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Approximate solution to the Navier-Stokes equations for flow through a rectangularly packed bed of spheres Item Info
- 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:
- Rights to the digital resource are held by the University of Idaho. http://www.uidaho.edu/
- Publisher:
- University of Idaho
- Contributing Institution:
- University of Idaho
- Type:
- Text
- Format:
- application/pdf
- Cataloger:
- wbv
- Date Digitized:
- 2012
Source
- 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:
- Rights to the digital resource are held by the University of Idaho. http://www.uidaho.edu/