| Abstract: | Flow within a packed bed is normally calculated by attempting to simultaneously satisfy the continuity and Ergun equations. However, the presence of gas sources/sinks within the bed escalates the complexity of the problem, particularly when the flow is two-dimensional and a solution to the full Ergun equation is required. In quest of an efficient and dependable algorithm for the calculation of gas flow, a critical review of existing solution methods was undertaken and a new method, ‘FLOW’, is now proposed. The technique retains the viscous and inertial pressure gradient terms of the Ergun equation, and both are treated as linear functions of the flow. Solutions are approached iteratively; using finite difference techniques, the continuity and linearized Ergun equations are solved for the pressure field; a new flow field is then calculated from which is derived an adjustment to the inertial resistance term of the Ergun equation. The sequence is repeated until satisfactory convergence is obtained. Relatively few iterations are normally required and, for the case of negligible inertial pressure drop, one calculation cycle is sufficient. A comparison of results obtained using the ‘FLOW’, modified ‘SIMPLE’ and vorticity procedures is presented. The proposed method allow flexibility in the specification of boundary conditions and can be applied to compressible or incompressible flow, as well as for the case of nonisothermal beds. |
