Stem Boundary-Layer Flow on 

 Axisymmetric Bodies 



T. T. Huang, N. Santelli, and G. Belt 



David W. Taylor Naval Ship Research and Development 



Center, Bethesda, Maryland 



ABSTRACT 



Measurements of static pressure distributions, mean 

 velocity profiles, and distributions of turbulence 

 intensities and Reynolds stress were made across the 

 stern boundary-layers on two axisymmetric bodies. 

 In order to avoid tunnel blockage, the entire after- 

 body was placed in the open-jet test section of the 

 DTNSRDC Anechoic Wind Tunnel. The numerical itera- 

 tion scheme which uses the boundary layer and open 

 wake displacement body is found to model satisfac- 

 torily the interaction between the thick stern bound- 

 ary layer and the external potential flow. The 

 measured static pressure distributions across the 

 entire stern boundary layer and the near wake are 

 predicted well by potential flow computations for 

 the displacement bodies. The measured distributions 

 of mean velocity and eddy viscosity over the stern, 

 except in the tail region (X/L > 0.90), are also 

 well-predicted when the Douglas CS differential 

 boundary-layer method is used in conjunction with 

 the inviscid pressure distribution on the displace- 

 ment body. However, the measured distributions of 

 turbulence intensity, eddy viscosity, and mixing- 

 length parameters in the tail region are found to 

 be much smaller than those of a thin boundary layer. 

 An approximate similarity characteristic for the 

 thick axisymmetric stern boundary layer is obtained 

 when the mixing-length parameters in the tail region 

 are normalized by the square-root of the boundary- 

 layer cross-sectional area instead of the boundary- 

 layer thickness. 



1. INTRODUCTION 



Many single-screw ship propellers operate inside of 

 thick stern boundary layers . An accurate prediction 

 of velocity inflow to the propeller is essential to 

 meet the ever- increasing demand for improving pro- 

 peller performance. Huang et al . (1976) used a 

 Laser Doppler Velocimeter (LDV) to measure the ve- 



locity profiles on axisymmetric models with and 

 without a propeller in operation. The measured 

 difference between these velocity profiles has 

 provided the necessary clues to formulate an inviscid 

 interaction theory for propellers and thick boundary 

 layers. An iterative scheme was employed to compute 

 the velocity profiles of the thick axisymmetric 

 boundary layer. In this approach, the initial 

 boundary- layer computation proceeds making use of 

 the potential-flow pressure distribution on the body 

 [Hess and Smith (1966) ] . The flow calculations are 

 then repeated for a modified body and wake geometry, 

 by adding the computed local displacement thickness 

 as suggested by Preston (1945) and Lighthill (1958) . 

 Potential-flow methods are then used to compute the 

 pressure distribution around the modified body and 

 the boundary- layer calculations are repeated using 

 the new pressure distribution. The basic iterative 

 scheme is continued until the pressure distributions 

 on the body from two successive approximations agree 

 to within a given error criterion (1 percent) . 



The Douglas CS differential boundary-layer method 

 [Cebeci and Smith (1974) ] , modified to properly ac- 

 acount for the effects of transverse curvature, was 

 used to calculate the boundary-layer over the axi- 

 symmetric body. The integral wake relations given 

 by Granville (1958) were used to calculate the dis- 

 placement thickness in the wake. In the stern/ 

 near-wake region (0.95 - X/L - 1.05), where X is the 

 axial distance from the nose and L is the total 

 length, a fifth-degree polynomial was used, with 

 the constants determined by the condition that the 

 thickness, slope, and curvature be equal to those 

 calculated by the boundary- layer method at X/L = 

 0.95 and by the integral wake relations at X/L = 

 1.05. Comparison with experimental results of Huang 

 et al. (1976) show that the potential- flow/boundary- 

 layer interaction computer program predicts accurate 

 values of pressure, shear stress, and velocity pro- 

 files over the forward 90 percent of the bodies, 

 where the boundary layers are thin compared with 

 the radii of the bodies. Over the last 10 percent 



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