Laminar-turbulent transition and velocity profiles of oscillatory rectangular duct flows

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 using two parameters defined in terms of hydraulic diameter, cross-sectional mean velocity amplitude, kinematic viscosity, and 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 duct flows are well described by these solutions.