Overview

The CFD optimization of different car components has the potential of significantly shortening the design process (Othmer & Grahs, 2005).  The adjoint method recently implemented in PAM-FLOW^TM is an advanced approach which aims to compute the sensitivities of the cost function and to plug them into a gradient-based optimization algorithm.

The purpose of this user tip is to demonstrate the ability of PAM-FLOW^TM to compute the sensitivities of the pressure drop cost function via an adjoint state and to optimize the duct shape.

Optimization Loop

Figure 1.  Adjoint optimization loop 

Sensitivities computation with adjoint states

The adjoint approach to optimal design consists of computing the sensitivities of the cost function via an adjoint state, and plugging these sensitivities into a gradient based optimization algorithm.

The advantage of the adjoint state is the following: for any number of design variables, only two solver calls are necessary (one for the CFD solver and one for the adjoint solver). For the duct optimization, the cost function used is to minimize the pressure drop.

In Figure 2 , the pressure field is shown for the initial design.

Figure 2.  Pressure field for the initial shape	Figure 3.  Gradients of the objective function

Figure 3 represents the gradient of the objective function. The red/magenta colors show the areas for which any geometrical change will modify the pressure drop significantly.

In the same figure, the gradient vectors are depicted. The arrow indicates the direction of the positive sensitivity, i.e. the direction of the node movement that produces an increase of the objective function which is the pressure drop. To reduce it, we have to move the walls in the opposite direction.

At the end of the sensitivity run, the 3D mesh is deformed (morphed) with respect to the design variables. Using the optimized mesh, we have to perform a new flow simulation in order to check the improvement of the cost function.

Figure 4.  Initial and optimized shape on the centerline (red, optimized shape)	Figure 5.  Initial and optimized shape (blue, optimized shape)

The maximum displacement of boundary nodes is around 3mm. In the Figures 4 and 5, the initial shape and the optimized shape are shown.  The pressure drop is reduced by 20% after one optimization loop.

Conclusions

The steady flow simulation in a duct has been performed using PAM-FLOW^TM incompressible solver. Starting from this flow solution, the adjoint solver has been applied in order to calculate the sensitivities for the cost function.

The obtained sensitivities results offer the opportunity to perform a shape change in order to optimize the pressure drop. After one optimization loop, an improvement by around 20% was obtained. This study shows that the adjoint method implemented in PAM-FLOW is a very powerful approach for industrial optimization tasks.

Regards,
Daniel Vinteler
ESI CFD Support Team - France

References

“Approaches to Fluid Dynamic Optimization in the Car Development Process”, C. Othmer and T. Grahs, EUROGEN 2005, FLN Munich 2005

“An Adjoint-Based Design Methodology for CFD Optimization Problems”, R. Lohner and all, AIAA-03-0200, 2003

PAM-GEN3D^TM Theory Manual, 2006
PAM-GEN3D^TM Reference Manual, 2006
PAM-FLOW^TM SOLVER, Theory Manual, 2006
PAM-FLOW^TM SOLVER, Reference Manual, 2006
PRE-FLOW, Reference Manual, 2006
POST-FLOW, Reference Manual, 2006