A Bandwidth and Order Optimized WENO Interpolation Scheme for Compressible Turbulent Flows

2018

J. Fluid Mech.

Comprehensive experimental and computational investigations have revealed possible mechanisms underlying low-frequency unsteadiness observed in spanwise homogeneous shock-wave/turbulent-boundary-layer interactions (STBLI). In the present work, we extend this understanding by examining the dynamic linear response of a moderately separated Mach 2.3 STBLI to small perturbations. The statistically stationary linear response is analysed to identify potential time-local and time-mean linear tendencies present in the unsteady base flow: these provide insight into the selective amplification properties of the flow at various points in the limit cycle, as well as asymmetry and restoring mechanisms in the dynamics of the separation bubble. The numerical technique uses the synchronized large-eddy simulation method, previously developed for free shear flows, significantly extended to include a linear constraint necessary for wall-bounded flows. The results demonstrate that the STBLI fosters a global absolute linear instability corresponding to a time-mean linear tendency for upstream shock motion. The absolute instability is maintained through constructive feedback of perturbations through the recirculation: it is self-sustaining and insensitive to external forcing. The dynamics are characterized for key frequency bands corresponding to high–mid-frequency Kelvin–Helmholtz shedding along the separated shear layer $(St_{L}\sim 0.5)$, low–mid-frequency oscillations of the separation bubble $(St_{L}\sim 0.1)$ and low-frequency large-scale bubble breathing and shock motion $(St_{L}\sim 0.03)$, where the Strouhal number is based on the nominal length of the separation bubble, $L$: $St_{L}=fL/U_{\infty }$. A band-pass filtering decomposition isolates the dynamic flow features and linear responses associated with these mechanisms. For example, in the low-frequency band, extreme shock displacements are shown to correlate with time-local linear tendencies toward more moderate displacements, indicating a restoring mechanism in the linear dynamics. However, a disparity between the linearly stable shock position and the mean shock position leads to an observed asymmetry in the low-frequency shock motion cycle, in which upstream motion occurs more rapidly than downstream motion. This is explained through competing linear and nonlinear (mass depletion through shedding) mechanisms and discussed in the context of an oscillator model. The analysis successfully illustrates how time-local linear dynamics sustain several key unsteady broadband flow features in a causal manner.

Section: Theoretical and Numerical Modelmentioning

confidence: 99%

Dynamic linear response of a shock/turbulent-boundary-layer interaction using constrained perturbations

Adler

2018

J. Fluid Mech.

“…In this work, we invoke a recently developed fifth order bandwidth and order optimized WENO scheme with Roe fluxes (see Ref. 26 for the inviscid fluxes, together with a sixth order compact scheme for the viscous fluxes. The time integration is performed with the implicit Beam-Warming scheme using two sub-iterations and approximate factorization.…”

Section: Theoretical and Numerical Modelmentioning

confidence: 99%

Analysis of Unsteady Behavior in Shock/Turbulent Boundary Layer Interactions with Large-Eddy Simulations

Mullenix

51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

2013

Self Cite

Various numerical and physical aspects of shock/turbulent boundary layer interactions (STBLI) are discussed in the context of Large-Eddy Simulations (LES). A spatially developing incoming equilibrium turbulent boundary layer is obtained with a force based tripping mechanism. Previous results are augmented with a detailed analysis of this procedure. In particular, it is shown that relatively coarser meshes may be employed if the strength of the trip is increased, together with an adjustment of the wall thermal condition for a short distance downstream of the trip. This approach yields both adiabatic as well as constant wall temperature results. Additionally, it is shown that precursor events provide estimates for the size of the trip with only a small portion of the domain in the vicinity of the trip, thus yielding an efficient technique. A simulation of a STBLI using this spatially developing incoming turbulent boundary layer confirms the low frequency signal observed in the STBLI by other approaches which use recycling techniques, and reproduces the particular unsteadiness shown in a reference experiment. A detailed analysis is performed of the evolution of the Reynolds stresses through the interaction. The amplification of turbulence energy is quantified, and the evolution of two point correlations is explored. The resultsindicate that the spanwise decorrelation distance first decreases and then increases through the interaction. A preliminary assessment of the effect of pulsed arc filament based actuators is provided. The results indicate a reduction in the separation length when pulsed at a St corresponding to the peak frequency near the reattachment point.

“…The governing equations are solved with very high-order methods. The inviscid fluxes are obtained with a highly accurate, band-width optimized fifth-order Weighted Essentially Non-Oscillatory (WENO) scheme described by Mullenix and Gaitonde [22]. The viscous flux terms are computed using a sixthorder compact difference, spectral-like scheme [36].…”

Section: Theoretical and Numerical Modelmentioning

confidence: 99%

A body-force based method to generate supersonic equilibrium turbulent boundary layer profiles

Waindim

Journal of Computational Physics

2016

We further develop a simple counterflow body force-based approach to generate an equilibrium spatially developing turbulent boundary layer suitable for Direct Numerical Simulations (DNS) or Large Eddy Simulations (LES) of viscous-inviscid interactions. The force essentially induces a small separated region in an incoming specified laminar boundary layer. The resulting unstable shear layer then transitions and breaks down to yield the desired unsteady profile. The effects of wall thermal conditions are explored to demonstrate the capability of the method for both fixed wall and adiabatic wall conditions. We then describe an efficient method to select parameters that ensure transition by examining precursor signatures using generalized stability variables. These precursors are shown to be evident in a computational domain spanning only a small region around the trip and can also be detected using 2D simulations. Finally, the method is tested for different Mach numbers ranging from 1.7 to 2.9, with emphasis on flow field surveys, Reynolds stresses, and energy spectra. These results provide guidance on boundary conditions for desired boundary layer thickness at each Mach number. The consequences of using a much lower Reynolds number in computation relative to experiment are evident at the higher Mach number, where a self sustaining turbulent boundary layer is more difficult to obtain.