Similaritylaw entrainment method for thick axisymmetric turbulent boundary layers in pressure gradients
Abstract
Analytical relations have been derived for calculating developing thick, axisymmetric, turbulent boundary layer in a pressure gradient from two simultaneous differential equations: momentum and shape parameter. An entrainment method is used to obtain the shape parameter equation. Both equations incorporate the velocity similarity laws that provide a twoparameter velocity profile general enough to include any range of Reynolds numbers. Newly defined quadratic shape parameters which arise from the geometry of the thick axisymmetric boundary layer are analytically related to the twodimensional shape parameter by means of these velocity similarity laws. The variation of momentum loss, boundarylayer thickness, local skin friction, and local velocity profile may be calculated for the axisymmetric turbulent boundary layers on underwater bodies, including the thick boundary layers on the tails. The various formulations are shown to correlate well with available experimental data.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 December 1975
 Bibcode:
 1975STIN...7720396G
 Keywords:

 Pressure Gradients;
 Similarity Theorem;
 Turbulent Boundary Layer;
 Differential Equations;
 Equations Of Motion;
 Momentum;
 Skin Friction;
 Fluid Mechanics and Heat Transfer