Designing an effective fluid flow system such as a wind turbine or an aircraft wing requires a detailed understanding of the sensitivity of the objective function (for example, efficiency, lift, etc,) to a host of input parameters (for example the parameters determining the aerodynamic shape). Adjoint methods provide the sensitivity of the objective function to any number of input parameters at a reasonable cost. They are usually based on Reynolds-Averaged Navier-Stokes (RANS) models, which can be very inaccurate, especially in the presence of complex flow features such as flow separation. Thus, when the flow prediction itself has a significant error, the sensitivity obtained from the RANS-based adjoint method may not be useful in designing optimal aerodynamic configurations.
Our first objective was to improve the accuracy of the RANS turbulence model for separated flows using high-fidelity LES data, that accurately captures the flow physics. The adjoint methodology was used to spatially vary the turbulence-model parameters such that the RANS flow matches the corresponding LES flow. Our next goal was to use the improved RANS turbulence model in shape optimization. The geometry considered was a 3D U-Bend geometry widely studied in literature and integral to gas-turbine cooling channels. The final shape obtained using the improved RANS model was seen to be distinctly different from a shape obtained using an uncorrected baseline RANS model clearly demonstrating the potential of our approach. Our third goal was to study the effect of a refined parametrization of the U-Bend geometry. To bring out the full potential of the KAFKA strategy, we formulated a four-fold increase in the design variables for U-Bend geometry creation and carried out a shape optimization using the LES-aided RANS model, which brought forth much richer design features unseen in a low-parameter design space.
