Sinusoidal Roughness Elements in a Square Cavity

Authors: M. Yousaf, S. Usman

Abstract:

Numerical studies were conducted using Lattice Boltzmann Method (LBM) to study the natural convection in a square cavity in the presence of roughness. An algorithm based on a single relaxation time Bhatnagar-Gross-Krook (BGK) model of Lattice Boltzmann Method (LBM) was developed. Roughness was introduced on both the hot and cold walls in the form of sinusoidal roughness elements. The study was conducted for a Newtonian fluid of Prandtl number (Pr) 1.0. The range of Ra number was explored from 10^3 to 10^6 in a laminar region. Thermal and hydrodynamic behavior of fluid was analyzed using a differentially heated square cavity with roughness elements present on both the hot and cold wall. Neumann boundary conditions were introduced on horizontal walls with vertical walls as isothermal. The roughness elements were at the same boundary condition as corresponding walls. Computational algorithm was validated against previous benchmark studies performed with different numerical methods, and a good agreement was found to exist. Results indicate that the maximum reduction in the average heat transfer was 16.66 percent at Ra number 10^5.

Keywords: Lattice Boltzmann Method Natural convection, Nusselt Number Rayleigh number, Roughness.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1100092

References:

[1] B. Gebhart, Y. Jaluria, R. L. Mahajan, B. Sammakia, Buoyancy-induced flows and transport, 1988.
[2] M. R. Amin, The effect of adiabatic wall roughness elements on natural convection heat transfer in vertical enclosures, International journal of heat and mass transfer, 34(11) (1991) 2691-2701.
[3] O. Shishkina, C. Wagner, Modelling the influence of wall roughness on heat transfer in thermal convection, Journal of Fluid Mechanics, 686 (2011) 568-582.
[4] S. Bhavnani, A. Bergles, Natural convection heat transfer from sinusoidal wavy surfaces, Wärme-und Stoffübertragung, 26(6) (1991) 341-349.
[5] S. Elsherbiny, K. Hollands, G. Raithby, Free convection across inclined air layers with one surface V-corrugated, Journal of Heat Transfer, 100(3) (1978) 410-415.
[6] S. Bajorek, J. Lloyd, Experimental investigation of natural convection in partitioned enclosures, Journal of Heat Transfer, 104(3) (1982) 527-532.
[7] H. Dixit, V. Babu, Simulation of high Rayleigh number natural convection in a square cavity using the lattice Boltzmann method, International journal of heat and mass transfer, 49(3) (2006) 727-739.
[8] X. Yang, B. Shi, Z. Chai, Generalized modification in the lattice Bhatnagar-Gross-Krook model for incompressible Navier-Stokes equations and convection-diffusion equations, Physical Review E, 90(1) (2014) 013309.
[9] M.C. Sukop, D.T. Thorne, Lattice Boltzmann modeling: an introduction for geoscientists and engineers, Springer, 2007.
[10] G. de Vahl Davis, Natural convection of air in a square cavity: a bench mark numerical solution, International Journal for Numerical Methods in Fluids, 3(3) (1983) 249-264.
[11] M. Ruhul Amin, Natural convection heat transfer and fluid flow in an enclosure cooled at the top and heated at the bottom with roughness elements, International journal of heat and mass transfer, 36(10) (1993) 2707-2710.
[12] S. Pretot, B. Zeghmati, P. Caminat, Influence of surface roughness on natural convection above a horizontal plate, Advances in Engineering Software, 31(10) (2000) 793-801.