Acoustic streaming in closed thermoacoustic devices

Abstract

A derivation of acoustic streaming in a steady-state thermoacoustic device is presented in the case of zero second-order time-averaged mass flux across the resonator section (nonlooped device). This yields analytical expressions for the time-independent second-order velocity, pressure gradient, and time-averaged mass flux in a fluid supporting a temperature gradient and confined between widely to closely separated solid boundaries, both in the parallel plate and in the cylindrical tube geometries (two-dimensional problem). From this, streaming can be evaluated in a thermoacoustic stack, regenerator, pulse tube, main resonator of a thermoacoustic device, or in any closed tube that supports a mean temperature gradient, providing only that the acoustic pressure, the longitudinal derivative of the pressure, and the mean temperature variation are known.

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

“…In order to be able to compare our experimental and numerical results to a reference, in the following section, two available models for streaming flow are briefly presented: a linear model developed by Bailliet et al 6 (used for quantitative comparison with direct numerical simulations and experiments in the slow streaming regime) and a nonlinear model developed by Menguy and Gilbert 8 (used for the description of the evolution of the streaming flow for moderate streaming regime). The latter shows that when dealing with streaming flow, an additional dimensionless number has to be considered, as discussed in the following.…”

“…In this paper, the model developed by Bailliet et al 6 is used. This model is based on the fundamental equations presented above.…”

“…For a better application to thermoacoustics, this theoretical description has evolved in order to refine thermal effect description and to remove the restrictions to wide channels and to slow streaming. Concerning the first two points, during the last decades, thermoacoustic applications have motivated several theoretical works to take into account thermal effects 4,5 and/or to remove the restriction to large channels 6,7 . However, all these theoretical developments were restricted to slow streaming where fluid inertia is neglected.…”

Weakly Nonlinear Propagation in Thermoacoustic Engines: A Numerical Study of Higher Harmonics Generation up to the Appearance of Shock Waves

“…Acoustic streaming is accounted for in models by higher-order developments of the basic equations [12,13], and experimental solutions are implemented to limit its effects [14,15]. The aerodynamical effects at geometrical singularities have been extensively studied numerically [16] and experimentally [17,18] in thermoacoustic systems, but are often analytically disregarded because of the complexity of the involved phenomena.…”

Experimental investigation of thermal performance of random stack materials for use in standing wave thermoacoustic refrigerators

“…The impact of the Page 3 of 31 operating frequency and temperature difference between the stack ends on the refrigeration power was studied using network and thermodynamic models, as well as experimental approaches (Jebali et al, 2004). Another important strand of research involves looking at the physics of the thermoacoustic effect, for example the experimental demonstration of the thermoacoustic effect (Biwa et al, 2004) and the nonlinear acoustic streaming that often takes place in such systems (Bailliet et al, 2001). …”