Mathematical and Simulation of Lid Driven Cavity Flow at Different Aspect Ratios Using Single Relaxation Time Lattice Boltzmann Technique

Anil Kumar; S P Agrawal

doi:doi:10.11648/j.ajtas.20130203.17

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Mathematical and Simulation of Lid Driven Cavity Flow at Different Aspect Ratios Using Single Relaxation Time Lattice Boltzmann Technique

Anil Kumar, S P Agrawal

Published in American Journal of Theoretical and Applied Statistics (Volume 2, Issue 3)

Received: 30 May 2013 Published: 20 June 2013

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Abstract

In this paper we, consider a restrictions on the choice of relaxation time in single relaxation time (SRT) models, simulation of flows is generally limited base on this technique. In the current study of the SRT lattice Boltzmann equation have been used to simulate lid driven cavity flow at various Reynolds numbers (100-5000) and three aspect ratios, K=1, 1.5 and 4. The point which is vital in convergence of this technique is how the boundary conditions will be implemented. Two kinds of boundary conditions which imply no-slip and constant inlet velocity, imposed in the present work. For square cavity, results show that with increasing the Reynolds number, bottom corner vortices will grow but they won’t merge together. In this case which the aspect ratio equals four, and Reynolds number reaches over 1000, simulations predicted four primary vortices, which have not predicted by previous single relaxation time models. The results have been compared by previous multi relaxation model.

Published in	American Journal of Theoretical and Applied Statistics (Volume 2, Issue 3)
DOI	10.11648/j.ajtas.20130203.17
Page(s)	87-93
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2013. Published by Science Publishing Group

Keywords

Cavity Flow, Lattice Boltzmann, Aspect Ratio, Vortex Integration

References

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[9]	Erturk, E., Corke, T.C., Gökçöl, C., "Numerical Solutions of 2-D Steady Incompressible Driven Cavity Flow at High Reynolds Numbers", Int. J. Numer. Meth. Fluids, Vol. 48 (2005), 747-774.
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[12]	Patil, D., Lakshmisha, K., Rogg, B., "Lattice Boltzmann simulation of lid-driven ﬂow in deep cavities", Comput Fluids, Vol. 35(10) (2006), 1116-1125.
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[14]	Lin, L.S., Chen, Y.C., Lin, C.A., "Multi relaxation time lattice Boltzmann simulations of deep lid driven cavity ﬂows at different aspect ratios", Computers & Fluids, Vol. 45(1) (2011), 233-240.
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[16]	JN Reddy : Applied functional analysis and variational methods in Engineering, Mc Graw Hill Book Company New York 1986.
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[18]	D. Arumuga Perumal, Anoop K. Dass "Application of lattice Boltzmann method for incompressible viscous ﬂows, Applied Mathematical Modeling vol. 14, 23-39, 2013.
[19]	Reyad Omari "CFD simulation of Lid Driven cavity flow at moderate Reynolds Number, European Scientific Journal May 2013 edition vol.9 (15) 45-60.
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Anil Kumar, S P Agrawal. (2013). Mathematical and Simulation of Lid Driven Cavity Flow at Different Aspect Ratios Using Single Relaxation Time Lattice Boltzmann Technique. American Journal of Theoretical and Applied Statistics, 2(3), 87-93. https://doi.org/10.11648/j.ajtas.20130203.17

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ACS Style

Anil Kumar; S P Agrawal. Mathematical and Simulation of Lid Driven Cavity Flow at Different Aspect Ratios Using Single Relaxation Time Lattice Boltzmann Technique. Am. J. Theor. Appl. Stat. 2013, 2(3), 87-93. doi: 10.11648/j.ajtas.20130203.17

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AMA Style

Anil Kumar, S P Agrawal. Mathematical and Simulation of Lid Driven Cavity Flow at Different Aspect Ratios Using Single Relaxation Time Lattice Boltzmann Technique. Am J Theor Appl Stat. 2013;2(3):87-93. doi: 10.11648/j.ajtas.20130203.17

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@article{10.11648/j.ajtas.20130203.17,
  author = {Anil Kumar and S P Agrawal},
  title = {Mathematical and Simulation of Lid Driven Cavity Flow at Different Aspect Ratios Using Single Relaxation Time Lattice Boltzmann Technique},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {2},
  number = {3},
  pages = {87-93},
  doi = {10.11648/j.ajtas.20130203.17},
  url = {https://doi.org/10.11648/j.ajtas.20130203.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20130203.17},
  abstract = {In this paper we, consider a restrictions on the choice of relaxation time in single relaxation time (SRT) models, simulation of flows is generally limited base on this technique. In the current study of the SRT lattice Boltzmann equation have been used to simulate lid driven cavity flow at various Reynolds numbers (100-5000) and three aspect ratios, K=1, 1.5 and 4. The point which is vital in convergence of this technique is how the boundary conditions will be implemented. Two kinds of boundary conditions which imply no-slip and constant inlet velocity, imposed in the present work. For square cavity, results show that with increasing the Reynolds number, bottom corner vortices will grow but they won’t merge together. In this case which the aspect ratio equals four, and Reynolds number reaches over 1000, simulations predicted four primary vortices, which have not predicted by previous single relaxation time models. The results have been compared by previous multi relaxation model.},
 year = {2013}
}

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TY  - JOUR
T1  - Mathematical and Simulation of Lid Driven Cavity Flow at Different Aspect Ratios Using Single Relaxation Time Lattice Boltzmann Technique
AU  - Anil Kumar
AU  - S P Agrawal
Y1  - 2013/06/20
PY  - 2013
N1  - https://doi.org/10.11648/j.ajtas.20130203.17
DO  - 10.11648/j.ajtas.20130203.17
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 87
EP  - 93
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20130203.17
AB  - In this paper we, consider a restrictions on the choice of relaxation time in single relaxation time (SRT) models, simulation of flows is generally limited base on this technique. In the current study of the SRT lattice Boltzmann equation have been used to simulate lid driven cavity flow at various Reynolds numbers (100-5000) and three aspect ratios, K=1, 1.5 and 4. The point which is vital in convergence of this technique is how the boundary conditions will be implemented. Two kinds of boundary conditions which imply no-slip and constant inlet velocity, imposed in the present work. For square cavity, results show that with increasing the Reynolds number, bottom corner vortices will grow but they won’t merge together. In this case which the aspect ratio equals four, and Reynolds number reaches over 1000, simulations predicted four primary vortices, which have not predicted by previous single relaxation time models. The results have been compared by previous multi relaxation model.
VL  - 2
IS  - 3
ER  -

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Author Information

Anil Kumar

Department of Applied Mathematics, World Institute of Technology Sohna Gurgaon, India
S P Agrawal

Department of Civil Engineering, World Institute of Technology Sohna Gurgaon, India

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APA Style

Anil Kumar, S P Agrawal. (2013). Mathematical and Simulation of Lid Driven Cavity Flow at Different Aspect Ratios Using Single Relaxation Time Lattice Boltzmann Technique. American Journal of Theoretical and Applied Statistics, 2(3), 87-93. https://doi.org/10.11648/j.ajtas.20130203.17

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ACS Style

Anil Kumar; S P Agrawal. Mathematical and Simulation of Lid Driven Cavity Flow at Different Aspect Ratios Using Single Relaxation Time Lattice Boltzmann Technique. Am. J. Theor. Appl. Stat. 2013, 2(3), 87-93. doi: 10.11648/j.ajtas.20130203.17

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AMA Style

Anil Kumar, S P Agrawal. Mathematical and Simulation of Lid Driven Cavity Flow at Different Aspect Ratios Using Single Relaxation Time Lattice Boltzmann Technique. Am J Theor Appl Stat. 2013;2(3):87-93. doi: 10.11648/j.ajtas.20130203.17

Copy | Download

@article{10.11648/j.ajtas.20130203.17,
  author = {Anil Kumar and S P Agrawal},
  title = {Mathematical and Simulation of Lid Driven Cavity Flow at Different Aspect Ratios Using Single Relaxation Time Lattice Boltzmann Technique},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {2},
  number = {3},
  pages = {87-93},
  doi = {10.11648/j.ajtas.20130203.17},
  url = {https://doi.org/10.11648/j.ajtas.20130203.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20130203.17},
  abstract = {In this paper we, consider a restrictions on the choice of relaxation time in single relaxation time (SRT) models, simulation of flows is generally limited base on this technique. In the current study of the SRT lattice Boltzmann equation have been used to simulate lid driven cavity flow at various Reynolds numbers (100-5000) and three aspect ratios, K=1, 1.5 and 4. The point which is vital in convergence of this technique is how the boundary conditions will be implemented. Two kinds of boundary conditions which imply no-slip and constant inlet velocity, imposed in the present work. For square cavity, results show that with increasing the Reynolds number, bottom corner vortices will grow but they won’t merge together. In this case which the aspect ratio equals four, and Reynolds number reaches over 1000, simulations predicted four primary vortices, which have not predicted by previous single relaxation time models. The results have been compared by previous multi relaxation model.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - Mathematical and Simulation of Lid Driven Cavity Flow at Different Aspect Ratios Using Single Relaxation Time Lattice Boltzmann Technique
AU  - Anil Kumar
AU  - S P Agrawal
Y1  - 2013/06/20
PY  - 2013
N1  - https://doi.org/10.11648/j.ajtas.20130203.17
DO  - 10.11648/j.ajtas.20130203.17
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 87
EP  - 93
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20130203.17
AB  - In this paper we, consider a restrictions on the choice of relaxation time in single relaxation time (SRT) models, simulation of flows is generally limited base on this technique. In the current study of the SRT lattice Boltzmann equation have been used to simulate lid driven cavity flow at various Reynolds numbers (100-5000) and three aspect ratios, K=1, 1.5 and 4. The point which is vital in convergence of this technique is how the boundary conditions will be implemented. Two kinds of boundary conditions which imply no-slip and constant inlet velocity, imposed in the present work. For square cavity, results show that with increasing the Reynolds number, bottom corner vortices will grow but they won’t merge together. In this case which the aspect ratio equals four, and Reynolds number reaches over 1000, simulations predicted four primary vortices, which have not predicted by previous single relaxation time models. The results have been compared by previous multi relaxation model.
VL  - 2
IS  - 3
ER  -

Copy | Download