Abstract: The Aim of the Work: This intrinsic study was made with the aim of improving and enriching the knoledges about the local physical phenomena encountered in both fluid mechanics and magneto-fluid dynamics, elaborating a new mathematical model.
Key-Words and Phrases: rotational flows, steady and unsteady flows, virtual isentropic (Bernoulli’s) surfaces, inviscid and viscous fluids, compressible fluids, flow of an electroconducting fluid in an external magnetic field
2000 Mathematics Subject Classification: 70 Mechanics of particles and systems; 76 Fluid mechanics; 78 Optics, electromagnetic theory; 80 Classical thermodynamics, heat transfer; 85 Astronomy and astrophysics
Extended Abstract: This work studies and clarifies some local phenomena in fluid mechanics as well as in magnetofluid dynamics, representing a continuation and completion of works [1] - [2] with the viscous effects.
Part One: A model of a certain isoenergetic flow of an inviscid fluid is introduced, in order to establish a simpler form for the general PDE of the velocity potential. It consists mainly in using a new three-orthogonal system of curvilinear coordinates (one of them being tied to the local specific entropy value). The choice of this system (with two coordinate curves lying on the “isentropic” surfaces) enables the treatment of any 3-D flow (rotational, steady and unsteady) as a potential 2-D one, introducing a 2-D velocity “quasi-potential”, specific to any isentropic surface. The dependence of the specific entropy on this velocity “quasi-potential” was also established. On the above surfaces the streamlines are orthogonal paths of a family of lines of equal velocity “quasi-potential”. The model can be also extended to the rotational flow of a viscous compressible fluid, finding the path for having a first integral, introducing the 0-work (made by the non-conservative terms in the Navier-Stokes equation of motion with a special virtual elementary displacement vector) surfaces and a new physical quantity – Selescu’s roto-viscous Ş vector.
Part Two: The model can be extended to some special (but usual) cases in magneto-plasma dynamics (taking into account the flow vorticity effects and those of the Joule-Lenz heat losses), considering a non-isentropic flow of a barotropic inviscid electroconducting fluid in an external magnetic field. There always are some space curves along which the equation of motion admits a first integral, making evident a new physical quantity – Selescu’s magneto-hydrodynamic $ vector. For a fluid having an infinite electric conductivity, these curves are the isentropic lines of the flow, also enabling the treatment of any 3-D flow as a “quasi-potential” 2-D one. Some surfaces of 0-work made by the non-conservative elementary forces with a special virtual elementary displacement vector were also introduced. Even if it does not seem to conform with the title, the case of the unsteady rotational flow (and electric field and charge, and magnetic field as well) of an inviscid and then viscous electroconducting liquid (incompressible fluid) was also studied (the case of the MHD generator with liquid), giving an exact first integral for the equation of motion. The model was extended to the unsteady (rotational flow, electric and magnetic field) case of a neutral perfect electroconducting viscous compressible fluid (including the highly ionized plasma).
In all treated cases the new found first integrals are similar to D. Bernoulli and D. Bernoulli-Lagrange ones. The differential equations of the virtual isentropic surfaces and those of Selescu’s roto-viscous – Ş and magneto-hydrodynamic – $ vector lines and virtual 0-work surfaces are also given.
The Original Contribution of the Work: A new mathematical model of flow was elaborated, making evident some new physical properties and quantities, being also given new first integrals for the equation of motion, integrals obtained by a procedure of eliminating the non-conservative terms in this equation (usually these ones depending upon the path of displacement of the fluid particle, here finding the most general class of the virtual paths for having 0-work of the terms above). Intersecting the 0-work surfaces with the isentropic ones (also virtual, as a rule they existing), the flow isentropic lines (along which the equation of motion also admits a first integral) were found. There is only one case for which the virtual 0-work surfaces coincide with the isentropic ones, namely the isoenergetic steady and unsteady rotational flows of an inviscid fluid, such that the virtual isentropic lines rest undetermined (there being an infinity of such kind of lines, among which one can find the true isentropic one).
 

Brief Biography of the Speaker:
Senior researcher Richard Selescu graduated as an engineer from the Polytechnic Institute Bucharest, the Faculty of Mechanics, Department of Aircraft Engineering in 1970. He is working in the National Institute for Aerospace Research “Elie Carafoli’’ – INCAS, Department of Aerodynamics, at the Trisonic Wind Tunnel Laboratory. He received his PhD degree in Aerodynamics and Fluid Mechanics at the Aerospace Engineering Faculty of the “Politehnica” University Bucharest in 1999. Among the research fields of interest, he approached the analytic modeling in aerodynamics, fluid mechanics and magnetofluid dynamics. Thus, he introduced the following nomenclature: the isentropic surfaces and a 2-D velocity quasi-potential function on these surfaces (in fluid mechanics); the 0-work surfaces for the non-conservative terms in the motion equation (in fluid mechanics and magnetofluid dynamics); a new physical quantity - the MHD vector and its vector lines (in magnetofluid dynamics); a new shock-free axisymmetric supersonic flow - the tronconical flow (in the supersonic aerogasdynamics); the similarity depth for satisfying the gas-hydrodynamic analogy (in the supercritical hydrodynamics).

 

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