A Discrete Immersed Boundary Method for the numerical simulation of heat transfer in compressible flows

Abstract

In the present study, a discrete forcing Immersed Boundary Method (IBM) is proposed for the numerical simulation of high-speed flow problems including heat exchange. The flow field is governed by the compressible Navier-Stokes equations, which are resolved by using the open source library OpenFOAM. The numerical solver is modified to include source terms in the momentum equation and in the energy equation, which account for the presence of the immersed body. The method is validated on some benchmark test cases dealing with forced convection problems and moving immersed bodies. The results obtained are in very good agreement with data provided in the literature. The method is further assessed by investigating three-dimensional high Mach flows around a heated sphere with different wall temperature. Even for this more complex test case, the method provides an accurate representation of both thermal and velocity fields.

Assessment of volume penalization and immersed boundary methods for compressible flows with various thermal boundary conditions

“…The Mach number (x-z plane) and the temperature (x-y plane) fields are depicted in Figure 21b. The drag coefficient C d , the recirculation length L, the separation angle θ s and the shock stand-off distance ∆ s are presented in Table 11 and show a good agreement with the results of Nagata et al [63] and Riahi et al [64]. Since the Nusselt number is highly dependent on the mesh size, smaller differences between the present Nusselt number and the one found by Nagata et al [63] may be expected by using a finer computational grid.…”

“…Nagata et al[63] 1.44 0.29 154 0.22 3.5 Riahi et al[64] ) 1.48 0.28 156 0.23 4.0 Supersonic flow past a heated sphere, M∞ = 2 , Re∞ = 300 (Tw = 2T∞): drag coefficient C d , recirculation length L, separation angle θs, shock stand-off distance ∆s and average Nusselt number N u.…”