Understanding Tow Tank Measurements of Total Drag for Long Thin Circular Cylinders

Abstract

Both the experimental measurements and numerical computations tell us that thin circular cylinders own turbulent boundary layer (TBL) characteristics which are dissimilar from planar geometries once the TBL thickness (δ) exceeds the cylinder radius. But the exceedingly long cylinders that serve as acoustic array systems have resorted to tow tank measurements due to the experimental complexities of axial sag or the required simplifications for efficient predictions. One key measurement in the tow tank experiments is the total drag, where the respective average tangential coefficients have been assessed relative to various scaled cylinder lengths, such as the length-based Reynolds number. We now know that the skin friction whose axial summation provides the total drag is governed by the radius-based Reynolds number as well. Herein, we revisit the many tow tank experiments to isolate the measurement discrepancies attributed to these two distinct Reynolds numbers. Once separated, these measurements provide a vital answer to the transformation of the TBL spatial growth to a temporal one (no additional net δ growth). This final stage is readily identifiable by a streamwise constant skin friction as given by near-wall flow homogeneity. This understanding lends subsequent evaluation of the TBL momentum thickness at the cylinder trailing edge. The present process involves applying several semiempirical expressions formed from the experimental and numerical evidence that supply the spatially evolving TBL characteristics along thin cylinders. Besides gaining an enhanced understanding of the TBL behavior, these semiempirical expressions are further clarified to form a final set that are helpful for design engineers of tow array devices in the military and oceanographic communities.