59717 - Structurally Constrained Aerodynamic Adjoint Optimisation of Highly Loaded Compressor Blades 

Adjoint aerodynamic optimisation has recently gained increased popularity for turbomachinery applications due to the large number of parameters that can be used without incurring additional computational costs. This work presents an adjoint based aero-structural optimisation method having efficiency as objective function and maximum von Mises stress set as a constraint. The full optimisation loop was set up and tests were carried out on a highly loaded compressor blade. The geometry parameterisation method used is the free form deformation method. A discrete adjoint approach was used to obtain the gradients of the objective function with respect to each design parameter and the search direction, along with a sequential least squares programming algorithm used as the optimizer.

To further benefit from reduced computational costs, the evaluation and constraining of the maximum stress was done by using a response surface generated beforehand. To enable the use of a large number of points in our design of experiments, a meshless tool was used for performing the stress analysis and building up the response surface. Two design of experiments were generated by the latin hypercube sampling method, using 2000 and 20000 points, respectively. For each of these design of experiments, three different response surfaces were created by using the polynomial, kriging and radial basis function methods, resulting in six different response surfaces. These response surfaces were then compared in terms of the Pearson correlation coefficient, the root mean square error and computational time based on two test cases. The first test case consisted of an additional 200 geometries also generated by the latin hypercube method in our design space. The second test consisted of 30 geometries generated in an optimisation process. Based on the results of both tests, it was concluded that the 20000 points polynomial response surface gives the best results.

This response surface was further used as a surrogate model in the structurally constrained aerodynamic adjoint optimisation of the highly loaded compressor blade under consideration. It was found that the method successfully increases the efficiency by more than 3% while maintaining the maximum stress under the imposed value, corresponding to the maximum von Mises stress of the datum. The results showed that the constrained optimization leads to a design with 1% lower efficiency than that obtained through the unconstrained optimisation. However, in the unconstrained optimal geometry the maximum stress value doubled, rendering the design completely unfeasible. Constraining the maximum stress at 130% of the datum value led to an efficiency value for the optimum almost as high as that of the unconstrained optimal geometry. This shows the effectiveness of the method in increasing the efficiency of compressor blades while maintaining a low value for the maximum von Mises stress and the importance of using structural constraints early in the optimization process.

Overall, the work provides a methodology for conducting structurally constrained adjoint aerodynamic optimisation that can be applied for large number of design parameters while maintain low computational costs. It also provides reference for constructing and selecting a response surface to be used in the optimisation process.