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Cooler Model

by Annette Brickley (Submitted: 01/29/2010)

[screen shot]

Download Cooler Model
If clicking does not initiate a download, try right clicking or control clicking and choosing "Save" or "Download".

(You can also run this model in your browser, but we don't recommend it; details here.)

WHAT IS IT?

Dynamical systems models are powerful tools for
studying many phenomena in Earth Science. These
models (often rather sophisticated) are in increasingly
wide use as research tools in hydrology, geochemistry,
petrology, oceanography and climatology. This
is a simple dynamical model used to develope
insight into seemingly complex physical phenomena.

HOW IT WORKS

Computer models developed in combination with simple physical
models allow students to better understand systems behavior. They gain confidence
in computer modeling, and learn how theoretical
models can be extended to study more complicated
systems.

HOW TO USE IT

Each time you run the model, if you want to start with the intitial conditions, begin with "setup" each time.
When you are ready to run the model with your parameter (either initial or modified), click "go" to watch the model run. When you want to stop the model, click "go" again.
If you would like to change the "inflow" into the "cooler", you may use the "adjust_inflow" slider to change the rate of water flowing into the cooler system. But don't do this until you've observed the steady state system and are ready to make predictions.
One plot, "water_volumes" will show the volume of water in the cooler. The second plot, "water_flows" will show how the "inflow" and "outflow" change and adjust to reach steady state.
The black box does nothing, but I can't get it off the screen!

THINGS TO NOTICE

One important point for the students to understand
about the steady state system is that although water
continually enters the reservoir and continually flows
out, none of the parameters of the system change with
time. This system is dynamically maintained, as
opposed to one that is static. The input and output
will not change and the volume of the system will
remain at 8 liters indefinitely.

THINGS TO TRY

What if we were to change the parameters of the
system? What would happen if we were to double the
amount of water input to the reservoir?
Before you begin adjusting the inflow, make a prediction about what you think will happen if you double the inflow rate. Write down your prediction. Then adjust the slider to double the original flow and click "go". Observe what happens and describe the response (shape of the curves).

EXTENDING THE MODEL

What happens if the input is tripled rather than doubled?
What is the new steady state volume?
How long did the system take to adjust?

Try these inputs to the System Dynamics Model rather than using the slider:
Parameters input into the model for this
perturbation are: Cooler = 8, Input =
0.011+STEP(0.011,600), Output = Cooler/720.

Add some physics:
If comparing to a physical model, you will find that, according to Bernoulli's equation for flow through a gravitationally fed pipe, the output rate should depend on the square root of the volume in a vertically walled container (e.g. Sears, Zemansky and Young, 1984, Ch.13). Our model may be easily modified to incorporate this relationship. The new output term is outflow = (8 / 720) * SQRT( cooler / 8). Now we have a model that not only accurately predicts the behavior of our particular cooler, but does so based on a fundamental understanding of the processes that control its behavior.

You can add a seasonality to the water inflow by changing
inflow = SIN(2 * PI)

Add additional inflows and outflows, depending on the system you are now trying to model. Each time, try to make the system reach steady state. Good luck!

NETLOGO FEATURES

NetLogo is not actually designed to best run this type of model, but it's free and available. Other models like this are more often created using STELLA.

RELATED MODELS

This section could give the names of models in the NetLogo Models Library or elsewhere which are of related interest.

CREDITS AND REFERENCES

The educational pedagogy and concepts as well as comparison to a physical model are from the following article published in the Journal of Geological Education, 1995, v.43, p. 153. The article is available online:
http://www.geo.cornell.edu/geology/research/derry/publications/JGE95.pdf

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