Curved Turbulent Mixing Layer

Abstract

The radial pressure gradient in combination with either a positive or negative radial gradient of angular momentum makes possible the realization of two dynamically different flows. When the angular momentum gradient is positive, the flow is stable; when it is negative, the flow is unstable. Mean velocity, turbulence intensity, and shear correlation measurements were made in both cases. The one-dimensional streamwise energy spectra of the lateral and transverse turbulent velocities were also measured. The turbulent energy balances for both cases reveal that the dominant terms are the production of turbulent energy and its spacial transport by the turbulent velocities. The effect of the centripetal acceleration field is to inhibit the spectral transport of turbulent energy in the unstable case. The dissipation rates are an order of magnitude greater than the dissipation rates in the unstable case. The one-dimensional streamwise energy spectra display a (-5/3) dependence almost two decades long in the unstable case and one decade long in the stable case. Furthermore, the spectra reveal that the constant in the Kolmogorov form of the spectrum is not universal and that it depends on the ratio of the rate of production to the rate of dissipation of turbulent energy. In this study this ratio ranged from 1.5–27, and the values of the Kolmogorov constant varied from 0.4–2.4.

Effects of Streamline Curvature on Laminar and Turbulent Wakes

“…With this objective in view, qualitative and quantitative studies have been made on both laminar and turbulent wakes behind a circular cylinder which could be located either transversely or spanwise in a curved potential flow field. Similar work has been reported, for example, Margolis and Lumley [17] on a curved turbulent mixing layer; by Fette [18] on flow around a sphere placed in a rotating curved potential flow; by Raj and Lakshminarayana [19] on the turbulent wake behind a cascade of blades; and by Sarpkaya [20] and Perryet al [21] on the Karman vortex street.…”

Mixing layer in open-channel junction flows

“…Oppositely, if the fastest flow is in the outer part of the curve, the mixing layer is "stable", the Görtler mode becomes negligible and flow curvature reduces the growth rate of the Kelvin-Helmholtz mode. The main modifications of the mixing layer characteristics due to curvature are that, when compared to the straight case, the mixing layer thickness increases much faster for the unstable case and much slower for the stable case (Margolis andLumley, 1965, Gibson andYounis, 1983 or Plesniak et al 1996). Moreover, the magnitude of turbulent intensity and Reynolds shear stress increases with distance from the initial condition in the unstable case and remains constant in the stable case.…”

“…In the literature, the coordinate system mainly used to investigate the curved mixing layers is the cylindrical coordinate system (as for Margolis and Lumley, 1965). This system is well adapted to describe a flow within a curved conduit for which the center of curvature is the same for the sidewalls and the centerline of the conduit, i.e.…”

Turbulent boundary layers with large streamline curvature effects

“…These simplifications reduce the transport equations to a set of algebraic equations for the Reynolds stresses which can be solved in terms of the mean flow quantities and surface curvature. The result obtained by So and Mellor [10] for the Reynolds shear stress, -uv, can be written as __ c kU(#U/#y + kU)) 3/2 kU (aU kU~ (11) J where 72(/t/A) /~ _ (12) 1 -6(ll/A) (13) and lt, A are length scales introduced through the turbulence models. The interested reader should refer to the work of So and Mellor [10] and So [303 for more detailed discussion on the model.…”

“…Measurements of two-dimensional turbulent boundary layers along plane surfaces lend support to this assumption [2]. However, investigations on turbulent flows in curved channels [4][5][6] and along curved surfaces [6][7][8][9][10][11][12][13][14] showed that curvature of the mean flow not only gives rise to an appreciable change in the measured mean velocity and wall shear stress, but more importantly, it also gives rise to a substantial change in the turbulent flow structure [9][10][11][12][13][14]. The reason is that existing two-dimensional methods neglect the effects of the curvature of the mean flow streamlines.…”