Comparison of Different Approaches to Predict the Performance of Pumps As Turbines (PATs)

This paper compares different approaches aimed at predicting the performance curves of pumps as turbines (PATs). The considered approaches are four, i.e. one physics-based simulation model (“white box” model), two “gray box” models, which integrate theory about turbomachines with specific data correlations, and one “black box” model. Namely, the modeling approaches are: 1) a physics-based simulation model developed by the same authors, which implements the equations for estimating head, power and efficiency and makes use of loss coefficients and specific parameters; 2) a model developed by Derakhshan and Nourbakhsh, which makes use of relations to predict the best efficiency point of a PAT and two equations to estimate their complete characteristic curves; 3) a prediction model, also taken from literature and developed by Singh and Nestmann, which requires only the pump shape and size as input parameters for bringing out the complete turbine characteristics; 4) an Evolutionary Polynomial Regression model, which is a data-driven hybrid technique, which allows the identification of the explicit mathematical relationship between PAT and pump curves, if data for training the EPR model are available. All approaches are tested against literature data, reporting both pump and PAT performance curves for head, power and efficiency over the entire range of operation. The performance data were taken experimentally by Derakhshan and Nourbakhsh on four different turbomachines, running in both pump and PAT mode and characterized by specific speed values in the range 1.53 - 5.82. The reliability of the predictions of the considered approaches is quantitatively assessed, as well as prediction consistency from a physical point of view. The advantages and drawbacks of each approach are also highlighted and discussed, in order to identify the most suitable methodology for predicting the performance curves of pumps as turbines (PATs).