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Topology Optimization of Cooling Channels Using Dual-Type Moving Morphable Components

Shunsuke Hirotani, Kunitaka Shintani, Yoshikatsu Furusawa, Kentaro Yaji

Abstract

Efficient thermal management in high-power electronic devices requires cooling channel designs that provide high heat removal while satisfying strict spatial and manufacturing constraints. This study presents a two-stage hierarchical topology optimization framework for cooling channels based on the Moving Morphable Components (MMC) method. The optimization is performed sequentially: in the first stage, only wall components are optimized to establish the global flow network and insignificant components are removed; in the second stage, the global structure is fixed and fin components are optimized to improve local thermal performance. The method is coupled with a two-layer thermofluid model using the Brinkman approximation and solved with the adjoint sensitivity approach. Across multiple inlet pressure conditions, the proposed framework consistently generates designs with clear functional separation. The results demonstrate that exploring such clearly separated structures through a two-stage optimization strategy leads to a further reduction in the objective function. Compared with simultaneous MMC optimization and conventional density-based topology optimization, the proposed method produces geometries that are more interpretable, controllable, and suitable for manufacturing.

Topology Optimization of Cooling Channels Using Dual-Type Moving Morphable Components

Abstract

Efficient thermal management in high-power electronic devices requires cooling channel designs that provide high heat removal while satisfying strict spatial and manufacturing constraints. This study presents a two-stage hierarchical topology optimization framework for cooling channels based on the Moving Morphable Components (MMC) method. The optimization is performed sequentially: in the first stage, only wall components are optimized to establish the global flow network and insignificant components are removed; in the second stage, the global structure is fixed and fin components are optimized to improve local thermal performance. The method is coupled with a two-layer thermofluid model using the Brinkman approximation and solved with the adjoint sensitivity approach. Across multiple inlet pressure conditions, the proposed framework consistently generates designs with clear functional separation. The results demonstrate that exploring such clearly separated structures through a two-stage optimization strategy leads to a further reduction in the objective function. Compared with simultaneous MMC optimization and conventional density-based topology optimization, the proposed method produces geometries that are more interpretable, controllable, and suitable for manufacturing.

Paper Structure

This paper contains 16 sections, 15 equations, 12 figures, 1 table.

Table of Contents

  1. Introduction
  2. Optimization Framework
  3. Proposed Optimization Framework
  4. Thermofluid Model
  5. Formulation
  6. Design Variables of Individual Components
  7. Topology Description Functions and Projection Functions
  8. Optimization Formulation and Numerical Implementation
  9. Optimization Problem
  10. Numerical Implementation
  11. Numerical Examples
  12. Numerical Model
  13. Results of the Two-Stage Optimization at Different Inlet Pressures
  14. Comparison Between Simultaneous Optimization and Two-Stage Optimization
  15. Comparison with Density-Based Topology Optimization
  16. ...and 1 more sections

Figures (12)

  • Figure 1: Conceptual diagram of the proposed optimization framework.
  • Figure 2: Wall components and fin components used in the optimization.
  • Figure 3: Geometry model and boundary conditions for the two-dimensional cooling device.
  • Figure 4: Results at each inlet pressure during wall optimization: (a) $p_\text{in}=50$ Pa, (b) $p_\text{in}=100$ Pa, (c) $p_\text{in}=200$ Pa. The top row shows the material distribution, the middle row shows the flow velocity distribution, and the bottom row shows the temperature distribution of the solid layer.
  • Figure 5: Objective function histories during wall-component optimization for multiple inlet pressure conditions.
  • ...and 7 more figures