Effect of wall slip on laminar flow past a circular cylinder

TL;DR

This study numerically investigates how wall slip, characterized by the Knudsen number, affects laminar flow past a confined circular cylinder, revealing scaling laws and the dominant drag reduction mechanisms at various flow conditions.

Contribution

It introduces a detailed numerical analysis of wall slip effects on flow past a cylinder, establishing new scaling laws and clarifying the dominant drag reduction mechanisms at different Reynolds and Knudsen numbers.

Findings

Tangential velocity distribution fits a specific formula with Re and Kn dependence.

Scaling laws relate maximum tangential velocity and drag reduction to Re and Kn.

Different drag reduction mechanisms dominate at low and high Re and Kn.

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 ($\bar{\theta_s}$), dimensionless recirculation length ($\bar{L_s}$) and the tangential velocity ($\bar{u_{\tau}}$) distributed on the cylinder's wall, drag coefficient ($\bar{C_d}$) and drag reduction ($DR$) are investigated. The time-averaged tangential velocity distribution on the cylinder's wall fit well with the formula $\bar{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, $log(\bar{u_{{\tau}max}})\sim{log(Re)}$ and $\bar{u_{{\tau}max}}\sim{Kn}$ for low $Kn$, ($\bar{u_{{\tau}max}}$ is the maximum tangential velocity on the cylinder's wall), $log(DR)\sim{log(Re)}$ ($Re\leq45$ and $Kn\leq0.1$), $log(DR)\sim{log(Kn)}$ ($Kn\leq0.05$). At low $Re$, $DR_v$ (the friction drag reduction) is the main source of $DR$. However, $DR_p$ (the differential pressure drag reduction) contributes the most to $DR$ at high $Re$ ($Re>\sim60$) and $Kn$ over a critical number. $DR_v$ is found almost independent to $Re$.