path: root/Basic_Engineering_Thermodynamics_by_R_Joel/14-Air_and_gas_compressors.ipynb

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 {
		   "cell_type": "markdown",
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	   "source": [
       "# Chapter 14: Air and gas compressors"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 14.1: EX14_1.sce"
		   ]
		  },
  {
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"clear;\n",
"clc;\n",
"disp(' Example 14.1');\n",
"\n",
"// aim : To determine \n",
"// (a) the free air delivered\n",
"// (b) the volumetric efficiency\n",
"// (c) the air delivery temperature\n",
"// (d) the cycle power\n",
"// (e) the isothermal efficiency\n",
"\n",
"// given values\n",
"d = 200*10^-3;// bore, [m]\n",
"L = 300*10^-3;// stroke, [m]\n",
"N = 500;// speed, [rev/min]\n",
"n = 1.3;// polytropic index\n",
"P1 = 97;// intake pressure, [kN/m^2]\n",
"T1 = 273+20;// intake temperature, [K]\n",
"P3 = 550;// compression pressure, [kN/m^2]\n",
"\n",
"// solution\n",
"// (a)\n",
"P4 = P1;\n",
"P2 = P3;\n",
"Pf = 101.325;// free air pressure, [kN/m^2]\n",
"Tf = 273+15;// free air temperature, [K]\n",
"SV = %pi/4*d^2*L;// swept volume, [m^3]\n",
"V3 = .05*SV;// [m^3]\n",
"V1 = SV+V3;// [m^3]\n",
"V4 = V3*(P3/P4)^(1/n);// [m^3]\n",
"ESV = (V1-V4)*N;// effective swept volume/min, [m^3]\n",
"// using PV/T=constant\n",
"Vf = P1*ESV*Tf/(Pf*T1);// free air delivered, [m^3/min]\n",
"mprintf('\n (a) The free air delivered is  =  %f  m^3/min\n',Vf);\n",
"\n",
"// (b)\n",
"VE = Vf/(N*(V1-V3));// volumetric efficiency\n",
"mprintf('\n (b) The volumetric efficiency is  =  %f  percent\n',VE*100);\n",
"\n",
"// (c)\n",
"T2 = T1*(P2/P1)^((n-1)/n);//  free air temperature, [K]\n",
"mprintf('\n (c) The air delivery temperature is  =  %f  C\n',T2-273);\n",
"\n",
"//  (d)\n",
"CP = n/(n-1)*P1*(V1-V4)*((P2/P1)^((n-1)/n)-1)*N/60;// cycle power, [kW]\n",
" mprintf('\n (d) The cycle power is  =  %f  kW\n',CP);\n",
"\n",
"// (e)\n",
"// neglecting clearence\n",
"W = n/(n-1)*P1*V1*((P2/P1)^((n-1)/n)-1)\n",
"Wi = P1*V1*log(P2/P1);// isothermal efficiency\n",
"IE = Wi/W;// isothermal efficiency\n",
"mprintf('\n (e) The isothermal efficiency neglecting clearence  is  =  %f percent\n',IE*100);\n",
"\n",
"// End"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 14.2: intermediate_pressure_volume_and_cycle_power.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
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"clear;\n",
"clc;\n",
"disp(' Example 14.2');\n",
"\n",
"// aim : To determine \n",
"// (a) the intermediate pressure\n",
"// (b) the total volume of each cylinder\n",
"// (c) the cycle power\n",
"\n",
"// given values\n",
"v1 = .2;// air intake, [m^3/s]\n",
"P1 = .1;// intake pressure, [MN/m^2]\n",
"T1 = 273+16;// intake temperature, [K]\n",
"P3 = .7;// final pressure, [MN/m^2]\n",
"n = 1.25;// compression index\n",
"N = 10;// speed, [rev/s]\n",
"\n",
"// solution\n",
"// (a)\n",
"P2 = sqrt(P1*P3);// intermediate pressure, [MN/m^2]\n",
"mprintf('\n (a) The intermediate pressure is  =  %f  MN/m^2\n',P2);\n",
"\n",
"// (b)\n",
"V1  = v1/N;// total volume,[m^3]\n",
"// since intercooling is perfect so 2 lie on the isothermal through1, P1*V1=P2*V2\n",
"V2 = P1*V1/P2;// volume, [m^3]\n",
"mprintf('\n (b) The total volume of the HP cylinder is  =  %f  litres\n',V2*10^3);\n",
"\n",
" // (c)\n",
" CP = 2*n/(n-1)*P1*v1*((P2/P1)^((n-1)/n)-1);// cycle power, [MW]\n",
"  mprintf('\n (c) The cycle power is  =  %f  MW\n',CP*10^3);\n",
" \n",
" // there is calculation mistake in the book so answer is not matching\n",
" \n",
" //  End"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 14.3: intermediate_pressures_effective_swept_volume_temperature_and_work_done.sce"
		   ]
		  },
  {
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	   "execution_count": null,
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	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"disp(' Example 14.3');\n",
"\n",
"// aim : To determine \n",
"// (a) the intermediate pressures\n",
"// (b) the effective swept volume of the LP cylinder\n",
"// (c) the temperature and the volume of air delivered per stroke at 15 bar\n",
"// (d) the work done per kilogram of air\n",
"\n",
"// given values\n",
"d = 450*10^-3;//  bore , [m]\n",
"L = 300*10^-3;//  stroke, [m]\n",
"cl = .05;//  clearence\n",
"P1 = 1; // intake pressure, [bar]\n",
"T1 = 273+18;// intake temperature, [K]\n",
"P4 = 15;// final delivery pressure, [bar]\n",
"n = 1.3;//  compression and expansion index\n",
"R = .29;// gas constant, [kJ/kg K]\n",
"\n",
"// solution\n",
"// (a)\n",
"k=(P4/P1)^(1/3); \n",
"// hence\n",
"P2 = k*P1;//  intermediare pressure, [bar]\n",
"P3 = k*P2;//  intermediate pressure, [bar]\n",
"\n",
"mprintf('\n (a) The intermediate pressure is P2 =  %f  bar\n',P2);\n",
"mprintf('\n     The intermediate pressure is  P3=  %f  bar\n',P3);\n",
"\n",
"// (b)\n",
"SV = %pi*d^2/4*L;//  swept volume of LP cylinder, [m^3]\n",
"// hence\n",
"V7 = cl*SV;// volume, [m^3]\n",
"V1 = SV+V7;// volume, [m^3]\n",
"// also\n",
"P7 = P2;\n",
"P8 = P1;\n",
"V8 = V7*(P7/P8)^(1/n);//  volume, [m^3]\n",
"ESV = V1-V8;// effective swept volume of LP cylinder, [m^3]\n",
"\n",
"mprintf('\n (b) The effective swept volume of the LP cylinder is  =  %f litres\n',ESV*10^3);\n",
"\n",
"// (c)\n",
"T9 = T1;\n",
"P9 = P3;\n",
"T4 = T9*(P4/P9)^((n-1)/n);// delivery temperature, [K]\n",
"// now using P4*(V4-V5)/T4=P1*(V1-V8)/T1\n",
"V4_minus_V5 = P1*T4*(V1-V8)/(P4*T1);// delivery volume, [m^3]\n",
" \n",
"mprintf('\n (c) The delivery temperature is =  %f  C\n',T4-273);\n",
"mprintf('\n      The delivery volume is =  %f  litres\n',V4_minus_V5*10^3);\n",
"\n",
"//  (d)\n",
"\n",
"W = 3*n*R*T1*((P2/P1)^((n-1)/n)-1)/(n-1);//  work done/kg ,[kJ]\n",
"mprintf('\n (d) The work done per kilogram of air is =  %f  kJ\n',W);\n",
" \n",
"// End"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 14.4: pressure_temperature_and_energy.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"disp(' Example 14.4');\n",
"\n",
"// aim : To determine \n",
"// (a) the final pressure and temperature\n",
"// (b) the energy required to drive the compressor\n",
"\n",
"// given values\n",
"rv = 5;// pressure compression ratio\n",
"m_dot = 10;// air flow rate, [kg/s]\n",
"P1 = 100;// initial pressure, [kN/m^2]\n",
"T1 = 273+20;// initial temperature, [K]\n",
"n_com = .85;// isentropic efficiency of compressor\n",
"Gama = 1.4;// heat capacity ratio\n",
"cp = 1.005;// specific heat capacity, [kJ/kg K]\n",
"\n",
"// solution\n",
"// (a)\n",
"T2_prim = T1*(rv)^((Gama-1)/Gama);// temperature after compression, [K]\n",
"// using isentropic efficiency=(T2_prim-T1)/(T2-T1)\n",
"T2 = T1+(T2_prim-T1)/n_com;//  final temperature, [K]\n",
"P2 = rv*P1;// final pressure, [kN/m^2]\n",
"mprintf('\n (a) The final temperature is  =  %f  C\n',T2-273);\n",
"mprintf('\n (b) The final pressure is  =  %f  kN/m^2\n',P2);\n",
"\n",
"// (b)\n",
"E = m_dot*cp*(T1-T2);// energy required, [kW]\n",
"mprintf('\n (b) The energy required to drive the compressor is  =  %f  kW',E);\n",
"if(E<0)\n",
"    disp('The negative sign indicates energy input');\n",
"else\n",
"    disp('The positive sign indicates energy output');\n",
"end\n",
"\n",
" //  End\n",
"\n",
""
   ]
   }
,
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		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 14.5: power_developed.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"disp(' Example 14.5');\n",
"\n",
"// aim : To determine \n",
"//  the power absorbed in driving the compressor\n",
"\n",
"// given values\n",
"FC = .68;// fuel consumption rate, [kg/min]\n",
"P1 = 93;// initial pressure, [kN/m^2]\n",
"P2 = 200;// final pressure, [kN/m^2]\n",
"T1 = 273+15;// initial temperature, [K]\n",
"d = 1.3;// density of mixture, [kg/m^3]\n",
"n_com = .82;// isentropic efficiency of compressor\n",
"Gama = 1.38;// heat capacity ratio\n",
"\n",
"// solution\n",
"R = P1/(d*T1);// gas constant, [kJ/kg K]\n",
"// for mixture\n",
"cp = Gama*R/(Gama-1);// heat capacity, [kJ/kg K]\n",
"T2_prim = T1*(P2/P1)^((Gama-1)/Gama);// temperature after compression, [K]\n",
"// using isentropic efficiency=(T2_prim-T1)/(T2-T1)\n",
"T2 = T1+(T2_prim-T1)/n_com;//  final temperature, [K]\n",
"m_dot = FC*15/60;// given condition, [kg/s]\n",
"P = m_dot*cp*(T2-T1);// power absorbed by compressor, [kW]\n",
"mprintf('\n The power absorbed by compressor is  =  %f kW\n',P);\n",
"\n",
"// End"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 14.6: power.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"disp(' Example 14.6');\n",
"\n",
"// aim : To determine \n",
"//  the power required to drive the blower\n",
"\n",
"// given values\n",
"m_dot = 1;// air capacity, [kg/s]\n",
"rp = 2;// pressure ratio\n",
"P1 = 1*10^5;// intake pressure, [N/m^2]\n",
"T1 = 273+70;// intake temperature, [K]\n",
"R = .29;// gas constant, [kJ/kg k]\n",
"\n",
"// solution\n",
"V1_dot = m_dot*R*T1/P1*10^3;// [m^3/s]\n",
"P2 = rp*P1;// final pressure, [n/m^2]\n",
"P = V1_dot*(P2-P1);// power required, [W]\n",
"mprintf('\n The power required to drive the blower is  =  %f kW\n',P*10^-3);\n",
"\n",
"// End"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 14.7: power.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"disp(' Example 14.7');\n",
"\n",
"// aim : To determine \n",
"//  the power required to drive the vane pump\n",
"\n",
"// given values\n",
"m_dot = 1;// air capacity, [kg/s]\n",
"rp = 2;// pressure ratio\n",
"P1 = 1*10^5;// intake pressure, [N/m^2]\n",
"T1 = 273+70;// intake temperature, [K]\n",
"Gama = 1.4;// heat capacity ratio\n",
"rv = .7;// volume ratio\n",
"\n",
"// solution\n",
"V1 = .995;// intake pressure(as given previous question),[m^3/s] \n",
"// using P1*V1^Gama=P2*V2^Gama, so\n",
"P2 = P1*(1/rv)^Gama;// pressure, [N/m^2]\n",
"V2 = rv*V1;// volume,[m^3/s]\n",
"P3 = rp*P1;// final pressure, [N/m^2]\n",
"P = Gama/(Gama-1)*P1*V1*((P2/P1)^((Gama-1)/Gama)-1)+V2*(P3-P2);// power required,[W]\n",
"mprintf('\n The power required to drive the vane pump is  =  %f  kW\n',P*10^-3);\n",
"\n",
"//  End"
   ]
   }
,
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		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 14.8: power_temperature_and_pressure.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
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"clear;\n",
"clc;\n",
"disp(' Example 14.8');\n",
"\n",
"// aim : To determine \n",
"//  the total temperature and pressure of the mixture\n",
"\n",
"// given values\n",
"rp = 2.5;// static pressure ratio\n",
"FC = .04;// fuel consumption rate, [kg/min]\n",
"P1 = 60;// inilet pressure, [kN/m^2]\n",
"T1 = 273+5;// inilet temperature, [K]\n",
"n_com = .84;// isentropic efficiency of compressor\n",
"Gama = 1.39;// heat capacity ratio\n",
"C2 = 120;//exit velocity from compressor, [m/s]\n",
"rm = 13;// air-fuel ratio\n",
"cp = 1.005;// heat capacity ratio\n",
"\n",
"// solution\n",
"P2 = rp*P1;// given condition, [kN/m^2]\n",
"T2_prim = T1*(P2/P1)^((Gama-1)/Gama);// temperature after compression, [K]\n",
"// using isentropic efficiency=(T2_prim-T1)/(T2-T1)\n",
"T2 = T1+(T2_prim-T1)/n_com;//  final temperature, [K]\n",
"m_dot = FC*(rm+1);// mass of air-fuel mixture, [kg/s]\n",
"P = m_dot*cp*(T2-T1);// power to drive compressor, [kW]\n",
"mprintf('\n The power required to drive compressor is  =  %f  kW\n',P);\n",
"\n",
"Tt2 = T2+C2^2/(2*cp*10^3);// total temperature,[K]\n",
"Pt2 = P2*(Tt2/T2)^(Gama/(Gama-1));// total pressure, [kN/m^2]\n",
"mprintf('\n The temperature in the engine is  =  %f  C\n',Tt2-273);\n",
"mprintf('\n The pressure in the engine cylinder is  =  %f  kN/m^2\n',Pt2);\n",
"\n",
"//  There is calculation mistake in the book\n",
"\n",
"\n",
"//  End"
   ]
   }
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