# 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

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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