{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 2: Analysis of Steam Cycles" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 2.1: Power_output_and_efficiency.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "//Input data\n", "p1=40//Initial pressure of steam in bar\n", "T1=500//Initial temperature of steam in degree C\n", "m1=5500//Rate of steam in kg/h\n", "p2=2//Pressure of steam after expansion in bar\n", "n1=0.83//Isentropic efficiency \n", "q=0.87//Quality\n", "m2=2700//Mass flow rate in kg/h\n", "p3=0.1//Pressure of steam after expansion in l.p turbine in bar\n", "n2=0.78//Isentropic efficiency\n", "\n", "//Calculations\n", "h1=3445.3//Enthalpy in kJ/kg\n", "s1=7.0901//Entropy in kJ/kg.K which is 1.5301+x2s*5.5970\n", "x2s=(5.5600/5.5970)//dryness fraction\n", "h2s=(504.7+(x2s*2201.9))//Enthalpy in kJ/kg\n", "h2=h1-(n1*(h1-h2s))//Enthalpy in kJ/kg\n", "h3=(504.7+(q*2201.9))//Enthalpy in kJ/kg\n", "h4=((m2*h3+m1*h2)/(m1+m2))//Enthalpy in kJ/kg\n", "x4=(2183.78/2201.9)//dryness fraction\n", "s4=(1.5301+x4*5.5970)//Entropy in kJ/kg.K\n", "x5s=0.8574//dryness fraction\n", "h5s=(191.84+x5s*2392.5)//Enthalpy in kJ/kg\n", "dh4h5=(n2*(h4-h5s))//Difference in enthalpy (h4-h5) in kJ/kg\n", "h6=191.83//Enthalpy in kJ/kg\n", "W1=((m1*(h1-h2))+((m1+m2)*dh4h5))/3600//Power output of the plant in kW\n", "Q1=(m1*(h1-h6))/3600//Heat input in kW\n", "n1=(W1/Q1)*100//Efficiency in percent\n", "WT=(m1*(h1-h2))/3600//Power output without the geothermal heat supply in kW\n", "Q2=(m1*(h1-h6))/3600//Heat input without the geothermal heat supply in kW\n", "n2=(WT/Q2)*100//Efficiency of the cycle without the geothermal heat supply in percent\n", "\n", "//Output\n", "printf('(a)Power output of the cycle is %3.1f kW \n Efficiency of the cycle is %3.1f percent \n\n (b)Without geothermal heat supply \n Power output of the cycle is %3.2f kW \n Efficiency of the cycle is %3.2f percent',W1,n1,WT,n2)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 2.2: Mass_flow_rate.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "//Input data\n", "p1=90//Initial pressure of steam in bar\n", "T1=500//Initial temperature of steam in degree C\n", "O=(500*1000)//Output in kW\n", "T2=40//Condensation temperature in degree C\n", "nhp=0.92//Efficiency of h.p turbine\n", "nlp=0.9//Efficiency of l.p turbine\n", "np=0.75//Isentropic efficiency of the pump \n", "TTD=-1.6//Temperature in degree C\n", "\n", "//Calculations\n", "p2=(0.2*p1)//Optimum reheat pressure in bar\n", "h1=3386.1//Enthalpy in kJ/kg\n", "s1=6.6576//Entropy in kJ/kg.K\n", "s2s=s1//Entropy in kJ/kg.K\n", "h2s=2915//Enthalpy in kJ/kg\n", "h3=3469.8//Enthalpy in kJ/kg\n", "s3=7.4825//Entropy in kJ/kg.K\n", "x4s=(s3-0.5725)/7.6845//Dryness fraction\n", "h4s=(167.57+x4s*2406.7)//Enthalpy in kJ/kg\n", "h5=167.57//Enthalpy in kJ/kg\n", "h7=883.42//Enthalpy in kJ/kg\n", "Wps=(0.001008*p1*10)//Workdone by the pump in kJ/kg\n", "h6s=176.64//Enthalpy in kJ/kg\n", "dh1h2=(nhp*(h1-h2s))//Difference in enthalpy (h1-h2) in kJ/kg\n", "h2=h1-dh1h2//Enthalpy in kJ/kg\n", "dh3h4=(nlp*(h3-h4s))//Difference in enthalpy (h3-h4) in kJ/kg\n", "h4=h3-dh3h4//Enthalpy in kJ/kg\n", "Wp=(Wps/np)//Workdone by the pump in kJ/kg\n", "h6=(Wp+h5)//Enthalpy in kJ/kg\n", "tsat=207.15//Saturation temperature at 18 bar in degree C\n", "t9=(tsat-TTD)//Temperature in degree C\n", "h9=875//Enthalpy in kJ/kg\n", "m=((h9-h6)/(h2-h7))//Mass of steam in kg\n", "WT=(dh1h2+(1-m)*dh3h4)//Workdone by the turbine in kJ/kg\n", "Wnet=(WT-Wp)//Net workdone in kJ/kg\n", "ws=(O/Wnet)//Mass flow rate of steam at turbine inlet in kg/s\n", "Q1=((h1-h9)+(1-m)*(h3-h2))//Heat input in kJ/kg\n", "n=(Wnet/Q1)*100//Efficiency of the cycle in percent\n", "Wr=(Wnet/WT)//Work ratio\n", "\n", "//Output\n", "printf('(a)Mass flow rate of steam at turbine inlet is %3.0f kg/s \n (b)The cycle efficiency is %3.2f percent \n (c)Work ratio is %3.3f',ws,n,Wr)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 2.3: Optimum_pressures_and_temperatures.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "//Input data\n", "p1=70//Pressure at which an ideal seam power plant operates in bar\n", "T1=550//Temperature at which an ideal seam power plant operates in degrees C\n", "p2=0.075//Pressure at which an ideal seam power plant operates in bar\n", "\n", "//Calculations\n", "TB=285.9//Saturation temperature at 70 bar in degree C\n", "TC=40.3//Saturation temperature at 0.075 bar in degree C\n", "Tr=(TB-TC)/(7+1)//Temperature rise per heater for maximum cycle efficiency in degree C\n", "t1=(TB-Tr)//Temperature at heater 1 in degree C\n", "P1=4.33//Pressure at heater 1 in MPa\n", "t2=(t1-Tr)//Temperature at heater 2 in degree C\n", "P2=2.5318//Pressure at heater 2 in MPa\n", "t3=(t2-Tr)//Temperature at heater 3 in degree C\n", "P3=1.367//Pressure at heater 3 in MPa\n", "t4=(t3-Tr)//Temperature at heater 4 in degree C\n", "P4=0.6714//Pressure at heater 4 in MPa\n", "t5=(t4-Tr)//Temperature at heater 5 in degree C\n", "P5=0.2906//Pressure at heater 5 in MPa\n", "t6=(t5-Tr)//Temperature at heater 6 in degree C\n", "P6=0.108//Pressure at heater 6 in MPa\n", "t7=(t6-Tr)//Temperature at heater 7 in degree C\n", "P7=32.65//Pressure at heater 7 in kPa\n", "\n", "//Output\n", "printf('The optimum pressure and temperature at different heaters are: \n Heater 1: t1 = %3.1f degree C and p1 = %3.2f MPa\n Heater 2: t2 = %3.1f degree C and p2 = %3.4f MPa\n Heater 3: t3 = %3.1f degree C and p3 = %3.3f MPa\n Heater 4: t4 = %3.1f degree C and p4 = %3.4f MPa\n Heater 5: t5 = %3.1f degree C and p5 = %3.4f MPa\n Heater 6: t6 = %3.1f degree C and p6 = %3.3f MPa\n Heater 7: t7 = %3.1f degree C and p7 = %3.2f kPa',t1,P1,t2,P2,t3,P3,t4,P4,t5,P5,t6,P6,t7,P7)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 2.4: Percentage_of_total_electricity.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "//Input data\n", "ng=0.97//Efficiency of electric generator \n", "nt=0.95//Efficiency of turbine\n", "nb=0.92//Efficiency of boiler\n", "nc=0.42//Efficiency of cycle\n", "no=0.33//Efficiency of overall plant\n", "\n", "//Calculations\n", "na=(no/(ng*nt*nb*nc))//Efficiency of auxiliaries\n", "n=(1-na)*100//Percentage of total electricity generated which is consumed in running the auxiliaries\n", "\n", "//Output\n", "printf('Percentage of total electricity generated which is consumed in running the auxiliaries is %3.2f percent',n)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 2.5: Percentage_of_total_heat_absorption.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "//Input data\n", "T1=140//Temperature with which feed water enters into economiser in degree C\n", "T2=[25,250]//Temperature from air is preheated to in degree C\n", "P1=60//Pressure with which steam leaves the drum in bar\n", "x1=0.98//Dryness fraction\n", "T3=450//Temperature with which steam leaves the superheater in degree C\n", "cc=25.2//Calorific value of coal in MJ/kg\n", "r=8.5//Rate of evaporation of steam per kg coal \n", "wf=1//Mass of coal in kg\n", "R=15//Air fuel ratio by mass\n", "Cpa=1.005//Specific heat of air at constant pressure in kJ/kg.K\n", "Cpw=4.2//Specific heat of water at constant pressure in kJ/kg.K\n", "\n", "//Calculations\n", "h1=(T1*Cpw)//Enthalpy in kJ/kg\n", "hf=1213.35//Enthalpy in kJ/kg\n", "h2=hf//Enthalpy in kJ/kg\n", "hfg=1571//Enthalpy in kJ/kg\n", "h4=3301.8//Enthalpy in kJ/kg\n", "h3=(hf+x1*hfg)//Enthalpy in kJ/kg\n", "n=((r*(h4-h1))/(wf*cc*1000))*100//Efficiency\n", "he=(r*(h2-h1))/wf*10^-3//Heat transfer in the economiser in MJ/kg\n", "hb=(r*(h3-h2))/wf*10^-3//Heat transfer in the boiler in MJ/kg\n", "hs=(r*(h4-h3))/wf*10^-3//Heat transfer in the superheater in MJ/kg\n", "ha=(R*Cpa*(T2(2)-T2(1)))/wf*10^-3//Heat transfer in the air preheater in MJ/kg\n", "pe=((h2-h1)/(h4-h1))*100//Percentage of total heat absorbed in the economiser in percent\n", "pb=((h3-h2)/(h4-h1))*100//Percentage of total heat absorbed in the boiler in percent\n", "ps=((h4-h3)/(h4-h1))*100//Percentage of total heat absorbed in the superheater in percent\n", "\n", "//Output\n", "printf('Efficiency of steam generator is %3.2f percent \n\n Heat transfer per kg fuel in \n (i)economiser is %3.4f MJ/kg \n (ii)boiler is %3.3f MJ/kg \n (iii)superheater is %3.3f MJ/kg \n (iv)air pre-heater is %3.3f MJ/kg \n\n Percentage of total heat absorption taking place in \n (i)economiser is %3.2f percent \n (ii)boiler is %3.2f percent \n (iii)superheater is %3.2f percent',n,he,hb,hs,ha,pe,pb,ps)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 2.6: Cycle_efficiency.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "//Input data\n", "p1=150//Pressure of inlet steam in bar\n", "T1=550//Temperature of steam in degree C\n", "p2=20//Pressure after expansion in bar\n", "T2=500//Reheat temperature in degree C\n", "pc=0.075//Condenser pressure in bar\n", "php=50//Pressure of steam in h.p turbine in bar\n", "pip=[10,5,3]//Pressure of steam in i.p turbines in bar\n", "plp=1.5//Pressure of steam in l.p turbine in bar\n", "m=300*1000//Steam flow rate in kg/h\n", "\n", "//Calculations\n", "h1=3448.6//Enthalpy in kJ/kg\n", "h4=3467.6//Enthalpy in kJ/kg\n", "s1=6.5119//Entropy in kJ/kg.K\n", "s2=s1//Entropy in kJ/kg.K\n", "s3=s1//Entropy in kJ/kg.K\n", "s4=7.4317//Entropy in kJ/kg.K\n", "s5=s4//Entropy in kJ/kg.K\n", "s6=s5//Entropy in kJ/kg.K\n", "s7=s6//Entropy in kJ/kg.K\n", "s8=s7//Entropy in kJ/kg.K\n", "s9=s8//Entropy in kJ/kg.K\n", "t2=370//Temperature in degree C\n", "t3=245//Temperature in degree C\n", "t5=400//Temperature in degree C\n", "t6=300//Temperature in degree C\n", "t7=225//Temperature in degree C\n", "t8=160//Temperature in degree C\n", "h2=3112//Enthalpy in kJ/kg\n", "h3=2890//Enthalpy in kJ/kg\n", "h5=3250//Enthalpy in kJ/kg\n", "h6=3050//Enthalpy in kJ/kg\n", "h7=2930//Enthalpy in kJ/kg\n", "h8=2790//Enthalpy in kJ/kg\n", "x9=(s9-0.5764)/7.6751//Dryness fraction\n", "h9=168.79+x9*2406////Enthalpy in kJ/kg\n", "h10=168.79//Enthalpy in kJ/kg\n", "h11=h10+0.001*pip(2)*100//Enthalpy in kJ/kg\n", "h12=467.11//Enthalpy in kJ/kg\n", "t14=111.37//Temperature in degree C\n", "h14=467//Enthalpy in kJ/kg\n", "h13=h12//Enthalpy in kJ/kg\n", "h14=h13//Enthalpy in kJ/kg\n", "h15=h14//Enthalpy in kJ/kg\n", "h16=561.47//Enthalpy in kJ/kg\n", "h17=h16//Enthalpy in kJ/kg\n", "h18=640.23//Enthalpy in kJ/kg\n", "h19=h18+0.001*(p1-pip(2))*100//Enthalpy in kJ/kg\n", "h20=762.8//Enthalpy in kJ/kg\n", "h21=h20//Enthalpy in kJ/kg\n", "h22=1154.23//Enthalpy in kJ/kg\n", "h23=h22//Enthalpy in kJ/kg\n", "m1=((h23-h21)/(h2-h22))//Mass in kg\n", "m2=((h21-h19)-(m1*(h22-h20)))/(h5-h20)//Mass in kg\n", "m3=(((1-m1-m2)*(h18-h17))-((m1+m2)*(h20-h18)))/(h6-h18+h18-h17)//Mass in kg\n", "m4=((1-m1-m2-m3)*(h17-h15))/(h7-h16)//Mass in kg\n", "m5=(((1-m1-m2-m3-m4)*(h14-h11))-(m4*(h16-h12)))/(h8-h12+h14-h11)//Mass in kg\n", "WT=(h1-h2)+(1-m1)*(h2-h3)+(1-m1)*(h4-h5)+(1-m1-m2)*(h5-h6)+(1-m1-m2-m3)*(h6-h7)+(1-m1-m2-m3-m4)*(h7-h8)+(1-m1-m2-m3-m4-m5)*(h8-h9)//Workdone by turbine in kJ/kg\n", "Wp=(0.5+14.5+0.15)//Workdone in kJ/kg\n", "Wnet=(WT-Wp)//Net workdone in kJ/kg\n", "Q1=(h1-h23)+(1-m1)*(h4-h3)//Heat supplied in kJ/kg\n", "ncy=(Wnet/Q1)*100//Cycle efficiency in percent\n", "t23=264//Temperature in degree C\n", "sr=(3600/Wnet)//Steam rate in kJ/kWh\n", "hr=((Q1/Wnet)*3600)//Heat rate in kJ/kWh\n", "P=((Wnet*m)/3600)/10^3//Power output in MW\n", "\n", "//Output\n", "printf('(a) The cycle efficiency is %3.2f percent \n (b) The feedwater temperature is %i degree C \n (c) The steam rate is %3.2f kJ/kWh \n (d) The heat rate is %3.0f kJ/kWh \n (e) The quality of steam at turbine exhaust is %3.4f \n (f) The power output is %3.2f MW',ncy,t23,sr,hr,x9,P)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 2.7: Steam_condition.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "//Input data\n", "m=10000//Mass flow rate of steam in kg/h\n", "p=3//Pressure of steam in bar\n", "P=1000//Power in kW\n", "n=0.7//Internal efficiency of turbine\n", "\n", "//Calculations\n", "dh=(P*3600)/m//Change in enthalpy in kJ/kg\n", "h2=2725.3//Enthalpy in kJ/kg from Fig. E2.7 \n", "h1=dh+h2//Enthalpy in kJ/kg \n", "dh1h2s=dh/n//Change in enthalpy in kJ/kg\n", "h2s=h1-dh1h2s//Enthalpy in kJ/kg\n", "x2s=(h2s-561.47)/2163.8//Dryness fraction\n", "s2s=1.6718+x2s*(6.999-1.6718)//Entropy in kJ/kg.K\n", "s1=s2s//Entropy in kJ/kg.K\n", "p1=37.3//Pressure in bar from Mollier diagram\n", "t1=344//Temperature in degree C\n", "\n", "//Output\n", "printf('The steam condition required at inlet of the turbine: \n Enthalpy is %3.1f kJ/kg \n Entropy is %3.4f kJ/kg.K \n Pressure is %3.1f bar \n Temperature is %i degree C',h1,s1,p1,t1)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 2.8: Steam_generation_capacity.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "//Input data\n", "Pl=5.6//Power load in MW\n", "Hl=1.163//Heat load in MW\n", "p1=40//Pressure in bar\n", "T1=500+273//Temperature in K\n", "p2=0.06//Pressure in bar\n", "p3=2//Pressure in bar\n", "CV=25//Calorific value in MJ/kg\n", "n=88//Boiler efficiency in percent\n", "T=6//Temperature rise in degree C\n", "\n", "//Calculations\n", "h1=3445.3//Enthalpy in kJ/kg\n", "s1=7.0901//Entropy in kJ/kg.K\n", "s2=s1//Entropy in kJ/kg.K\n", "s3=s1//Entropy in kJ/kg.K\n", "x2=(s2-1.5301)/5.5970//Dryness fraction\n", "h2=2706.7//Enthalpy in kJ/kg\n", "h26=2201.9//Difference in enthalpy in kJ/kg\n", "w=(Hl*10^3)/h26//Rate of steam extraction in kg/h\n", "x3=(s1-0.52)/7.815//Dryness fraction\n", "h3=(149.79+x3*2416)//Enthalpy in kJ/kg\n", "h4=149.79//Enthalpy in kJ/kg\n", "ws=((Pl*10^3+(w*(h2-h3)))/((h1-h2)+(h2-h3)))//Steam generation capacity in kg/s\n", "ws1=(ws*3600)/1000//Steam generation capacity in t/h\n", "h7=(504.7+(1.061*10^-3*(p1-p3)*100))//Enthalpy in kJ/kg\n", "h5=(149.79+(1.006*100*p1*10^-3))//Enthalpy in kJ/kg\n", "Q1=(((ws-w)*(h1-h5))+(w*(h1-h7)))//Heat input in kW\n", "wf=((Q1/1000)/((n/100)*CV))*(3600/1000)//Fuel burning rate in t/h\n", "Q2=((ws-w)*(h3-h4))//Heat rejected to the condensor in kW\n", "wc=(Q2/(4.187*T))/1000//Rate of flow of cooling water in m^3/s\n", "\n", "//Output\n", "printf('(a) the steam generation capacity of the bolier is %3.2f t/h \n (b) the heat input to the boiler is %3.1f kW \n (c) the fuel burning rate of the bolier is %3.3f t/h \n (d) the heat rejected to the condensor is %3.0f kW \n (e) the rate of flow of cooling water in the condensor is %3.3f m^3/s',ws1,Q1,wf,Q2,wc)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 2.9: Power_developed.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "//Input data\n", "m=21000//Steam rate in kg/h\n", "p1=17//Pressure in bar\n", "T1=230+273//Temperature in K\n", "P=132.56//Power in kW\n", "x2=0.957//Dryness fraction\n", "p2=3.5//Pressure in bar\n", "Pl=1337.5//Power in l.p turbine in kW\n", "p3=0.3//Pressure in bar\n", "x3=0.912//Dryness fraction\n", "\n", "//Calculations\n", "h1=2869.7//Enthalpy in kJ/kg\n", "s1=6.5408//Entropy in kJ/kg.K\n", "h2=(870.44+x2*1924.7)//Enthalpy in kJ/kg\n", "h3=h2//Enthalpy in kJ/kg\n", "h56=(Pl*3600)/m//Difference in Enthalpy in kJ/kg\n", "h6=(289.23+x3*2336.1)//Enthalpy in kJ/kg\n", "h5=2649.04//Enthalpy in kJ/kg\n", "s4s=s1//Entropy in kJ/kg.K\n", "x4s=(s4s-1.7275)/5.2130//Dryness fraction\n", "h4s=584.33+x4s*2148.1//Enthalpy in kJ/kg\n", "w=(P/(h1-h2))//Flow rate in kg/s\n", "ws=(m/3600)//Steam flow rate in kg/s\n", "h4=((ws*h5)-(w*h3))/(ws-w)//Enthalpy in kJ/kg\n", "x4=(h4-584.33)/2148.1//Dryness fraction\n", "W=(ws-w)*(h1-h4)//Power developed by h.p turbine in kW\n", "n=((h1-h4)/(h1-h4s))*100//Isentropic efficiency in percent\n", "\n", "//Output\n", "printf('(a) the steam quality at the exhaust of the h.p turbine is %3.3f \n (b) the power developed by the h.p turbine is %3.2f kW \n (c) the isentropic efficiency of the h.p turbine is %3.2f percent',x4,W,n)" ] } ], "metadata": { "kernelspec": { "display_name": "Scilab", "language": "scilab", "name": "scilab" }, "language_info": { "file_extension": ".sce", "help_links": [ { "text": "MetaKernel Magics", "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" } ], "mimetype": "text/x-octave", "name": "scilab", "version": "0.7.1" } }, "nbformat": 4, "nbformat_minor": 0 }