Xavier Gloerfelt

Direct computation of the noise radiated by a subsonic cavity flow and application of integral methods

Abstract The goal of this paper is to investigate the acoustic field generated by the flow over a cavity using two different and complementary numerical methods. First, a Direct Numerical Simulation of the 2-D compressible Navier–Stokes equations is performed to obtain directly the radiated noise. The results of the acoustic and aerodynamic fields are compared to the experimental data in the literature. Second, this reference solution is compared to solutions provided by hybrid methods using the flowfield computed inside the cavity combined with an integral formulation to evaluate the far-field noise. Numerical issues of three integral methods are studied: the Ffowcs Williams and Hawkings analogy that extends Lighthills theory to account for solid boundaries and two Wave Extrapolation Methods from a control surface, the Kirchhoff and porous Ffowcs Williams and Hawkings methods. All methods show a good agreement with the Direct Numerical Simulation, but the first one is more expensive owing to an additional volume integral. However, the analogy can help in the analysis of wave patterns, by separating the direct waves from the reflected ones. The wave extrapolation methods from a surface are more efficient and provide a complementary tool to extend Computational Aeroacoustics near field to the very far field.

Numerical evidence of mode switching in the flow-induced oscillations by a cavity

A Direct Noise Computation (DNC) has been performed for a turbulent boundary layer past a rectangular cavity, matching one configuration of Karamcheti1 experiments. An LES approach with periodic boundary conditions in the spanwise direction is used to evaluate the solution at a reasonable computational cost. The two components in the pressure spectra found experimentally are well reproduced. The acoustic field appears to be dominated by the low-frequency component whereas the experimental visualization indicates a radiation at the higher frequency. The mechanism giving rise to the lower frequency is investigated providing evidence on the possibility of switching between two cavity modes and that the strong coupling of the separated shear layer with the recirculation flow within the cavity is likely to participate to the low-frequency modulation. Moreover, an extrapolation method is proposed and applied to obtain the far-field from the near acoustic field.

Aerodynamic noise induced by laminar and turbulent boundary layers over rectangular cavities

The structure of an unsteady o w past a rectangular, open cavity is investigated using numerical simulations. Particular attention is drawn to the three-dimensional geometry eects, and to the turbulent state of the incoming boundary layer. The consequences on noise generation are studied. Two-dimensional DNS allows a reconstruction of the feedback loop giving rise to the selfsustained oscillations, but DNS is restricted to thick laminar upstream boundary layers. Cavity o ws with higher Reynolds numbers are computed by 3-D Large Eddy Simulations, based on high order algorithms, by considering that the interactions of coherent structures with the downstream edge are predominant in such o ws. The three-dimensional structure of the recirculating zone is illustrated and its inuence on the shear layer dynamics is shown . In the same way as the incoming turbulence level, these modulations induce jittering of vortex-corner interactions, a decrease in feedback coherence, and thus a reduction of the radiated noise.

Large-Eddy Simulation of Broadband Unsteadiness in a Shock/Boundary-Layer Interaction

The simulation of low-frequency unsteadiness in shock wave/turbulent boundary-layer interactions constitutes a challenging case insofar as very long time integrations are required to describe these broadband motions at frequencies two orders of magnitude lower than those of the turbulent motions. A relatively low-cost numerical strategy is established in the present study. The use of quasi-spectral centered finite differences in conjunction with high-order selective filtering provides an efficient method for compressible large-eddy simulations based on explicit filtering regularization. This strategy is extended to flows containing discontinuities by switching between the high-order filter used in regular zones and a low-order filter acting selectively near the shock locations. The accuracy of the current strategy is assessed for a developing turbulent supersonic boundary layer. The case of an oblique shock wave impinging on a flat plate is then successfully validated against previous experimental and num...

Trailing edge noise from an isolated airfoil at a high Reynolds number

A multi-size mesh multi-time step strategy is used to perform three dimensional direct noise computations (DNC) around airfoils at high Reynolds numbers. This method allows to realize local grid refinements in conjonction with high order numerical methods commonly used in Computational AeroAcoustics (CAA). In order to analyse broadband trailing edge noise, the configuration consists in a truncated NACA0012 airfoil at high Reynolds 2.32 × 10 6 with an angle of attack of 2.5 ◦ and with triggered turbulent boundary layers both sides. This challenging case implies a wide variety of scales, and tackle the limit of the current computational capabilities. Two grids have been designed to test Large Eddy Simulations based on explicit filtering. In the present work, two of the five self-noise mechanisms due to specific boundary-layer phenomena identified and modeled by Brooks et al.[NASA Tech. Rep., 1989] are studied numerically. Namely, the noise radiation comes from the diffraction of the kinetic energy of evanescent waves advected in the turbulent boundary layers passing in the vicinity of the trailing edge in conjonction with the vortex shedding from the truncated trailing edge. First comparisons are made with an experimental database realized by the french aerospace agency ONERA. Particular attention is drawn to the characteristics of the wall pressure, in order to relate it with the acoustic field, obtained directly in the present approach.

Direct Computation of Turbulent Boundary Layer Noise

Aerodynamic noise from a turbulent boundary layer, also known as flow noise is a fundamental topic in flow-induced noise insofar as it determines the structural response of a surface submitted to this turbulent buffeting. For example, in the automotive applications, sound waves transmitted inside the interior of the vehicle come from two contributions: the direct transfer of the acoustic radiation, and the indirect transfer by the incompressible pressure loading which can excite the vibrational modes of the structure. The first one has a low efficiency but a transfer function close to one, whereas the second is more energetic but the transfer function becomes very weak at high wavenumbers. For the flow around a A-pillar, Alam et al. have shown that the mechanism associated with structural responses to turbulent wall flow is preponderant, but no study has quantified precisely the contributions of the direct and indirect transfers, and the question whether the acoustic part should be considered remains an open question.

Reliable reduced-order models for time-dependent linearized Euler equations

Development of optimal reduced-order models for linearized Euler equations is investigated. Recent methods based on proper orthogonal decomposition (POD), applicable for high-order systems, are presented and compared. Particular attention is paid to the link between the choice of the projection and the efficiency of the reduced model. A stabilizing projection is introduced to induce a stable reduced-order model at finite time even if the energy of the physical model is growing. The proposed method is particularly well adapted for time-dependent hyperbolic systems and intrinsically skew-symmetric models. This paper also provides a common methodology to reliably reduce very large nonsymmetric physical problems.

Aeroacoustic computations using a high-order shock-capturing scheme

For aeroacoustic computations in the supersonic regime, it is necessary to use a numerical scheme that can represent shock waves without generating spurious numerical oscillations. The centered schemes that are usually used with success in the subsonic case, combined with a selective filtering, will generally oscillate in the presence of discontinuities. A new class of shock-capturing schemes, the one-step monotonicity-preserving schemes, combine the high accuracy and the nonoscillating property. It is thus a good candidate for supersonic aeroacoustic applications. The good spectral properties of these schemes are illustrated in the scalar linear case. Results of aeroacoustic test problems for the Euler and Navier-Stokes equations are compared with a dispersion-relation-preserving scheme. The application to a supersonic cavity flow, which induces a complex pattern of moving shocks, shows that the one-step monotonicity-preserving schemes capture the moving discontinuities without spurious oscillations and preserve a high accuracy at the same time.

Large-eddy simulation of a high Reynolds number ∞ow over a cavity including radiated noise

The large-eddy simulation of a high Reynolds number cavity flow is investigated. The configuration is a L/D = 2, M∞ = 0.4, ReL = 1.52×10, studied experimentally by Kegerise et al., because this case presents significant nonlinearities between the modes of oscillations, and displays mode-switching between the Rossiter modes. The LES strategy relies on the conjoint use of a finite-difference scheme and a selective filter, both optimized in the wavenumber space up to k∆x = π/2, in order to ensure a clear separation between resolved and unresolved scales. The dissipative effect of the subgrid-scale is provided implicitely by the selective filtering. The first LES results with a coarse grid capture the main features of the cavity flow.

Numerical Investigation of the Coexistence of Multiple Tones in Flow-induced Cavity Noise

Flow-induced cavity oscillations are often characterized by the presence of multiple simultaneous peaks in the spectra. This phenomenon is investigated numerically by using Direct Noise Computations for Mach 0.6 o ws over cavities with a length-to-depth ratio of L=D = 1. Two parameters are studied : the width of the cavity in the spanwise direction, and the thickness of the incoming boundary layer. The dominant oscillation frequencies correspond to the number of vortices in the shear layer. Low-frequency components and higher harmonics are also identiable in the spectra. Time-frequency analyses show that the multiple tones do coexist. Even if some low frequencies can be associated to lower Rossiter modes, the coexistence is not attributable to switching between competitive modes. In general, the lowfrequency components do not result directly from vortex coalescence, although such interaction are not precluded. They arise instead from severe modulations in the vortex-corner interactions, leading to remarkably ordered cycling patterns. To understand to what extent quadratic nonlinearities are important, bispectral analysis has been performed. All the components observed in the spectra may be related to the sum and dierence of the primary cavity modes, and eventual harmonics, through nonlinear interactions. This mutual interaction involving nonlinear triads is a candidate explanation for the coexistence of multiple self-sustained cavity tones.