This paper presents a topology optimization algorithm based on the lattice Boltzmann method coupled with a level-set method for increasing the efficiency of reactive fluid flows. The multi-relaxation time model is considered for the lattice Boltzmann collision operator, allowing higher Reynolds numbers flow simulations compared to the ordinary single-relaxation time model. The cost function gradient is obtained with the derivation of the adjoint-state formulation for the fully coupled problem. The proposed method is tested successfully on several numerical applications involving Reynolds numbers from 10 up to 1,000, as well as with different Damkohler and Peclet numbers. A limitation of the maximal pressure drop is also applied. The obtained results demonstrate that the proposed numerical method is robust and efficient for solving topology optimization problems of reactive fluid flows, in different operating conditions.

本文提出了一种基于格子玻尔兹曼方法和水平集方法的拓扑优化算法，以提高反应流体的效率。晶格Boltzmann碰撞算子考虑了多重弛豫时间模型，与普通的单一弛豫时间模型相比，可以进行更高的雷诺数流模拟。通过导出完全耦合问题的伴随状态公式，可以获得成本函数梯度。所提出的方法已在包括10到1,000的雷诺数以及不同的Damkohler和Peclet数在内的多个数值应用程序上成功进行了测试。还施加最大压降的限制。