Experimental validation of inviscid linear stability theory applied to an axisymmetric jet

Abstract

We study the development of perturbations in a submerged air jet with a round cross-section and a long laminar region (five jet diameters) at a Reynolds number of 5400 by both inviscid linear stability theory and experiments. The theoretical analysis shows that there are two modes of growing axisymmetric perturbations, which are generated by three generalized inflection points of the jet's velocity profile. To validate the results of linear stability theory, we conduct experiments with controlled axisymmetric perturbations to the jet. The characteristics of growing waves are obtained by visualization, thermoanemometer measurements and correlation analysis. Experimentally measured wavelengths, growth rates and spatial distributions of velocity fluctuations for both growing modes are in good agreement with theoretical calculations. Therefore, it is demonstrated that small perturbations to the laminar jet closely follow the predictions of inviscid linear stability theory.

Development of Disturbances in a Circular Submerged Jet with Two Instability Modes

“…The results obtained of the development of axisymmetric perturbations contradict the experiment [7]. In the calculations it was shown that the development of axisymmetric perturbations leads to establishment of regular oscillations, whereas in the experiments not only the fact of turbulence transition but also reduction in the length of laminar section under the action of an artificial axisymmetric perturbation was established.…”

“…In the present study we will give the results of investigations that correspond to the experimental conditions [4,7,8] at Re = 2850 (in the above-mentioned studies the Reynolds number is calculated on the base of the nozzle diameter but not on the base of the nozzle radius; therefore, it takes twice values). The profile of the longitudinal velocity component at the nozzle exit , that is implemented at this Re, takes the form reproduced in Fig.…”

“…In [7] the experiments carried out on the facility in the Institute of Mechanics of Moscow State University were described in detail. In these experiments the development of a jet subject to artificial perturbations of axisymmetric form was studied.…”

“…In this case, probably, transition is initiated by the development of perturbations of the outer mode of linear stability. We can also assume that reduction in the length of transition region in applying artificial axisymmetric perturbations with the amplitude ~10 -2 , observed in the experiment [6,7], is initiated not so much by the development of the axisymmetric perturbations themselves, as by their influence on the growth rate of background three-dimensional perturbations. The fact mentioned above that the θ ω ' v growth of three-dimensional low-amplitude perturbations strengthens against the background of the axisymmetric perturbation when the perturbation amplitude reaches the value of the order of 10 -2 testifies in favor of this fact.…”

“…In this case, the dimension of the device is equal to approximately only . The characteristic feature of the jets generated by the device at various Reynolds numbers is the presence of two modes of unstable perturbations which differ significantly with respect to their growth rates in propagating downstream [6,7]. In introducing artificial axisymmetric perturbations, it was revealed that the length of the jet laminar section depends on the perturbation frequency reaching the minimum at frequencies that correspond to the maximum growth of small perturbations.…”