This brief paper describes and illustrates the performance of three key features
in the RELAP53D
computer code: the multidimensional hydrodynamic model, the multidimensional
reactor kinetics model, and the BPLU matrix solver.
A comprehensive description of the code can be found in
Volume I of the Users Manual.
Background
The RELAP53D
code is an outgrowth of the onedimensional RELAP5/MOD3 code developed at the
Idaho National Laboratory (INL) for the U.S. Nuclear Regulatory Commission
(NRC). The U.S. Department of Energy (DOE) began sponsoring additional RELAP5
development in the early 1980s to meet its own reactor safety assessment needs.
Following the accident at Chernobyl, DOE undertook a reassessment of the
safety of all of its test and production reactors throughout the United States.
The RELAP5 code was chosen as the thermalhydraulic analysis tool because of
its widespread acceptance.
The application of RELAP5 to these various reactor designs created the need for
new modeling capabilities. In particular, the analysis of the Savannah River
reactors necessitated a threedimensional flow model. Later, under
laboratorydiscretionary funding, the multidimensional reactor kinetics was
added. Altogether, DOE sponsored improvements and enhancements have amounted to
a multimilliondollar investment in the code.
Up until the end of 1995, the INL maintained NRC and DOE versions of the code
in a single source code that could be partitioned before compilation. It became
clear by then, however, that the efficiencies realized by the maintenance of a
single source were being overcome by the extra effort required to accommodate
sometimes conflicting requirements. The code was therefore "split" into two
versions, one for NRC and the other for DOE. The DOE version maintained all of
the capabilities and validation history of the predecessor code, plus the added
capabilities that had been sponsored by the DOE before and after the split.
The most prominent attribute that distinguishes the DOE code from the NRC code
is the fully integrated, multidimensional thermalhydraulic and kinetic
modeling capability in the DOE code. This removes any restrictions on the
applicability of the code to the full range of postulated reactor accidents.
Other enhancements include a new matrix solver for 3D problems, new water
properties, and improved time advancement for greater robustness. The balance
of this paper focuses on the capabilities and bench marking of the
threedimensional hydrodynamic model and the multidimensional kinetics model.
MultiDimensional Hydrodynamic Model
The multidimensional component in RELAP53D was developed to allow
the user to more accurately model the multidimensional flow behavior that can
be exhibited in any component or region of a LWR system. Typically, this will
be the lower plenum, core, upper plenum and downcomer regions of an LWR.
However, the model is general, and is not restricted to use in the reactor
vessel. The component defines a one, two, or threedimensional array of volumes
and the internal junctions connecting them. The geometry can be either
Cartesian (x, y, z) or cylindrical (r, q
, z). An orthogonal, threedimensional grid is defined by mesh interval input
data in each of the three coordinate directions.
The functionality of the multidimensional component has been under testing and
refinement since it was first applied to study the K reactor at Savannah River
in the early 1990s. A set of approximately twenty verification test problems
was devised to demonstrate the correctness of the numerical conservation
equation formulation. All of these problems have closed form solutions. Until
recently, application of the model to experiments was limited to tests carried
out in the L reactor at Savannah River. A program is currently underway to
expand the validation base to include a wide variety of experiments that
exhibit multidimensional flow behavior. One example is a series of experiments
conducted at the Rensselaer Polytechnic Institute to examine the flow patterns
in a twodimensional test section connected to an airwater loop^{1}
.
Figure 1. Observed and computed flow patterns in the RPI
TwoPhase Test Section
The test section (Figure 1, left) consisted of a thin vertical channel that
simulated a twodimensional slice through the core of a pressurized water
reactor. The test section was 0.91 m (3 ft) tall, 0.91 m (3 ft) wide, and 0.013
m (0.5 in.) thick. Singlephase and twophase flows were supplied to the test
section in an asymmetric manner to generate a twodimensional flow field. An
airwater mixture was injected at port 4 and liquid was injected at port 1.
Ports 2 and 3 served as outlets and port 5 was closed. A traversing gamma
densitometer was used to measure void fraction at many locations in the test
section. High speed photographs provided information on the flow patterns and
flow regimes. Figure 1, left, shows the observed flow patterns observed in the
experiments, where the arrows indicate the direction of flow but not the
magnitude.
The RPI test section was modeled^{2} using the multidimensional
component in RELAP53D . Cartesian geometry was selected and
the test section was represented with 1 interval in the xdirection, 17
intervals in the ydirection, and 16 intervals in the zdirection. The
zcoordinate was selected to be in the vertical direction. Figure 1, right,
shows the steadystate flow pattern predicted by RELAP53D for
Test 2AN4. The direction and length of each vector was computed based on
resolving the liquid and air flow velocities in the y and z directions as
follows:
where a is the void fraction, v_{gy}and
v_{gz} are the gas velocities in the y and z directions
respectively, and v_{fy} and v_{fz} are the
liquid velocities in the y and z directions, respectively.
The predicted flow pattern is seen to closely match that observed in the
experiment, exhibiting a general upward flow in the center towards the port 2
outlet, and recirculation regions on either side.
MultiDimensional Neutron Kinetics
The multidimensional neutron kinetics model in RELAP53D is
based on the NESTLE code^{3} developed by Paul Turinsky and coworkers
at North Carolina State University under an INL initiative. The NESTLE code
solves the two or four group neutron diffusion equations in either Cartesian or
hexagonal geometry using the Nodal Expansion Method (NEM) and the nonlinear
iteration technique. Three, two, or onedimensional models may be used. Several
different core symmetry options are available including quarter, half, and full
core options for Cartesian geometry and 1/6, 1/3, and full core options for
hexagonal geometry. Zero flux, nonreentrant current, reflective, and cyclic
boundary conditions are available. The steadystate eigenvalue and time
dependent neutron flux problems can be solved by the NESTLE code as implemented
in RELAP53D
.
The implementation of the NESTLE neutron kinetics has been verified by the
simulation of the NEACRP^{4} three dimensional benchmark problems^{5}.
Four of the PWR rod ejection scenarios, ejection of a control rod and a
peripheral rod from Hot Zero Power (HZP) and Hot Full Power (HFP) conditions
were simulated by RELAP53D . Quarter core symmetry was used
for the simulation. The RELAP53D core model for the benchmark
problem consisted of a sequence of 47 parallel pipes, each consisting of a
series of heat structures and control volumes to model the fuel and coolant
from a single assembly. The results of the two HFP rod ejection cases are
compared with the reference results in Figure 2. As shown, excellent agreement
was obtained.
Figure 2. Comparisons of RELAP53D and PANTHER
Predictions of Power Excursions Following Rod Ejection from Hot Full Power
BPLU Matrix Solver
The Border Profiled Lower Upper (BPLU) matrix solver ^{6} is used to
efficiently solve sparse linear systems of the form AX = B. BPLU is designed to
take advantage of pipelines, vector hardware, and sharedmemory parallel
architecture to run fast. BPLU is most efficient for solving systems that
correspond to networks, such as pipes, but is efficient for any system that it
can permute into borderbanded form.
Speedups are achieved for RELAP53D; running with BPLU over the
default solver. For almost all onedimensional problems, there is no speedup;
however, for problems with wider bandwidths, especially those with
threedimensional regions, significant speedups can be achieved. One of the
standard installation problems, "3dflown.i" illustrates the reduction in run
time that can be achieved. The problem is a simple cube subdivided into a 3x3
region in each of the Cartesian coordinate directions. There are nine cases
examined with this model, comprised of flow in each coordinate direction
(x,y,z) of vapor only, liquid only, and a twophase mixture. Table 1 compares
the run times for the default and BPLU solvers.
Table 1. CPU Times for 3dflown.i Problem Using Default and BPLU Solvers
Case

Default Solver
(CPU sec.)

BPLU Solver
(CPU sec.)

Ratio

1 
7.180 
2.437 
2.946 
2 
7.142 
2.110 
3.385 
3 
6.903 
2.718 
2.540 
4 
6.142 
2.422 
2.536 
5 
5.513 
2.117 
2.604 
6 
5.818 
2.698 
2.156 
7 
6.167 
2.432 
2.535 
8 
7.404 
2.116 
3.499 
9 
6.396 
2.697 
2.372 
Note: All times on a DEC Alpha 4100
Workstation 
The results show speedups ranging from 2.1 to 3.5 for this simple
threedimensional problem.
References
1. 
K. M. Bukhari and R. T. Lahey, "The Measurement of Countercurrent Phase
Separation and Distribution in a TwoDimensional Test Section," Rensselaer
Polytechnic Institute, Department of Nuclear Engineering, NUREG/CR3577,
January, 1984. 
2. 
C. B. Davis, "Assessment of RELAP53D Using Data from
TwoDimensional RPI Flow Tests," Proceedings from the 1998 RELAP5 International
Users Seminar, College Station, Texas, May 1721, 1998. 
3. 
R. M. AlChalabi, et al., "NESTLE: A Nodal Kinetics Code," Transactions of the
American Nuclear Society, Volume 68, June, 1993. 
4. 
H. Finnemann and A. Galati, "NEACRP 3D LWR Core Transient Benchmark – Final
Specifications," NEACRPL335 (Revision 1), January, 1992. 
5. 
J. L. Judd, W. L. Weaver, T. Downar, and J. G. Joo, "A Three Dimensional Nodal
Neutron Kinetics Capability for RELAP5," Proceedings of the 1994 Topical
Meeting on Advances in Reactor Physics, Knoxville, TN, April 1115, 1994, Vol.
II, pp 269280. 
6. 
G. L. Mesina, "BorderProfile LU Solver for RELAP53D," Proceedings of the 1998
RELAP5 International Users Seminar, College Station, Texas, May 1721, 1998.

A more detailed paper on RELAP53D is available as a
MS Word document or as an
Adobe PDF file
.
The more detailed paper is also available in three parts in HTML format.
Part 1 includes the introduction and
discusses the threedimensional hydrodynamics.
Part 2 discusses the validation of the
threedimensional hydrodynamics using data from LOFT Test L25.
Part 3
discusses the multidimensional neutron kinetics model and the Border
Profiled Lower Upper (BPLU) sparse matrix solver.
Download
the free Acrobat Reader to view or print the PDF version of the
detailed paper.
Questions or problems regarding this web site should be directed to
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