Wall heat flux estimation using the Cartesian cut-cell method

Abstract

The Cartesian cut-cell method evaluates wall-fluid interactions by using the fluxes through a wall. This wall treatment by the Cartesian cut-cell method is expected to overcome the mass and energy conservation problems of the immersed boundary method. A wall flux evaluation using the image point is proposed in this study to avoid volume center estimation. The Cartesian cut-cell method that uses the proposed wall flux evaluation is validated by the numerical simulations of supersonic flows past simple shapes. In the numerical simulations of the supersonic flow past a cylinder with an isothermal wall, the shorter displacement dIP of the image point from the wall provided a better estimation of the wall heat flux. Furthermore, the wall heat flux distributions and the amount of heat converged with grid refinement. In the numerical simulations of the supersonic flow past a wedge, the minimum grid resolution of the Cartesian cut-cell method for wall flux estimation was suggested. Furthermore, the results of the isothermal wall condition, the adiabatic wall condition, and the inviscid condition were compared.

Keywords

• computational fluid dynamics
• cartesian grid solvers
• cartesian cut-cell method
• compressible flows
• wall-heat flux