An Integrated RELAP5-3D and Multiphase CFD Code System Utilizing a Semi Implicit Coupling Technique Page: 4 of 12
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2001 RELAP5 International Users Seminar
Sun Valley, Idaho
September 5-7, 2001
program has no formal time step size requirements for
numerical stability. This is not to say that the iterative
solution procedure will converge for any size time step;
it will not. However, since the material Courant limit
does not determine stability, the nodalization of the CFD
program can be small enough to resolve the fluid flow
patterns in a manner typical for CFD calculations
without violating any formal stability criteria.
It should be noted that the semi-implicit coupling
algorithm can be implemented as a master process for
any number of system codes. However, the
implementation into the RELAP series of codes is easier
since they use a "single-shot" linearization technique.
By only linearizing the conservation equations once per
time step, the coupling coefficients remain fixed during
the course of the time step. If the conservation equations
are linearized more than once per time step, new
coupling coefficients would be calculated at each
iteration in the master process and the slave process
would need to recalculate the flow field for each new set
of coupling coefficients. In the present implementation
in the CFD program, this additional requirement would
result in significantly longer execution times.
Implementation in the CFD Program
The CFD program which was chosen to be coupled with
RELAP5-3D was based on the CFDS-FLOW3D
(Harwell Laboratory, 1992) (now CFX) program. The
program has been extensively modified to provide
multidimensional, multifield, heated, two-phase flow
capability. A four-field formulation [continuous liquid,
dispersed vapor (bubbles), continuous vapor and
dispersed liquid (drops)] is used to represent the
complete range of two-phase flow patterns from bubbly
through annular flow more accurately.
As stated previously, the role of the CFD program in this
coupling algorithm is to calculate the phasic flow rates
of mass, energy, volume and gaseous non-condensables
across the coupling plane. (For the remainder of this
paper, the phrase "net phasic flows rate" will refer to the
net phasic flow rates of mass, energy, volume, and the
mass flow rate of a non-condensable gas). Using the
CFD program to calculate the net phasic flow rates
across the coupling plane instead of calculating volume
conditions has many advantages. The first of these is the
ability to integrate the CFD results over the flow area at
the coupling plane. Since the coupling algorithm is a
function of only the net phasic flow rates, this technique
readily permits the coupling of one RELAP5-3D
volume to numerous CFD volumes. This is a
requirement of any coupled system/CFD code suite,
since the nodalization of system programs, such as
RELAP5-3D, is usually much coarser than the
nodalization used for the CFD programs.
The semi-implicit coupling in the CFD program is
implemented as an extension of a standard pressure
boundary condition. At the beginning of each time step,
RELAP5-3D passes the old-time volume parameters
(pressure, void fraction, phasic densities, phasic internal
energies and non-condensable quality) to the CFD
program. Using these conditions, the CFD program then
performs the spatial differencing (upwind differencing
was used in this example) of the quantities convected
across the boundary (void fraction, phasic densities,
phasic internal energies, phasic velocities and non-
condensable quality). Since the CFD program may use
many more cells and a larger number of fields to
represent the fluid conditions, an averaging scheme is
required to define the two-phase state variables required
by RELAP5-3D. In the current implementation, the
upwind quantity for each of the CFD cells is computed
as a simple volume weighted average. Note that this
implementation will correctly handle counter-current
phasic flow situations since each small cell is
At this point in the solution scheme, the convected
quantities are fixed for the time step. Using these
convected quantities, RELAP5-3D creates the pressure
matrix as described above and transmits coefficients a
through h to the CFD program. The CFD program uses
these coefficients in conjunction with the net phasic flow
rates at the coupling plane. These net phasic flow rates
are calculated using
Net Phasic Flow = 1 AV i, j
where nfld, is the number of fields that are present for
the given phase, and nfac is the number of faces in the
CFD program that comprise the coupling junction, Aj is
the flow area for the face, Via is the velocity and $i is
the convected quantity (e.g., macroscopic density for the
mass equation). This has been implemented in such a
way as to maintain the use of symmetry boundary
conditions in the CFD program by using a multiplier (1,
2 or 4) depending on how many symmetry planes are
used in the problem.
Note that this definition integrates over the number of
fields in a given phase. This allows the CFD program to
calculate counter-current phasic flows (i.e., a falling
liquid film and rising liquid drops) at the coupling plane
and determine the net phasic flow rates.
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Aumiller, D.L.; Tomlinson, E.T. & Weaver, W.L. An Integrated RELAP5-3D and Multiphase CFD Code System Utilizing a Semi Implicit Coupling Technique, article, June 21, 2001; United States. (digital.library.unt.edu/ark:/67531/metadc783173/m1/4/: accessed October 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.