Turbulent heat and mass transfer inside closed and open cavities

Abstract

The main objective of this work is to investigate the turbulent heat and mass transfer inside open and closed cavities. For two-dimensional cavities, a modified Rayleigh number was defined. The LES (Large Eddy Simulation) turbulence model and Boussinesq approximation were employed. On modified Rayleigh number definition, the buoyant force driven by concentration difference was included beside the buoyant force driven by temperature difference. The non-dimensionalized equations were obtained and stream junction-vorticity approach was utilized to solve two-dimensional continuity, Navier-Stokes, energy and concentration equations. Finite Difference method was utilized for discretization the non-dimensionalized equations. Successice Over-relaxation technique was used to calculate stream function. To obtain the boundary layer, non-homogenous grid was generated. For the range of $10^8-5.10^{10}$ of the modified Rayleigh number, numerical simulations were run. For the numerical analyses, a code was written in Fortran programming language. The code was paralellized and run on a supercomputer. Stream function, vorticily, horizontal and vertical velocities, isoterms and isoconcentrations were obtained. The results showed that increasing modified Rayleigh number causes higher Nusselt and Sherwood numbers and the hydrodynamic, thermal and concentration boundary layers become thinner for increasing modified Rayleigh number. The results were reported as correlations of Nusselt and Sherwood numbers for both open and closed cavity problems.

Özet

Bu çalışmanın amacı, kapalı ve açık kavitelerde oluşan türbülanslı doğal taşınım problemini, ısı ve kütle transferinin birada olduğu durum için incelemektir. Bu amaçla, LES (Large Eddy Simulation) türbülans modeli kullanılarak, iki boyutlu kavile geometrilerinde, Boussinesq yaklaşımı kullanılarak, bir modifiye Rayleigh sayısı tanımı yapılmıştır. Bu tanımda, sıcaklık farkından kaynaklanan kaldırma kuvvetinin yanısıra, konsantrasyon farkından kaynaklanan kaldırma kuvveti de yer almaktadır. Modifiye Rayleigh sayısının $10^8-5.10^{10}$ ' aralığı için, LES (Large Eddy Simulation) modeli kullanılarak, nümerik analizlerle türbülanslı akış durumu incelenmiştir. Nümerik analizler için, Fortran programlama dilinde kod yazılmış ve bu kod çok-işlemcili bilgisayarlarda çalışacak şekilde paralelleştirilerek, süperbilgisayarda çözümleme yapılmıştır. Elde edilen sonuçlar, Nusselt sayısı ve Sherwood sayısı korelasyonları olarak ifade edilmiştir.