Dissipation of intense vortices

2009 ◽  
Vol 87 (6) ◽  
pp. 685-689 ◽  
Author(s):  
Yasser Aboelkassem
Keyword(s):  
Steady State ◽  
Stokes Equations ◽  
Similarity Transformation ◽  
Navier Stokes ◽  
Time Decay ◽  
Navier Stokes Equations ◽  
Mathematical Algorithm ◽  
Vortex Model ◽  
Burgers Vortex ◽  
Time Analogy

In this article, we extend the space-time analogy shared by viscous vortices to generalize the dissipation of intense vortices Vatistas and Aboelkassem (Am. Inst. Aeronaut. Astronaut. J. 44, 912 (2006)). The main objective is to layout a mathematical algorithm that can be used to transform vortices into their dissipative phase or into a steady-state counterpart via a similarity transformation to Navier–Stokes equations. The method is applied to examine the time decay of eddies that belong to the Oseen-like concentrated type of viscous vortices. The steady-state Burgers’ vortex model was used to validate the transformation approach. This analysis shows that, upon variable transformation, Burgers’ vortex model has changed into the Oseen–Lamb class of decaying vortices. The approach is simple, general, and applicable to all kinds of viscous incompressible vortices like those of Sullivan, Rott, Bellamy-Knights, Vatistas, and Scully.

Performance analysis of a finite noncircular floating ring bearing in turbulent flow regime

2016 ◽  
Vol 231 (7) ◽  
pp. 869-888 ◽  
Author(s):  
Sandeep Soni ◽  
DP Vakharia
Keyword(s):  
Steady State ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Speed Ratio ◽  
Turbulent Regime ◽  
New Variety ◽  
Navier Stokes Equations ◽  
Turbulent Flow Regime ◽  
Oil Flow ◽  
Steady State Performance

The present paper investigates the turbulence effect on the steady-state performance of a new variety of journal bearing, i.e. the noncircular floating ring bearing. This particular bearing consists of the journal, floating ring, as well as lower and upper lobes. The shaft and the floating ring are cylindrical while surfaces of the bearing are noncircular. The classical Navier–Stokes equations and continuity equation in cylindrical coordinates are being satisfactorily adapted with the linearized turbulent lubrication model of Ng and Pan. These improved equations are being solved by the finite element method using Galerkin’s technique and an appropriate iteration strategy. The proposed bearing has a length-to-diameter ratio of 1 and operates over different values of the ratio of clearances (i.e. 0.70 and 1.30). The steady-state performance parameters computed are presented in terms of an inner and outer film eccentricity ratios, load-carrying capacity, attitude angle, speed ratio, friction coefficient variable, oil flow, and temperature rise variable for the Reynolds number up to 9000. The present analysis predicts better performance in the turbulent regime as compared to the laminar regime for the noncircular floating ring bearing.

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