Modeling a Simple Flow in a Pipe

Goals

  1. Introduce you to basic modeling of conduction and heat transfer.
  2. Check SNAPís ease of use

Preliminaries

 

One team member should open a word processor to record the steps used in this exercise,  while the other(s) setup a SNAP session on an adjacent computer.  Start by creating a directory for the exercise and opening a copy of the model that you generated for exercise 2.

Problem Definition

 

This is a series of three extensions to Exercise 2.  The first is designed to give you a feel for the impact of number of finite volumes used in the system model, and the relative behavior of available numerical methods.  This is a qualitative study of mesh size, and does not use the more rigorous approaches from lectures on error analysis and verification.  The second portion of the exercise adds effects of the pipe wall on the transient, and the third part gives you experience adding power to a metal structure and extracting the heat through the fluid flow.


Part 1


Flow and basic geometry are the same as in exercise 2.  
Flow is through a 10 meter section of 0.25 m diameter circular pipe. Initially, water flows into the test section at 1 m/s with a temperature of 300K. From 1 to 2 seconds into the transient, the inlet temperature increases linearly from 300K to 330K. The pressure at the exit is 2.0x105 Pa.   Now locate the renodalization option for the pipe generated in exercise 2.  Change from 10 fluid volumes in the pipe to 100.  Run the problem and plot the temperature of volume 45 (close to center of volume 5 in the 10 cell problem), on the same axes with your 10 cell results.  Alter the Namelist Variable labeled "SETS Numerics" from "SETS" to "Semi-Implicit" and repeat the 10 and 100 volume runs.  Create a plot with the cell 5 temperature history for both methods in the 10 cell problem, and  volume 45 temperatures for the 100 cell runs.  Edit the legends associated with the plot to clearly describe the curves.  Which curve is closest to the expected results?  Notice how a change in the numerical solution method for the flow equations can significantly effect results. 


Part 2


Now add a bit more reality to the problem.  Model the pipe wall with a heat structure.  The wall is Inconel 600, 0.01 m thick.  Take its initial temperature as 300K, and assume that the outside of the pipe wall is perfectly insulated. Place 6 evenly spaced radial temperature nodes in the wall, and be certain that there are a total of 100 rows of these radial nodes, one corresponding to each fluid volume. Alter the model properties so that the transient runs for 100 seconds.   Select the
"SETS Numerics" type that gave the best results in the first portion of this exercise.


Plot temperature in fluid volume 45 versus time for this calculation and for the corresponding run without a wall model on the same axes. Limit the time axis in this plot to 0-10 s.  What causes the differences in fluid temperature?  Plot the wall temperature (rftn) in radial node 6 and axial node 45 (4.5 meters from the inlet).  Note that metal structures require the longest time to reach steady state.


Part  3


Assume that the pipe wall is electrically heated with power distributed uniformly through the volume.  Use your knowledge of thermodynamics and fluid dynamics to calculate the total power required to give a temperature at the pipe exit of 360K when a transient with the above initial and boundary conditions is run to a steady state.  Modify your previous model to include that power and plot temperature in the last fluid volume as a function of time for a 50 second run.  If necessary adjust your power, and rerun the calculation until the temperature in the last pipe cell is within 0.5K of 360
K.



Procedure

Parts 2 and 3 involve new experience with the model editor.  To model the pipe wall, add a heat structure by right clicking the pipes drawing, selecting "Edit Heat structures", and then "New".


An initialization window will appear allowing you to set the basic geometry, temperature, material, and nodalization for the pipe wall.


Initialization Dialog

When you click OK, a full properties window will appear for the heat structure.  Give it the usual text information for a name, description, and comments.  For this simple case you won't need to change anything else. Expand the "Meshpoints",and "Initial Temperature" items to check location and initial conditions for your  6 temperature nodes and 5 material zones between them, and set the initial metal temperature to 300K.  Also take a look at the "Axial Nodes / Surface BCs" to see how it models the outer pipe wall as perfectly insulated, and links the inner wall to the fluid.



With the metal pipe wall represented, all that remains is to supply a power source.  This is a separate component found on the Component Navigator window.  Expand the "Power Data" item, then right click on "Power Components", and select new.




The power component has a great deal of flexibility and a corresponding long list of possible inputs in its properties.  For this exercise only a few of the items need to be set.  As usual provide the Component Name, Description, and Comments.  For the "Power Option" select "Constant Power", and set the "Initial Power" to the value that you calculated to produce the required temperature rise in the liquid.




Expand the "Powered Components" item, and move your wall heat structure from the unpowered to the powered list. 



Since there is only one heat structure, you should assign its power fraction to 1.0 and close this window.


The last thing that you normally need to do is to provide a profile (or profiles) describing the axial distribution of the power in the heat structure.  Input here is a little confusing because of the flexibility provided to users.  You have the capability to provide profiles at any set of times, and to interpolate between these profiles during a transient (this is basically a table with two independent variables).   For this exercise, the power profile is flat, and constant with time.  Because of the way the time table is handled internally, the time independence can be accomplished by providing only one time entry for t=0.0, which already has a default uniform distribution


Click the + to expand the Power Shape box and expand the "Power Shape Table" row.
The axial locations for power table entries are already provided from the axial nodalization of the wall heat structure.   In the resulting window, the Abscissa to Problem Time (signal variable 1), and click the "Add Shape" button.  The "Abscissa-Coordinate Value" is just the point in time at which this power shape is evaluated and should be set to 0.0.  Because only one profile will be entered, all times greater than zero will also use this profile.  The right column of the power shape table should default to 1.0, to give uniform distribution of the power.  The program will automatically normalize this distribution.



At this point you should save your project and run the problem to see if you can get results.



The written summary of your activities, should include: 

  1. The successful steps that you  took to produce the final model;
  2. The dead end paths that you followed;
  3. Your comments on aspects of the Model Editor that are misleading or not sufficiently clear;
  4. Your suggestions for improvements (junking the Model Editor is not an option). 


Clean up the summary of your adventures, and submit it with your plots and answers to my questions as Homework 6.

 

 


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