| OCR Text |
Show - 6 - walls. At x = ± L, there is symmetry. Hence, Ft =F; (14) and fH/ax = 0 . (IS) METHOD OF SOLUTION Even a single vertical section of the heater could be complex, because it represents a multi-connected region in which numerous tubes could be embedded in the porous medium. As an illustration, a computational module consisting of a single tube is considered. Because of the difficulty of handling simultaneously rectangular Cartesian and cylindrical geometries in the mesh, the tube is assumed to be square (Fig.I). Due to symmetry of the computational module a uniform rectangular grid is used. A grid independence study was conducted, and after some trials a 61X41 grid, in the x- and ydirections, respectively, was selected for the calculations. This grid represented a good compromise between accuracy and computational effort. The volumetric heat generation (source term) due to release of the heat of combustion was placed along the x-axis, midway between the entrance and the duct. It was assumed that heat generation takes place within a strip of one mesh size in height. The model equations, Eqs.(1-5), (9) and (10) together with appropriate boundary conditions were finite-differenced using the control volume approach as discussed by Patankar (1980). The SIMPLER algorithm in terms of primitive variables was used in the solution of the model equations. Strict convergence criteria were required to satisfy the conservation equations. To improve the rate of convergence, initial gas velocity in the porous medium was set to the inlet velocity. Also, the results of the previous simulation were used as the initial approximation for the next one. Even under these circumstances, 400 to 500 iterations were required to obtain converged solutions. RESULTS AND DISCUSSION Model Parameters There are a large number of independent parameters governing the problem, and the parameters used in the sample calculations are summarized in Table 1. Representative values of parameters and properties, including those for the porous matrix, were used to obtain the sample results reported in the paper. The main objective of the calculations is to identify the opacities (To) and the heat transfer parameter hAe for which the surface combustor-heater yields optimum performance. The distribution plate is not modeled, and the heat release, simulating the combustion of fuel is assumed to take place in the region half-way between the bottom of the bed and the square tube. The "combustion zone" is assumed to be one node high (Le., D.y = 1.6 mm). |
