Cosserat Modeling of Turbulent Plane-Couette and Pressure-Driven Channel Flows

2007 ◽  
Vol 129 (6) ◽  
pp. 806-810 ◽  
Author(s):  
Amin Moosaie ◽  
Gholamali Atefi
Keyword(s):  
Stokes Equations ◽  
Irreversible Thermodynamics ◽  
Channel Flows ◽  
Navier Stokes ◽  
Flat Plates ◽  
Navier Stokes Equations ◽  
Micropolar Fluids ◽  
Cosserat Model ◽  
Dissipative Boundary ◽  
Pressure Driven

The theory of micropolar fluids based on a Cosserat continuum model is utilized for analysis of two benchmarks, namely, plane-Couette and pressure-driven channel flows. In the obtained theoretical velocity distributions, some new terms have appeared in addition to linear and parabolic distributions of classical fluid mechanics based on the Navier-Stokes equations. Utilizing the principles of irreversible thermodynamics, a new dissipative boundary condition is developed for angular velocity at flat plates by taking the couple-stress vector into account. The obtained results for the velocity profiles have been compared to results of recent and classical experiments. This paper demonstrates that continuum mechanical theories of higher orders, for instance Cosserat model, are able to describe a complex phenomenon, such as hydrodynamic turbulence, more precisely.

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.

Double diffusive effects on pressure-driven miscible displacement flows in a channel

2012 ◽  
Vol 712 ◽  
pp. 579-597 ◽  
Author(s):  
Manoranjan Mishra ◽  
A. De Wit ◽  
Kirti Chandra Sahu
Keyword(s):  
Stokes Equations ◽  
Miscible Displacement ◽  
Interfacial Instability ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Finite Volume Approach ◽  
Diffusive Effects ◽  
The Moment ◽  
Double Diffusive ◽  
Pressure Driven

AbstractThe pressure-driven miscible displacement of a less viscous fluid by a more viscous one in a horizontal channel is studied. This is a classically stable system if the more viscous solution is the displacing one. However, we show by numerical simulations based on the finite-volume approach that, in this system, double diffusive effects can be destabilizing. Such effects can appear if the fluid consists of a solvent containing two solutes both influencing the viscosity of the solution and diffusing at different rates. The continuity and Navier–Stokes equations coupled to two convection–diffusion equations for the evolution of the solute concentrations are solved. The viscosity is assumed to depend on the concentrations of both solutes, while density contrast is neglected. The results demonstrate the development of various instability patterns of the miscible ‘interface’ separating the fluids provided the two solutes diffuse at different rates. The intensity of the instability increases when increasing the diffusivity ratio between the faster-diffusing and the slower-diffusing solutes. This brings about fluid mixing and accelerates the displacement of the fluid originally filling the channel. The effects of varying dimensionless parameters, such as the Reynolds number and Schmidt number, on the development of the ‘interfacial’ instability pattern are also studied. The double diffusive instability appears after the moment when the invading fluid penetrates inside the channel. This is attributed to the presence of inertia in the problem.

Flow past a row of flat plates at large Reynolds numbers

1993 ◽  
Vol 441 (1912) ◽  
pp. 211-235 ◽  
Keyword(s):  
Stokes Equations ◽  
Solution Procedure ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
Flat Plates ◽  
Navier Stokes Equations ◽  
Element Discretization ◽  
Flow Past ◽  
High Reynolds ◽  
Outflow Boundary

The steady, incompressible, high Reynolds number, viscous flow past a row of flat plates is computed by a Galerkin finite element discretization of the Navier-Stokes equations in the streamfunction/vorticity formulation. A novel implementation of the inflow and outflow boundary conditions is described, which combines numerical stability with computational economy in the solution procedure. The calculations reported here cover the range of medium and small blockage ratios, i. e. 5 ≼ a ≼ 25 (where a is the inverse blockage ratio). A transition is found from narrow wake eddies for small values of a , to wide wake eddies for values of a above a crit ≈ 15. This transition is in general agreement with the trends reported earlier by Fornberg (1991), for the related problem of flow past a row of circular cylinders (for which a crit was approximately 8).

Numerical Solution of the Three-Dimensional Navier-Stokes Equations With Applications to Channel Flows and a Buoyant Jet in a Cross Flow

1975 ◽  
Vol 42 (3) ◽  
pp. 575-579 ◽  
Author(s):  
J. C. Chien ◽  
J. A. Schetz
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Cross Flow ◽  
Boussinesq Approximation ◽  
Channel Flows ◽  
Navier Stokes ◽  
Buoyant Jet ◽  
Navier Stokes Equations ◽  
Eddy Viscosity Model ◽  
Good Agreement

The steady, three-dimensional, incompressible Navier-Stokes equations written in terms of velocity, vorticity, and temperature are solved numerically for channel flows and a jet in a cross flow. Upwind differencing of the convection term was used in the computation for convergence and simplicity. Comparisons were made with experimental results for laminar flow in the entrance region of a square channel, and good agreement was obtained. The method was also applied to a turbulent, buoyant jet in a cross-flow problem with the Boussinesq approximation and a constant Prandtl eddy viscosity model. Good agreement with experiment was obtained in this case also.

Steady two-dimensional flow through a row of normal flat plates

1990 ◽  
Vol 210 ◽  
pp. 281-302 ◽  
Author(s):  
D. B. Ingham ◽  
T. Tang ◽  
B. R. Morton
Keyword(s):  
Finite Difference ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Corner Singularities ◽  
Flat Plates ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
Good Agreement

A numerical and experimental study is described for the two-dimensional steady flow through a uniform cascade of normal flat plates. The Navier–Stokes equations are written in terms of the stream function and vorticity and are solved using a second-order-accurate finite-difference scheme which is based on a modified procedure to preserve accuracy and iterative convergence at higher Reynolds numbers. The upstream and downstream boundary conditions are discussed and an asymptotic solution is employed both upstream and downstream. A frequently used method for dealing with corner singularities is shown to be inaccurate and a method for overcoming this problem is described. Numerical solutions have been obtained for blockage ratio of 50 % and Reynolds numbers in the range 0 [les ]R[les ] 500 and results for both the lengths of attached eddies and the drag coefficients are presented. The calculations indicate that the eddy length increases linearly withR, at least up toR= 500, and that the multiplicative constant is in very good agreement with the theoretical prediction of Smith (1985a), who considered a related problem. In the case ofR= 0 the Navier–Stokes equations are solved using the finite-difference scheme and a modification of the boundary-element method which treats the corner singularities. The solutions obtained by the two methods are compared and the results are shown to be in good agreement. An experimental investigation has been performed at small and moderate values of the Reynolds numbers and there is excellent agreement with the numerical results both for flow streamlines and eddy lengths.

scholarly journals ON NONISOTHERMAL TWO‐FLUID CHANNEL FLOWS

2007 ◽  
Vol 12 (1) ◽  
pp. 143-156
Author(s):  
Jajanek Sokolowsky
Keyword(s):  
Thermocapillary Convection ◽  
Stokes Equations ◽  
Boussinesq Approximation ◽  
Channel Flows ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Free Boundary Value Problems ◽  
Fluid Channel ◽  
Stationary Problems ◽  
Two Fluid

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 or their modifications. In this paper we are concerned with the so‐called Boussinesq‐approximation of the coupled heat‐ and mass transfer. Thermocapillary convection is included. The solvability of two related stationary problems is discussed. The solution techniques of both problems are quite different. The obtained results generalize previous results for similar isothermal problems.

A numerical study of vortex shedding from flat plates with square leading and trailing edges

1992 ◽  
Vol 236 ◽  
pp. 445-460 ◽  
Author(s):  
Yuji Ohya ◽  
Yasuharu Nakamura ◽  
Shigehira Ozono ◽  
Hideki Tsuruta ◽  
Ryuzo Nakayama
Keyword(s):  
Shear Layer ◽  
Vortex Shedding ◽  
Stokes Equations ◽  
Numerical Study ◽  
Vortical Flow ◽  
Navier Stokes ◽  
Shear Layer Instability ◽  
Flat Plates ◽  
Navier Stokes Equations ◽  
Trailing Edges

This paper describes a numerical study of the flow around flat plates with square leading and trailing edges on the basis of a finite-difference analysis of the two-dimensional Navier—Stokes equations. The chord-to-thickness ratio of a plate, d/h, ranges from 3 to 9 and the value of the Reynolds number based on the plate's thickness is constant and equal to 103. The numerical computation confirms the finding obtained in our previous experiments that vortex shedding from flat plates with square leading and trailing edges is caused by the impinging-shear-layer instability. In particular, the Strouhal number based on the plate's chord increases stepwise with increasing d/h in agreement with the experiment. Numerical analyses also provide some crucial information on the complicated vortical flow occurring near the trailing edge in conjunction with the vortex shedding mechanism. Finally, the mechanism of the impinging-shear-layer instability is discussed in the light of the experimental and numerical findings.

Pressure-driven flow of a thin viscous sheet

1995 ◽  
Vol 292 ◽  
pp. 359-376 ◽  
Author(s):  
B. W. Van De Fliert ◽  
P. D. Howell ◽  
J. R. Ockenden
Keyword(s):  
Shell Theory ◽  
Stokes Equations ◽  
Thin Sheet ◽  
Theory Model ◽  
Navier Stokes ◽  
Coordinate Frame ◽  
Leading Order ◽  
Navier Stokes Equations ◽  
Pressure Driven Flow ◽  
Pressure Driven

Systematic asymptotic expansions are used to find the leading-order equations for the pressure-driven flow of a thin sheet of viscous fluid. Assuming the fluid geometry to be slender with non-negligible curvatures, the Navier–Stokes equations with appropriate free-surface conditions are simplified to give a ‘shell-theory’ model. The fluid geometry is not known in advance and a time-dependent coordinate frame has to be employed. The effects of surface tension, gravity and inertia can also be incorporated in the model.

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