WSEAS Transactions on Fluid Mechanics
Print ISSN: 1790-5087, E-ISSN: 2224-347X
Volume 9, 2014
First Integrals for Crocco’s Equation and Hence for the Motion Equation
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Abstract: This work studies and clarifies some local phenomena in fluid mechanics, in the form of an intrinsic analytic study, regarding Crocco’s equation and the motion one, for inviscid compressible fluid flows (both steady and unsteady), and finds new first integrals. It continues a series of works presented at some conferences and a congress during 2006 – 2012, representing a real deep insight into the still hidden theory of the isoenergetic rotational flow. Unlike the geometrical point of view (using a smart intrinsic coordinate system tied to flow’s isentropic surfaces) previously approached to eliminate the rotational non-conservative term, this time a thermodynamic point of view is used, to evidence the above term first as a biscalar one, and further as a conservative one. Several new functions and surfaces were introduced: the 2-D velocity quasi-potential, the isentropic 3-D (V, Ω) surfaces, the polytropic integral ones, and the quasi-incompressible quasi-potential (Laplace) lines, for a quasi-uniform rotational pseudoflow of an inviscid compressible fluid. The dependence of gas particle specific entropy on the 2-D velocity quasipotential was established. The PDE of the polytropic special integral surfaces, and that of the isentropic ones (both in Cartesian system) were given. The newly found first integrals for the motion equation are related to D. Bernoulli’s and D. Bernoulli–Lagrange ones. An extension of the new intrinsic model to MHD of a neutral plasma was also given.
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Keywords: conservative (irrotational, potential) and biscalar vectors, rotational flows, steady and unsteady flows, inviscid fluids, compressible fluids, isentropic surfaces, polytropic integral surfaces, quasi-Laplace lines
Pages: 1-18
WSEAS Transactions on Fluid Mechanics, ISSN / E-ISSN: 1790-5087 / 2224-347X, Volume 9, 2014, Art. #1