LES Investigation of the Interaction between Compressible Flows and Fractal Structures

Previous experimental and numerical studies focused on incompressible flow interactions with multi-scale fractal structures targeting the generation of turbulence at multiple scales. Depending on various flow conditions, it was found that these fractal structures are able to enhance mixing and scalar transport, and in some cases reduce flow generated sound in certain frequency ranges. The interaction of compressible flows with multi-scale fractal structures, however, did not receive attention as the focus was entirely on the incompressible regime. The objective of this study is to conduct large eddy simulations (LES) of flow interactions with a class of fractal plates in the compressible regime, and to extract and analyze different flow statistics in an attempt to determine the effect of compressibility. Immersed boundary methods (IBM) will be employed to overcome the difficulty of modeling the fractal structures via a bodyitted mesh, with adequate mesh resolution around small features of the fractal shapes

Nonlinear centrifugal instabilities in curved free shear layers

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

Nonlinear centrifugal instabilities in curved free shear layers:American Institute of Aeronautics and Astronautics (AIAA) SciTech Forum

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

Simulating and investigating compressible flows interaction with fractal structures:71st Annual Meeting of the APS Division of Fluid Dynamics

Previous experimental and numerical studies have investigated incompressible flow interactions with multi-scale fractal structures with the objective of generating turbulence at multiple scales. Depending on various flow conditions, it was found that these fractal structures are able to enhance mixing and scalar transport, and in some cases to contribute to the reduction of flow generated sound in certain frequency ranges. The interaction of compressible flows with multi-scale fractal structures did not receive much attention as the focus was entirely on the incompressible regime. The objective of this study is to conduct large eddy simulations of flow interactions with various fractal structures in the compressible regime and to extract and analyze different flow statistics in an attempt to determine the effect of compressibility. Immersed boundary methods will be employed to overcome the difficulty of modeling the fractal structures, with adequate mesh resolution around small features of the fractal shapes

Investigation of Görtler vortices in high-speed boundary layers via an efficient numerical solution to the non-linear boundary region equations

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 into feedback control in reasonable total computational times. We investigate the development of the Görtler vortex system via the BRE solution with feedback control parametrically at various freestream Mach numbers M∞ and spanwise separations λ of the inflow disturbances

Streamwise Pressure Gradient Effect on Görtler Vortices:a Numerical Study in the Compressible Regime

We investigate the influence of streamwise pressure gradient on the Görtler vortex system initiation and development in high-speed compressible boundary layers. We conduct a parametric study in which we vary the pressure gradient in a supersonic flow at Mach number 3. Preliminary results include velocity and temperature plots, vortex energy distributions, and velocity profiles

Simulating and investigating compressible flows interaction with fractal structures

Previous experimental and numerical studies have investigated incompressible flow interactions with multi-scale fractal structures with the objective of generating turbulence at multiple scales. Depending on various flow conditions, it was found that these fractal structures are able to enhance mixing and scalar transport, and in some cases to contribute to the reduction of flow generated sound in certain frequency ranges. The interaction of compressible flows with multi-scale fractal structures did not receive much attention as the focus was entirely on the incompressible regime. The objective of this study is to conduct large eddy simulations of flow interactions with various fractal structures in the compressible regime and to extract and analyze different flow statistics in an attempt to determine the effect of compressibility. Immersed boundary methods will be employed to overcome the difficulty of modeling the fractal structures, with adequate mesh resolution around small features of the fractal shapes

Lagrange Multiplier-Based Optimal Control Technique for Streak Attenuation in High-Speed Boundary Layers

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. Previous articl

Control of Görtler vortices in high-speed boundary layer flows using nonlinear boundary region equations

We formulate a mathematical framework for the optimal control of compressible boundary layers to suppress the growth rate of the streamwise vortex system before breakdown occurs. We introduce flow instabilities to the flow either through roughness elements equally separated in the spanwise direction or via freestream disturbances. We reduce the compressible Navier-Stokes equations to the boundary region equations (BRE) in a high Reynolds number asymptotic framework wherein the streamwise wavelengths of the disturbances are assumed to be much larger than the spanwise and wall-normal counterparts. We apply the method of Lagrange multipliers to derive the adjoint compressible boundary region equations and the associated optimality conditions. The wall transpiration velocity represents the control variable while the wall shear stress or the vortex energy designates the cost functional. The control approach induces a significant reduction in the kinetic energy and wall shear stress of the boundary layer flow. Contour plots visually demonstrate how the primary instabilities gradually flatten out as more control iterations are applied

Control of streamwise vortices developing in compressible boundary layers

We derive and test an optimal control algorithm in the context of compressible boundary layers, in an attempt to suppress or at least limit the growth of streamwise vortices caused by high-amplitude freestream disturbances. We aim to reduce the vortex energy and ultimately delay the transition to turbulent flow. We introduce flow instabilities to the flow either through roughness elements equally separated in the spanwise direction or via freestream disturbances. We analytically reduce the compressible Navier-Stokes equations to the compressible boundary region equations (CBRE) in a high Reynolds number asymptotic framework, based on the assumption that the streamwise wavenumber of the streaks is much smaller than the cross-flow wavenumbers. We employ Lagrange multipliers to derive the adjoint compressible boundary region equations, and the associated optimality conditions. The wall transpiration velocity represents the control variable, whereas the wall shear stress or the vortex energy designates the cost functional. We report and discuss results for different Mach numbers, wall conditions, and spanwise separations