Three-dimensional finite element modelling of coupled free/porous flows: applications to industrial and environmental flows
journal contribution
posted on 2012-12-07, 12:08authored byNavraj S. Hanspal, Vahid Nassehi, A. Kulkarni
Conjunctive modelling of free/porous flows provides a powerful and cost-effective tool for designing industrial
filters used in the process industry and also for quantifying surface–subsurface flow interactions, which
play a significant role in urban flooding mechanisms resulting from sea-level rise and climate changes. A
number of well-established schemes are available in the literature for simulation of such regimes; however,
three-dimensional (3D) modelling of such flow systems still presents numerical and practical challenges.
This paper presents the development of a fully 3D, transient finite element model for the prediction and
quantitative analyses of the hydrodynamic behaviour encountered in industrial filtrations and environmental
flows represented by coupled flows. The weak-variational formulation in this model is based on the
use of C0 continuous equal-order Lagrange polynomial functions for velocity and pressure fields represented
by 3D hexahedral finite elements. A mixed UVWP finite element scheme based on the standard
Galerkin technique satisfying the Ladyzhenskaya–Babuska–Brezzi stability criterion through incorporation
of an artificial compressibility term in the continuity equation has been employed for the solution of coupled
partial differential equations. We prove that the discretization generates unified stabilization for both the
Navier–Stokes and Darcy equations and preserves the geometrical flexibility of the computational grids.
A direct node-linking procedure involving the rearrangement of the global stiffness matrix for the interface
elements has been developed by the authors, which is utilized to couple the governing equations in a
single model. A variety of numerical tests are conducted, indicating that the model is capable of yielding
theoretically expected and accurate results for free, porous and coupled free/porous problems encountered
in industrial and environmental engineering problems representing complex filtration (dead-end and
cross-flow) and interacting surface–subsurface flows. The model is computationally cost-effective, robust,
reliable and easily implementable for practical design of filtration equipments, investigation of land use
for water resource availability and assessment of the impacts of climatic variations on environmental
catastrophes (i.e. coastal and urban floods). The model developed in this work results from the extension
of a multi-disciplinary project (AEROFIL) primarily sponsored by the European aerospace industries for
development of a computer simulation package (Aircraft Cartridge Filter Analysis Modelling Program),
which was successfully utilized and deployed for designing hydraulic dead-end filters used in Airbus
A380.
History
School
Aeronautical, Automotive, Chemical and Materials Engineering
Department
Chemical Engineering
Citation
HANSPAL, N.S., NASSEHI, V. and KULKARNI, A., 2013. Three-dimensional finite element modelling of coupled free/porous flows: applications to industrial and environmental flows. International Journal for Numerical Methods in Fluids, 71 (11), pp. 1382-1421.