In this study, a computational method for the coupled four-field problem of thermo-fluid–structure interaction (TFSI) using finite elements for all fields is proposed. Residual-based variational multiscale formulations are used for ensuring stable and accurate solutions of the flow as well as the temperature-transport problems. Adequate formulations for considering both the flow of gases and liquids are included in the computational method, with the most prominent representatives of each explicitly considered in the numerical examples contained in this article, that is, air and water, respectively. For air, a variable-density formulation of the Navier–Stokes equations at low Mach number, and for water, an incompressible formulation of the Navier–Stokes equations are utilized. Each of them is coupled to fully nonlinear dynamic equations for the structural field, along with the corresponding nonlinear dynamic equations for temperature transport in both fluid and solid domain. For the two surface couplings and the two volume couplings, a partitioned-monolithic strategy is pursued, in that the surface-coupled problems are solved monolithically, and the volume-coupled problems in partitioned form. On the one hand, choosing a monolithic scheme for the surface-coupled problems is particularly due to the improved performance of such a scheme compared to a partitioned scheme for FSI, as demonstrated by various studies published earlier. On the other hand, by using a partitioned algorithm for the volume-coupled problems, a potentially very large overall system of linear equations encompassing all fields can be avoided, for the time being, by splitting it up into two smaller monolithic systems. The choice is also motivated by the fact that the interaction is typically stronger for the surface-coupled fields in the applications of main interest. The computational method is applied to four numerical examples of increasing complexity, ranging from a rather simple problem of a plate which is subjected to tangential flow via channel flow with single and double elastic walls to the simplified configuration of a complex tube-bundle heat exchanger. The presented approach proves to be robust, and accurate results are obtained for all test cases. In particular, it is shown that the proposed method is capable of simulating a complex technical device such as a heat exchanger under its nominal working conditions.

在这项研究中，提出了一种使用有限元计算所有场的热-流体-结构相互作用 (TFSI) 耦合四场问题的计算方法。基于残差的变分多尺度公式用于确保流动以及温度传递问题的稳定和准确的解决方案。计算方法中包含了考虑气体和液体流动的充分公式，本文中包含的数值示例中明确考虑了每个公式的最突出代表，即分别为空气和水。对于空气，Navier-Stokes 方程在低马赫数下的变密度公式，对于水，使用 Navier-Stokes 方程的不可压缩公式。它们中的每一个都与结构场的完全非线性动力学方程以及流体和固体域中温度传输的相应非线性动力学方程耦合。对于两个表面耦合和两个体积耦合，采用分区单片策略，即单片解决表面耦合问题，分区形式解决体积耦合问题。一方面，为表面耦合问题选择整体方案特别是由于与 FSI 的分区方案相比，这种方案的性能有所提高，如先前发表的各种研究所示。另一方面，通过对体积耦合问题使用分区算法，单片系统。该选择还受到以下事实的推动：在主要感兴趣的应用中，表面耦合场的相互作用通常更强。该计算方法应用于四个复杂度不断增加的数值示例，从一个相当简单的板件问题（通过具有单层和双层弹性壁的通道流经受切向流）到复杂管束换热器的简化配置。所提出的方法被证明是稳健的，并且对于所有测试用例都获得了准确的结果。特别是，表明所提出的方法能够在其标称工作条件下模拟复杂的技术设备，例如热交换器。