Expander model validation
The parameters of the expander model are identified using test results. They are adjusted to fit the three model outputs (supply pressure, exhaust temperature, shaft power) to experimental data. The input variables of this calculation are: expander rotation speed, fluid flow rate, supply temperature and exhaust pressure. An error-objective function is defined, that should be minimized: this error function is a weighted sum of the relative errors for each output. It is defined as follows:
The parameters that minimize the objective function F are identified by means of a genetic algorithm. Given these parameters, the predicted and measured outputs can be compared:
• A maximum error of 3 K is reached for the prediction of the exhaust temperature.
• The supply pressure is predicted with a maximum relative error of 2.3%.
The expander shaft power is predicted with a maximum deviation of 6% (Figure 6).