Multimoment Hydrodynamics in Problem on Flow around a Sphere: Entropy Interpretation of the Appearance and Development of Instability

Lebed, I. V.

doi:10.4236/ojfd.2014.42015

Cited by 10 publications

(15 citation statements)

References 25 publications

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“…The multimoment hydrodynamics equations were used to study the phenomenon of instability appearance and development in the problem of flow around a solid sphere at a wide range of Reynolds number values (Lebed, 1997;1998;2014a;2014b). It was found that solutions to these equations lead the development of instability in the direction compatible with experiment.…”

Section: Introductionmentioning

confidence: 98%

“…They are the disintegration of the Gibbs ensemble (Lebed, 1997;2014b), the breakage of unstable solution (Lebed, 1997;2014b), the movement of a system at an extremely unlikely direction described by the reverse multimoment hydrodynamics equations (Lebed, 2014b;2014c;2015b).It was discovered that system entropy begins to play the key role to predict the direction of instability development. The calculation of the system evolution becomes impossible without participation of the entropy.…”

Section: Introductionmentioning

confidence: 99%

“…The multimoment hydrodynamics equations find a large number of ways for system evolution. Just the entropy shows the single way, in which the system evolution goes (Lebed, 2014b;2015b).…”

Section: Introductionmentioning

confidence: 99%

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Derivation of the Multimoment Hydrodynamics Equations for a Gas Mixture

Lebed¹

2016

APR

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The equations for pair distribution functions are used to derive the multimoment hydrodynamics equations for gas mixture. The gas mixture pair distribution functions are specified. The equations for pair functions are derived directly from the general statistical mechanics concepts. The basic property of the pair functions is established. In conformity with basic property, these functions remain unchanged in time along the trajectory of the center of inertia of a pair. The basic property of the pair distribution functions reveals the existence of an infinite number of principle hydrodynamic values. Multimoment hydrodynamics equations are constructed using 3 4 L + principle hydrodynamic values, where L is the number of gas mixture components. Just these principle values specify measurable moments. The measurable moments are represented by linear combination of principle and non-principle hydrodynamic values. The general structure of constructed multimoment conservation laws is identical to the structure of appropriate multimoment conservation laws in a gas of identical particles. Each of the multimoment conservation laws is divided into two separate equations. The first group of conservation equations corresponds to convective phenomena. The second group of conservation equations corresponds to dissipative phenomena. Derived multimoment hydrodynamics equations are designed for interpreting the behavior of unstable systems. As is shown previously, classic hydrodynamics equations are incapable of reproducing flows after they lose stability. That is, the solutions to the classic hydrodynamics equations do not find the direction of instability development correctly. The possibility of improvement of classic hydrodynamics equations for a gas mixture is sought on the way toward an increase in the number of principle hydrodynamic values.

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Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Derivation of the Multimoment Hydrodynamics Equations for a Gas Mixture

Lebed¹

2016

APR

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“…The problems encountered by classic hydrodynamics when interpreting observed evolution of unstable process, are proposed to be solved on the way toward an increase in the number of principle hydrodynamic values [4]. In [5]- [8], the multimoment hydrodynamics equations are used to study the phenomena of instability appearance and development in problem on flow around a solid sphere at a wide range of Reynolds number values.…”

Section: Introductionmentioning

confidence: 99%

“…The studies [5]- [8] demonstrated that when interpreting each of unstable regimes in problem on flow around a sphere the need emerges to involve the so-called reverse multimoment hydrodynamics equations [9]. The evolution of the system after losing its stability that is described by the direct hydrodynamics equations advances in direction of the system departure from the statistical equilibrium state.…”

Section: Introductionmentioning

confidence: 99%

About Appearance of the Irreversibility

Lebed¹

2014

OJFD

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The inevitability of arising in equations of kinetics and hydrodynamics irreversibility not contained in original equations of classic mechanics is substantiated. It is established that transfer of information about the direction of system evolution from initial conditions to resulting equations is the consequence of losing information about the position of an individual particle in space, which takes place at roughening description. It is shown that the roughening with respect to impact parameters of colliding particles is responsible for appearance of the irreversibility in resulting equations. Direct equations of kinetics and hydrodynamics are the result of roughening distribution functions with respect to impact parameters of particles, which have not yet reached the domain of their interaction. The direct equations are valid for the progressive direction of timing on the time axis pointing from the past to the future. Reverse equations of kinetics and hydrodynamics are the result of roughening distribution functions with respect to impact parameters of particles, which have already left the domain of their interaction. The reverse equations are valid for the progressive direction of timing on the time axis pointing from the future to the past.

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