Class Introduction

Assignment :

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 knowledge 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 performed at much smaller scales than a nuclear power plant. Nuclear System simulation codes (e.g. TRACE, RELAP5, CATHARE, and RETRAN) are then used 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 finite 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 experience 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 the 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 detail, 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, they decided to produce an analysis package combining the capabilities of RELAP5, TRAC-PWR, TRAC-BWR, and a special purpose BWR code named Ramona. The result is a software package called the TRAC/RELAP Advanced Computational Engine (TRACE).

The Basics

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 a 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 a balancing act with this discretization of space. The more (smaller) cells that you use in your system, the closer your answer will 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 to 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 a variable cross-sectional area.

Exercises

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.