Direct Numerical Simulation of Mixed Convection Flow in Lid-Driven Cavities

Noura Ben Mansour *

Physics Department, Faculty of Science, Al-Baha University, 65779-7738 Alaqiq, Kingdom of Saudi Arabia.

Ridha Jmai

Laboratory of Fluid Dynamics, Physics Department, Faculty of Sciences of Tunis, Campus Universitaire, 2092 El-Manar II, Tunisia and Al Baha Private College of Science, 3347 6615, Al Bahah 65724, Kingdom of Saudi Arabia.

*Author to whom correspondence should be addressed.


Abstract

The mixed convection of heat transfer and fluid flow in a - lid drivencubical cavity filled with air is investigated numerically in this study. The computational procedure is based on the finite volume method and a full multigrid acceleration solver. The top wall of the cavity is maintained at a constant high temperature - Th, and it can move with a constant velocity U0. The bottom wall is immobile and maintained at a cold temperature Tc. While, the remaining boundary parts of the cavity are motionless and kept thermally insulated. Several numerical simulations were conducted to investigate mixed convection heat transfer in a sliding cubical cavity for a range of Reynolds numbers from 1000 to 5000 and Richardson numbers from 0.001 to 10. The influence of mixed convection parameters, Reynolds number, Richardson number, and heat transfer rate on the flow behavior was analyzed through parametric studies. The results include flow and heat transfer characteristics, iso-surfaces, and streamlines for the entire range of Richardson numbers and Reynolds numbers investigated. The study shows that as Reynolds number is increased beyond a critical value, the flow becomes unstable and bifurcates.

Keywords: Mixed convection, Richardson number, lid-driven cavity


How to Cite

Mansour, Noura Ben, and Ridha Jmai. 2024. “Direct Numerical Simulation of Mixed Convection Flow in Lid-Driven Cavities”. Physical Science International Journal 28 (3):50-65. https://doi.org/10.9734/psij/2024/v28i3831.

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References

Wong KL, Baker AJ. A 3D incompressible Navier–Stokes velocity–vorticity weak form finite element algorithm, Int. J. Numer. Meth. Fluids. 2002;3899-123. Available: https://doi.org/10.1002/fld.204

Hussein AK, Hussain SH. Mixed convection through a lid-driven air-filled square cavity with a hot wavy wall, Int. J. Mech. Mater. Eng. 2010;5:222-235. Available:https://www.researchgate.net/publication/289168743

Nemati H, Farhadi M, Sedighi K, Fattahi E, Darzi AAR. Lattice Boltzmann simulation of nanofluid in lid-driven cavity. Int. Commun. Heat Mass Transf. 2010;37:1528-1534. Available:https://doi.org/10.1016/j.icheatmasstransfer.2010.08.004

Sheikhzadeh GA, Ebrahim Qomi M, Hajialigol N, Fattahi A. Numerical study of mixed convection flows in a lid-driven enclosure filled with nanofluid using variable properties, Results Phys. 2012;2: 5-13. vhttps://doi.org/10.1016/j.rinp.2012.01.001

Hassanzadeh Afrouzi H, Farhadi M. Mix convection heat transfer in a lid driven enclosure filled by nanofluid, Iran. J. Energy Environ. 2013;4:376-384. DOI: 10.5829/idosi.ijee.2013.04.04.09

Arash Karimipour, Mohammad Hemmat Esfe, Mohammad Reza Safaei, Davood Toghraie Semiromi, Saeed Jafari Kazi SN. Mixed convection of Copper-Water nanofluid in a shallow inclined lid driven cavity using lattice Boltzmann method, Physica A. 2014;402:150-168. Available:https://doi.org/10.1016/j.physa.2014.01.057

Rehena Nasrin MA, Alim Ali, Chamkha J. Modeling of mixed convective heat transfer utilizing nanofluid in a double lid driven chamber with internal heat generation, Int. J. Numer. Methods Heat Fluid Flow. 2014; 24:36-57. Available:http://dx.doi.org/10.1108/HFF-11-2011-0239

Abdelkader Boutra, Karim Raguia and Youb Khaled Benkahla, Numerical study of mixed convection heat transfer in a lid driven cavity filled with a nanofluid, Mech. Ind. 2015;16. Available:https://doi.org/10.1051/meca/2015027

Bakar NA, Karimipour A, Roslan R. Effect of magnetic field on mixed convection heat transfer in a lid-driven square cavity, J. Thermodyn. 2016;1:1-14. Available:https://doi.org/10.1155/2016/3487182

Mohammad Mastiani, Myeongsub Mike Kim, Ali Nematollah, Density maximum effects on mixed convection in a square lid-driven enclosure filled with Cu-water nanofluids Adv. Powder Technol. 2017;28: 197–214. Available:https://doi.org/10.1016/j.apt.2016.09.009

Moallemi MK, Jang KS. Prandtl number effects on laminar mixed convection heat transfer in a lid-driven cavity. Int. J. Heat Mass Transf. 1992;35:1881-1892. Available:https://doi.org/10.1016/0017-9310(92)90191-T

Mohamed AA, Viskanta R. Flow and heat transfer in a lid-driven cavity filled with a stably stratified fluid, Appl. Math. Model. 1995;19:465-472. Available:https://doi.org/10.1016/0307-904X(95)00030-N

Iwatsu R, Hyun JM. Three-dimensional driven-cavity flows with a vertical temperature gradient, Int. J. Heat Mass Transf. 1995;38:3319–3328. Available:https://doi.org/10.1016/0017-9310(95)00080-S

Prasad AK, Koseff JR. Combined forced and natural convection heat transfer in a deep lid-driven cavity flow. Int. J. Heat Fluid Flow. 1996;17;460-467. Available:https://doi.org/10.1016/0142-727X(96)00054-9

Cheng TS, Liu WH. Effect of temperature gradient orientation on the characteristics of mixed convection flow in a lid-driven square cavity, Comput. Fluids. 2010;39: 965-978.

Aydin O, Yang WJ. Mixed convection in cavities with a locally heated lower wall and moving sidewalls, Numer. Heat Transfer A Appl. 2000;37:695-710. Available:https://doi.org/10.1080/104077800274037

Oztop HF, Dagtekin I. Mixed convection in two-sided lid-driven differentially heated square cavity, Int. J. Heat Mass Transfer. 2004;47:1761-1769. Available:https://doi.org/10.1016/j.ijheatmasstransfer.2003.10.016

Sharif MAR. Laminar mixed convection in shallow inclined driven cavities with hot moving lid on top and cooled from bottom, Appl. Therm. Eng. 2007;27:1036-1042. Available:https://doi.org/10.1016/j.applthermaleng.2006.07.035

Abbasian Arani AA, Mazrouei Sebdani S, Mahmoodi M, Ardeshiri A, Aliakbari M. Numerical study of mixed convection flow in a lid-driven cavity with sinusoidal heating on sidewalls using nanofluid, Superlattices Microstruct. 2012;51:893-911. Available:https://doi.org/10.1016/j.spmi.2012.02.015

Cheng TS, Liu WH. Effects of cavity inclination on mixed convection heat transfer in lid-driven cavity flows, Comput. Fluids. 2014;100:108-122. Available:http://dx.doi.org/10.1016/j.compfluid.2014.05.004

Khorasanizade S, Sousa JM. A detailed study of lid-driven cavity flow at moderate Reynolds numbers using Incompressible SPH, Int. J. Numer. Meth. Fluids. 2014;76: 653-668. Available:https://doi.org/10.1002/fld.3949

Jmai R, Ben-Beya B, Lili T. Numerical analysis of mixed convection at various walls speed ratios in two-sided lid-driven cavity partially heated and filled with nanofluid, J. Mol. Liq. 2016;221;691-713. Available:http://dx.doi.org/10.1016/j.molliq.2016.05.076

Ismael MA. Numerical solution of mixed convection in a lid-driven cavity with arc-shaped moving wall, Eng. Comput. 2017; 34:869-891. Available:http://dx.doi.org/10.1108/EC-11-2015-0368

Rahman MM, Pop I, Saghir MZ. Steady free convection flow within a titled nanofluid saturated porous cavity in the presence of a sloping magnetic field energized by an exothermic chemical reaction administered by Arrhenius kinetics, Int. J. Heat Mass Transf. 2019; 129:198-211. Available:https://doi.org/10.1016/j.ijheatmasstransfer.2018.09.105

Lamarti H, Mahdaoui M, Bennacer R, Chahboun A. Numerical simulation of mixed convection heat transfer of fluid in acavity driven by an oscillating lid using lattice Boltzmann method, Int. J. Heat Mass Transf. 2019;137:615-629. Available:https://doi.org/10.1016/j.ijheatmasstransfer.2019.03.057

Keya ST, Yeasmin S, Rahman MM, Karim MF, Amin MR. Mixed convection heat transfer in a lid-driven enclosure with a double-pipe heat exchanger, Int. J. of Thermofluids. 2022;13:100-131. Available:https://doi.org/10.1016/j.ijft.2021.100131

Ammar I, Alsabery, Mohammad H, Yazdi Ali, Abosinnee S, Ishak Hashim, Evgeny Solomin. Impact of partial slip condition on mixed convection of nanofluid within lid-driven wavy cavity and solid inner body, Propul. Power Res. 2022;11:544-564. Available:https://doi.org/10.1016/j.jppr.2022.09.001

Brown DL, Cortez R, Minion ML. Accurate projection methods for the incompressible Navier–Stokes equations, J. Comput. Phys. 2001;168;464-499. Available:https://doi.org/10.1006/jcph.2001.6715

Patankar SV. A calculation procedure for two-dimensional elliptic situations, Numer. Heat Transfer. 1981;34:409-425. Available:https://doi.org/10.1080/01495728108961801

Moukhalled F, Darwish M. A unified formulation of the segregated class of algorithm for fluid flow at all speeds, Numer. Heat Transfer B Fundam. 2000;37: 103-139. Available:https://doi.org/10.1080/104077900275576

Kobayachi MH, Pereira JMC, Pereira JCF. A conservative finite-volume second-order-accurate projection method on hybrid unstructured grids, J. Comput. Phys. 1999; 150:40-75. Available:https://doi.org/10.1006/jcph.1998.6163

Hayase T, Humphrey JAC, Greif R. A consistently formulated QUICK scheme for fast and stable convergence using finite-volume iterative calculation procedures, J. Comput. Phys. 1992;98;108-118. Available:https://doi.org/10.1016/0021-9991(92)90177-Z

Ben-Cheikh N, Ben-Beya B, Lili T. Benchmark solution for time-dependent natural convection flows with an accelerated full-multigrid method, Numer. Heat Transfer B Fundam. 2007;52:131-151. Available:https://doi.org/10.1080/10407790701347647

Barrett R, Berry M, Chan TF, et al. Templates for the solution of linear systems: Building Blocks for Iterative Methods, SIAM; 1994. DOI:10.1137/1.9781611971538

Ouertatani N, Ben-Cheikh N, Ben-Beya B, Lili T. Mixed convection in a double lid-driven cubic cavity, Int. J. Thermal Sci. 2009;48:265-1272. Available:https://doi.org/10.1016/j.ijthermalsci.2008.11.020

Al-Atawi NO, Mashat DS. A Computational Investigation of the Lid-Driven Cavity Flow, Am. J. Comput. Mathematics. 2022;12: 283-296. Available:https://doi.org/10.4236/ajcm.2022.122018