Different methods have been developed to solve fluid flow-related problems over moving and complex boundaries. In particular, the immersed boundary (IB) technique is considered to be potential to replace the conventional body-fitted methods as it is more efficient and can handle complex flows over static Eulerian grids. Generally, the IB method is classified into two: sharp-interface and diffusion interface depending on the approach used to calculate the additional force. It is widely used to model laminar flow over complex bodies with flexile or rigid boundaries. With the increase in computational capabilities, the IB method has been combined with other turbulent models such as the large-eddy simulations (LES) method to model turbulent flows. Unfortunately, a combination of IB and LES requires the location of the IB forcing points within the viscous sublayer while maintaining a similar cartesian should be the same in the three directions. Thus, the combined method is limited to low-Reynolds-number turbulent flows because it requires expensive refining grids for resolving the near-wall turbulent structure of flows at high Reynolds number.
Previous findings revealed that using a hybrid wall model to combining the IB and the LES method is a more practical and promising approach for overcoming its limitations. This model utilizes the off-wall velocity to establish the wall shear stress without having to resolve the associated near-wall turbulent structures. Recently, a combination of IB and wall model methods have been extensively studied in different contexts, producing remarkable results. Nonetheless, most of the methods reported were performed at low-to-moderate Reynolds numbers, while turbulent flow simulation at high Reynolds numbers still remains underexplored.
Herein, Dr. Ming Ma, Professor Wei-Xi Huang, Professor Chun-Xiao Xu and Professor Gui-Xiang Cui from Tsinghua University developed a hybrid IB-LES approach in conjunction with wall model for simulation of high-Reynolds-number turbulent flows over moving/complex boundaries. It was based on the assumption that the occurrence of wall shear stress at high Reynolds number is mainly dependent on near-wall viscous flux. When applying the hybrid method, the near-wall velocity deviation was induced by combining the sub-grid scale viscosity and mixing-length model. Thus, a new scheme for modifying the sub-grid scale viscosity was proposed to match the wall-modeling induced shear stress and near-wall viscous flux directly. Finally, the feasibility of the proposed approach was verified by testing it on a number of numerical examples. Their work is currently published in the International Journal of Heat and Fluid Flow.
The research team showed that the shear stress associated with the wall-model LES was significantly enhanced at high-Reynolds number turbulent flows attributed to the correction of the deviation. Tests were carried out on several numerical examples, all of which produced satisfactory results in good agreement with the experimental data. For instance, the turbulent flows in a pipe, over a circular cylinder, over a sphere (figure 1), and over pitching airfoil were tested at Reynolds numbers up to 1.0 ×105, 1.4 ×105, 1.0 ×104, and 4.8 ×104, respectively. Furthermore, it was noted that the calculation of the wall shear stress was highly dependent on the non-equilibrium terms related to the wall model, while the grid resolution influenced the distribution of the near-wall pressure.
In summary, the authors successfully developed an improved wall model for the simulation of turbulent flow at high Reynold number in a hybrid IB/LES framework. The applicability of the proposed method was successfully tested in turbulent flows on several numerical examples. Compared with the previous results, the obtained results agreed well with the experimental data besides providing reasonable predictions. In a statement to Advances in Engineering, Professor Wei-Xi Huang said that the study findings would pave the way for developing next-generation robust and reliable models for engineering flows with moving and complex boundaries.
Ma, M., Huang, W., Xu, C., & Cui, G. (2021). A hybrid immersed boundary/wall-model approach for large-eddy simulation of high-Reynolds-number turbulent flows. International Journal of Heat and Fluid Flow, 88, 108769.