Flow in a Tube With a Circumferential Wall Cavity

1973 ◽  
Vol 40 (2) ◽  
pp. 355-361 ◽  
Author(s):  
J. F. Stevenson
Keyword(s):  
Stokes Equations ◽  
Separated Flow ◽  
Mesh Size ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Tube Radius ◽  
Cavity Depth ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
Stress Profiles

Streamlines, velocity profiles, and wall shear stress profiles are presented for a numerical solution of the Navier-Stokes equations for steady flow through a tube (radius = 1) with a circumferential wall cavity (depth = 1.33, length = 1.33). For tube Reynolds numbers equal to 0, 50, and 200, the numerical calculations show that a region of separated flow with closed streamlines exists in the cavity and that the attachment points for the separating streamline are located along the cavity wall. An assessment is made of the dependence of the numerical results on mesh size and the type of vorticity boundary condition applied at the protruding corners.

scholarly journals Quantifying Compressibility and Slip in Multiparticle Collision (MPC) Flow Through a Local Constriction

2021 ◽  
Author(s):  
Tahmina Akhter ◽  
Katrin Rohlf
Keyword(s):  
Stokes Equations ◽  
Equations Of Motion ◽  
Wall Slip ◽  
Reynolds Numbers ◽  
Ideal Gas ◽  
Navier Stokes ◽  
Numerical Work ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
Generalized Boundary Condition

The flow of a compressible fluid with slip through a cylinder with an asymmetric local constriction has been considered both numerically, as well as analytically. For the numerical work, a particle-based method whose dynamics is governed by the multiparticle collision (MPC) rule has been used together with a generalized boundary condition that allows for slip at the wall. Since it is well known that an MPC system corresponds to an ideal gas and behaves like a compressible, viscous flow on average, an approximate analytical solution has been derived from the compressible Navier–Stokes equations of motion coupled to an ideal gas equation of state using the Karman–Pohlhausen method. The constriction is assumed to have a polynomial form, and the location of maximum constriction is varied throughout the constricted portion of the cylinder. Results for centerline densities and centerline velocities have been compared for various Reynolds numbers, Mach numbers, wall slip values and flow geometries.

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 Quantifying Compressibility and Slip in Multiparticle Collision (MPC) Flow Through a Local Constriction

2021 ◽  
Author(s):  
Tahmina Akhter ◽  
Katrin Rohlf
Keyword(s):  
Stokes Equations ◽  
Equations Of Motion ◽  
Wall Slip ◽  
Reynolds Numbers ◽  
Ideal Gas ◽  
Navier Stokes ◽  
Numerical Work ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
Generalized Boundary Condition

The flow of a compressible fluid with slip through a cylinder with an asymmetric local constriction has been considered both numerically, as well as analytically. For the numerical work, a particle-based method whose dynamics is governed by the multiparticle collision (MPC) rule has been used together with a generalized boundary condition that allows for slip at the wall. Since it is well known that an MPC system corresponds to an ideal gas and behaves like a compressible, viscous flow on average, an approximate analytical solution has been derived from the compressible Navier–Stokes equations of motion coupled to an ideal gas equation of state using the Karman–Pohlhausen method. The constriction is assumed to have a polynomial form, and the location of maximum constriction is varied throughout the constricted portion of the cylinder. Results for centerline densities and centerline velocities have been compared for various Reynolds numbers, Mach numbers, wall slip values and flow geometries.

The flow of a viscous incompressible fluid past a normal flat plate at low and intermediate Reynolds numbers: the wake

1985 ◽  
Vol 160 ◽  
pp. 369-383 ◽  
Author(s):  
J. D. Hudson ◽  
S. C. R. Dennis
Keyword(s):  
Flat Plate ◽  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Separated Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Good Comparison ◽  
Method Of Solution ◽  
Vortex Centre

The Navier-Stokes equations are solved numerically for the steady separated flow past a normal flat plate for Reynolds numbers in the range 0.1 ≤ R ≤ 20. Eddy dimensions together with the position of the vortex centre are presented and compared with the few other estimates and predictions available. Streamlines and equivorticity lines are also given. The main result of interest is the extremely good comparison with experimental results over this range of Reynolds numbers. The method of solution is based on an artificial time-dependent procedure using a distorted time. Results are given only for the steady-state flow.

Numerical Solutions of Viscous Flow through a Pipe Orifice at Low Reynolds Numbers

1968 ◽  
Vol 10 (2) ◽  
pp. 133-140 ◽  
Author(s):  
R. D. Mills
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Axially Symmetric ◽  
Navier Stokes Equations ◽  
Low Reynolds Numbers ◽  
Flow Through ◽  
Good Agreement

Numerical solutions of the Navier-Stokes equations have been obtained in the low range of Reynolds numbers for steady, axially symmetric, viscous, incompressible fluid flow through an orifice in a circular pipe with a fixed orifice/pipe diameter ratio. Streamline patterns and vorticity contours are presented as functions of Reynolds number. The theoretically determined discharge coefficients are in good agreement with experimental results of Johansen (2).

Steady flow through a channel with a symmetrical constriction in the form of a step

1980 ◽  
Vol 372 (1750) ◽  
pp. 393-414 ◽  
Keyword(s):  
Asymptotic Theory ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Volumetric Flow Rate ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Uniform Grids ◽  
Flow Through ◽  
Good Agreement

Numerical solutions of the Navier-Stokes equations are given for the steady, two-dimensional, laminar flow of an incompressible fluid through a channel with a symmetric constriction in the form of a semi-infinite step change in width. The flow proceeds from a steady Poiseuille velocity distribution far enough upstream of the step in the wider part of the channel to a corresponding distribution downstream in the narrower part and is assumed to remain symmetrical about the centre line of the channel. The numerical scheme involves an accurate and efficient centred difference treatment developed by Dennis & Hudson (1978) and results are obtained for Reynolds numbers, based on half the volumetric flow rate, up to 2000. For a step that halves the width of the channel it is found that very fine uniform grids, with 80 intervals spaced across half of the wider channel upstream, are necessary for resolution of the solution for the flow downstream of the onset of the step. Slightly less refined grids are adequate to resolve the flow upstream. The calculated flow ahead of the step exhibits very good agreement with the asymptotic theory of Smith (1979 b)for Reynolds numbers greater than about 100; indeed, comparisons of the upstream separation position and of the wall vorticity nearby are believed to yield the best agreement between numerical and asymptotic solutions yet found. Downstream there is also qualitative agreement regarding separation and reattachment as the grid size is refined in the numerical results.

scholarly journals An Alternative HSS Preconditioner for the Unsteady Incompressible Navier-Stokes Equations in Rotation Form

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Jia Liu
Keyword(s):  
Iterative Method ◽  
Krylov Subspace ◽  
Stokes Equations ◽  
Mesh Size ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Preconditioned Iterative ◽  
Preconditioned Iterative Methods

We study the preconditioned iterative method for the unsteady Navier-Stokes equations. The rotation form of the Oseen system is considered. We apply an efficient preconditioner which is derived from the Hermitian/Skew-Hermitian preconditioner to the Krylov subspace-iterative method. Numerical experiments show the robustness of the preconditioned iterative methods with respect to the mesh size, Reynolds numbers, time step, and algorithm parameters. The preconditioner is efficient and easy to apply for the unsteady Oseen problems in rotation form.

Simulation of Unsteady Flow Around a Cylinder

2015 ◽  
Vol 3 (2) ◽  
pp. 28-49
Author(s):  
Ridha Alwan Ahmed
Keyword(s):  
Stokes Equations ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Mean Value ◽  
Navier Stokes ◽  
Cylinder Surface ◽  
Navier Stokes Equations ◽  
Flow Around A Cylinder ◽  
Numerical Grid ◽  
Good Agreement

       In this paper, the phenomena of vortex shedding from the circular cylinder surface has been studied at several Reynolds Numbers (40≤Re≤ 300).The 2D, unsteady, incompressible, Laminar flow, continuity and Navier Stokes equations have been solved numerically by using CFD Package FLUENT. In this package PISO algorithm is used in the pressure-velocity coupling.        The numerical grid is generated by using Gambit program. The velocity and pressure fields are obtained upstream and downstream of the cylinder at each time and it is also calculated the mean value of drag coefficient and value of lift coefficient .The results showed that the flow is strongly unsteady and unsymmetrical at Re>60. The results have been compared with the available experiments and a good agreement has been found between them

scholarly journals Transient Pressure-Driven Electroosmotic Flow through Elliptic Cross-Sectional Microchannels with Various Eccentricities

Computation ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 27
Author(s):  
Nattakarn Numpanviwat ◽  
Pearanat Chuchard
Keyword(s):  
Laplace Transform ◽  
Electroosmotic Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Mathieu Functions ◽  
Navier Stokes Equations ◽  
Flow Rates ◽  
Elliptic Cross ◽  
Flow Through ◽  
Relative Errors

The semi-analytical solution for transient electroosmotic flow through elliptic cylindrical microchannels is derived from the Navier-Stokes equations using the Laplace transform. The electroosmotic force expressed by the linearized Poisson-Boltzmann equation is considered the external force in the Navier-Stokes equations. The velocity field solution is obtained in the form of the Mathieu and modified Mathieu functions and it is capable of describing the flow behavior in the system when the boundary condition is either constant or varied. The fluid velocity is calculated numerically using the inverse Laplace transform in order to describe the transient behavior. Moreover, the flow rates and the relative errors on the flow rates are presented to investigate the effect of eccentricity of the elliptic cross-section. The investigation shows that, when the area of the channel cross-sections is fixed, the relative errors are less than 1% if the eccentricity is not greater than 0.5. As a result, an elliptic channel with the eccentricity not greater than 0.5 can be assumed to be circular when the solution is written in the form of trigonometric functions in order to avoid the difficulty in computing the Mathieu and modified Mathieu functions.

Burgers turbulence model for a channel flow

1971 ◽  
Vol 47 (2) ◽  
pp. 321-335 ◽  
Author(s):  
Jon Lee
Keyword(s):  
Channel Flow ◽  
Stokes Equations ◽  
Turbulent Channel Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Amplitude Equations ◽  
Fourier Amplitude ◽  
Navier Stokes Equations ◽  
Burgers Model ◽  
Model Dynamics

The truncated Burgers models have a unique equilibrium state which is defined continuously for all the Reynolds numbers and attainable from a realizable class of initial disturbances. Hence, they represent a sequence of convergent approximations to the original (untruncated) Burgers problem. We have pointed out that consideration of certain degenerate equilibrium states can lead to the successive turbulence-turbulence transitions and finite-jump transitions that were suggested by Case & Chiu. As a prototype of the Navier–Stokes equations, Burgers model can simulate the initial-value type of numerical integration of the Fourier amplitude equations for a turbulent channel flow. Thus, the Burgers model dynamics display certain idiosyncrasies of the actual channel flow problem described by a truncated set of Fourier amplitude equations, which includes only a modest number of modes due to the limited capability of the computer at hand.

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