1. OPTIMIZING A CYCLE GasTurb 12 – Tutorial 4 Copyright © GasTurb GmbH

2. GasTurb 12 Main Window For this tutorial we will use a Turbojet. Copyright © GasTurb GmbH

3. We Need Some Data Copyright © GasTurb GmbH Select the engine model Open the engine model

4. Input Data Page First we run a single cycle Copyright © GasTurb GmbH

5. Starting Point of the Optimization Copyright © GasTurb GmbH

6. Optimization Task: Find the Compressor Pressure Ratio for Minimum SFC The SFC minimum is at pressure ratio 65 Copyright © GasTurb GmbH The optimization feature allows finding the SFC minimum without doing a parametric study. A parametric study with Pressure Ratio as the only parameter yields…

7. Selecting Optimization Now we go for Optimize. Copyright © GasTurb GmbH

8. Optimization Input Window The Min Value must be lower than the Start Value The Max Value must be higher than the Start Value Copyright © GasTurb GmbH First drag the Optimization Variable to the input grid. Next enter boundaries for the variables. Finally define the Figure of Merit

9. Optimization Input Window The Figure of Merit can be maximized or minimized. Of course SFC shall be minimized Copyright © GasTurb GmbH Drag your Figure of Merit to the box. Now run the optimization

10. The Optimization Window The upper boundary (Max Value) for the variable The lower boundary (Min Value) for the variable Click to run the optimization Copyright © GasTurb GmbH Let us have a look at the result.

11. SFC Optimum Copyright © GasTurb GmbH This result is somewhat unrealistic for a turbojet - among other reasons because the turbine pressure ratio is almost 24.

12. Repeating the Optimization Copyright © GasTurb GmbH

13. Repeating the Optimization Copyright © GasTurb GmbH

14. Introducing Constraints The Min Value must be lower than the Start Value The Max Value must be higher than the Start Value Copyright © GasTurb GmbH We introduce as Constraint the Turbine Pressure Ratio. We enter for the upper boundary (Max Value) 4. This is a reasonable limit for a single stage turbine. The Min Value is of no relevance for this optimization problem. Then we re-run the optimization. We enter for the upper boundary (Max Value) 4. This is a reasonable limit for a single stage turbine. The Min Value is of no relevance for this optimization problem. Then we re-run the optimization.

15. End of the Constrained Optimization The value of the optimization variable is within the Min and Max Values The value of the optimization constraint is equal to the Max Value Copyright © GasTurb GmbH

16. Result of the Constrained Optimization Turbine Pressure Ratio is 4 Copyright © GasTurb GmbH This introduction to optimization was very simple. The problem could have been solved also with a simple parametric study. Next we go for a more complex task which would require many parametric studies for finding the optimal solution. Applying numerical optimization leads quickly to the result. This introduction to optimization was very simple. The problem could have been solved also with a simple parametric study. Next we go for a more complex task which would require many parametric studies for finding the optimal solution. Applying numerical optimization leads quickly to the result.

17. GasTurb 12 Main Window Copyright © GasTurb GmbH The file opening menu will appear automatically, read the file Demo_gtf.CYG After reading the data, the design input window opens. The file opening menu will appear automatically, read the file Demo_gtf.CYG After reading the data, the design input window opens. We will consider a Geared Unmixed Flow Turbofan.

18. Input Data Page First we run a single cycle Copyright © GasTurb GmbH

19. Starting Point of the Optimization Copyright © GasTurb GmbH After closing this window click Optimization. Then, hit the Optimize button. After closing this window click Optimization. Then, hit the Optimize button.

20. Optimization Input There are five optimization variables… … and three Constraints. Copyright © GasTurb GmbH The Figure of Merit is again SFC

21. Optimization Status Copyright © GasTurb GmbH Let us have a look at the optimum Status at the begin of the optimization Status at the end of the optimization

22. Result of the Optimization LPT Pressure Ratio <=12 T45 <=1300K Net Thrust >= 31 kN Copyright © GasTurb GmbH The solution fulfills the Constraints The SFC was previously 16,60, Optimization has reduced it by 4.6%. The SFC was previously 16,60, Optimization has reduced it by 4.6%.

23. Optimization Input Do all of these constraints really apply to Cruise conditions? Copyright © GasTurb GmbH We have optimized the cycle for minimum SFC at cruise conditions. However, … No ! the LPT Inlet Temperature T45 Limit must not be exceeded during a hot day Take-Off. Next we will show how this can be taken into account. Go back to the GasTurb Main Window. When asked to restore the old data, chose “Yes”. No ! the LPT Inlet Temperature T45 Limit must not be exceeded during a hot day Take-Off. Next we will show how this can be taken into account. Go back to the GasTurb Main Window. When asked to restore the old data, chose “Yes”.

24. GasTurb 12 Main Window Select Off Design… …and Standard Maps Copyright © GasTurb GmbH

25. Select the Mission Option Copyright © GasTurb GmbH

26. Mission Input Copyright © GasTurb GmbH Choose a Single Point Mission and enter the Take-Off operating conditions as well as the required thrust of 145kN Run the Single Point Mission and check if the off-design iteration converges. Close the Mission Windows and go back to the GasTurb12 Main Window. Switch back to the Calculation Mode Design and select Performance. In the Design Input Window click Optimization and Run. Run the Single Point Mission and check if the off-design iteration converges. Close the Mission Windows and go back to the GasTurb12 Main Window. Switch back to the Calculation Mode Design and select Performance. In the Design Input Window click Optimization and Run.

27. Design and Off-Design Constraints These dropdown lists are visible only if a mission is defined. Select “Case 1” to apply the T45 constraint to the off-design condition. Click Constraints Copyright © GasTurb GmbH

28. After the Optimization Run Copyright © GasTurb GmbH

29. The Cycle Design Point LPT Pressure Ratio <=12 T45 is not constrained at the cycle design point Net Thrust >= 31 kN Copyright © GasTurb GmbH The SFC was previously 16,60. Single Point Optimization yielded 15,83. but T45 at Hot Day Take-Off was 1324K. With additional constraint for Off Design (T45 <= 1300K), SFC is reduced by 3.9%. The SFC was previously 16,60. Single Point Optimization yielded 15,83. but T45 at Hot Day Take-Off was 1324K. With additional constraint for Off Design (T45 <= 1300K), SFC is reduced by 3.9%.

30. Hot Day Sea Level Take-Off T45 <=1300K Copyright © GasTurb GmbH This slide ends the Control System Optimization Tutorial This slide ends the Control System Optimization Tutorial