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The ongoing digitalization of the energy sector, which will make a large amount of data available, should not be viewed as a passive ICT application for energy technology or a threat to thermodynamics and fluid dynamics, in the light of the competition triggered by data mining and machine learning techniques. These new technologies must be posed on solid bases for the representation of energy systems and fluid machinery. Therefore, mathematical modelling is still relevant and its importance cannot be underestimated. The aim of this Special Issue was to collect contributions about mathematical modelling of energy systems and fluid machinery in order to build and consolidate the base of this knowledge.

Technology: general issues --- centrifugal pump --- double hidden layer --- Levenberg–Marquardt algorithm --- performance prediction --- thermal energy storage --- stratification --- dynamic simulation --- heating --- double-channel sewage pump --- critical wall roughness --- numerical calculation --- external characteristics --- axial-flow pump --- impeller --- approximation model --- optimization design --- multi-disciplinary --- blade slot --- orthogonal test --- numerical simulation --- Francis turbine --- anti-cavity fins --- draft tube --- vortex rope --- low flow rates --- internal flow characteristics --- unsteady pressure --- energy recovery --- turboexpander --- throttling valves --- CFD --- modelling techniques --- Kaplan turbine --- draft tube optimization --- CFD analysis --- DOE --- response surface --- single-channel pump --- CFD-DEM coupling method --- particle features and behaviors --- solid-liquid two-phase flows --- computational fluid dynamics (CFD) --- artificial neural network (ANN) --- subcooled boiling flows --- uncertainty quantification (UQ) --- Monte Carlo dropout --- deep ensemble --- deep neural network (DNN) --- intake structures --- physical hydraulic model --- free surface flow --- free surface vortices --- vertical pump --- design considerations --- magnetocaloric effect --- coefficient of performance --- refrigeration --- capacity --- mathematical modelling --- energy systems