Axial Flutter Effects on the Axisymmetric Turbulent Boundary Layer Along Long Thin Circular Cylinders

Abstract

Experimental observations of towed sonar arrays as characterized by long thin circular cylinders indicate transverse motions that are clearly identified by low-amplitudes, low-wavelengths, and low-frequencies. Although the cylinder length (L) to radius (a) is commonly large [L/a = O(103)] with high Reynolds numbers [O(104)], the corresponding length scale involving the average skin friction [CfL/a = O(10)] remains within the many experimental determinations of short to moderate length cylinders that experience oscillatory instabilities. Prior to the present investigation, any detrimental effects of these oscillatory instabilities on the thin cylinder flow physics that serve construction of the respective semi-empirical and semi-analytical models remained chiefly unknown. Herein, we began examining those turbulent statistics via fine-scale numerical simulations to critique the pragmatic adequacy of the representative design models. We were concerned in particular about the streamwise effects on the turbulent boundary layer (TBL), skin friction and wall pressure evolutions as well as the radial distributions of the leading normal and shear Reynolds stresses. Fortunately, no major deviations (within 10%) were discovered in the TBL statistics over a characteristic range of Reynolds numbers and TBL thicknesses as compared to the axisymmetric state. However, acute spikes (both subharmonics and harmonics) were detected in the wall pressure autospectra similar to that suspected in the towed cylinder experiments, which were conducted in large tow tanks and lake-type basins. These spikes are of paramount importance and should be explored further because they may lead to signal-to-noise ratios above acceptable limits.