A Computational Investigation of Vortex Flows Across Shockwaves

No doubt, current CFD tools have a great many limitations, and active research is being done to overcome these limitations. One of the primary limitation is in the area of turbulent flows. In general, turbulent flows are unsteady solutions to the fluid dynamic equations, and instances of these solutions can be computed directly from the equations. One of the approaches commonly implemented is known as the ‘direct numerical simulation’, DNS. This approach requires a spatial grid that is fine enough to capture the smallest length scale of the turbulent fluid motion. This approach is called the ‘Kolmogorov scale’ model. In is of interest to note that the Kolmogorov scale model must be captured throughout the domain of interest, and at a correspondingly small time step as well. In typical problems of industrial interest, the ratio of the length scale of the domain to the Kolmogorov length scale is so great that the required grid is prohibitively large. As a result, the available computational resources are usually inadequate for DNS related tasks. As such, DNS is not applicable to industrial problems except for the case of relatively simple problems. In this research, an attempt is made to develop a numerical technique that can deliver DNS quality solutions. To date, this technique has delivered preliminary results for both steady and unsteady, inviscid and viscous, compressible and incompressible, for both high and low Reynolds number flow fields that are very accurate. Herein, The IDS formulation was successfully used to solve a wide class of 2D compressible flow problems that included shocks and vortex interactions. The IDS simulated flow fields were compared to corresponding flow fields generated from the fifth order weighted essentially non-oscillatory (WENO) scheme. The purpose in this paper was to use the IDS formulation to simulate the aforementioned flow fields, investigate that these flow fields revealed the physics of the prescribed interactions, and compared the IDS numerical data with those from reputable CFD/experimental sources. These expectations were met.