{ "metadata": { "name": "", "signature": "sha256:1fcefba58d1aff268f075c74fd2cddb1b329d45775f950b8a0c675f9e594fddf" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 9:GAS CYCLES" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9.1, Page No:425" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "r=8; # Compression ratio of an engine\n", "p1=100; # Pressure of air before compression in lPa\n", "T1=300; # Temperature air before compression in kelvin\n", "qH=1800; # Heat added to the air in kJ/kg\n", "k=1.4; # Index of reversible adiabatic process\n", "Cvo=0.7165; # Specific heat at constant volume in kJ/kg K\n", "Cpo=1.0035; # Specific heat at constant pressure in kJ/kg K\n", "R=0.287; # characteristic gas constant of air in kJ/kg K\n", "\n", "#Calculation for (1)\n", "# Otto cycle\n", "# (1) state 2\n", "p2=p1*(r)**k; # Pressure at the end of compression\n", "T2=T1*(p2/p1)**((k-1)/k);# Temperature at the end of compression\n", "# state 3\n", "T3=(qH/Cvo)+T2; # Temperatue after heat addition\n", "p3=p2*(T3/T2); # Pressure after heat addition\n", "# state 4\n", "p4=p3*(1/r)**k; # Pressure after expansion\n", "T4=T3*(p4/p3)**((k-1)/k);# Temperature after expansion\n", "\n", "#Result for (1)\n", "print \"(1).state 1\",\"\\n Pressure of air before compression = \",p1,\"kPa\",\"\\n Temperature air before compression =\",T1,\"K\"\n", "print \"state 2\",\"\\n Pressure of air at the end of compression = \",round(p2,0),\"kPa\"\n", "print \" Temperature at the end of compression =\",round(T2,1),\"K\"\n", "print \"state 3\",\"\\n Pressure after heat addition = \",round(p3,0),\"kPa (round off error)\"\n", "print \" Temperature after heat addition =\",round(T3,1),\"K (round off error)\"\n", "print \"state 4\",\"\\n Pressure after expansion = \",round(p4,1),\"kPa (round off error)\"\n", "print \" Temperature after expansion =\",round(T4,1),\"K (round off error)\"\n", "\n", "#Calculation for (2)\n", "# (2).Thermal efficiency\n", "qL=Cvo*(T4-T1); # Heat rejected\n", "eff_th=1-qL/qH; # thermal efficiency\n", "\n", "#Result for (2)\n", "print \"\\n(2).Thermal efficienvy = \",round(eff_th*100,2),\"% (round off error)\"\n", "\n", "#Calculation for (3)\n", "# (3). Mean effective pressure\n", "wnet=qH-qL; # net work\n", "v1=R*T1/p1; # Specific volume at state 1\n", "v2=v1/r; # Specific volume at state 2\n", "pm=wnet/(v1-v2); # Mean effective pressure\n", "\n", "#Result for (3)\n", "print \"\\n(3).Mean effective pressure = \",round(pm,0),\"kPa\"\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(1).state 1 \n", " Pressure of air before compression = 100 kPa \n", " Temperature air before compression = 300 K\n", "state 2 \n", " Pressure of air at the end of compression = 1838.0 kPa\n", " Temperature at the end of compression = 689.2 K\n", "state 3 \n", " Pressure after heat addition = 8537.0 kPa (round off error)\n", " Temperature after heat addition = 3201.4 K (round off error)\n", "state 4 \n", " Pressure after expansion = 464.5 kPa (round off error)\n", " Temperature after expansion = 1393.5 K (round off error)\n", "\n", "(2).Thermal efficienvy = 56.47 % (round off error)\n", "\n", "(3).Mean effective pressure = 1349.0 kPa\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9.2, Page No:430" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Variable declaration\n", "r=18; # Compression ratio of an engine\n", "p1=100; # Pressure of air before compression in lPa\n", "T1=300; # Temperature air before compression in kelvin\n", "qH=1800; # Heat added to the air in kJ/kg\n", "k=1.4; # Index of reversible adiabatic process\n", "Cvo=0.7165; # Specific heat at constant volume in kJ/kg K\n", "Cpo=1.0035; # Specific heat at constant pressure in kJ/kg K\n", "R=0.287; # characteristic gas constant of air in kJ/kg K\n", "\n", "#Calculation\n", "# Diesel cycle\n", "# state 2\n", "T2=T1*(r)**(k-1); # Temperature at the end of compression\n", "p2=p1*(r)**k; # Pressure at the end of compression\n", "# state 3\n", "T3=(qH/Cpo)+T2; # Temperatue after heat addition\n", "p3=p2; #constant pressure\n", "Tmax=T3; # maximum temperature\n", "Pmax=p3; # Maximum pressure\n", "# state 4\n", "v3=R*T3/p3; # Specific volume at state 3\n", "v4=R*T1/p1; # Specific volume at state 4\n", "T4=T3*(v3/v4)**(k-1); # Temperature after expansion\n", "p4=p3*(v3/v4)**k; # Pressure after expansion\n", "qL=Cvo*(T4-T1); # Heat rejected\n", "wnet=qH-qL; # net work\n", "eff_th=wnet/qH; # thermal efficiency\n", "v1=R*T1/p1; # Specific volume at state 1\n", "v2=v1/r; # Specific volume at state 2\n", "pm=wnet/(v1-v2); # Mean effective pressure\n", "\n", "#Results\n", "print \"Maximum pressure = \",Pmax,\"kPa\",\"Maximum Temperature = \",Tmax,\"K\"\n", "print \"Thermal efficienvy = \",round(eff_th*100,1),\"%\"\n", "print \"Mean effective pressure = \",round(pm,0),\"kPa (Error in textbook)\"\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Maximum pressure = 5719.80874166 kPa Maximum Temperature = 2747.02343004 K\n", "Thermal efficienvy = 59.4 %\n", "Mean effective pressure = 1315.0 kPa (Error in textbook)\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9.3, Page No: 440" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Variable declaration\n", "p1=0.1; # Pressure of air at inlet in MPa\n", "T1=300; # Temperature of air at inlet in kelvin\n", "p2=0.6; # Pressure of air at exit in MPa\n", "T3=1200; # Maximun temperature of air in kelvin\n", "k=1.4; # Index of reversible adiabatic process\n", "Cvo=0.7165; # Specific heat at constant volume in kJ/kg K\n", "Cpo=1.0035; # Specific heat at constant pressure in kJ/kg K\n", "R=0.287; # characteristic gas constant of air in kJ/kg K\n", "\n", "#Calculation\n", "# Brayton cycle\n", "rp=p2/p1; # pressure ratio\n", "T2=T1*(p2/p1)**((k-1)/k);# Temperature at the end of compression\n", "wc=Cpo*(T2-T1); # compressor work\n", "T4=T3*(p1/p2)**((k-1)/k);# Temperature at the end of expansion\n", "wT=Cpo*(T3-T4); # Turbine work\n", "qH=Cpo*(T3-T2); # heat addition\n", "wnet=wT-wc; # net work\n", "eff_th=wnet/qH; # thermal efficiency\n", "rw=wnet/wT; # worh ratio\n", "\n", "#Result \n", "print \"Thermal Efficiency = \",round(eff_th*100,1),\"%\"\n", "print \"Work Ratio = \",round(rw,3)\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Thermal Efficiency = 40.1 %\n", "Work Ratio = 0.583\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9.4, Page No: 441" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Variable declaration\n", "p1=0.1; # Pressure of air at inlet in MPa\n", "T1=300; # Temperature of air at inlet in kelvin\n", "p2=0.6; # Pressure of air at exit in MPa\n", "T3=1200; # Maximun temperature of air in kelvin\n", "k=1.4; # Index of reversible adiabatic process\n", "Cvo=0.7165; # Specific heat at constant volume in kJ/kg K\n", "Cpo=1.0035; # Specific heat at constant pressure in kJ/kg K\n", "R=0.287; # characteristic gas constant of air in kJ/kg K\n", "eff_t=0.85; # Turbine efficiency\n", "eff_c=0.8; # Compressor efficienct\n", "\n", "#Calculation\n", "# Brayton cycle\n", "rp=p2/p1; # pressure ratio\n", "T2s=T1*(p2/p1)**((k-1)/k);# Isentropic Temperature at the end of compression\n", "T2=((T2s-T1)/eff_c)+T1; # Actual Temperature at the end of compression\n", "p3=0.585; # as per given in MPa\n", "p4s=0.11; # As per given in MPa\n", "T4s=T3*(p4s/p3)**((k-1)/k); # Isentropic temperature after reversible adiabatic expansion\n", "T4=T3-(eff_t*(T3-T4s));# Actual temperature at state 4\n", "wc=Cpo*(T2-T1); # compressor work\n", "wT=Cpo*(T3-T4); # Turbine work\n", "qH=Cpo*(T3-T2); # heat addition\n", "wnet=wT-wc; # net work\n", "eff_th=wnet/qH; # thermal efficiency\n", "rw=wnet/wT; # worh ratio\n", "\n", "#Result \n", "print \"Thermal Efficiency = \",round(eff_th*100,0),\"%\"\n", "print \"Work Ratio = \",round(rw,3)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Thermal Efficiency = 21.0 %\n", "Work Ratio = 0.353\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9.5, Page No: 448" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Variable declaration\n", "p1=0.1; # Pressure of air at inlet in MPa\n", "T1=300; # Temperature of air at inlet in kelvin\n", "p2=0.6; # Pressure of air at exit in MPa\n", "T3=1200; # Maximun temperature of air in kelvin\n", "k=1.4; # Index of reversible adiabatic process\n", "Cvo=0.7165; # Specific heat at constant volume in kJ/kg K\n", "Cpo=1.0035; # Specific heat at constant pressure in kJ/kg K\n", "R=0.287; # characteristic gas constant of air in kJ/kg K\n", "\n", "#Calculation\n", "# Brayton cycle\n", "rp=p2/p1; # pressure ratio\n", "T2=T1*(p2/p1)**((k-1)/k);# Temperature at the end of compression\n", "T4=T3*(p1/p2)**((k-1)/k);# Temperature at state 4\n", "Tx=T4; Ty=T2; # regenerator temperatures\n", "qH=Cpo*(T3-Tx); # Heat added in the cycle with regenerator\n", "qL=Cpo*(Ty-T1);# Heat rejected in the cycle with regenerator\n", "eff_th=1-qL/qH; # Thermal efficiency\n", "\n", "#Result\n", "print \"Thermal efficiency with regenerator = \",round(eff_th*100,1),\"%\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Thermal efficiency with regenerator = 58.3 %\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9.6, Page No: 453" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "V1=250; # Velocoty of jet aircraft in m/s\n", "p1=60; # Atmospheric pressure in kPa\n", "T1=260; # Atmospheric temperature in kelvin\n", "rp=8; # Pressure ratio of compressor\n", "T4=1350; # Temperature of gas at turbine inlet in kelvin\n", "k=1.4; # Index of reversible adiabatic process\n", "Cvo=0.7165; # Specific heat at constant volume in kJ/kg K\n", "Cpo=1.0035; # Specific heat at constant pressure in kJ/kg K\n", "R=0.287; # characteristic gas constant of air in kJ/kg K\n", "\n", "#Calculation for (a)\n", "# (a).The pressure and temperature at each point of the cycle\n", "# process 1-2 isentropic diffusion\n", "T2=T1+(V1**2)/(2*Cpo*10**3); # Temperature at state 2\n", "p2=p1*(T2/T1)**(k/(k-1)); # Pressure at state 2\n", "# process 2-3 isentropic compression\n", "p3=rp*p2; # perssure at state 3\n", "T3=T2*(p3/p2)**((k-1)/k); # Temperature at state 3\n", "wc=Cpo*(T3-T2); # compressor work\n", "# process 3-4 Constant pressur heat addition\n", "qH=Cpo*(T4-T3); # heat addition\n", "p4=p3; # constant pressure\n", "# process 4-5 isentropic expansion in turbine\n", "wT=wc;\n", "T5=T4-(wT/Cpo); # Temperature at state 5\n", "p5=p4*(T5/T4)**(k/(k-1)); # Pressure at state 5\n", "# process 5-6 Isentropic expansion in nozzle\n", "p6=p1;\n", "T6=T5*(p6/p5)**((k-1)/k); # Temperature at state 6\n", "\n", "#Result for (a)\n", "print \"(a).The pressure and temperature at each point of the cycle\",\"\\n State 1\",\"\\n p1 =\",p1,\"kPa\",\"\\n T1 =\",T1,\"K\"\n", "print \"\\n State 2\",\"\\n p2 =\",round(p2,1),\"kPa\",\"\\n T2 =\",round(T2,1),\"K\",\n", "print \"\\n State 3\",\"\\n p3 =\",round(p3,0),\"kPa\",\"\\n T3 =\",round(T3,1),\"K\"\n", "print \"\\n State 4\",\"\\n p4 =\",round(p4,0),\"kPa\",\"\\n T4 =\",T4,\"K\"\n", "print \"\\n State 5\",\"\\n p5 =\",round(p5,0),\"kPa (roundoff error)\",\"\\n T5 =\",round(T5,1),\"K (roundoff error)\"\n", "print \" State 6\",\"\\n p6 =\",p6,\"kPa\",\"\\n T6 =\",round(T6,0),\"K\"\n", "\n", "#Calculation for (b)\n", "# (b).Exit velocity of jet\n", "V6=math.sqrt (2*Cpo*10**3*(T5-T6)); # Exit velocity of jet\n", "\n", "#Result for (b)\n", "print \"\\n\\n(b).Exit velocity of jet =\",round(V6,0),\"m/s (roundoff error)\"\n", "\n", "#Calculation for (c)\n", "# (c).Specific thrust and work output\n", "F_mair=(V6-V1); # Specific thrust \n", "w=F_mair*V1/1000; # Work output\n", "\n", "#Result for (c)\n", "print \"\\n\\n(c).Specific thrust and work output\",\"\\nSpecific thrust =\",round(F_mair,0),\"N (roundoff error)\"\n", "print \"Work output = \",round(w,1),\"kJ/kg\"\n", "\n", "#Calculation for (d)\n", "# (d).Propulsion efficiency\n", "eff_p=w/(w+(V6**2-V1**2)/2000);# Propulsion efficiency\n", "\n", "#Result for (d)\n", "print \"\\n\\n(d).Propulsion efficiency =\",round(eff_p*100,1),\"%\"\n", "\n", "#Calculation for (e)\n", "# (e).Overall thermal efficiency\n", "eff_th=w/qH; # Overall thermal efficiency\n", "\n", "#Result for (e)\n", "print \"(e).Overall thermal efficiency =\",round(eff_th*100,1),\"%\"\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a).The pressure and temperature at each point of the cycle \n", " State 1 \n", " p1 = 60 kPa \n", " T1 = 260 K\n", "\n", " State 2 \n", " p2 = 89.1 kPa \n", " T2 = 291.1 K \n", " State 3 \n", " p3 = 713.0 kPa \n", " T3 = 527.4 K\n", "\n", " State 4 \n", " p4 = 713.0 kPa \n", " T4 = 1350 K\n", "\n", " State 5 \n", " p5 = 364.0 kPa (roundoff error) \n", " T5 = 1113.8 K (roundoff error)\n", " State 6 \n", " p6 = 60 kPa \n", " T6 = 666.0 K\n", "\n", "\n", "(b).Exit velocity of jet = 948.0 m/s (roundoff error)\n", "\n", "\n", "(c).Specific thrust and work output \n", "Specific thrust = 698.0 N (roundoff error)\n", "Work output = 174.6 kJ/kg\n", "\n", "\n", "(d).Propulsion efficiency = 29.4 %\n", "(e).Overall thermal efficiency = 21.2 %\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9.7, Page No:458" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Variable declaration\n", "p1=100; # Pressure of air at inlet in kPa\n", "T1=288; # Temperature of air at inlet in kelvin\n", "rp=12; # Pressure ratio of the compressor\n", "k=1.4; # Index of reversible adiabatic process\n", "Cvo=0.7165; # Specific heat at constant volume in kJ/kg K\n", "Cpo=1.0035; # Specific heat at constant pressure in kJ/kg K\n", "R=0.287; # characteristic gas constant of air in kJ/kg K\n", "T3=T1; # From figure\n", "\n", "#Calculation\n", "# process 1-2\n", "p2=12*p1; # Pressure at state 2\n", "T2=T1*(p2/p1)**((k-1)/k); # Temperature at state 2\n", "wc=Cpo*(T2-T1); # Compressor work\n", "# process 2-3\n", "qH=Cpo*(T2-T3); # Heat added\n", "# process 3-4\n", "T4=T3*(1/rp)**((k-1)/k); # Temperature at state 4\n", "# process 4-1 Refrigerating coil\n", "qL=Cpo*(T1-T4); # heat rejected\n", "wnet=qH-qL; # net work\n", "cop=qL/wnet; # Cop of plant\n", "pc=wnet/qL; # Power consumption per kW of refrigeration\n", "\n", "#Result\n", "print \"COP of the cycle =\",round(cop,3),\"\\nPower consumption per kW of refrigeration =\",round(pc,3),\"kW/kW\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "COP of the cycle = 0.967 \n", "Power consumption per kW of refrigeration = 1.034 kW/kW\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9.8, Page No:459" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Variable declaration\n", "p1=100; # Pressure of air at inlet in kPa\n", "T1=288; # Temperature of air at inlet in kelvin\n", "rp=12; # Pressure ratio of the compressor\n", "T4=223; # Temperature at state 4\n", "k=1.4; # Index of reversible adiabatic process\n", "Cvo=0.7165; # Specific heat at constant volume in kJ/kg K\n", "Cpo=1.0035; # Specific heat at constant pressure in kJ/kg K\n", "R=0.287; # characteristic gas constant of air in kJ/kg K\n", "T3=T1; # From figure\n", "\n", "#Calculation\n", "# process 1-2\n", "p2=12*p1; # Pressure at state 2\n", "T2=T1*(p2/p1)**((k-1)/k); # Temperature at state 2\n", "wc=Cpo*(T2-T1); # Compressor work\n", "# process 2-3\n", "qH=Cpo*(T2-T3); # Heat added\n", "# process 3-4 cooling in regenerative heat exchanger\n", "qregen=Cpo*(T3-T4); # cooling in regenerative heat exchanger\n", "# process 4-5 Expander\n", "T5=T4*(1/rp)**((k-1)/k); # Temperature at state 5\n", "wE=Cpo*(T4-T5); # Expander work\n", "# process 5-6 Refrigerating coil\n", "T6=T4; # From figure 9.32\n", "qL=Cpo*(T6-T5); # Heat rejected\n", "# process 6-1 Heating in regenerative heat exchanger\n", "qregen=Cpo*(T1-T6); # Heat supplied\n", "wnet=qH-qL; # net work\n", "cop=qL/wnet; # Cop of plant\n", "\n", "#Result\n", "print \"COP of the modified cycle =\",round(cop,3)\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "COP of the modified cycle = 0.615\n" ] } ], "prompt_number": 8 } ], "metadata": {} } ] }