Internal laminar flow

2018 ◽  
Author(s):  
Marcel Escudier
Keyword(s):  
Poiseuille Flow ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Concentric Cylinder ◽  
Navier Stokes Equations ◽  
Concentric Cylinders ◽  
Constant Viscosity ◽  
Pressure Driven Flow

In this chapter it is shown that solutions to the Navier-Stokes equations can be derived for steady, fully developed flow of a constant-viscosity Newtonian fluid through a cylindrical duct. Such a flow is known as a Poiseuille flow. For a pipe of circular cross section, the term Hagen-Poiseuille flow is used. Solutions are also derived for shear-driven flow within the annular space between two concentric cylinders or in the space between two parallel plates when there is relative tangential movement between the wetted surfaces, termed Couette flows. The concepts of wetted perimeter and hydraulic diameter are introduced. It is shown how the viscometer equations result from the concentric-cylinder solutions. The pressure-driven flow of generalised Newtonian fluids is also discussed.

New boundary conditions in the transition régime

1968 ◽  
Vol 2 (3) ◽  
pp. 293-310 ◽  
Author(s):  
Carlo Cercignani ◽  
Gino Tironi
Keyword(s):  
Boundary Conditions ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Slip Flow ◽  
Navier Stokes ◽  
Main Body ◽  
Parallel Plates ◽  
Navier Stokes Equations ◽  
Concentric Cylinders ◽  
Flow Heat

Starting from the Boltzmann equation, new boundary conditions are derived to be matched with the Navier—Stokes equations, that are supposed to hold in the main body of a gas. The idea upon which this method is based goes back to Maxwell and Langmuir. Since the distribution function is supposed to be completely determined by the Navier—Stokes equations, this new set of boundary conditions extends in some sense the validity of the macroscopic equations to the transition and free molecular régimes. In fact, it is shown that the free molecular and slip flow régimes are correctly described by this method; the latter is also supposed to give a reasonable approximation for the complete range of Knudsen numbers. The new procedure is applied to different problems such as plane Couette flow, plane and cylindrical Poiseuile flow, heat transfer between parallel plates and concentric cylinders. Results are obtained and compared with the exact numerical solutions for the above-mentioned problems.

Stability of Hagen-Poiseuille flow with superimposed rigid rotation

1976 ◽  
Vol 73 (1) ◽  
pp. 153-164 ◽  
Author(s):  
P.-A. Mackrodt
Keyword(s):  
Poiseuille Flow ◽  
Pipe Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Neutral Curve ◽  
Rigid Rotation ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Navier Stokes Equations

The linear stability of Hagen-Poiseuille flow (Poiseuille pipe flow) with superimposed rigid rotation against small three-dimensional disturbances is examined at finite and infinite axial Reynolds numbers. The neutral curve, which is obtained by numerical solution of the system of perturbation equations (derived from the Navier-Stokes equations), has been confirmed for finite axial Reynolds numbers by a few simple experiments. The results suggest that, at high axial Reynolds numbers, the amount of rotation required for destabilization could be small enough to have escaped notice in experiments on the transition to turbulence in (nominally) non-rotating pipe flow.

scholarly journals Asymptotically based self-similarity solution of the Navier–Stokes equations for a porous tube with a non-circular cross-section

2017 ◽  
Vol 826 ◽  
pp. 396-420 ◽  
Author(s):  
M. Bouyges ◽  
F. Chedevergne ◽  
G. Casalis ◽  
J. Majdalani
Keyword(s):  
Cross Section ◽  
Similarity Solution ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Internal Flow ◽  
Navier Stokes ◽  
Solid Rocket Motor ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Radial Deviation

This work introduces a similarity solution to the problem of a viscous, incompressible and rotational fluid in a right-cylindrical chamber with uniformly porous walls and a non-circular cross-section. The attendant idealization may be used to model the non-reactive internal flow field of a solid rocket motor with a star-shaped grain configuration. By mapping the radial domain to a circular pipe flow, the Navier–Stokes equations are converted to a fourth-order differential equation that is reminiscent of Berman’s classic expression. Then assuming a small radial deviation from a fixed chamber radius, asymptotic expansions of the three-component velocity and pressure fields are systematically pursued to the second order in the radial deviation amplitude. This enables us to derive a set of ordinary differential relations that can be readily solved for the mean flow variables. In the process of characterizing the ensuing flow motion, the axial, radial and tangential velocities are compared and shown to agree favourably with the simulation results of a finite-volume Navier–Stokes solver at different cross-flow Reynolds numbers, deviation amplitudes and circular wavenumbers.

scholarly journals Subcritical transition in channel flows

2002 ◽  
Vol 451 ◽  
pp. 35-97 ◽  
Author(s):  
S. JONATHAN CHAPMAN
Keyword(s):  
Poiseuille Flow ◽  
Stokes Equations ◽  
Domain Of Attraction ◽  
Reynolds Numbers ◽  
Linear Instability ◽  
Laminar Flows ◽  
Navier Stokes ◽  
Plane Poiseuille Flow ◽  
Navier Stokes Equations ◽  
Laminar State

Certain laminar flows are known to be linearly stable at all Reynolds numbers, R, although in practice they always become turbulent for sufficiently large R. Other flows typically become turbulent well before the critical Reynolds number of linear instability. One resolution of these paradoxes is that the domain of attraction for the laminar state shrinks for large R (as Rγ say, with γ < 0), so that small but finite perturbations lead to transition. Trefethen et al. (1993) conjectured that in fact γ <−1. Subsequent numerical experiments by Lundbladh, Henningson & Reddy (1994) indicated that for streamwise initial perturbations γ =−1 and −7/4 for plane Couette and plane Poiseuille flow respectively (using subcritical Reynolds numbers for plane Poiseuille flow), while for oblique initial perturbations γ =−5/4 and −7/4 Here, through a formal asymptotic analysis of the Navier–Stokes equations, it is found that for streamwise initial perturbations γ =−1 and −3/2 for plane Couette and plane Poiseuille flow respectively (factoring out the unstable modes for plane Poiseuille flow), while for oblique initial perturbations γ =−1 and −5/4. Furthermore it is shown why the numerically determined threshold exponents are not the true asymptotic values.

Nanofluidic transport and formation of nano-emulsions

2008 ◽  
Vol 2 (1) ◽  
Author(s):  
P.A. Chando ◽  
S.S. Ray ◽  
A.L. Yarin
Keyword(s):  
Stokes Equations ◽  
Theoretical Calculations ◽  
Ccd Camera ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Flow Rates ◽  
Fluid Layers ◽  
Pressure Driven Flow ◽  
Two Fluid

The focus of this research is to study fluidic transport through carbon nanotubes. The nanotubes studied were formed by electrospinning Polycaplrolactone (PCL) nanofibers and then using them as channel templates in colyacrylamide blocks which were carbonized. A pressure driven flow is initiated through the nanochannels and the rate of emulsion formation is recorded with a CCD camera. Theoretical calculations are conducted for nanochannels because in many experiments, the nanochannels studied have two-phase flows, which make direct application of Poiseuille law impossible. The model used for the calculations is a slit with two fluid layers in between. In particular, in many experiments, decane-air system is of interest. The calculations are carried out using the Navier-Stokes equations. The results of the model are used to evaluate experimental volumetric flow rates and find the distribution of air and decane in the nanochannels.

scholarly journals CENTRIFUGAL DESTABILIZATION AND RESTABILIZATION OF PLANE SHEAR FLOWS

1996 ◽  
Vol 06 (02) ◽  
pp. 409-413
Author(s):  
A. J. CONLEY
Keyword(s):  
Viscous Fluid ◽  
Linear Stability ◽  
Stokes Equations ◽  
Path Following ◽  
Incompressible Viscous Fluid ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Plane Shear ◽  
Navier Stokes Equations ◽  
Spectral Techniques

The flow of an incompressible viscous fluid between parallel plates becomes unstable when the plates are tumbled. As the tumbling rate increases, the flow restabilizes. This phenomenon is elucidated by path-following techniques. The solution of the Navier-Stokes equations is approximated by spectral techniques. The linear stability of these solutions is studied.

Flow Through Rough Microchannels: A Lubrication Perspective

2003 ◽  
Author(s):  
S. Boedo
Keyword(s):  
Poiseuille Flow ◽  
Stokes Equations ◽  
Upper And Lower Bounds ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Test Setup ◽  
One Dimensional ◽  
Reference Velocity ◽  
Sample Application ◽  
Flow Through

This paper provides concise specifications where idealized Poiseuille flow is applicable in representing one-dimensional flow through wide, thin, rough microchannels subjected to prescribed pressures at the channel ends. Starting with the general (compressible) form of the Navier-Stokes equations, new expressions which discuss the effect of body forces on flow through thin channels are first presented, leading to upper and lower bounds on channel reference velocity where idealized Poiseuille flow dominates. These results are combined with previously published studies related to the predicability of flow through stochastically rough surfaces. An arbitrarily chosen microchannel model based loosely on a previously published experimental test setup is used as a sample application.

scholarly journals An Axisymmetric Squeezing Fluid Flow between the Two Infinite Parallel Plates in a Porous Medium Channel

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
S. Islam ◽  
Hamid Khan ◽  
Inayat Ali Shah ◽  
Gul Zaman
Keyword(s):  
Differential Equation ◽  
Porous Medium ◽  
Fluid Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Transform Method ◽  
Navier Stokes Equations ◽  
Differential Transform ◽  
Fluid Parameters

The flow between two large parallel plates approaching each other symmetrically in a porous medium is studied. The Navier-Stokes equations have been transformed into an ordinary nonlinear differential equation using a transformationψ(r,z)=r2F(z). Solution to the problem is obtained by using differential transform method (DTM) by varying different Newtonian fluid parameters and permeability of the porous medium. Result for the stream function is presented. Validity of the solutions is confirmed by evaluating the residual in each case, and the proposed scheme gives excellent and reliable results. The influence of different parameters on the flow has been discussed and presented through graphs.

Normal modes for a stratified viscous fluid layer

2002 ◽  
Vol 132 (3) ◽  
pp. 611-625 ◽  
Author(s):  
K. F. Gurski ◽  
R. L. Pego
Keyword(s):  
Stokes Equations ◽  
Fluid Layer ◽  
Normal Modes ◽  
Internal Gravity Waves ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Damped Oscillations ◽  
Small Constant ◽  
Constant Viscosity ◽  
Stratified Viscous Fluid

We consider internal gravity waves in a stratified fluid layer with rigid horizontal boundaries and periodic boundary conditions on the sides at constant temperature with a small constant viscosity, modelled using the incompressible Navier-Stokes equations. Using operator-theoretic methods to study the damping rates of internal waves we prove there are non-oscillatory wave modes with arbitrarily small damping rates. We provide an asymptotic approximation for these non-oscillatory modes. Additionally, we find that the eigenvalues for damped oscillations are in an explicitly describable half-ring.

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