Finish HW10
Steam generators come in many configurations and are used well
beyond the nuclear industry. For nuclear power plants, there are
three dominant types: U-Tube; Once-through; and Horizontal Tube.
U-Tube are the most prevalent. Once-through steam generator were
used on B&W plants, but lost favor due to TMI and the attention
that it brought to the lower secondary water inventory of this
design. Horizontal tube steam generators occur in Russian
reactors (VVER). This discussion will focus on U-Tube steam
generators, but most of what I say can be applied to all designs.
During Loss of Coolant Accidents (LOCAs), steam generators can
provide significant cooling, although conditions can exist where the
pressure in the secondary side is greater than the pressure in the
primary, and heat flows into the primary. One important cooling
source is "Reflux Cooling". In this situation steam travels from
the core to the steam generator tubes. Some or all of the steam
is condensed in the upward path through the U-Tubes and flows back down
into the hot leg, returning to to the reactor vessel via horizontally
stratified counter-current flow. A similar counter-current flow
can occur in single phase during severe accidents with hot steam
flowing out from the hot leg through some tubes and returning cooler to
the hot leg via other tubes. The hot and cold streams mix to some
degree in the steam generator inlet plenum. If insufficient
mixing occurs, temperatures in the hottest flow can result in tube
failure and release of radiation outside of containment.
When simulating a steam generator the primary is generally modeled
with a single 1-D
component covering the inlet and outlet plenums, and average tube
geometry. For the tubes the
hydraulic diameter must be that of an individual tube, but the modeled
flow area and wall area
must be total for all tubes. For accidents where voiding at the top of
the U-tubes has an
important impact on results, you should consider using at least three
1-D flow paths to model
long, medium, and short tubes in the bundle. This is particularly
valuable when cooling during some phase of the transient depends on
natural circulation in the loops with the steam generator secondary as
the heat sink. Another key consideration is the number of tubes
modeled. You need to know that the stress-corrosion cracking
requires utilities to plug tubes during outages. Number of actual
tubes in use varies from plant to plant, and over time for a given
plant.
The secondary side of the steam generator is normally modeled with
1-D dimensional flow,
but the flow topology is more complex. In addition to the boiling tube
bundle region, it is
necessary to model the steam dome, the downcomer, feedwater connection,
and beginning of the
steam line. TRACE and RELAP5 have options to model the complete
secondary side. However,
you should realize that this capability has never been seriously
exercised. In particular the
turbine models may have problems preserving proper energy balance, and
wall condensation processes in condensers could restrict time step
sizes.
One feature of steam generators is an adjustable gate at the bottom
of the downcomer to
permit tuning of the recirculation flow. When modeling a steam
generator, you will need to
introduce and adjust a loss coefficient at this point to obtain the
appropriate recirculation flow
through the downcomer. You will normally be asked to match a
quoted "recirculation ratio" for the steam generator. This is the
ratio of mass flow recirculated to the downcommer to the mass flow of
steam exiting the steam generator. Normally this ratio is
substantially greater than one, insuring that liquid entering the tube
bundle is very close to the saturation temperature, even though the
feedwater flow is significantly subcooled.
One problem with the use of 1-D modeling in the secondary is
non-physical thermal
stratification during some accidents. Watch the output of the secondary
for colder temperatures
at higher elevations in the bundle region. If the accident can be shown
to be particularly
sensitive to steam generator heat transfer, you might consider using a
3-D model for the
secondary, or a carefully selected pair of cross-connected pipes in the
bundle region. This will create a circulation
path, and will at least produce a more uniform temperature
distribution. Correct circulation
velocities are possible, but not likely in the cross-junction model.
The 3-D model
has a better chance of
modeling the balance of gravitational buoyancy and frictional damping
forces, to obtain a good
circulation pattern. However, I am not aware of anyone who has spent
the necessary time
including good cross-flow loss coefficients in a 3-D steam generator
model.
Remember that modeling natural circulation in a tube (or rod) bundle is a special case for the TRACE 3-D flow model. It has a chance of working because damping forces are a result of wall and form losses. TRAC has no chance of modeling circulation in an open 3-D region because it only solves the Euler equations. No attempt is made to specifically include viscous or turbulent damping forces.
Study and test the two classes of steam generator models that I have provided. The deck stgen.inp provides a generic model of a Westinghouse steam generator, including all important features. Unfortunately, it does not lend itself to quick renodalization of the tubes and boiler region (I'll discuss this in class), so I have also created a variant stgenSS3.inp that is easier to renodalize. The deck stgen1.inp is a simpler model of a scaled experiment.
At this point you have examples (and perhaps knowledge) of enough bits and pieces to assemble the PWR model necessary for your final project. Do yourself a big favor and start working aggressively on the project NOW. If you do, you will have ample time and opportunity to finish before the last week of classes, giving you time to concentrate on final exams in other classes. If you ignore this advice, don't blame me for all-night work sessions at the end of the semester.
Your starting point should be a text book or SAR for a general description of geometry and operating conditions of a typical PWR. Next scale and assemble components from class examples to create an initial model of the system. Learn to use the duplicate feature in SNAP to create multiple loops, but also exercise caution and check components created by SNAP.