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Figure 6.12: Comparison of the analytical solution to the Schumann equations with the explicit numerical solution Solution Stability When the simplified explicit solution is used with an insufficient number of nodes, the solution becomes unstable because the time and distance steps are coupled. In the interest of minimizing computational overhead with the explicit model, a method for predicting both the stability and accuracy of the solution is investigated. This method can help to choose appropriate mesh and timestep sizes for rapid and accurate simulation. Two dimensionless groups are related to the stability of this explicit numerical solution. They are defined here as: NTUfluid,node =hAnode m& f C f [6.3.28] [6.3.29] NTU solid ,node = hAnode∆t msCs Notice that NTUfluid,node is simply a nodal version of the previously defined NTUfluid. In the context of solution stability it is most useful to think of both nodal NTU values as “sensitivity” parameters to temperature change. Defining these terms allows equations [6.3.26] and [6.3.27] to be reformulated as follows: 109PDF Image | Organic Rankine Cycle Solar-Thermal Powerplants
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