| There are prevalent existences of turbulent boundary layers subjected to longitudinal surface curvature,the study of which is significant for novel high-speed vechile design and effective flow control strategy.The main objective of the present numerical study is systematically investigating the influences of longitudianl concave and convex curvatures on the passing supersonic turbulent boundary layers.We conduct direct numerical simulations of a canonical turbulent boundary layer at supersonic regime M?=2.87,which is the prelude of more chanllenging studies of supersonic flows over curved surface geometries.The excellent agreement with literature well-accepted data confirms that our DNS reproduces a genuine zero-pressure-gradient turbulent boundary layer,which is free from artificial effects and post-transitional effects.The collected DNS databases are used to address the issue of hairpin vortex model.We conduct conditional analyses based on an event of ejections,and the conditional flow fields reveal a hairpin vortex with increasingly larger inclination as departing the wall,which is meanwhile significant in organizing the production of Reynolds stresses.We conduct direct numerical simulations of supersonic turbulent boundary layers(M_?=2.87)subjected to a longitudinal concave wall surface.Two novel approaches are employed to reasonably define the edges of the distorted boundary layer:one relies on the total pressure,the other uses the intermittency functions.Results show the two sets of boundary layer thicknesses are physically consistent.It is shown that the many scalings well-established in canonical wall turbulence are violated in these distorted turbulent boundary layers,such as the universal logarithmic velocity distribution,the universal average spacing of near-wall streaks,and the characteristic lengthscales of outer-layer turbulent structures.The analyses of Reynolds stresses and turbulent kinetic energy reveal that the concave wall imposes a general destabilizing effect on the passing turbulent boundary layers.These destabilizing effects can be traced to the energization of outer-layer large-scale motions,and meanwhile can be understood from the budgets of mean and turbulent kinetic energy.Paricularly,the concave surface incurs enhanced inner-outer interactions:the overlaid large-scale footprint onto the near-wall region intensifies the linear energy superposition and nonlinear amplitude modulation.As a result,the outer-scaled motions are endowed with a more prominent role in the turbulence dynamics,which may have implications for flow control strategies.We further conduct DNS regarding the convex wall surface,to complete the list of wall curvature effects.It is found in many aspects of the turbulent statistics and structures,the influences of convex wall is contrary to the concave one.In general the convex wall surface imposes stablizing effects on the turbulent boundary layer.More in-depth understanding is gained by investigating the turbulent/non-turbulent interfaces.We first found similarity of the interfacial physics between the supersonic and incompressible case,which can be considered as an extension of Morkovin's weak compressibility hypothesis.We find the convex wall highly influences the properties of TNTI in several aspects,such as the geometries,the interfacial dynamics,and the entrainment processes.It is counterintuitive to observe detrainment of rotational fluids from turbulent boundary layer,and this is explained by inspecting the modifications of interfacial physics.We find that the vortical structures in TNTI layer are weakened on the convex wall.Consequently the ultimate stage of turbulence entainment,i.e.,the nibbling process,is damped,meaning that the turbulent boundary layer is losing its capability of entraining irrotational fluids from the potential flow.These analyses collectively point towards that the detablizing or stabilizing effects of surface wall can reach as far as to the outermost boundaries of turbulent flows. |
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