Experimental demonstration of Boltzmann equation.

Let us apply the principle of worst action.

Using a supersonic nozzle A; the method of characteristics allows to define the gas state at each point. The number of characteristics can be very large, and thus the network can be much finer than the one presented. In the relaxation domain, flow properties (speed, direction of velocity, static temperature, etc.) are significantly different between two any location 1 and 2.

Take an other supersonic nozzle B, similar to the space rocket propelling nozzles, operating between the same Mach numbers than the previous.


Between points 1 and 1′ (or 2 and 2′) corresponding to the two nozzles, the various properties of the fluid are obviously different.
Now build a sandwich structure, endowed with a certain thickness, using these two nozzles. With such stratification, everything changes. Flow breaks into a huge number of complexions W. Each of countless particles is surrounded by particles whose velocities, directions of velocities, etc. are different from his own.

In this curious use of supersonic flows, two flows initially almost reversible lead almost instantly to an abundant increase of entropy. What could be considered an experimental demonstration of Boltzmann equation.
Finally apply this process, called simply a vistemboir, to a model of control valve. In certain functionning situations, tens of megawatts should be degraded. The confrontation between the reference version A (issue of a consensus among french steam turbines manufacturers and EDF) and version B with vistemboirs gives remarkable results, and this on the first attempt. An experimenter who falls (for the only time in his life) on such a blatant outcome remains taken aback. This brilliant observation should further advance the Boltzmann ideas in energetics.


– In the first case A, the fluid has any freedom to dissipate itself its kinetic energy. Then the chaos is achieved and the dissipative structures of Prigogine appear, who generally admired by men but that can become very dangerous in valves and other energetics applications.
– In the second case B, molecular system is forced to immediately join the final equilibrium point, thanks to the geometry used. Unknown transport phenomena create intense energy degradation. The huge number of complexions generates a lot of entropy and exhausts the kinetic power contained in the fluid. All unsteady characteristics of flow are wiped out.

Conclusion : by introducing a massive disorder in the microscopic world, the chaos can be avoided in our macroscopic world. The application of the principle of worst action allows an ultra-high dissipation of kinetic energy in the supersonic flows and thus calms the valve flows.

About the Author Michel Pluviose

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.

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