Solutions for Steady and Nonsteady Entrance Flow in a Semi-Infinite Circular Tube at Very Low Reynolds Numbers

Goldberg, Irwin S.; Folk, R.

doi:10.1137/0148044

Cited by 15 publications

(14 citation statements)

References 15 publications

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“…Analytically, the exact solution of the Navier-Stokes equations is not possible due to their nonlinear nature. However, Abarbanel et al [13], Li and Ludford [14], Benson and Trogdon [15], and Goldberg and Folk [16] have solved the Stokes equations for entry flow using different analytical approaches. They found bulges in the velocity profile, indicating that they are part of the exact solution and inevitable.…”

Section: Introductionmentioning

confidence: 99%

Numerical Study of the Flow Behavior in the Uniform Velocity Entry Flow Problem

Darbandi

Schneider

1998

Numerical Heat Transfer, Part A: Applications

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Section: Introductionmentioning

confidence: 99%

Numerical Study of the Flow Behavior in the Uniform Velocity Entry Flow Problem

Darbandi

Schneider

1998

Numerical Heat Transfer, Part A: Applications

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“…Langhaar (1942) obtained an analytical solution by linearising the non-linear terms in the momentum equations. More recently, Goldberg and Folk (1988) obtained analytical solutions for the Stokes and continuity equations for the case of very low Re (i.e. creeping flow), steady and nonsteady entrance flow in a semi-infinite circular tube using Fourier transform methods.…”

mentioning

confidence: 99%

The influence of reynolds number on the entry length and pressure drop for laminar pipe flow

et al. 1993

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A numerical analysis of the laminar flow of a Newtonian fluid in the inlet section of a circular pipe has been carried out for a Reynolds number range of 0 to 500, employing a finite element based CFD code. A new flow phenomenon has been identified at low Reynolds numbers (<50), viz, the existence of a peak in the axial pressure profile at a small distance from the entrance. Existing correlations for the entry length are shown to be insufficient and a new correlation for the entry length is proposed.

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“…The integrals in the correspondence relation containing the expression Uo(R) given by equation (19) could not be evaluated in closed form, unlike the situation for the problem given by Goldberg and Folk. 3 Consequently, Gaussian quadrature was introduced for the numerical evaluation of these integral expressions. The solutions presented in this paper were obtained with 200 modes contained in the correspondence relations.…”

Section: Analytical Resultsmentioning

confidence: 99%

Periodic viscous flow: A bench‐mark problem

Goldberg

Carey

McLay

et al. 1990

Numerical Methods in Fluids

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SUMMARYA double-transform technique provides a semi-analytic solution in the form of a series expansion for unsteady axisymmetric Stokes flow in the entrance region of a semi-infinite rigid cylindrical tube. This in turn offers an appropriate bench-mark problem for evaluating the quality of numerical approximations. To illustrate this, periodic axial flow in a circular cylinder is considered. Some aspects of the bench-mark problem that are of interest include the reverse flow in the wall layers, the accuracy of the approximate method in different flow regimes and the mesh grading. This bench-mark problem and the numerical study provide some insight into practical issues pertinent to the approximate solution of unsteady and periodic flows.

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Solutions for Steady and Nonsteady Entrance Flow in a Semi-Infinite Circular Tube at Very Low Reynolds Numbers

Cited by 15 publications

References 15 publications

Numerical Study of the Flow Behavior in the Uniform Velocity Entry Flow Problem

Numerical Study of the Flow Behavior in the Uniform Velocity Entry Flow Problem

The influence of reynolds number on the entry length and pressure drop for laminar pipe flow

Periodic viscous flow: A bench‐mark problem

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