Adjoint-Based Design Optimization of a Volute for Radial Compressor

Authors

Romain Hottois  - von Karman Institute for Fluid Dynamics, Belgium
Tom Verstraete - von Karman Institute for Fluid Dynamics, Belgium
Arnaud Châtel - von Karman Institute for Fluid Dynamics, Belgium

Abstract

Nowadays, numerical methods are widely used within the framework of design optimization of turbomachinery components due to the cost and time savings that they provide. Gradient-based optimization methods generally offer the benefit of a faster convergence at a lower computational cost, especially in the case of complex geometries where the number of design parameters can be significant. This is typically true for the parametrization of a full-stage radial compressor that can include the impeller, a vaneless or vaned diffuser and a volute. In the available literature, shape optimization is mainly focused on the improvement of the impeller alone. However, it is recommended to optimize the entire stage in one single process to directly consider flow interactions between the different components of the compressor. In previous research work led at von Karman Institute, the adjoint-based optimization of the SRV2-O wheel was performed and resulted in notable increase of the total-to-total efficiency. As a second step towards full-stage optimization, this paper aims to perform the adjoint-based optimization of a volute. The CAD of the volute is first created, using a parametrization of 30 design parameters. Then, a butterfly topology is applied to mesh the computational domain with a multi-block structural grid, and an elliptic smoothing procedure is then used to improve the quality of the fluid grid. A steady-state RANS CFD solver with Spalart-Allmaras turbulence model is used to solve the Navier-Stokes equations, and flow sensitivities are computed with an adjoint solver. The objective function consists in minimizing the loss coefficient of the volute. The gradients of this performance parameter with respect to the design variables are compared against complex step computations to validate the gradients accuracy before running the optimization. The optimization is performed to obtain an improved design with 5% reduction of losses expected. Detailed flow and design analysis is carried out to highlight the loss reduction mechanisms followed by the optimizer. Finally, the efficiency of the full stage with and without optimized volute is assessed through CFD computations using a mixing plane interface. This research will provide further development for the design of efficient radial compressors, using adjoint-based methods.