# Catherine Weisman's research while affiliated with French National Centre for Scientific Research and other places

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## Publications (34)

Complex coupling between thermal effects and Rayleigh streaming in a standing wave guide at high acoustic levels is analyzed numerically. The approach is guided by the recent analytical study, showing that reverse streaming cells can form if the nonlinear Reynolds number exceeds a value depending on the wave frequency and thermophysical properties...

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...

Acoustic streaming generated by a plane standing wave between two infinite plates or inside a cylindrical tube is considered, under the isentropic flow assumption. A two-dimensional analysis is performed in the linear case of slow streaming motion, based on analytical formal solutions of separate problems, each associated with a specific source ter...

This study focuses on natural convection flows within a cylindrical guide containing a porous medium. This configuration is applicable to standing-wave thermoacoustic engines, usually composed of an acoustic resonator where a (short) stack (or porous medium) is inserted, with a heat exchanger placed at one of its ends. The resulting horizontal temp...

Rayleigh streaming is a second order mean flow generated by the interaction between a standing wave and a solid wall. At moderate acoustic levels, the streaming flow is slow, composed of two cells along a quarter wavelength: an inner cell close to the tube wall and an outer cell in the core. When increasing the acoustic level, the streaming flow in...

The effect of inertia on Rayleigh streaming generated inside a cylindrical resonator where a mono-frequency standing wave is imposed, is investigated numerically and experimentally. To this effect, time evolutions of streaming cells in the near wall region and in the resonator core are analyzed. An analogy with the lid-driven cavity in a cylindrica...

Rayleigh streaming is a mean flow generated by the interaction between a standing wave and a solid wall. In the case of a low amplitude wave inside a cylindrical resonator, the streaming pattern along a quarter wavelength is composed of two toroidal cells: An inner cell close to the tube wall and an outer cell in the core. In the present work the e...

The interaction between an acoustic wave and a solid wall generates a mean steady flow called Rayleigh streaming, generally assumed to be second order in a Mach number expansion. This flow is well known in the case of a stationary plane wave at low amplitude: it has a half-wavelength spatial periodicity and the maximum axial streaming velocity is a...

Rayleigh streaming is a steady flow generated by the interaction between an acoustic wave and a solid wall, generally assumed to be second order in a Mach number expansion. Acoustic streaming is well known in the case of a stationary plane wave at low amplitude: it has a half-wavelength spatial periodicity and the maximum axial streaming velocity i...

The effect of inertia on nonlinear streaming generated inside a cylindrical resonator where a mono-frequency standing wave is imposed, is investigated numerically using two codes: A code solving the full Navier-Stokes compressible equations, assuming that the flow is isentropic in order to exclude thermal effects, and a code solving the time-averag...

The influence of a resistive load on the starting performance of a standing-wave thermoacoustic engine is investigated numerically. The model used is based upon a low Mach number assumption; it couples the two-dimensional nonlinear flow and heat exchange within the thermoacoustic active cell with one-dimensional linear acoustics in the loaded reson...

Flow dynamics in the stack and heat exchangers of a standing wave thermoacoustic engine is studied using two-dimensional direct numerical simulations. The numerical approach is based on asymptotic coupling in the low Mach number limit of a nonlinear dynamic model in the active cell with linear acoustics in the resonator. Computed results of the ini...

Rayleigh streaming in a cylindrical acoustic standing waveguide is studied both experimentally and numerically for nonlinear Reynolds numbers from 1 to 30 [ReNL=(U0/c0)(2)(R/δν)(2), with U0 the acoustic velocity amplitude at the velocity antinode, c0 the speed of sound, R the tube radius, and δν the acoustic boundary layer thickness]. Streaming vel...

The acoustic streaming associated to standing waves in a cylindrical resonator is studied for increasing nonlinear Reynolds numbers by numerically solving the compressible Navier-Stokes equations, using a high resolution finite difference scheme. The resonator is excited by shaking it along the axis at imposed frequency, corresponding to the fundam...

A model of an idealized thermoacoustic engine is formulated, coupling nonlinear flow and heat exchange in the heat exchangers and stack with a simple linear acoustic model of the resonator and load. Correct coupling results in an asymptotically consistent global model, in the small Mach number approximation. A well-resolved numerical solution is ob...

An asymptotically consistent small Mach number model of a standing wave thermoacoustic engine has been developed. A simple thermoacoustic engine consists of a resonating tube within which is inserted an acoustically compact assembly, composed of a stack of conducting plates, placed between two heat exchangers. The model couples one-dimensional line...

The role of unavoidable space between heat exchangers and stack inside a thermoacoustic standing wave generator is investigated. A two-dimensional Low Mach number viscous and heat conducting flow model of the active thermoacoustic cell, comprising heater and cooler separated by a stack made of parallel conducting plates, is described. Three differe...

We performed a numerical study of the thermal and physical phenomena occurring in thermoacoustic wave generators. The goal of the simulation is to predict the amplification due to thermoacoustics of a wave initially of small amplitude. Therefore, we focus on the stack and the two heat exchangers, which we call the active cell, which is acoustically...

There are very few reference solutions in the literature on non-Boussinesq natural convection flows. We propose here a test case problem which extends the well-known De Vahl Davis differentially heated square cavity problem to the case of large temperature differences for which the Boussinesq approximation is no longer valid. The paper is split in...

In the second part of the paper, we compare the solutions produced in the framework of the conference “Mathematical and numerical aspects of low Mach number flows” organized by INRIA and MAB in Porquerolles, June 2004, to the reference solutions described in Part 1. We make some recommendations on how to produce good quality solutions, and list a n...

This study focuses on natural convection flows of air in a two-dimensional differentially heated cavity under large temperature differences. The model equations are the low Mach approximation equations ob-tained by Paolucci which filter sound waves. The transition to unsteadiness is investigated using a finite volume code, with fractional time step...

Natural convection of air in a differentially heated cavity with large temperature gradients can be described by the low Mach approximation equations obtained by Paolucci allowing for filtering of sound waves with the fluid viscosity a nonlinear function of temperature. Numerical simulations exhibit intriguing time-dependent solutions. The transiti...

The object of this study is the heat transfer associated to a buoyancy-induced flow developing in a rectangular cavity, partly filled with porous medium, with given heat flux from the sides. Numerical experiments show the existence of a quasi parallel solution away from the top and bottom end walls, characterized by a linear vertical temperature pr...

Natural convection of air inside a rectangular cavity, differentially heated under large temperature gradients, is considered. The low Mach approximation equations are those obtained by Paolucci allowing for filtering of sound waves. Transition to unsteadiness is studied with numerical simulation, with a finite volume code based on a fractional tim...

This study deals with the steady flow structure and temperature field in a rectangular cavity including a layer of porous medium adjacent to the heated side, with uniform heat flux from the sides. The Navier-Stokes and energy equations in the Boussinesq approximation are written with an extra term accounting for the Darcy effect within the porous m...

This study is devoted to the experimental and numerical simulations of thermoacoustic heat transfer. We focus on the time dependence of the temperature in the vicinity of a stack of plates interacting with a fluid subjected to a monochromatic acoustic wave. The experimental setup is a Heat Driven Ther-moAcoustic Refrigerator where acoustic temperat...

## Citations

... In the more recent numerical 13,14 and theoretical studies, 15,16 it was shown that a transverse mean temperature gradient has a huge impact: ...

... Besides theoretical and experimental studies, numerical simulations and modeling have become a suitable alternative for studying thermoacoustic phenomena involved in SWTAE [24][25][26][27][28]. To this end, Hireche et al. [29] recently performed a 3D numerical study of natural convection flow using a finite volume method to solve the mixed Navier-Stokes and Darcy-Brinkman equations under Boussinesq approximation in a thermoacoustic device with a porous medium. They highlighted thermal conductivity, permeability, and anisotropy influence of the porous medium on the dynamic and thermal fields. ...

... In § 2 the effect of a transversely stratified temperature distribution on the streaming flow is analysed in the plane case of low acoustic amplitude. The analytical model developed in Baltean-Carlès et al. (2019) for isentropic flow is extended here to the case of variable mean temperature for a perfect gas. As in Baltean-Carlès et al. (2019), the symbolic computational software Mathematica (Wolfram Research Inc. 2018) is used to solve the equations throughout this study. ...

... Daru et al. [30] analyzed different streaming flow regimes in a resonant waveguide and pointed out two regimes which are function of the acoustic amplitude. Likewise, Daru et al. [31] assessed both numerically and theoretically the interaction between a standing wave and a solid wall resolving the averaged Navier-Stokes equations with acoustic correlation source terms whose effects have been highlighted. Along this same line, Rahpeima and Ebrahimi [32] numerically investigated the effects of different geometric parameters and thermophysical properties of the stack. ...

... Also, as shock waves are known for generating entropy, their effect was expected to be small in these isentropic simulations. 9,12 A similar evolution of the streaming flow, as in Ref. 11, was observed but at a higher Re NL . 9 These results highlighted the main role of the nonlinear coupling between the acoustic and streaming flows 12 and showed that the inertia affected the streaming flow only slightly (in accordance with the theoretical results of Ref. 10). ...

... They highlighted thermal conductivity, permeability, and anisotropy influence of the porous medium on the dynamic and thermal fields. Daru et al. [30] analyzed different streaming flow regimes in a resonant waveguide and pointed out two regimes which are function of the acoustic amplitude. Likewise, Daru et al. [31] assessed both numerically and theoretically the interaction between a standing wave and a solid wall resolving the averaged Navier-Stokes equations with acoustic correlation source terms whose effects have been highlighted. ...

... Dans le stack, avec l'hypothèse de stack court, on peut montrer que la vitesse débitante s'exprime par [12] : (5) où A est l'aire de la section fluide transversale dans le stack. En appliquant les conditions aux limites et de continuité, on obtient une équation de dispersion. ...

... Solution of the coupled equations providing velocity boundary conditions from resonator acoustic are appropriately integrated in the solution sequence. An extensive validation of the current implementation was performed with satisfactory results [8]. Initial conditions considered fluid at rest and temperature profiles obtained numerically, corresponding to steady conduction in the walls and in fluid at rest. ...

... The comparison of numerical results with the theoretical analysis obtained in [29,30] was presented both in [4] as well as in [31,32]. The authors of [31] performed 2D numerical compressible simulations, while [32] used COMSOL software and also investigated the streaming flow in more complex geometries such as inclined channel or circular cross-section. ...

... In the last decade, our team has worked on this distortion of the streaming flow in the fast regime. A first joint experimental and numerical study (based on the fully compressible Navier-Stokes equations) of the evolution of the Rayleigh streaming was performed 11 from the slow to the fast regime. It was found that the experimental and numerical streaming patterns evolved in a similar manner and that new counterrotating vortices appeared near the velocity acoustic antinodes for a similar value of the nonlinear Reynolds number. ...