SPIV measurements of axisymmetric turbulent boundary layers

This paper presents a description of turbulent boundary layer velocity measurements made on an experimental towed array during testing at the David Taylor Model Basin, Naval Surface Warfare Center Carderock Division in June 2007. The experimental array had an aspect ratio L/a = 7 × 10
³
and was towed at Reynolds numbers Re
_θ
varying from 4.6 × 105 to 8.9 × 105. This range falls well outside that which has been investigated to date in laboratories or with computational fluid dynamics. Previous lake tests of this array were performed and documented in Cipolla and Keith [1]. However, details of the high Reynolds turbulent boundary layer were not obtained during these tests. The goal of the follow-on tow tank testing was to obtain measurements of the mean and turbulent flow field which are not feasible in lake or sea trial testing. A stationary stereo-particle image velocimetry (SPIV) system was used to obtain three-dimensional velocity measurements and evaluate the boundary layer flow development along full-scale fleet towed array modules. Measurements were collected at discrete transverse planes along the length at tow speeds between 6.2 and 15.4 m/s. Algorithms for image pre-processing and filtering were applied to enhance the instantaneous images and mask the array and its shadow. The data will be analyzed to extract mean velocity profiles and compared with wind tunnel measurements on cylinders [2]. Further, relevant boundary layer parameters will be used to refine the scaling of the wall pressure measurements obtained simultaneously as reported by [3]. Independent load cell measurements of the total drag on the towed model provided the momentum thickness at the end of the model and the spatially-averaged friction velocity u
_τ
. These data supplement the SPIV data near the array wall, completing the velocity profile over the entire boundary layer. The load cell also provided a highly accurate value of the mean wall shear stress which is traditionally very difficult to obtain. The velocity profiles can be compared with existing models for the mean velocity which include the velocity defect law and Clauser's log law. In particular, the velocity defect law is expected to provide the best collapse of the data in the outer region of the boundary layer, while the log law relation is expected to provide a good collapse very close to the surface of the towed array (near wall region). Trends in the data with Reynolds number will be evaluated. In addition, the boundary layer thickness and mean wall shear stress at particular streamwise locations along the array will be quantified. The growth of the turbulent boundary layer over the length of the array is an important metric with regard to estimating the maximum turbulent boundary layer thickness which exists over a fleet towed array. The underlying structure of the axisymmetric boundary layer, which leads to significant increases in wall shear stress with respect to flat plate cases, is of primary importance. These new insights will facilitate efforts toward towed array reliability and an accurate prediction of drag and flow noise for any towed array application.