Industrial compressors suffer from strong aerodynamic instability that arises when low ranges of flow rate are achieved; this instability is called surge. This phenomenon creates strong vibrations and forces acting on the compressor and system components due to the fact that it produces variable time-averaged mass flow and pressure. Therefore, surge is dangerous not only for aerodynamic structures but also for mechanical parts. Surge is usually prevented in industrial plants by means of anti-surge systems, which act as soon as surge occurs; however, some rapid transients or system upsets can lead the compressor to surge anyway. Despite the fact that surge can be classified as mild, classic, or deep, depending on the amplitudes and frequency of the fluctuations, operators are used to simply referring to surge, without making a distinction between the three main classes. This is one of the reasons why, when surge occurs in industrial plants, it is a common practice to stop the machine to perform inspections and check if any damage occurred. Obviously, this implies maintenance costs and time, during which the machine does not operate. On the other hand, not all surge events are dangerous in terms of damage, and they can be tolerated by the mechanical structures of the compressor; thus, in these cases, inspections would not be required. Unfortunately, a method for establishing the potential damage of a surge event is not available in literature. In order to fill this gap, this paper proposes a final formulation of a surge severity index, which was only preliminarily formulated by the authors in a previous work. The preliminary form of this coefficient demonstrated some limitations, which are overcome in this paper. The surge severity index derives from an energy-force based analysis. The coefficient demonstration is carried out in this paper by means of (i) the application of the Buckingham's Pi-theorem, and (ii) a careful analysis of the causative and restorative factors of surge. Finally, some simple practical evaluations are shown by means of a sensitivity analysis, using simulation results of an existing model, to effectively further highlight the consistency of this coefficient for industry.

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