path: root/Turbines_by_Compressors_And_Fans/2-Thermodynamics.ipynb

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	   "source": [
       "# Chapter 2: Thermodynamics"
	   ]
	},
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		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 2.1: Calculation_on_a_Diffuser.sce"
		   ]
		  },
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"// scilab Code Exa 2.1 Calculation on a Diffuser \n",
"\n",
"p1=800; // Initial Pressure in kPa\n",
"T1=540;  // Initial Temperature in K\n",
"p2=580;  // Final Pressure in kPa\n",
"gamma=1.4; // Specific Heat Ratio\n",
"cp=1005; // Specific Heat at Constant Pressure in J/(kgK)\n",
"R=0.287; // Universal Gas Constant in kJ/kgK\n",
"g=9.81; // Gravitational acceleration in m/s^2\n",
"sg=13.6; // Specific Gravity of mercury\n",
"n=0.95; // Efficiency in %\n",
"AR=4; // Area Ratio of Diffuser\n",
"delp=(367)*(1e-3)*(g)*(sg); // Total Pressure Loss Across the Diffuser in kPa\n",
"pr=p1/p2; // Pressure Ratio\n",
"T2s=T1/(pr^((gamma-1)/gamma));\n",
"T2=T1-(n*(T1-T2s));\n",
"c2=sqrt(2*cp*(T1-T2));\n",
"ro2=p2/(R*T2);\n",
"c3=c2/AR;\n",
"m=0.5*1e-3*ro2*((c2^2)-(c3^2));\n",
"n_D=1-(delp/m);\n",
"disp ('%',n_D*1e2,' Efficiency of the diffuser is')\n",
"p3=(p2+n_D*m)*1e-2;\n",
"disp('m/s',c2,'the velocity of air at diffuser entry is')\n",
"disp('m/s',c3,'the velocity of air at diffuser exit is')\n",
"disp('bar',p3,'static pressure at the diffuser exit is')"
   ]
   }
,
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		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 2.2: Determining_the_infinitesimal_stage_efficiencies.sce"
		   ]
		  },
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"// Exa 2.2 Determining the infinitesimal stage efficiencies\n",
"p1=1.02; // Initial Pressure in bar\n",
"T1=300;  // Initial Temperature in K\n",
"\n",
"// part(a)\n",
"T2=315;  // Final Temperature in K\n",
"gamma=1.4; // Specific Heat Ratio\n",
"g=9.81; // Gravitational acceleration in m/s^2\n",
"sg=1; // Specific Gravity of air\n",
"delp=(1500)*(0.001)*(g)*(sg); // Total Pressure Loss Across the Diffuser in kPa\n",
"p2=p1+(0.01*delp);\n",
"pr=p2/p1; // Pressure Ratio\n",
"T2s=T1*(pr^((gamma-1)/gamma));\n",
"n_c=(T2s-T1)/(T2-T1); // Efficiency in %\n",
"n_p=((gamma-1)/gamma)*((log(p2/p1))/(log(T2/T1)));\n",
"disp ('%',n_c*100,'(a)Efficiency of the compressor is')\n",
"disp ('%',n_p*100,'and infinitesimal stage Efficiency or polytropic efficiency of the compressor is')\n",
"\n",
"// part(b) Determining the infinitesimal stage efficiency\n",
"\n",
"p2_b=2.5;  // Final pressure in bar\n",
"n_b=0.75; // Efficiency\n",
"pr_b=p2_b/p1; // Pressure Ratio\n",
"T2s_b=T1*(pr_b^((gamma-1)/gamma));\n",
"T2_b=T1+((T2s_b-T1)/n_b);\n",
"n_p_b=((gamma-1)/gamma)*((log(p2_b/p1))/(log(T2_b/T1)));\n",
"disp ('%' ,n_p_b*100,'(b)infinitesimal stage Efficiency or polytropic efficiency of the compressor is')"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 2.3: Calculations_on_air_compressor.sce"
		   ]
		  },
  {
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"// scilab Code Exa 2.3 Calculation on a compressor\n",
"p1=1.0; // Initial Pressure in bar\n",
"t1=40;  // Initial Temperature in degree C\n",
"T1=t1+273; // in Kelvin\n",
"s=8; // number of stages\n",
"m=50; // mass flow rate through the compressor in kg/s\n",
"pr=1.35; // equal Pressure Ratio in each stage\n",
"opr=pr^s; // Overall Pressure Ratio\n",
"gamma=1.4; // Specific Heat Ratio\n",
"cp=1.005; // Specific Heat at Constant Pressure in kJ/(kgK)\n",
"n=0.82; // Overall Efficiency\n",
"\n",
"// part(a) Determining state of air at the compressor exit\n",
"p9=opr*p1;\n",
"delTc=T1*(opr^((gamma-1)/gamma)-1)/n;\n",
"T9=T1+delTc;\n",
"disp('bar',p9,'(a)Exit Pressure is')\n",
"disp('K',T9,'and Exit Temperature is')\n",
"\n",
"// part(b) Determining the polytropic or small stage efficiency\n",
"n_p=((gamma-1)/gamma)*((log(p9/p1))/(log(T9/T1)));\n",
"disp('%',n_p*100,'(b)small stage Efficiency or polytropic efficiency of the compressor is')\n",
"\n",
"// part(c) Determining efficiency of each stage\n",
"n_st=(pr^((gamma-1)/gamma)-1)/(pr^(((gamma-1)/gamma)/n_p)-1);\n",
"disp ('%',n_st*100,'(c)Efficiency of each stage is')\n",
"\n",
"// part(d) Determining power required to drive the compressor\n",
"n_d=0.9; // Overall efficiency of the drive\n",
"P=m*cp*delTc/n_d;\n",
"disp ('MW' ,P/1e3,'(d)Power required to drive the compressor is')"
   ]
   }
,
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		   "metadata": {},
		   "source": [
			"## Example 2.4: compressor_with_same_temperature_rise.sce"
		   ]
		  },
  {
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"// Exa 2.4 compressor with same temperature rise\n",
"\n",
"p1=1.0; // Initial Pressure in bar\n",
"t1=40;  // Initial Temperature in degree C\n",
"T1=t1+273; // in Kelvin\n",
"s=8; // number of stages\n",
"pr=1.35;\n",
"opr=pr^s; // Overall Pressure Ratio\n",
"n=0.82; // Overall Efficiency \n",
"p9=opr*p1;\n",
"gamma=1.4;\n",
"delTc=(T1*(opr^((gamma-1)/gamma)-1)/n);\n",
"delTi=delTc/s;\n",
"T9=T1+delTc;\n",
"n_p=((gamma-1)/gamma)*((log(p9/p1))/(log(T9/T1))); // small stage Efficiency or polytropic efficiency\n",
"m=8;\n",
"T(1)=T1;\n",
"for i=1:m\n",
"    T(i+1)=T(i)+delTi;\n",
"    pr(i)=(1+(delTi/T(i)))^(n_p/((gamma-1)/gamma));\n",
"    n_st(i)=(pr(i)^((gamma-1)/gamma)-1)/(pr(i)^(((gamma-1)/gamma)/n_p)-1);\n",
"disp(T(i),'T is');\n",
"disp(pr(i),'pressure ratio is')\n",
"disp(n_st(i),'efficiency is' )\n",
"end"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 2.5: Calculations_on_three_stage_gas_turbine.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
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	   "outputs": [],
"source": [
"// scilab Code Exa 2.5 Calculation on three stage gas turbine\n",
"\n",
"p1=1.0; // Initial Pressure in bar\n",
"gamma=1.4;\n",
"T1=1500;  // Initial Temperature in K\n",
"s=3; // number of stages\n",
"opr=11; // Overall Pressure Ratio\n",
"\n",
"// part(a)Determining pressure ratio of each stage\n",
"pr=opr^(1/s); // equal Pressure Ratio in each stage\n",
"disp (pr,'(a)Pressure ratio of each stage is')\n",
"\n",
"// part(b)Determining the polytropic or small stage efficiency\n",
"n_o=0.88; // Overall Efficiency \n",
"delT=T1*(1-opr^(-((gamma-1)/gamma)))*n_o;\n",
"T2=T1-delT;\n",
"n_p=(log(T1/T2))/(((gamma-1)/gamma)*(log(opr)));\n",
"disp ('%',n_p*100,'(b)small stage Efficiency or polytropic efficiency of the turbine is')\n",
"\n",
"// part(c) Determining mass flow rate\n",
"P=30000; // Power output of the Turbine in kW\n",
"n_d=0.91; // Overall efficiency of the drive\n",
"cp=1.005; // Specific Heat at Constant Pressure in kJ/(kgK)\n",
"m=P/(cp*delT*n_d);\n",
"disp ('kg/s',m,'(c)mass flow rate is')\n",
"\n",
"// part(d) Determining efficiency of each stage\n",
"n_st=(1-pr^(n_p*(-((gamma-1)/gamma))))/(1-pr^(-((gamma-1)/gamma)));\n",
"disp ('%',n_st*100,'(d)Efficiency of each stage is')\n",
"d=3;\n",
"T(1)=T1;\n",
"for i=1:d\n",
"    delT(i)=T(i)*(1-pr^(n_p*(-((gamma-1)/gamma))));\n",
"    T(i+1)=T(i)-delT(i);\n",
"    P(i)=m*cp*delT(i);\n",
"printf('\n P(%d)=%f MW',i,P(i)*1e-3)\n",
"end"
   ]
   }
,
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		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 2.6: Calculations_on_a_Gas_Turbine.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
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"source": [
"// scilab Code Exa 2.6 calculation on a gas turbine\n",
"\n",
"funcprot(0);\n",
"p1=5; // Inlet Pressure in bar\n",
"p2=1.2; // Exit Pressure in bar\n",
"T1=500;  // Initial Temperature in K\n",
"gamma=1.4;\n",
"m=20; // mass flow rate of the gas in kg/s\n",
"cp=1.005; // Specific Heat at Constant Pressure in kJ/(kgK)\n",
"n_T=0.9; // Overall Efficiency \n",
"pr=p1/p2; // Pressure Ratio\n",
"// part(a)\n",
"T2s=T1/(pr^((gamma-1)/gamma));\n",
"T2=T1-(n_T*(T1-T2s));\n",
"n_p=(log(T1/T2))/(log(T1/T2s));\n",
"disp('%',n_p*100,'(a)small stage Efficiency or polytropic efficiency of the expansion is')\n",
"P=m*cp*(T1-T2);\n",
"disp('kW',P,'and Power developed is')\n",
"\n",
"// part(b)\n",
"AR=2.5; // Area Ratio of Diffuser\n",
"R=0.287; // Universal Gas Constant in kJ/kgK\n",
"p3=1.2; // Exit Pressure for diffuser in bar\n",
"c2=75; // Velocity of gas at turbine exit in m/s\n",
"c3=c2/AR;\n",
"n_d=0.7; // Efficiency of the diffuser\n",
"ro2=p2/(R*T2);\n",
"delp=n_d*(0.5*0.001*ro2*((c2^2)-(c3^2))); // delp=p3-p2d\n",
"disp('mm W.G.',delp*100000/9.81,'(b)static pressure across the diffuser is')\n",
"p2d=p3-delp;\n",
"prd=p1/p2d;\n",
"T2sd=T1/(prd^((gamma-1)/gamma));\n",
"T2d=T1-(n_T*(T1-T2sd));\n",
"Pd=m*cp*(T1-T2d);\n",
"disp('kW',Pd-P,'and Increase in the power output of the turbine is')\n",
"\n",
"disp('Comment: Error in Textbook, Answers vary due to Round-off Errors')"
   ]
   }
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