Research Fellows
Ismael Sānchez Torreguitart
Early Stage Researcher 13 at Von Karman Institute
The originalities of this research are related to:
1. The way the CAD model is used within the gradient based shape optimization loop
Defining the design variables in the CAD system requires computing the derivatives of the grid coordinates with respect to the CAD design variables. This was done by differentiating the CAD kernel and grid generator of the VKI’s in-house software CADO using the ADOL-C tool in forward and reverse modes of algorithmic differentiation. In this way, it was possible to compute accurate gradients whilst avoiding the topology and label renaming issues that can arise with the finite difference approach. Using algorithmic differentiation for the derivative computation requires more memory than the finite differences approach, but it performs significantly faster specially for large number of design variables.
The VKI LS89 axial turbine cascade is selected as a demonstrator to test the methodology. The profile is parameterized by 24 design parameters (Fig. 1) and the geometrical as well as grid sensitivities are obtained for each parameter, showing the influence of each design parameter on the profile and on the profile surface X-Y grid coordinates.
For example, Fig.2a shows the magnitude and direction of the geometrical sensitivities obtained for the suction side first Bézier control point position relative to the camber line (i.e., t1SS). The magnitude of the grid sensitivities obtained for the tSS1 parameter is computed using Eq. 1 and is shown in Fig. 2b for t1SS.
Figure 3a and 3b show the maximum error in magnitude between the FD approximated and the exact AD sensitivities for the t1SS design parameter. The sensitivities obtained by AD are compared against second order accurate central finite difference approximations through changing the perturbation step. The error is very sensitive to the chosen step size and the step size needs to be relatively small to have a small error.
