Assessment of optimization methods for aeroacoustic prediction of trailing-edge interaction noise in axisymmetric jets

Our concern in this paper is in the fine-tuning of the arbitrary parameters within the upstream turbulence structure for the acoustic spectrum of a rapid-distortion theory (RDT)-based model of trailing-edge noise. RDT models are based on an appropriate asymptotic limit of the Linearized Euler Equations and apply when the interaction time of the turbulence with the surface edge discontinuity is small compared to the eddy turnover time. When an arbitrary transversely sheared jet mean flow convects a finite region of nonhomogeneous turbulence, the acoustic spectrum of the pressure field scattered by the trailing-edge depends on (among other things) the upstream turbulence via the Fourier transform of the correlation function, R 22 (where subscript 2 refers to a co-ordinate surface normal to the plate). We show that the length and time scale parameters that govern the spatial and temporal de-correlation of R 22 can be found using formal optimization methods to avoid any uncertainty in their selection by hand-tuning. We assess various optimization methods that are broadly categorized into an ‘evolutionary’ and ‘non-evolutionary’ paradigm. That is, we optimize the acoustic spectrum using the Multi-Start algorithm, Particle Swarm Optimization and the Multi-Population Adaptive Inflationary Differential Evolution Algorithm. The optimization is based upon different objective functions for the acoustic spectrum and/or turbulence structure. We show that this approach, while resulting in the total modest increase in computation time (on average 2 h), gives excellent prediction over most frequencies (within 2–4 dB) where the trailing-edge noise associated amplification in sound exists

Modelling and prediction of the peak-radiated sound in subsonic axisymmetric air jets using acoustic analogy-based asymptotic analysis

This paper uses asymptotic analysis within the generalized acoustic analogy formulation (Goldstein 2003 JFM488, 315–333. (doi:10.1017/S0022112003004890)) to develop a noise prediction model for the peak sound of axisymmetric round jets at subsonic acoustic Mach numbers (Ma). The analogy shows that the exact formula for the acoustic pressure is given by a convolution product of a propagator tensor (determined by the vector Green's function of the adjoint linearized Euler equations for a given jet mean flow) and a generalized source term representing the jet turbulence field. Using a low-frequency/small spread rate asymptotic expansion of the propagator, mean flow non-parallelism enters the lowest order Green's function solution via the streamwise component of the mean flow advection vector in a hyperbolic partial differential equation. We then address the predictive capability of the solution to this partial differential equation when used in the analogy through first-of-its-kind numerical calculations when an experimentally verified model of the turbulence source structure is used together with Reynolds-averaged Navier–Stokes solutions for the jet mean flow. Our noise predictions show a reasonable level of accuracy in the peak noise direction at Ma = 0.9, for Strouhal numbers up to about 0.6, and at Ma = 0.5 using modified source coefficients. Possible reasons for this are discussed. Moreover, the prediction range can be extended beyond unity Strouhal number by using an approximate composite asymptotic formula for the vector Green's function that reduces to the locally parallel flow limit at high frequencies

Effect of wall temperature on the growth of Gortler vortices in high-speed boundary layers

Boundary layer flows over concave surfaces are subject to a centrifugal instability that leads to spatially growing longitudinal vortices known as Gortler vortices. From the practical standpoint, this phenomenon can be encountered, for example, in flows evolving over the concave part of a wing or turbomachinery blade, or on the walls of diverging-converging nozzles such as those utilized in supersonic/hypersonic wind tunnels. Depending on the curvature, the Reynolds number of the flow, and the level of environmental disturbances, these vortices can first lead to secondary instabilities, potential vortex breakdown, and eventual transition to turbulence. Here, we investigate the effect of varying the wall temperature on the development of Gortler vortices in high-speed boundary layer flows (with free-stream Mach number ranging from 1.5 to 7), using direct numerical simulations of the Navier-Stokes equations. The results reveal that the cooling of the wall can reduce the wall skin friction commensurately with the decrease in wall temperature, but at the same time increases the energy of the Gortler vortices

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

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

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

Effect of plate trailing edge deformations on jet flow and noise : an LES investigation

One approach to reduce jet noise generated by rectangular jets is to include flat surfaces that are parallel to the jet axis, but previous experimental work indicated that there is an increase in the noise generated by these configurations, mainly associated with the effect that the plate trailing edge exerts on the flow. In this work, we use large eddy simulations to investigate the potential of trailing edge deformations to reduce jet noise. We consider a high aspect ratio rectangular nozzle exhausting a jet over a flat surface in different configurations, and estimate the noise propagating to the farfield. Because of the high aspect ratio of the rectangular nozzle, we approximate the jet as being two-dimensional, and use periodic boundary conditions in the spanwise direction. For the configurations that we considered here, the trailing edge deformations did not seem to affect the noise significantly; an overall sound pressure level in the order of 1-2 dB was observed for some selected cases

Active control of high-speed boundary layer flows

High-amplitude freestream disturbances, as well as surface roughness elements, trigger streamwise oriented vortices and streaks of varying amplitudes in laminar boundary layers, which can lead to secondary instabilities and ultimately to transition to turbulence. In this project we aim at deriving and testing a control algorithm based on the adjoint compressible boundary region equations, which are obtained in the assumption that the streamwise wavenumber of the disturbances is much smaller the the crossflow wavenumbers. In our control algorithm, the wall transpiration velocity represents the control variable, whereas the wall shear stress or the vortex energy designates the cost functional. We anticipate the optimal control of the streamwise vortices approach to lessen vortex energy and subsequently cause a delay of the occurrence of transition from laminar to turbulent flow. Here, we report the progress on the project

A compressible boundary layer optimal control approach using nonlinear boundary region equations

High-amplitude free-stream turbulence and large surface roughness elements can excite a laminar boundary layer sufficiently enough to cause streamwise oriented vortices to form. The latter is accompanied by streaks of varying amplitudes that ‘wobble’ through inviscid secondary instabilities and, ultimately, transition to turbulence. In this paper, we formu- late a mathematical framework for the optimal control of compressible boundary layers to suppress the growth rate of the streamwise vortex system before breakdown occurs. This has a commensurate impact on the wall shear stress and heat transfer at the wall. Flow instabilities are introduced either through roughness elements equally separated in the spanwise direction or via free-stream disturbances. The compressible Navier-Stokes equations are reduced 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. The method of La- grange multipliers is used to derive the adjoint compressible boundary region equations via an appropriate transformation of the original constrained optimization problem into an unconstrained form. In the present formulation, the wall transpiration velocity represents the control variable while the wall shear stress or the vortex energy represents the cost functional. Our study shows that this kind of control approach induces a significant reduc- tion 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