Direct numerical simulation of compressible turbulence in a counter-flow channel configuration

Abstract

Counter-flow configurations, whereby two streams of fluid are brought together from opposite directions, are highly efficient mixers due to the high turbulence intensities that can be maintained.In this paper, a simplified version of the problem is introduced that is amenable to direct numerical simulation. The resulting turbulent flow problem is confined between two walls, with one non-zero mean velocity component varying in the space direction normal to the wall, corresponding to a simple shear flow. Compared to conventional channel flows, the mean flow is inflectional and the maximum turbulence intensity relative to the maximum mean velocity is nearly an order of magnitude higher. The numerical requirements and turbulence properties of this configuration are first determined. The Reynolds shear stress is required to vary linearly by the imposed forcing, with a peak at the channel centreline. A similar behaviour is observed for the streamwise Reynolds stress, the budget of which shows an approximately uniform distribution of dissipation, with large contributions from production, pressure-strain and turbulent diffusion. A viscous sublayer is obtained near the walls and with increasing Reynolds number small-scale streaks in the streamwise momentum are observed, superimposed on the large-scale structures that buffet this region. When the peak local mean Mach number reaches 0.55, turbulent Mach numbers of 0.6 are obtained, indicating that this flow configuration can be useful to study compressibility effects on turbulence. I. INTRODUCTIONCounter-flow shear layers, also known as counter-current flows, have been previously recognised as efficient flow configurations for mixing [1-4], thrust vectoring (flow control)[5-7] and combustion [8,9]. Strykowski and Wilcoxon [2] showed that counter-current configurations could be used to control axisymmetric jet flows and enhance their mixing characteristics using global oscillations produced by self-excitation within shear layers. Strykowski and colleagues [8,9] also showed that a counter-current flow configuration can be used in swirl combustors to efficiently control the turbulent burning velocity (flame speed) and reduce pollutant emissions. The use of counter-flow configurations for fundamental flow studies was first recognised by Humphrey and Li [1] and later by various researchers including most notably Forliti et al. [3] who studied planar shear layers. A shear layer develops

Direct numerical simulations of shocklet-containing turbulent channel counter-flows

“…The dimensionless governing equations of a compressible Newtonian fluid flow that conserve mass, momentum and energy are solved (Hamzehloo et al, 2021). The latter two equations containing the shear-forcing term are given as: where ρ represents the density, u i (i = 1, 2, 3) denotes the velocity component (u, v and w, respectively) in the i th direction (x, y and z, respectively), E is the total energy, and p and δ denote the pressure and the Kronecker delta, respectively.…”

“…In order to accurately resolve the near wall region, the grid is stretched in the y direction. We have previously identified an optimum domain size of 12H × 2H × 6H with a grid resolution of 240 × 151 × 200 (Hamzehloo et al, 2021). This domain size is used with a Reynolds number of Re = 400.…”

“…Counter-flows are highly efficient mixers due to the high turbulence intensities that can be maintained (Humphrey & Li, 1981;Strykowski & Wilcoxon, 1993;Forliti et al, 2005). Previously, we introduced (Hamzehloo et al, 2021) a wall-bounded counter-flow turbulent channel configuration, amenable to Direct Numerical Simulation (DNS), and demonstrated that it could overcome the above-mentioned barriers associated with free shear layers and Poiseuille/Couette type flows. Specifically, it retains a statistically stationary onedimensional solution, in common with conventional channel flows, but contains an inflectional mean flow, representative of free shear layers.…”

“…Our earlier study (Hamzehloo et al, 2021) was limited to a maximum Mach number of M = 0.4 (defined based on a reference velocity deduced from the forcing as discussed in the next section) since higher values necessitated using a shockcapturing method. Here, by applying an appropriate numerical treatment for flow discontinuities, we extend our previous DNS study to a Mach number of M = 0.7.…”

The Effect of Turbulence on Dynamic Radar Cross Section of Chaff Clouds

“…Various Cutting Edge Turbulence Simulation methods for wind energy and aerospace problems have been reported in (4) . Direct numerical simulation of compressible turbulence in counter flow channel configuration, in which two streams of fluid are brought together from opposite directions is discussed in (5) . Bistatic scattering evaluation method for chaff cloud in airflow is presented in (6) .…”