Computational simulations of oblique shock induced laminar boundary layer separations

The main objective of present computational study is to model and investigate an impinging oblique shock wave induced laminar boundary layer separations over a flat plate. Mechanism of the flow was observed for steady-state or unsteady separations. Surface temperature of the flat plate has been changed to prevent undesired unsteady interaction region. A parametric study that covers a wide range of impinging shock angle as well as free stream Mach number is considered here. Number of simulations for 2-dimensional flows utilizing a density based finite volume Navier-Stokes solver of open source CFD solver of OpenFOAM, rhoCentralFoam. Preliminary results show that the shock-induced separation can result in steady or unsteady separations depending on the impingement angle of the shock and the freestream Mach number. Although the influence of free stream Mach number and shock impingement angle on separation have already been studied extensively, relatively high Mach number range of this study has a potential to contribute the literature. Computational grids include quadratic, non-conformal elements and precise refinement regions were handled to capture discontinuities of the flow quantities around incident and reflected oblique shock waves. Computational simulation results are evaluated in terms of number and location of the separation bubble/s; shear stress and pressure variation along the wall. In addition, visualization of vortices will be covered by Q-Criterion Method. Mechanism of shock wave laminar boundary layer interaction on a flat plate can be summarized as an incident shock impinges on a laminar boundary layer, its strength decreases and an adverse pressure gradient occurs. Then, the boundary layer thickens because of the pressure gradient; thus, compression waves are occurred as merging and forming a single oblique shock wave. This wave is called first reflected shock wave. When the direction of the flow changes in the boundary layer due to shock impingement, stress on the wall become zero and local separation takes place. The incident shock loses its strength as it penetrates the boundary layer. Expansion fans occur downstream of the impingement point. Then second reflected shock forms due to thinning boundary layer. In here, reattachment is observed in the boundary layer. Besides, the region of probable transition to turbulence can be seen at the downstream right after interaction zone. As an introduction, phenomenon of the interaction is described to understand characteristic of the flow. After investigating results of computational simulations, both numerical and analytical expressions were matched to obtain a comparison. In the section of geometrical properties, it is described how angle data range were selected to generate a SWBLI zone. Beyond limits of wave angle, there will be no single oblique shock and/or induced and reflected shock wave interaction anymore. The set of angle includes values close to upper and lower limits of oblique shock and interaction zone generation. In this set, middle value of β which matches half of maximum deflection angle value as well describes a transition from stable and relatively steady boundary layer to unstable and possible detached boundary layer Before generating geometries depend on various wave angle (β), analytical calculations were supplied to make a reference for numerical analyses. Regarding to these calculations, parametric geometries were created to keep location of impingement point of incident shock wave constant. Therefore, the flow regime can be kept as laminar. Computational domain and grid structure were generated on X-Y plane for a 2-D case. Inlet, outlet, freestream and flat plate regions are defined as H1, H2, f and L sections respectively. Besides, wall of shock generator section is defined to induce an oblique shock wave onto the flat plate. Inclination of the shock generator is provided due to avoiding interaction of reflected shock waves from flat plate and shock generator. It should be considered as a modelling technique to obtain shock wave boundary layer interaction zone only. Reducing number of the mesh elements is another advantage of this approach. In the grid structure, there are numerous of refinement regions to capture discontinuities of flow quantities for critical regions such as incident and reflected shock areas, boundary layer, stagnation point and interaction zone. Edges of the intersections between these refinement and regular grid regions are implemented to provide better transition. Mesh generation has been conducted in a commercial software, namely NUMECA HEXPRESS. Grid has a non-conformal structure which requires interpolation around intersections. On the other hand, it maintains best quality of the mesh elements which have 2E+5 number of quadrilateral cells. In third dimension which lies on Z direction, single cell block is placed due to solver requirement. The most common definition of the fluid flow is derived by the time dependent compressible Navier-Stokes equations which state the conservations laws for mass, momentum and energy for viscous fluids. In the first step, unsteady and viscous effects were also included into solution with steady boundary conditions. And then, unsteady boundary conditions will be implemented to see reactions and behaviours of two introducing induced shock waves in time. Therefore, time dependent and compressible flow regime is applied on Navier-Stokes equations for the primary study. Before generating simulations of main set, mesh and time independent analyses were performed due to avoiding numerical errors. A gradual mesh refinement on the region of the interaction were applied by splitting into two parts on both X and Y directions. And every mesh level which includes coarse, medium, fine and finest were compared to reach mesh independent analysis result. As a conclusion, fine and finest levels were observed as well-fitted results of each other. Therefore, fine level of mesh was taken as reference for the simulations of main set. Other refinement was generated on time step to capture time independent results. Unsurprisingly, when the time step decreases, time independent results were obtained. Time step set include 2.5 E-9 s, 5E-9s, 10E-9s and 15E-9s. Biggest value of time step has slightly different results in terms of pressure distribution along the wall. All other time steps have same characteristics and closer values of both pressure and wall shear stress. Medium level of time step which is 10E-9s was chosen as reference for the next simulations of main set. The computational analyses have been performed by using compressible Navier-Stokes and open source solver, namely OpenFOAM. The capabilities of solver about adaptive mesh refinement and types of discretization techniques allow to solve time dependent compressible Navier-Stokes equations. Central-Upwind Scheme of Kurganov and Tadmor has been used as a scheme of discretization and rhoCentralFoam has density-based solver structure is defined as the solver type. Coupled system of conservation equations are solved by implicit formulation. Besides, time and space have 1st and 2nd order accuracy, respectively. All the preliminary simulations presented here are obtained utilizing 2-dimensional, unsteady, compressible Navier-Stokes solver. The complex flow physics may require 3-dimensional unsteady flow simulations with high impingement angle. A rise in the shock impingement angle causes an increase in the number of separation bubble, an increase the size of separation bubble and longer distance between the separation and reattachment points. In addition, it should be considered that relatively complex around impingement point may have 3-D effects in boundary layer. Following computational studies will cover up these predictions and higher Mach number interactions.