Proper Orthogonal Decomposition of Streamwise-Velocity Fluctuations in a Compression-Corner Shock-Wave/Turbulent Boundary-Layer Interaction

Author(s):  
M. A. Mustafa ◽  
N. J. Parziale
2019 ◽  
Vol 863 ◽  
pp. 1091-1122 ◽  
Author(s):  
M. A. Mustafa ◽  
N. J. Parziale ◽  
M. S. Smith ◽  
E. C. Marineau

In this work, we study the effect of the compression-corner angle on the streamwise turbulent kinetic energy (sTKE) and structure in Mach 2.8 flow. Krypton tagging velocimetry (KTV) is used to investigate the incoming turbulent boundary layer and flow over$8^{\circ }$,$16^{\circ }$,$24^{\circ }$and$32^{\circ }$compression corners. The experiments were performed in a 99 %$\text{N}_{2}$and 1 % Kr gas mixture in the Arnold Engineering Development Complex (AEDC) Mach 3 Calibration Tunnel (M3CT) at$Re_{\unicode[STIX]{x1D6E9}}=1750$. A figure of merit is defined as the wall-normal integrated sTKE ($\overline{\text{sTKE}}$), which is designed to identify turbulence amplification by accounting for the root-mean-squared (r.m.s.) velocity fluctuations and shear-layer width for the different geometries. We observe that the$\overline{\text{sTKE}}$increases as an exponential with the compression-corner angle near the root when normalized by the boundary-layer value. Additionally, snapshot proper orthogonal decomposition (POD) is applied to the KTV results to investigate the structure of the flow. From the POD results, we extract the dominant flow structures and compare each case by presenting mean-velocity maps that correspond to the largest positive and negative POD mode coefficients. Finally, the POD spectrum reveals an inertial range common to the boundary-layer and each compression-corner flow that is present after the first${\approx}10$dominant POD modes.


1984 ◽  
Vol 143 ◽  
pp. 23-46 ◽  
Author(s):  
S. Agrawal ◽  
A. F. Messiter

The local interaction of an oblique shock wave with an unseparated turbulent boundary layer at a shallow two-dimensional compression corner is described by asymptotic expansions for small values of the non-dimensional friction velocity and the flow turning angle. It is assumed that the velocity-defect law and the law of the wall, adapted for compressible flow, provide an asymptotic representation of the mean velocity profile in the undisturbed boundary layer. Analytical solutions for the local mean-velocity and pressure distributions are derived in supersonic, hypersonic and transonic small-disturbance limits, with additional intermediate limits required at distances from the corner that are small in comparison with the boundary-layer thickness. The solutions describe small perturbations in an inviscid rotational flow, and show good agreement with available experimental data in most cases where effects of separation can be neglected. Calculation of the wall shear stress requires solution of the boundary-layer momentum equation in a sublayer which plays the role of a new thinner boundary layer but which is still much thicker than the wall layer. An analytical solution is derived with a mixing-length approximation, and is in qualitative agreement with one set of measured values.


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