## THERMAL SCIENCE

International Scientific Journal

### SIMULATION OF FLOW IN SINGLE AND DOUBLE-SIDED LID DRIVEN SQUARE CAVITIES BY DIRECT SIMULATION MONTE CARLO METHOD

**ABSTRACT**

The gaseous flow of monoatomic Argon in a double-sided lid-driven square cavity is investigated using the direct simulation Monte Carlo method for different degrees of rarefaction. The effect of the direction of wall motion and the magnitude of wall velocities on the flow physics are analyzed. Unlike the single-sided cavity flow, the double-sided cavity flow generates different vortex formations especially for the parallel wall motion of the wall. The problem, therefore, merits a thorough study, which is attempted in the present paper using the direct simulation Monte Carlo method. Certain complex flow phenomena which are not captured using the numerical methods for continuum flows are revealed by the current method employed in the study. Two counter-rotating vortices are observed for the parallel wall motion whereas only one primary vortex can be observed for the antiparallel case. The variation in the flow and thermal properties is found to be significant at the onset of the transition regime and much smaller in the free molecular regime.

**KEYWORDS**

PAPER SUBMITTED: 2018-09-06

PAPER REVISED: 2019-02-16

PAPER ACCEPTED: 2019-02-20

PUBLISHED ONLINE: 2019-03-09

**THERMAL SCIENCE** YEAR

**2020**, VOLUME

**24**, ISSUE

**5**, PAGES [3031 - 3045]

- A. Y. Gelfgat, "Linear instability of the lid-driven flow in a cubic cavity," Theoretical and Computational Fluid Dynamics, vol. 33, no. 1, pp. 59-82, Feb. 2019.
- E. M. Wahba, "Multiplicity of states for two-sided and four-sided lid driven cavity flows," Computers & Fluids, vol. 38, no. 2, pp. 247-253, Feb. 2009.
- U. Ghia, K. N. Ghia, and C. T. Shin, "High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method," Journal of Computational Physics, vol. 48, no. 3, pp. 387-411, Dec. 1982.
- C. Barbaros and B. Ozgur, "Evaluation of Nusselt number for a flow in a microtube using second-order slip model," Thermal Science, vol. 15, no. suppl. 1, pp. 103-109, 2011.
- N. Rahbar, M. Taherian, M. Shateri, and S. Valipour, "Numerical investigation on flow behavior and energy separation in a micro-scale vortex tube," Thermal Science, vol. 19, no. 2, pp. 619-630, 2015.
- A. Miguel, "Non-Darcy porous media flow in no-slip and slip regimes," Thermal Science, vol. 16, no. 1, pp. 167-176, 2012.
- S. Milicev and N. Stevanovic, "Navier-Stokes-Fourier analytic solutions for non-isothermal Couette slip gas flow," Thermal Science, vol. 20, no. 6, pp. 1825-1833, 2016.
- G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Oxford, New York: Oxford University Press, 1994.
- M. Cheng and K. C. Hung, "Vortex structure of steady flow in a rectangular cavity," Computers & Fluids, vol. 35, no. 10, pp. 1046-1062, Dec. 2006.
- S. Hamimid, M. Guellal, and M. Bouafia, "Numerical study of natural convection in a square cavity under non-boussinesq conditions," Thermal Science, vol. 20, no. 5, pp. 1509-1517, 2016.
- R. Bennacer, M. Reggio, N. Pellerin, and X. Ma, "Differentiated heated lid driven cavity interacting with tube: A lattice Boltzmann study," Thermal Science, vol. 21, no. 1 Part A, pp. 89-104, 2017.
- C.-C. Su, M. R. Smith, F.-A. Kuo, J.-S. Wu, C.-W. Hsieh, and K.-C. Tseng, "Large-scale simulations on multiple Graphics Processing Units (GPUs) for the direct simulation Monte Carlo method," Journal of Computational Physics, vol. 231, no. 23, pp. 7932-7958, Oct. 2012.
- H. C. Kuhlmann, M. Wanschura, and H. J. Rath, "Flow in two-sided lid-driven cavities: non-uniqueness, instabilities, and cellular structures," Journal of Fluid Mechanics, vol. 336, pp. 267-299, Apr. 1997.
- D. Arumuga Perumal and A. K. Dass, "Multiplicity of steady solutions in two-dimensional lid-driven cavity flows by Lattice Boltzmann Method," Computers & Mathematics with Applications, vol. 61, no. 12, pp. 3711-3721, Jun. 2011.
- S. B. R., D. A. Perumal, and A. K. Yadav, "Computation of fluid flow in double sided cross-shaped lid-driven cavities using Lattice Boltzmann method," European Journal of Mechanics - B/Fluids, vol. 70, pp. 46-72, Jul. 2018.
- D. Auld and Y. Lan, "Simulation of Lid-Driven Cavity Flow by Parallel DSMC Method," in 24th AIAA Applied Aerodynamics Conference, San Francisco, California, 2006.
- A. Alkhalidi, S. Kiwan, W. Al-Kouz, A. Alshare, and M. Sari, "Rarefaction and scale effects on heat transfer characteristics for enclosed rectangular cavities heated from below," Thermal Science, no. 00, pp. 234-234, 2017.
- A. Mohammadzadeh, E. Roohi, H. Niazmand, S. Stefanov, and R. S. Myong, "Thermal and second-law analysis of a micro-or nanocavity using direct-simulation Monte Carlo," Physical review E, vol. 85, no. 5, p. 056310, 2012.
- A. Mohammadzadeh, E. Roohi, and H. Niazmand, "A Parallel DSMC Investigation of Monatomic/Diatomic Gas Flows in a Micro/Nano Cavity," Numerical Heat Transfer, Part A: Applications, vol. 63, no. 4, pp. 305-325, Jan. 2013.
- H. Liu et al., "Monte Carlo simulations of gas flow and heat transfer in vacuum packaged MEMS devices," Applied Thermal Engineering, vol. 27, no. 2, pp. 323-329, Feb. 2007.
- C. Cai, "Heat transfer in vacuum packaged microelectromechanical system devices," Physics of Fluids, vol. 20, no. 1, p. 017103, Jan. 2008.
- A. Rana, M. Torrilhon, and H. Struchtrup, "A robust numerical method for the R13 equations of rarefied gas dynamics: Application to lid driven cavity," Journal of Computational Physics, vol. 236, pp. 169-186, Mar. 2013.
- E. Y. Moghadam, E. Roohi, and J. A. Esfahani, "Heat transfer and fluid characteristics of rarefied flow in thermal cavities," Vacuum, vol. 109, pp. 333-340, Nov. 2014.
- M. Eskandari and S. S. Nourazar, "On the time relaxed Monte Carlo computations for the lid-driven micro cavity flow," Journal of Computational Physics, vol. 343, pp. 355-367, Aug. 2017.
- B. John, X.-J. Gu, and D. R. Emerson, "Investigation of Heat and Mass Transfer in a Lid-Driven Cavity Under Nonequilibrium Flow Conditions," Numerical Heat Transfer, Part B: Fundamentals, vol. 58, no. 5, pp. 287-303, Nov. 2010.
- B. John, X.-J. Gu, and D. R. Emerson, "Effects of incomplete surface accommodation on non-equilibrium heat transfer in cavity flow: A parallel DSMC study," Computers & Fluids, vol. 45, no. 1, pp. 197-201, Jun. 2011.
- S. Naris and D. Valougeorgis, "The driven cavity flow over the whole range of the Knudsen number," Physics of Fluids, vol. 17, no. 9, p. 097106, Sep. 2005.
- K. Aoki, S. Takata, H. Aikawa, and F. Golse, "A rarefied gas flow caused by a discontinuous wall temperature," Physics of Fluids, vol. 13, no. 9, pp. 2645-2661, Sep. 2001.
- J.-C. Huang, K. Xu, and P. Yu, "A Unified Gas-Kinetic Scheme for Continuum and Rarefied Flows II: Multi-Dimensional Cases," Communications in Computational Physics, vol. 12, no. 3, pp. 662-690, Sep. 2012.
- V. Venugopal and S. S. Girimaji, "Unified Gas Kinetic Scheme and Direct Simulation Monte Carlo Computations of High-Speed Lid-Driven Microcavity Flows," Communications in Computational Physics, vol. 17, no. 05, pp. 1127-1150, May 2015.
- L. Wu, J. M. Reese, and Y. Zhang, "Oscillatory rarefied gas flow inside rectangular cavities," Journal of Fluid Mechanics, vol. 748, pp. 350-367, Jun. 2014.
- P. Wang, W. Su, L. Zhu, and Y. Zhang, "Heat and mass transfer of oscillatory lid-driven cavity flow in the continuum, transition and free molecular flow regimes," International Journal of Heat and Mass Transfer, vol. 131, pp. 291-300, Mar. 2019.
- C. Cercignani, The Boltzmann Equation and Its Applications. New York: Springer-Verlag, 1988.
- S. Milanovic, M. Jovanovic, Z. Spasic, and B. Nikolic, "Two-phase flow in channels with non-circular cross-section of pneumatic transport of powder material," Thermal Science, vol. 22, no. Suppl. 5, pp. 1407-1424, 2018.
- M. Hssikou, J. Baliti, and M. Alaoui, "Extended Macroscopic Study of Dilute Gas Flow within a Microcavity," Modelling and Simulation in Engineering, vol. 2016, pp. 1-9, 2016.