Structure of an axisymmetric turbulent boundary layer under adverse pressure gradient: a large-eddy simulation study

Abstract

The spatial characteristics and structure of an axisymmetric turbulent boundary layer under strong adverse pressure gradient and weak transverse curvature are investigated using incompressible large-eddy simulation. The boundary layer is on a $20^{\circ}$ tail cone of a body of revolution at a length-based Reynolds number of $1.9\times10^6$. The simulation results are in agreement with the experimental measurements of Balantrapu et al. (J. Fluid Mech., vol. 929, 2021) and significantly expand the experimental results with new flow-field details and physical insights. The mean streamwise velocity profiles exhibit a shortened logarithmic region and a longer wake region compared with planar boundary layers at zero pressure gradient. With the embedded-shear-layer scaling, self-similarity is observed for the mean velocity and all three components of turbulence intensity. The azimuthal-wavenumber spectra of streamwise velocity fluctuations possess two peaks in the wall-normal direction, an inner peak at the wavelength of approximately 100 wall units and an outer peak in the wake region with growing strength, wavelength and distance to the wall in the downstream direction. Two-point correlations of streamwise velocity fluctuations show significant downstream growth and elongation of turbulence structures with increasing inclination angle. However, relative to the boundary-layer thickness, the correlation structures decrease in size in the downstream direction. The distributions of streamwise and wall-normal integral lengths across the boundary-layer thickness resemble those of zero-pressure-gradient planar boundary layers, whereas the azimuthal integral length deviates from the planar boundary-layer behavior at downstream stations.