Numerical simulation of a compressible mixing layer past an axisymmetric trailing edge is carried out for a Reynolds number based on the diameter of the trailing edge approximately equal to 2.9 × 106. The free-stream Mach number at separation is equal to 2.46, which corresponds to experiments and leads to high levels of compressibility. The present work focuses on the evolution of the turbulence field through extra strain rates and on the unsteady features of the annular shear layer. Both time-averaged and instantaneous data are used to obtain further insight into the dynamics of the flow. An investigation of the time-averaged flow field reveals an important shear-layer growth rate in its initial stage and a strong anisotropy of the turbulent field. The convection velocity of the vortices is found to be somewhat higher than the estimated isentropic value. This corroborates findings on the domination of the supersonic mode in planar supersonic/subsonic mixing layers. The development of the shear layer leads to a rapid decrease of the anisotropy until the onset of streamline realignment with the axis. Due to the increase of the axisymmetric constraints, an adverse pressure gradient originates from the change in streamline curvature. This recompression is found to slow down the eddy convection. The foot shock pattern features several convected shocks emanating from the upper side of the vortices, which merge into a recompression shock in the free stream. Then, the flow accelerates and the compressibility levels quickly drop in the turbulent developing wake. Some evidence of the existence of large-scale structures in the near wake is found through the domination of the azimuthal mode m = 1 for a Strouhal number based on trailing-edge diameter equal to 0.26.

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a b s t r a c tThe present paper focus on the stochastic response of a two-dimensional transonic airfoil to parametric uncertainties. Both the freestream Mach number and the angle of attack are considered as random parameters and the generalized Polynomial Chaos (gPC) theory is coupled with standard deterministic numerical simulations through a spectral collocation projection methodology. The results allow for a better understanding of the flow sensitivity to such uncertainties and underline the coupling process between the stochastic parameters. Two kinds of non-linearities are critical with respect to the skin-friction uncertainties: on one hand, the leeward shock movement characteristic of the supercritical profile and on the other hand, the boundary-layer separation on the aft part of the airfoil downstream the shock. The sensitivity analysis, thanks to the Sobol' decomposition, shows that a strong non-linear coupling exists between the uncertain parameters. Comparisons with the one-dimensional cases demonstrate that the multi-dimensional parametric study is required to get the correct shape and magnitude of the standard deviation distributions of the flow quantities such as pressure and skin-friction.