– Close to initial equilibrium, this is the area of linear thermodynamics. Agitation in the molecular world leads to the transport phenomena. These processes are irreversible: this is particularly the case for viscosity. Entropy grows. Flows are laminar in this zone.
– More far from equilibrium, one enters the non-linear field. The flow becomes irregular and complex: it is the turbulent regime. But this is not a complete disorder.
– Then, the system has a deterministic chaotic behavior. The chaotic zone appears after a bifurcation, accompanied by fluctuations and dissipative structures. These new ordered structures appear far from equilibrium; an example is the supersonic jet escaping from Denis Papin’s safety valve.
– Finally, going still further from initial equilibrium, one enters the really chaotic area, where anarchy is total.
At the opening of a safety valve, the internal flows pass through all these troubled areas. A safety valve must open when conditions so require, but it must be able to close. During the opening, all the internal turmoil due to motive power which degrades by converting kinetic energy of the fluid in other forms (energy thermal, vibration, sound, etc.) attack the mechanical structure and sometimes deforms it.
Because we have not been able to destroy enough kinetic energy, the flow degrade energy themselves. The principle of worst action allows to avoid chaotic areas and quickly destroys the kinetic power of internal jets. The valves are then calmed down.
Michel Pluviose is Honorary Professor of Le Conservatoire National des Arts et Métiers (CNAM), and formerly Chair of Turbomachines who received his Doctor of Sciences from Université Pierre et Marie Curie - Paris VI. A hands-on engineer, Michel has worked with leading institutions, including as an engineer at Hispano-Suiza, SNECMA, Head of the laboratory at ATTAG (Association technique pour les turbomachines et turbines à gaz), Manager for compressible fluid activities at CETIM (Centre technique des industries mécaniques), and manager of the treaty « Machines hydrauliques et thermiques » at the « Techniques de l’Ingénieur » publications.
The principle of worst action applied to valves
The principle of worst action applied to a perforated plate.
The principle of worst action
Aircraft carrier Charles-de-Gaulle: Safety Valve Incident (October 15th, 2010)
Fessenheim Power Plant (april 2014)
Experimental demonstration of Boltzmann equation.