GasTurb 13 – Tutorial 4 Optimizing a Cycle Copyright © GasTurb GmbH

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

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

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

Starting Point of the Optimization Copyright © GasTurb GmbH

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

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

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

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

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

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

Repeating the Optimization Copyright © GasTurb GmbH

Repeating the Optimization Copyright © GasTurb GmbH

Introducing Constraints The Min Value must be lower than the Start Value The Max Value must be higher than the Start Value 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. Copyright © GasTurb GmbH

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

Result of the Constrained Optimization 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. Turbine Pressure Ratio is 4 Copyright © GasTurb GmbH

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

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

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

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

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

Result of the Optimization The SFC was previously 16.51, Optimization has reduced it by 6.3%. Net Thrust >= 31 kN T45 <=1300K Copyright © GasTurb GmbH LPT Pressure Ratio <=12 The solution fulfills the Constraints

Optimization Input Copyright © GasTurb GmbH Do all of these constraints really apply to Cruise conditions? 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”. Copyright © GasTurb GmbH We have optimized the cycle for minimum SFC at cruise conditions. However, …

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

Select the Mission Option Copyright © GasTurb GmbH

In the Design Input Window click Optimization and Run. Mission Input 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. Choose a Single Point Mission and enter the Take-Off operating conditions as well as the required thrust of 145kN Copyright © GasTurb GmbH

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

After the Optimization Run Copyright © GasTurb GmbH

The Cycle Design Point Copyright © GasTurb GmbH The SFC was previously 16,51. Single Point Optimization yielded 15,47. but T45 at Hot Day Take-Off was 1351K. With additional constraint for Off Design (T45 <= 1300K), SFC is reduced by 5.3%. Net Thrust >= 31 kN T45 is not constrained at the cycle design point Copyright © GasTurb GmbH LPT Pressure Ratio <=12

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