ME 200 - Chapter 8

ME 200 - Chapter 8 - ME 200 – Thermodynamics 1 Chapter 8...

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Unformatted text preview: ME 200 – Thermodynamics 1 Chapter 8 In In-Class Notes for Spring 2011 Notes Spring 2011 Vapor Power Cycles • • • • Background Carnot Vapor Power Cycles Vapor Power Cycles Basic Rankine Cycle Rankine Cycle Trends and Improvements Simple Combustion Power Plant Vapor Power Cycle Background Goal: generate electricity from heat input Vapor Cycles: Employ working fluid that changes Cycles Employ working fluid that changes phase (typically water/steam for conventional cycles) A Variety of Sources for Heat Input: Fossil fuels (coal, oil) Geothermal Ocean thermal gradients Methane gas from land fills - Nuclear fission fi - Solar radiation - Garbage Carnot Vapor Power Cycle Vapor Power Cycle • All processes are totally reversible • Maximum possible power plant efficiency QH 1 Comp. Boiler 2 Turb. Wnet Heat Rejection: ambient air, lakes, or ocean Environmental Issues - Air pollution - Waste products (nuclear) - Thermal pollution - CO2 production - Safety Vapor Power Cycles - Page 1 4 Condenser 3 QL Vapor Power Cycles - Page 2 Carnot Efficiency Ideal Rankine Vapor Power Cycle ηth = WT − Wc Wnet QH − QL m ⋅ qL = = = 1− m ⋅ qH QH QH QH Reversible + isothermal heat transfer ⇒ q = T Δs So, Carnot efficiency is ηcarnot = 1 − TH ( s2 − s1 ) TL ( s3 − s4 ) = 1− TL TH • All processes are internally reversible • Basis for most steam power plants How does plant efficiency vary with source temp.? What is max. efficiency for TL = 212 F, TH = 450 F Actual Rankine Vapor Power Cycle Implementation Problems for Carnot Vapor Cycle Problems for Carnot Vapor Cycle • • • • Heat addition temperature, TH, limited to fluid critical temperature 2-phase compressors are difficult to build diffi Turbines will only tolerate a small amount of liquid (want χ > 0.9) Need temperature differences between source temperature differences between source and boiler and between condenser and sink Vapor Power Cycles - Page 3 Vapor Power Cycles - Page 4 Typical Rankine Cycle Analysis Assump: Pump SSSF, Δke=Δpe=0, adiabatic, incomp. ηP,TC or PC,TB or PB, P1=PC & sat. liq., P2=PB wpump,in = h2 – h1 s2s = s1, h2 = h1 + (h2s - h1)/ηP Typical Rankine Cycle Analysis Assump: Given: Turbine SSSF, Δke=Δpe=0, adiabatic ηT, P4=PC, h3 & s3 from boiler analysis boiler analysis wturb,out = h3 – h4 s4s = s3, h4 = h3 +ηT(h4s- h3) Given: 1st Law: 1st 2nd Law: Law: 2nd Law: Properties: h2s-h1=v(P2 - P1), v= vf,1, h1= hf,1 v= Assump: Given: Boiler SSSF, Δke=Δpe=0 TB or PB, P3= P2=PB, T3 or qin h2 from pump analysis qin = h3 – h2 Properties: h4s=h(P4, s4s) Assump: Given: Condenser SSSF, Δke=Δpe=0 TC or PC, P1=P4=PC, h4 from turbine anal. qout = h4 – h1 1st Law: 1st Law: Properties: h3 = h(P3,T3), s3 = h(P3,T3) h(P h(P Vapor Power Cycles - Page 5 Overall Efficiency ηth = or ηth = wT − w p qin wnet qin − qout q = = 1 − out qin qin qin Vapor Power Cycles - Page 6 Simple Rankine Cycle Example Given: 1 MW power plant State 3: T3 =450 F and sat. vapor State 1: T1 = 212 F and sat. liquid ηp = ηT = 0.80 Find: steam flow rate (lbm/hr), heat input (Btu/hr), fl (lb (Bt cycle efficiency Assumptions: Rankine Cycle Model State 1 2 2s 3 4s 4 P (psia) T(F) 212 h (Btu/lbm) s (Btu/lbm-R) X 0 450 1 Vapor Power Cycles - Page 7 Vapor Power Cycles - Page 8 Vapor Power Cycles - Page 9 Vapor Power Cycles - Page 10 Lecture 35 More on Vapor Power Cycles Simple Steam Power Plant Rankine Cycle Trends Effect of Boiler Superheating What’s the impact on plant efficiency of increasing boiler superheat? What can we do to improve the efficiency of this plant? Why is a cooling tower used for heat rejection rather than just a heat exchanger? Vapor Power Cycles - Page 11 Vapor Power Cycles - Page 12 Why not increase boiler temperature (TB) instead? • want χ4 > 0.9 to limit erosion • there is a limit on boiler pressure due to materials is limit on boiler pressure due to materials and safety For previous example: TB = 450 F, TC = 212 F previous example: 450 F, 212 ηp = ηt = 0.8 T3(F) 450 550 950 η χ4 For previous example with: TC = 150 F (PC=3.7 psia) χ4 = 0.95 (specifies T3), PB = Psat @ TB TB (F) 450 550 650 PB (psia) 422 1046 2216 T3 (F) η Notes • T3 must increase to maintain constant χ4 • Maximum boiler pressure dictated by maximum T3 Effect of Condensing Pressure What’s the impact on plant efficiency of decreasing condensing temperature? Effect of Boiler Pressure (i.e., Temperature, TB) What’s the impact on plant efficiency of increasing efficiency of increasing boiler pressure? How do you change condensing pressure? condensing pressure? Vapor Power Cycles - Page 13 Vapor Power Cycles - Page 14 For previous example with: TB = 650 F χ4 = 0.95 PC = Psat @ TC TC (F) 200 150 100 PC (psia) 11.5 3.7 0.95 T3 (F) η Rankine Cycle Improvements Ideal Reheat Cycle Summary • • Want high TB and low TC Better to raise TB than T3, but need superheat to achieve desired χ4 Vapor Power Cycles - Page 15 Vapor Power Cycles - Page 16 ...
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