{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Appendix A"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 1"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"('Temperature T2 = %.1f K', 556.4270854641527)\n",
"(' Compressor work = %.1f kJ/kg ', 269.2999938060093)\n",
"(' Temperature T3 = %.1f K', 1373.2)\n",
"(' Temperature T4 = %.1f K', 711.24546295203)\n",
"(' Turbine work = %.1f kJ/kg', 664.6023551961619)\n",
"(' Net work = %.1f kJ/kg', 395.30236139015256)\n",
"(' Thermal Efficiency of cycle = %.1f percent', 48.205253207687875)\n"
]
}
],
"source": [
"# -*- coding: utf8 -*-\n",
"from __future__ import division\n",
"#Example: 12.1\n",
"''' '''\n",
"\n",
"#Variable Declaration: \n",
"\n",
"\n",
"\t\t#1-Inlet for compressor\n",
"\t\t#2-Exit for compressor\n",
"\t\t#T-Temperature at a state\n",
"\t\t#P-Pressure at a state\n",
"T1 = 288.2\t\t#K\n",
"P2 = 1000\t\t#kPa\n",
"P1 = 100\t\t#kPa\n",
"k = 1.4\n",
"T2 = T1*(P2/P1)**(1-1/k)\t\t#K\n",
"Cp = 1.004\t\t#Specific heat at constant pressure in kJ/kg\n",
"wc = Cp*(T2-T1)\t\t#compressor work in kJ/kg\n",
"print ('Temperature T2 = %.1f K',T2)\n",
"print (' Compressor work = %.1f kJ/kg ',wc)\n",
"\t\t#3-Turbine Inlet\n",
"\t\t#4-Turbine Exit\n",
"P4 = P1\n",
"P3 = P2\n",
"T3 = 1373.2\t\t#K\n",
"T4 = T3*(P4/P3)**(1-1/k)\t\t#K\n",
"wt = Cp*(T3-T4)\n",
"wnet = wt-wc\n",
"print (' Temperature T3 = %.1f K',T3)\n",
"print (' Temperature T4 = %.1f K',T4)\n",
"print (' Turbine work = %.1f kJ/kg',wt)\n",
"print (' Net work = %.1f kJ/kg',wt-wc)\n",
"\t\t#2-Also high temperature heat exchanger Inlet\n",
"\t\t#3-(-do-) Exit\n",
"qh = Cp*(T3-T2)\t\t#Heat of source in kJ/kg\n",
"\t\t#4-high temp heat exchanger inlet\n",
"\t\t#1-(-do-) Exit\n",
"ql = Cp*(T4-T1)\t\t#Heat of sink in kJ/kg\n",
"nth = wnet/qh\n",
"print (' Thermal Efficiency of cycle = %.1f percent',nth*100)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"('Temperature T2 = %.1f K', 623.4838568301909)\n",
"(' Compressor work = %.1f kJ/kg ', 336.6249922575117)\n",
"(' Temperature T3 = %.1f K', 1373.2)\n",
"(' Temperature T4 = %.1f K', 810.5386435092256)\n",
"(' Turbine work = %.1f kJ/kg', 564.9120019167375)\n",
"(' Net work = %.1f kJ/kg', 228.28700965922582)\n",
"(' Thermal Efficiency of cycle = %.1f percent', 30.32847854912508)\n"
]
}
],
"source": [
"# -*- coding: utf8 -*-\n",
"from __future__ import division\n",
"#Example: 12.2\n",
"''' '''\n",
"\n",
"#Variable Declaration: \n",
"\t\t#Standard brayton cycle\n",
"\n",
"\n",
"\t\t#Calculation mistake in book\n",
"\t\t#1-Inlet for compressor\n",
"\t\t#2-Exit for compressor\n",
"\t\t#T-Temperature at a state\n",
"\t\t#P-Pressure at a state\n",
"T1 = 288.2\t\t#K\n",
"P2 = 1000\t\t#kPa\n",
"P1 = 100\t\t#kPa\n",
"k = 1.4\n",
"T2s = T1*(P2/P1)**(1-1/k)\t\t#K\n",
"nc = .80\t\t#Compressor Efficiency\n",
"T2 = T1+(T2s-T1)/0.80\n",
"Cp = 1.004\t\t#Specific heat at constant pressure in kJ/kg\n",
"wc = Cp*(T2-T1)\t\t#compressor work in kJ/kg\n",
"print ('Temperature T2 = %.1f K',T2)\n",
"print (' Compressor work = %.1f kJ/kg ',wc)\n",
"\t\t#3-Turbine Inlet\n",
"\t\t#4-Turbine Exit\n",
"P4 = P1\n",
"P3 = P2\n",
"T3 = 1373.2\t\t#K\n",
"T4s = T3*(P4/P3)**(1-1/k)\t\t#K\n",
"nt = 0.85\t\t#turbine Efficiency\n",
"T4 = T3-(T3-T4s)*0.85\n",
"wt = Cp*(T3-T4)\n",
"wnet = wt-wc\n",
"print (' Temperature T3 = %.1f K',T3)\n",
"print (' Temperature T4 = %.1f K',T4)\n",
"print (' Turbine work = %.1f kJ/kg',wt)\n",
"print (' Net work = %.1f kJ/kg',wt-wc)\n",
"\t\t#2-Also high temperature heat exchanger Inlet\n",
"\t\t#3-(-do-) Exit\n",
"qh = Cp*(T3-T2)\t\t#Heat of source in kJ/kg\n",
"\t\t#4-high temp heat exchanger inlet\n",
"\t\t#1-(-do-) Exit\n",
"ql = Cp*(T4-T1)\t\t#Heat of sink in kJ/kg\n",
"nth = wnet/qh\n",
"print (' Thermal Efficiency of cycle = %.1f percent',nth*100)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"('Thermal efficiency = %.1f percent', 59.42413919202417)\n"
]
}
],
"source": [
"# -*- coding: utf8 -*-\n",
"from __future__ import division\n",
"#Example: 12.3\n",
"''' '''\n",
"\n",
"#Variable Declaration: \n",
"\n",
"\n",
"wnet = 395.2\t\t#kJ/kg from example no 1\n",
"\t\t#Tx = T4\n",
"Tx = 710.8\t\t#K from example no 1\n",
"T3 = 1373.2\t\t#K from example no 1\n",
"Cp = 1.004\t\t#specific heat in kJ/kg \n",
"qh = Cp*(T3-Tx)\n",
"nth = wnet/qh\n",
"print ('Thermal efficiency = %.1f percent',nth*100) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"('Isothermal work in compressor = %.1f kJ/kg ', -190.4546418308537)\n",
"(' Isothermal work in turbine = %.1f kJ/kg', 907.4681268637344)\n"
]
}
],
"source": [
"# -*- coding: utf8 -*-\n",
"from __future__ import division\n",
"#Example: 12.4\n",
"''' '''\n",
"from math import log\n",
"#Variable Declaration: \n",
"\n",
"\n",
"R = 0.287\t\t#gas constant \n",
"T1 = 288.2\t\t#compressor temperature K\n",
"T2 = 1373.2\t\t#K turbine temperature K\n",
"\t\t#Pe/Pi = c = 10, Pi/Pe = 1/c from example 12.1\n",
"c = 10\n",
"wc = -R*T1*log(c)\n",
"print ('Isothermal work in compressor = %.1f kJ/kg ',wc)\n",
"wt = -R*T2*log(1/c)\n",
"print (' Isothermal work in turbine = %.1f kJ/kg',wt) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"('Velocity of air leaving the nozel = %.0f m/s', 889.4375751001304)\n"
]
}
],
"source": [
"# -*- coding: utf8 -*-\n",
"from __future__ import division\n",
"#Example: 12.5\n",
"''' '''\n",
"from math import sqrt\n",
"#Variable Declaration: \n",
"\n",
"\n",
"\t\t#1-compressor inlet\n",
"\t\t#2-Compressor exit\n",
"\t\t#P-Pressure at given point\n",
"\t\t#T-Temperature at given point\n",
"P1 = 100\t\t#kPa\n",
"P2 = 1000\t\t#kPa\n",
"T1 = 288.2\t\t#K\n",
"T2 = 556.8\t\t#K\n",
"wc = 269.5\t\t#from ex 12.1 work done in compressor in kJ/kg\n",
"\t\t#2-Burner inlet\n",
"\t\t#3-Burner exit\n",
"P3 = 1000\t\t#kPa\n",
"T3 = 1373.2\t\t#K\n",
"\t\t#wc = wt\n",
"Cp = 1.004\t\t#specific enthalpy of heat at constant pressure in kJ/kg\n",
"k = 1.4\n",
"T4 = T3-wc/Cp\n",
"P4 = P3*(T4/T3)**(1-1/k)\n",
"\t\t#from s4 = s5 and h4 = h5+v2/2 we get\n",
"T5 = 710.8\t\t#K, from second law\n",
"v = sqrt(2*Cp*1000*(T4-T5))\t\t#m/s\n",
"print ('Velocity of air leaving the nozel = %.0f m/s',v)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 6"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"('Coefficient of performance = %.3f ', 1.712857850240205)\n",
"(' Rate at which the air enter the compressor = %.3f kg/s ', 0.013985866348928795)\n"
]
}
],
"source": [
"# -*- coding: utf8 -*-\n",
"from __future__ import division\n",
"#Example: 12.6\n",
"''' '''\n",
"\n",
"#Variable Declaration: \n",
"\n",
"\n",
"\t\t#1-compressor inlet\n",
"\t\t#2-compressor exit\n",
"P1 = 100\t\t#kPa\n",
"P2 = 500\t\t#kPa\n",
"k = 1.4\n",
"rp = P2/P1\n",
"cop = (rp**(1-1/k)-1)**-1\n",
"print ('Coefficient of performance = %.3f ',cop)\n",
"\t\t#3-Expander inlet\n",
"\t\t#4-Expander exit\n",
"P3 = P2\n",
"P4 = P1\n",
"T3 = 288.23\t\t#K, given and fixed\n",
"T4 = T3/(P3/P4)**(1-1/k)\n",
"T1 = 253.2\t\t#K, given\n",
"Cp = 1.004\t\t#Specific heat at cons pressure in kJ/kg\n",
"ql = Cp*(T1-T4)\t\t#heat released in kJ/kg\n",
"P = 1\t\t#power required in kW \n",
"ms = P/ql\t\t#kg/s\n",
"print (' Rate at which the air enter the compressor = %.3f kg/s ',ms) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 7"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Temperature at compressor exit, T2 = %.1f K 723.925669561\n",
" Pressure at compressor exit, P2 = %.3f MPa 2.51188643151\n",
" Initial Temperature during heat additon process, T3 = %.0f K 3234.38592061\n",
" Initial pressure during heat addition process, P3 = %.3f MPa 11.222713118\n",
" Final temperature during heat addition process, T4 = %.1f K 1287.63222733\n",
" Final pressure during heat addition process, P4 = %.4f MPa 0.446784256534\n",
" Thermal efficiency = %.1f percent 96.0189282945\n",
" Mean effective pressure = %.0f kPa 1455.36957602\n"
]
}
],
"source": [
"# -*- coding: utf8 -*-\n",
"from __future__ import division\n",
"#Example: 12.7\n",
"''' '''\n",
"\n",
"#Variable Declaration: \n",
"\n",
"\n",
"\t\t#1-compressor inlet\n",
"\t\t#2-compressor exit\n",
"P1 = 100\t\t#kPa\n",
"T1 = 288.2\t\t#K\n",
"R = 0.287\t\t#gas constant\n",
"v1 = R*T1/P1\t\t#specific volume at inlet in m**3/kg\n",
"rv = 10\t\t#compression ratio given\n",
"k = 1.4\t\t#constant\n",
"T2 = T1*rv**(k-1)\t\t#K\n",
"print 'Temperature at compressor exit, T2 = %.1f K ',T2\n",
"P2 = P1*rv**k\t\t#kPa\n",
"print ' Pressure at compressor exit, P2 = %.3f MPa ',P2/1000\n",
"v2 = v1/rv\t\t#specific heat at exit in m**3/kg\n",
"\t\t#23-heat addition process\n",
"\t\t#q23 = Cv*(T3-T2) = 1800 kJ/kg given\n",
"q23 = 1800\t\t#kJ/kg heat addition, given\n",
"Cv = 0.717\t\t#specific heat at constant volume in kJ/kg\n",
"T3 = T2+q23/Cv\t\t#K\n",
"print ' Initial Temperature during heat additon process, T3 = %.0f K ',T3\n",
"P3 = P2*(T3/T2)\t\t#kPa\n",
"print ' Initial pressure during heat addition process, P3 = %.3f MPa ',P3/1000\n",
"r = 10\t\t#k = V4/V3 = P3/P4\n",
"T4 = T3*(1/r)**(k-1)\n",
"print ' Final temperature during heat addition process, T4 = %.1f K ',T4\n",
"P4 = P3/r**k\t\t#kPa\n",
"print ' Final pressure during heat addition process, P4 = %.4f MPa ',P4/1000\n",
"nth = 1-1/r**k\t\t#thermal efficiency\n",
"print ' Thermal efficiency = %.1f percent ',nth*100\n",
"q41 = Cv*(T1-T4)\t\t#/heat for process 4-1 in kJ/kg\n",
"wnet = q23+q41\n",
"mep = wnet/(v1-v2)\t\t#effective mean pressure n kPa\n",
"print ' Mean effective pressure = %.0f kPa ',mep"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 8"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Temperature at compressor exit, T2 = %.1f K 955.225647797\n",
" Pressure at compressor exit, P2 = %.3f MPa 6.62890803468\n",
" Initial Temperature during heat addition process, T3 = %.0f K 2748.05433306\n",
" Final temperature during heat addition process, T4 = %.0f K 1265.26371322\n",
" Thermal efficiency = %.1f percent 61.0802954233\n",
" Mean effective pressure = %.0f kPa 1399.18182622\n"
]
}
],
"source": [
"# -*- coding: utf8 -*-\n",
"from __future__ import division\n",
"#Example: 12.8\n",
"''' '''\n",
"\n",
"#Variable Declaration: \n",
"\n",
"\n",
"\t\t#1-compressor inlet\n",
"\t\t#2-compressor exit\n",
"P1 = 100\t\t#kPa\n",
"T1 = 288.2\t\t#K\n",
"R = 0.287\t\t#gas constant\n",
"v1 = R*T1/P1\t\t#specific volume at inlet in m**3/kg\n",
"rv = 20\t\t#compression ratio given\n",
"k = 1.4\t\t#constant\n",
"T2 = T1*rv**(k-1)\t\t#K\n",
"print 'Temperature at compressor exit, T2 = %.1f K ',T2\n",
"P2 = P1*rv**k\t\t#kPa\n",
"print ' Pressure at compressor exit, P2 = %.3f MPa ',P2/1000\n",
"v2 = v1/rv\t\t#specific heat at exit in m**3/kg\n",
"\t\t#23-heat addition process\n",
"\t\t#q23 = Cv*(T3-T2) = 1800 kJ/kg given\n",
"q23 = 1800\t\t#kJ/kg heat addition, given\n",
"Cv = .717\n",
"Cp = 1.004\t\t#specific heat at constant pressure in kJ/kg\n",
"T3 = T2+q23/Cp\t\t#K\n",
"print ' Initial Temperature during heat addition process, T3 = %.0f K ',T3\n",
"r = T3/T2\t\t#T3/T2 = V3/V2 = r\n",
"v3 = r*v2\n",
"T4 = T3/(v1/v3)**(k-1)\n",
"print ' Final temperature during heat addition process, T4 = %.0f K ',T4\n",
"q41 = Cv*(T1-T4)\t\t#/heat for process 4-1 in kJ/kg\n",
"wnet = q23+q41\n",
"mep = wnet/(v1-v2)\t\t#effective mean pressure in kPa\n",
"qh = 1800\t\t#heat transfer in kJ/kg\n",
"nth = wnet/qh\t\t#thermal efficiency\n",
"\n",
"print ' Thermal efficiency = %.1f percent ',nth*100\n",
"print ' Mean effective pressure = %.0f kPa ',mep"
]
}
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