A Wall Nodalization Study, and a Heat Transfer Experiment
Assignment :
Finish Homework 8, and
start Homework 9
Nodalization Study
We just had a discussion of numerical modeling of wall conduction in
which I pointed out the need for care in setting locations for wall
temperature nodes near a surface. To experience
this for yourself, make a directory for this exercise, and put
the file
2WallNodes.inp into that file. For speed, I recommend that
you run 2WallNodes.inp
with a command line from a Bash window or from the TRACE icon.
Run this base case with
2 wall
temperature nodes, and plot the total power from the wall to fluid
(tpowi) with AcGrace. Now try to remember how you changed numbers
of wall nodes during the exercise with Richardson
extrapolation. If you simply want to edit the input file, set
"nodes" in the
heat structure to 20, and change the line giving location of
temperature nodes from
* radrd * 0.0 0.200000e
to
* radrd * i18 0.0 0.200000e
Rerun the problem and add the new values of tpowi to your AcGrace
plot. Repeat this with nodes = 50 and 100. See anything
interesting? Alter the legends on your plot to give the number of
conduction nodes associated with each curve, and add a meaningful title
to the graph. Set the range on the x axis to 0-100s, and print to
a PNG or PDF file. Reset the x-axis range to 0-5, and print to a
second file.
A Heat Transfer Experiment
We will be working with a simulation of a real experiment, Bennet test
5358. This is flow through a tube that is heated by a DC electric
current in the wall. The model takes the measured electrical
power delivered to the tube and distributes it uniformly through the
metal volume. Copy bennet.inp
to your TRACE execution directory (or make a new one and change the
TRACE icon properties). The experiment is configured to go to a
steady state, so I'm introducing use of the basic TRACE steady state
option. This differs from a transient in that the time step size
used in the conduction solution is a factor "rtwfp" greater than the
time step used for the fluid calculation. This settles out the
conduction solutions quicker, but results in the same steady solution
that you would get running a real transient for a longer time
period. Other side-effects of choosing the steady option don't
impact this particular model, but are worth knowing. If a model
contains Trips, only those with negative identification numbers are
evaluated during a steady state. Component action tables (e.g.
Fill velocity vs. time) are not evaluated, unless they are triggered by
a trip, and the trip is in the ON state. Some special controllers
are available during a steady state (see Section 3.7 of the User's
Guide). If a pressurizer component is used in a steady state
model, it is replaced automatically by a break component to set the
system pressure (see Section 4.5 of the User's Guide). Namelist options
(IPOWR, TPOWR) allow you to get flow established in a steady state,
before engaging power to rods. This can prevent a non-physical
onset of film boiling from which you never return. To permit longer
time step sizes and hence faster runs, a less time accurate approach to
time averaging of heat transfer coefficients is taken during a steady
state than during a transient. In addition,
you will notice that any successful steady state calculation resets the
transient time to zero before producing the final ASCII edit and
restart dump.
Steady state is determined by comparing the maximum fractional change
in various key system state variables to the input criterion
EPSS. You should always set EPSS greater than the iteration
convergence criterion EPSO. You should also make a habit of
plotting the time history of sensitive system variables (I like steam
generator water level) vs. time to confirm that a steady state has been
achieved. If the code does not declare a steady state, these
plots may tell you that you are close enough to a steady state to move
on to your transient calculation. It is not unusual for a system
to have low level oscillations about fixed values. Use your
judgment, but these cases are usually not going to improve regardless
of how long you run the steady state. If the oscillation
amplitude is low enough, move on to your transient. If not, you
may need to examine your system model more closely.
Run bennet.inp and list
for me all heat transfer regimes that you see
and the range of axial cells in which they occur. Also plot the
wall surface temperatures (tsurfi) at cells 1, 13, and 25. Rerun
the problem with 20 temperature nodes in the wall and plot the same set
of surface temperatures on the same graph as the run with the 5 node
wall model. You should see that nodalization is not a problem in
this case. Why the difference? At any given axial location,
the conduction problem rapidly goes to a steady balance between heat
flux to the fluid and power generated at that location. You can
get an analytic solution to this steady problem, and it gives a
temperature profile that varies quadratically in the radial
direction. Remember when we concluded that the conduction
solution was second order accurate. Among other things,
that means that it can exactly reproduce quadratic solutions to the
corresponding differential equation. In the case of vessel
wall above, it never reached a steady state, and if you look at any
radial temperature profile you won't see a quadratic curve.
Aside from intentional heat transfer experiments, it's generally not a
good idea to run heat transfer devices in the film boiling
regime. Do a study and find (within 5%) the largest power to the
tube for which no film boiling occurs.
Maintained by John Mahaffy : jhm@psu.edu