Octant Analysis of the Reynolds Stresses in the Three Dimensional Turbulent Boundary Layer of a Prolate Spheroid
Madden, Michael Mark Jr.
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The Reynolds stresses in a three-dimensional turbulent boundary layer were examined using octant analysis. The representative flow was a pressure driven, three-dimensional turbulent boundary layer on the leeside (x/L=0.76-0.78, f=105Â°-130Â°) of a 6:1 prolate spheroid at 10Â° angle of attack. The Reynolds number for the flow was Re=4.2x10E+6. The LDV data of Chesnakas, Simpson, and Madden (1994) were the basis of examination. This data set employed a post-processing technique for refining the radial location of the measurments. A least-squares fit of the Spalding wall law was used to both correct the measurement locations and estimate the wall shear stress. This paper presents a previously unpublished assesment of the techinque. Octant analysis was performed on the corrected data under free-stream and wall-collateral coordinates. (The wall-collateral coordinate system is aligned with the mean tangential velocity in the buffer-layer.) The octant analysis led to the development of a structural model that extends the sweep/ejection process to three dimensions. Ejections and sweeps produce w' through the same mechanism that produces u'; they transport fluid across a spanwise velocity gradient. The model's results remain consistent with coordinate rotation. The model also describes the asymmetries that evolve between ejections and sweeps with spanwise fluctuations (w') of opposite sign. These asymmetries cause non-zero u'w' and v'w' in the buffer layer. Comparison of the two coordinate systems reveals that wall-collateral coordinates provides a simpler foundation for octant analysis. The sweep and ejection octants maintain a nearly equal distribution of velocity events throughout the buffer and lower log layers. Also, the spanwise velocity profile monotonically decreases to a constant value at the boundary layer edge, simplifying application of the sweep/ejection model to spanwise fluctuations. Comparison with other 3DTBL experiments suggests that the wall-collateral coordinates are more closely aligned with the quasi-streamwise vortex structures than free-stream coordinates. The octant analysis also reveals structural behavior consistent with the four mechanisms revealed by the direct numerical simulation of Sendstad and Moin (1992).
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