IMAGE-BASED MODELING OF THE SKIN-FRICTION COEFFICIENT IN COMPRESSIBLE BOUNDARY-LAYER TRANSITIONWenjie Zheng AbstraktWe report a geometric study of Lagrangian structures in compressible, spatially evolving transitional boundary layers at two Mach numbers Ma_{∞} = 2.25 and 6, and develop a simple model of the skin-friction coefficient based the geometric analysis of two-dimensional scalar images. The velocity fields are obtained by the direct numerical simulation (DNS). The Lagrangian structures in the transition process are extracted from the Lagrangian scalar field by a sliding window filter in compact frames. The multi-scale and multi-directional geometric analysis is applied to characterize the averaged inclination angles of Lagrangian structures at different scales ranging from the boundary layer thickness to several viscous length scales, where the inclination angle is on the plane of the streamwise and wall-normal directions. In general, the averaged inclination angle is increased along the streamwise direction, and the variation of the angles for large-scale structures is smaller than that for small-scale structures. We develop a simple model of skinfriction coefficient based on the inclination angle statistics of the filtered component fields on the streamwise and wallnormal plane at different scales. The trend of the increasing averaged inclination angle is qualitatively similar to the rise of the skin-friction coefficient, and our modelled skinfriction coefficient agrees well quantitatively with the DNS results for the two Mach numbers. |
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