Octant Analysis of the Reynolds Stresses in the Three-Dimensional Turbulent Boundary Layer of a Prolate Spheroid

摘要

The Reynolds stress contributions to each of the 8 octants of combinations of u, v, and w fluctuations were examined in local free-stream and local wall-collateral co-ordinates for a pressure-driven three-dimensional turbulent wall-bounded shear flow on the leeside (x/L=0.76 - 0.78, pi=105 - 130 deg from the windward side) of a 6:1 prolate spheroid at 10 deg angle of attack and Reynolds number Re(L) = 4.2x10 to the 6th power. The laser-Doppler velocimeter data of Chesnakas, Simpson, and Madden (1994) were used in this examination of the sweep/ejection concepts for a 3-D mean flow. As described and assessed here, a post-processing technique for fitting the data to the Spalding composite law-of-the-wall velocity profile was used to both reduce the measurement location uncertainty and estimate the wall shear stress. In the resulting flow model, ejections and sweeps produce w' with the same mechanism that produces u'; they transport fluid across a spanwise velocity gradient. Asymmetries that evolve between ejections and sweeps with spanwise fluctuations (w') of opposite sign cause non-zero u'w' and v'w' in the buffer layer. While the model results remain consistent with co-ordinate rotation, wall-collateral coordinates are simpler for octant analysis and are more closely aligned with the quasi-streamwise vortex structures than free-stream coordinates. The sweep and ejection octants maintain a nearly equal distribution of velocity events throughout the buffer and lower log layers. The model's results remain consistent with the four mechanisms revealed by the direct numerical simulation of Sendstad and Moin (1992).