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 the cylinder wall. The Reynolds number (Re) and Knudsen number (Kn) ranges considered are Re = [1, 180] and Kn = [0, ∞), respectively. Time-averaged flow separation angle ($\overline{{\theta_{{\text{s}}} }}$), dimensionless recirculation length ($\overline{{L_{{\text{s}}} }}$), and tangential velocity ($\overline{{u_{\tau } }}$) distributed on the cylinder’s wall, drag coefficient ($\overline{{C_{{\text{d}}} }}$) and drag reduction (DR) are investigated. The time-averaged tangential velocity distributed on the cylinder’s wall fits well with the formula $\overline{{u_{\tau } }} = U_{\infty } \cdot \left[ {\frac{\alpha }{{1 + \beta e^{{ - \gamma \left( {\pi - \theta } \right)}} }} + \delta } \right] \cdot \sin \theta$, where the coefficients (α, β, γ, δ) are related to Re and Kn, and U∞ is the incoming velocity. Several scaling laws are found, log($\overline{{u_{\tau \max } }}$) ~ log(Re) and $\overline{{u_{\tau \max } }}$ ~ Kn for low Kn ($\overline{{u_{\tau \max } }}$ is the maximum tangential velocity on the cylinder’s wall), log(DR) ~ log(Re) (Re ≤ 45 and Kn ≤ 0.1) and log(DR) ~ log(Kn) (Kn ≤ 0.05). At low Re, DR_v (the friction drag reduction) is the main source of DR. However, DR_p (the differential pressure drag reduction) contributes most to DR at high Re (Re > $\sim60$) and Kn over a critical number. DR_v is found almost independent of Re.