Improving the accuracy of the topology optimization of turbulent flows

Abstract

Silicon based power semiconductors have
long been used as the standard in ‘semiconductor technology in power conversion
applications’. Recent developments replaces the Silicon with Silicon Carbide as
it results in superior performance of the power conversion applications.
However, due to the increased performance, challenges regarding heat
dissipation emerge and the lifetime of the power semiconductor packaging or
power module is compromised. Since this leads to an increase power density, the
cooling of the power module is becoming of more importance and the heat sink
becomes an interesting component to optimize. The best performance of a heat
sink can be obtained when the flow through the device is turbulent. Developing
turbulent flow heat sinks by using topology optimization methods can
significantly improve the cooling performance compared to the current designs.
This work is thus aimed towards improving methods for topology optimization of
turbulent flow cooling devices. However, this work focuses on turbulent flow
topology optimization only and aims to improve the accuracy of current methods.
It is important that the flow physics are accurate since the thermal energy
transfer is dependent on the flow field. The current state-of-the-art method
based on the 𝑘−𝜔 turbulence model developed by Dilgen et al. is investigated. A
design domain is subdivided into elements since the finite element method (FEM)
is used, such that an optimization algorithm is able to turn every element into
either fluid or solid with the goal of finding the best performing structure.
This density based approach, models the solid domain as a highly impermeably
porous material. To inhibit flow in the solid domain a Darcy penalization is
added to the momentum equation. Moreover, in the method by Dilgen et al.
boundary conditions in the other turbulent fields are also enforced using a
similar penalization approach. Weaknesses and errors in the density based
method are investigated by comparing solutions to ones computed on a body
fitted mesh. It has been found that the largest errors in the solution, by
using the state-of-the-art method, appear at the solid/fluid interface in the design.
In these regions the penalizations are not applied correctly for the desired
boundary conditions. Therefore, in this work it is improved on by the
enforcement of the boundary condition by using the Dilation method. The
Dilation method focuses on the solid/fluid region where it shifts the boundary
conditions for the specific dissipation rate (𝜔) and ensures it reaches the desired value at the solid/fluid
interface. Secondly, severe flow leakage is found in the “porous” solid domains
using the state-of-the-art method. Flow leakage is reduced by using an improved
formulation of the maximum Darcy penalization in the solid domain. Finally, the
improved approach is investigated in several topology optimization cases and
compared to the state-of-the-art Dilgen method. It is shown that by using the
new approach, different designs with a better accuracy can be obtained. In an
extreme test case, the Dilgen method resulted in an infeasible design which disconnects
the flow inlets from the outlets while the new and improved method resulted in
a feasible design.