Acoustic source terms study for non-isothermal flows using an aeroacoustic hybrid approach

This paper presents a numerical study of noise source term in non-isothermal flows in the context of an aeroacoustic hybrid technique at low Mach numbers. Asymptotic analysis applied to the fully compressible Navier–Stokes equations provides separated sets of equations for the dynamic of the flow and the production and propagation of acoustic waves. Comparisons with analytical dipole and quadrupole distributions are performed, confirming the dipole type of non-isothermal source distribution. This paper is a preliminary work for some more extensive studies on the topic. To cite this article: F. Golanski, C. Prax, C. R. Mecanique 333 (2005).     

Effective equations describing the flow of a viscous incompressible fluid through a long elastic tubeEquations efficaces décrivant l'écoulement d'un fluide visqueux incompressible dans un tuyau long et élastique

We study the flow of a viscous incompressible fluid through a long and narrow elastic tube whose walls are modeled by the Navier equations for a curved, linearly elastic membrane. The flow is governed by a given small time dependent pressure drop between the inlet and the outlet boundary, giving rise to creeping flow modeled by the Stokes equations. By employing asymptotic analysis in thin, elastic, domains we obtain the reduced equations which correspond to a Biot type viscoelastic equation for the effective pressure and the effective displacement. The approximation is rigorously justified by obtaining the error estimates for the velocity, pressure and displacement. Applications of the model problem include blood flow in small arteries. We recover the well-known Law of Laplace and provide a new, improved model when shear modulus of the vessel wall is not negligible. To cite this article: S. ?ani?, A. Mikeli?, C. R. Mecanique 330 (2002) 661–666.     

An adaptation of the low Mach number approximation for supercritical fluid buoyant flows

This Note describes an acoustic filtering of the equations governing the supercritical fluid buoyant flow driven by a weak heating. The resulting low Mach number approximation takes into account the compressibility of the fluid with respect to the hydrostatic pressure. Using the direct numerical simulation of a supercritical fluid flow in the Rayleigh–Bénard configuration, we show that the density stratification may be taken into account without further numerical effort and is fundamental for the prediction of the convective instability threshold induced by a weak heating. To cite this article: G. Accary et al., C. R. Mecanique 333 (2005).     

Computational aeroacoustics using the B-spline collocation method

One of the major problems in computational aero-acoustics is the disparity in length scales between the flow field and the acoustic field. As a result, a mapping function is normally used to achieve a non-uniform grid distribution. In this paper, a B-spline collocation method with an arbitrary grid placement capability is proposed. This capability not only allows an optimum grid distribution but also avoids the numerical complexities associated with the mapping function. The B-spline collocation method is applied to the case of spinning co-rotating vortices. The result agrees well with the matched asymptotic solution. To cite this article: R. Widjaja et al., C. R. Mecanique 333 (2005).     

Étude numérique du champ de vitesse dans un échangeur à vortexNumerical study of the velocity field in a vortex heat exchanger

Flow through a cylindrical flat chamber, a model of some particular heat exchanger, is investigated numerically using the CFD-ACE code. Turbulence is modelled using the classical k–ε model. A better understanding of the secondary flow is then obtained: the k–ε model shows a strong dependence of the secondary flow velocity field with Reynolds number as was pointed out with precedent experimental results. Variations of the number of vortexes composing the secondary flow, giving a symmetrical or asymmetrical aspect, will influence the fluid particle trajectories and time residence. To cite this article: S. Petitot et al., C. R. Mecanique 330 (2002) 749–756.     

Amelioration de technique d'intensimetrie hydroacoustiqueImprovement of hydro-acoustic intensity technique

For industrial applications, a transfer matrix model can be used to study pressure and flow rate fluctuations propagation within ducts. If none analytical model exists, this matrix has to be identified according to acoustic intensity techniques.Pressure waves exert forces, which cause a compliant system to move, the motion causes pressure waves in return (fluid–structure interaction). An extension of acoustic intensity technique using several transducers is presented. To cite this article: J. Charley, C. R. Mecanique 331 (2003).     

Using Vorticity as an Indicator for the Generation of Optimal Coarse Grid Distribution

An improved vorticity-based gridding technique is presented and applied to create optimal non-uniform Cartesian coarse grid for numerical simulation of two-phase flow. The optimal coarse grid distribution (OCGD) is obtained in a manner to capture variations in both permeability and fluid velocity of the fine grid using a single physical quantity called “vorticity”. Only single-phase flow simulation on the fine grid is required to extract the vorticity. Based on the fine-scale vorticity information, several coarse grid models are generated for a given fine grid model. Then the vorticity map preservation error is used to predict how well each coarse grid model reproduces the fine-scale simulation results. The coarse grid model which best preserves the fine-scale vorticity, i.e. has the minimum vorticity map preservation error is recognized as an OCGD. The performance of vorticity-based optimal coarse grid is evaluated for two highly heterogeneous 2D formations. It is also shown that two-phase flow parameters such as mobility ratio have only minor impact on the performance of the predicted OCGD.     

三维非均匀不稳定渗流方程的二维不均匀粗化算法

在无源汇条件下,根据流过某一个横截面的流体流量等于流过这一横截面内所有精细网格的流体流量之和这一特点提出了粗化网格等效渗透率的计算方法。在粗化区内,利用直接解法求解二维渗流方程,再用这些解合成粗化网格的三维合成解,并由合成解计算粗化网格的等效渗透率。根据精度的要求采用了不均匀网格粗化,在流体流速大的区域采用精细网格。利用所得等效渗透率计算了粗化网格的某三维非均匀不稳定渗流场的压降解,结果表明三维非均匀不稳定渗流方程的二维不均匀粗化解非常逼近采用精细网格的解,但计算的速度比采用精细网格提高了80倍。     

Selection of two-dimensional nonlinear strain waves in micro-structured mediaSelection d'ondes de déformation non linéaires à deux dimensions dans des milieux à microstructure

It is shown that the micro-displacement gradient allows the propagation of two-dimensional localized long nonlinear strain waves in a medium with microstructure. These waves may exist even in the presence of dissipation and energy input in the microstructured medium but with selected values of the wave amplitude and velocity. An increase or a decrease in the wave amplitude and velocity happens faster at the initial stage than that of the plane localized wave. However, their steady values selected by the energy input/output, are higher for the plane waves. To cite this article: A.V. Porubov et al., C. R. Mecanique 332 (2004).     

Prolongation of two phases in the model of fluid displacement through a capillaryProlongement de deux phases dans le modèle du déplacement d'un fluide dans un capillaire

The problem of a piston-like displacement of a fluid by another in a capillary is examined. It is suggested that each fluid is prolonged into the domain occupied by the other fluid. This enables the replacement of the two-phase flow problem by a transient single-phase flow problem, with discontinuity in velocity and pressure on a film interface. The problems related to the triple point are solved by introducing a limit fluid near the pore wall. The demonstration of the Washburn equation contributes to the physical justification of our model. To cite this article: Y. Lucas et al., C. R. Mecanique 334 (2006).     

Computational aeroacoustics applications based on a discontinuous Galerkin method

caa simulation requires the calculation of the propagation of acoustic waves with low numerical dissipation and dispersion error, and to take into account complex geometries. To give, at the same time, an answer to both challenges, a Discontinuous Galerkin Method is developed for Computational AeroAcoustics. Euler's linearized equations are solved with the Discontinuous Galerkin Method using flux splitting technics. Boundary conditions are established for rigid wall, non-reflective boundary and imposed values. A first validation, for induct propagation is realized. Then, applications illustrate: the Chu and Kovasznay's decomposition of perturbation inside uniform flow in term of independent acoustic and rotational modes, Kelvin–Helmholtz instability and acoustic diffraction by an air wing. To cite this article: Ph. Delorme et al., C. R. Mecanique 333 (2005).     

Computation of the mean velocity field above a stack plate in a thermoacoustic refrigeratorSimulation numérique de la vitesse moyenne près d'une plaque de l'empilement d'un réfrigérateur thermoacoustique.

A numerical simulation of the unsteady flow above one stack plate in a thermoacoustic refrigerator was performed. The second order mean velocity field was computed. Two regions could be distinguished. In the first region, located at the plate extremities, the mean flow is essentially vortical and results from the resonator/plate transition. In the second region, located above the plate, the mean velocity field corresponds to a streaming flow which results from the interaction of the acoustic wave with the plate boundaries. The effects of stack plates spacing on the streaming flow pattern is studied. To cite this article: D. Marx, Ph. Blanc-Benon, C. R. Mecanique 332 (2004).     

Experimental evidence of energy pumping in acousticsMise en évidence expérimentale de pompage énergétique en acoustique

This Note presents an experimental vibro-acoustic set-up that aims to reproduce the energy pumping phenomenon between an acoustic medium and an essentially nonlinear oscillator. It shows a one-way irreversible transfer of energy between the first acoustic mode in a tube and a thin visco-elastic membrane. To cite this article: B. Cochelin et al., C. R. Mecanique 334 (2006).     

Simulation of peristaltic flow of chyme in small intestine for couple stress fluid

In this article couple stress fluid have been considered for the peristaltic flow of chyme in intestine. Problem under consideration have been formulated assuming that two non-periodic sinusoidal wave of different wavelength propagate with same speed c along the outer wall of the tube. Governing equations have been simplified under the assumptions of long wavelength and low Reynolds number approximation (such assumption are consistent that Re (Reynold number) is very small and long wavelength approximation also exists in the small intestine). Exact solutions have been evaluated for velocity and pressure rise. Physical behaviour of different parameter of couple stress fluid have been presented graphically for velocity, pressure rise, pressure gradient and frictional forces. The stream lines are also made against different parameters.     

Proper Orthogonal Decomposition of the mixing layer flow into coherent structures and turbulent Gaussian fluctuations

The Proper Orthogonal Decomposition is used to decompose fluctuating turbulent flows into a coherent non-Gaussian component and background fluctuations. An application is performed from 2D experimental data of a turbulent plane mixing layer flow. The analyses of the energy spectra and the Probability Density Function of the velocity field show that POD extracts an incoherent part approaching the quasi-Gaussian distribution properties. The background fluctuations are homogeneous with small amplitude. New future applications are then conceivable like the modeling of the incoherent part for particular inflow condition generation methodology and the analysis of the cyclic velocity field variabilities in Internal Combustion engine flow. To cite this article: Ph. Druault et al., C. R. Mecanique 333 (2005).     

Verification of higher-order discontinuous Galerkin method for hexahedral elements

A high-order implementation of the Discontinuous Galerkin (dg) method is presented for solving the three-dimensional Linearized Euler Equations on an unstructured hexahedral grid. The method is based on a quadrature free implementation and the high-order accuracy is obtained by employing higher-degree polynomials as basis functions. The present implementation is up to fourth-order accurate in space. For the time discretization a four-stage Runge–Kutta scheme is used which is fourth-order accurate. Non-reflecting boundary conditions are implemented at the boundaries of the computational domain.The method is verified for the case of the convection of a 1D compact acoustic disturbance. The numerical results show that the rate of convergence of the method is of order $p+1$ in the mesh size, with p the order of the basis functions. This observation is in agreement with analysis presented in the literature. To cite this article: H. Özdemir et al., C. R. Mecanique 333 (2005).     

Flow in wavy tube structure: asymptotic analysis and numerical simulationÉcoulement dans une structure tubulaire ondulée : analyse asymptotique et résolution numérique

This paper deals with the study of the stationary, incompressible, 2D flow of a fluid in a thin wavy tube. In this work, we consider a domain which is the union of two wavy tubes depending on a small parameter. The asymptotic expansion is constructed. The method of partial asymptotic decomposition is applied. The numerical implementation of this method for the extrusion process is developed. The new physical effects are discussed. To cite this article: A. Ainser et al., C. R. Mecanique 331 (2003).     

Contrôle des profils de vitesse par déformation de parois dans une conduiteControl of velocity profils by walls deformation in a deformed conduit

Starting from a study of perturbation equations for stationary Newtonian fluid flow in deformed axisymmetric tubes, we propose a semi-analytical method allowing to generate in a given section of the conduit, an arbitrary velocity profil previously defined. We get this velocity profile by geometrical modification of the duct walls on a given length. Doing this, we create a specific perturbation of the upstream profile wich allows to generate the chosen velocity profile. To cite this article: M. Sijelmassi, J. Khalid Naciri, C. R. Mecanique 330 (2002) 153–158.     

UNSTEADY LIFT AND SOUND PRODUCED BY AN AIRFOIL IN A TURBULENT BOUNDARY LAYER

An analysis is made of the unsteady lift exerted on a stationary rigid body immersed in an incompressible, plane-wall turbulent boundary layer. The lift is expressed as a surface integral over the body involving theupwash velocity induced by the “free” vorticity Ω (found by taking explicit account of the interaction of the body with the flow and excluding the bound vorticity) and a harmonic function X₂that depends only on the shape of the body. The upwash velocity is the free-field velocity given in terms of Ω by the Biot–Savart formula, augmented by the velocity field of a conventional distribution of image vortices in the wall. The function X₂can be interpreted as the velocity potential of flow past the body, produced by motion of the wall at unit speed towards the body. Detailed predictions are made of the lift on a slender airfoil placed in the outer region of the boundary-layer. When the airfoil chord is large compared to the boundary-layer thickness, vortex shedding into the wake causes the magnitude of the net upwash velocity near the trailing edge to be small. The main contributions to the surface integral are then from the nose region, where the upwash velocity may be estimated independently of the fluctuations near the trailing edge. Analytical results for a thin plate airfoil of chord 2a at distance h from the wall show that the lift increases as a/h increases; it is ultimately independent of a and scales with the ratio of h to the hydrodynamic wavelength. Application is made to determine the sound generated by the airfoil in a weakly compressible boundary layer flow over a finite elastic plate.     

Residual‐based turbulence models for moving boundary flows: hierarchical application of variational multiscale method and three‐level scale separation

This paper presents residual‐based turbulence models for problems with moving boundaries and interfaces. The method is developed via a hierarchical application of variational multiscale ideas and the models are cast in an arbitrary Lagrangian–Eulerian (ALE) frame to accommodate the deformation of domain boundaries. An overlapping additive decomposition of velocity and pressure fields into coarse and fine scale components leads to coarse and fine scale mixed‐field problems. The problem governing fine scales is subjected to a further decomposition of the fine scale velocity into overlapping components termed as fine scales level I and level II. In turn, in the bottom‐up integration of scales, the model for level II fine scales serves to stabilize the problem governing level I fine scales, and model for level I fields yields the turbulence models. From the computational perspective, the coarse scales are represented in terms of the standard Lagrange shape functions, whereas level I and level II scales are represented via quadratic and fourth order polynomial bubbles, respectively. Because of the bubble functions approach employed in the consistently derived fine scale models, the resulting method is free of any embedded or tunable parameters. The proposed turbulence models share a common feature with the LES models in that the largest scales in the flow are numerically resolved, whereas the subgrid scales are modeled. The method is applied to flow around a plunging airfoil at Re = 40,000, and results are compared with experimental and numerical data published in the literature. Also presented are the results for the plunging airfoil at Re = 60,000 to show the robustness and range of applicability of the method. Copyright © 2013 John Wiley & Sons, Ltd.