Effect of wall slip on laminar flow past a circular cylinder

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 (θ_s¯), dimensionless recirculation length (L_s¯), and tangential velocity (u_τ¯) distributed on the cylinder’s wall, drag coefficient (C_d¯) and drag reduction (DR) are investigated. The time-averaged tangential velocity distributed on the cylinder’s wall fits well with the formula uτ¯=U∞·[α1+βe-γ(π-θ)+δ]·sinθ, 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(u_τmax¯) ~ log(Re) and u_τmax¯ ~ Kn for low Kn (u_τmax¯ 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 > ∼ 60) and Kn over a critical number. DR_v is found almost independent of Re.