CFD analysis of natural convective non-Darcy flow in porous medium

In this study, the fluid dynamics in porous media is treated as a non-Darcy flow condition that the inertial resistance and the viscous resistance must be considered. According to Niven, the porosity and particle size determine the flow condition, whether it is Darcy or non-Darcy flow. From this, Ergun developed the well-known equation of the relation between momentum loss and the geometrical parameters. When Darcy equation is introduced, the permeability, Forchheimer's coefficient b, and momentum loss can be expressed. Based on these, the governing equations of mass, momentum and energy were implemented in ANSYS CFX-11.0. The physical domain is a square rectangular enclosure. The mesh was generated with hexagonal mesh and included 50 x 50 nodes, uniformly. In transient analysis, zero velocity and the reference temperature was applied as an initial value. The convergence criterion was below 10-5 for all averaged residual RMS value. The temperature and velocity were calculated. For validation, the porous media with constant temperature on side wall and with the heat generating inside was modeled. The results of numerical analysis for validation of the case of only constant side wall temperature were compared with the previous results of Nithiarasu et al. Most of the data agreed with the data of Nithiarasu et al. and reasonable trends were found. For the case of the porous media with heat generating inside as well as the constant temperature on side wall, the results showed a good agreement with the previous works. The influence of Darcy number was examined and we found that the natural circulation can be depressed more by the denser porous media. For deeper level of validation, transient analysis was also conducted. The steady state was attained at about 1 or 2 minutes as the natural circulation became stable. To describe the flow behavior, previous works applied the Darcy flow assumption. However, non-Darcy flow is also important and must be considered. By conducting Scale Analysis, Nusselt number correlation in terms of Rayleigh number can be derived. Nu = C1(Ra-A)1/2 / 1-C2(Ra-A)-1/6 where Nu = Sd2/2kΔT, A = ραK1/2d2CF / μδ3 and δH = α(CFK1/2 / gβKΔT)1/2. C1 and C2 are constants of order 1 and could be determined empirically or analytically. Based on Ergun equation, CFD methodology was developed to understand the natural convection within the porous media for, both Darcy flow and non-Darcy flow condition. Furthermore, the physical model and numerical method was validated showing good agreements with the previous works. To suggest a theoretical base for non-Darcy flow case, Nusselt number correlation was derived by the scale analysis. As an extension of this study, the further analysis on applications, such as core catcher in LMFBR will be added to complement the study