Experimental study on mean velocity and turbulence characteristics of plane Couette flow: low-Reynolds-number effects and large longitudinal vortical structure

Abstract

Experimental work to investigate plane Couette flow has been performed in the Reynolds number range of $750\,{\leq}\,\hbox{\it Re}\,(\,{=}\,hU_b/(2\nu))\,{\leq}\, 5000$ or $50\,{\leq}\, \hbox{\it Re}_*\,(\,{=}\,hu_*/\nu)\,{\leq}\, 253$, where $U_b$, $u_*$ and $h$ are moving wall speed, friction velocity and channel half-height, respectively. The low-Reynolds-number effect on the wall friction coefficient $C_f$, mean velocity profile and statistical turbulence quantities is discussed in relation to the turbulent Poiseuille flow properties. Since the shear stress is constant in Couette flow, the flow is free from the effect of shear stress gradient and the Reynolds number effect therefore can be seen explicitly, uncontaminated by this effect. A flow region diagram is given to show how the low-Reynolds-number effect penetrates into the wall region. The area of the buffer region is contracted by the low-Reynolds-number effect when $\hbox{\it Re}_*\leq 150$, so that the additive constant $B$ of the log law decrease as $\hbox{\it Re}_*$ decreases. Also, $C_f$ has a larger value than in Poiseuille flow in the low $\hbox{\it Re}_*$ range. The log-law area in Couette flow is 2–3 times as wide as that in Poiseuille flow. The defect law is $\hbox{\it Re}_*$-dependent and the non-dimensional velocity gradient at the core, $Rs=({\rm d}U_1/{\rm d}x_2)(h/u_*)$, increases from 3 to 4.2 as $\hbox{\it Re}_*$ increases from 50 to 253. The peak value of streamwise turbulence intensity $u_{1p}^+$ has a constant value of 2.88 but decreases sharply as $\hbox{\it Re}_*$ reduces below 150.

The large longitudinal vortices extending the entire height of the channel are shown to be sustained in Couette flow that is oscillating around their average position. This causes a slow fluctuation with large amplitude in the streamwise velocity component. These vortices make the Couette flow three-dimensional and the skin friction coefficient varies 20% sinuously in the spanwise direction, for example. Also, the zero-crossing time separation of streamwise velocity auto-correlation $R_{11}(\tau)$ becomes longer as $\tau=40h/U_b$, which is 3 times as long as that in Poiseuille flow.