The development of concentrated vortices: a numerical study

1971 ◽  
Vol 48 (1) ◽  
pp. 1-21 ◽  
Author(s):  
L. M. Leslie
Keyword(s):  
Steady State ◽  
Numerical Experiment ◽  
Laboratory Experiments ◽  
Body Force ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Quasi Steady State ◽  
Navier Stokes Equations ◽  
Flow Parameters ◽  
Axis Of Rotation

Amongst the more important laboratory experiments which have produced concentrated vortices in rotating tanks are the sink experiments of Long and the bubble convection experiments of Turner & Lilly. This paper describes a numerical experiment which draws from the laboratory experiments those features which are believed to be most relevant to atmospheric vortices such as tornadoes and waterspouts.In the numerical model the mechanism driving the vortices is represented by an externally specified vertical body force field defined in a narrow neighbourhood of the axis of rotation. The body force field is applied to a tank of fluid initially in a state of rigid rotation and the subsequent flow development is obtained by solving the Navier–Stokes equations as an initial-value problem.Earlier investigations have revealed that concentrated vortices will form only for a restricted range of flow parameters, and for the numerical experiment this range was selected using an order-of-magnitude analysis of the steady Navier–Stokes equations for sink vortices performed by Morton. With values of the flow parameters obtained in this way, concentrated vortices with angular velocities up to 30 times that of the tank are generated, whereas only much weaker vortices are formed at other parametric states. The numerical solutions are also used to investigate the comparative effect of a free upper surface and a no-slip lid.The concentrated vortices produced in the numerical experiment grow downwards from near the top of the tank until they reach the bottom plate whereupon they strengthen rapidly before reaching a quasi-steady state. In the quasi-steady state the flow in the tank typically consists of the vortex at the axis of rotation, strong inflow and outflow boundary layers at the bottom and top plates respectively, and a region of slowly-rotating descending flow over the remainder of the tank. The flow is cyclonic (i.e. in the same sense as the tank) in the vortex core and over most of the bottom half of the tank and is anticyclonic over the upper half of the tank away from the axis of rotation.

Mathematical modeling of steady stratified flows

2003 ◽  
Vol 3 ◽  
pp. 195-207
Author(s):  
A.M. Ilyasov ◽  
V.N. Kireev ◽  
S.F. Urmancheev ◽  
I.Sh. Akhatov
Keyword(s):  
Stokes Equations ◽  
Approximate Model ◽  
Immiscible Liquid ◽  
Stratified Flows ◽  
Navier Stokes ◽  
Flat Channel ◽  
Navier Stokes Equations ◽  
Two Fluids ◽  
Flow Parameters ◽  
Direct Numerical Solution

The work is devoted to the analysis of the flow of immiscible liquid in a flat channel and the creation of calculation schemes for determining the flow parameters. A critical analysis of the well-known Two Fluids Model was carried out and a new scheme for the determination of wall and interfacial friction, called the hydraulic approximation in the theory of stratified flows, was proposed. Verification of the proposed approximate model was carried out on the basis of a direct numerical solution of the Navier–Stokes equations for each fluid by a finite-difference method with phase-boundary tracking by the VOF (Volume of Fluid) method. The graphical dependencies illustrating the change in the interfase boundaries of liquids and the averaged over the occupied area of the phase velocities along the flat channel are presented. The results of comparative calculations for two-fluid models are also given, according to the developed model in the hydraulic approximation and direct modeling. It is shown that the calculations in accordance with the hydraulic approximation are more consistent with the simulation results. Thus, the model of hydraulic approximation is the most preferred method for calculating stratified flows, especially in cases of variable volumetric content of liquids.

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.

ON THE EXISTENCE AND UNIQUENESS OF TWO‐FLUID CHANNEL FLOWS

2005 ◽  
Vol 9 (1) ◽  
pp. 67-78 ◽  
Author(s):  
J. Socolowsky
Keyword(s):  
Stokes Equations ◽  
Channel Flows ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Parameters ◽  
Free Boundary Value Problems ◽  
Fluid Channel ◽  
Density Ratios ◽  
Steady State Solutions ◽  
Two Fluid

iscous two‐fluid channel flows arise in different kinds of coating technologies. The corresponding mathematical models represent two‐dimensional free boundary value problems for the Navier‐Stokes equations. In this paper the solvability of the related stationary problems is discussed and computational results are presented. Furthermore, it is shown that depending on the flow parameters like viscosity or density ratios and on the fluxes there can happen nonexistence of steady‐state solutions. For other parameter sets the solution is even unique. Dvieju, tekančiu kanale, klampiu skysčiu srauto uždavinys iškyla taikant ivairias skirtingu rušiu paviršiu padengimo technologijas. Atitinkamas matematinis modelis išreiškiamas dvimačiu kraštiniu uždaviniu su laisvu paviršiumi Navje-Stokso lygtims. Straipsnyje nagrinejamas santykinai stacionaraus uždavinio išsprendžiamumas ir pateikiami skaičiavimo rezultatai. Be to parodoma, kad priklausomai nuo sroves parametru kaip ir nuo klampumo ir tankio santykio stacionarus sprendiniai gali neegzistuoti. Su kitais parametrais egzistuoja tiksliai vienas sprendinys.

Sign in / Sign up

Export Citation Format

Share Document