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diff --git a/Turbomachines_by_A._V._Arasu/Ch5.ipynb b/Turbomachines_by_A._V._Arasu/Ch5.ipynb new file mode 100644 index 00000000..8d6309b4 --- /dev/null +++ b/Turbomachines_by_A._V._Arasu/Ch5.ipynb @@ -0,0 +1,1195 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:b3c6b5b9437eb9e3bff13119283daec451a9bdb3f3f492bbf38ecac5c3f69e9c" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 5 - Axial flow steam & gas turbines" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex 5.1 Page 211" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\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", + "print '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", + "print '\\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 %0.1f %%'%(b1,C2,a2,Wm,AT,W,Ndia*100)\n", + "# the answer in the textbook is not correct for axial thrust." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The scale of the velocity vector diagram is 1:50\n", + "\n", + "The following values are obtained from the velocity vector diagram\n", + "\n", + "\n", + "(a)Moving blade inlet angle is 33 degree\n", + "(b)\n", + " Exit velocity of the steam is 160 m/s\n", + " Direction of steam at the exit is 56 degree\n", + "(c)Work done per kg of steam is 111 kW/kg\n", + "(d)\n", + " Axial thrust is 200 N\n", + " Power developed is 555 kW\n", + "(e)Diagram or blade efficiency is 88.8 %\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex 5.2 Page 213" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sin, pi\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", + "print '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=(sin((90-a)*pi/180))**(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", + "print '\\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 %0.1f %%\\n Maximum blade efficiency under optimum conditions is %0.1f %%\\n Stage efficiency is %0.2f %%\\n(d)Energy loss in blade friction is %3.3f kJ/kg'%(AT,Wm,P,m,Ndia*100,MNdia*100,Ns1*100,E)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The scale of the velocity vector diagram is 1:100\n", + "\n", + "The following values are obtained from the velocity vector diagram\n", + "\n", + "\n", + "(a)Axial thrust is 100 N/kg\n", + "(b)\n", + " Work developed per kg of steam/sec is 279 kW/(kg/s)\n", + " Power developed per kg of steam/sec is 251.1 kW/(kg/s)\n", + " Steam rate per kW.hr is 14.3 kg\n", + "(c)\n", + " Diagram or blade efficiency is 69.4 %\n", + " Maximum blade efficiency under optimum conditions is 88.3 %\n", + " Stage efficiency is 58.99 %\n", + "(d)Energy loss in blade friction is 98.022 kJ/kg\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex 5.3 Page 215" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#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", + "print '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", + "print '\\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", + "print '\\n\\n(a)Velocity of steam at exit from nozzle is %3.2f m/s\\n(b)Diagram efficiency is %0.2f\\n(c)Relative velocity ratio is %3.3f\\n(d)\\n Stage efficiency in method 1 is %0.2f\\n Stage efficiency in method 2 is %0.2f'%(C1,Ndia*100,RV,Ns1*100,Ns2*100)\n", + "# the answer in the textbook is not accurate." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Assuming isentropic expansion the enthalpy drop can be found from steam table\n", + "\n", + "The following values are obtained from steam tables\n", + "\n", + "\n", + "The scale of the velocity vector diagram is 1:50\n", + "\n", + "The following values are obtained from the velocity vector diagram\n", + "\n", + "\n", + "(a)Velocity of steam at exit from nozzle is 440.65 m/s\n", + "(b)Diagram efficiency is 84.87\n", + "(c)Relative velocity ratio is 0.857\n", + "(d)\n", + " Stage efficiency in method 1 is 76.61\n", + " Stage efficiency in method 2 is 76.39\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex 5.4 Page 218" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#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", + "print '\\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=(sin((90-a1)*pi/180))**2#Maximum diagram efficiency\n", + "\n", + "#output\n", + "print '\\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 %0.1f\\n(e)Maximum diagram efficiency is %0.1f'%(b1,b11,dWx1,dWx11,dW,AT,DP,DE*100,MDE*100)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + "The scale of the velocity vector diagram is 1:50\n", + "\n", + "The following values are obtained from the velocity vector diagram\n", + "\n", + "\n", + "(a)\n", + " Blade inlet angle for first row of moving blade is 20 degree\n", + " Blade inlet angle for second row of moving blade is 35 degree\n", + "(b)\n", + " Driving force for first stage is 870 m/s\n", + " Driving force for second stage is 295 m/s\n", + " Total driving force for unit mass flow rate is 1165 N\n", + "Total axial thrust for unit mass flow rate is 45 N\n", + "(c)Diagram power is 139.8 kW\n", + "(d)Diagram efficiency is 77.7\n", + "(e)Maximum diagram efficiency is 92.4\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex 5.5 Page 220" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import cos\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*cos((90-a1)*pi/180)#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", + "print '\\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", + "print '\\n\\n(a)The rotor speed is %3i rpm\\n(b)The diagram power is %3.2f kW\\n(c)The diagram efficiency is %0.1f\\n(d)Percentage increase in relative velocity is %0.1f\\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*100,RV*100,dH,H)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + "The scale of the velocity vector diagram is 1:10\n", + "\n", + "The following values are obtained from the velocity vector diagram\n", + "\n", + "\n", + "(a)The rotor speed is 2226 rpm\n", + "(b)The diagram power is 17.99 kW\n", + "(c)The diagram efficiency is 78.4\n", + "(d)Percentage increase in relative velocity is 69.5\n", + "(e)\n", + " Enthalpy drop in the moving blades is 3.260 kJ/kg\n", + " Total enthalpy drop in two stages is 6.519 kJ/kg\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex 5.6 Page 222" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#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*sin((90-a1)*pi/180))-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*cos((90-a1)*pi*180)#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", + "print '(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)\n", + "# the answer in the textbook is not correct." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a)Mass flow rate of steam is 18.63 kg/s\n", + "(b)Mean blade velocity is 136.8 m/s \n", + "(c)Blade mean diameter is 0.767 m \n", + "(d)Rotor speed is 3407 rpm\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex 5.7 Page 224" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import tan, pi, degrees, atan\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/((tan(a1m*pi/180))-(tan(b1m*pi/180)))#Flow velocity in m/s\n", + "Cx1m=Ca*tan(a1m*pi/180)#Velocity of whirl at inlet at mid height in m/s\n", + "Cx2m=Ca*tan(b2m*pi/180)-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=degrees(atan(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=degrees(atan(tan(a1h*pi/180)-(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=degrees(atan((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=degrees(atan(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=degrees(atan(tan(a1t*pi/180)-(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=degrees(atan((Ut+Cx2t)/Ca))#Outlet angle of the rotor blade at hub in degree\n", + "Rh=(Ca/(2*Uh))*(tan(b2h*pi/180)-tan(b1h*pi/180))#Degree of reaction at hub\n", + "Rt=(Ca/(2*Ut))*(tan(b2t*pi/180)-tan(b1t*pi/180))#Degree of reaction at tip\n", + "\n", + "#output\n", + "print '(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 %0.2f %%\\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 %0.2f'%(a1h,b1h,b2h,Rh*100,a1t,b1t,b2t,Rt*100)\n", + "# Answer for degree of reaction is not correct in the textbook." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a)for hub\n", + " (1)Inlet angle of the nozzle blade at hub height is 79.4 degree\n", + " (2)Inlet angle of the rotor blade at hub is 72 degree\n", + " (3)Outlet angle of the rotor blade at hub is 72.75 degree\n", + " (4)Degree of reaction at hub is 2.93 %\n", + "(b)for tip\n", + " (1)Inlet angle of the nozzle blade at tip height is 72.69 degree\n", + " (2)Inlet angle of the rotor blade at tip is -29 degree\n", + " (3)Outlet angle of the rotor blade at tip is 77 degree\n", + " (4)Degree of reaction at tip is 65.04\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex 5.8 Page 228" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#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*tan(a1*pi/180)#Inlet whirl velocity in m/s\n", + "b11=degrees(atan((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=degrees(atan((2*R/pi))+tan(b11*pi/180))#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=degrees(atan(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*(tan(b22*pi/180)-tan(b12*pi/180)))/2#Degree of reaction \n", + "#output\n", + "print '(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)\n", + "# Answer in the textbook is not correct for some part." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a)blade angles\n", + " Inlet angle of the rotor blade at inlet velocity triangle is 43.9 degree\n", + " Outlet angle of the rotor blade at inlet velocity triangle is 59 degree\n", + "(b)Degree of reaction is 0.0032\n", + "(c)Inlet angle of the rotor blade at outlet velocity triangle is 45 degree\n", + "(d)Outlet angle of the rotor blade at outlet velocity triangle is 43.9 degree\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex 5.9 Page 229" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import cos\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*tan(a1*pi/180))-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/cos(a1*pi/180)#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", + "print '(a)Power developed by turbine is %3.1f kW\\n(b)Degree of reaction is %0.2f %%\\n(c)Blade efficiency is %0.2f %%\\n'%(W,R*100,nb*100)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a)Power developed by turbine is 502.5 kW\n", + "(b)Degree of reaction is 184.35 %\n", + "(c)Blade efficiency is 51.03 %\n", + "\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex 5.10 Page 230" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\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)/(tan(b2*pi/180)-tan(b1*pi/180))#Axial velocity in m/s\n", + "W=m*U*Ca*(tan(a1*pi/180)+tan(a2*pi/180))*10**-3#Power output in kW\n", + "dh=W/ns#Stage enthalpy drop in kJ/kg\n", + "\n", + "#output\n", + "print '(a)Power output is %3.2f kW\\n(b)Stage enthalpy drop is %3.2f kJ/kg'%(W,dh)\n", + "# Answer in the textbook is not correct." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a)Power output is 12.59 kW\n", + "(b)Stage enthalpy drop is 14.31 kJ/kg\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex 5.11 Page 231" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\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=degrees(atan(tan(a1*pi/180)/2))#Inlet angle of the rotor blade in degree\n", + "b2=b1#Outlet angle of the rotor blade in degree\n", + "pi=2/tan(a1*pi/180)#Flow coefficient\n", + "psil=pi*(tan(b1*pi/180)+tan(b2*pi/180))#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", + "print '(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)\n", + "# Answer in the textbook is not accurate." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a)Rotor blade angles\n", + " Inlet angle of the rotor blade is 12.12 degree\n", + " Outlet angle of the rotor blade is 12.12 degree\n", + "(b)Flow coefficient is 4.658\n", + "(c)Blade loading coefficient is 3\n", + "(d)Power developed is 13.8 MW\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex 5.12 Page 233" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sin, pi\n", + "#Ex Page\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=(pi*D*N)/60#Mean blade speed in m/s\n", + "C1=(2*U)/sin(a1*pi/180)#Velocity of steam at exit from nozzle in m/s \n", + "b11=degrees(atan(tan(a1*pi/180)/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", + "print '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*cos(a1*pi/180)#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", + "print '\\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)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The values of enthalpy and specific volume are taken from the mollier chart at inlet and exit conditions respectively\n", + "\n", + "\n", + "(a)rotor blade angles\n", + " Inlet angle of the rotor blade is 53.95 degree\n", + " Outlet angle of the rotor blade is 53.95 degree\n", + " Inlet angle of the rotor blade in second stage is 53.95 degres\n", + " Outlet angle of the rotor blade in second stage is 53.95 degree\n", + "(b)Total work done or Power developed in both the stages is 9.87 MW\n", + "(c)final state of steam\n", + " Enthalpy at beginning of first stage is 3370 kJ/kg\n", + " Enthalpy at the end of first stage is 3320.65 kJ/kg\n", + " Isentropic enthalpy at the end of first stage is 3306.73 kJ/kg\n", + " Specific volume at the end of first stage is 0.041 m**3/kg\n", + " Enthalpy at beginning of second stage is 3271.3 kJ/kg\n", + " Isentropic enthalpy at the end of second stage is 3257.39 kJ/kg\n", + " Specific volume at the end of second stage is 0.05 m**3/kg\n", + "(d)blade height\n", + " Blade height at first stage rotor exit is 0.0114 m\n", + " Blade height at second stage rotor exit is 0.0139 m\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex 5.13 Page 236" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#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)/sin(a1*pi/180)#Velocity of steam at exit from nozzle in m/s\n", + "Ca=C1*cos(a1*pi/180)#Axial velocity in m/s\n", + "Wx1=3*U#Inlet whirl velocity in m/s\n", + "b11=degrees(atan(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=degrees(atan(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", + "print '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", + "print '\\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)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The values of enthalpy and specific volume are taken from the mollier chart at inlet and exit conditions respectively\n", + "\n", + "\n", + "(a)rotor blade angles\n", + " Inlet angle of the rotor blade is 64.11 degree\n", + " Outlet angle of the rotor blade is 64.11 degree\n", + " Inlet angle of the rotor blade in second stage is 34.48 degres\n", + " Outlet angle of the rotor blade in second stage is 34.48 degree\n", + "(b)Total work done or Power developed in both the stages is 19.74 MW\n", + "(c)final state of steam\n", + " Enthalpy at beginning of first stage is 3370 kJ/kg\n", + " Enthalpy at beginning of stage is 3172.6 kJ/kg\n", + " Isentropic enthalpy at the end of stage is 3066.34 kJ/kg\n", + " Specific volume at the end of stage is 0.105 m**3/kg\n", + "(d)rotor blade height is 0.0146 m\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex 5.14 Page 238" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#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*tan(a1*pi/180)#Velocity of whirl at inlet in m/s\n", + "b1=degrees(atan((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", + "print '(a)Blade angle at inlet is %3i degree\\n(b)Blade angle at exit is %3i degree'%(b1,b2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a)Blade angle at inlet is 10 degree\n", + "(b)Blade angle at exit is 60 degree\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex 5.15 Page 239" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#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/sin(a1*pi/180)#Velocity of steam at exit from nozzle in m/s\n", + "Ca=C1*cos(a1*pi/180)#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", + "print '(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)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a)Rotor blade angles\n", + " Absolute air angle at first stage nozzle exit is 70 degree\n", + " Blade angle at outlet is 70 degree\n", + " Blade angle at inlet is 0 degree\n", + " Stator exit angle is 0 degree\n", + "(b)Power developed is 1.92 MW\n", + "(c)Isentropic enthalpy drop is 30.12 kJ/kg\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex 5.16 Page 240" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "from math import pi\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=(pi*DhDt*N)/60#Mean blade speed in m/s\n", + "Ca=Um/(tan(a1m*pi/180)-tan(b1m*pi/180))#Axial velocity in m/s\n", + "fi=Ca/Um#Flow coefficient\n", + "psil=fi*(tan(b1m*pi/180)+tan(b2m*pi/180))#Blade loading coefficient\n", + "a1h=degrees(atan(tan(a1m*pi/180)*((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=degrees(atan(tan(a1h*pi/180)-(Uh/Ca)))#Rotor blade angle at entry at root section in degree\n", + "a2h=degrees(atan(tan(a2m*pi/180)*((Dm/2)/(Dh/2))))#Stator angle at exit at root section in degree\n", + "b2h=degrees(atan((Uh/Ca)+tan(a2h*pi/180)))#Rotor blade angle at exit at root section in degree\n", + "pih=Ca/Uh#Flow coefficient at root section\n", + "Rh=(pih/2)*(tan(b2h*pi/180)-tan(b1h*pi/180))#Degree of reaction at root section\n", + "psilh=pih*(tan(b1h*pi/180)+tan(b2h*pi/180))#Blade loading coefficient at root section\n", + "\n", + "#output\n", + "print '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)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Mean section\n", + " (a)Degree of reaction is 0.5\n", + " (b)Blade loading coefficient is 1.77\n", + "Root section (a)Degree of reaction is 0.11\n", + " (b)Blade loading coefficient is 3.14\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex 5.17 Page 242" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#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*cos(a1*pi/180)#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=degrees(atan(((Dm/2)/(Dh/2))*tan(a1*pi/180)))#Discharge angle at hub in degree\n", + "C1h=Ca/cos(a1h*pi/180)#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=degrees(atan(((Dm/2)/(Dt/2))*tan(a1*pi/180)))#Gas discharge angle at tip in degree\n", + "C1t=Ca/cos(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", + "print '(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)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a)At mid section\n", + " Gas velocity is 682.2 m/s\n", + " Gas temperature is 771.6 K\n", + " Gas discharge angle is 62 degree\n", + "(b)At hub section\n", + " Gas velocity is 742.0 m/s\n", + " Gas temperature is 734.80 K\n", + " Gas discharge angle is 64.43 degree\n", + "(c)At tip section\n", + " Gas velocity is -320.3 m/s\n", + " Gas temperature is 928.61 K\n", + " Gas discharge angle is 59.68 degree\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex 5.18 Page 244" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sin, cos, atan, tan, pi, degrees\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/((sin(a1*pi/180))/2)#Velocity of steam at exit from nozzle in hub in m/s\n", + "Cah=C1h*cos(a1*pi/180)#Axial velocity at hub in m/s\n", + "Cx1h=C1h*sin(a1*pi/180)#Whirl component of velocity at inlet in hub in m/s\n", + "b1h=degrees(atan((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=sin(a1*pi/180)/2#Blade to gas speed ratio at hub\n", + "rm=((Dh/2)+(Df/2))/2#Mean radius in m\n", + "rmrh=(rm/(Dh/2))**((sin(a1*pi/180))**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=degrees(atan((Cx1m-Um)/Ca1m))#Rotor blade angle at entry at mean section in degree\n", + "b2m=degrees(atan(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))*(tan(b2m*pi/180)-tan(b1m*pi/180))#Degree of reaction of mean section\n", + "rmrt=((rm)/(Df/2))**((sin(a1*pi/180))**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=degrees(atan((Cx1t-Ut)/Ca1t))#Rotor blade angle at entry at tip section in degree\n", + "b2t=degrees(atan(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))*(tan(b2t*pi/180)-tan(b1t*pi/180))#Degree of reaction of tip section\n", + "\n", + "#output\n", + "print '(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)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(1)Hub section\n", + " (a)\n", + " Absolute air angle is 61.81 degree\n", + " Relative air angle is 61.81 degree\n", + " (b)Blade to gas speed ratio is 0.483\n", + " (c)Degree of reaction is 0\n", + "(2)Mean section\n", + " (a)\n", + " Absolute air angle is 25.55 degree\n", + " Relative air angle is 72.92 degree\n", + " (b)Blade to gas speed ratio is 0.842\n", + " (c)Degree of reaction is 0.427\n", + "(3)Tip section\n", + " (a)\n", + " Absolute air angle is -51.94 degree\n", + " Relative air angle is 78.71 degree\n", + " (b)Blade to gas speed ratio is 1.296\n", + " (c)Degree of reaction is 0.627\n", + "\n" + ] + } + ], + "prompt_number": 23 + } + ], + "metadata": {} + } + ] +}
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