{ "metadata": { "name": "", "signature": "sha256:c31b3e182c94546bee565a2d8036e956b36a8e464b50b24f4e687e55ce855452" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 8:VAPOUR CYCLE" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.1, Page No: 362" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Variable declaration\n", "TH=311.06; # Source temperature in degree celcius\n", "pb=10; # Boiler pressure in MPa\n", "TL=32.88; # Sink temperature in degree celcius \n", "pc=5; # Condenser pressure in kPa\n", "# From steam tables at pb\n", "h2=1407.56; # specific enthalpy in kJ/kg \n", "h3=2724.7; # specific enthalpy in kJ/kg \n", "s2=3.3596; # specific entropy in kJ/kg K\n", "s3=5.6141; # specific entropy in kJ/kg K\n", "# From steam tables at pc\n", "hf=137.82; hfg=2423.7; # specific enthalpy in kJ/kg \n", "sf=0.4764; sfg=7.9187; # specific entropy in kJ/kg K\n", "\n", "#Calculation\n", "x1=(s2-sf)/sfg; # quality of steam at state 1\n", "x4=(s3-sf)/sfg; # quality of steam at state 4\n", "h1=hf+x1*hfg; # specific enthalpy at state 1\n", "h4=hf+x4*hfg; # specific enthalpy at state 4\n", "wT=h3-h4; # Turbine work\n", "wC=h2-h1; # Compressor work\n", "wnet=wT-wC; # Net work output\n", "qH=h3-h2; # Heat added\n", "rw=wnet/wT; # Ratio of net work to trbine work\n", "eff_th=wnet/qH; # Thermal efficiency\n", "SSC=3600/wnet; # specific steam consumption\n", "\n", "#Result\n", "print \"Ratio of net work to trbine work =\",round(rw,3),\"\\nThermal efficiency =\",round(eff_th*100,1),\"%\"\n", "print \"specific steam consumption =\",round(SSC,3),\"kg/kWh\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Ratio of net work to trbine work = 0.618 \n", "Thermal efficiency = 47.6 %\n", "specific steam consumption = 5.741 kg/kWh\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.2, Page No:366" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Variable declaration\n", "TH=311.06; # Source temperature in degree celcius\n", "p2=10; # Boiler pressure in MPa\n", "TL=32.88; # Sink temperature in degree celcius \n", "p1=5; # Condenser pressure in kPa\n", "# From steam tables at p2\n", "h3=2724.7; # specific enthalpy in kJ/kg \n", "s3=5.6141; # specific entropy in kJ/kg K\n", "# From steam tables at p1\n", "hf=137.82; hfg=2423.7; # specific enthalpy in kJ/kg \n", "sf=0.4764; sfg=7.9187; # specific entropy in kJ/kg K\n", "\n", "#Calculations\n", "x4=(s3-sf)/sfg; # quality of steam at state 4\n", "h4=hf+x4*hfg; # specific enthalpy at state 4\n", "h1=137.82; # specific enthalpy at state 1 in kJ/kg \n", "s1=0.4764; # specific entropy at state in kJ/kgK\n", "v1=0.001005; # specific volume in m^3/kg\n", "wp=abs (v1*(p2*10**3-p1)); # Pump work (absolute value)\n", "h2=h1+wp; # specific enthalpy at state 2\n", "wT=h3-h4; # Turbine work\n", "wnet=wT-wp; # Net work output\n", "qH=h3-h2; # Heat added\n", "rw=wnet/wT; # Ratio of net work to trbine work\n", "eff_th=wnet/qH; # Thermal efficiency\n", "SSC=3600/wnet; # specific steam consumption\n", "\n", "#Results\n", "print \"Ratio of net work to trbine work =\",round(rw,2),\"\\nThermal efficiency =\",round(eff_th*100,0),\"%\"\n", "print \"specific steam consumption =\",round(SSC,3),\"kg/kWh\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Ratio of net work to trbine work = 0.99 \n", "Thermal efficiency = 39.0 %\n", "specific steam consumption = 3.585 kg/kWh\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.3, Page No:369" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Variable declaration\n", "TH=311.06; # Source temperature in degree celcius\n", "p2=10; # Boiler pressure in MPa\n", "TL=32.88; # Sink temperature in degree celcius \n", "p1=5; # Condenser pressure in kPa\n", "# (a).Actual carnot cycle\n", "eff_Tur=0.8; # Efficiency of turbine\n", "eff_com=0.6; # Efficiency of compressure\n", "# From steam tables at p2\n", "h3=2724.7; # specific enthalpy in kJ/kg \n", "s3=5.6141; # specific entropy in kJ/kg K\n", "s2=3.3596; # specific entropy in kJ/kg K\n", "h2=1407.56; # specific enthalpy in kJ/kg \n", "# From steam tables at p1\n", "hf=137.82; hfg=2423.7; # specific enthalpy in kJ/kg \n", "sf=0.4764; sfg=7.9187; # specific entropy in kJ/kg K\n", "\n", "#Calculations for (a)\n", "x1=(s2-sf)/sfg; # quality of steam at state 1\n", "x4=(s3-sf)/sfg; # quality of steam at state 4\n", "h1=hf+x1*hfg; # specific enthalpy at state 1\n", "h4=hf+x4*hfg; # specific enthalpy at state 4\n", "wTs=h3-h4; # Turbine work\n", "wT=eff_Tur*wTs; # Actual turbine work\n", "wCs=h2-h1; # Compressor work\n", "wC=wCs/eff_com; # Actual compressor work\n", "wnet=wT-wC; # Net work output\n", "h2a=h1+wC; # specific enthalpy\n", "qH=h3-h2a; # Heat added\n", "rw=wnet/wT; # Ratio of net work to trbine work\n", "eff_th=wnet/qH; # Thermal efficiency\n", "SSC=3600/wnet; # specific steam consumption\n", "\n", "#Results for (a)\n", "print \"(a).Actual carnot cycle\",\"\\nRatio of net work to trbine work =\",round(rw,4),\"\\nThermal efficiency =\",round(eff_th*100,2),\"%\"\n", "print \"specific steam consumption =\",round(SSC,1),\"kg/kWh\"\n", "\n", "#Variable declaration for (b)\n", "# (b).Actual Rankine cycle\n", "eff_Tur=0.8; # Efficiency of turbine\n", "eff_pump=0.9; # Efficiency of Pump\n", "# From steam tables at p1\n", "h1=137.82; # specific enthalpy at state 1 in kJ/kg \n", "s1=0.4764; # specific entropy at state in kJ/kgK\n", "v1=0.001005; # specific volume in m^3/kg\n", "\n", "#Calculations for (b)\n", "wps=abs (v1*(p2*10**3-p1)); # Pump work (absolute value)\n", "wp=wps/eff_pump; # Actual pmp work\n", "h2a=h1+wp; # # specific enthalpy at state 2\n", "wnet=wT-wp; # Net work output\n", "qH=h3-h2a; # Heat added\n", "rw=wnet/wT; # Ratio of net work to trbine work\n", "eff_th=wnet/qH; # Thermal efficiency\n", "SSC=3600/wnet; # specific steam consumption\n", "\n", "#Results for (b)\n", "print \"\\n\\n(b).Actual Rankine cycle\",\"\\nRatio of net work to trbine work =\",round(rw,3),\"\\nThermal efficiency =\",round(eff_th*100,0),\"%\"\n", "print \"specific steam consumption =\",round(SSC,1),\"kg/kWh\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a).Actual carnot cycle \n", "Ratio of net work to trbine work = 0.2046 \n", "Thermal efficiency = 15.68 %\n", "specific steam consumption = 21.7 kg/kWh\n", "\n", "\n", "(b).Actual Rankine cycle \n", "Ratio of net work to trbine work = 0.986 \n", "Thermal efficiency = 31.0 %\n", "specific steam consumption = 4.5 kg/kWh\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.4, Page No:379 " ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Variable declaration\n", "T3=450; # temperature of steam at state 3 in degree celcius\n", "p3=10; # Boiler pressure in MPa \n", "p6=5; # Condenser pressure in kPa\n", "# From steam tables at state 1\n", "hf=137.82; hfg=2423.7; # specific enthalpy in kJ/kg \n", "sf=0.4764; sfg=7.9187; # specific entropy in kJ/kg K\n", "h1=137.82; # specific enthalpy at state 1 in kJ/kg \n", "s1=0.4764; # specific entropy at state in kJ/kgK\n", "v1=0.001005; # specific volume in m^3/kg\n", "\n", "#Calculations for (a)\n", "wp=abs (v1*(p3*10**3-p6)); # Pump work (absolute value)\n", "h2=h1+wp; # specific enthalpy at state 2\n", "# (a).Rankine cycle with superheat\n", "# From steam tables at state 3\n", "h3=3240.9;# specific enthalpy in kJ/kg\n", "s3=6.419; # specific entropy in kJ/kg K\n", "# State 4_1\n", "x4_1=(s3-sf)/sfg; # Quality of steam at state 4_1\n", "h4_1=hf+x4_1*hfg; # specific enthalpy at state 4_1\n", "wT=h3-h4_1; # Turbine work\n", "wnet=wT-wp; # Net work output\n", "qH=h3-h2; # Heat added\n", "eff_th=wnet/qH; # Thermal efficiency\n", "SSC=3600/wnet; # specific steam consumption\n", "\n", "#Results for (a)\n", "print \"(a).Rankine cycle with superheat\",\"\\nQuality of steam at exhaust = \",round(x4_1,2),\"\\nThermal efficiency =\",round(eff_th*100,1),\"%\"\n", "print \"specific steam consumption =\",round(SSC,3),\"kg/kWh\"\n", "\n", "#Variable declaration for (b)\n", "# (b).Reheat cycle\n", "s4=s3; # isentropic expansion\n", "x4=0.975; # Quality of steam at state 4\n", "# from steam table intermediate pressure is selected for s4 & x4 by interpolation and assumed by round value\n", "p4=1.2; # Intermediate pressure in MPa\n", "# From steam tables at state 4\n", "hf4=798.6; hfg4=1986.2; # specific enthalpy in kJ/kg \n", "h4=hf4+x4*hfg4; # specific enthalpy in kJ/kg \n", "# From steam tables at state 5\n", "h5=3368.5;# specific enthalpy in kJ/kg\n", "s5=7.5266; # specific entropy in kJ/kg K\n", "\n", "#Calculations for (b)\n", "x6=(s5-sf)/sfg; # Quality of steam at state 6\n", "h6=hf+x6*hfg; # specific enthalpy in kJ/kg \n", "wT=(h3-h4)+(h5-h6); # Turbine work\n", "wnet=wT-wp; # Net work output\n", "qH=(h3-h2)+(h5-h4); # Heat added\n", "eff_th=wnet/qH; # Thermal efficiency\n", "SSC=3600/wnet; # specific steam consumption\n", "\n", "#Results for (b)\n", "print \"\\n\\n(b).Reheat cycle\",\"\\nQuality of steam at exhaust = \",round(x6,2),\"\\nThermal efficiency =\",round(eff_th*100,1),\"%\"\n", "print \"specific steam consumption =\",round(SSC,3),\"kg/kWh\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a).Rankine cycle with superheat \n", "Quality of steam at exhaust = 0.75 \n", "Thermal efficiency = 41.2 %\n", "specific steam consumption = 2.825 kg/kWh\n", "\n", "\n", "(b).Reheat cycle \n", "Quality of steam at exhaust = 0.89 \n", "Thermal efficiency = 42.1 %\n", "specific steam consumption = 2.295 kg/kWh\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.5, Page No:386 " ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Variable declaration\n", "T5=311.06; # temperature of steam at state 5 in degree celcius\n", "p5=10; # Boiler pressure in MPa\n", "p4=p5;\n", "T7=32.88; # temperature of steam at state 7 in degree celcius \n", "p7=5; # Condenser pressure in kPa\n", "p1=p7;\n", "# From steam tables at p7\n", "h1=137.82; # specific enthalpy at state 1 in kJ/kg \n", "s1=0.4764; # specific entropy at state 1 in kJ/kgK\n", "v1=0.001005; # specific volume in m^3/kg\n", "\n", "#Calculations\n", "wp=abs (v1*(p5*10**3-p7)); # Pump work (absolute value)\n", "h2=h1+wp; # specific enthalpy at state 2\n", "T6=(T5+T7)/2; # Temperature of bleed system\n", "h5=2724.7; # specific enthalpy at state 5 in kJ/kg \n", "s5=5.6141; # specific entropy at state 5 in kJ/kgK\n", "# From steam tables at state 6\n", "p6=791.5; # bleed steam pressure in kPa\n", "p2=p6; p3=p6;\n", "vf6=0.00114; # specific volume in m^3/kg\n", "v3=vf6;\n", "hf6=719.21; hfg6=2049.5; # specific enthalpy in kJ/kg \n", "sf6=2.0419; sfg6=4.6244; # specific entropy in kJ/kg K\n", "x6=(s5-sf6)/sfg6; # quality of steam at state 6\n", "h6=hf6+x6*hfg6; # specific enthalpy at state 6\n", "h3=hf6; # specific enthalpy at state 3\n", "m1=(h3-h2)/(h6-h2); # Fraction of bleed steam\n", "wLP=abs (v1*(p2-p1)); # LP work\n", "wHP=abs (v3*(p4*10**3-p3)); # HP work\n", "wp=(1-m1)*wLP+wHP; # Total pump work\n", "h2=h1+wp; h4=h3+wp; # Specific Enthalpies of water\n", "# From steam tables at pc\n", "hf7=137.82; hfg7=2423.7; # specific enthalpy in kJ/kg \n", "sf7=0.4764; sfg7=7.9187; # specific entropy in kJ/kg K\n", "x7=(s5-sf7)/sfg7; # quality of steam at state 7\n", "h7=hf7+x7*hfg7; # specific enthalpy at state 4\n", "wT=(h5-h6)+(1-m1)*(h6-h7); # Turbine work\n", "wnet=wT-wp; # Net work output\n", "qH=h5-h4; # Heat added\n", "eff_th=wnet/qH; # Thermal efficiency\n", "SSC=3600/wnet; # specific steam consumption\n", "\n", "#Result\n", "print \"Thermal efficiency =\",round(eff_th*100,1),\"%\",\"\\nspecific steam consumption =\",round(SSC,3),\"kg/kWh\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Thermal efficiency = 42.4 % \n", "specific steam consumption = 4.254 kg/kWh\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.6, Page No:389" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Variable declaration \n", "ps=6.89+1; # Pressure of steam produced in bar (Absolute)\n", "x=0.96; # Quality of steam produced\n", "f=75; # Steady flow of water in litres\n", "t=9.5; # Time consumption of water in minutes\n", "tf=685; #Time consumption of 10 litre fuel in seconds\n", "Vf=10; # consumption of fuel in litres\n", "Sf=0.85; # specific gravity of water\n", "CV=43125; # Calorific value of fuel in kJ/kg\n", "\n", "#Calculation\n", "ms=f/(t*60);# Steam generation\n", "mf=Vf*Sf/tf; # consumption of fuel\n", "# From steam tables at ps\n", "hf=718.5; hfg=2050; # specific enthalpy in kJ/kg \n", "hs=hf+x*hfg; # specific enthalpy of steam produced\n", "hFW=146.7; # Enthalpy of feed water at 35 degree celcius\n", "eff_boiler=(ms*(hs-hFW))/(mf*CV); # Boiler Efficiency\n", "\n", "#Result\n", "print \"Boiler Efficiency = \",round(eff_boiler*100,2),\"%\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Boiler Efficiency = 62.45 %\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.7, Page No:394" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Variable declaration \n", "TL=-15; # Source temperature in degree celcius\n", "TH=40; # Sink temperature in degree celcius\n", "# From the table of properties of Freon - 12\n", "h2=203.05; h3=74.53; hf4=22.31; hg4=180.85; # specific enthalpy in kJ/kg \n", "s1=0.682; s3=0.2716; sf4=0.0906; sg4=0.7046; sfg4=sg4-sf4;# specific entropy in kJ/kg K\n", "\n", "#Calculations\n", "sf1=sf4; sfg1=sfg4; s2=s1; s4=s3; hf1=hf4; hg1=hg4; hfg4=hg4-hf4; hfg1=hfg4;# refer figure 8.20 \n", "x1=(s1-sf1)/sfg1; # Dryness fraction at state 1\n", "x4=(s4-sf4)/sfg4; # dryness fraction at state 4\n", "h1=hf1+x1*hfg1; h4=hf4+x4*hfg4; # specific enthalpy in kJ/kg \n", "wc=h2-h1; # work of compression\n", "wE=h3-h4; # Work of expansion\n", "qL=h1-h4; # Refrigerating effect\n", "qH=h2-h3; # Heat rejected\n", "wnet=wc-wE; # Net work\n", "COPc=qL/wnet; # COP of the cycle\n", "\n", "#Results\n", "print \"Work of compression = \",round(wc,2),\"kJ/kg\",\"\\nWork of expansion =\",round(wE,2),\"kJ/kg\"\n", "print \"Refrigerating effect = \",round(qL,2),\"kJ/kg\"\n", "print \"Heat rejected =\",qH,\"kJ/kg\",\"\\nCOP of the cycle =\",round(COPc,3)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Work of compression = 28.04 kJ/kg \n", "Work of expansion = 5.48 kJ/kg\n", "Refrigerating effect = 105.97 kJ/kg\n", "Heat rejected = 128.52 kJ/kg \n", "COP of the cycle = 4.699\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.8, Page No:400 " ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Variable declaration\n", "TL=-15; # Source temperature in degree celcius\n", "TH=40; # Sink temperature in degree celcius\n", "# From the table of properties of Freon - 12\n", "h3=74.53; h1=180.85; h4=h3; # specific enthalpy in kJ/kg \n", "s1=0.7046; s2=0.682; # specific entropy in kJ/kg K\n", "\n", "# (a) \n", "\n", "#Calculation for (i)\n", "# (i).Condensor and Evaporator pressure\n", "pc=0.9607; # Saturation pressure at TH in MPa\n", "pE=0.1826; # Saturation pressure at TL in MPa\n", "\n", "#Results for (i)\n", "print \"(a)\",\"\\n(i).Condensor and Evaporator pressure\",\"\\nCondensor pressure = \",pc,\"MPa\"\n", "print \"Evaporator pressure = \",pE,\"MPa\"\n", "\n", "#Calculation for (ii)\n", "# (ii).Compressor discharge temperature & Enthalpy\n", "p2=pc; # Condensor pressure\n", "s2=s1; # refer figure 8.25\n", "# From the table of properties of Freon - 12 at pc\n", "t2=46.8; # Compressor discharge temperature in degree celcius\n", "h2=208.3; # specific enthalpy in kJ/kg \n", "\n", "#Results for (ii)\n", "print \"\\n(ii).Compressor discharge temperature & Enthalpy\",\"\\nCompressor discharge temperature = \",t2,\"oC\"\n", "print \"Enthalpy = \",h2,\"kJ/kg\"\n", "\n", "#Calculation for (iii)\n", "# (iii).Ratio of COP of the cycle to Carnot COP\n", "w=h2-h1; # Compressor work\n", "qL=h1-h4; # Refrigeration effect\n", "COP=qL/w; # COP of the cycle\n", "COPc=4.68; # COP of carnot cycle from example 8.7\n", "r=COP/COPc; # Ratio of COP of the cycle to Carnot COP\n", "\n", "#Results for (iii)\n", "print \"\\n(iii).Ratio of COP of the cycle to Carnot COP = \",round(r,2)\n", "\n", "#Calculation for (b)\n", "# (b) \n", "QL=0.440; # Capacity of refrigerator in kW (1/8 ton of refrigeration)\n", "m=QL/qL; # Mass flow rate of refrigerant\n", "W=m*w; # Power consumption of compressor\n", "QH=QL+W; # Heat rejected\n", "\n", "#Results for (b)\n", "print \"\\n\\n(b)\",\"\\nMass flow rate of refrigerant = \",round(m,5),\"kg/s\",\"\\nPower consumption of compressor = \",round(W,4),\"kW\"\n", "print \"Heat rejected to surroundings = \",round(QH,4),\"kW (Error in textbook answer)\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a) \n", "(i).Condensor and Evaporator pressure \n", "Condensor pressure = 0.9607 MPa\n", "Evaporator pressure = 0.1826 MPa\n", "\n", "(ii).Compressor discharge temperature & Enthalpy \n", "Compressor discharge temperature = 46.8 oC\n", "Enthalpy = 208.3 kJ/kg\n", "\n", "(iii).Ratio of COP of the cycle to Carnot COP = 0.83\n", "\n", "\n", "(b) \n", "Mass flow rate of refrigerant = 0.00414 kg/s \n", "Power consumption of compressor = 0.1136 kW\n", "Heat rejected to surroundings = 0.5536 kW (Error in textbook answer)\n" ] } ], "prompt_number": 8 } ], "metadata": {} } ] }