Marcello A. F. Medeiros

Sparse Techniques in Global Flow Instability with Application to Compressible Leading-Edge Flow

Investigation of linear instability mechanisms is essential for understanding the process of transition from laminar to turbulent flow. Many studies over several decades have reported results in simple one-dimensional steady laminar basic flows, such as the boundary and shear layers. However, most flows of practical engineering significance remain unexplored. The main reason is that the geometry and underlying basic state in most applications depend on an inhomogeneous manner on more than one spatial direction, which does not permit use of simplified equations. The consideration of two or three inhomogeneous directions in the stability problem formulation results in formidable computational costs for completing parametric studies, which are, on the other hand, mandatory from a physical point of view.

On the Small Effect of Boundary Layer Thicknesses on Slat Noise

In landing procedure the airframe noise is comparable to the noise generated by the engines of an aircraft, being the leading edge slat one of the most important components. Experiments on slat noise generation usually are limited to much lower Reynolds numbers than those obtained in ight conditions. The present paper describes analyses made to evaluate numerically the in uence of the boundary layer thickness on the unsteady ow and noise generation at the slat cove. Time accurate simulations were done using a LatticeBoltzmann solver. Grid independence studies of the Power Spectral Density (PSD) are presented. Slat boundary layer thicknesses were found to have little in uence on turbulence and pressure spectra at the slat cove, leading to investigations of the use of free-slip walls at the slat. Very small level di erences were obtained in the slat noise produced. This assumption allowed not only a coarser grid to be employed in certain regions but also the possibility to predict slat noise in high Reynolds number ows with no major increase in simulation cost.

Numerical investigation of the three-dimensional secondary instabilities in the time-developing compressible mixing layer

Mixing layers are present in very different types of physical situations such as atmospheric flows, aerodynamics and combustion. It is, therefore, a well researched subject, but there are aspects that require further studies. Here the instability of two-and three-dimensional perturbations in the compressible mixing layer was investigated by numerical simulations. In the numerical code, the derivatives were discretized using high-order compact finite-difference schemes. A stretching in the normal direction was implemented with both the objective of reducing the sound waves generated by the shear region and improving the resolution near the center. The compact schemes were modified to work with non-uniform grids. Numerical tests started with an analysis of the growth rate in the linear regime to verify the code implementation. Tests were also performed in the non-linear regime and it was possible to reproduce the vortex roll-up and pairing, both in two-and three-dimensional situations. Amplification rate analysis was also performed for the secondary instability of this flow. It was found that, for essentially incompressible flow, maximum growth rates occurred for a spanwise wavelength of approximately 2/3 of the streamwise spacing of the vortices. The result demonstrated the applicability of the theory developed by Pierrehumbet and Widnall. Compressibility effects were then considered and the maximum growth rates obtained for relatively high Mach numbers (typically under 0.8) were also presented.

Linear instability of orthogonal compressible leading-edge boundary layer flow

Instability analysis of compressible orthogonal swept leading-edge boundary layer flow was performed in the context of BiGlobal linear theory. 1, 2 An algorithm was developed exploiting the sparsity characteristics of the matrix discretizing the PDE-based eigenvalue problem. This allowed use of the MUMPS sparse linear algebra package 3 to obtain a direct solution of the linear systems associated with the Arnoldi iteration. The developed algorithm was then applied to efficiently analyze the effect of compressibility on the stability of the swept leading-edge boundary layer and obtain neutral curves of this flow as a function of the Mach number in the range 0 ≤ Ma ≤ 1. The present numerical results fully confirmed the asymptotic theory results of Theofilis et al. 4 Up to the maximum Mach number value studied, it was found that an increase of this parameter reduces the critical Reynolds number and the range of the unstable spanwise wavenumbers.

Slat Noise from an MD30P30N Airfoil at Extreme Angles of Attack

This study investigates the slat noise of a two-dimensional scaled, unswept, and untapered MD30P30N high-lift model. The experimental data refer to aeroacoustic and aerodynamic measurements in a cl...

On Detrimental Effects of Excrescences on the Slat Noise

In airplane landing the slat noise is already a barrier to the development of quieter commercial airplanes. Investigations have been made by several research groups to understand the mechanism of noise generation in slat and develop better tools to predict it. Most of the published works related to slat noise considers clean idealized geometries, whereas real slats contain some imperfections to enable its operation. The in uence of a protrusion on the slat cavity surface on the unsteady ow around the slat and on the propagated sound was here investigated via numerical calculation. The protrusion was a sealing device to avoid metal-metal contact. Lattice-Boltzmann method was used in the computations. The e ect of the seal on the mean surface pressure distribution is limited to the region close to it. When the seal is positioned inside the recirculation zone, the region next to the cusp present less uctuation intensity and the vortices formed in the mixing layer keep two-dimesionality for a longer distance in the way to the reattachment point. The noise propagated to fareld also present more intense low frequency tonal peaks. Although discretization as ne was 0:15mm was employed, uctuations of a speci c frequency band were still mesh dependent.

Natural Transition in Plane Poiseuille Flow

We present numerical and theoretical results on the natural transition in a plane Poiseuille flow. The natural transition is often studied in boundary layers, but the analysis in a parallel flow allows the use of the Reynolds number as a control parameter. The results indicated that the classical scenarios described in the literature play a role in natural transition and can lead to turbulent spots. In natural transition the wave systems are modulated in streamwise and spanwise directions and cause premature nonlinearity [1]. Spikes and turbulent spots are often present in natural transition, but the classical routes, namely, K-type and H-type instabilities and the oblique transition, have not been linked to these phenomena. Therefore, many questions remain regarding the relevance of these studies to natural transition. For instance, it is unknown whether such classical routes actually occur in natural transition, whether they occur simultaneously or interact, whether there is a dominant mechanism under some circumstances, etc. Such questions motivated the present work. Numerical simulation of the incompressible three-dimensional Navier-Stokes equations in a vorticity velocity formulation was performed using high accurate numerical schemes. Owing to the complexity of the natural transition, the streamwise modulation was initially not considered. Therefore, only the three dimensionality was studied yielding spanwise modulated wavetrains. Two cases were judiciously selected at Re = 8000. One case was located near the first branch of the two-dimensional stability diagram where the linear process is dominated by three-dimensional Tollmien-Schlichting (TS) waves. The other case was located far from the first branch where the linear process is dominated by a two-dimensional TS waves. Preliminary results can be found in [2]. Similar studies, but for boundary layers, can be found in [3].

A Study of the Sources of Slat Noise using Proper Orthogonal Decomposition

Airframe noise is already a barrier in the expansion of commercial aviation. Among airframe noise sources, the leading-edge slats play an important role since it is a source distributed along almost the whole wingspan. Although the high-frequency tonal peak is already known to be generated by trailing-edge vortex shedding, the origin of other elements of the spectrum of slat noise is not fully understood yet. The present work considers an unsteady Lattice-Boltzmann simulation of the flow around a typical threeelement high-lift configuration, and performs an analysis of the flow structures existing inside of the slat cove at the peak frequencies of the far-field noise radiation. Proper orthogonal decomposition (POD), widely used in the identification of coherent structures in turbulent flows, is employed here in order to filter out the fluctuations without a significant correlation on the slat cove region.i Different inner products are investigated in the POD formulation, using not only the most standard turbulent kinetic energy norm but also pressure norms, more adequate to the study of noise generation phenomena. The results show that, at the dominant tonal peaks, the flow inside the cove is dominated by vortical structures generated by the inflectional instability of the mixing-layer.

Non-conservative implicit large-eddy simulation method for predicting the noise radiated by subsonic jets

In this paper was developed and validated an implicit Large-Eddy Simulation (LES) method for predicting the noise radiated by subsonic jets. Unlike the traditional LES methods based on eddy-viscosity models, the present approach is based on the Approximate Deconvolution Model (ADM) and a non-conservative form of ow governing equations. The use of non-conservative form avoids the need of density weighting (Favre avareging) of ow variables and also reduces the sensitivity to aliasing errors, providing strong nonlinear stability for high-order non-dissipative compact schemes. Stringent requirements of Computational Aeroacoustics (CAA) were satised by employing sixth-order accurate compact schemes for spatial discretization and implicit ltering, and a fourth-order RungeKutta method for time integration. Boundary conditions and buer zone treatments were prescribed by a characteristic-based formulation and a conceptual model based on the characteristic analysis. Computations of the jet were carried out with a high performance multi-block Message Passing Interface (MPI) parallel solver with nite sized overlap interface communication. Mean ow parameters of the jet where found to be in excellent agreement with previous LES data at similar ow conditions and the theoretical decay law.

Wavepackets in a compressible subsonic adverse pressure gradient boundary layer

yMost studies of natural transition report the occurrence of wavepackets prior to transition. The packets are therefore regarded as a good model of natural transition. Nevertheless, in natural transition the packets are not likely to happen in isolation, but can interact. This paper covers a fairly comprehensive and systematic study of the eect of modulation on the evolution of waves in compressible adverse pressure gradient boundary layers. The three-dimensional direct numerical simulation (DNS) method has been used and the natural transition scenario was modeled by three-dimentional wavepackets. The simulations was performed at Mach number 0:5 and a mild adverse pressure gradient was used to verify the earliest eect of pressure. It was possible to identify many relevant features to characterize the regime. The nonlinear regime that was observed was consistent with oblique transition, both in physical and Fourier space.