Numerical simulation of the viscous shock tube problem by using a high resolution monotonicity-preserving scheme

International audienceThis work deals with the flow generated in a shock tube after the shock wave has reflected at the end wall. For a viscous fluid, a complex unsteady interaction takes place between the incident boundary layer and reflected shock wave. The numerical simulation of this complex flow requires both robust and accurate numerical schemes. In this work, we rely on the one-step high-order scheme recently proposed by Daru and Tenaud [Daru V, Tenaud C. High order one-step monotonicity preserving schemes for unsteady flow calculations. J Comput Phys 2004;193]. With this scheme, converged results are obtained for Reynolds numbers in the range 200-1000. The interaction mechanisms are carefully analyzed as well as the flow dynamics

Two-dimensional numerical simulations of nonlinear acoustic streaming in standing waves

Numerical simulations of compressible Navier–Stokes equations in closed two-dimensional channels are performed. A plane standing wave is excited inside the channel and the associated acoustic streaming is investigated for high intensity waves, in the nonlinear streaming regime. Significant distortion of streaming cells is observed, with the centers of streaming cells pushed toward the end-walls. The mean temperature evolution associated with the streaming motion is also investigated

Fast acoustic streaming in standing waves : Generation of an additional outer streaming cell

Rayleigh streaming in a cylindrical acoustic standing waveguide is studied both experimentally and numerically for nonlinear Reynolds numbers from 1 to 30. Streaming velocity is measured by means of laser Doppler velocimetry in a cylindrical resonator filled with air at atmospheric pressure at high intensity sound levels. The compressible Navier-Stokes equations are solved numerically with high resolution finite difference schemes. The resonator is excited by shaking it along the axis at imposed frequency. Results of measurements and of numerical calculation are compared with results given in the literature and with each other. As expected, the axial streaming velocity measured and calculated agrees reasonably well with the slow streaming theory for small ReNL but deviates significantly from such predictions for fast streaming (ReNL > 1). Both experimental and numerical results show that when ReNL is increased, the center of the outer streaming cells are pushed toward the acoustic velocity nodes until counter-rotating additional vortices are generated near the acoustic velocity antinodes

Simulation numérique du décollement et recollement turbulent autour d'une plaque plane épaisse

Nous présentons la simulation numérique de l'écoulement turbulent autour d'une plaque épaisse pour étudier les mécanismes d'interaction entre les structures énergétiques et la génération du champ de pression instationnaire. Les résultats statistiques se comparent très favorablement aux résultats expérimentaux. Les LES retrouvent les fréquences caractéristiques (de « shedding » et « flapping » et des modes de Kelvin-Helmholtz) qui ont été mesurées expérimentalement. C'est à notre connaissance la première fois que l'ensemble de ces fréquences est prédit numériquement

3d conservative coupling method between a compressible fluid flow and a deformable structure

In this work, we present a conservative method for three-dimensional inviscid fluid-structure interaction problems. On the fluid side, we consider an inviscid Euler fluid in conservative form. The Finite Volume method uses the OSMP high-order flux with a Strang operator directional splitting [1]. On the solid side, we consider an elastic deformable solid. In order to examine the issue of energy conservation, the behavior law is here assumed to be linear elasticity. In order to ultimately deal with rupture, we use a Discrete Element method for the discretization of the solid [2]. An immersed boundary technique is employed through the modification of the Finite Volume fluxes in the vicinity of the solid. Since both fluid and solid methods are explicit, the coupling scheme is designed to be globally explicit too. The computational cost of the fluid and solid methods lies mainly in the evaluation of fluxes on the fluid side and of forces and torques on the solid side. The coupling algorithm evaluates these only once every time step, ensuring the computational efficiency of the coupling. Our approach is an extension to the three-dimensional deformable case of the conservative method developed in [3]. We focus herein numerical results assessing the robustness of the method in the case of a undeformable solid with large displacements subjected to a compressible fluid flow

On wall pressure fluctuations and their coupling with vortex dynamicsin a separate d–reattache d turbulent flow over a blunt flat plate

This study deals with the numerical predictions through Large-Eddy Simulation ( LES ) of the separated–reattached turbulent flow over a blunt flat plate for analyzing main coherent structure features and theirrelation to the unsteady pressure field. A compressible approach that inherently includes acoustic prop- agation is here followed to describe the relationship between pressure fluctuations and vortex dynam- ics around the separation bubble. The objective of the present work is then to contribute to a betterunderstanding of the coupling between the vortex dynamics and the wall pressure fluctuations. The fil- tered compressible Navier–Stokes equations are then solved with a numerical method that follows a Lax–Wendroffapproach to recover a high accuracy in both time and space. For validations, the present numer- ical results are compared to experimental measurements, coming from both the Pprime laboratory (Sicotel al., 2012) and the literature (Cherry et al., 1984; Kiya and Sasaki, 1985; Tafti and Vanka,1991; Sicotet al., 2012). Our numerical results very well predict mean and fluctuating pressure and velocity fields.Flapping, shedding as well as Kelvin–Helmholtz characteristic frequencies educed by present simulationsare in very good agreement with the experimental values generally admitted. These characteristic modesare also visible on unsteady pressure signatures even far away from the separation. Spectral, POD andEPOD (extended POD) analyses are then applied to these numerical data to enhance the salient featuresof the pressure and velocity fields, especially the unsteady wall pressure in connection with either thevortex shedding or the low frequency shear-layer flapping. A contribution to the understanding of thecoupling between wall pressure fluctuations and eddy vortices is finally proposed

Coherent structures in the boundary layer of a flat thick plate

International audienceWe use POD and EPOD (extended POD) analysis to extract the main features of the flow over a thick flat plate simulated with a LES. Our goal is to better understand the coupling between the velocity field and the surface pressure field. We find that POD modes based on the full velocity and energy fields contain both flapping and shedding frequencies. Pressure modes are found to be uniform in the spanwise direction and the most intense variations take place at the mean reattachment point. Velocity modes educed from the pressure modes with EPOD are seen to correspond to eddies shed by the recirculation bubble. Résumé : Onconsi ere l ecoulementau-dessusd'uneplaqueplanéepaisse.Nousutilisonslasimulationauxgrandeechellesetl'analysePOD/EPODpourcomprendrelecouplageentrelechampdevitesseetlechampdepres-sioalaparoi.LesmodesPODextraitsdelavitessecontiennentdesfréquencescorrespondantauxphénoenesdeflappingetdeshedding.Lesmodesdepressionsontuniformesdansladirectiontransverseetlesvariationslesplusintensessontobservéesaupointderéattachement.Lesmodesdevitesseconstruitapartirdesmodesdepressionavecl'approcheEPODcorrespondenadestourbillonsassociéalabullederecirculation

Méthode de frontière immérgée pour la simulation d'écoulements visqueux compressibles.

La difficulté de prendre en compte des corps mobiles de géométries complexes en maillage cartésien a favorisé le développement de méthodes de frontières immergées (MFI). Les applications MFI multidimensionnelles ont principalement été menées en incompressible. Nous présentons ici une technique de conditions immergées pour des écoulements compressibles. La validation de la méthode est effectuée en écoulements 3D compressibles autour de géométries « complexes »

Acoustically induced thermal effects on Rayleigh streaming

The present study focuses on acoustically induced thermal effects on Rayleigh streaming inside a resonator. Firstly, we consider the effect of the transverse (or wall-normal) mean temperature gradient on the acoustic streaming flow generated by a standing wave between two parallel plates. Analytical expressions for acoustic quantities are developed and used to express the sources of linear streaming. The influence of a transverse temperature variation on the streaming velocity is clearly identified through a term proportional to the temperature difference and to the square of the half-width of the guide. This term modifies the Rayleigh streaming pattern and may generate an additional vortex. On the other hand, the longitudinal (or wall-parallel) temperature difference is calculated as a cumulated effect of thermoacoustic heat transport in the fluid, heat conduction in the wall and heat convection of the air outside the resonator. At high acoustic levels, heat is significantly convected by the streaming flow and the resulting transverse temperature difference is proportional to the longitudinal temperature difference. Combining these expressions brings out a new criterion parameter for the nonlinear Reynolds number (ReNL) characterizing the transition in streaming patterns at high acoustic levels. This result explains previous experimental and numerical observations of the streaming flow dynamics at high acoustic amplitudes, under different temperature boundary conditions, and can provide a powerful prediction tool for streaming pattern transitions

Etude numérique du vent acoustique non linéaire dans un résonateur à ondes stationnaires

Le vent acoustique associé aux ondes stationnaires dans un résonateur rectangulaire est étudié pour des nombres de Reynolds non-linéaires croissants, par résolution numérique des équations de Navier-Stokes compressibles moyennées sur une période. Pour des vitesses acoustiques assez grandes, des chocs sont visibles. Lorsque le Reynolds non linéaire augmente, les centres des tourbillons sont repoussés vers les parois latérales du tube. Ce résultat est en accord avec plusieurs résultats expérimentaux existants qui divergent des modèles linéaires