Week 4. Gas Power Cycles IV
Objecties. Ealuate the performance of gas power cycles for which the working fluid remains a gas throughout the entire cycle 2. Deelop simplifying assumptions applicable to gas power cycles 3. Discuss both approximate and exact analysis of gas power cycles 4. Reiew the operation of reciprocating engines 5. Sole problems based on the Otto, Diesel, Stirling, and Ericsson cycles 6. Sole problems based on the Brayton cycle; the Brayton cycle with regeneration; and the Brayton cycle with intercooling, reheating, and regeneration 7. Analyze jet-propulsion cycles 8. Identify simplifying assumptions for second-law analysis of gas power cycles 9. Perform second-law analysis of gas power cycles
Stirling And Ericsson Cycles II Stirling Cycle proposed by Robert Stirling in 828 Process 2 : isothermal expansion : heat addition from external source Process 2 3 : constant olume regeneration : internal heat transfer from the working fluid to the regenerator Process 3 4 : isothermal compression : heat rejection to the external sink Process 4 : constant olume regeneration : internal heat transfer from the regenerator back to the working fluid Stirling Engine http://www.youtube.com/watch?=srm7gcal3de&feature=related http://www.youtube.com/watch?=cjjkj-ugbom http://www.youtube.com/watch?=rnnlyikxlc&nr= http://www.youtube.com/watch?=7q4uengn_yk http://www.youtube.com/watch?=furb7krxuk&feature=fw
Stirling And Ericsson Cycles I Stirling Engine (Video Clips). How a Stirling engine works 2. Laminar Flow Stirling Engine 3. The Stirling Motor 4. Solar powered Stirling Engine with Fresnel Lens
Solar Dish/Stirling Power Systems ) 2) ) California Edison 25 kw dish/stirling system 3) 2) Adnco/Vanguard 25 kw dish/stirling system installed at Rancho Mirage, California 3) 25 kw power conersion system under test at Sandia National Laboratories
Stirling And Ericsson Cycles III Thermal efficiency of Stirling cycle q = c ( T T ) 4 4 q = c ( T T ) 23 2 3 T = T, T = T q = q 2 4 3 4 23 Supplied heat Emitted heat th,stirling 2 in out 3 4 th,stirling ln 2 ln Process 2 3, 4 are isometric process =, = η is η q q = = RT H = RT L q 3 4 out = = q in T T L H 4 2 3
Stirling And Ericsson Cycles IV The Ericsson cycle is ery much like the Stirling cycle, except that the two constantolume processes are replaced by two constant-pressure processes Process 2 : isothermal expansion : heat addition from external source Process 2 3 : constant pressure regeneration : internal heat transfer from the working fluid to the regenerator Process 3 4 : isothermal compression : heat rejection to the external sink Process 4 : constant pressure regeneration : internal heat transfer from the regenerator back to the working fluid A steady-flow Ericsson engine
Stirling And Ericsson Cycles V Thermal efficiency of Ericson cycle q = c ( T T ) 4 P 4 q = c ( T T ) 23 P 2 3 T = T, T = T q = q 2 4 3 4 23 P RT ln q P T η th,ericsson = = = T Process 2; T = T, P = P 4 L out 3 q P in RTH ln P2 2 2 2 2 2 Process 3 4; T = T, P = P P = P 3 4 4 3 3 4 3 3 4 4 P = P L H
Ex 4) Thermal Efficiency of the Ericsson Cycle Using an ideal gas as the working fluid, show that the thermal efficiency of an Ericsson cycle is identical to the efficiency of a Carnot cycle operating between the same temperature limits.
Brayton Cycle: The ideal Cycle for Gas-Turbine Engines Proposed by George Brayton in 870s It is an open cycle, but it can be modeled as a closed cycle by utilizing the air-standard assumptions The two major application areas of gasturbine engines are aircraft propulsion and electric power generation It is made up of four internally reersible processes: Process 2 : Isentropic compression (in a compressor) Process 2 3 : Constant pressure heat addition Process 3 4 : Isentropic expansion (in a turbine) Process 4 : Constant-pressure heat rejection An open-cycle gas-turbine engine A closed-cycle gas-turbine engine
Summary
Brayton Cycle: Thermal Efficiency The energy balance for a steady-flow process, when ke pe 0 ( ) ( ) q q + w w = h h in out in out exit inlet heat transfers to and from the working fluid are ( ) ( ) q = h h = c T T in 3 2 p 3 2 q = h h = c T T out 4 p 4 The thermal efficiency of the ideal Brayton Cycle T T 4 ( ) wnet q c out p T4 T T ηth,brayton = = = = qin qin cp ( T3 T2 ) T T 3 2 T 2 Process -2 and 3-4 : isentropic process, and P = P, P = P p ( ) ( ) k k k k T 2 P 2 P 3 T3 = = = T P P4 T4 P2 Thus, η = - r ( k ) k p = P th,brayton rp 2 3 4 where, r is the pressure ratio and k is the specific heat ratio T-s and P- diagrams for the ideal Brayton cycle
Summary Process 2 : isentropic compression Otto Cycle Process 2 3 : constant olume heat addition Process 3 4 : isentropic expansion Process 4 : constant olume heat rejection Process 2 : isentropic compression Diesel Cycle Process 2 3 : constant pressure heat addition Process 3 4 : isentropic expansion Process 4 : constant olume heat rejection Process 2 : isentropic compression Brayton Cycle Process 2 3 : constant pressure heat addition Process 3 4 : isentropic expansion Process 4 : constant pressure heat rejection
Brayton Cycle: Thermal Efficiency II The thermal efficiency of an ideal Brayton cycle depends on the pressure ratio of the gas turbine and the specific heat ratio of the working fluid. (The thermal efficiency increases with both of these parameters.) In most common designs, the pressure ratio of gas turbines ranges from about to 6 Back work ratio: the ratio of the compressor work to the turbine work w c ( T2 T ) c h2 h p bwr = = = w h h c T T t 3 4 ( ) Deelopment of Gas Turbines. Increasing the turbine inlet temperatures 540 425 (new materials & innoatie cooling techniques) 2. Increasing the efficiencies of turbo machinery components 3. Adding modifications to the basic cycle (e.g. intercooling regeneration and reheating) p 3 4 Gas Turbine Thermal efficiency of the ideal Brayton cycle as a function of the pressure ratio with K=.4
Ex 5) The Simple Ideal Brayton Cycle A gas-turbine power plant operating on an ideal Brayton cycle has a pressure ratio of 8. The gas temperature is 300 K at the compressor inlet and 300 K at the turbine inlet. Utilizing the air-standard assumptions, determine (a) the gas temperature at the exits of the compressor and the turbine, (b) the back work ratio, and (c) the thermal efficiency.
Deiation of Actual Gas-Turbine Cycles from Idealized Ones Some pressure drop during the heat-addition and heat rejection processes is ineitable The actual work input to the compressor is more The actual work output from the turbine is less because of irreersibilities The deiation can be accounted for by using the isentropic efficiencies of the turbine and compressor η η c T = = w w w w s a a s h h h h 2 s 2 a 3 3 h h h h 4 a 4 s The deiation of an actual gas-turbine cycle from the ideal Brayton cycle as a result of irreersibilities