1. Chalmers University of Technology 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. Chalmers University of Technology 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 corresponds to new engine design - new turbine/compressor blading nozzle areas etc Design = rubber engines

3. Chalmers University of Technology The off design problem 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 running line Shows proximity to surge line

4. Chalmers University of Technology The off design simulation - component models 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) Obtained from experiments

5. Chalmers University of Technology 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. Chalmers University of Technology Part load importance 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 WR21 better fuel efficiency than simple cycle

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

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

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

10. Chalmers University of Technology 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 problem exam 2003

11. Chalmers University of Technology Gas generator performance Poses the same restriction on upstream components Jet engine Free turbine engine Derive common procedure for both engines - GAS GENERATOR matching!

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

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

14. Chalmers University of Technology 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. Chalmers University of Technology Off-design of free turbine engine - load match For the free turbine we obtain a corrected mass flow as input: where: The free turbine pressure ratio is obtained from (power turbine exit pressure is approximately p a ):

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

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

20. Chalmers University of Technology Use of fminbnd 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. % Solve non-linear 1D equation by minimization fa = fminbnd( 'fa_err',faair,fastoch,[],t02,t03,Qnet);

21. Chalmers University of Technology 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; ….. Use of non-dimensional numbers

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

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

24. Chalmers University of Technology Theory 11.1 – Simplified turbojet running line Assume that both exhaust nozzle and turbine operate choked: 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. Exhaust nozzle Nozzle choked and efficiency approx. const. => temperature and pressure ratio is constant over turbine

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

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

27. Chalmers University of Technology Learning goals 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