity triangle in degree\n", +"b12=b11//Inlet angle of the rotor blade at outlet velocity triangle in degree as np change in rotor inlet conditions \n", +"R=(pi*(tand(b22)-tand(b12)))/2//Degree of reaction \n", +"\n", +"//output\n", +"printf('(a)blade angles\n Inlet angle of the rotor blade at inlet velocity triangle is %3.1f degree\n Outlet angle of the rotor blade at inlet velocity triangle is %3.f degree\n(b)Degree of reaction is %3.4f\n(c)Inlet angle of the rotor blade at outlet velocity triangle is %3.f degree\n(d)Outlet angle of the rotor blade at outlet velocity triangle is %3.1f degree',b11,b21,R,b22,b12)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.9: POWER_DEVELOPED.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"U=300//Blade speed of turbine in m/s\n", +"m=2.5//Mass flow rate in kg/s\n", +"T0=773//Gas temperature at turbine inlet in K\n", +"T2=573//Gaas temperature at turbine outlet in K\n", +"a1=70//Fixed blade outlet angle in degree\n", +"Ca=200//Axial velocity in m/s\n", +"Cp=1.005//Specific heat of gas at constant pressure in kJ/kg.K\n", +"//calculations\n", +"W=m*Cp*(T0-T2)//Power developed by turbine in kW\n", +"Wm=Cp*(T0-T2)//Stage work done per unit mass flow rate in kJ/kg\n", +"Wx1Wx2=Wm*10^3/U//Sum of whirl components of velocity at inlet and outlet in m/s\n", +"Wx1=(Ca*tand(a1))-U//Inlet whirl velocity in m/s\n", +"Wx2=Wx1Wx2-Wx1//Outlet whirl velocity in m/s\n", +"R=(Wx2-Wx1)/(2*U)//Degree of reaction\n", +"Wx2Wx1=Wm*10^3*R//Energy input due to whirl component velocity in (m/s)^2\n", +"C1=Ca/cosd(a1)//Velocity of steam at exit from nozzle in m/s \n", +"nb=(Wm*10^3)/(((C1^2)/2)+Wx2Wx1)//Blade efficiency\n", +"\n", +"//output\n", +"printf('(a)Power developed by turbine is %3.1f kW\n(b)Degree of reaction is %3.3f\n(c)Blade efficiency is %3.4f\n',W,R,nb)" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |