This paper discusses the aerodynamic optimization of low-pressure axial fans using adjoint Computational Fluid Dynamics (CFD).

In the first part, a typical CFD-based fan optimization problem is introduced. The focus is on the CFD model and potential objective functions.

The adjoint system of equations and the adjoint boundary conditions for this optimization problem are derived in the second part. Moreover, the software implementation in the open source CFD code OpenFOAM v3.0.x is described. The existing OpenFOAM solver “adjointShapeOptimizationFoam” serves as the basis and is customized to the optimization of fans. The code solves both the primal and the adjoint incompressible Reynolds-averaged Navier-Stokes (RANS) equations from which a sensitivity map of the objective function with respect to the grid topology can be derived. The main extension of the existing code deals with the consideration of a rotating frame of reference leading to additional source terms in both the primal and the adjoint RANS equations. Moreover, the implementation of new boundary conditions is performed to handle the distinct objective functions.

In the third part, the customized adjoint solver is applied to improve an existing baseline fan. Two adjoint simulations of the baseline fan are performed aiming at maximization of pressure and efficiency, respectively. The resulting surface sensitivities on the blade are used to modify the blade shape accordingly. Eventually, the performance of the two optimized fans is predicted by RANS to quantify the improvements. The first fan features a pressure rise which is 3.6 % higher as compared to the baseline fan. The second fan features an efficiency improvement of 0.1 percentage points as compared to the baseline fan. Hence, the functionality of the adjoint method is proven. A more substantial improvement would require further optimization loops with repeated adjoint simulations that, however, are not part of this paper.

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