Research

Topology Optimization of Heat Sink for 3D Integrated Power Converters

This paper proposes a density-based topology optimization scheme to design a heat sink for the application of a 3D integrated SIC-based 75 kVA Intelligent Power Stage (IPS). The heat sink design considers the heat conduction and convection effects with forced air cooling. The objective function is to minimize the thermal compliance of the whole structure. A volume constraint is imposed to reduce the overall volume of the designed heat sink to make it conformal to the underlying power devices. Some numerical techniques like filtering and projection schemes are employed to render a crisp design. Some 2D benchmarks examples are first provided to demonstrate the effectiveness of the proposed method. Then a 3D heat sink, especially designed for the 3D IPS, is topologically optimized. The classic tree-like structure is reproduced to reinforce the convection effect. Some comparisons with the intuitive baseline designs are made through numerical simulation. The optimized heat sinks are shown to provide a more efficient cooling performance for the 3D integrated power converter assembly.

Topology Optimization of Thermal Cloaks in Euclidean Spaces and Manifolds using an Extended Level Set Method

 Thermal cloaks are devices designed to shield an object against thermal detection, which have attracted growing interest in research. This paper proposes to design thermal cloaks using the level-set-based shape and topology optimization in the context of pure heat conduction. The cloaking effect is achieved by optimizing the distribution of two bulk heat conductive materials to eliminate the temperature disturbance induced by the introduction of the insulator (cloaking region) into a homogeneous thermal conduction medium. The optimized thermal cloaks are free of high anisotropy and non-homogeneity commonly seen in the popular transformation thermotics or scattering cancellation methods. Due to the clear boundary characteristic of the level set representation, no sophisticated filtering techniques are required to suppress the appearance of  “gray regions” as opposed to the density-based topology optimization methods. Considering the fact that the device components that need to be thermally cloaked, e.g., sensors, can take an arbitrary free-form shape, a conformal thermal cloak on the manifold is also topologically optimized using the extended level set method (X-LSM), which has not been reported in the literature. The structural boundary is evolved by solving the (modified) Hamilton-Jacobi equation. The feasibility and robustness of the proposed method to design thermal meta-devices with cloaking functionality are demonstrated through a number of 2D and 3D (solid and shell) numerical examples with different cloaking regions (circular, human-shaped, spherical, and curved circular). This work may shed light on further exploration of the thermal meta-devices in the heat flux manipulation regime.

Shape and Topology Optimization of Conformal Thermal Control Structures on Free-form Surfaces: A Dimension Reduction Level Set Method (DR-LSM)

In this paper, the authors propose a dimension reduction level set method (DR-LSM) for shape and topology optimization of heat conduction problems on general free-form surfaces utilizing the conformal geometry theory. The original heat conduction optimization problem defined on a free-form surface embedded in the 3D space can be equivalently transferred and solved on a 2D parameter domain utilizing the conformal invariance of the Laplace equation along with the extended level set method (X-LSM). Reducing the dimension can not only significantly reduce the computational cost of finite element analysis but also overcome the hurdles of dynamic boundary evolution on free-form surfaces. The equivalence of this dimension reduction method rests on the fact that the covariant derivatives on the manifold can be represented by the Euclidean gradient operators multiplied by a scalar with the conformal mapping. The proposed method is applied to the design of conformal thermal control structures on free-form surfaces. Specifically, both the Hamilton–Jacobi equation and the heat equation, the two governing PDEs for boundary evolution and thermal conduction phenomena, are transformed from the manifold in 3D space to the 2D rectangular domain using conformal parameterization. The objective function, constraints, and the design velocity field are also computed equivalently with FEA on the 2D parameter domain with properly modified forms. The effectiveness and efficiency of the proposed method are systematically demonstrated through five numerical examples of heat conduction problems on the manifolds.

Topology Optimization of Multi-material Thermoelectric Structures

A large amount of energy from power plants, vehicles, oil refining, and steel or glass making process is released to the atmosphere as waste heat. The thermoelectric generator (TEG) provides a way to reutilize this portion of energy by converting temperature differences into electricity using Seebeck phenomenon. Because the figures of merit zT of the thermoelectric materials are temperature-dependent, it is not feasible to achieve high efficiency of the thermoelectric conversion using only one single thermoelectric material in a wide temperature range. To address this challenge, the authors propose a method based on topology optimization to optimize the layouts of functional graded TEGs consisting of multiple materials. The multimaterial TEG is optimized using the solid isotropic material with penalization (SIMP) method. Instead of dummy materials, both the P-type and N-type electric conductors are optimally distributed with two different practical thermoelectric materials. Specifically, Bi2Te3 and Zn4Sb3 are selected for the P-type element while Bi2Te3 and CoSb3 are employed for the N-type element. Two optimization scenarios with relatively regular domains are first considered with one optimizing on both the P-type and N-type elements simultaneously, and the other one only on single P-type element. The maximum conversion efficiency could reach 9.61% and 12.34% respectively in the temperature range from 25 °C to 400 °C. CAD models are reconstructed based on the optimization results for numerical verification. A good agreement between the performance of the CAD model and optimization result is achieved, which demonstrates the effectiveness of the proposed method.