Velocity and temperature fields in oscillating boundary layers

Abstract

The response of boundary layer velocity and temperature distributions to small amplitude oscillations imposed by the free-stream is investigated. A straightforward combination of perturbation and numerical methods is applied. The analysis of the effect of the frequency of oscillations shows that in many respects the response of the boundary layer to the oscillations in time is periodic in ξ (ξ = frequency parameter), with the period Δξ ≈ 4.0 and the first harmonic manifesting itself strongly at ξ ≈ 1.15. The available experimental data seem to confirm this finding.

Second-order effects of oscillations on velocity and temperature fields are studied for laminar flows. In general the steady-streaming contributions are small, but it appears from the present results that for large Eckert numbers the wall heat transfer may be altered up to 40% by the streaming phenomena. Unfortunately there is no experimental data on this subject.

Several models of the oscillatory Reynolds stress (eddy viscosity type) are tested for oscillating turbulent boundary layer flow on a flat plate. Satisfactory results are obtained by decoupling the mean and oscillatory Reynolds stresses. It appears that theoretical profiles of oscillating velocity in low or high frequency regions are relatively insensitive to the details of the models used. This is not the case for intermediate frequencies for which in fact the performance of the present models is not very good. It is concluded that the interaction between the random turbulent motion and oscillations is probably too strong to be neglected and therefore more complex models, capable of incorporating the interaction process, are required to successfully predict the behavior of oscillatory turbulent boundary layers.