Numerical Study Of The Vortex Shedding From A Square Cylinder And Its Effects On The Heat Transfer Of Mixed Convection

In the field of computational heat transfer, the subject of unsteady mixed convection about a square cylinder is of relevance to the flow and heat transfer around a sharp-edged rectangular cross-sectional cylinder. For several decades, the problem has been a subject of great attention among applied mathematicians, fluid dynamicists and heat transfer analysts owing to its numerous engineering applications such as the cooling of electronic components, energy conservation, structural design and acoustic emissions. Based on a review of its current condition and development home and abroad, the thesis systematically expounds some achievements in the numerical arithmetic and the methodology that facilitate the study of the flow around a square cylinder and heat transfer of unsteady mixed convection by using the primitive-variable-time-dependent approach.Firstly, based on the method of pressure-velocity coupling introduced by SIMPLE algorithm and a revised method of solving the unsteady equation of stream function and vorticity on uniform grid, a special algorithm called primitive-variable-time-dependent approach is formed in the present study. In this algorithm the Navier-Stokes equation in primitive variable form is solved by using the time-dependent approach on non-uniform staggered grid system. The second-order accuracy finite difference is used for the first and second partial derivatives of all variables of the convective terms and diffusion terms. The finite difference equations are solved with ADI method. Outer-node method is used to form the computational grid. The pressure on the wall and the nearest velocity normal to the wall are computed from the momentum equations in special form, and for the corners of the wall, the pressure is averaged by the value gained from the alternating direction calculation of the momentum equations. To validate the algorithm, two classical test problems are studied: namely, the driven cavity flow and the laminar natural convection flow in a square cavity. The calculation results are consistent with the results of the other numerical methods. It is valuable that a new law of laminar natural convection flow and heat transfer is summarized on the basis of previous scholar's works and Ra=5×104 is accurately proposed as the flow transition point between the laminar flow predominated by the heat conduct and the laminar flow cooperated by the convection and the heat conduct.Secondly, the primitive-variable-time-dependent approach is used to compute the steady and unsteady two-dimensional flow around a square cylinder at different Reynolds numbers. The appropriate length of the calculation domain is selected by comparing the results calculated by using some different outlet boundary condition. Several computational parameters, such as Xu(distance from body to inlet), Xd(distance from body to outlet), blockage parameter B, lateral and outlet boundary conditions, are taken into consideration to analyze their effects on vortex shedding frequency scaled by the Strouhal number St and drag coefficient CD. Ranges of blockage parameters are studied for the different lateral boundary conditions to demonstrate where its effects can be ignored numerically, and then the effects of the lateral boundaries are compared. A set of optimized computational domain and artificial boundary conditions are selected to study the fluid flow and heat transfer around a square cylinder by using the primitive-variable-time-dependent approach. Numerical calculations of the steady flow around a square cylinder have been reported, and the onset of vortex shedding is predicted in between Re=50~55. To validate the algorithm, the unsteady process of vortex formation and shedding from the square cylinder for Re=100 is simulated successfully and the strict Kármán vortex street is also obtained.Finally, based on the simulation of the flow around a square cylinder, the energy equation is taken into consideration and the vortex shedding from a square cylinder and its effects on the heat transfer of laminar forced c...