Asymptotic solution of the Navier-Stokes equations for radial fluid flow in the gap between two rotating disks

1983 ◽  
Vol 24 (1) ◽  
pp. 8-12
Author(s):  
P. I. San'kov ◽  
E. M. Smirnov
Keyword(s):  
Fluid Flow ◽  
Asymptotic Solution ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Rotating Disks ◽  
Navier Stokes Equations

Fluid flow over and through a regular bundle of rigid fibres

2016 ◽  
Vol 792 ◽  
pp. 5-35 ◽  
Author(s):  
Giuseppe A. Zampogna ◽  
Alessandro Bottaro
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Flow Field ◽  
Stokes Equations ◽  
Transversely Isotropic ◽  
Navier Stokes ◽  
Leading Order ◽  
Macroscopic Scale ◽  
Navier Stokes Equations ◽  
Homogenized Model

The interaction between a fluid flow and a transversely isotropic porous medium is described. A homogenized model is used to treat the flow field in the porous region, and different interface conditions, needed to match solutions at the boundary between the pure fluid and the porous regions, are evaluated. Two problems in different flow regimes (laminar and turbulent) are considered to validate the system, which includes inertia in the leading-order equations for the permeability tensor through a Oseen approximation. The components of the permeability, which characterize microscopically the porous medium and determine the flow field at the macroscopic scale, are reasonably well estimated by the theory, both in the laminar and the turbulent case. This is demonstrated by comparing the model’s results to both experimental measurements and direct numerical simulations of the Navier–Stokes equations which resolve the flow also through the pores of the medium.

Fluid Structure Interaction Modelling for the Vibration of Tube Bundles: Part I—Analysis of the Fluid Flow in a Tube Bundle

2011 ◽  
Author(s):  
Quentin Desbonnets ◽  
Daniel Broc
Keyword(s):  
Fluid Flow ◽  
Stokes Equations ◽  
Tube Bundle ◽  
Nuclear Industry ◽  
Navier Stokes ◽  
Inertial Effects ◽  
Navier Stokes Equations ◽  
Dissipative Effects ◽  
Tube Bundles ◽  
Interaction Modelling

It is well known that a fluid may strongly influence the dynamic behaviour of a structure. Many different physical phenomena may take place, depending on the conditions: fluid flow, fluid at rest, little or high displacements of the structure. Inertial effects can take place, with lower vibration frequencies, dissipative effects also, with damping, instabilities due to the fluid flow (Fluid Induced Vibration). In this last case the structure is excited by the fluid. Tube bundles structures are very common in the nuclear industry. The reactor cores and the steam generators are both structures immersed in a fluid which may be submitted to a seismic excitation or an impact. In this case the structure moves under an external excitation, and the movement is influence by the fluid. The main point in such system is that the geometry is complex, and could lead to very huge sizes for a numerical analysis. Homogenization models have been developed based on the Euler equations for the fluid. Only inertial effects are taken into account. A next step in the modelling is to build models based on the homogenization of the Navier-Stokes equations. The papers presents results on an important step in the development of such model: the analysis of the fluid flow in a oscillating tube bundle. The analysis are made from the results of simulations based on the Navier-Stokes equations for the fluid. Comparisons are made with the case of the oscillations of a single tube, for which a lot of results are available in the literature. Different fluid flow pattern may be found, depending in the Reynolds number (related to the velocity of the bundle) and the Keulegan-Carpenter number (related to the displacement of the bundle). A special attention is paid to the quantification of the inertial and dissipative effects, and to the forces exchanges between the bundle and the fluid. The results of such analysis will be used in the building of models based on the homogenization of the Navier-Stokes equations for the fluid.

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.

Cellular‐automaton fluids: A model for flow in porous media

Geophysics ◽  
1988 ◽  
Vol 53 (4) ◽  
pp. 509-518 ◽  
Author(s):  
Daniel H. Rothman
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Numerical Methods ◽  
Boundary Conditions ◽  
Pressure Gradient ◽  
Cellular Automaton ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Cellular Automaton Fluids

Numerical models of fluid flow through porous media can be developed from either microscopic or macroscopic properties. The large‐scale viewpoint is perhaps the most prevalent. Darcy’s law relates the chief macroscopic parameters of interest—flow rate, permeability, viscosity, and pressure gradient—and may be invoked to solve for any of these parameters when the others are known. In practical situations, however, this solution may not be possible. Attention is then typically focused on the estimation of permeability, and numerous numerical methods based on knowledge of the microscopic pore‐space geometry have been proposed. Because the intrinsic inhomogeneity of porous media makes the application of proper boundary conditions difficult, microscopic flow calculations have typically been achieved with idealized arrays of geometrically simple pores, throats, and cracks. I propose here an attractive alternative which can freely and accurately model fluid flow in grossly irregular geometries. This new method solves the Navier‐Stokes equations numerically using the cellular‐automaton fluid model introduced by Frisch, Hasslacher, and Pomeau. The cellular‐ automaton fluid is extraordinarily simple—particles of unit mass traveling with unit velocity reside on a triangular lattice and obey elementary collision rules—but is capable of modeling much of the rich complexity of real fluid flow. Cellular‐automaton fluids are applicable to the study of porous media. In particular, numerical methods can be used to apply the appropriate boundary conditions, create a pressure gradient, and measure the permeability. Scale of the cellular‐automaton lattice is an important issue; the linear dimension of a void region must be approximately twice the mean free path of a lattice gas particle. Finally, an example of flow in a 2-D porous medium demonstrates not only the numerical solution of the Navier‐Stokes equations in a highly irregular geometry, but also numerical estimation of permeability and a verification of Darcy’s law.

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