Coupling methodology for thermal fluid-solid simulations through a full transient flight cycle. (March 2023) - Lazareff, Marc; Moretti, Rocco; Errera, Marc-Paul
Highlights: An adaptive heuristic fluid-solid interface condition is proposed for the first time. This new condition, called "X-R", has been developed to switch automatically between the Dirichlet-Robin (D-R) and Neumann-Robin (N-R) conditions on the basis of the Biot number. A temporal interpolation of the fluid conditions for dealing with "non-coupling instants" is defined on the basis of a physics-based approach by naturally considering the flux-temperature linearity. This approach replaces the generally adopted time-dependent linearity, which cannot be justified. The first test case demonstrates that the adaptive interface condition always produces smooth solutions, which is not the case when fixed conditions like D-R or N-R are adopted. The second test case shows that the physics-base approach based on the flux-temperature linearity is by far the most satisfactory. However, this interpolation method remains valid only if each ramp defined initially remains in a linear domain. Indeed, a full transient cycle, entirely based on the existence of particular time points can lead to non-linear problems, difficult to deal with. As a direct consequence of the previous point and shown in the third test case, the initial problem can be not well-posed. In this case, adding a small number of temporal points can keep the coupling algorithm in a quasi-linear domain. Abstract: This paper is devoted to the study of numerical methods used in the analysis of a thermal transient flight cycle. Two priorities are stressed. The first one concerns a stability issue, namely the fluid-solid interface conditions. The main properties of the Dirichlet-Robin and Neumann-Robin conditions are first recalled, before proposing for the first time an adaptive heuristic condition combining them. The second line of research is dedicated to an accuracy issue, the temporal interpolation of the fluid conditions for dealing with non-coupling instants. We propose here to adopt a physics-based approach by naturally considering the flux-temperature linearity. Then, using a simple numerical test under severe thermal boundary conditions, three test cases are proposed. The first one demonstrates that the adaptive interface condition always produces smooth solutions. The other two cases show that the physical interpolation approach is much more accurate than the one based on temporal linearity, using a costly but accurate reference solution built for the validation. Moreover, important improvements were made by adequately defining the integral contribution of the boundary condition using the Gauss points in the finite element solid code. It was also revealed that a relevant approximation of the heat transfer requires a sufficiently fine solid mesh at the interface. Finally, potential improvements are proposed at the end of this paper and more particularly two other interface conditions. One of them has the remarkable property of not using the convective heat transfer coefficient.