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Multi-Scale Digital Holographic Interferometry for Studying a Thermoacoustic Resonator
Abstract
This paper proposes a digital holographic set-up with two wavelengths and two image sensors, having different acquisition frame rates, to characterize the acoustic auto-oscillations generated in a standing-wave thermo-acoustic generator.
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A model for the description of the transient regime leading to steady-state sound in a quarter-wavelength thermoacoustic prime mover is proposed, which is based on the description of the unsteady heat transfer in the system, coupled with an ordinary differential equation describing wave amplitude growth/attenuation. The equations are derived by considering a cross-sectional averaged temperature distribution along the resonator, and by assuming that both the characteristic time associated with heat diffusion through the stack and that associated with the thermoacoustic amplification are much larger than the acoustic period. Attention is here focused on the only mechanism of saturation due to heat transport by sound within the stack. The numerical solving of the governing equations leads to the prediction of the transient regime, which is compared with experimental results for several values of the heat power supplied to the system and for several positions of the stack in the resonator. The model reproduces the experiments quite well, notably showing that a small diminution of the temperature in the vicinity of the hot end of the stack is associated to an overshoot of wave amplitude growth, while heat diffusion through the whole stack impacts the subsequent evolution of wave amplitude leading to steady state. Additional experimental results exhibiting complicated regimes of wave amplitude evolution are provided, which are not reproduced by the present model.
Heat fluxes close to the edge of a heated solid plate aligned parallel to the axis of an acoustic standing wave were measured for drive ratios DR≡P
A/p
m
of 1, 2 and 3. It was found that at the highest drive ratio (3), the resulting heat flux vector at the edge of the plate is directed into the plate, opposite to the direction of the heat flux imposed by the resistive heaters within the plate. This observation confirms the thermoacoustic effect previously detected in the visualized temperature fields and discussed in part I of this paper. Through the energy balance the magnitudes of the heat fluxes into the plate, caused by the thermoacoustic effect, were determined. The measured data are in good agreement with numerical and analytical predictions.
The flow inside a thermoacoustic couple is investigated experimentally using particle image velocimetry. Measurements show the oscillation of the shear layers flowing out of a single stack, thus forming an asymmetric vortex street at high driving amplitudes. Development of vortices is also observed within the gap of a thermoacoustic couple. It causes the flow not to repeat from one acoustic period to another. The nonperiodicity of the flow will lead to unsteady heat transfer between the stack and heat exchangers and to the oscillation of the cooling load.
A digital three-color holographic interferometer was designed to analyze the variations in refractive index induced by a candle flame. Color holograms are generated and recorded with a three layer photodiode stack sensor allowing a simultaneous recording with a high spatial resolution. Phase maps are calculated using Fourier transform and spectral filtering is applied to eliminate parasitic diffraction orders. Then, the contribution along each color is obtained with the simultaneous three wavelength measurement. Results in the case of the candle flame are presented. Zero order fringe, meaning zero optical path difference, can be easily extracted from the experimental data, either by considering a modeled colored fringe pattern or the wrapped phases along the three wavelengths.
The present Note deals with the identification and tracking of vortices in a time-resolved unsteady flow. The approach is based on the combination of two existing post-processing tools that are Galilean invariant functions: feature flow field f and vortex identification algorithm γ2. An analytical development shows that the joint use of γ2 and the streamlines of f allows to identify and track the location of the center of a vortex core with a non-zero convection velocity. We discuss the applicability of this procedure to actual flows for which the assumptions of the analytical approach may not be strictly valid. The procedure is validated using PIV measurements performed in an oscillating flow in a model of thermoacoustic refrigerator. This method proves to be efficient for the automated analysis of convection processes when large numbers of vortices are involved. To cite this article: A. Berson et al., C. R. Mecanique 337 (2009).
The thermal interaction between a heated solid plate and the acoustically driven working fluid was investigated by visualizing
and quantifying the temperature fields in the neighbourhood of the solid plate. A combination of holographic interferometry
and high-speed cinematography was applied in the measurements. A better knowledge of these temperature fields is essential
to develop systematic design methodologies for heat exchangers in oscillatory flows. The difference between heat transfer
in oscillatory flows with zero mean velocity and steady-state flows is demonstrated in the paper. Instead of heat transfer
from a heated solid surface to the colder bulk fluid, the visualized temperature fields indicated that heat was transferred
from the working fluid into the stack plate at the edge of the plate. In the experiments, the thermoacoustic effect was visualized
through the temperature measurements. A novel evaluation procedure that accounts for the influence of the acoustic pressure
variations on the refractive index was applied to accurately reconstruct the high-speed, two-dimensional oscillating temperature
distributions.