Frontiers in Aerospace Science

In this chapter, an introduction of shock-boundary layer interaction (SBLI) is given. A paper review about the driven mechanism of pressure fluctuation caused by shock induced flow separation on a ramp corner is presented and a research history on micro vortex generator (MVG) is briefly reviewed. In particular, a series of new findings made by the LES team at the Center of Numerical Simulation and Modeling led by Dr. Chaoqun Liu under the support of US Air Force Office of Scientific Research (AFOSR) is briefly reported. These new findings are milestone work which have made a breakthrough in understanding the physics of SBLI, shock-vortex ring interaction, control of shock induced flow separation and noise generation.

In this chapter, the dimensional and non-dimensional 3-D time-dependent Navier-Stokes equations in curvilinear coordinates are given in details. The flux splitting scheme and non-reflecting boundary conditions are discussed and provided.

In this chapter, a brief introduction of algebraic grid generation, transfinite interpolation and elliptic grid generation is given. In particular, a two-step elliptic grid generation method developed by Spekreijse [121] is introduced, which can generate high quality and orthogonal grids near the boundary. The smooth and orthogonal grid for the LES case of MVG and Ramp is generated by the above method.

In this chapter, a series of high order shock capturing schemes including WENO scheme, weighted compact scheme, modified upwinding compact scheme are introduced, which can get sharp shock capturing but keep high order accuracy in the smooth area. These schemes are particularly useful for LES of shock-turbulence interaction where both high resolution and sharp shock capturing are important. All these schemes are somehow successful in high order LES for SBLI. An efficient shock detector is introduced as a part of weighted compact and modified upwinding schemes. In addition, the accuracy, truncation errors, dissipation and dispersion of these schemes are analyzed.

In this chapter, a high order direct numerical simulation (DNS) is applied to generate fully developed turbulent inflow. The fully developed inflow was taken from a case of DNS for flow transition. The inflow condition is carefully checked with the velocity profile and ratio of boundary layer thickness, ensuring that it is a fully developed turbulent flow in order to compare with the wind tunnel test.

In this chapter, we propose a series of new discoveries from our high order LES, including the spiral point near the leading edge, the origin of the momentum loss, the vortex structure, the topology of the flow separation, and some conclusions of other physics in the flow. Although there are some studies of experiments and numerical simulations on fluid flow controlled by MVG recently, only two-dimensional flow information was provided and confirmed by those studies. The three dimensional flow field behind MVG is still unclear. To better understand the flow structure especially the vortex structure in the downstream of the MVG, the flow field around the MVG and surrounding areas has been investigated in details. In addition, the 3D shock wave structure in the flow field is also studied in this book.

In this chapter, interaction of shock and vortex rings which were generated by MVG is described and analyzed in details. The change of vorticity, vortex, shock strength and location is described in details. The physics of shock and vortex interaction and its influence on the flow structure is also discussed.

In this chapter, a new mechanism of SBLI control by MVG is presented. Traditionally, people consider the reduction of shock-induced separation is caused by streamwise vortex which mixes the boundary layer flow and makes the velocity profile to be more able to withstand the flow separation. The new mechanism shows the spanwise vortex rings are critical which are quickly moving and fast rotating to destroy or undermine the shock and ease up the shock-induced flow separation significantly. Potentially, this study could contribute to some technology revolution in control of SBLI, flow separation and interference reduction.

In this chapter, the correlation between density and pressure fluctuation and vortex motion is studied. The correlation between flow separation and vortex motion is studied as well. The correlation clearly shows the vortex ring generation, size, frequencies, and strength are closely related to the fluctuation of density and pressure. This would provide a powerful tool for SBLI control and noise reduction.

An implicit Large Eddy Simulation (ILES) is carried out for a Micro Vortex Generator (MVG) controlled supersonic ramp flow at Ma = 2.5 and Re = 5760 based on inflow momentum boundary thickness. The results are validated against the TU Delft experiment on the same MVG geometry and Mach number. Several techniques are used to analyze the coherent structures in the MVG wake. The vortex system in the MVG wake is visualized using vortex identification method and it is found that two primary counter rotating streamwise vortex pair are induced by the MVG, which would further lead to a trail of vortex rings through K-H instability. The average distance between adjacent vortex rings is determined by a spatial auto-correlation of vorticity, which is estimated as 1.5 MVG height. Two dimensionality reduction algorithms, namely Proper Orthogonal Decomposition (POD), and Dynamic Mode Decomposition (DMD) are applied to a set of flow field sequences on the spanwise symmetry plane. POD modes identify structures containing most of the turbulent kinetic energy and DMD modes, capturing single frequency structures which are most essential to the unsteady dynamics.