Methodology of numerical coupling for transient conjugate heat transfer

Abstract

This paper deals with the construction of a conservative method for coupling a fluid mechanics solver and a heat diffusion code. This method has been designed for unsteady applications. Fluid and solid computational domains are simultaneously integrated by dedicated solvers. A coupling procedure is periodically called to compute and update the boundary conditions at the solid/fluid interface. First, the issue of general constraints for coupling methods is addressed. The concept of interpolation scheme is introduced to define the way to compute the interface conditions. Then, the case of the Finite Volume Method is thoroughly studied. The properties of stability and accuracy have been optimized to define the best coupling boundary conditions: the most robust method consists in assigning a Dirichlet condition on the fluid side of the interface and a Robin condition on the solid side. The accuracy is very dependent on the interpolation scheme. Moreover, conservativity has been specifically addressed in our methodology. This numerical property is made possible by the use of both the Finite Volume Method and the corrective method proposed in the current paper. The corrective method allows the cancellation of the possible difference between heat fluxes on the two sides of the interface. This method significantly improves accuracy in transient phases. The corrective process has also been designed to be as robust as possible. The verification of our coupling method is extensively discussed in this article: the numerical results are compared with the analytical solution of an infinite thick plate in a suddenly accelerated flow (and with the results of other coupling approaches).

An Adaptive Simplex Cut-Cell Method for High-Order Discontinuous Galerkin Discretizations of Conjugate Heat Transfer Problems

“…⌦ (1) ⌦ (2) ⌦ (3) ⌃ (13) ⌃ (12) ⌃ (23) (a) Example multi-regioned problem In this paper, we propose a solution framework for CHT simulations that autonomously provides reliable output predictions. More specifically, the framework is comprised of a cut-cell technique that allows mesh generation to be decoupled from the design geometry, a high-order discontinuous Galerkin (DG) discretization, and an anisotropic output-based adaptation method that autonomously adapts the mesh to minimize the error in an output of interest.…”

An Acceleration Method for Numerical Studies of Conjugate Heat Transfer With a Self-Adaptive Coupling Time Step Method: Application to a Wall-Impinging Flame

“…The study of conjugate heat transfer (CHT), not necessarily involving combustion, is an active area of research. Using code coupling between separate solvers used for the solid part and the fluid flow have been carried out for RANS simulations [1][2][3][4] and for Large Eddy Simulations (LES) [5][6][7][8][9][10] . When studying turbulent reactive flows, the more and more maturing LES framework offers great accuracy [11] compared to RANS, at the cost of consuming large computational resources.…”

“…For unsteady CHT studies with flow and solid solvers that are both unsteady, a standard approach is the Neumann-Dirichlet coupling method where, between coupling events, one solver is given a fixed temperature at the interface (Dirichlet condition) while the other one uses a Neumann condition with a given value of the wall heat flux from the first solver. The stability of this approach has been studied [12] and enhanced [6,8,[13][14][15].…”

Multi‐scale time integration for transient conjugate heat transfer

“…Although an unsteady flow solver can be used, and the coupling between the two solvers can be conducted in time, such as [9]; the direct coupling of this kind between the fluid and solid domains integrated in parallel in time tends to be very difficult. Although an unsteady flow solver can be used, and the coupling between the two solvers can be conducted in time, such as [9]; the direct coupling of this kind between the fluid and solid domains integrated in parallel in time tends to be very difficult.…”

“…Loosely coupled CHT methods, where the fluid and solid domains are solved by separate solvers and coupled together at an interface iteratively, have been more commonly adopted. Although an unsteady flow solver can be used, and the coupling between the two solvers can be conducted in time, such as [9]; the direct coupling of this kind between the fluid and solid domains integrated in parallel in time tends to be very difficult. On the other hand, the apparent scale disparity between the fluid and solid provides a seemingly justifiable motivation for a quasi-steady transient CHT approach, that is, coupling a steady flow solver quasi-steadily with an unsteady solid conduction solver.…”