Complete Homework 1
Course Content and Expectations
Review the class syllabus.
Purpose of Simulation
Computer Simulation allows us to study the behavior of physical
systems when experiments are either too expensive, too time consuming,
or not possible due to safety or technical considerations (you don't
want to run variations on Three Mile Island). Even when
experiments are available, computer simulation can enhance our
of the system by providing information on state variables that can't be
experimentally measured. Simulation programs are created with the
best available knowledge of the physical world, providing a form of
virtual reality. In our world of Nuclear Reactors, this knowledge is
obtained from careful analysis of experiments, generally
at much smaller scales than a nuclear power plant. Nuclear System
simulation codes (e.g. TRACE, RELAP5, CATHARE, and RETRAN) are then
to scale this knowledge up to power plant applications. Unfortunately
accuracy of results can be and often is degraded by the effects of
incomplete knowledge of two-phase flow (including the way that certain
behavior scales to different system sizes), and by the effects of
volume computer approximations on the solution of fluid dynamics
equations. For this reason, the computer code user needs to understand
the limits and anomalies of the virtual experiment provided by the
simulation code, just as standard experimentalists must have such an
understanding of their hardware and data acquisition devices.
One major shortcoming in the area of computer simulation is in the
background of code users and developers. The vast majority have
strong theoretical and/or computer backgrounds, and very weak
with experiments. When you apply a simulation code, you are
performing an experiment. If you expect to go into this business,
pay attention to the experimental training that you do get, and take
time to read about the subject. Think about design of good
controlled experiments, interpretation of data, and analysis or
errors. Be prepared to use all of your theoretical and
experimental background to interpret and justify the results of your
computer simulation. The most important thing that you should
learn from this class is to never trust the results of a computer
simulation until you have checked it very carefully. This is in
fact very good news for you. If results of computer simulations
were foolproof, vendors, utilities and regulatory agencies could hire
high school students to analyze reactor systems.
Brief History of Reactor Simulation
The early history is cloudy, including various industry design codes,
but the two roots with the most obvious impact on current codes were
Bettis FLASH code and a family of Los Alamos codes based on a method
called ICE (Implicit Continuous Eulerian). The FLASH code family has
been part of classified Naval Reactor Design, but formed the starting
point for the openly available RELAP code family. The most recent of
these (RELAP5) is the most widely used program in the world for the
analysis of the safety of nuclear power plants.
Early versions of RELAP included conservative assumptions to meet
the US Nuclear Regulatory Commission's Appendix K requirements for
licensing of reactors. Systems were modeled with 1-Dimensional flow
equations which averaged over fairly large volumes of the reactors.
In the early 70's the Nuclear Regulatory Commission (NRC) became
interested in "best estimate" (BE) calculations of reactor behavior in
which Appendix K assumptions were replaced with the best knowledge of
physical behavior. This path was followed because:
- NRC was worried that Appendix K is not always conservative;
- NRC wanted estimates of margins of safety;
- more knowledge leads to fewer unpleasant surprises.
Recent modifications to licensing rules permit use of BE codes for
licensing purposes, provided the uncertainty of the code is properly
quantified. It is very important to remember a best estimate is not
always a good estimate.
The second major code family in this country (TRAC) began with a
research proposal to the NRC by Kay Lathrop and Bill Reed from Los
Alamos Scientific Laboratory (now LANL) in 1974. The product was meant
to include significantly more detail than RELAP, including 3-D flow
equations, but as a consequence of computational complexity, was to be
used for spot checks on RELAP results. Around 1980, TRAC split into PWR
and BWR versions, that looked very different to code users. Over
the years, TRAC became much faster than expected without loss of
and RELAP became significantly more detailed. As a result, the codes
evolved very similar in capabilities.
About 1996, the NRC realized that they had too many codes doing
about the same thing. To reduce maintenance costs, and the number
of people required to carry the expertise in all of these products,
decided to produce an analysis package combining the capabilities of
RELAP5, TRAC-PWR, TRAC-BWR, and a special purpose BWR code named
The result is a software package called the TRAC/RELAP Advanced
Computational Engine (TRACE).
By now you know that the standard theoretical model for fluid flow
is the Navier-Stokes equation set, and that heat conduction is modeled
with the Poisson Equation. These are partial differential
equations (PDEs) solved over some domain in space and time.
Regardless of the size of the domain, it is a continuum with an
infinite number of points at which values are available for the
solutions. Computers have only a finite amount of memory, so
solution methods are required that only evaluate solution variables at
finite number of locations in space and time. We will look at
details of the numerical solution procedure later. For now the
important thing to know is that the code user must choose how space is
broken up into a finite number of regions (often referred to as cells,
nodes, or volumes). The code will worry about sampling of time
with some guidance from you on the maximum and minimum permitted steps
forward in time from one solution to the next.. You will be engaged in
balancing act with this discretization of space. The more
(smaller) cells that you use in your system, the closer your answer
be to the correct solution of the PDEs. However, the more cells
that you use, the more computer time it will take to solve the problem.
TRACE and its predecessors use Finite Volume solution methods.
For now we will work with 1-D pipe flow. You are required
provide input that breaks each 1-D section into some number of volumes.
To fully describe your discretization, you provide the length
along the pipe center line of each of your volumes, the total
volume of each volume, and the area available to fluid flow at the ends
of each volume. This may seem like an over specification of
conditions to you, but permits "1-D" flow modeling in pipes with
variable cross-sectional area.
For the computer lab sessions this week you will construct and analyze
models of some simple flows. The first exercise is steady flow in
an pipe with an abrupt abrupt area expansion. You will learn that
with a little help, codes like TRACE can do a pretty good job of
capturing the pressure change along a flow path. Without this
capability, serious problems would arise in reproducing flow rates in a
pump driven system. The second
exercise models injection of boron into a pipe. During some
accidents, timing of the arrival of boron in the core can have a
strong effect on fuel rod temperatures.
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