COMPUTATION OF TURBULENT NATURAL CONVECTION IN A RECTANGULAR CAVITY WITH THE FINITE-VOLUME BASED LATTICE BOLTZMANN METHOD

A numerical study of a turbulent natural convection in an enclosure with the lattice Boltzmann method (LBM) is presented. The primary emphasis of the present study is placed on investigation of accuracy and numerical stability of the LBM for the turbulent natural convection flow. A HYBRID method in which the thermal equation is solved by the conventional Reynolds averaged Navier-Stokes equation method while the conservation of mass and momentum equations are resolved by the LBM is employed in the present study. The elliptic-relaxation model is employed for the turbulence model and the turbulent heat fluxes are treated by the algebraic flux model. All the governing equations are discretized on a cell-centered, non-uniform grid using the finite-volume method. The convection terms are treated by a second-order central-difference scheme with the deferred correction way to ensure accuracy and stability of solutions. The present LBM is applied to the prediction of a turbulent natural convection in a rectangular cavity and the computed results are compared with the experimental data commonly used for the validation of turbulence models and those by the conventional finite-volume method. It is shown that the LBM with the present HYBRID thermal model predicts the mean velocity components and turbulent quantities which are as good as those by the conventional finite-volume method. It is also found that the accuracy and stability of the solution is significantly affected by the treatment of the convection term, especially near the wall.

[1]  Paul A. Durbin,et al.  Toward Improved Prediction of Heat Transfer on Turbine Blades , 2002 .

[2]  K. J. King.  Turbulent natural convection in rectangular air cavities , 1989 .

[3]  유홍선,et al.  혈액 투석시 충혈방법에 따른 인조혈관 내 유동 특성에 관한 수치해석 연구 , 2010 .

[4]  Shiyi Chen,et al.  LATTICE BOLTZMANN METHOD FOR FLUID FLOWS , 2001 .

[5]  Ilya Staroselsky,et al.  Numerical simulation of laminar and turbulent buoyancy-driven flows using a lattice Boltzmann based algorithm , 2004 .

[6]  Ching-Long Lin,et al.  A Simple Finite-Volume Formulation of the Lattice Boltzmann Method for Laminar and Turbulent Flows , 2010 .

[7]  C. Teixeira.  INCORPORATING TURBULENCE MODELS INTO THE LATTICE-BOLTZMANN METHOD , 1998 .

[8]  Chang Shu,et al.  A 3D incompressible thermal lattice Boltzmann model and its application to simulate natural convection in a cubic cavity , 2004 .

[9]  Orestis Malaspinas,et al.  Straight velocity boundaries in the lattice Boltzmann method. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Brian Launder,et al.  On the computation of buoyancy-driven turbulent flows in rectangular enclosures , 1989 .

[11]  K. Hanjalic,et al.  Prediction of turbulent thermal convection in concentric and eccentric horizontal annuli , 1995 .

[12]  Chen,et al.  Lattice Boltzmann thermohydrodynamics. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  Seong-O Kim,et al.  Comparative Analysis of Thermal Models in the Lattice Boltzmann Method for the Simulation of Natural Convection in a Square Cavity , 2011 .

[14]  Xiaowen Shan,et al.  SIMULATION OF RAYLEIGH-BENARD CONVECTION USING A LATTICE BOLTZMANN METHOD , 1997 .

[15]  Q. Zou,et al.  On pressure and velocity boundary conditions for the lattice Boltzmann BGK model , 1995, comp-gas/9611001.

[16]  Seong-O Kim,et al.  COMPUTATION OF TURBULENT NATURAL CONVECTION IN A RECTANGULAR CAVITY WITH THE k–ϵ– –f MODEL , 2004 .

[17]  Shiyi Chen,et al.  A Novel Thermal Model for the Lattice Boltzmann Method in Incompressible Limit , 1998 .

[18]  S. G. Rubin,et al.  A diagonally dominant second-order accurate implicit scheme , 1974 .