This paper deals with the comparison of different methods which can be used for the prediction of 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 on turbomachines with specific data correlations, and one “black box” model. More in detail, the modeling approaches are: (1) a physics-based simulation model developed by the same authors, which includes the equations for estimating head, power, and efficiency and uses loss coefficients and specific parameters; (2) a model developed by Derakhshan and Nourbakhsh, which first predicts the best efficiency point of a PAT and then reconstructs their complete characteristic curves by means of two ad hoc equations; (3) the prediction model developed by Singh and Nestmann, which predicts the complete turbine characteristics based on pump shape and size; (4) an Evolutionary Polynomial Regression model, which represents a data-driven hybrid scheme which can be used for identifying the explicit mathematical relationship between PAT and pump curves. All approaches are applied to literature data, relying on both pump and PAT performance curves of head, power, and efficiency over the entire range of operation. The experimental data were provided by Derakhshan and Nourbakhsh for four different turbomachines, working in both pump and PAT mode with specific speed values in the range 1.53–5.82. This paper provides a quantitative assessment of the predictions made by means of the considered approaches and also analyzes consistency from a physical point of view. Advantages and drawbacks of each method are also analyzed and discussed.
A symbolic data-driven technique based on evolutionary polynomial regression
