Three dimensional hydrodynamic modelling of combined free/porous flow regimes

In the present scenario, as advances in research, technology and engineering application have been on a rise , thus persuading researchers and engineers to employ new computer modelling techniques for the design and analysis, mainly due to time, environmental and economic constraints. Moreover it also forms a basis for any observed anomalies, when comparing with the simulated and experimental results and taking steps to develop optimum design strategies. The present research work deals with the development of novel ftlter designs when employed in aeronautical hydraulic systems. These pleated cartridge ftlters would be fabricated using eco-friendly fIltering media supported by unconventional disposable or reusable solid components. The primary focus of the present research work to develop a robust cost-effective simulating tools for simulating the results in the hydrodynamic behaviour of the fluid in pleated cartridge ftlters. As observed in any ftltration process, it comprises of two flow regimes namely free flow and porous flow regimes. For over five decades, it had been a subject of intense research and investigation for researchers, scientist and engineers to resolve some of the critical and vital issues related to filtration process. The main problems, when compared to others, that are associated with such processes are the free/porous interfacial constraints along with boundary conditions and their mathematical representation with respect to the industrial applications. A three dimensional model has been developed to represent the momentum and mass conservation for creeping incompressible flow in coupled free/porous flow regimes. In order to take into consideration the rheological behaviour of the fluid, power law model has been included, which forms the constitutive equation, and the viscosity of the fluid has been updated for the highly viscous specially formulated hydraulic fluid. For any numerical technique of analysis, on vital aspect is the boundary conditions that are imposed on the surface/volume/edge of the domain under consideration. The free (Stokes) and porous flow (Darey) regimes have been linked and solved in conjunction with continuity equations on a perturbed continuity scheme based on the standard Galerkin weighted residual finite element method. The perturb continuity UVWP finite element scheme is based On the equal order interpolation approximations and the discretized working equations are then transformed into the local coordinate system using iso-parametric mapping. The elements used are linear (8 nodded) hexahedral elements. The integrals in the elemental stiffness equations were calculated using Gauss-Legendre quadrature. After evaluation of the members of the elemental stiffness matrix, they are assembled over the common nodes in the computational grid to obtain a system of algebraic equations. After substituting the boundary conditions, the system becomes determinate and the algebraic equations can be solved using a frontal solution method. The described simulations are carried out using an in-house developed lnte! Visual FORTRAN code. The time stepping technique used here is second order Taylor-Galerkin method. The concept of compression permeability model developed by Nassehi et aL Nassehi et aL, 2005J ( developed for two dimensional case and now extended to three dimensional case) has been used to into the flow model to take into account the effects arising due to the mtration area loss in pleated cartridge filters and degree or extent of compression of the fUter medium. Significant over-use of media material or the need for changes to the geometric or mechanical design can be identified using the procedures described.