This brief paper describes and illustrates the performance of three key features
in the RELAP5-3D
computer code: the multidimensional hydrodynamic model, the multi-dimensional
reactor kinetics model, and the BPLU matrix solver.
A comprehensive description of the code can be found in
Volume I of the Users Manual.
code is an outgrowth of the one-dimensional 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 re-assessment of the
safety of all of its test and production reactors throughout the United States.
The RELAP5 code was chosen as the thermal-hydraulic 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 three-dimensional flow model. Later, under
laboratory-discretionary funding, the multi-dimensional reactor kinetics was
added. Altogether, DOE sponsored improvements and enhancements have amounted to
a multimillion-dollar 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, multi-dimensional thermal-hydraulic 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
three-dimensional hydrodynamic model and the multi-dimensional kinetics model.
Multi-Dimensional Hydrodynamic Model
The multi-dimensional component in RELAP5-3D was developed to allow
the user to more accurately model the multi-dimensional 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 three-dimensional 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, three-dimensional grid is defined by mesh interval input
data in each of the three coordinate directions.
The functionality of the multi-dimensional 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 multi-dimensional flow behavior. One example is a series of experiments
conducted at the Rensselaer Polytechnic Institute to examine the flow patterns
in a two-dimensional test section connected to an air-water loop1
Figure 1. Observed and computed flow patterns in the RPI
Two-Phase Test Section
The test section (Figure 1, left) consisted of a thin vertical channel that
simulated a two-dimensional 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. Single-phase and two-phase flows were supplied to the test
section in an asymmetric manner to generate a two-dimensional flow field. An
air-water 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
The RPI test section was modeled2 using the multi-dimensional
component in RELAP5-3D . Cartesian geometry was selected and
the test section was represented with 1 interval in the x-direction, 17
intervals in the y-direction, and 16 intervals in the z-direction. The
z-coordinate was selected to be in the vertical direction. Figure 1, right,
shows the steady-state flow pattern predicted by RELAP5-3D 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
where a is the void fraction, vgyand
vgz are the gas velocities in the y and z directions
respectively, and vfy and vfz 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.
Multi-Dimensional Neutron Kinetics
The multi-dimensional neutron kinetics model in RELAP5-3D is
based on the NESTLE code3 developed by Paul Turinsky and co-workers
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 non-linear
iteration technique. Three, two, or one-dimensional 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, non-reentrant current, reflective, and cyclic
boundary conditions are available. The steady-state eigenvalue and time
dependent neutron flux problems can be solved by the NESTLE code as implemented
The implementation of the NESTLE neutron kinetics has been verified by the
simulation of the NEACRP4 three dimensional benchmark problems5.
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 RELAP5-3D . Quarter core symmetry was used
for the simulation. The RELAP5-3D 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
Figure 2. Comparisons of RELAP5-3D 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 shared-memory 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 border-banded form.
Speed-ups are achieved for RELAP5-3D; running with BPLU over the
default solver. For almost all one-dimensional problems, there is no speed-up;
however, for problems with wider bandwidths, especially those with
three-dimensional regions, significant speed-ups 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 two-phase 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
| Note: All times on a DEC Alpha 4100
The results show speed-ups ranging from 2.1 to 3.5 for this simple
||K. M. Bukhari and R. T. Lahey, "The Measurement of Countercurrent Phase
Separation and Distribution in a Two-Dimensional Test Section," Rensselaer
Polytechnic Institute, Department of Nuclear Engineering, NUREG/CR-3577,
||C. B. Davis, "Assessment of RELAP5-3D Using Data from
Two-Dimensional RPI Flow Tests," Proceedings from the 1998 RELAP5 International
Users Seminar, College Station, Texas, May 17-21, 1998.
||R. M. Al-Chalabi, et al., "NESTLE: A Nodal Kinetics Code," Transactions of the
American Nuclear Society, Volume 68, June, 1993.
||H. Finnemann and A. Galati, "NEACRP 3-D LWR Core Transient Benchmark – Final
Specifications," NEACRP-L-335 (Revision 1), January, 1992.
||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 11-15, 1994, Vol.
II, pp 269-280.
||G. L. Mesina, "Border-Profile LU Solver for RELAP5-3D," Proceedings of the 1998
RELAP5 International Users Seminar, College Station, Texas, May 17-21, 1998.
A more detailed paper on RELAP5-3D 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 three-dimensional hydrodynamics.
Part 2 discusses the validation of the
three-dimensional hydrodynamics using data from LOFT Test L2-5.
discusses the multidimensional neutron kinetics model and the Border
Profiled Lower Upper (BPLU) sparse matrix solver.
the free Acrobat Reader to view or print the PDF version of the
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Last modified: May 17, 2011.