Heat Cycles, Heat Engines, & Real Devices John Jechura – [email protected] Updated: January 4, 2015 Topics • Heat engines / heat cycles . Review of ideal‐gas efficiency equations . Efficiency upper limit –Carnot Cycle • Water as working fluid in Rankine Cycle . Role of rotating equipment inefficiency • Advanced heat cycles . Reheat & heat recycle • Organic Rankine Cycle • Real devices . Gas & steam turbines 2 Heat Engines / Heat Cycles • Carnot cycle . Most efficient heat cycle possible Hot Reservoir @ T H • Rankine cycle Q H . Usually uses water (steam) as working fluid W . Creates the majority of electric power used net throughout the world Q C . Can use any heat source, including solar thermal, Cold Sink @ T coal, biomass, & nuclear C • Otto cycle . Approximates the pressure & volume of the combustion chamber of a spark‐ignited engine WQQ • Diesel cycle net H C th QQ . Approximates the pressure & volume of the HH combustion chamber of the Diesel engine 3 Carnot Cycle • Most efficient heat cycle possible • Steps . Reversible isothermal expansion of gas at TH. Combination of heat absorbed from hot reservoir & work done on the surroundings. Reversible isentropic & adiabatic expansion of the gas to TC. No heat transferred & work done on the surroundings. Reversible isothermal compression of gas at TC. Combination of heat released to cold sink & work done on the gas by the surroundings. Reversible isentropic & adiabatic compression of the gas to TH. No heat transferred & work done on the gas by the surroundings. • Thermal efficiency QQHC TT HC T C th th 1 QTTHHH 4 Rankine/Brayton Cycle • Different application depending on working fluid . Rankine cycle to describe closed steam cycle. Brayton cycle approximates gas turbine operation. • Steps . Heat at constant PH. Heat absorbed from hot reservoir & no work done. Isentropic & adiabatic expansion to PL. Work done on surroundings. Cool at constant PL. Heat released to cold sink & no work done. Isentropic & adiabatic compression to PH. Work done on fluid by surroundings. • Ideal gas thermal efficiency –not appropriate for condensing water 1/ TPLL th 11 TPHH 5 Thermal Efficiency Ideal‐Gas Brayton Cycle 0.8 Argon, =1.7 0.7 Air, =1.4 0.6 ) ( 0.5 0.4 Efficiency 0.3 Propane, =1.1 Thermal 0.2 0.1 0 0 5 10 15 20 25 30 35 Compression Ratio (P2/P1) 6 Otto Cycle • Steps . Reversible isentropic compression from V1 to V2. No heat transferred & work done on the fluid. Initial conditions are TL & PL. Heat at constant volume. Heat absorbed from hot reservoir & no work done. Reversible isentropic & adiabatic expansion from V2 to V1. No heat transferred & work done by the fluid on the surroundings. Cool at constant volume to TL with resulting pressure PL. Heat released to cold sink & no work done. • Thermal efficiency –ideal gas 1 1 where RV /V is the volumetric compression ratio th R1 12 • This cycle ignores input of new air/fuel mixture, change in composition with combustion, & exhaust of combustion products 7 Thermal Efficiency Ideal‐Gas Otto Cycle 60% 600 Inlet Conditions: 25°C & 1.0 bar =1.3 (typical air+fuel) 50% 500 40% 400 30% 300 Temperature [°C] Temperature Thermal Efficiency Thermal 20% 200 10% 100 0% 0 0 5 10 15 20 25 Volumetric Compression Ratio 8 Diesel Cycle • Steps . Reversible isentropic compression from V1 to V2. No heat transferred & work done on the fluid. Initial conditions are TL & PL. Heat at constant pressure. Heat absorbed from hot reservoir & no work done. Volume increases from V2 to V3. Reversible isentropic & adiabatic expansion from V3 to V1. No heat transferred & work done by the fluid on the surroundings. Cool at constant volume to TL with resulting pressure PL. Heat released to cold sink & no work done. • Thermal efficiency –ideal gas 11 1 th 1 R 1 where R=V1/V2 (the compression ratio) & =V3/V2 (the cut‐off ratio). • This cycle ignores input of new air, injection of fuel, change in composition with combustion, & exhaust of combustion products 9 Thermal Efficiency Ideal‐Gas Diesel Cycle 80% 800 Inlet Conditions: 25°C & 1.0 bar =1.4 (air) 70% =3.0 700 60% 600 50% 500 40% 400 30% 300 [°C] Temperature Thermal Efficiency Thermal 20% 200 10% 100 0% 0 0 5 10 15 20 25 Volumetric Compression Ratio 10 Example: Actual Gasoline Engine Thermal Efficiency • BMW M54B30 (2,979 cc) engine stated to produce 228 hp @ 5900 rpm (with 10.2:1 compression ratio) • Calculation steps to determine thermal efficiency . Unit conversion: 228 hp = 10,200 kJ/min 1.729 kJ/rev . 2 revolutions needed for full volume displacement: 1.161 kJ/L . Air+fuel mix has LHV of 3.511 kJ/L (ideal gas) • Assumptions o Characterize air as 21 mol% O2 / 79 mol% N2 & gasoline as isooctane (iC8, C8H18, LHV of 5065 kJ/mol) o Air+fuel mix an ideal‐gas stoichiometric mixture of @ 1.0 bar & 25°C o Air+fuel mix molar density is 0.0403 mol/L (i.g.) with 1.72 mol% iC8 • Thermal efficiency is 33% at these stated conditions . Ideal‐gas Otto Cycle shows upper limit of 50.2% (=1.3) 11 Gasoline Thermal Efficiency Using Aspen Plus 25 1 100 0.00 B1 7 HEATVAL FUEL 1 HIERARCHY 6052 FUELMIX 1.00 B2 W W-12 25 384 2674 1 24 116 5952 6052 6487 1.00 1.00 1.00 BURN-1 FLAMEVAL AIR MIX-HP 2A CMBSTGAS HIERARCHY B4 W Temperature (C) W-34 Pressure (bar) 1544 25 Molar Flow Rate (kmol/hr) Q-RESID 7 1 6487 6487 Vapor Fraction Q 1.00 0.89 Duty (kJ/sec) Power(kW) LOSTHEAT EXHAUST AMBIENT • 44.7% thermal efficiency assuming isentropic compression & expansion . Care must be taken to calculate heats & works from internal energy values, not enthalpy values . iC8 as model gasoline component . 10:1 volumetric compression ratio . 33% thermal efficiency & 33% lost heat to exhaust using 89% isentropic efficiency & 5% mechanical losses during compression & expansion 12 Water as Working Fluid in Rankine Cycle • Aspen Plus flowsheet . Flow system • Energy considerations from enthalpy, not internal energy . Cycle represented by once‐through flow system • LP‐WATER must match conditions of LP‐ WATR2 • “Out” direction of Energy & Work streams represent calculated values • Can use arbitrary flow rate for thermal efficiency calculation . Thermal efficiency from heat & work values Wnet W‐TURBIN W‐PUMP th Qin Q‐BOILER 13 Typical operating parameters • TURBINE exhaust fully condensed in CONDSR • BOILER increases temperature & changes phase . Outlet saturated liquid (i.e., vapor fraction is zero) or (liquid vapor) subcooled . At minimum, exit at saturated vapor conditions (i.e., • No vapor to PUMP to prevent cavitation vapor fraction is one). Temperature controlled by available cooling media . May be superheated to much higher temperature. • 15 –35oC (60 –95oF) typical for cooling water . Exit temperature controlled by heat source available & materials of construction –maximum about 420 – • 45 –50oC (110 – 125oF) typical for air cooling 580oC (790 – 1075oF) . Pressure will “float” to match this saturation • Highest temperatures require expensive nickel & temperature cobalt alloys • PUMP increases pressure of water to high‐ • Shaft work produced in TURBINE when pressure of pressure conditions steam let down to CONDSR inlet conditions . Pressure chosen to match common TURBINE inlet . Very complicated rotating machinery that can have pressures – 1500, 1800, & 2400 psig for large power multiple number of stages, multiple entry & applications extraction points, … . Real isentropic efficiencies 75 – 90% at optimal . Real isentropic efficiencies 70 – 90% at optimal flowrates flowrates • Inefficiency causes temperature rise in water . May be designed to exhaust gas phase or water/steam phase (condensing turbine) . Mechanical efficiency represents energy loss in drive train . Mechanical efficiency represents energy loss in drive train 14 Example #1 Steam Turbine Operation • Operating conditions . Condenser outlet saturated liquid @ 35oC • No pressure loss through exchanger . Pump outlet 1500 psig • Ideal compression . Boiler outlet saturated vapor • No pressure loss through exchanger . Turbine • Ideal expansion . No pressure losses through piping . No mechanical losses in rotating equipment W‐TURBIN W‐PUMP 2789 29 0.388 th Q‐BOILER 7111 15 Example #2 Steam Turbine Operation • Operating conditions . Condenser outlet saturated liquid @ 35oC • No pressure loss through exchanger . Pump outlet 1500 psig • 80% isentropic efficiency . Boiler outlet saturated vapor • No pressure loss through exchanger . Turbine • 75% isentropic efficiency . No pressure losses through piping . No mechanical losses in rotating equipment W‐TURBIN W‐PUMP 2092 36 0.289 th Q‐BOILER 7104 16 Advanced Heat Cycles • Reheat . Multiple step expansion, turbine exhaust reheated before next step . Keep the steam gas‐phase for as much of the process as possible . Increased thermal efficiency with increased capital cost • Heat recycle . Multiple step expansion, turbine exhaust split before next step • Majority sent to low‐pressure turbine • Remainder condensed against the high‐pressure boiler feed water . Trades off the heat of vaporization relative to power from expansion process 17 Example Steam Turbine With Reheat • Operating conditions . Condenser outlet saturated liquid @ 45oC • No pressure loss through exchanger . Pump outlet 120 bar‐a • Ideal compression . Boiler outlet 150oC superheat • No pressure loss through exchanger . Turbine intermediate 24 bar • 80% isentropic efficiency . Reheat to 475oC • No pressure loss through exchanger . No pressure losses through piping . No mechanical losses in rotating equipment 921 2465 34 th 0.341 8555 1277 18 Example Steam Turbine With Reheat 19 Example Steam Turbine With Heat Recycle • Operating conditions . Condenser outlet saturated liquid @ 45oC • No pressure loss through exchanger . Pump outlet 120 bar‐a • Ideal compression . Boiler outlet 150oC superheat • No pressure loss through exchanger . Turbine intermediate 10 bar • 80% isentropic efficiency . 10% split to recycle . No pressure losses through piping . No mechanical losses in rotating equipment 1306 1414 34 0.336 th 7986 20 Example Steam Turbine With Heat Recycle 21.