Upwind algorithm

The advection—diffusion equation with a source term can be solved by CFD algorithms in general. Patankar provided an excellent introduction to numerical fluid flow and heat transfer. Oran and Boris discussed numerical solutions of diffusion—convection problems with chemical reactions. Since fuel cells feature an aspect ratio of the order of 100, 0(100), the upwind scheme for the flow-field solution is applicable and proves to be very effective. Unstructured meshes are commonly employed in commercial CFD codes. 

The finite volume methods have been used to discretised the partial differential equations of the model using the Simple method for pressure-velocity coupling and the second order upwind scheme to interpolate the variables on the surface of the control volume. The segregated solution algorithm was selected. The Reynolds stress turbulence model was used in this model due to the anisotropic nature of the turbulence in cyclones. Standard fluent wall functions were applied and high order discretisation schemes were also used. 

Several schemes and algorithms for solving the fluid dynamic part of the model have been published. This work has been concentrated on several items. Most important, one avoids using the very diffusive first order upwind schemes discretizing the convective terms in the multi-fluid transport equations. Instead higher order schemes that are more accurate have been implemented into the codes [62, 139, 140, 65, 105, 66[. The numerical truncation errors induced by the discretization scheme employed for the convective terms may severely alter the numerical solution and this can destroy the physics reflected... 

The order of accuracy of the upwind scheme can be improved by using a higher-order accurate scheme such as QUICK (quadratic upwind interpolation for convective kinematics).The concentration at an interface is interpolated by means of a parabola instead of a straight line. The use of QUICK or similar methods may, however, complicate implementation of boundary conditions or lessen the convergence rate of the solution algorithm. 

Stability is a problem associated with most explicit advection algorithms. The explicit algorithm of (25.130) has the worst behavior. The upwind scheme is stable if... 

Based on the finite volume method, the control equation can be converted to a numerical method for solving algebraic equations. Convection of equation use second-order upwind difference during the discrete process, the solver is based on the pressure, the pressure-velocity coupling adopt the SIMPLE algorithm, pressure interpolation scheme use PRESTO Format. 

The employed oxygen is compressible fluid, and the flow between inlet and outlet is called isentropic flow. The pressure at the inlet is 0.9 MPa. The temperature is 293 K. The pressure at the outlet is 0.13 MPa. The flow speed around the wall is calculated through standard wall functions with consideration of no wall slippage. The flow field is calculated by the PISO which belongs to coupled algorithm with using Second Order Upwind as array of difference and VOF model as two phase flow. 

The model equations were solved numerically by using the commercial software FLUENT 6.2 with finite volume method. The SIMPLEC algorithm was used to solve the pressure-velocity coupling problem in the momentum equations. The second-order upwind spatial discretization scheme was employed for all differential equations. 

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