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The Carnot Cycle

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The Ericsson cycle Reversible isothermal process: Entropy changes for process 1-2 and 3-4: The efficiencies of all reversible heat engines operating between the same two reservoirs are the same

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Industrial gas turbines – aeroderivatives Early installations: small, typically 10MW, efficiency less than 30% even with heat exchanger Aero-derivatives: –Higher powers –Much development cost already paid Strengthening bearings Burner mods. => allow natural gas or diesel fuel Power turbine (drive pipeline compressors and alternators directly) De-rate for longer life (decrease TIT) Reduction gearbox (e.g. marine propeller) –Early installations typically 15MW, 25%

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Aero-derivatives – The Trent Similar fan pressure ratio –”Bypass power requirement” converted to shaft output. Tip-speed of fan limits rot. speed. to about 3600 rpm!!! NO X requirement => re-design of burner necessity.

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Aero-derivatives – applications Pipeline pumping (up to 10 per cent of through-put for typical pipeline) Peak-load and emergency electricity generation (full power from cold in under two minutes, expensive fuel, low efficiency) Off-shore platforms (base load) Naval propulsion (more to come…)

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Large industrial units Today output of 250 MW possible –Maximum width to permit transport by rail –Limited by disk forgings Reason for success…

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Example Cengel/Boles - Thermodynamics - an engineering approach r = pressure ratio = 8 t 1 =300 K, t 3 = 1300 K, a =1.4, g =1.333 T 2a = 604.29 K

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Example Cengel/Boles - Thermodynamics - an engineering approach T 4a = 852.29K. Compressor and turbine work:

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Example Cengel/Boles: Thermodynamics - an engineering approach Burner temperature rise: Ideal fuel flow requirement:

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TKMCE Fig. 2-17

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Why not use exhaust gases to boil water ?

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Example Rankine Cycle (40.8%) Steam cycle (example 9-8b): h 2 =144.85 kJ/s h 3 =3410.3 kJ/s w net = 1331.4 kJ/s= w turb,out -w pump,in Energy balance (how much steam can be generated from 1 kg/s of air ?) : T5 (=T9) given in C&B=450 K

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Improved efficiency The efficiency is improved:

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TKMCE HRSG (Heat Recovery Steam Generator) configuration

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Cogeneration Combined production of Heat and Power (CHP) –Very high net efficiency can be obtained –The Rya Combined Heat and Power (CHP) plant Many industrial processes require large quantities of steam and hot water –Breweries, paper mills, chemical industry Microturbines!!! –Small gas turbines for small users such as supermarkets –Powers around 100 kW –Low pressure ratio regenerative cycle => cheap and efficient

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TKMCE Rya combined heat and power plant Cleaned flue gas District heat Electric power Condensers Steam turbine and electrical generator Heat Recovery Steam Generator (HRSG) Gas turbine and electrical generator Air

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Rya gas turbine 600 MW output –261MW electric (43.5%) –294MW district heat production (49%) –Losses 7.5% Total efficiency of 92.5%! SCR (selective catalytic reduction) for low NO x emissions –More on SCR in burner chapter π = 19.2 T 3 = 1570 K

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Closed cycles + Can use high pressures => reduce turbomachinery size + Part load by variation of pressure − External heating system => bulky plant, allowable temperature in heating system limits power output + Avoid erosion/corrosion (cheap fuels) + No filtration of incoming air + Other gases can be used

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Closed cycles – air vs. helium (section 2.6) Heat transfer coefficient of Helium is almost twice the coefficient for air => smaller heat exchangers Higher Mach numbers in turbomachinery offsets unfavorable specific heats => turbomachinery sizing comparable Sealing will be a problem and helium is a scarce resource (at least compared to air) Helium gas is very inert: –does not burn –absorbs neutrons only weakly – small cross section

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Closed cycles – HTR application PBMR = Pebble Bed Modular Reactor –Silicon carbide coated uranium granules are compacted into billiard-ball-like graphite spheres –Fuel for reactors operating at high temperature –Gas turbine => long maintenance intervals (6 years between overhauls) –Operation in Germany was discontinued after Chernobyl –CRS: ”it follows that gas turbines are unlikely to be used in any nuclear power plant in the foreseeable future…. (section 1.3) Resurfacing in South Africa –The first commercial PBMR will be available from 2013.

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TKMCE The pebbles

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Closed cycles – some application areas 800 K 1200 K 500000 pebbles

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TKMCE Theory 2.1 - Simple cycle efficiency

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TKMCE Theory 2.1 - Simple cycle efficiency Independent of T 3 !!! Raising average temperature at which heat is added => temperature at which heat is rejected is also increased r = pressure ratio = P 2 /P 1

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TKMCE Theory 2.2 - Simple cycle specific work Today typical values of t is around 5-6 t = temperature ratio = T 3 /T 1

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TKMCE Theory 2.3 - Simple cycle optimal pressure ratio Introduce the auxiliary variable according to: Differentiate with respect to and set to zero: but:

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بسم الله الرّحمن الرّحیم

بسم الله الرّحمن الرّحیم

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