Measurements of velocity–acceleration statistics in turbulent boundary layers

Abstract

An advanced laser Doppler velocimetry system is developed to acquire measurements of fluctuating velocity–acceleration statistics in turbulent boundary layers. These correlations are enabled by customized burst signal processing that estimates both the Doppler frequency and the rate-of-change of Doppler frequency, which are related to the particle velocity and acceleration by the interference fringe spacing. The measurements give important insight into the near-wall turbulence structure since the statistical correlations of interest, u i a j ¯ appear directly in the Reynolds stress transport equations as a sum of the velocity–pressure gradient correlation, - 1 ρ u i ∂ p ∂ x j + u j ∂ p ∂ x i ¯ , the dissipation rate, 2 ν ∂ u i ∂ x k ∂ u j ∂ x k ¯ , and the viscous diffusion, ν ∇ 2 u i u j ¯ . The immediate power of such measurements is that combinations of terms in the Reynolds stress transport equation may be characterized by a single statistical measurement at one location in the flow—no gradients need be computed. In the present paper, data are presented for a constant-pressure 2D turbulent boundary layer at Re θ = 6800. Near-wall results for the dominant term in the velocity–acceleration tensor, the streamwise correlation ua x ¯ , compare favorably with DNS for the same quantity at Re θ = 1410 and Re τ = 640; furthermore, the quantity exhibits no Reynolds number effects within experimental uncertainties. The balance of the velocity–acceleration equation in the streamwise direction is presented, giving the first measurements for the profile of the velocity–pressure gradient correlation with this technique. This study exhibits the potential of the technique to be applied to more complex flows, particularly those 3D separating flows in which the motions contributing to the velocity–acceleration correlations become dominant.