Effect of wall slip on laminar flow past a circular cylinder

Abstract

A numerical study of two-dimensional flow past a confined circular cylinder with slip wall is performed. A dimensionless number, Knudsen number ($Kn$) is used to describe the slip length of cylinder wall. The Reynolds number ($Re$) and Knudsen number ($Kn$) ranges considered are $Re=[1,180]$ and $Kn=[0,\infty )$, respectively. Time-averaged flow separation angle ($\overline{{\theta }_s}$), dimensionless recirculation length ($\overline{L_s}$) and the tangential velocity ($\overline{u_{\tau }}$) distributed on the cylinder's wall, drag coefficient ($\overline{C_d}$) and drag reduction ($DR$) are investigated. The time-averaged tangential velocity distribution on the cylinder's wall fit well with the formula $\overline{u_{\tau }}=[\frac{\alpha }{1+\beta e^{-\gamma (\pi -\theta )}}+\delta ]sin(\theta )$, where the coefficients ($\alpha$, $\beta$, $\gamma$, $\delta$) are related with $Re$ and $Kn$. Several scaling-laws are found, $log(\overline{u_{\tau max}})\sim log(Re)$ and $\overline{u_{\tau max}}\sim Kn$ for low $Kn$, ($\overline{u_{\tau max}}$ is the maximum tangential velocity on the cylinder's wall), $log(DR)\sim log(Re)$ ($Re\le 45$ and $Kn\le 0.1$), $log(DR)\sim log(Kn)$ ($Kn\le 0.05$). At low $Re$, $D{R}_v$ (the friction drag reduction) is the main source of $DR$. However, $D{R}_p$ (the differential pressure drag reduction) contributes the most to $DR$ at high $Re$ ($Re>\sim 60$) and $Kn$ over a critical number. $D{R}_v$ is found almost independent to $Re$.

Acta Mech (2022)

References in corpus (1)

• Influence of slip on the dynamics of two-dimensional wakes