Catherine Weisman

Heat Transfer Associated to Natural Convection Flow in a Partly Porous Cavity

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 profile. Analytical expressions are derived for the velocity and temperature which, combined with an energy balance, enable us to relate the stratification to the other governing parameters. Influence of the porous layers permeability and width, and of the Rayleigh number on the flow structure and heat transfer is thoroughly investigated, and summarized in simple relationships

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 [Re(NL)=(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 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.

Low Mach number analysis of idealized thermoacoustic engines with numerical solution

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 obtained for two-dimensional heat exchangers and stack. The model assumes that the heat exchangers and stack are shorter than the overall length by a factor of the order of a representative Mach number. The model is well-suited for simulation of the entire startup process, whereby as a result of some excitation, an initially specified temperature profile in the stack evolves toward a near-steady profile, eventually reaching stationary operation. A validation analysis is presented, together with results showing the early amplitude growth and approach of a stationary regime. Two types of initial excitation are used: Random noise and a small periodic wave. The set of assumptions made leads to a heat-exchanger section that acts as a source of volume but is transparent to pressure and to a local heat-exchanger model characterized by a dynamically incompressible flow to which a locally spatially uniform acoustic pressure fluctuation is superimposed.

Inertial effects on non linear acoustic streaming

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-averaged equations where the linear acoustic flow field is used as a source term. It is shown that the sole effect of inertia cannot be responsible for the acoustic streaming behavior observed for large values of the nonlinear Reynolds number.

Effect of a resistive load on the starting performance of a standing wave thermoacoustic engine: A numerical study

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 resonator. For a given engine geometry, prescribed temperatures at the heat exchangers, prescribed mean pressure, and prescribed load, results from a simulation in the time domain include the evolution of the acoustic pressure in the active cell. That signal is then analyzed, extracting growth rate and frequency of the dominant modes. For a given load, the temperature difference between the two sides is then varied; the most unstable mode is identified and so is the corresponding critical temperature ratio between heater and cooler. Next, varying the load, a stability diagram is obtained, potentially with a predictive value. Results are compared with those derived from Rotts linear theory as well as with experimental results found in the literature.

Evolution of Rayleigh streaming flow velocity components in a resonant waveguide at high acoustic levels

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 quadratic function of the acoustic velocity amplitude at the antinode. For higher acoustic levels, additional streaming cells have been observed. In the present study, results of LDV and PIV measurements are compared to direct numerical simulations. The evolution of axial and radial velocity components for both acoustic and streaming flows is studied from low to high acoustic amplitudes. Two streaming flow regimes are pointed out, the axial streaming dependency upon acoustics going from quadratic to linear. The hypothesis of the radial streaming velocity being of second order in a Mach number expansion is shown to be invalid at high amplitudes. The change of re...

Acoustic and streaming velocity components in a resonant waveguide at high acoustic levels

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 is a quadratic function of the acoustic velocity amplitude at antinode. For higher acoustic levels, additional streaming cells have been observed. Results of laser Doppler velocimetry measurements are here compared to direct numerical simulations. The evolution of axial and radial velocity components for both acoustic and streaming velocities is studied from low to high acoustic amplitudes. Two streaming flow regimes are pointed out, the axial streaming dependency on acoustics going from quadratic to linear. The evolution of streaming flow is different for outer cells and for inner cells. Also, the hypothesis of radial streaming velocity being of second order in a Mach number expansion, is not valid at high amplitudes. The change of regime occurs when the radial streaming velocity amplitude becomes larger than the radial acoustic velocity amplitude, high levels being therefore characterized by nonlinear interaction of the different velocity components.

Acoustic Rayleigh streaming: Comprehensive analysis of source terms and their evolution with acoustic level

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 inside the inner cells is marginally modified, while the outer cells are strongly distorted. The emergence of an extra cell was observed both in previous numerical simulations and experiments and it has been shown that inertia is not responsible for this behavior, which is rather due to nonlinear interactions between streaming and acoustics. In the present work these interactions are analyzed both numerically and theoretically. The averaged Navier-Stokes equations are numerically solved with acoustic correlation source terms obtained from previous full instantaneous simulations. The effect of each source term is highlighted and the source term responsible for the ...

Numerical and experimental investigation of the role of inertia on acoustic Rayleigh streaming in a standing waveguide

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 effect of inertia on Rayleigh streaming at high acoustic level 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. For the analysis of the outer cell, an analogy with the lid-driven cavity in a cylindrical geometry is proposed. It is shown that the outer cell is distorted due to convection, but the previously observed emergence of an extra cell cannot be recovered. Inertial effects on the established streaming flow pattern are further investigated numerically by solving time averaged Navier-Stokes equations with an imposed acoustic source. Results are si...

Numerical study of nonlinear streaming inside a standing wave resonator

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 fundamental resonance frequency of the waveguide. For sufficiently large acoustic velocities, shocks are visible. The mean field is computed by time-averaging over the main acoustic period. When the nonlinear Reynolds number increases, the center of the outer streaming cells are pushed toward the acoustic velocity nodes and two additional vortices per quarter-wavelength are generated on the axis, near the velocity antinodes. This result differs from linear models and is in agreement with several recent experimental measurement performed in the nonlinear regime. The mean temperature field evolution within the resonator is also investigated.