An Asymptotic Solution for the Laminar Flow of a Thin Film on a Rotating Disk

1973 ◽  
Vol 40 (1) ◽  
pp. 43-47 ◽  
Author(s):  
J. W. Rauscher ◽  
R. E. Kelly ◽  
J. D. Cole
Keyword(s):  
Thin Film ◽  
Asymptotic Solution ◽  
Radial Direction ◽  
Stokes Equations ◽  
Fluid Flows ◽  
Rotating Disk ◽  
Navier Stokes ◽  
Rossby Number ◽  
Navier Stokes Equations ◽  
Higher Order Terms

An analysis on the basis of the Navier-Stokes equations is made of the flow of a liquid in a thin film on a rotating disk. Fluid flows outward in the radial direction due to the centrifugal force. An asymptotic solution valid for small values of the Rossby number is presented. Higher-order terms correcting for the effects of convection, Coriolis acceleration, radial diffusion, surface curvature, and surface tension are found and discussed on a physical basis.

Numerical Integration of the Navier-Stokes Equations for a Disk Rotating in a Housing

1985 ◽  
Vol 40 (8) ◽  
pp. 789-799 ◽  
Author(s):  
A. F. Borghesani
Keyword(s):  
Boundary Layer ◽  
Cylindrical Cavity ◽  
Boundary Layer Thickness ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Rotating Disk ◽  
Infinite Medium ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Viscous Torque

The Navier-Stokes equations for the fluid motion induced by a disk rotating inside a cylindrical cavity have been integrated for several values of the boundary layer thickness d. The equivalence of such a device to a rotating disk immersed in an infinite medium has been shown in the limit as d → 0. From that solution and taking into account edge effect corrections an equation for the viscous torque acting on the disk has been derived, which depends only on d. Moreover, these results justify the use of a rotating disk to perform accurate viscosity measurements.

scholarly journals 3D Hydrodynamic Modelling Enhances the Design of Tendaho Dam Spillway, Ethiopia

Water ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 82
Author(s):  
Getnet Kebede Demeke ◽  
Dereje Hailu Asfaw ◽  
Yilma Seleshi Shiferaw
Keyword(s):  
Stokes Equations ◽  
Flow Behavior ◽  
Fluid Flows ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Hydraulic Structures ◽  
Hydrodynamic Modelling ◽  
Navier Stokes Equations ◽  
Pressure Distributions ◽  
Computational Fluid Dynamics Cfd

Hydraulic structures are often complex and in many cases their designs require attention so that the flow behavior around hydraulic structures and their influence on the environment can be predicted accurately. Currently, more efficient computational fluid dynamics (CFD) codes can solve the Navier–Stokes equations in three-dimensions and free surface computation in a significantly improved manner. CFD has evolved into a powerful tool in simulating fluid flows. In addition, CFD with its advantages of lower cost and greater flexibility can reasonably predict the mean characteristics of flows such as velocity distributions, pressure distributions, and water surface profiles of complex problems in hydraulic engineering. In Ethiopia, Tendaho Dam Spillway was constructed recently, and one flood passed over the spillway. Although the flood was below the designed capacity, there was an overflow due to superelevation at the bend. Therefore, design of complex hydraulic structures using the state-of- art of 3D hydrodynamic modelling enhances the safety of the structures. 3D hydrodynamic modelling was used to verify the safety of the spillway using designed data and the result showed that the constructed hydraulic section is not safe unless it is modified.

scholarly journals Generalized Navier–Stokes equations with nonlinear anisotropic viscosity

2019 ◽  
Vol 17 (06) ◽  
pp. 977-1003
Author(s):  
H. B. de Oliveira
Keyword(s):  
Stokes Equations ◽  
Fluid Flows ◽  
Ekman Layer ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Very Weak Solutions ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Nonlinear Viscosity ◽  
Anisotropic Viscosity

The purpose of this work is to study the generalized Navier–Stokes equations with nonlinear viscosity that, in addition, can be fully anisotropic. Existence of very weak solutions is proved for the associated initial and boundary-value problem, supplemented with no-slip boundary conditions. We show that our existence result is optimal in some directions provided there is some compensation in the remaining directions. A particular simplification of the problem studied here, reduces to the Navier–Stokes equations with (linear) anisotropic viscosity used to model either the turbulence or the Ekman layer in atmospheric and oceanic fluid flows.

Two-Fluid Flow Between Rotating Annular Disks

1976 ◽  
Vol 98 (2) ◽  
pp. 214-222 ◽  
Author(s):  
J. E. Zweig ◽  
H. J. Sneck
Keyword(s):  
Annular Flow ◽  
Stokes Equations ◽  
Fluid Flows ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Two Fluids ◽  
Small Clearance ◽  
Annular Disks ◽  
Two Fluid

The general hydrodynamic behavior at small clearance Reynolds numbers of two fluids of different density and viscosity occupying the finite annular space between a rotating and stationary disk is explored using a simplified version of the Navier-Stokes equations which retains only the centrifugal force portion of the inertia terms. A criterion for selecting the annular flow fields that are compatible with physical reservoirs is established and then used to determine the conditions under which two-fluid flows in the annulus might be expected for specific fluid combinations.

Attractors for the modifications of the three-dimensional Navier-Stokes equations

1994 ◽  
Vol 346 (1679) ◽  
pp. 173-190 ◽  
Keyword(s):  
Viscous Fluid ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Fluid Flows ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Initial Boundary Value ◽  
Dimensional Domain

The modifications of the three-dimensional Navier-Stokes equations, which I suggested earlier for the description of viscous fluid flows with large gradients of velocities, are considered. It is proved that the first initial-boundary value problem for these equations in any bounded three-dimensional domain has a compact minimal global B-attractor. Some properties of the attractor are established.

Inward Flow Between Stationary and Rotating Disks

2014 ◽  
Vol 136 (10) ◽  
Author(s):  
Achhaibar Singh
Keyword(s):  
Laminar Flow ◽  
Flow Field ◽  
Velocity Distribution ◽  
Stokes Equations ◽  
Tangential Velocity ◽  
Rotating Disk ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Rotating Disks ◽  
Navier Stokes Equations

The present study predicts the flow field and the pressure distribution for a laminar flow in the gap between a stationary and a rotating disk. The fluid enters through the peripheral gap between two concentric disks and converges to the center where it discharges axially through a hole in one of the disks. Closed form expressions have been derived by simplifying the Navier– Stokes equations. The expressions predict the backflow near the rotating disk due to the effect of centrifugal force. A convection effect has been observed in the tangential velocity distribution at high throughflow Reynolds numbers.

Melting From a Horizontal Rotating Disk

1989 ◽  
Vol 56 (1) ◽  
pp. 47-50 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Heat Transfer ◽  
Numerical Integration ◽  
Stokes Equations ◽  
Rotating Disk ◽  
Similarity Solutions ◽  
Navier Stokes ◽  
Relative Importance ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Transfer Rates

Melting of a disk is facilitated by rotation. The problem is governed by a nondimensional parameter α which represents the relative importance of injection (melt) rate and rotation times viscosity. The nonlinear governing equations are solved by perturbations for small α and numerical integration for arbitrary α. Torque and heat transfer rates are found. The solution is one of the rare exact similarity solutions of the Navier-Stokes equations.

scholarly journals On singular limits arising in the scale analysis of stratified fluid flows

2016 ◽  
Vol 26 (03) ◽  
pp. 419-443 ◽  
Author(s):  
Eduard Feireisl ◽  
Rupert Klein ◽  
Antonín Novotný ◽  
Ewelina Zatorska
Keyword(s):  
Transport Equation ◽  
Stokes System ◽  
Stokes Equations ◽  
Potential Temperature ◽  
Fluid Flows ◽  
Navier Stokes ◽  
Flat Torus ◽  
Navier Stokes Equations ◽  
Singular Limits ◽  
Order Variation

We study the low Mach low Freude numbers limit in the compressible Navier–Stokes equations and the transport equation for evolution of an entropy variable — the potential temperature [Formula: see text]. We consider the case of well-prepared initial data on “flat” torus and Reynolds number tending to infinity, and the case of ill-prepared data on an infinite slab. In both cases, we show that the weak solutions to the primitive system converge to the solution to the anelastic Navier–Stokes system and the transport equation for the second-order variation of [Formula: see text].

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