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


*   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.

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