Theoretical Computation and Model and 

 Full-Scale Correlation of the Flow at the 

 Stem of a Submerged Body 



A. W. Moore 



Admiralty Marine Technology Establishment 



Teddington, England 



C. B. Wills 



Admiralty Marine Technology Establishment 



Haslar , England 



©British Crown Copyright 1979. 



ABSTRACT 



This paper describes an empirical method devised 

 for modifying measurements made at a propeller 

 position at the rear of unpowered bodies such that 

 the flow at the same position on a full-scale self- 

 propelled body may be predicted. 



A boundary layer calculation procedure for esti- 

 mating boundary-layer velocity profiles at the 

 tail region of a body of revolution is discussed, 

 and the inclusion of a simple representation of a 

 propeller is described. Comparisons between 

 velocities measured at Reynolds numbers of order 

 10 and calculated velocities show reasonable 

 correlation both for unpowered and for powered 

 bodies of revolution. It is shown how the results 

 of boundary-layer velocity calculations are used 

 to derive a method for modifying flow measurements 

 at model scale to represent full-scale flow over 

 the propeller disc area. Comparisons are made 

 between predictions based on this method and 

 measurements on powered and unpowered bodies at 

 high and low Reynolds numbers. 



1 . INTRODUCTION 



For many applications a self-propelled marine 

 vehicle has a propeller fitted at the rear of the 

 body where it gains in propulsive performance and 

 in cavitation performance by operating in the 

 relatively slow moving fluid in the hull boundary 

 layer. It follows that a fundamental requirement 

 for propeller design is a knowledge of the boundary 

 layer flow at the propeller position. This infor- 

 mation is not usually known since there are no 

 theoretical methods presently available for calcu- 

 lating the boundary flow at the rear of a powered 

 asymmetric body with appendages. An estimate of 

 the required flow field can be obtained from 

 measurements at model scale but as the Reynolds 

 number based on model length is considerably lower 



than the full-scale value, it is necessary to make 

 some modification to the measurements to simulate 

 the effect of a thinner boundary layer at full 

 scale. If the flow field is measured on an un- 

 powered model, as is often the case, further 

 modification is required to allow for flow acceler- 

 ation due to the propeller. 



This paper describes an approximate method 

 which has been developed for estimating corrections 

 required to flow measurements on unpowered bodies. 

 A boundary layer calculation procedure is briefly 

 outlined and then compared with data from tests on 

 axisymmetric bodies at low Reynolds numbers and 

 non axisymmetric bodies at both low and high 

 Reynolds niombers . 



2. BOUNDARY LAYER CALCULATION 



The method is based on the work of Myring (1973) 

 and only a brief outline is presented herein. An 

 iterative scheme is adopted in which a boundary 

 layer calculation is done for a given pressure 

 distribution over the body and a potential flow 

 calculation is done to calculate the pressure 

 distribution over the body with boundary layer dis- 

 placement thickness added. In the boundary layer 

 calculation procedure, an integral method is used 

 in which the laminar flow region is calculated 

 using the method of Luxton and Young (1962) and the 

 turbulent flow is calculated using a method similar 

 to that due to Head {I960) . The transition point 

 must be specified and it is assiomed that momentum 

 area and a shape parameter are continuous at 

 transition. 



An important feature in Myring 's method is his 

 treatment of the turbulent boundary layer in the 

 region of the tail. The usual boundary layer 

 assumptions become invalid in this region where the 

 ratio of boundary layer thickness to body radius 

 tends to infinity so Myring defines a momentum 

 area and a displacement area which overcomes the 



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