Lumped Parameter Models

Question 1

What is the purpose of using an LPM?

Answer 1

Provides ability to simplify the system by treating it as a big bucket (control volume). Combines spatial complexity into one ‘lump’ and then solve an ODE for how its state changes over time.

Question 2

What questions should you ask yourself when forming an LPM?

Answer 2

What is the thing inside our volume? What are the flows in and out? What is the dependent variable?

Question 3

What are the types of flows in/out of the control volume?

Answer 3

Fixed rate (e.g Law of cooling)
Specified rate (e.g extraction)

Question 4

What are the ODEs produced by the different conservation equations?

Answer 4

Mass: ODE for pressure
Energy: ODE for temperature
Solute: ODE for concentration
Momentum: ODE for displacement

Question 5

The control volume approach states:

Answer 5

The rate of change of quantity inside a volume is equal to the net flow of quantity into or out of the volume.

Question 6

What are the two methods for solving an LPM?

Answer 6

Numerical solution - iterative time stepping.
Analytical solution - simplifying assumptions under particular conditions.

Question 7

When are coupled LPMs used?

Answer 7

When we want to track more than one quantity within a control volume.