Mbu Waindim

Results and Analysis of Implicit Large Eddy Simulations of Equilibrium Spatially Developing Turbulent Boundary Layers at Multiple Mach Numbers

Equilibrium turbulent flat plate boundary layers with time invariant statistics were obtained at Mach numbers 1.7, 2.3, and 2.9. These are to be used as the initial condition for Large Eddy Simulations (LES) or Direct Numerical Simulations (DNS) of shock wave/turbulent boundary layer interactions utilizing a body force-based method. The results obtained are supplemented by an analysis of the mean and statistical properties of the respective boundary layers. The spanwise extent of the domain required to allow adequate decorrelation between the centerline and the boundaries is investigated by extensively probing the flowfields obtained. This is done to quantify the coherent structures of the turbulent flow. Specifically, two point correlations and integral length scales are used to investigate spanwise decorrelation distances in an attempt to pick a computational domain which is large enough to permit decorrelation downstream but small enough to minimize computational costs. It is shown that by examining the precursor events in the upstream region, namely the generalized stability criterion, it is possible to provide estimates for the force field parameters necessary for transition for a given flow, with only a small portion of the domain in the neighborhood of the trip. The technique is made even more efficient by investigating the possibility of determining these parameters using a two-dimensional simulation. Additionally, the three flow fields obtained are surveyed to confirm that they are suitable for subsequent SBLI simulations. We check that (i)they possess the expected turbulent characteristics and (ii)there is no signature of the tripping mechanism.Copyright

Further Development of the Navier-Stokes Equations-Based Mean Flow Perturbation Technique

The evolution of disturbances in a mean basic state can be accomplished in several different ways. A relatively recent approach proposed by Touber and Sandham1 for shock-turbulent boundary layer interaction (STBLI) performs this task by advancing the Navier-Stokes equations and factoring out the changes associated with the mean basic state. In a recent effort,2 we have shown that this Navier-Stokes based Mean Flow Perturbation (NS-MFP) method reverts to the Parabolized, Linear and Global stability methods under appropriate conditions. NS-MFP solves an initial boundary value problem and is in principle capable of tracking the complete spatio-temporal evolution of disturbances in any 3-D mean flow. Here, we further analyze NS-MFP in the presence of (a) strong-gradient/discontinuities and (b) viscous stresses with the ultimate aim of using it for tracking disturbance evolution in 3-D swept STBLI. To analyze the effects of strong gradient and/or discontinuities, we investigate the interaction of an entropic spot with a Mach 2 normal shock using NS-MFP. The results obtained are quantitatively compared with corresponding theoretical linear interaction analysis (LIA) presented in the literature. To illustrate that NS-MFP captures the viscous terms accurately and is applicable to wall bounded flows; we examine the evolution of pressure perturbations on a Mach 2.0 laminar flat plate boundary layer. Finally, we apply the method to a 2-D STBLI problem, where an impinging shock with 9◦ wedge angle interacts with a Mach 2.3 turbulent boundary layer (Reynolds number 17, 500). Our results successfully capture the biglobal mode reported by other researchers, along with the intermediate frequencies characteristic of Kelvin-Helmholtz shedding in the mixing layer. Finally, we establish the suitability of the approach in analyzing a Reynolds Averaged Navier Stokes (RANS) generated basic state as an initial exercise to extend the technique to fully 3-D swept STBLI, for which LES are expensive.

Conditional analysis of unsteadiness in shock boundary layer interactions

The features of the interaction between an oblique shock wave and a Mach 2.3 turbulent boundary layer are examined in an effort to differentiate the dynamics of bubble dilation (upstream shock motions) from bubble collapse (downstream shock motions). A dataset obtained from Large Eddy Simulations, which has been validated against experiments is used for the analysis. A relatively new technique, Empirical Mode Decomposition (EMD), is used for low-pass filtering to facilitate separation of upstream shock motions from downstream shock motions. To examine the dynamics of bubble dilation versus collapse, three Dynamic Mode Decomposition (DMD) analyses are carried out: considering the full dataset, considering strictly upstream motions, and considering only downstream motions. For each case, results of DMD are shown for the pressure field to accentuate different aspects of the physics. The results highlight differences in the dynamics of dilation and collapse, which aid in the understanding of unsteadiness in these interactions. A comparison of the speeds at which either process occurs is also shown to yield similar conclusions as the DMD analyses.

Budget of Turbulent Kinetic Energy in a Shock Wave Boundary-Layer Interaction

Implicit large-eddy simulation (ILES) of a shock wave/boundary-layer interaction (SBLI) was performed. Quantities present in the exact equation of the turbulent kinetic energy transport were accumulated and used to calculate terms like production, dissipation, molecular diffusion, and turbulent transport. The present results for a turbulent boundary layer were validated by comparison with direct numerical simulation data. It was found that a longer development domain was necessary for the boundary layer to reach an equilibrium state and a finer mesh resolution would improve the predictions. In spite of these findings, trends of the present budget match closely with that of the direct numerical simulation. Budgets for the SBLI region are presented at key axial stations. These budgets showed interesting dynamics as the incoming boundary layer transforms and the terms of the turbulent kinetic energy budget change behavior within the interaction region.