Direct simulations of low-Reynolds-number turbulent flow in a rotating channel

Abstract

Direct numerical simulations of fully developed pressure-driven turbulent flow in a rotating channel have been performed. The unsteady Navier–Stokes equations were written for flow in a constantly rotating frame of reference and solved numerically by means of a finite-difference technique on a 128 × 128 × 128 computational mesh. The Reynolds number, based on the bulk mean velocity Um and the channel half-width h, was about 2900, while the rotation number Ro = 2|Ω|h/Um varied from 0 to 0.5. Without system rotation, results of the simulation were in good agreement with the accurate reference simulation of Kim, Moin & Moser (1987) and available experimental data. The simulated flow fields subject to rotation revealed fascinating effects exerted by the Coriolis force on channel flow turbulence. With weak rotation (Ro = 0.01) the turbulence statistics across the channel varied only slightly compared with the nonrotating case, and opposite effects were observed near the pressure and suction sides of the channel. With increasing rotation the augmentation and damping of the turbulence along the pressure and suction sides, respectively, became more significant, resulting in highly asymmetric profiles of mean velocity and turbulent Reynolds stresses. In accordance with the experimental observations of Johnston, Halleen & Lezius (1972), the mean velocity profile exhibited an appreciable region with slope 2Ω. At Ro = 0.50 the Reynolds stresses vanished in the vicinity of the stabilized side, and the nearly complete suppression of the turbulent agitation was confirmed by marker particle trackings and two-point velocity correlations. Rotational-induced Taylor-Görtler-like counter-rotating streamwise vortices have been identified, and the simulations suggest that the vortices are shifted slightly towards the pressure side with increasing rotation rates, and the number of vortex pairs therefore tend to increase with Ro.

Large-eddy simulation of turbulent flows in a heated streamwise rotating channel

“…According to Xun et al [14], the effects of the Coriolis forces on the resolved turbulent stresses and TKE can be further studied using their transport equations. As revealed in the experimental study of Johnston et al [23] and DNS study of Kristoffersen and Andersson [35], the production terms in the transport equations of the resolved turbulent stresses TABLE 4.1: Production terms due to the mean turbulent shear (P ij ) and rotation (G ij ) stresses for a fullydeveloped rotating plane channel flow.…”

“…The Among the studies of turbulent channel flows subjected to these three types of system rotations, the spanwise rotating turbulent channel flows have been studied extensively through experiments [23,24] and numerical simulations [14,[25][26][27][28][29][30][31][32][33][34][35][36][37]. It is reported that as the rotation number increases, turbulence is gradually enhanced on the pressure side and reduced on the suction side, further resulting in asymmetric distributions in the mean flow and Reynolds stresses [14,[23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. At the same time, large-scale roll cells come forth as a result of the Taylor-Görtler (T-G) instability [14,23,25,35].…”

“…It is reported that as the rotation number increases, turbulence is gradually enhanced on the pressure side and reduced on the suction side, further resulting in asymmetric distributions in the mean flow and Reynolds stresses [14,[23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. At the same time, large-scale roll cells come forth as a result of the Taylor-Görtler (T-G) instability [14,23,25,35]. These large-scale roll cells dominate the secondary flow pattern in a channel, and shift towards the pressure side.…”

“…These large-scale roll cells dominate the secondary flow pattern in a channel, and shift towards the pressure side. The number of the pairs of such cells tends to increase as the rotation number increases [35]. At high rotation numbers, turbulence on the suction side reduces significantly, and the roll cells become much smaller and eventually disappear due to thickening of the relaminarized region on the suction side [36,37].…”

Application of the Turbulent Potential Model to Complex Flows

“…The model has been compared to the DNS results of Kristoffersen & Andersson (1993). The DNS has a turbulent Reynolds number t Re u h / τ = υof 194 where h is the channel half width and u τ = wall dv / dy υ is the shear velocity.…”