Purpose

This paper aims to present a topology optimization (TopO) method for designing heat exchangers (HEx) with two working fluids to be kept apart. The introduction of cut–cells gives rise to the cut-cell TopO method, which computes the optimal distribution of an artificial impermeability field and successfully overcomes the weaknesses of the standard density-based TopO (denTopO) by computing the fluid–solid interface (FSI) at each cycle. This allows to accurately solve the flow and conjugate heat transfer (CHT) problem by imposing exact boundary conditions on the computed FSI and results to correct performances computed without the need to re-evaluate the optimized solutions on a body-fitted grid.

Design/methodology/approach

The elements of an artificial impermeability distribution field defined on a background grid act as the design variables and allow topological changes to take place. Post-processing them yields two fields indicating the location of the two flow streams inside the HEx. At each TopO cycle, the FSIs computed based on these two fields are used as the cutting surfaces of the cut-cell grid. On the so-computed grid, the incompressible Navier–Stokes equations, coupled with the Spalart–Allmaras turbulence model, and the temperature equation are solved. The derivatives of the objective and constraint functions with respect to the design variables of TopO are computed by the continuous adjoint method, using consistent discretization schemes devised thanks to the “Think Discrete – Do Continuous” (TDDC) adjoint methodology.

Findings

The effectiveness of the cut-cell–based TopO method for designing HEx is demonstrated in 2D parallel/counter flow and 3D counter flow HEx operating under both laminar and turbulent flow conditions. Compared to the standard denTopO, its ability to compute FSIs along which accurate boundary conditions are imposed, increases the accuracy of the flow solver, which usually leads to optimal, rather than sub-optimal, solutions that truly satisfy the imposed constraints.

Originality/value

This work proposes a new/complete methodology for the TopO of two-fluid systems including CHT that relies on the cut-cell method. This successfully combines aspects from both TopO and Shape Optimization (ShpO) in a single framework thus overcoming the well-known downsides of standard denTopO regarding its accuracy or the need for a follow-up ShpO after TopO. Instead of adding the well-known Brinkman penalization terms into the flow equations, it computes the FSIs at each optimization cycle allowing the solution of the CHT problem on a cut-cell grid.

中文翻译：

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用于双流体换热器拓扑优化的连续伴随切割单元公式

 目的

本文旨在提出一种拓扑优化 （TopO） 方法，用于设计两种工作流体分开的换热器 （HEx）。切割单元的引入产生了切割单元 TopO 方法，该方法计算人工不渗透场的最佳分布，并通过计算每个循环的流固界面 （FSI） 成功克服了基于密度的标准 TopO （denTopO） 的弱点。这允许通过在计算的 FSI 上施加精确的边界条件来准确求解流动和共轭传热 （CHT） 问题，并得出校正计算的性能，而无需在体拟合网格上重新评估优化的解决方案。

设计/方法/方法

在背景网格上定义的人工不渗透分布场的元素充当设计变量，并允许发生拓扑更改。对它们进行后处理会产生两个字段，指示 HEx 内两个流的位置。在每个 TopO 循环中，基于这两个字段计算的 FSI 用作切割单元网格的切割表面。在计算的网格上，求解不可压缩的 Navier-Stokes 方程，耦合 Spalart-Allmaras 湍流模型和温度方程。关于 TopO 设计变量的目标函数和约束函数的导数是通过连续伴随方法计算的，使用“离散思考 - 执行连续”（TDDC） 伴随方法设计的一致离散化方案。

 发现

在层流和湍流条件下运行的 2D 平行/逆流和 3D 逆流 HEx 证明了基于切割单元的 TopO 方法在设计 HEx 方面的有效性。与标准 denTopO 相比，它能够计算施加精确边界条件的 FSI，从而提高了流动求解器的精度，这通常会导致真正满足施加约束的最优解，而不是次优解。

 原创性/价值

这项工作提出了一种新的/完整的方法，用于依赖于切割单元方法的双流体系统（包括 CHT）的 TopO。这成功地将 TopO 和形状优化 （ShpO） 的各个方面结合在一个框架中，从而克服了标准 denTopO 在准确性或需要在 TopO 之后进行后续 ShpO 的众所周知的缺点。它没有将众所周知的 Brinkman 惩罚项添加到流方程中，而是计算每个优化周期的 FSI，从而允许在切割单元网格上求解 CHT 问题。