Multiphase flows are characterized by flows with a mixture
of fluids and solids that have unique velocity fields. Common examples
are rain falling in air, the transport of coal in a liquid in a pipe,
the initial mixing of milk in coffee. Interpenetration of the different
phases pose significant problems with traditional methods for handling
flows with single phases or multiple phases with well-behaved interfaces
(e.g., air about water in a cup). These challenging interpenetration problems
are just now being simulated and understood by specially developed codes
for multiphase flows.
The numerical origins of the CFDLIB collection of codes began with a thesis
study [Kashiwa, 1987] in T-3 to find a stable, well-coupled,
Finite Volume integration scheme for incompressible flow with co-located
primitive variables. Two possibilities emerged [Kashiwa, 1986]
[Kashiwa, 1986], neither of which seemed fully satisfactory.
This was because both schemes required solving two Poisson equations at
each time step, rather than one Poisson solution, as in the original MAC
scheme. Nevertheless, these schemes both represented cell-centered Finite
Volume schemes for incompressible flow.
On another front was an internally supported project to develop a computer
code, CAVEAT, for two and three dimensional, compressible flows with resolved
material interfaces and large deformation that used co-located primitive
variables and an ALE split computational cycle. The CAVEAT code [Addessio
et al, 1992] in its final incarnation included both a Godunovs method
and the so-called Total Variation Diminishing (TVD) Finite Volume method.
Because of CAVEAT's versatile block structure and highly efficient computational
approach, it furnished the basic data structure that was ultimately to
One of the goals of the research project was to develop a capability for
integrating the compressible multiphase flow equations, and this effort
focused on the TVD schemes, because Godunov's method, an explicit scheme,
had not yet been applied to multiphase flows. One of the fundamental features
of TVD schemes is the use of space-time centered fluxes for advancing
a cell-centered state vector. When these fluxes are exactly centered in
space and time, the method is second-order accurate, and is known as the
Lax-Wendroff scheme. The TVD approach was to devise a 'limiter' to sense
when the state is tending toward new extrema, and to use the limiter to
introduce a first order fluxing in such localities. During this development
it became clear that classical staggered meshes and TVD space-time centered
fluxes were two different ways of accomplishing the same coupling of the
momentum and pressure fields. Hence, the next step was to examine a space-time
centered fluxing scheme for incompressible flow. What emerged is what
is now called CCMAC; a cell-centered generalization of the MAC method,
which requires a single Poisson pressure solution each time step [Kashiwa
et al, 1994].
The CCMAC scheme was the key development that provided a common numerical
treatment for CFDLIB: a collection of hydrocodes that are suitable for
compressible flow, incompressible flow, multiphase flow of all kinds,
magnetohydrodynamic forces and multi-fluid solutions, each with their
own set of conservation equations. The design of each code volume in the
library is modular, making the development of codes for specialized applications
exceptionally fast. For example, a k-e model of the Reynolds stress, developed
for one code volume, is easily inserted into another because of the common
data structure among the codes.
The FLIP approach is now being installed into CFDLIB as an option, so
one can take full advantage of the nondiffusive Lagrangian approach (see
section 3.3 on Particle Methods below). With the FLIP option, one can
simulate the motion of a Lagrangian projectile, passing through an Eulerian
gas, penetrating a Lagrangian wall, and into an Eulerian liquid.
A current area of application of CFDLIB is the modeling of a reactive
flow in multiphase, multi-field problems, such as encountered in oil refining,
chemicals manufacturing, metals production, and fiber processing [Kashiwa,
1996]. Fig. 3.2-1 illustrates one time of a full simulation of the
startup and operation of a recirculating fast-fluidized bed (FFB) reactor.
Here, the goal is to model the interpenetration of gases and liquids,
relative to a field of solid catalyst grains. Solid catalyst grains circulate
in a flow loop consisting of a cyclone separator with a gas exit. A realistic
simulation of the FFB reactor is dependent upon the physical models used
to represent the effects of chemical species conversion, physical kinetics
of phase change, granular flow, and multiphase fluid turbulence. The equations
that embody these physical models are developed using a combination of
detailed mathematics, definitive laboratory experiments, and physical
intuition. The large-scale simulation is a means of bringing together
these diverse sets of information in order to test the validity of the
theories, and to provide important guidance to the design and operation
of modern equipment.
There also exist many applications [Apen et al, 1996]
that are a subset of the FFB application, such as the two-phase flow in
human cardiovascular systems, or the dynamics associated with a lifeboat
dropped onto the sea from a search-and-rescue aircraft [Lewis
et al, 1994]. These and many other contemporary applications in modern
technology are addressable by the Los Alamos code library CFDLIB. Some
current applications include the smelting of iron ore, alumina precipitation,
combined granular and fiber flow in manufacturing, and the effects of
a near-miss in the performance of defensive missiles.
Los Alamos Multi-Phase Fluids Projects
All of the filled circles are linkable projects.
All of the empty circles are navigational guides.
- Interfacial phenomena
- Loss of Circulation in 3-Phase Draft-Tube
- Interface reconstruction methods
- Thermomechanical Response of Solids
- Multiphase interpenetration
- Loss of Circulation in 3-Phase Draft-Tube
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This is from "The Legacy and Future of CFD at Los Alamos"
(LAUR#LA-UR-1426)(365Kb pdf file)
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