Brief introduction on the issue:

FLUENT’s shape optimizer doesn’t appear to be giving the correct direction for optimizing the case with an energy objective function, but works fine with a momentum based objective function.

Section 1: Model introduction

The model is a tunnel, with the liquid flowing through it as shown in the figure 1 attached..

Boundary conditions:

Top surface: insulated wall.

Bottom surface: heat flux wall.

Side surfaces: symmetry.

Inlet: Mass flow rate.

Outlet: pressure outlet.

The objective function is minimizing the temperature of the bottom surface.

I already did a parametric study to validate the direction the optimizer should go: I simulate a case with smaller thickness and find that the smaller thickness can lead to the bottom surface temperature smaller:

Initial case, objective value: 449.51416K

Case with smaller thickness: 431.62213K

To do the shape optimization for this case, I use the adjoint based shape optimization in FLUENT.

Section 2: Sensitivity of optimal displacement

I made vector plots of sensitivity of optimal displacement for two cases, one is the case with the objective function that minimizing the bottom surface’s temperature, same as the section 1, and the other one is the case with objective function that maximizing the pressure drop between inlet and outlet.

From the plots, the geometry cannot change in y direction (thickness direction) when the objective function is temperature, but for objective function as the pressure drop, the design will be changed in y direction. These plots are also shown in the figure 2, attached

Section 3 Optimization process

For the case, the objective function is minimizing the temperature of the bottom surface, I set all the surfaces, except for the bottom surface, can be moved and the surfaces movement is constrained only in y direction, which is the thickness direction. The movement freedom is 1. The optimization results are shown below:

Initial case: 449.51416K

Optimized case: 439.35349K

There are two steps during the optimization, first running with -1% as target change and subsequently running with -0.3%. The residuals for first step are below 1e-10. As for the second step, the continuity residual is around 1e-5, other residuals are below 1e-7.

When I set larger target change, there is an error: negative cell volume detected.

Based on the optimized design, there is negligible change of the design, I also cannot find the expected design change in y direction (thickness direction).

Issue:

Based on the sections above, My question is why the optimizer does not make the geometry of energy on case (objective is minimizing the temperature) change in y direction(thickness direction) but can make the geometry of energy off case (objective is maximizing the pressure drop) change in y direction(thickness direction)?

How to resolve the error properly: negative cell volume detected so that I can use larger target change.

Thank you for any reply!

Zhengda Yao