希薄気体流れを利用したマイクロ流体デバイスのトポロジー最適化

抄録

The gas in microfluidic devices is likely to be rarefied because the characteristic length of the channel is relatively short compared with its mean free path. Recently, some devices utilize the properties of rarefied gas flows in a positive way. Therefore, in this study, we propose the topology optimization for designing such devices. We use Bhatnagar-Gross-Krook (BGK) equation as the governing equation to analyze rarefied gas flows. Moreover, for the implementation of the boundary condition on the gas-sollid interfaces in the optimization process, the BGK equation is extended to the entire design domain composed of both the gas and solid domains, using the shape representation by the level-set function. We use the Hamilton-Jacobi equation and shape sensitivity to update the channel structure, according to the procedure of a level set-based topology optimization method. The shape sensitivity is derived based on the adjoint variable method. Finally, we show the validity of the method through a numerical example of pump design problem.