{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter10:CI Engines-Fuel Injection System"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.1 page no: 332"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"bsfc=0.3 #The brake specific fuel consumption in kg/kWh\n",
"bp=250 #The brake power in kW\n",
"N=1500 #Number of cycles per min in rpm\n",
"CA=15 #Crank angle in degrees\n",
"pi1=30 #The pressure of air in the cylinder at the beginning of the injection in bar\n",
"pi2=60 #The pressure of air in the cylinder at the end of the injection in bar\n",
"pf1=220 #The fuel injection pressure at the beginning in bar\n",
"pf2=550 #The fuel injection pressure at the end in bar\n",
"Cd=0.65 #The coefficient of discharge for the injector \n",
"df=850 #The density of the fuel in kg/m**3\n",
"p1=1.013 #The atmospheric pressure in bar\n",
"n=4.0 #The number of orifices used in the nozzle\n",
"x=6.0 #Number of cylinders\n",
"\n",
"#Calculations\n",
"import math\n",
"mf=bsfc*bp/60.0 \n",
"F=(mf/(N/2.0))*(1/x) \n",
"s=(CA/360.0)/(N/60.0) \n",
"mf1=F/s \n",
"p1=pf1-pi1 \n",
"p2=pf2-pi2\n",
"pa=(p1+p2)/2.0\n",
"Af=(mf1/(Cd*(2*df*pa*10.0**5)**(1/2.0)))*10**6\n",
"do=((Af/n)*(4/math.pi))**(1/2.0)\n",
"\n",
"#Output\n",
"print\"The nozzle area required per injection = \" ,round(Af,3),\"mm**2\"\n",
"print\"The diameter of the orifice = \",round(do,3), \"mm\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The nozzle area required per injection = 1.067 mm**2\n",
"The diameter of the orifice = 0.583 mm\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.2 page no: 333"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"bp=30 #The brake power of the engine in kW\n",
"N=3000 #The engine speed in rpm \n",
"bsfc=0.28 #The brake specific fuel consumption in kg/kWh \n",
"Api=35 \n",
"p2=160 #The pressure at which fuel is injected in bar\n",
"CA=28 #The crank angle in degrees\n",
"p1=35 #The pressure in the combustion chamber in bar\n",
"Cv=0.92 #The coefficient of velocity \n",
"\n",
"#Calculations\n",
"import math\n",
"S=141.5/(131.5+Api) \n",
"df=S*1000 \n",
"D=(CA/360.0)/(N/60.0)\n",
"F=(bsfc*bp)/((N/2.0)*60)\n",
"mf=F/D\n",
"Cf=Cv*((2*(p2-p1)*10**5)/df)**(1/2.0)\n",
"Af=(mf/(df*Cf))*10**6\n",
"d=(4*Af/math.pi)**(1/2.0) \n",
"\n",
"#Output\n",
"print\"The velocity of injection of the fuel = \",round(Cf,1),\"m/s \"\n",
"print\"The diameter of the fuel orifice = \",round(d,3),\" mm \"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The velocity of injection of the fuel = 157.8 m/s \n",
"The diameter of the fuel orifice = 0.755 mm \n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.3 Page no 334"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"d=0.8*10**-3 #The diameter of an orifice in m\n",
"A=1.65*10**-6 #The cross sectional area in m**2\n",
"Cd=0.9 #The discharge coefficient of the orifice \n",
"Cp=0.85 #The coefficient of the passage\n",
"p1=170 #The injection pressure in bar\n",
"p2=25 #The compression pressure of the discharge in bar\n",
"df=850 #The density of the fuel in kg/m**3\n",
"\n",
"#Calculations\n",
"Q=((145/(22.931*10.0**9))**(1/2.0))*10**6 \n",
"p=170-(2.161*10**9*(Q/10.0**6)**2)\n",
"Cf=Cd*((2*(p-p2)*10**5)/df)**(1/2.0)\n",
"\n",
"#Output\n",
"print\"The discharge of fuel through the injector = \",round(Q,1),\"cm**2/s\" \n",
"print\"The jet velocity through the orifice = \",round(Cf,1),\" m/s\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The discharge of fuel through the injector = 79.5 cm**2/s\n",
"The jet velocity through the orifice = 158.2 m/s\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.4 page no: 336"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"s=20 #Spray penetration in cm\n",
"t1=15.7 #The spray penetration of 20 cm in ms\n",
"pi1=150 #The injection pressure in bar\n",
"pi2=450.0 #The injection pressure to be used in bar\n",
"p2=15 #The combustion chamber pressure in bar\n",
"d1=0.34 #The diameter of the orifice in mm\n",
"s1=20 #The penetration for an orifice in cm\n",
"d2=0.17 #If the diameter of the orifice in cm\n",
"t11=12 #The spray penetration in ms\n",
"\n",
"#Calculations\n",
"t2=(t1*(pi1-p2)**(1/2.0))/(pi2-p2)**(1/2.0)\n",
"s2=d2*(s1/d1)\n",
"t21=t11*(d2/d1)\n",
"\n",
"#Output\n",
"print\"(a) The time required for the spray to penetrate = \",round(t2,3),\"ms\"\n",
"print\"(b) The spray penetration of the orifice = \",round(s2,3),\"cm\"\n",
"print\"The time required for the spray to penetrate = \",round(t21,3),\"ms\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) The time required for the spray to penetrate = 8.746 ms\n",
"(b) The spray penetration of the orifice = 10.0 cm\n",
"The time required for the spray to penetrate = 6.0 ms\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.5 page no: 336"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"v=6.5 #The volume of fuel in the barrel in cc\n",
"d=0.3 #The dimeter of fuel pipe line in cm\n",
"l=65 #The length of the fuel pipe line in cm \n",
"vi=2.5 #The volume of fuel in the injection valve in cc\n",
"K=78.5*10**-6 #The coefficient of compressibility of the oil per bar\n",
"p1=1 #The atmospheric pressure in bar\n",
"p2=180 #The pressure due to pump in bar\n",
"v3=0.1 #The pump displacement necessary for the fuel in cc\n",
"e=0.75 #The effective stroke of the plunger in cm\n",
"\n",
"#Calculations\n",
"import math\n",
"V1=v+((math.pi*d**2)/4.0)*l+vi\n",
"V=K*V1*(p2-p1)\n",
"T=(V)+v3\n",
"L=T*(4/math.pi)*(1/(e**2))\n",
"\n",
"#Output\n",
"print\"(a) The total displacement of the plunger = \",round(T,3),\"cc\" \n",
"print\"(b) The effective stroke of the plunger = \",round(L,3),\"cm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) The total displacement of the plunger = 0.291 cc\n",
"(b) The effective stroke of the plunger = 0.659 cm\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.6 page no: 337"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"n=4.0 #Number of cylinders \n",
"N=2500 #The engine speed in rpm \n",
"P=90 #The power produced by the engine in kW\n",
"bsfc=0.28 #The brake specific fuel consumption in kg/kWh\n",
"v=3.5 #The volume of fuel in the barrel in cc\n",
"vp=2.5 #Volume of fuel in the pipe line in cc\n",
"vi=2.0 #The fuel inside the injector in cc\n",
"p1=280.0 #The average injection pressure in bar\n",
"p2=30.0 #The compression pressure of air during injection in bar\n",
"df=850.0 #The density of the fuel in kg/m**3\n",
"K=80*10**-6 #The coefficient of compressibility of fuel per bar\n",
"pi=1.0 #The pressure with which fuel enter into the barrel in bar\n",
"\n",
"#Calculations\n",
"import math\n",
"F=(bsfc*P)/((N/2.0)*60)\n",
"F1=F/n\n",
"Vf=(F1/df)*10**6\n",
"V1=v+vp+vi\n",
"V=K*V1*(p1-math.pi)\n",
"Vp=Vf+V\n",
"W=((1/2.0)*(p1-math.pi)*10**5*V*10**-6)+((p1-p2)*10**5*Vf*10**-6)\n",
"P1=(W*N)/(2*60*1000) #Power lost per cylinder in kW\n",
"P2=P1*4 #Total power lost for pumping the fuel in kW\n",
"\n",
"#Output \n",
"print\"The displacement volume of one plunger per cycle = \",round(Vp,3),\"cc\" \n",
"print\"Total power lost for pumping the fuel = \",round(P2,3),\"kW\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The displacement volume of one plunger per cycle = 0.276 cc\n",
"Total power lost for pumping the fuel = 0.41 kW\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.7 page no: 339"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"v1=0.3 #Velocity of the pump plunger in m/s\n",
"l=0.575 #The length of the fuel pipe in m\n",
"A=1/20.0 #The cross sectional area of pipe to the plunger cylinder\n",
"a=1/40.0 #The area of nozzle hole to the pipe \n",
"p1=27.6 #Initial pressure in the line in bar \n",
"p2=27.6 #The compression pressure of the engine\n",
"K=17830*10**5 #The bulk modulus of fuel in N/m**2\n",
"df=860.0 #The density of the fuel in kg/m**3\n",
"\n",
"#Calculations\n",
"Vs=(K/df)**(1/2.0)\n",
"t=l/Vs\n",
"Vp=(1/A)*v1\n",
"p=((K/Vs)*Vp)/10.0**5\n",
"pi=p+p1\n",
"po=p1+p\n",
"vc=Vp-(a*((2*(po-p2))/df)**(1/2.0))\n",
"pr=26.8 #By trial , Pressure\n",
"Vc=pr*(Vs/(K/10.0**5))\n",
"po1=p1+p+pr\n",
"vo=a*((2*(po1-p2)*10**5)/df)**(1/2.0)\n",
"\n",
"#Output\n",
"print\"(a)The velocity of the pressure disturbance = \",round(Vs,0),\"m/s\"\n",
"print\"(b) The time taken by the disturbance to travel through the pipe line = \",round(t,4),\" s\" \n",
"print\"(c) The velocity at the pump end of the pipe line as the plunger moves = \",round(Vp,2),\" m/s\"\n",
"print\"The pressure at the pump end of pipe line as the plunger moves = \",round(pi,2),\"bar\"\n",
"print\"(d)The magnitude of the first reflected pressure = \",round(pr,2),\"bar\" \n",
"print\"The magnitude of the first reflected velocity wave =\",round(Vc,2),\"m/s\" \n",
"print\"(e)The pressure at the oriface end of the pipe line after the first reflection = \",round(po1,1),\"bar\"\n",
"print\"The velocity at the oriface end of the pipe line after the first reflection = \",round(vo,2),\" m/s \"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)The velocity of the pressure disturbance = 1440.0 m/s\n",
"(b) The time taken by the disturbance to travel through the pipe line = 0.0004 s\n",
"(c) The velocity at the pump end of the pipe line as the plunger moves = 6.0 m/s\n",
"The pressure at the pump end of pipe line as the plunger moves = 101.9 bar\n",
"(d)The magnitude of the first reflected pressure = 26.8 bar\n",
"The magnitude of the first reflected velocity wave = 2.16 m/s\n",
"(e)The pressure at the oriface end of the pipe line after the first reflection = 128.7 bar\n",
"The velocity at the oriface end of the pipe line after the first reflection = 3.83 m/s \n"
]
}
],
"prompt_number": 30
}
],
"metadata": {}
}
]
}