{
"metadata": {
"name": ""
},
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter15:Air Capacity and SuperCharging"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 15.1 page no: 474"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Input data\n",
"Vs=0.0028 #Swept volume in m**3\n",
"N=3000 #Speed of the engine in rpm\n",
"ip=12.5 #The average indicated power developed in kW/m**3\n",
"nv=85 #Volumetric efficiency in percent\n",
"p1=1.013 #The atmospheric pressure in bar\n",
"T1=288 #The atmospheric temperature in K\n",
"ni=74 #Isentropic efficiency in percent\n",
"pr=1.6 #The pressure ratio\n",
"nm=78 #All mechanical efficiencies in percent\n",
"g=1.4 #Adiabatic index\n",
"R=287 #Real gas constant in J/kgK\n",
"Cp=1.005 #The specific heat of gas in kJ/kgK\n",
"\n",
"#Calculations\n",
"Vs1=(Vs*(N/2.0)) #Volume swept by the piston per minute in m**3/min\n",
"Vi=(nv/100.0)*Vs1 #Unsupercharged induced volume in m**3/min\n",
"p2=pr*p1 #Blower delivery pressure in bar\n",
"T21=T1*(p2/p1)**((g-1)/g) #Temperature after isentropic compression in K\n",
"T2=T1+((T21-T1)/((ni/100.0))) #Blower delivery temperature in K\n",
"Ve=(Vs1*p2*T1)/(T2*p1) #Equivalent volume at 1.013 bar and 15 degree centigrade in m**3/min\n",
"nv1=(Ve/Vs1)*100 #Volumetric efficiency of supercharged engine in percent\n",
"Vii=Ve-Vi #Increase in induced volume in m**3/min\n",
"ipa=ip*Vii #Increase in ip from air induced in kW\n",
"ipi=((p2-p1)*10**5*Vs1)/(60*1000) #Increase in ip due to increased induction pressure in kW\n",
"ipt=ipa+ipi #Total increase in ip in kW\n",
"bp=ipt*(nm/100.0) #Increase in engine bp in kW\n",
"ma=(p2*(Vs1/60.0)*10**5)/(R*T2) #Mass of air delivered per second by blower in kg/s\n",
"P=ma*Cp*(T2-T1) #Power input to blower in kW\n",
"Pd=P/(nm/100.0) #Power required to drive the blower in kW\n",
"bpn=bp-Pd #Net increase in bp in kW\n",
"bpu=ip*Vi*(80/100.0) #The bp of unsupercharged engine in kW\n",
"bpp=(bpn/(bpu))*100 #Percentage increase in bp in percent\n",
"\n",
"#Output\n",
"print\"The volumetric efficiency of supercharged engine = \",round(nv1,0),\"percent\"\n",
"print\"The increase in brake power by supercharging = \",round(bpn,1),\" kW \"\n",
"print\"The percentage increase in brake power = \",round(bpp,1),\" percent \"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The volumetric efficiency of supercharged engine = 134.0 percent\n",
"The increase in brake power by supercharging = 15.1 kW \n",
"The percentage increase in brake power = 42.3 percent \n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 15.2 page no: 477"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Input data\n",
"p=1.013 #The pressure at the sea level in bar\n",
"T=283 #The temperature at the sea level in K\n",
"bp=275.0 #Brake power in kW\n",
"N=1800.0 #The speed of the engine in rpm\n",
"a=20 #Air fuel ratio \n",
"R=287 #The real gas constant in J/kgK\n",
"bsfc=0.24 #Brake specific fuel consumption in kg/kWh\n",
"nv=80 #Volumetric efficiency in percent\n",
"p2=0.75 #The atmospheric pressure at altitude in bar\n",
"P=9 #The power consumed by supercharger of the total power produced by the engine in percent\n",
"T2=303 #The temperature of air leaving the supercharger in K\n",
"\n",
"#Calculations\n",
"mf=(bsfc*bp)/60.0 \n",
"ma1=mf*a \n",
"ma=(2/N)*ma1 \n",
"dai=(p*10**5)/(R*T) \n",
"Vd=(ma/(dai*(nv/100.0))) \n",
"pmb=(bp*2*60*1000)/(Vd*N*10**5) \n",
"GP=bp/(1-0.09) \n",
"ma2=(ma1/bp)*GP \n",
"ma1=(ma2*2)/N \n",
"p21=((R*T2*ma1)/((nv/100.0)*Vd))/10.0**5 \n",
"pi=p21-p2 \n",
"\n",
"#Output\n",
"print\"(a) The engine capacity Vd = \",round(Vd,3),\"m**3\" \n",
"print\"The bmep of the unsupercharged engine = \",round(pmb,3),\"bar\" \n",
"print\"(b) Increase in air pressure required in the supercharged = \",round(pi,3),\"bar\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) The engine capacity Vd = 0.024 m**3\n",
"The bmep of the unsupercharged engine = 7.483 bar\n",
"(b) Increase in air pressure required in the supercharged = 0.442 bar\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 15.3 page no: 479"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Input data\n",
"Vs=0.003 #Swept volume in m**3\n",
"bmep=9 #Brake mean effective pressure in bar\n",
"N=4000 #The speed of the engine in rpm\n",
"ni=30.0 #Indicated thermal efficiency in percent\n",
"nm=90 #Mechanical efficiency in percent\n",
"bmep1=12 #The brake mean effective pressure of other engine in bar\n",
"N1=4000 #The speed of other engine in rpm\n",
"ni1=25 #The indicated thermal efficiency of other engine in percent\n",
"nm1=91 #The mechanical efficiency of other engine in percent\n",
"m=200 #The mass of naturally aspired engine in kg\n",
"m1=220 #The mass of supercharged engine in kg\n",
"CV=44000 #The calorific value of the fuel in kJ/kg\n",
"\n",
"#Calculations\n",
"bp=(bmep*10**5*Vs*N)/(2.0*60.0*1000) \n",
"ip=bp/(nm/100.0) \n",
"mf=(ip)/((ni/100.0)*CV) \n",
"bp1=(bmep1*10**5*Vs*N1)/(2.0*60.0*1000) \n",
"ip1=bp1/(nm1/100.0) \n",
"mf1=ip1/((ni1/100.0)*CV) \n",
"mf2=mf*3600 \n",
"mf3=mf1*3600 \n",
"x=((200/90.0)-(220/120.0))/((43.2/120.0)-(27.27/90.0)) \n",
"\n",
"#Output\n",
"print\"The maximum hours required for supply of sufficient fuel = \",round(x,3),\"hr\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The maximum hours required for supply of sufficient fuel = 6.823 hr\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 15.4 Page no 480"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Input data\n",
"d=0.1 #The diameter of the bore in m\n",
"L=0.12 #The length of the stroke in m\n",
"N=3000 #The speed of the engine in rpm\n",
"n=4 #Number of cylinders\n",
"R=287 #Real gas constant in J/kgK\n",
"t=120 #Output Torque in Nm\n",
"nm=85 #The mechanical efficiency of the engine in percent\n",
"T1=288 #The inlet temperature of air into compressor in K\n",
"p1=1 #The inlet pressure of air into compressor in bar\n",
"Q=1200 #Heat rejected rate in kJ/min\n",
"T=328 #The outlet temperature of air in K\n",
"p=1.7 #The outlet pressure of air in bar\n",
"nv=90 #Volumetric efficiency in percent\n",
"Cp=1.005 #Specific heat of gas in kJ/kg\n",
"\n",
"#Calculations\n",
"import math\n",
"bp=(2*math.pi*N*t)/(60.0*1000.0) #The brake power in kW\n",
"ip=bp/(nm/100.0) #The indicated power in kW\n",
"pmi=((ip*2*60*1000*4)/(L*(math.pi*d**2)*N*n))/10.0**5 #The mean effective pressure in bar\n",
"Vs=(math.pi/4.0)*d**2*L #Swept volume in m**3\n",
"Vs1=Vs*(N/2.0)*n #Volume swept by the piston per min \n",
"V1=(nv/100.0)*Vs1 #Rate of volume flow of air into the engine in m**3/min\n",
"me=((p*10**5*V1)/(R*T))*60 #Rate of mass flow of air into the engine in kg/h\n",
"E=Q/60.0 #Energy balance in the after cooling in kJ/s\n",
"T2=((bp/E)*T-T1)/((bp/E)-1) #The outlet temperature of air in K\n",
"mc=((bp)/(Cp*(T2-T1)))*3600 #Mass flow rate in kg/h\n",
"maf=mc-me #Rate of air flow available to the consumer in kg/h\n",
"\n",
"#Output\n",
"print\"(a) The imep of the supercharged engine = \",round(pmi,3),\"bar\"\n",
"print\"(b) The rate of air consumed by the engine = \",round(me,1),\"kg/h\" \n",
"print\"(c) The rate of air flow available to the consumer = \",round(maf,1),\"kg/h\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) The imep of the supercharged engine = 4.706 bar\n",
"(b) The rate of air consumed by the engine = 551.5 kg/h\n",
"(c) The rate of air flow available to the consumer = 1033.5 kg/h\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 15.5 page no: 482"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Input data\n",
"Vs=0.0045 #Swept volume in m**3\n",
"N=4000.0 #The speed of the engine in rpm \n",
"nv=150.0 #Overall volumetric efficiency in percent\n",
"ni=90.0 #Isentropic efficiency of the compressor in percent\n",
"nm=85.0 #Mechanical efficiency in percent\n",
"T=330.0 #The temperature of compressed air after cooler in K\n",
"p2=1.8 #The pressure of the compressed air in bar\n",
"T1=290.0 #The ambient temperature of air in K\n",
"p1=1.0 #The pressure of the ambient condition in bar\n",
"R=287.0 #The real gas constant in J/kgK\n",
"g=1.4 #Adiabatic index\n",
"Cp=1.005 #The specific heat of gas in kJ/kgK\n",
"\n",
"#Calculations\n",
"T21=T1*(p2/p1)**((g-1)/g) \n",
"T2=T1+((T21-T1)/(ni/100.0)) \n",
"Vs1=Vs*(N/(2*60)) # m**3/s\n",
"Va=(nv/100)*Vs1 \n",
"d=(p1*10**5)/(R*T1) # kg/m**3\n",
"ma=d*Va # kg/s\n",
"Q=ma*Cp*(T2-T) # kJ/s\n",
"P=ma*Cp*(T2-T1) # kW\n",
"Pa=P/(nm/100.0) \n",
"\n",
"#Output\n",
"print \"(a) The rate of heat rejected from the engine after cooler = \",round(Q,2),\"kJ/s\" \n",
"print\"(b) The power absorbed by the supercharger from the engine = \",round(Pa,1),\"kW\" \n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) The rate of heat rejected from the engine after cooler = 5.14 kJ/s\n",
"(b) The power absorbed by the supercharger from the engine = 18.8 kW\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 15.6 page no: 483"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Input data\n",
"p1=0.98 #The inlet pressure of air in bar\n",
"T1=290.0 #The inlet temperature of air in K\n",
"p2=1.8 #The pressure of air delivered to the engine in bar\n",
"a=20.0 #The air fuel ratio \n",
"T3=850.0 #The temperature of the exhaust gases leaving the engine in K\n",
"p3=1.6 #The pressure of the exhaust gases leaving the engine in bar\n",
"p4=1.03 #The turbine exhaust pressure in bar\n",
"nc=80.0 #The isentropic efficiency of compressor in percent\n",
"nt=85.0 #The isentropic efficiency of turbine in percent\n",
"Cpa=1.005 #The specific heat of air in kJ/kgK\n",
"Cpg=1.15 #The specific heat of gas in kJ/kgK\n",
"g=1.33 #isentropic index\n",
"h=1.0 #Adiabatic index\n",
"\n",
"#Calculations\n",
"T21=T1*(p2/p1)**(0.286) #value taken in book (g-1/g)=0.286 \n",
"T2=T1+((T21-T1)/(nc/100.0)) \n",
"T22=T2-273 \n",
"T41=T3*(p4/p3)**((g-1)/g) \n",
"T4=T3-((nt/100.0)*(T3-T41)) \n",
"T44=T4-273 \n",
"mf=1.0 # kg/s\n",
"ma=mf*a # kg/s\n",
"Wc=ma*Cpa*(T2-T1) # kW\n",
"mg=ma+mf #Mass flow rate of gas in kg/s\n",
"Wt=mg*Cpg*(T3-T4) \n",
"Pt=(Wc/Wt)*100 \n",
"\n",
"#Output\n",
"print\"(a) The temperature of the air leaving the compressor = \",round(T22,0),\"degree centigrade\" \n",
"print\"(b) The temperature of gases leaving the turbine = \",round(T44,0),\"degree centigrade\" \n",
"print\"(c) The mechanical power used to run the turbocharger = \",round(Pt,1),\"percent\" \n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) The temperature of the air leaving the compressor = 86.0 degree centigrade\n",
"(b) The temperature of gases leaving the turbine = 502.0 degree centigrade\n",
"(c) The mechanical power used to run the turbocharger = 76.6 percent\n"
]
}
],
"prompt_number": 22
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 15.7 page no: 485"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Input data\n",
"a=14.0 #Air fuel ratio \n",
"T1=288 #The ambient temperature of air in K\n",
"T2=(288-23) #The evaporation of fuel cause 23 degree C drop in mixture temperature in K\n",
"p=1.3 #Pressure ratio \n",
"nc=75 #The isentropic efficiency of the compressor in percent\n",
"Cpm=1.05 #The specific heat of the mixture in kJ/kgK\n",
"Cpa=1.005 #The specific heat of air in kJ/kgK\n",
"g=1.33 #Adiabatic index\n",
"h=1.4 #Isentropic index\n",
"ma=1 #Mass flow rate of air in kg/s\n",
"\n",
"#Calculations\n",
"T31=T2*p**((g-1)/g) \n",
"T3=T2+((T31-T2)/(nc/100.0))\n",
"mm=1+(1/a)\n",
"Wc1=mm*Cpm*(T3-T2)\n",
"T21=T1*p**((h-1)/h)\n",
"T4=T1+((T21-T1)/(nc/100.0))\n",
"T4_=317 #approx value taken in book of T4=317\n",
"Wc2=ma*Cpa*(T4_-T1) \n",
"T5=T4-23\n",
"Ps=((Wc2-round(Wc1,0))*100)/Wc2\n",
"\n",
"#Output\n",
"print\"(a) The power required by the compressor before the supercharger = \",round(Wc1,0),\"kW/kg of air per second\"\n",
"print\"(b) The power required by the compressor after the supercharger = \",round(Wc2,1),\"kW/kg of air per second\" \n",
"print\"Percentage of turbine power used to run the compressor = \",round(Ps,3),\"percent\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) The power required by the compressor before the supercharger = 27.0 kW/kg of air per second\n",
"(b) The power required by the compressor after the supercharger = 29.1 kW/kg of air per second\n",
"Percentage of turbine power used to run the compressor = 7.36 percent\n"
]
}
],
"prompt_number": 34
}
],
"metadata": {}
}
]
}