Laminar-Turbulent Transition and Velocity Profiles of Oscillatory Rectangular Duct Flows

Abstract

Oscillatory air flows in ducts of rectangular cross-section with aspect ratios 1, 5 and 10 are investigated experimentally. On the basis of the inspections of hot-wire signals, flow types can be classified into laminar, transitional and turbulent regimes, and these regimes are well delimitated by using two parameters, Re_os=D_h|u_m, os, 1|/ν and √(ω')=(D_h/2) √(ω/ν), where D_h : hydraulic diameter, |u_m, os, 1| : cross-sectional mean velocity amplitude, ν : kinematic viscosity, ω : angular frequency. For fully developed steady turbulent flows in a square and a two-dimensional duct, the approximate solutions for the axial mean velocity profiles are derived on the assumption of eddy viscosity distributions. In the phase when turbulent bursts occur, instantaneous velocity profiles of measured oscillatory duet flows are well described by the above-mentioned solutions.