Simulation of turbulent flow subjected to conjugate heat transfer via a dual immersed boundary method

Abstract

In the context of turbulent flows, this study presents a new methodology for the high-fidelity simulation of conjugate heat transfer between solid and fluid. The numerical strategy is mainly based on the immersed boundary method to ensure the expected thermal boundary condition at the fluid/solid interface. The approach is dual since the solid domain is the immersed region for the fluid and, conversely, the fluid for the solid. The resulting method is an extension of an already existing immersed boundary method based on the reconstruction of the solution inside the immersed region. The duality of the technique requires to define one temperature field for the fluid and another one for the solid. The interaction between the two temperature fields is ensured, at the fluid/solid interface, through an efficient weak coupling preserving numerical stability and accuracy. Thanks to the reconstruction in its own immersed zone, each temperature field solution is perceived as smooth by the numerical differentiation method, for any fluid-to-solid ratio of thermal conductivities and diffusivities, while representing a desirable sharp interface. This feature is crucial for the high-order finite difference schemes used in this work. The method is validated for the plane channel and pipe flow configurations and a demanding pure conduction case with variable conductivity in a composite wall. Its ability to preserve second-order accuracy in space is checked in the laminar and pure conduction cases by comparison with analytical solutions. In the turbulent case, the assessment is based on comparisons of basic turbulent statistics with reference data obtained by direct numerical simulation. The step-by-step analysis of thermal statistics shows that the present immersed boundary method can ensure accurately imposed temperature, imposed heat flux, and conjugate heat transfer conditions at the fluid/solid interface.