Similarity laws of velocity profiles and turbulence characteristics of Couette–Poiseuille turbulent flows

Abstract

Similarity laws of mean velocity profiles and turbulence characteristics of Couette–Poiseuille turbulent flow (C-P flow) have been studied experimentally. The global parameters of C-P flow are the Reynolds number $\hbox{\it Re}^{\ast}$ and the dimensionless shear stress gradient $\mu$ and flow parameter $\beta $. The effects of these parameters on the turbulence structure have also been considered in the wall region and turbulent core region, respectively. In the wall region, the wall law varies greatly with $\mu $ but slightly with $\hbox{\it Re}^{\ast}$. Typically, the additive constant $B$ of the logarithmic law (or Van Driest damping factor $A^{+}$) is shown to depend only on $\mu $. Turbulence characteristics are also strongly influenced by $\mu $, but not much by $\hbox{\it Re}^{\ast}$. Because the relation $\mu \,{=}\, {-}\hbox{\it Re}^{\ast}$ holds in plane Poiseuille flow and $\hbox{\it Re}^{\ast}$ has little effect on the similarity laws for C-P flows, the low-Reynolds-number effect on the additive constant and turbulence quantities for plane Poiseuille flow can be attributed to the $\mu $ effect. In the turbulent core region, however, there is a great difference in the defect law of the velocity profile and the distribution of turbulence intensity between Poiseuille (P)- and Couette (C)-types flows. For P-type flow, an effective friction velocity $u^{\ast}_{e}$ and a new coordinate $\eta \,{=}\,y- h_{s}$ are recommended for the universal profile, where $y\,{=}\,h_{s}\,{=}\,\delta _{p}$ is the position of $\tau \,{=}\,0$ and $\delta _{p}$ is considered to be appropriate as a characteristic length scale of turbulence. For C-type flow, a different effective friction velocity $u^{\ast}_{c,}$ the characteristic length scale 2$h$ and the wall coordinate $y$ are preferred. The turbulence activity away from the wall is extremely high for $\mu \,{>}\,0$ and low for $\mu \,{<}\,0$. A strong sweep event plays a dominant role in the Reynolds shear stress when $0\,{<}\,\mu \,{<}\,50$, whereas strong ejection from the near-wall region prevails in the case of negative $\mu$ with a small absolute value.