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Boundary conditions with adjustable slip length for the lattice Boltzmann simulation of liquid flow

Boundary conditions with adjustable slip length for the lattice Boltzmann simulation of liquid flow
Boundary conditions with adjustable slip length for the lattice Boltzmann simulation of liquid flow
The phenomenon of liquid slip has been studied by many researchers using the lattice Boltzmann method. However, boundary conditions for the lattice Boltzmann simulation of liquid flow are far from perfect and how to specify the boundary conditions for liquid flow with slip accurately is still a challenge. In this work, we introduce four widely used slip boundary conditions in gaseous flow into the simulation of liquid flow, two half-way schemes and two modified schemes. Theoretical analysis shows that all half-way schemes are equivalent in principle, so are the modified schemes. According to the equivalence of these schemes, these slip boundary conditions are improved by expanding the range of the combination parameters from [0,1] to [0,2] to surmount the barrier of limited simulated slip length. And the relations between the combination parameters and the slip length are deduced strictly in theory. The specified combination parameter is decided by the given slip length and the relaxation time. The discrete effects of these slip boundary conditions are analysed. If the grid is fine enough, the discrete effects can be ignorable and the local flow at the wall can be approximated as flow with linear velocity gradient. The accuracy and reliability of our method have been verified by the simulations of the Couette flow, the Poiseuille flow and the unsteady Womersley flow. The cylindrical Couette flow is also implemented to explore the possibility of simulating liquid flows with curved boundary.
liquid slip boundary conditions, Navier's slip model, slip length, lattice Boltzmann simulation
0045-7930
200-212
Yang, Liuming
00488c19-ed5a-4376-bb99-2130699942c3
Yang, Yu
0c11efa6-b9f8-4871-bb02-478180ce0c98
Hou, Guoxiang
33d256fc-597b-4778-839c-ebdcc52e14f6
Wang, Kai
7fae7b01-7cee-4537-aa5b-7b5445c82291
Xiong, Yeping
51be8714-186e-4d2f-8e03-f44c428a4a49
Yang, Liuming
00488c19-ed5a-4376-bb99-2130699942c3
Yang, Yu
0c11efa6-b9f8-4871-bb02-478180ce0c98
Hou, Guoxiang
33d256fc-597b-4778-839c-ebdcc52e14f6
Wang, Kai
7fae7b01-7cee-4537-aa5b-7b5445c82291
Xiong, Yeping
51be8714-186e-4d2f-8e03-f44c428a4a49

Yang, Liuming, Yang, Yu, Hou, Guoxiang, Wang, Kai and Xiong, Yeping (2018) Boundary conditions with adjustable slip length for the lattice Boltzmann simulation of liquid flow. Computers & Fluids, 174, 200-212. (doi:10.1016/j.compfluid.2018.08.002).

Record type: Article

Abstract

The phenomenon of liquid slip has been studied by many researchers using the lattice Boltzmann method. However, boundary conditions for the lattice Boltzmann simulation of liquid flow are far from perfect and how to specify the boundary conditions for liquid flow with slip accurately is still a challenge. In this work, we introduce four widely used slip boundary conditions in gaseous flow into the simulation of liquid flow, two half-way schemes and two modified schemes. Theoretical analysis shows that all half-way schemes are equivalent in principle, so are the modified schemes. According to the equivalence of these schemes, these slip boundary conditions are improved by expanding the range of the combination parameters from [0,1] to [0,2] to surmount the barrier of limited simulated slip length. And the relations between the combination parameters and the slip length are deduced strictly in theory. The specified combination parameter is decided by the given slip length and the relaxation time. The discrete effects of these slip boundary conditions are analysed. If the grid is fine enough, the discrete effects can be ignorable and the local flow at the wall can be approximated as flow with linear velocity gradient. The accuracy and reliability of our method have been verified by the simulations of the Couette flow, the Poiseuille flow and the unsteady Womersley flow. The cylindrical Couette flow is also implemented to explore the possibility of simulating liquid flows with curved boundary.

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Computers and Fluids_2018 - Accepted Manuscript
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More information

Accepted/In Press date: 6 August 2018
e-pub ahead of print date: 7 August 2018
Published date: 30 September 2018
Keywords: liquid slip boundary conditions, Navier's slip model, slip length, lattice Boltzmann simulation

Identifiers

Local EPrints ID: 424121
URI: http://eprints.soton.ac.uk/id/eprint/424121
ISSN: 0045-7930
PURE UUID: caef981f-a3b0-471e-9fdf-f2be06885611
ORCID for Yeping Xiong: ORCID iD orcid.org/0000-0002-0135-8464

Catalogue record

Date deposited: 04 Oct 2018 16:30
Last modified: 07 Oct 2020 04:13

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