Reynolds Stress as an Indicator of the Laminar-Turbulent Transition of a Boundary Layer and a Linear Disturbance Development in It

摘要

This paper describes a method for estimating of disturbances development and the laminar-turbulent transition location on a base of the linear stability theory in presence of the acoustic field. In a stable region amplitudes of perturbation velocities near the location of a stability loss are determined by disturbances which are excited by external sound waves. Because of proximity of a sound wave and eigen fluctuations parameters, the received value of amplitude is accepted equal to amplitude of the growing boundary layer wave. At some point down the Reynolds stress becomes equal to several percents of the laminar boundary layer stress. On the basis of experimental data the criterion is accepted according to which the Reynolds stress equal to 12% of the laminar stress in the beginning of the laminar-turbulent transition. On the basis of a spectrum of external disturbances and the accepted criterion the satisfactory consent of the calculated and experimental transition Reynolds numbers of is received. Up to transition the disturbance increase in a boundary layer is described by linear stability equations well enough.