Two coupled problems are investigated: a complete description of long-wave vortex ring oscillations in an ideal incompressible fluid, and an examination of sound radiation by these oscillations in a weakly compressible fluid.The first part of the paper relates to the problem of eigen-oscillations of a thin vortex ring (μ[Lt ]1) in an ideal incompressible fluid. The solution of the problem is obtained in the form of an asymptotic expansion in the small parameter μ. The complete set of three-dimensional eigen-oscillations and axisymmetric modes (two-dimensional oscillations) is obtained. It is shown that, unlike the vortex column oscillations which have the form of simple angular harmonics, the majority of eigen-oscillations of a thin vortex ring have a more complex form which is a combination of two harmonics in the leading approximation. This leads to dramatic changes in the efficiency of sound radiation produced by modes of the vortex ring in comparison with the corresponding modes of the vortex column.In the second part of the paper the solution obtained is used to investigate the process of sound radiation by vortex perturbations in a weakly compressible fluid. The vortex ring eigen-oscillations are classified according to their sound radiation efficiency. It is shown that the modes with the dimensionless frequency ω≈1/2 radiate sound most efficiently. They are two isolated modes, two infinite families of Bessel modes and a set of axisymmetric modes. The frequencies of these modes are in the interval Δω=O(μ).The results obtained are compared with known experimental data on acoustic radiation of a turbulent vortex ring. Within the limits of the theory derived an explanation of the main characteristics of sound radiation is presented.
The mechanisms of noise generation by turbulent jets associated with a cascade of turbulent per turbations are considered from generation of primary eddies to their disintegration. A new correlation model proposed for describing these mechanisms is based on simulation of their generation as a random process with deterministic description of individual eddies. The model makes it possible to analyze available correlation models based on experimental modeling of the correlation function: monopoles, dipoles, or quadrupoles. The main difference between these models is both the different multipole structure of assumed sources and implicit "hard" and "soft" variants of source generation, as well as in the main variable for which the corre lation function is developed. This approach is used for developing the correlation model of the noise genera tion mechanism related to oscillations of surface eddies. The jet noise inferred from the proposed model is well consistent with experimental data on circular jet noise.
The main goal of the paper is to assess the contribution of large-scale vortices to the noise of the subsonic turbulent jet (M = 0.35, Re = 3.2•10 5) in the selected frequency bands (Sh~0.2-0.45). The mechanism of sound radiation according to which a separate vortex structures itself can be a significant sound source is considered. Vortex core eigen-modes are responsible for noise radiation according to this mechanism. The work is subdivided on three coupling items: (i) theoretical investigation of noise radiation of separate vortex ring (especially little-known octupole contribution to sound radiation), (ii) visualization of large vortices in excited jet and (iii) experimental investigation of turbulent jet noise (subsonic jet with velocity 120m/s excited at 2000Hz) decomposed on the separate azimuthal components with the help of azimuthal decomposition technique (ADT). On the final stage the careful comparison of these results gives the quantitative assessment of the contribution of vortex rings to the jet noise in a tone-excited turbulent jet under consideration.
In the modeling of the noise sources in turbulent jets two open questions are still remain. The first, what is the multipole type of the sources? The second, what kind of stochastic fields can be used for the noise source description. These issues are analyzed in this work. Two-point crosscorrelation of the jet noise is used to determine the multipole type of sources. Modeling of the cross-correlation provides clear evidence in favor of the quadrupole type of the jet noise sources. In the context of the second issue the recently developed two-stage correlation model is tested on the basis of measurements of azimuthally decomposed jet noise. The results show a promising agreement in a wide range of parameters.
The effect of a non-uniform effective ion charge distribution on the dynamo contribution to the plasma resisitivity of a reversed field pinch is studied, based on a stationary energy or helicity balance. The radial distribution of the impurity is obtained from the ETA-BETA II line emission profiles. It is found that the main impurity ions are concentrated in the outer region of the plasma and, consequently, the effective ion charge, Z ff , is close to one everywhere, except in a small slab close to the plasma border, where it can be as high as three to four. The loop voltage required to sustain the RFP configuration with such 'hollow' Z eff profiles has to balance a higher dissipation in the outer region; hence, the apparent resistivity on axis is considerably greater than in the case of uniform Z eff . This effect could also be present in other RFP devices and might very well bridge the gap that was observed previously between the average effective ion charge and the resistivity anomaly factor, particularly for the low plasma density operation.
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