What is Topology Optimization ?

Topology optimization is a mathematical method to optimize the arrangement of materials in the design space under given analytical conditions and constraints.

We will not go into a detailed explanation of topology optimization in this article; please refer to the many explanatory materials available on the Web.

Please also check out the lectures by Dr. Kazuo Yonekura and Dr. Kentaro Yaji at our OpenNA event, where they explain the basics and applications of topology optimization.

Heat Sink Design

Topology optimization seems to be a universal method for generating geometry from scratch once the problem is set up, but in reality, some setups are difficult to solve, and solving the optimization may yield inappropriate results.

This article describes a heat sink design case study, along with design philosophy and examples of challenges faced in designing with thermo-fluid topology optimization and how to deal with them.

We used COMSOL Multiphysics® for topology optimization and took advantage of the topology optimization framework distributed by Dr. Kentaro Yaji.

Problem-Solving

As shown in the figure below, consider a system in which a cooling plate is placed above the heat source and liquid flows inside the cooling plate to cool it.

The topology optimization setup was as follows The detailed values are omitted.

• Topology optimization model
  • Cooling plate modeled in two layers: solid layer and fluid layer（reference paper：doi.org/10.1016/j.ijheatmasstransfer.2019.118462）
  • Use density method
• Boundary conditions
  • Inlet, Outlet：Pressure fixed boundary
  • Heat source：Constant energy sources
  • Wall：Insulation
• Objective function
  • Maximum temperature minimization of solid layer
• Constraints: None

Design Philosophy

The design was based on the idea of combining human knowledge with topology optimization to create a structure that could not have been conceived by humans alone.

Topology optimization alone is limited in its applicability to design problems because it is difficult to take into account various design constraints, and optimization of the entire design object cannot be solved in a realistic amount of time.

In addition, when design is based solely on human knowledge, the range of shapes that can be designed is limited because people can only think of shapes within the limits of what they can come up with.

We believe that topology optimization and people's respective strengths can be combined to create a better design.

Issue 1: Turbulence

One of the challenges is the effect of flow turbulence.

In general, a turbulence model is used with a boundary layer for analysis of turbulent conditions, but for topology optimization, where the wall surface changes during the optimization process, the entire design domain must be meshed with a size equivalent to that of the boundary layer.

Unsteady analysis may also be necessary when the degree of turbulence is strong.

Although topology optimization using turbulence models and unsteady state topology optimization has been done in research, there are still hurdles to overcome in its application to design.

In this design, topology optimization is positioned as a low-fidelity model in a multi-fidelity analysis, and topology optimization is performed in a state close to laminar and creep flow by correcting for physical properties and other factors.
As shown in the figure below, a change in the Reynolds number of the flow changes the local flow, but does not significantly change the global flow. The topology optimization was used to search for the global flow in laminar flow conditions, and the geometry was modified to reproduce the global flow in turbulent flow conditions.

Issue 2: Locally optimal solution

Because topology optimization is a multi-degree-of-freedom optimization, there can be a very large number of locally optimal solutions.

It would be nice if the locally optimal solution is a meaningful result for the design, but depending on the problem setting, it may not be meaningful.

For example, in this setup, different optimization results are obtained for each initial value, as shown in the following figure

In this design, the shape was guided to a meaningful solution in the design by running the topology optimization iteratively with the optimization results feedback to the initial values.

The topology optimization itself corresponds to a continuous, gradient-based design space, but the feedback of the optimization results to the initial values is a discontinuous change.

This discontinuous change was designed by human interpretation, search and optimization algorithms, and in-house design know-how in terms of the physics and optimization of the optimization results.

Issue 3: Manufacturability and readability

Topology optimization often cannot include all manufacturing constraints, so it is difficult to use the geometry obtained from optimization as is.

Therefore, it is essential to modify the geometry, but it is simply not clear how modifying the geometry will affect performance.

Even if the geometry obtained by topology optimization could be manufactured as is, it is highly likely that it would not be a valid design because the geometry is complex and quality control would be difficult, or design changes would be difficult because the intent of the geometry is unknown.

In this design, after interpreting the physical intent of the geometry obtained through topology optimization, the concept of the geometry was extracted and the geometry was modified to improve manufacturability and readability.

For example, we extracted the following concept and modified the shape as shown below.

• To reduce the heat transfer of fluid upstream where cooling is easier, the upstream space is narrower and the residence time of fluid is shorter.
• To increase fluid heat transfer downstream, where it is harder to cool, the downstream space is narrower and the fluid's residence time is longer.
• Bypass shape sends cold fluid downstream in a shorter path.

Design Results

Cooling with this design shape reduced the temperature rise by about 47% compared to the reference shape, and by 15% compared to the reference fins modified to the appropriate density.

Summary

In this article, we have presented a case study of a heat sink design that combines topology optimization and human hands.

With the development of analysis and optimization technologies, the way product design is conducted is changing.

We believe that better design can be achieved not only by using analysis and optimization technology in design, but also by having people supplement and provide appropriate feedback and correction to areas that cannot be reached by analysis and optimization technology.