Numerical Solution of Three-Dimensional Navier-Stokes Equations Showing Trailing Tip Vortices

AIAA Journal ◽  
1974 ◽  
Vol 12 (6) ◽  
pp. 787-794 ◽  
Author(s):  
J. F. THOMPSON ◽  
S. P. SHANKS ◽  
J. C. WU
Keyword(s):  
Numerical Solution ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Tip Vortices

scholarly journals Far Field of a Three-Dimensional Laminar Wall Jet

2021 ◽  
Vol 56 (6) ◽  
pp. 812-823
Author(s):  
I. I. But ◽  
A. M. Gailfullin ◽  
V. V. Zhvick
Keyword(s):  
Numerical Solution ◽  
Stokes Equations ◽  
Plane Surface ◽  
Three Dimensional ◽  
The Self ◽  
Similar Solution ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Self Similar Solution ◽  
Self Similar

Abstract We consider a steady submerged laminar jet of viscous incompressible fluid flowing out of a tube and propagating along a solid plane surface. The numerical solution of Navier–Stokes equations is obtained in the stationary three-dimensional formulation. The hypothesis that at large distances from the tube exit the flowfield is described by the self-similar solution of the parabolized Navier–Stokes equations is confirmed. The asymptotic expansions of the self-similar solution are obtained for small and large values of the coordinate in the jet cross-section. Using the numerical solution the self-similarity exponent is determined. An explicit dependence of the self-similar solution on the Reynolds number and the conditions in the jet source is determined.

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