Skip to main content Accessibility help
×
Home
Hostname: page-component-544b6db54f-bkjnw Total loading time: 0.355 Render date: 2021-10-19T09:21:36.343Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

The first effects of fluid inertia on flows in ordered and random arrays of spheres

Published online by Cambridge University Press:  26 November 2001

REGHAN J. HILL
Affiliation:
School of Chemical Engineering, Cornell University, Ithaca, NY 14853, USA
DONALD L. KOCH
Affiliation:
School of Chemical Engineering, Cornell University, Ithaca, NY 14853, USA
ANTHONY J. C. LADD
Affiliation:
Department of Chemical Engineering, University of Florida, Gainesville, FL 32611, USA

Abstract

Theory and lattice-Boltzmann simulations are used to examine the effects of fluid inertia, at small Reynolds numbers, on flows in simple cubic, face-centred cubic and random arrays of spheres. The drag force on the spheres, and hence the permeability of the arrays, is determined at small but finite Reynolds numbers, at solid volume fractions up to the close-packed limits of the arrays. For small solid volume fraction, the simulations are compared to theory, showing that the first inertial contribution to the drag force, when scaled with the Stokes drag force on a single sphere in an unbounded fluid, is proportional to the square of the Reynolds number. The simulations show that this scaling persists at solid volume fractions up to the close-packed limits of the arrays, and that the first inertial contribution to the drag force relative to the Stokes-flow drag force decreases with increasing solid volume fraction. The temporal evolution of the spatially averaged velocity and the drag force is examined when the fluid is accelerated from rest by a constant average pressure gradient toward a steady Stokes flow. Theory for the short- and long-time behaviour is in good agreement with simulations, showing that the unsteady force is dominated by quasi-steady drag and added-mass forces. The short- and long-time added-mass coefficients are obtained from potential-flow and quasi-steady viscous-flow approximations, respectively.

Type
Research Article
Copyright
© 2001 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)
250
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

The first effects of fluid inertia on flows in ordered and random arrays of spheres
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

The first effects of fluid inertia on flows in ordered and random arrays of spheres
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

The first effects of fluid inertia on flows in ordered and random arrays of spheres
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *