Study of interpolation methods for high-accuracy computations on overlapping grids

Overset strategy can be an efficient way to keep high-accuracy discretization by decomposing a complex geometry in topologically simple subdomains. Apart from the grid assembly algorithm, the key point of overset technique lies in the interpolation processes which ensure the communications between the overlapping grids. The family of explicit Lagrange and optimized interpolation schemes is studied. The a priori interpolation error is analyzed in the Fourier space, and combined with the error of the chosen discretization to highlight the modification of the numerical error. When high-accuracy algorithms are used an optimization of the interpolation coefficients can enhance the resolvality, which can be useful when high-frequency waves or small turbulent scales need to be supported by a grid. For general curvilinear grids in more than one space dimension, a mapping in a computational space followed by a tensorization of 1-D interpolations is preferred to a direct evaluation of the coefficient in the physical domain. A high-order extension of the isoparametric mapping is accurate and robust since it avoids the inversion of a matrix which may be ill-conditioned. A posteriori error analyses indicate that the interpolation stencil size must be tailored to the accuracy of the discretization scheme. For well discretized wavelengthes, the results show that the choice of a stencil smaller than the stencil of the corresponding finite-difference scheme can be acceptable. Besides the gain of optimization to capture high-frequency phenomena is also underlined. Adding order constraints to the optimization allows an interesting trade-off when a large range of scales is considered. Finally, the ability of the present overset strategy to preserve accuracy is illustrated by the diffraction of an acoustic source by two cylinders, and the generation of acoustic tones in a rotor–stator interaction. Some recommandations are formulated in the closing section

cPCWE -- Perturbed Convective Wave Equation based on Compressible Flows

This work derives a variant of the perturbed convective wave equation based on the acoustic perturbation equations for compressible flows. In particular, the derivation reformulates the relation of Helmholtz's decomposition to the acoustic and source potential definition. The detailed roadmap of a possible implementation is presented algorithmically. Finally, initial results on the sound prediction capabilities concerning a mixing layer example are presented.Comment: 5 pages, working paper, v0.

Turbulent boundary layer noise : direct radiation at Mach number 0.5

Boundary layers constitute a fundamental source of aerodynamic noise. A turbulent boundary layer over a plane wall can provide an indirect contribution to the noise by exciting the structure, and a direct noise contribution. The latter part can play a significant role even if its intensity is very low, explaining why it is hardly measured unambiguously. In the present study, the aerodynamic noise generated by a spatially developing turbulent boundary layer is computed directly by solving the compressible Navier-Stokes equations. This numerical experiment aims at giving some insight into the noise radiation characteristics. The acoustic wavefronts have a large wavelength and are oriented in the direction opposite to the flow. Their amplitude is only 0.7 % of the aerodynamic pressure for a flat-plate flow at Mach 0.5. The particular directivity is mainly explained by convection effects by the mean flow, giving an indication about the compactness of the sources. These vortical events correspond to low-frequencies, and have thus a large life time. They cannot be directly associated with the main structures populating the boundary layer such as hairpin or horseshoe vortices. The analysis of the wall pressure can provide a picture of the flow in the frequency-wavenumber space. The main features of wall pressure beneath a turbulent boundary layer as described in the literature are well reproduced. The acoustic domain, corresponding to supersonic wavenumbers, is detectable but can hardly be separated from the convective ridge at this relatively high speed. This is also due to the low frequencies of sound emission as noted previously

On compressibility assumptions in aeroacoustic integrals: a numerical study with subsonic mixing layers

Two assumptions commonly made in predictions based on Lighthill’s formalism are investigated: a constant density in the quadrupole expression, and the evaluation of the source quantity from incompressible simulations. Numerical predictions of the acoustic field are conducted in the case of a subsonic spatially evolving two-dimensional mixing layer at Re = 400. Published results of the direct noise computation (DNC) of the flow are use as reference and input for hybrid approaches before the assumptions on density are progressively introduced. Divergence free velocity fields are obtained from an incompressible simulation of the same flow case, exhibiting the same hydrodynamic field as the DNC. Fair comparisons of the hybrid predictions with the reference acoustic field valid both assumptions in the source region for the tested values of the Mach number. However, in the observer region, the inclusion of flow effects in the Lighthill source term is not preserved, which is illustrated through a comparison with the Kirchhoff wave-extrapolation formalism, and with the use of a convected Green function in the integration process

Near-field aero-acoustic shape optimization at low Reynolds number

Abstract: The Flux Reconstruction (FR) approach, is used to study the ?ow over two-dimensional objects at low Reynolds numbers. The Sound Pressure Level (SPL) is computed using a direct acoustic approach at an observer in the near ?eld. The aeroacoustic shape optimization is performed using the gradient-free Mesh Adaptive Direct Search (MADS) technique. NACA 4-digit airfoil is optimized at Re = 10, 000 and M? = 0.2 to reduce the trailing edge noise. The airfoil’s shape is optimized at an appropriate angle of attack to reduce the SPL while increasing the lift coef?cient. The optimized airfoil is quiet with 0 dB noise and the lift coef?cient is increased by more than 80%.Communication présentée lors du congrès international tenu conjointement par Canadian Society for Mechanical Engineering (CSME) et Computational Fluid Dynamics Society of Canada (CFD Canada), à l’Université de Sherbrooke (Québec), du 28 au 31 mai 2023

Parallel computation of aeroacoustics of industrially relevant complex-geometry aeroengine jets

Jet noise is still a distinct noise component when a commercial aircraft is taking off. A parallel high-fidelity simulation framework for industrial jet noise prediction is presented in this paper. This framework includes complex geometry meshing and Ffowcs Williams-Hawkings (FW-H) surface placement during preprocessing, a parallel hybrid RANS-LES flow solver coupled with an FW-H acoustic solver in the simulation and mean and unsteady data processing after the simulation. The use of this framework is demonstrated through two jet noise prediction cases: in-flight heated jets and installed ultra-high bypass-ratio (UHBPR) engines. These simulations can provide more insight than experimental tests into jet flow physics for engineering model improvement. Additional advantages are also shown in the cost and turn-around time. Thus there is great potential for high-fidelity jet noise simulations to partly replace rig tests for industrial use in the future

A General Method to Compute Numerical Dispersion Error

This article presents a new methodology to compute numerical dispersion error. The analysis here presented is not restricted to uniform structured meshes nor linear discrete operators as it does not rely on sinusoids to compute the associated error. When using uniform meshes, the results obtained with the present method collapse onto the obtained with the classic one via an easy change of basis. If non-uniform meshes are used, a new kind of results are obtained which shed some light onto the role stretching has on dispersion error.This work has been financially supported by the Ministerio de Economía y Competitividad, Spain (No. ENE2017-88697-R). J.R.P. is supported by a FI-DGR 2015 predoctoral contract financed by Generalitat de Catalunya, Spain.Peer ReviewedPostprint (published version

Acoustic far-field prediction of a controlled diffusion airfoil self-noise

Abstract: Direct Numerical Simulations (DNS) of the compressible flow over a Controlled Diffusion (CD) airfoil are conducted. To obtain far field predictions, the DNS are coupled to an acoustic solver based on the Ffowcs Williams & Hawkings formulation. The turbulent flow field at the vicinity of the trailing edge and its noise generation mechanisms is the object of study. The installation effects associated with wind tunnel conditions are included in the computations. Three noise sources have been found, the flow separation and reattachment, the interaction between the attached turbulent flow at the trailing edge and a secondary instability in the near wake.Communication présentée lors du congrès international tenu conjointement par Canadian Society for Mechanical Engineering (CSME) et Computational Fluid Dynamics Society of Canada (CFD Canada), à l’Université de Sherbrooke (Québec), du 28 au 31 mai 2023

Wall treatments for aeroacoustic measurements in closed wind tunnel test sections

Aeroacoustic tests in closed wind tunnels are affected by reflections in the tunnel circuit and background noise. Reflections can be mitigated by lining the tunnel circuit. The present study investigates if lining exclusively the most accessible segment of a closed wind tunnel circuit, in particular the test section, is an approach which improves acoustic measurements. Literature shows that a wind tunnel lining material should have high acoustic absorption, low inertial resistivity and low surface roughness. Therefore, the test section of TU Delft's closed Low Turbulence Tunnel is lined with melamine foam wall liners. A total of 4 test section configurations were tested: baseline; test section with lining on the floor and ceiling; test section with lined side--panels; and test section lined at all surfaces (floor, ceiling and side--panels). An omnidirectional speaker is used for evaluating the wind tunnel's acoustic performance. A geometric modelling algorithm, based on the mirror-source method, is used to predict the effect of lining on primary reflections in the test section. In addition, reflections in the test section and in the tunnel circuit are characterized experimentally. The results show that the closed loop of the tunnel circuit is responsible for a long reverberation time in the test section. However, reflections inside the test section itself are the dominant source of acoustic interference at the microphone array location. The low fidelity geometric modelling algorithm is shown to be a valuable approach for an initial estimation of the acoustic benefit of lining, for both flow--off and --on conditions. Lining of the test section walls significantly reduces reflections from the reference source, as well as the aerodynamic background noise that reaches the array