# 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, 2001program 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

individually examined.

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 usingnfld nfac

Net Phasic Flow = 1 AV i, j

i=1j=1(2)

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.3

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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.