# Analysis of vortical structures in a differentially heated lid driven cubical cavity

Analysis of vortical structures in a differentially heated lid driven cubical cavity

Hari P. RaniVekamulla Narayana Yadagiri Rameshwar

Department of Mathematics, National Institute of Technology, Warangal 506004, India

Department of Mathematics, College of Engineering, Osmania University, Hyderabad 500007

Corresponding Author Email:
hprani@nitw.ac.in
Page:
548-556
|
DOI:
https://doi.org/10.18280/ijht.360218
9 January 2018
|
Accepted:
20 April 2018
|
Published:
30 June 2018
| Citation

OPEN ACCESS

Abstract:

Analysis of the vortical structures arising in the system with respect to their control parameters is an important fundamental study. Studies in this regard have mostly been paid attention on a free convective cavity flow. Relatively few studies have been devoted on the characteristics of the vortical structures arising in the mixed convection cavity flows. Thus, it is aimed to analyse the vortical structures arising in a free and forced convective flow of air in a cubical cavity using the direct numerical simulations. Governing equations of this problem, expressed in dimensionless form are solved by using the finite volume method. The simulated results are corroborated with benchmark solutions. Numerical solutions are obtained for wide range of Reynolds number (Re) and Richardson number (Ri) (the mixed convection parameter). The flow and thermal characteristics are analysed using isotherms, velocity magnitude, vortex corelines and average Nusselt number. The simulated results show that the large values of Ri decrease the total heat transfer rate thus the conductive heat transfer prevails. While when Ri takes the small values and for amplified values of Re the complex 3D features are clearly seen and the vigorous forced convection enhances the global heat in the system.

Keywords:

mixed convection, Reynolds number, Richardson number, vortex coreline

1. Introduction
2. Physical System and Governing Equations
3. Validation
4. Results and Discussion
5. Conclusion
Nomenclature
References

[1] Moallemi MK, Jang KS. (1992). Prandtl number effects on laminar mixed convection heat transfer in a lid-driven cavity. Int. J. Heat Mass Transfer 35: 1881-1892. http://doi.org/10.1016/0017-9310(92)90191-t

[2] Sharif MAR. (2007). Laminar mixed convection in shallow inclined driven cavities with hot moving lid on top and cooled from bottom. Appl. Ther. Eng. 27: 1036-1042. http://doi.org/ 10.1016/j.applthermaleng.2006.07.035

[3] Prasad YS, Das MK. (2007). Hopf bifurcation in mixed flow inside a rectangular cavity. Int. J. Heat Mass Transfer 50: 3583-3598. http://doi.org/ 10.1016/j.ijheatmasstransfer.2006.11.048

[4] Mohammad AA, Viskanta R. (1992). Laminar flow and heat transfer in Rayleigh-Benard convection with shear. Phys. Fluids 4: 2131-2140. http://doi.org/ 10.1063/1.858509

[5] Koseff JR, Street RL. (1984). Visualization studies of a shear driven three dimensional recirculating flow. J. Fluids Eng. 106: 21-29. http://doi.org/ 10.1115/1.3242393

[6] Koseff JR, Street RL. (1984). On end wall effects in a lid driven cavity flow. J. Fluids Eng. 106: 385-389. http://doi.org/10.1115/1.3243135

[7] Koseff JR, Street RL. (1984). The lid-driven cavity Flow: A synthesis of qualitative and quantitative observations. J. Fluids Eng. 106: 385-389. http://doi.org/10.1115/1.3243136

[8] Ku HC, Hirish RS, Taylors TD. (1987). A Pseudospectral Method for solution of the Three-Dimensional Incompressible Navier-Stokes equations. J. Comput. Phys. 70: 439-462. http://doi.org/10.1016/0021-9991(87)90190-2

[9] Iwatsu R., Ishii K, Kawamura T, Kuwahara K, Hyun JM. (1989). Numerical simulation of three dimensional flow structure in a driven cavity. Flu. dynamic. Research 5:173-189. http://doi.org/10.1016/0169-5983(89)90020-8

[10] Iwatsu R, Hyun JM, Kuwahara K (1989). Analyses of three dimensional flow calculations in a driven cavity. Flu. dynamic. Research 6: 91-102. http://doi.org/10.1016/0169-5983(90)90030-3

[11] Iwatsu R, Hyun JM. (1995). Three dimensional driven-cavity flows with a vertical temperature gradient. Int. J. Heat Mass Transfer 38: 3319-3328. http://doi.org/10.1016/0017-9310(95)00080-s

[12] Aydin O, Yang WJ. (2000). Mixed convection in cavities with a locally heated lower wall and moving sidewalls. Numer. Heat Trans, Part A: Applications 37: 695-710. http://doi.org/10.1080/104077800274037

[13] Benkacem N, Cheikh NB, Beya BB. (2015). Three-dimensional analysis of mixed convection in a differentially heated lid-driven cubic enclosure. J Appl. Mech. Eng. 4: 159-162. http://doi.org/10.4172/2168-9873.1000159

[14] Ouertatani N, Cheikh NB, Beya BB, Taieb L, Antonio C. (2009). Mixed convection in a double lid-driven cubic cavity. Int. J. Thermal Sciences 48: 1265-1272. http://doi.org/10.1016/j.ijthermalsci.2008.11.020

[15] Robinson SK. (1991). Coherent motions in the turbulent boundary layer. Annual Review of Fluid Mechanics 23: 601-639. http://doi.org/10.1146/annurev.fl.23.010191.003125

[16] Tony Sheu WH, Rani HP, Tan TC, Tsai SF. (2008). Multiple states, topology and bifurcations of natural convection in a cubical cavity. Comput. and Fluids 37: 1011-1028. http://doi.org/10.1016/j.compfluid.2007.11.003