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Modeling Inflow and Outflow in a Coleman Cooler

Introduce the concept of systems thinking using a simple physical model of a Coleman Cooler. Explore the dynamics of inflow and outflow and learn how to model it in STELLA. Examine the impact of doubling the inflow rate and understand the limitations of the model. Videos and analytical solutions provided.

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Modeling Inflow and Outflow in a Coleman Cooler

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  1. The Moore and Derry (1995) Coleman Cooler Example •Introduce systems thinking with a simple physical model •Inflow = outflow, so steady state but dynamic, not static •How might we model this in STELLA? 0.011 Liters/sec 0.011 Liters/sec 8 Liters Moore, A., and Derry, L., 1995, Understanding Natural Systems through Simple Dynamical Systems Modeling, JGE, v. 43, p. 152-157.

  2. STELLA representation •dV/dt = inflow – outflow •At steady state, dV/dt = 0, so inflow = outflow •Residence time = V/inflow or V/outflow

  3. ½ dt rule • To ensure simulation is running properly, always check the time step. • First, run model with chosen time step. • Next, cut time step in half. • If results are identical, proceed with larger time step. • If results are different, continue halving time step until results are the same.

  4. What will happen if we double the inflow? Students typically predict overflow.

  5. In reality, outflow depends on the volume of water in the cooler. Opportunity to explain “Garbage In Garbage Out.” Bob Mackay (Clark University) videos: http://www.youtube.com/watch?v=CoTQ7LCpwgA - filling bucket http://www.youtube.com/watch?v=dVUh1JraiLk - draining bucket http://www.youtube.com/watch?v=CcHohK458XM - filling and draining http://www.youtube.com/watch?v=iYtDxf4V1lA - bucket too full to begin with

  6. Pink connector arrows show dependency of drain flow on cooler volume and rate constant drain = cooler * k but

  7. The analytical solution: at t = 0, V(t) = V0 so C = V0 – i/k at t = 0, V(t) = V0 as t  infinity, V(t)  i/k

  8. Let starting volume = 8 Liters and initial inflow and outflow = 0.011 Liters/sec At time = 600 seconds, double inflow to 0.022 Liters/sec 0.011 Liters/sec 0.011 Liters/sec 0.022 Liters/sec 32 Liters Note difference between true volume and STELLA model volume – indicates not all of the physics of the system are included in our simple model!

  9. Bernoulli’s equation for gravitationally fed pipe flow gives a better solution:

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