An improved immersed boundary method for computation of turbulent flows with heat transfer.

摘要

The immersed boundary (IB) method is a technique to enforce boundary conditions on surfaces not aligned with the mesh in a numerical simulation. This method has been used as a practical approach to model flow problems involving very complex geometries or moving bodies. Our objective is to assess the accuracy and efficiency of the IB method in simulations of turbulent flows, where the flow dynamics in the near-wall region is fundamental to correctly predict the overall flow. The first part of this work focuses on the development of a simulation tool based on the IB method that can correctly predict the wall temperature and pressure fluctuations in turbulent flows. In the second part, we illustrate the application of the method to a multi-material heat transfer problem where convective heat transfer of the fluid and conductive heat transfer of the solid are handled simultaneously.; This work achieves sufficient accuracy at the immersed boundary and overcomes deficiencies in previous IB methods by augmenting the formulation with additional constraints--a compatibility constraint relating the interpolated velocity boundary condition with mass conservation and a decoupling constraint for the pressure. We derived an IB method with a revised boundary interpolation and a strictly mass conserving scheme, which does not show pressure oscillations near the immersed boundary. Although accurate, the complexity of this method prompted the development of another variant--the immersed boundary-approximated domain method (IB-ADM). This approach satisfies the pressure decoupling constraint with an inexpensive computational overhead. The IB-ADM correctly predicts the near-wall velocity, pressure and scalar fields in several example problems. The IB-ADM is shown to successfully predict the flow around a very thin solid object for which incorrect results were obtained with previous IB methods. The IB-ADM has been successfully validated through computation of the wall-pressure space-time correlation in DNS of a turbulent channel flow. When applied to a turbulent flow around an airfoil, the computed flow statistics--the mean/RMS flow field and power spectra of the wall pressure--are in good agreement with a previous LES and experiment.; In order to establish the viability of the IB method as an efficient tool for LES/DNS of conjugate heat transfer applications, the problem of a heated cylinder in a channel with heating from below is considered. Here, the fluid-solid interface is constructed as a collection of disjoint faces of control volumes associated to different material zones. Coupling conditions for the material zones have been developed such that continuity and conservation of the scalar flux are satisfied by a second-order interpolation. The local mesh refinement technique is crucial to accommodate the large difference in length scales in the present application (i.e., small heated cylinder in a large channel). In the region upstream of the transition to turbulence, numerical predictions show a strong sensitivity to the mesh resolution and inlet condition. Predictions of the local Nusselt number show good agreement with the experimental data. The effect of the Boussinesq approximation on this problem was also investigated. Comparison with the variable density formulation suggests that, in spite of a small thermal expansion coefficient of water, the variable density formulation in a transitional flow with mixed convection is preferable, since it does not involve the uncertainty in the material properties required in the Boussinesq approximation.