Numerical investigation of lubrication force on a spherical particle moving to a plane wall at finite Reynolds numbers

San Yih Lin; Jeng Feng Lin

doi:10.1016/j.ijmultiphaseflow.2013.01.006

Numerical investigation of lubrication force on a spherical particle moving to a plane wall at finite Reynolds numbers

San Yih Lin
, Jeng Feng Lin

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

A direct-forcing immersed-boundary (IB) pressure correction method is used to investigate numerically the total hydrodynamic force for a solid sphere in normal approach to a plane wall. For constant approaches, Cox and Brenner's classic asymptotic formula in the lubrication regime was extended to cover particle Reynolds number Re. ≤. 50. An explicit force formula was proposed by fitting the current simulation results. We also consider gravity-induced decent of an immersed sphere towards a wall and an equation of motion was proposed containing quasi-steady viscous drag and two unsteady components-added mass force and history force. Possible effects from liquid inertia at finite-Re and wall at small gaps are described by least-square fitting of the simulation results. The proposed formula agrees to existing low-Re theories.

Original language	English
Pages (from-to)	40-53
Number of pages	14
Journal	International Journal of Multiphase Flow
Volume	53
DOIs	https://doi.org/10.1016/j.ijmultiphaseflow.2013.01.006
Publication status	Published - 2013 Jul

All Science Journal Classification (ASJC) codes

Mechanical Engineering
General Physics and Astronomy
Fluid Flow and Transfer Processes

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10.1016/j.ijmultiphaseflow.2013.01.006

Cite this

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title = "Numerical investigation of lubrication force on a spherical particle moving to a plane wall at finite Reynolds numbers",

abstract = "A direct-forcing immersed-boundary (IB) pressure correction method is used to investigate numerically the total hydrodynamic force for a solid sphere in normal approach to a plane wall. For constant approaches, Cox and Brenner's classic asymptotic formula in the lubrication regime was extended to cover particle Reynolds number Re. ≤. 50. An explicit force formula was proposed by fitting the current simulation results. We also consider gravity-induced decent of an immersed sphere towards a wall and an equation of motion was proposed containing quasi-steady viscous drag and two unsteady components-added mass force and history force. Possible effects from liquid inertia at finite-Re and wall at small gaps are described by least-square fitting of the simulation results. The proposed formula agrees to existing low-Re theories.",

author = "Lin, \{San Yih\} and Lin, \{Jeng Feng\}",

note = "Funding Information: The authors wish to extend their appreciation for the supports awarded by the National Science Council of the Republic of China under the contact NSC 100-2221-E-006-106 and by the Excellent Research Projects of National Taiwan University under award No. 97R0066-07 and 98R0066-07. The authors also thank the reviewers for their valuable suggestions. According to their suggestions, we add a test case for dynamics of the rear vortex ring and re-exam the meaning of Eq. (17) . We express our thanks to Professor F.L. Yang for reading the paper. Copyright: Copyright 2013 Elsevier B.V., All rights reserved.",

year = "2013",

month = jul,

doi = "10.1016/j.ijmultiphaseflow.2013.01.006",

language = "English",

volume = "53",

pages = "40--53",

journal = "International Journal of Multiphase Flow",

issn = "0301-9322",

publisher = "Elsevier BV",

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T1 - Numerical investigation of lubrication force on a spherical particle moving to a plane wall at finite Reynolds numbers

AU - Lin, San Yih

AU - Lin, Jeng Feng

N1 - Funding Information: The authors wish to extend their appreciation for the supports awarded by the National Science Council of the Republic of China under the contact NSC 100-2221-E-006-106 and by the Excellent Research Projects of National Taiwan University under award No. 97R0066-07 and 98R0066-07. The authors also thank the reviewers for their valuable suggestions. According to their suggestions, we add a test case for dynamics of the rear vortex ring and re-exam the meaning of Eq. (17) . We express our thanks to Professor F.L. Yang for reading the paper. Copyright: Copyright 2013 Elsevier B.V., All rights reserved.

PY - 2013/7

Y1 - 2013/7

N2 - A direct-forcing immersed-boundary (IB) pressure correction method is used to investigate numerically the total hydrodynamic force for a solid sphere in normal approach to a plane wall. For constant approaches, Cox and Brenner's classic asymptotic formula in the lubrication regime was extended to cover particle Reynolds number Re. ≤. 50. An explicit force formula was proposed by fitting the current simulation results. We also consider gravity-induced decent of an immersed sphere towards a wall and an equation of motion was proposed containing quasi-steady viscous drag and two unsteady components-added mass force and history force. Possible effects from liquid inertia at finite-Re and wall at small gaps are described by least-square fitting of the simulation results. The proposed formula agrees to existing low-Re theories.

AB - A direct-forcing immersed-boundary (IB) pressure correction method is used to investigate numerically the total hydrodynamic force for a solid sphere in normal approach to a plane wall. For constant approaches, Cox and Brenner's classic asymptotic formula in the lubrication regime was extended to cover particle Reynolds number Re. ≤. 50. An explicit force formula was proposed by fitting the current simulation results. We also consider gravity-induced decent of an immersed sphere towards a wall and an equation of motion was proposed containing quasi-steady viscous drag and two unsteady components-added mass force and history force. Possible effects from liquid inertia at finite-Re and wall at small gaps are described by least-square fitting of the simulation results. The proposed formula agrees to existing low-Re theories.

UR - https://www.scopus.com/pages/publications/84874570584

UR - https://www.scopus.com/pages/publications/84874570584#tab=citedBy

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DO - 10.1016/j.ijmultiphaseflow.2013.01.006

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VL - 53

SP - 40

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JO - International Journal of Multiphase Flow

JF - International Journal of Multiphase Flow

ER -

Numerical investigation of lubrication force on a spherical particle moving to a plane wall at finite Reynolds numbers

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