技術情報とプレゼンテーション

Topology optimization of conjugate heat transfer problems is an relatively intricate problem due to the coupled nature of Navier-Stokes equation, continuity equation and energy equation. In any density based topology optimization code, the major parts are finite element analysis, sensitivity analysis and core optimization algorithm like Method of Moving Asymptotes(MMA), Optimality Criteria method etc. Writing a complete code from scratch for topology optimization is cumbersome due to finite element analysis and it’s requirement of stabilization techniques for thermo-fluid problems. But most often, the problem requires rigorous tuning of parameters in interpolation schemes, sensitivity analysis and optimization algorithm which may be difficult to access in commercial softwares. COMSOL LiveLink for MATLAB enables us to couple the commercial COMSOL Multiphysics software with MATLAB programming via COMSOL Application Programming Interface(API). In this work, we demonstrate a comprehensive COMSOL LiveLink for MATLAB code for topology optimization of conjugate heat transfer inspired from (Junghwan Kook et al. 2021). In particular, we are focused on natural convection examples (natural convection pump) where finite element analysis is more complicated and unhandy to code. Figure 1 summarizes the LiveLink for MATLAB code in a flowchart.

COMSOL Laminar Flow interface will be used to solve the steady state Navier-Stokes equation and continuity equation. The COMSOL Heat Transfer Module will be used to solve energy equation for fluid and solid region. Study steps will be defined in COMSOL for finite element analysis and adjoint sensitivity analysis. A detailed description will be provided for extraction of state variables, nodal information, required matrices and vectors for adjoint sensitivity analysis from COMSOL to MATLAB. A governing equation for design variable field will be defined in COMSOL Weak Form PDE interface. The process for applying filtering and projection schemes will be clearly explained.

The code will be explained using numerical example of design of a micropump where fluid motion is due to differential heating of walls [2]. The objective function would be to maximize the flow rate at the objective boundary (see figure 2). The illustration of the layout and boundary conditions are given in figure 2. The problem will be investigated in several combinations of boundary conditions. The thermal boundary condition at any boundary would either be a given temperature or a zero heat flux. A study on effect of Grashof’s number will be done. A study on effect of parameters in the interpolation schemes on the final output will be done.

This work demonstrates that COMSOL LiveLink for MATLAB offers the possibility to reduce the effort of implementing finite element analysis while being able to control all the parameters in topology optimization of conjugate heat transfer problems.

REFERENCES

[1] Kook, J. and Chang, J.H., 2021, A high-level programming language implementation of topology optimization applied to the acoustic-structure interaction problem. Structural and Multidisciplinary Optimization, 64(6), pp.4387-4408.

[2] Alexandersen, J., Aage, N., Andreasen, C.S. and Sigmund, O., 2014. Topology optimisation for natural convection problems. International Journal for Numerical Methods in Fluids, 76(10), pp.699-721.