Oscillating flows, dynamics and transfers

S. Kouidri, F. Jebali Jerbi, G. Defresne, R. Paridaens.

We investigate the mechanisms generating secondary flows with our experimental thermoacoustic prime mover (see Illustration 1). In the previous stage, good agreement has been obtained between our LDV (Laser Doppler Velocimetry) experiments on the resonator and our numerical simulations with DeltaEC accounting for the changes in the cross sections. The analytical approach developed in the PhD thesis of R. Paridaens (see LIMSI’s previous reports) is thus validated. Now, we focus our interest on the annular part of the prime mover (see Illustration 2) and on the effect of the jetpump. The first results of the LDV measurements done in 2014 have shown that the amplitude of the streaming velocity is twice smaller than in the resonator. Further theoretical investigation of the jetpump effect on the secondary flow in the annulus will be developed in the one-year LaSIPS project ENERMODEON during a collaboration with LMT lab (ENS Cachan) .

Illustration 1: Thermoacoustic prime mover.
Illustration 2: Streaming velocity profiles in the annulus for resp. 165, 190 and 210W with a mean pressure of 10 bars.

Besides, the study of the thermal non-uniformity in the transverse direction is also an important issue for a better insight on the onset in thermoacoustic prime movers. Transverse temperature gradients occur in resonators, in stacks and in heat exchangers, but are ignored by the standard linear theory. In order to quantify their effects, we developed an asymptotic model generalizing the standard linear theory. Our approach does not add any assumption compared to the usual models, so that the analytical derivations introduce two generalized form functions, the viscous one f0 and the thermal one g1, that describe the effects of either type of diffusion. The amplitude and phase of those form functions are plotted vs the penetration depth δν in Illustration 3 for three values of the transverse temperature gradient. Showing that viscous diffusion tends to change the directions of the particle velocity and of the acoustic temperature related to f0 and g1.

Illustration 3: Viscous and thermal form functions, resp. f0 and g1

Besides, the analysis of our experimental data about hot wire anemometry in oscillating flows concluded that the dynamics of heat transfer must be taken into account in order to correctly interpret the experimental signal, especially the phase difference between wire temperature and fluid velocity.


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