Turbulence structures and statistics of a supersonic turbulent boundary layer subjected to concave surface curvature

Abstract

Supersonic turbulent flows at Mach 2.7 over concave surfaces for two different curvature radii were investigated and compared with a flat plate turbulent boundary layer using direct numerical simulations. The streamwise velocity reduces in the outer part of the boundary layer due to the compression while it increases near the wall due to curvature, with a higher shape factor for the concave cases. The near wall spanwise streak spacing reduces compared to the flat plate, with large scale streaks and turbulence amplification also observed. Streamwise velocity iso-surfaces and streamlines show the generation of Görtler-like vortices, consistent with significant centrifugal effects. Abundant small vortices are shown to be associated with large baroclinic production of vorticity that is caused by the density and pressure gradients that are associated with the concave compression. Profiles of turbulent kinetic energy (TKE) and turbulent Mach number exhibit a characteristic two-layer structure in the concave boundary layer cases. In the outer layer, turbulence is greatly amplified, whereas a local balance exists in the inner layer. Turbulent energy budget analysis shows that both production and dissipation increase near the concave wall, whereas in the outer part of the boundary layer, the production is increased and ultimately balanced by convection and turbulent transport.

Spatially developing supersonic turbulent boundary layer subjected to static surface deformations

“…6(c), corresponds to de-stabilization or stabilization of the boundary layer, respectively. This is consistent with the fact that convex curvature stabilizes the boundary layer, whereas concave curvature destabilizes the boundary layer [48,20]. Furthermore, after an initial adjustment, concave curvature leads to increase in the wall friction, heat transfer, and Reynolds stresses as well as it may give rise to Taylor-Görtler like vortices; on the other hand, the convex surface deformation typically results in opposite effects.…”

“…where δ * and θ are the displacement and momentum thicknesses of the boundary layer. A theoretical estimate of the shape factor of an equilibrium supersonic TBL may be obtained by using a power-law relation for the mean velocity of an incompressible TBL [46,20]. For instance, u/u ∞ = (y/δ x ) 1/n gives the velocity profile of a zero pressure gradient incompressible TBL, where n weakly depends on the Reynolds number (Re x ).…”

“…often employed with a threshold of M t ≈ 0.3 for the appearance of compressibility effects on turbulence [20], is plotted Fig. 8 at the different streamwise locations of Table 2.…”

“…For example, adverse pressure gradients and concave wall curvature destabilize the boundary layer and enhance turbulent mixing, in terms of the conservation of angular momentum [3,18]. The destabilization manifests as an increase in the turbulent fluctuations due to streamline curvature, adverse pressure gradients and bulk compression [19,20]. This contrasts with the stabilizing effects of favorable pressure gradients, which include weakening of coherent structures [21,22] and lead to a decrease in the turbulence, particularly in the outer region of the boundary layer [23].…”

A numerical study over the effect of curvature and adverse pressure gradient on development of flow inside gas transmission pipelines

“…It was found that, even in the turbulent flow, the boundary layer is destabilized due to the Gortler instability. Sun et al [4] used DNS method to study a supersonic TBL (STBL) in Mach number of 2.7 under the influence of a concave curvature with two curvature radii of 308 and 908 mm. The results of the velocity profiles showed that the velocity decreases in the outer region of the boundary layer, while it increases near the wall.…”