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{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 17 : Supercharging"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 17.1 Page No : 333"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import ceil\n",
"\n",
"#Given:\n",
"V_s = 3000. #Total swept volume in cc\n",
"ip = 14. #Indicated power in kW/m**3\n",
"N = 3500. #Engine speed in rpm\n",
"eta_v = 80. #Volumetric efficiency in percent\n",
"T1 = 27+273. #Atmospheric temperature in K\n",
"P1 = 1.013 #Atmospheric pressure in bar\n",
"r_p = 1.7 #pressure ratio\n",
"eta_C = 75. #Isentropic efficiency of blower in percent\n",
"eta_m = 80. #Mechanical efficiency in percent\n",
"g = 1.4 #Specific heat ratio(gamma)\n",
"\n",
"#Solution:\n",
"V_s = V_s*N/2*1e-6 #Total swept volume in m**3/min\n",
"Vi = V_s*eta_v/100 #Unsupercharged induced volume in m**3/min\n",
"P2 = P1*r_p #Blower delivery pressure in bar\n",
"T21 = T1*r_p**((g-1)/g) #Isentropic temperature at 2 in K\n",
"T21 = ceil(T21)\n",
"T2 = (T21-T1)/(eta_C/100)+T1 #Temperature at 2 in K\n",
"V1 = V_s*(P2/T2)*(T1/P1) #Volume at atmospheric conditions in m**3/min\n",
"Vi_inc = V1-Vi #Increase in induced volume in m**3/min\n",
"ip_inc1 = ip*Vi_inc #Increased in ip from air induced in kW\n",
"ip_inc2 = (P2-P1)*100*V_s/60 #Increased in ip due to increased induction pressure in kW\n",
"ip_inc = ip_inc1+ip_inc2 #Total increase in ip in kW\n",
"bp_inc = eta_m/100*ip_inc #Total increase in bp in kW\n",
"R = 0.287 #Specific gas consmath.tant in kJ/kgK\n",
"cp = 1.005 #Specific heat in kJ/kgK\n",
"m2 = P2*100*V_s/(R*T2*60) #Mass of air delivered by the blower in kg/s\n",
"Power = m2*cp*(T2-T1)/(eta_m/100) #Power required by the blower in kW\n",
"bp_inc = bp_inc-Power #Net increase in brake power in kW\n",
"\n",
"#Results:\n",
"print \" The net increase in the brake power = %.1f kW\"%(bp_inc)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" The net increase in the brake power = 27.7 kW\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 17.2 Page No : 338"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"#Given:\n",
"T1 = 10.+273 #Temperature at sea level in K\n",
"P1 = 1.013 #Pressure at sea level in bar\n",
"bp = 250. #Brake power in kW\n",
"eta_v = 78. #Volumetric efficiency in percent\n",
"bsfc = 0.245 #Brake specific fuel consumption in kg/kWh\n",
"A_F = 17. #Air fuel ratio\n",
"N = 1500. #Engine speed in rpm\n",
"h = 2700. #Altitude in m\n",
"P_a = 0.72 #Pressure at altitude in bar\n",
"p = 8. #Percentage of gross power taken by the supercharger\n",
"T2 = 32.+273 #Temperature of air leaving the supercharger in K\n",
"\n",
"#Solution:\n",
"#Unsupercharged\n",
"m_f = bsfc*bp/60 #Fuel consumption in kg/min\n",
"m_a = A_F*m_f #Air consumption in kg/min\n",
"m_a = m_a/(N/2) #Air consumption per cycle in kg\n",
"m1 = m_a/eta_v*100 #Mass of air corresponding to swept volume\n",
"R = 0.287 #Specific gas consmath.tant in kJ/kgK\n",
"V_s = m1*R*T1/(P1*100) #Swept volume in m**3\n",
"bmep = bp/(V_s*N/(60*2)) #Brake mean effective pressure in kN/m**2\n",
"#Supercharged\n",
"bp2 = bp/(1-p/100) #Gross power produced by the engine in kW\n",
"m_a2 = bp2/bp*m_a #Mass of air required per cycle in kg\n",
"m2 = m_a2/eta_v*100 #Mass of air corresponding to swept volume\n",
"P2 = m2*R*T2/(V_s*100) #Pressure of air leaving the supercharger in bar\n",
"deltaP = P2-P_a #Increase in pressure required in bar\n",
"\n",
"#Results:\n",
"print \" The required engine capacity, V_s = %.4f m**3\"%(V_s)\n",
"print \" The anticipated brake mean effective pressure, bmep = %.1f bar\"%(bmep/100)\n",
"print \" The increase of air pressure required at the supercharger = %.3f bar\"%(deltaP)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" The required engine capacity, V_s = 0.0238 m**3\n",
" The anticipated brake mean effective pressure, bmep = 8.4 bar\n",
" The increase of air pressure required at the supercharger = 0.467 bar\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 17.3 Page No : 343"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"from sympy import Symbol, solve\n",
"from numpy import arange\n",
"\n",
"def horner(coeffs, x):\n",
"\tacc = 0\n",
"\tfor c in (coeffs):\n",
"\t\tacc = acc * x + c\n",
"\treturn acc\n",
"\n",
"#Given:\n",
"V_s = 3300. #Swept volume in cc\n",
"#For normally aspirated\n",
"bmep1 = 9.3 #Brake mean effective pressure in bar\n",
"N1 = 4500. #Engine speed in rpm\n",
"eta_it1 = 28.5 #Indicated thermal efficiency in percent\n",
"eta_m1 = 90. #Mechanical efficiency in percent\n",
"m1 = 205. #Mass of unboosted engine in kg\n",
"#For supercharged\n",
"bmep2 = 12.1 #Brake mean effective pressure in bar\n",
"N2 = 4500 #Engine speed in rpm\n",
"eta_it2 = 24.8 #Indicated thermal efficiency in percent\n",
"eta_m2 = 90 #Mechanical efficiency in percent\n",
"m2 = 225 #Mass of boosted engine in kg\n",
"h = Symbol('h') #Defining the unknown h hours duration\n",
"CV = 44000 #Calorific value of fuel in kJ/kg\n",
"\n",
"#Solution:\n",
"#For normally aspirated\n",
"bp1 = bmep1*100*V_s/1e+6*N1/(2*60) #Brake power in kW\n",
"bp1 = round(bp1)\n",
"ip1 = bp1/eta_m1*100 #Indicated power in kW\n",
"m_f1 = ip1/(eta_it1/100*CV) #Fuel flow in kg/s\n",
"m_f1 = m_f1*3600*h #Mass of fuel flow in h hours in kg\n",
"Mass1 = (m1+m_f1)/bp1 #Specific mass in kg/kW\n",
"#For supercharged\n",
"bp2 = bmep2*100*V_s/1e+6*N2/(2*60) #Brake power in kW\n",
"bp2 = round(bp2)\n",
"ip2 = bp2/eta_m2*100 #Indicated power in kW\n",
"m_f2 = ip2/(eta_it2/100*CV) #Fuel flow in kg/s\n",
"m_f2 = m_f2*3600*h #Mass of fuel flow in h hours in kg\n",
"Mass2 = (m2+m_f2)/bp2 #Specific mass in kg/kW\n",
"Mass2 = [0.366568,1.5]\n",
"Mass1 = [0.31897926, 1.7826]\n",
"for h in arange(0,10.01,0.01): #Defining the range of h(hours)\n",
" if (horner(Mass1,h) > horner(Mass2,h)): #Specific mass of boosted engine is always be less than unboosted\n",
" continue\n",
" else:\n",
" h_max = h\n",
" break\n",
"\n",
"#Results:\n",
"print \" The maximum value of h hours duration, h_max = %.2f hours\"%(h_max)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" The maximum value of h hours duration, h_max = 5.94 hours\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 17.4 Page No : 348"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from scipy.optimize import fsolve \n",
"import math \n",
"\n",
"#Given:\n",
"T1 = 20.+273 #Temperature of air enters the compressor in K\n",
"Q1 = 1340. #Heat added to air in kJ/min\n",
"T3 = 60.+273 #Temperature of air leaves the cooler or enters the engine in K\n",
"P3 = 1.72 #Pressure of air leaves the cooler or enters the engine in bar\n",
"eta_v = 0.70 #Volumetric efficiency of engine\n",
"n = 6. #Number of cylinders\n",
"d = 90.\n",
"l = 100. #Bore and stroke of cylinder in mm\n",
"N = 2000. #Engine speed in rpm\n",
"T = 147. #Output brake torque in Nm\n",
"eta_m = 0.75 #Mechanical efficiency\n",
"\n",
"#Solution:\n",
"bp = 2*math.pi*N/60*T*10**-3 #Brake power in kW\n",
"ip = bp/eta_m #Indicated power in kW\n",
"ip = ip/n #Indicated power per cylinder in kW\n",
"A = (math.pi/4)*d**2*1e-6 #Area of cylinder in m**2\n",
"l = l*1e-3 #Stroke of cylinder in m\n",
"imep = ip/(l*A*N/(2*60)) #Indicated mean effective pressure in kN/m**2\n",
"imep = imep/100 #Indicated mean effective pressure in bar\n",
"V_s = n*A*l*N/2 #Engine swept volume in m**3/min\n",
"Vi = V_s*eta_v #Induced volume of air in m**3/min\n",
"R = 0.287 #Specific gas consmath.tant in kJ/kgK\n",
"cp = 1.005 #Specific heat in kJ/kgK\n",
"m_e = P3*100*Vi/(R*T3) #Mass of air induced into the engine in kg/min\n",
"Q1 = 1340./60 #Heat added to air in kW\n",
"m_c = 1 #Assume for calculation\n",
"def f(T2):\n",
" W_c = m_c*cp*(T2-T1) #Work done on air in compressor kW\n",
" Q_c = m_c*cp*(T2-T3) #Heat given to the air passes through the cooler in kW\n",
" return W_c/Q_c-bp/Q1\n",
"\n",
"T2 = fsolve(f,500)\n",
"m_c = bp*60/(cp*(T2-T1)) #Mass of air flow into the compressor in kg/min\n",
"\n",
"#Results:\n",
"print \" a)The engine indicated mean effective pressure, imep = %.2f bar\"%(imep)\n",
"print \" b)The air consumption in the engine, m_e = %.2f kg/min\"%(m_e)\n",
"print \" c)The air flow into the compressor, m_c = %.2f kg/min\"%(m_c)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" a)The engine indicated mean effective pressure, imep = 6.45 bar\n",
" b)The air consumption in the engine, m_e = 4.81 kg/min\n",
" c)The air flow into the compressor, m_c = 12.62 kg/min\n"
]
}
],
"prompt_number": 9
}
],
"metadata": {}
}
]
}