We investigate flows interacting with a square and a fractal shape multi-scale structures in the compressible regime for Mach numbers at subsonic and supersonic upstream conditions using large-eddy-simulations (LES). We also aim at identifying similarities and differences that these interactions have with corresponding interactions in the canonical incompressible flow problem. To account for the geometrical complexity associated with the fractal structures, we apply an immersed boundary method to model the no-slip boundary condition at the solid surfaces, with adequate mesh resolution in the vicinity of the small fractal features. We validate the numerical results through extensive comparisons with experimental wind tunnel measurements at a low Mach number. Similar to the incompressible flow case results, we find a break-up of the flow structures by the fractal plate and an increase in turbulent mixing in the downstream direction. As the Mach number increases, we observe noticeable wake meandering and higher spread rate of the wake in the lateral direction perpendicular to the streamwise-spanwise plane. Although not significant, we quantify the difference between the square and the fractal plates using two-point velocity correlations across the Mach number range. The wakes generated by the fractal plate in the compressible regime showed lower turbulent kinetic energy (TKE) and energy spectra levels compared to those of the square case. Moreover, results in terms of the near-field pressure spectra seem to indicate that the fractal plate has the potential to reduce the aerodynamic noise.Investigation of wakes generated by fractal plates in the compressible flow regime using large-eddy simulations (LES) Investigation of wakes generated by fractal plates in the compressible flow regime using large-eddy simulations (LES)
Streamwise vortices and the associated streaks evolve in boundary layers over flat or concave surfaces due to disturbances initiated upstream or triggered by the wall surface. Following the transient growth phase, the fully-developed vortex structures become susceptible to inviscid secondary instabilities resulting in early transition to turbulence via 'bursting' processes. In high-speed boundary layers, more complications arise due to compressibility and thermal effects, which become more significant for higher Mach numbers. In this paper, we study Görtler vortices developing in high-speed boundary layers using the boundary region equations (BRE) formalism, which we solve using an efficient numerical algorithm. Streaks are excited using a small transpiration velocity at the wall. Our BRE-based algorithm is found to be superior to direct numerical simulation (DNS) and ad-hoc nonlinear parabolized stability equation (PSE) models. BRE solutions are less computationally costly than a full DNS and have a more rigorous theoretical foundation than PSE-based models. For example, the full development of a Görtler vortex system in high-speed boundary layers can be predicted in a matter of minutes using a single processor via the BRE approach. This substantial reduction in calculation time is one of the major achievements of this work. We show, among other things, that it allows investigation
Curved free shear layers exist in many engineering problems involving complex flow geometries, such as the backward facing step flow, flows with wall injection, the flow inside side-dump combustors, or flows generated by vertical axis wind turbines, among others. Most of the studies involving centrifugal instabilities have been focused on wall flows where Taylor instabilities between two rotating concentric cylinders or Görtler vortices in boundary layers resulting from the imbalance between centrifugal effects and radial pressure gradients, are generated. Curved free shear layers, however, did not receive sufficient attention. An examination of the stability characteristics and the flow structures associated with curved free shear flows should provide a better understanding of these complex flow problems. In this work, we study the development of Görtler vortices inside a curved shear layer in both the incompressible and compressible regimes using a numerical solution to a parabolized form of the Navier-Stokes equations, in the assumption that the streamwise wavenumber associated with the vortex flow is much smaller than the crossstream wavenumbers. Various results consisting of contour plots of centrifugal instabilites in crossflow planes, and energy and streak amplitude distributions along the streamwise direction are reported and discussed. In addition, we conduct a biglobal stability analysis to study the growth rates and the eigenmodes associated with these flows.
High-amplitude upstream disturbances and wall surface roughness elements trigger streamwise/Görtler vortices and the associated streaks in boundary layers over flat or concave surfaces. Following the transient growth phase, the fully-developed vortices become sensitive to inviscid secondary instabilities, which ultimately result in a premature transition to turbulence. Our work aims at investigating the effect of cooling/heating on the initiation and development of such streaks in an attempt to gain a better understanding of the conditions and governing mechanisms leading to secondary instabilities in high-speed compressible boundary layers. We conduct a parametric study via a robust and efficient numerical solution to the non-linear compressible boundary region equations (NCBRE) to identify the impact of varying the wall temperature on the development of streaks in supersonic and hypersonic boundary layer flows.
High-amplitude freestream turbulence and surface roughness elements can excite a laminar boundary-layer flow sufficiently to cause streamwise-oriented vortices to develop. These vortices resemble elongated streaks having alternate spanwise variations of the streamwise velocity. Downstream, the vortices “wobble” through an inviscid secondary instability mechanism and, ultimately, transition to turbulence. We formulate an optimal control algorithm to suppress the growth rate of the streamwise vortex system. Considering a high-Reynolds-number asymptotic framework, we reduce the full compressible Navier–Stokes equations to the nonlinear compressible boundary-region equations. We then implement the method of Lagrange multipliers via an appropriate transformation of the original constrained optimization problem into an unconstrained form to obtain the disturbance equations in the form of the adjoint compressible boundary-region equations (ACBREs) and corresponding optimality conditions. Numerical solutions of the ACBRE approach for high-supersonic and hypersonic flows reveal a significant reduction in the kinetic energy and wall shear stress for all considered configurations. We present contour plots to demonstrate the qualitative effect of increased control iterations. Our results indicate that the primary vortex instabilities gradually flatten in the spanwise direction thanks to the ACBRE algorithm.
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