107,282 research outputs found
Solving the flow fields in conduits and networks using energy minimization principle with simulated annealing
In this paper, we propose and test an intuitive assumption that the pressure
field in single conduits and networks of interconnected conduits adjusts itself
to minimize the total energy consumption required for transporting a specific
quantity of fluid. We test this assumption by using linear flow models of
Newtonian fluids transported through rigid tubes and networks in conjunction
with a simulated annealing (SA) protocol to minimize the total energy cost. All
the results confirm our hypothesis as the SA algorithm produces very close
results to those obtained from the traditional deterministic methods of
identifying the flow fields by solving a set of simultaneous equations based on
the conservation principles. The same results apply to electric ohmic
conductors and networks of interconnected ohmic conductors. Computational
experiments conducted in this regard confirm this extension. Further studies
are required to test the energy minimization hypothesis for the non-linear flow
systems.Comment: 11 pages, 2 figures, 1 tabl
Chaotic Mixing in Three Dimensional Porous Media
Under steady flow conditions, the topological complexity inherent to all
random 3D porous media imparts complicated flow and transport dynamics. It has
been established that this complexity generates persistent chaotic advection
via a three-dimensional (3D) fluid mechanical analogue of the baker's map which
rapidly accelerates scalar mixing in the presence of molecular diffusion. Hence
pore-scale fluid mixing is governed by the interplay between chaotic advection,
molecular diffusion and the broad (power-law) distribution of fluid particle
travel times which arise from the non-slip condition at pore walls. To
understand and quantify mixing in 3D porous media, we consider these processes
in a model 3D open porous network and develop a novel stretching continuous
time random walk (CTRW) which provides analytic estimates of pore-scale mixing
which compare well with direct numerical simulations. We find that chaotic
advection inherent to 3D porous media imparts scalar mixing which scales
exponentially with longitudinal advection, whereas the topological constraints
associated with 2D porous media limits mixing to scale algebraically. These
results decipher the role of wide transit time distributions and complex
topologies on porous media mixing dynamics, and provide the building blocks for
macroscopic models of dilution and mixing which resolve these mechanisms.Comment: 36 page
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