scholarly journals On the free surface Navier-Stokes equation in the inviscid limit

2011 ◽  
pp. 1-14
Author(s):  
Frederic Rousset
Keyword(s):  
Free Surface ◽  
Stokes Equation ◽  
Inviscid Limit ◽  
Navier Stokes ◽  
Navier Stokes Equation

scholarly journals Drop formation in a one-dimensional approximation of the Navier–Stokes equation

1994 ◽  
Vol 262 ◽  
pp. 205-221 ◽  
Author(s):  
Jens Eggers ◽  
Todd F. Dupont
Keyword(s):  
Free Surface ◽  
Stokes Equation ◽  
Equation Of Motion ◽  
Navier Stokes ◽  
Liquid Jet ◽  
Drop Formation ◽  
Navier Stokes Equation ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
Dimensional Equation

We consider the viscous motion of a thin axisymmetric column of fluid with a free surface. A one-dimensional equation of motion for the velocity and the radius is derived from the Navier–Strokes equation. We compare our results with recent experiments on the breakup of a liquid jet and on the bifurcation of a drop suspended from an orifice. The equations form singularities as the fluid neck is pinching off. The nature of the singularities is investigated in detail.

Analysis of Flow in a Concentric Cylindrical Vessel Using Stream and Vorticity Function

2009 ◽  
Author(s):  
Sukanta Rakshit ◽  
Harsha Bojja
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Stokes Equation ◽  
Vortex Breakdown ◽  
Vortex Formation ◽  
Slip Boundary Condition ◽  
Cylindrical Vessel ◽  
Navier Stokes ◽  
Finite Difference Schemes ◽  
Navier Stokes Equation

This paper reports the numerical results of flow in a concentric cylindrical vessel. Velocity plots are shown to illustrate the swirling cylinder flow inside the cylinder having free surface on top and constant rotating bottom wall. The analysis is carried out axisymmetric using Stream function and Vorticity method by writing Navier-Stokes equation and continuity equation in cylindrical coordinates in form of stream functions and azimuthal vorticity components eliminating the pressure component. Using Finite Difference Schemes, modified Navier-Stokes equation and continuity equations are solved by explicit methods. No-slip boundary condition is assumed at wall to minimize the discontinuity. Vortex formation is shown using contour plots and variation in Reynolds number and dimensions are considered as variable for the system. As the Reynolds number is increased the system undergoes vortex breakdown. Result clearly indicates the formation of another vortex near the free surface illustrating the phenomena of vortex breakdown. Effect of aspect ratio in the nature flow is also shown in the paper. Comparison of numerically achieved results and experimental results are done for validation.

Flow domain identification from free surface velocity in thin inertial films

2013 ◽  
Vol 720 ◽  
pp. 338-356 ◽  
Author(s):  
C. Heining ◽  
T. Pollak ◽  
M. Sellier
Keyword(s):  
Free Surface ◽  
Stokes Equation ◽  
Surface Shape ◽  
Surface Velocity ◽  
Navier Stokes ◽  
Free Surface Velocity ◽  
Navier Stokes Equation ◽  
Domain Identification ◽  
Noisy Input ◽  
Flow Domain

AbstractWe consider the flow of a viscous liquid along an unknown topography. A new strategy is presented to reconstruct the topography and the free surface shape from one component of the free surface velocity only. In contrast to the classical approach in inverse problems based on optimization theory we derive an ordinary differential equation which can be solved directly to obtain the inverse solution. This is achieved by averaging the Navier–Stokes equation and coupling the function parameterizing the flow domain with the free surface velocity. Even though we consider nonlinear systems including inertia and surface tension, the inverse problem can be solved analytically with a Fourier series approach. We test our method on a variety of benchmark problems and show that the analytical solution can be applied to reconstruct the flow domain from noisy input data. It is also demonstrated that the asymptotic approach agrees very well with numerical results of the Navier–Stokes equation. The results are finally confirmed with an experimental study where we measure the free surface velocity for the film flow over a trench and compare the reconstructed topography with the measured one.

Wavelet-distributed approximating functional method for solving the Navier-Stokes equation

1998 ◽  
Vol 115 (1) ◽  
pp. 18-24 ◽  
Author(s):  
G.W. Wei ◽  
D.S. Zhang ◽  
S.C. Althorpe ◽  
D.J. Kouri ◽  
D.K. Hoffman
Keyword(s):  
Stokes Equation ◽  
Functional Method ◽  
Navier Stokes ◽  
Navier Stokes Equation

scholarly journals Generalized Navier–Stokes Equations and Dynamics of Plane Molecular Media

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 288
Author(s):  
Alexei Kushner ◽  
Valentin Lychagin
Keyword(s):  
Carbon Dioxide ◽  
Internal Structure ◽  
Stokes Equation ◽  
Hydrogen Cyanide ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations

The first analysis of media with internal structure were done by the Cosserat brothers. Birkhoff noted that the classical Navier–Stokes equation does not fully describe the motion of water. In this article, we propose an approach to the dynamics of media formed by chiral, planar and rigid molecules and propose some kind of Navier–Stokes equations for their description. Examples of such media are water, ozone, carbon dioxide and hydrogen cyanide.

Sign in / Sign up

Export Citation Format

Share Document