The Reduction of Skin Friction Drag 



TO THE LAMINAR 

 LAYER 



SAME STRUCTURE 

 CHANGE VISCOSITY 

 ONLY 

 HEATING WALL 



COMPLIANT 

 BOUNDARY 



DRAG REDUCTION 



IN LIQUIDS 



VIOLATE WALL 

 SIMILARITY 



PARTICLES 

 a FIBERS 



CHANGE STRUCTURE 



VIOLATE REYNOLDS 

 NUMBER SIMILARITY 



VISCO-ELASTIC 



NON-NEWTONIAN 



ADDITIVE 



CHANGE SUBLAYER 

 THICKNESS REYNOLDS 

 NUMBER 



PARTICLES 

 S FIBERS 



COMPLIANT 

 BOUNDARY 



VISCO-ELASTIC 

 NON-NEWTONIAN 

 ADDITIVE 



PARTICLES 

 a FIBERS 



Fig. 4 - Techniques to alter the structure of the turbulent boundary layer 



The Nonuniform Sublayer 



Some question may be raised about the possibility of having a nonuniform 

 value of ,u through the sublayer; it is not difficult to show that for a non- 

 Newtonian fluid of arbitrary constitutive equation in a zero-pressure gradient 

 boundary -layer the viscous shear stress near the wall is constant to terms of 

 third degree in distance from the wall, so that there will be a region of uniform 

 strain rate and hence uniform viscosity. Relations will, of course, not be simple 

 at the outer edge of the sublayer, but it seems unlikely that the picture developed 

 above, which ignores this transition region between sublayer and inertial region 

 (on the grounds that the transition is in a thin layer (Townsend (1956)) can be far 

 wrong. 



A hot wall (in a liquid) can produce a temperature (and hence viscosity) 

 variation in the sublayer, if the heat flux is large enough, and a mechanism by 

 which this could reduce drag has been suggested by G. B. Schubauer (private 

 communication). The ratio of the temperature drop in the sublayer to that through 

 the boundary layer is given to first order by (using a two-layer model) 



(AT) 



subl ay er 



aRu * U 



(AT) 



boundary layer 



1 + R,a* (c- - 1) U 



At moderate Fleynolds numbers (in liquids), most of this drop takes place in the 

 sublayer, and we may take the temperature (and hence the viscosity) at the outer 



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