Compressibility effects on the structural evolution of transitional high-speed planar wakes

Abstract

The compressibility effects on the structural evolution of the transitional high-speed planar wake are studied. The relative Mach number (Ma r ) of the laminar base flow modifies two fundamental features of planar wake transition: (i) the characteristic length scale defined by the most unstable linear mode; and (ii) the domain of influence of the structures within the staggered two-dimensional vortex array. Linear stability results reveal a reduced growth (approximately 30 % reduction up to Ma r = 2.0) and a quasilinear increase of the wavelength of the most unstable, two-dimensional instability mode (approximately 20 % longer over the same Ma r range) with increasing Ma. The primary wavelength defines the length scale imposed on the emerging transitional structures; naturally, a longer wavelength results in rollers with a greater streamwise separation and hence also larger circulation. A reduction of the growth rate and an increase of the principal wavelength results in a greater ellipticity of the emerging rollers. Compressibility effects also modify the domain of influence of the transitional structures through an increased cross-wake and inhibited streamwise communication as characteristic paths between rollers are deflected due to local Ma gradients. The reduced streamwise domain of influence impedes roller pairing and, for a sufficiently large relative Ma, pairing is completely suppressed. Thus, we observe an increased two-dimensionality with increasing Mach number: directly contrasting the increasing three-dimensional effects in high-speed mixing layers. Temporally evolving direct numerical simulations conducted at Ma = 0.8 and 2.0, for Reynolds numbers up to 3000, support the physical insight gained from linear stability and vortex dynamics studies.

Speed of a von Kármán point vortex street in a weakly compressible fluid

“…As discussed by Leppington [18], if wavelike problems are of interest, the analysis of the intermediate region presented here can be fed into a full calculation of the global flow by matching of this Rayleigh-Jansen solution to a far-field solution at large distances-where the wavelike nature of the compressible flow must be accounted for-and an inner core region near the vortex. This basic theoretical study may also help in understanding compressible wake structures behind bluff bodies where it has recently been indicated that planar models can play a role [7]. A consequence of our analysis is that the aspect ratio 0.28056, which is the isolated value for neutral stability in the incompressible case, is well below the critical value of 0.38187, meaning that making the fluid weakly compressible will speed up a street of small vortices with aspect ratio close to this physically important value.…”

“…where ν 0 is some constant reference density. Clearly, (4) and (7) together no longer constitute the Cauchy-Riemann equations for harmonic functions φ and ψ. Nevertheless, we continue to define a complex potential [29]…”

“…The study of incompressible vortex dynamics is a vital subfield of fluid mechanics, especially important for the study of wakes [1], and it plays a crucial role in aerodynamics, geophysics, astrophysics, turbulence theory [2], and biofluids [3][4][5]. A surprising circumstance, remarked upon by previous authors [6], is that the study of compressible vortex dynamics has received markedly less attention even though gaining an understanding of compressible vortex flows is of fundamental interest for compressible wakes [7,8] and the theory of vortex sound and aeroacoustics [9][10][11]. There have been a few fundamental studies of compressible vortices [12][13][14][15], but many basic theoretical questions remain to be answered.…”

Effects of the Mach number on the evolution of vortex-surface fields in compressible Taylor-Green flows

“…Virk et al [13] studied compressible vortex reconnection of two antiparallel vortex tubes, and found that the shocklets induce the earlier occurrence of the vortex reconnection in larger Ma flows, and reduce the reconnection degree and curvature of isosurfaces of the vorticity magnitude. Hickey et al [14] found that the compressibility effects inhibit the streamwise communication and increase the cross-wake communication of neighboring vortices in transitional high-speed planar wakes. In compressible turbulence, a series of studies of Lee et al [15][16][17] showed that shocklets change the vorticity and dilatation distribution in high-Ma turbulent flows, which leads to strong shocklet-vortex interactions.…”

The effect of core size on the speed of compressible hollow vortex streets

“…The effect of core size on compressible hollow vortex streets 821 trying to understand the effects of compressibility on the structural evolution of transitional high-speed planar wakes, with recent work (Hickey, Hussain & Wu 2016) indicating that quasi-two-dimensional planar wakes of the kind examined here have a role to play. The significance of the results herein to such studies has yet to be ascertained.…”