Principal Investigator Qiqi Wang
Multi-stage centrifugal compressors are widely used across industries and the demand is growing in the radial and axial compactness to reduce cost and increase reliability. Optimized design is therefore needed to reduce the loss caused by the innate 180 degree change in flow direction in the return bend. Conventional gradient-based optimization becomes computationally expensive when computing gradients in such a high dimensional problem, requiring a number of simulation runs equal to the number of design variables.
In contrast, adjoint method uses linear approximation to construct adjoint equations. By solving only once the flow equations and the adjoint equations, the sensitivity is obtained for an objective function, i.e. performance metric, with regard to any number of design variables.
In practice, a generalized free-form deformation algorithm has been developed for the geometry perturbation which is free from the traditional control point configuration constraints. The perturbation converts into residuals of the primal flow equations. Then the sensitivity is computed by integrating the product of adjoint equation solution and the residuals over the computational domain. The adjoint-based sensitivity is verified against that obtained using finite-difference method using a low Reynolds number, laminar flow case. The evolution of return bend geometry deformation is then automated based on the feedback of sensitivity, using a Quasi-Newton method, until an optimal design is reached within given constraints.
The adjoint-based optimization would ideally explore the design space more comprehensively, and cost-effectively. Future work could include implementing turbulence model and adaptive meshing.