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Lecture 11 – Performance of simple cycles

Lecture 11 – Performance of simple cycles. The off-design problem Off-design operation for: the single shaft engine free turbine engine the jet engine Design Task 3 description. Design = rubber engines. The off design problem. Chapter 1-3 describes the (on) design problem

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Lecture 11 – Performance of simple cycles

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  1. Lecture 11 – Performance of simple cycles The off-design problem Off-design operation for: the single shaft engine free turbine engine the jet engine Design Task 3 description

  2. Design = rubberengines The off design problem Chapter 1-3 describes the (on) design problem Downstream engine components are adapted to upstream. For instance: Turbine pressure ratio is selected to deliver power required by compressor Exhaust nozzle is sized to swallow flow exiting from turbine Every point correspondsto new engine design - new turbine/compressor blading nozzle areas etc

  3. The off design problem Shows proximity to surge line What happens when control signals are changed such as: Fuel flow Nozzle exit area Compressor variable geometry Conservation of mass flow, energy and turbine/compressor rotational speed compatibility Operating space reduced to an equilibrium runningline

  4. The off design simulation - component models Obtained from experiments Component performance Semi-empirical models Models with some constants set by measurements or design experience. Ex: Scaled maps Existing performance maps are scaled to new design point. Data from component rig tests Higher order models (2D or 3D simulation)

  5. The off design simulation - component models Engine system model is built by its component models Iteration is frequently required to determine the running line Some engine specific algorithms are found in chapter 8 and 9.

  6. Part load importance WR21 better fuel efficiency than simple cycle Aircraft High. Taxiing and landing. Power generation Low (except for ambient conditions). However, surge free starting and shut down as well as time to max. power is important. Naval High. Poor gas turbine part load performance has given rise to a number of combined cycles: CODOG, COSAG, COGAG Vehicular gas turbine High. 1% fuel efficiency idle

  7. Layout types to be studied off design Single shaft engine: Free turbine engine: Jet engine: Poses the same restriction on upstream components

  8. Off-design of single-shaft engine • By approximating the fuel flow as equal to bleeds, compatibility of flow gives: Select a constant speed line on compressor characteristic. Reading of point gives: • Turbine pressure ratio is obtained from (neglect inlet and exhaust losses):

  9. Off-design of single-shaft engine • Rotational speed and corrected mass flow gives turbine efficiency from turbine map. • The power output is then: The turbine rotational speed is now obtained:

  10. Off-design of single-shaft engine We have now determined the power output corresponding to the selected point in the compressor map. Does it match the load? Performance problemexam 2003

  11. Gas generator performance Free turbine engine Derive common procedure for bothengines - GAS GENERATORmatching! Poses the same restriction on upstream components Jet engine

  12. Off-design of gas generator • By approximating the fuel flow as equal to bleeds, compatibility of flow gives: Select a constant speed line on compressor characteristic. Reading of point gives: • Turbine pressure ratio is relatedto (neglect inlet and exhaust losses):

  13. Off-design of gas generator • Guess turbine pressure ratio and proceed as usual: Verify assumption with power balance

  14. Off-design of gas generator and load • Every point on compressor rotational speed has a matching point, but only one of these will match the exhaust nozzle/free turbine!!! • A simple nested iteration will do: match_load: DO match_gas_generator: DO ! gas generator simulation code END DO match_gas_generator ! load check simulation code END DO match_load

  15. Off-design of free turbine engine - load match • For the free turbine we obtain acorrected mass flow as input: where: Do they match ?? • The free turbine pressure ratio is obtained from (power turbine exit pressure is approximately pa):

  16. Off-design of jet engine • The characteristics of the turbine nozzles are the same as the exhaust nozzle => we have already solved the problem • Use same procedure but check with exhaust nozzle characteristic instead of turbine characteristic!

  17. Design Task 3 Klassens, Wood, Schuman “Experimental Performance of a …. Centrifugal Compressor Designed for a 6:1 Pressure Ratio”NASA TMX-3552 1977 You receive a Start Kit which contains characteristics Start by solving warm up task

  18. Design Task 3 – two nested iterations Gasgen. Odp.m (off-design performance) Turbojet.m Gasgen.m • Start with inner loop – gas generator • Check that you get (T3/T1)work=(T3/T1)flowwhen you run with Design Task 1 data • Then solve inner loop with fminbnd and continue with outer

  19. Design Task 3 • Predict off-design T5,Thrust and SFC • Determine engine conditions at 500 mph and 30000 feet

  20. Minimize a function of one variable on a fixed interval. Syntax: x = fminbnd(fun,x1,x2) x = fminbnd(fun,x1,x2,options) x = fminbnd(fun,x1,x2,options,P1,P2,...) Start by solving test example Fig217_test, that is make sure that you obtain fa = 0.01452 for t02=482.0 and t03=1046.0. (faair = 0.0, fastoch = 0.06760, Qnet=43200000 ) Make sure you understand the manual for fminbnd. Use of fminbnd % Solve non-linear 1D equation by minimization fa = fminbnd('fa_err',faair,fastoch,[],t02,t03,Qnet);

  21. Use of non-dimensional numbers function mfp4_err = Turbojet(rc,i,pa,P01,T01,eta_t,eta_m,eta_j,deltaP_b,A3,A5, … gamma_a,gamma_g,cp_a,cp_g,R) [mcorr1,eta_c,ncorr1] = CompChar(i,rc); % p02 = rc*P01; % p03 = p02*(1.0-deltaP_b); r_b = p03/p02; theta = T01/288.15; delta = P01/101325.0; m = (mcorr1*delta)/sqrt(theta); mfp1 = m*sqrt(T01)/P01; …..

  22. Approximation for two turbines in series • For the gas generator exit we have: Typically, variation in turbine efficiency will be limited we can plot outflow and inflow in same turbine map! Same effect with nozzle downstream of gas-generator turbine!!!

  23. Theory 11.1 – Simplified turbojet running line The compressible continuity function (x-function):

  24. Theory 11.1 – Simplified turbojet running line Assume that both exhaust nozzle and turbine operate choked: Exhaustnozzle Nozzle choked andefficiency approx. const. => temperature and pressure ratio is constant over turbine If the exhaust nozzle operates choked, the turbine will remain in the same non-dimensional point! Assuming a fixed efficiency => temperature ratio will then remain constant.

  25. Theory 11.1 – Simplified turbojet running line Finally, a work balance will be introduced: The compressor pressure ratio is obtained from: Combining yields:

  26. Theory 11.1 – Simplified turbojet running line Combining the two equations yield: We have derived an explicit expression for the running line!!!

  27. Master algorithms for calculating performance for: Single shaft engine Jet engine Free turbine engine Know how to derive an expression for the running line as well as to state the requirements for this expression to hold Learning goals

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