The structure of a highly decelerated axisymmetric turbulent boundary layer

Abstract

Experiments were performed over a body of revolution at a length-based Reynolds number of 1.9 million. While the lateral curvature parameters are moderate ( $\delta /r_s < 2, r_s^+>500$ , where $\delta$ is the boundary layer thickness and r s is the radius of curvature), the pressure gradient is increasingly adverse ( $\beta _{C} \in [5 \text {--} 18]$ where $\beta_{C}$ is Clauser’s pressure gradient parameter), representative of vehicle-relevant conditions. The mean flow in the outer regions of this fully attached boundary layer displays some properties of a free-shear layer, with the mean-velocity and turbulence intensity profiles attaining self-similarity with the ‘embedded shear layer’ scaling (Schatzman & Thomas, J. Fluid Mech., vol. 815, 2017, pp. 592–642). Spectral analysis of the streamwise turbulence revealed that, as the mean flow decelerates, the large-scale motions energize across the boundary layer, growing proportionally with the boundary layer thickness. When scaled with the shear layer parameters, the distribution of the energy in the low-frequency region is approximately self-similar, emphasizing the role of the embedded shear layer in the large-scale motions. The correlation structure of the boundary layer is discussed at length to supply information towards the development of turbulence and aeroacoustic models. One major finding is that the estimation of integral turbulence length scales from single-point measurements, via Taylor's hypothesis, requires significant corrections to the convection velocity in the inner 50 % of the boundary layer. The apparent convection velocity (estimated from the ratio of integral length scale to the time scale), is approximately 40 % greater than the local mean velocity, suggesting the turbulence is convected much faster than previously thought. Closer to the wall even higher corrections are required.

Energy transfer mechanisms in adverse pressure gradient turbulent boundary layers: production and inter-component redistribution

“…They proposed scaling parameters based on this idea of an embedded shear layer and obtained self-similar mean velocity and Reynolds stress profiles in their large-defect APG TBL, as well as in other large-defect cases. Balantrapu et al (2021) also obtained self-similar profiles with the same scaling in their highly decelerated axisymmetric turbulent boundary layer. However, Maciel et al (2017a) noted that they could not find any roller-like structures that are the sign of a Kelvin-Helmholtz type instability.…”

“…Balantrapu et al. (2021) also obtained self-similar profiles with the same scaling in their highly decelerated axisymmetric turbulent boundary layer. However, Maciel et al.…”

“…In addition, it is important to note that moderate-defect APG TBLs have an outer maximum of the Reynolds stresses without the presence of an inviscidly unstable inflection point in the mean velocity profile (Maciel et al 2018). It is still not known whether an inflection point instability exists, and furthermore if it is directly responsible for turbulent regeneration in large-defect APG TBLs, but it is possible that the presence of Reynolds stress peaks and an inflection point in the outer layer is simply correlated without any causality (Balantrapu et al 2021).…”

“…It is still not known whether an inflection point instability exists, and furthermore if it is directly responsible for turbulent regeneration in large-defect APG TBLs, but it is possible that the presence of Reynolds stress peaks and an inflection point in the outer layer is simply correlated without any causality (Balantrapu et al. 2021).…”

Wall-pressure fluctuations in an axisymmetric boundary layer under strong adverse pressure gradient

“…The object of our research is to provide an understanding of the strong APG axisymmetric boundary layers, in particular of the turbulence structure and the associated wall-pressure fluctuations. The companion paper (Balantrapu et al (2021), hereafter referred to as BHAD) presents the measurements of the mean flow and turbulence structure of a boundary layer over a body of revolution. BHAD found that the axisymmetric boundary layer behaved as if there is an embedded shear layer in the outer region.…”