Instability of vortical and acoustic modes in supersonic round jets

Abstract

The stability of ''top-hat'' and fully developed jet profiles is investigated by an inviscid linear stability theory for compressible flow. The study covers a wide range of the Mach number and the temperature ratio. Two types of instabilities are found: vortical and acoustic, each of which can be subdivided into non-radiating ͑subsonic͒ and radiating ͑supersonic͒ modes. The vortical mode is the continuation of the Kelvin-Helmholtz instability from incompressible flow. The acoustic mode is a compressible flow phenomenon, which becomes important at large Mach numbers. Temperature-ratio effects can be destabilizing or stabilizing, depending on the Mach number and mode of instability. A spectrum of unstable acoustic modes, including axisymmetric ones, are found to exist in the fully developed jet. For this jet, acoustic axisymmetric waves become more unstable than both vortical and acoustic helical waves at Mach numbers over about 3. Strong evidence of a resonance mechanism for acoustic modes is seen in the growth rate curves at high Mach numbers, where a spectrum of local peaks and valleys appears at regularly distributed frequencies. © 1997 American Institute of Physics.

Shear instability in a stratified fluid when shear and stratification are not aligned

“…Nevertheless, they have also shown that strong stratification has an effect on the three-dimensional character of the instability by making the width of the associated wavenumber band proportional to N. In a companion paper (Candelier 2010), we show that a horizontal Bickley jet also exhibits other less unstable threedimensional modes. These modes are similar to those found in supersonic jets (Mack 1990;Luo & Sandham 1997;Parras & Le Dizès 2010). The mechanism of instability of these modes is different from the shear instability and associated with the phenomenon of over-reflection (Basovich & Tsimring 1984;Le Dizès & Billant 2009).…”

The effect of upstream disturbance on the angle of sound emission in a supersonic round jet

“…Their results show that the plane jet (Mc =1.17) forced by a pair of oblique modes (the oblique mode is most unstable at high convective Mach numbers) with the subsonic phase speed suppresses the emitted Mach wave intensity. On the other hand, in high convective Mach number, the most unstable (first helical mode) modes have the supersonic phase speed in a round jet (Luo et al, 1997 andParras et al, 2010). The supersonic phase speed of the most unstable mode in a round jet makes the suppression of Mach waves more difficult.…”

“…The both unstable modes have the supersonic phase speed relative to the ambient fluid (Luo and Sandham, 1997). The supersonic phase speed of the modes is responsible to form Mach waves.…”

Numerical Algorithm for Computing Acoustic and Vortical Spatial Instability Waves

“…Following Boyd [34], the parameter L 1 for the mapping [Eq. (13)] must be of the same order of magnitude of the scale of variation of the solution. Thus, by choosing L 1 10 and y ∞ 1000, the number of grid nodes required to have at least π points per wavelength in the whole domain ranges between 2000 and 2500.…”

“…For supersonic jet flows, and in the framework of a spatial analysis (which is considered in what follows), a two-domain shooting method is commonly preferred [8][9][10][11][12][13]. The numerical algorithm including radiation boundary conditions appears to be easier to implement and generally provides the most accurate results.…”