A ghost-cell immersed boundary method for reacting flow simulations with conjugate heat transfer

This paper proposes a novel methodology based on a ghost-cell immersed boundary method (IBM) for simulating conjugate heat transfer (CHT) between solids and reacting fluids. The method employs a directional ghost-cell IBM, where ghost values are reconstructed along each discretization direction, to impose Dirichlet boundary conditions. A conventional ghost-cell IBM, where ghost values are extrapolated along the wall-normal direction, is used to enforce Neumann boundary conditions. Combining both, a partially directional ghost-cell IBM is then developed to describe the coupled heat transfer between solids and fluids along complex fluid-solid interfaces on a Cartesian grid, using a Neumann-Dirichlet weak coupling strategy. A series of validation cases - including heat conduction and forced convection along flat and curved fluid-solid interfaces - demonstrate the ability of the method to accurately impose CHT boundary conditions at fluid-solid interfaces. Additionally, a nearly second-order accuracy in space is preserved. Finally, simulations of reacting flow in a packed-bed reactor, considering heat exchange between the flame and the solid, further illustrate the performance of the proposed method for realistic applications.