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Approximate solution to the Navier-Stokes equations for flow through a rectangularly packed bed of spheres Item Info

Approximate solutions for the Navier -Stokes equations describing fluid fiow through a rectangular packing of spheres were obtained for Reynolds numbers of 0.1, 1, 7 and 35. Initial attempts to solve the Navier-Stokes equations with the inertia terms intact were unsuccessful. However, the methods used in these solution attempts are given in detail. The results reported are based on an Oseen linearization of the full Navier-Stokes equations. The solutions were approximated by triple trigonometric series and the unknown coefficients evaluated using the Galerkin method for error distribution. Velocity components and pressure in the void space of the bed are given as explicit functions of the spacial coordinates. Friction factors for the packed bed and superficial velocity were evaluated from the velocity functions and are shown to agree with the experimental observations of previous investigators. The viscous and kinetic contribution to the energy dissipation are partitioned using first principles of the mechanical energy balance and evidence is given khat the viscous and kinetic effects determined by semiempirical methods do not show the actual relationship between viscous and kinetic losses in the intermediate Reynolds number range. Based on friction factor and superficial velocity, the Oseen linearization is shown to be valid for packed flow at Reynolds numbers less than seven, and invalid for a Reynolds number of 35. Suggestions for future research are included.

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Title:
Approximate solution to the Navier-Stokes equations for flow through a rectangularly packed bed of spheres
Authors:
Carson Jr., William McKinley
Date Created (ISO Standard):
1970-08
Description:
Approximate solutions for the Navier -Stokes equations describing fluid fiow through a rectangular packing of spheres were obtained for Reynolds numbers of 0.1, 1, 7 and 35. Initial attempts to solve the Navier-Stokes equations with the inertia terms intact were unsuccessful. However, the methods used in these solution attempts are given in detail. The results reported are based on an Oseen linearization of the full Navier-Stokes equations. The solutions were approximated by triple trigonometric series and the unknown coefficients evaluated using the Galerkin method for error distribution. Velocity components and pressure in the void space of the bed are given as explicit functions of the spacial coordinates. Friction factors for the packed bed and superficial velocity were evaluated from the velocity functions and are shown to agree with the experimental observations of previous investigators. The viscous and kinetic contribution to the energy dissipation are partitioned using first principles of the mechanical energy balance and evidence is given khat the viscous and kinetic effects determined by semiempirical methods do not show the actual relationship between viscous and kinetic losses in the intermediate Reynolds number range. Based on friction factor and superficial velocity, the Oseen linearization is shown to be valid for packed flow at Reynolds numbers less than seven, and invalid for a Reynolds number of 35. Suggestions for future research are included.
Subjects:
fluid friction
Collection:
Boise Basin
IWRRI number:
197003
Rights:
In copyright, educational use permitted. Educational use includes non-commercial reproduction of text and images in materials for teaching and research purposes. For other contexts beyond fair use, including digital reproduction, please contact the University of Idaho Library Special Collections and Archives Department at libspec@uidaho.edu. The University of Idaho Library is not liable for any violations of the law by users.
Publisher:
University of Idaho
Contributing Institution:
University of Idaho
Type:
Text
Format:
application/pdf
Cataloger:
wbv
Date Digitized:
2012

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Preferred Citation:
"Approximate solution to the Navier-Stokes equations for flow through a rectangularly packed bed of spheres", Idaho Waters Digital Library, University of Idaho Library Digital Collections, https://www.lib.uidaho.edu/digital/iwdl/items/iwdl-197003.html
Rights
Rights:
In copyright, educational use permitted. Educational use includes non-commercial reproduction of text and images in materials for teaching and research purposes. For other contexts beyond fair use, including digital reproduction, please contact the University of Idaho Library Special Collections and Archives Department at libspec@uidaho.edu. The University of Idaho Library is not liable for any violations of the law by users.
Standardized Rights:
http://rightsstatements.org/vocab/InC-EDU/1.0/
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