共查询到20条相似文献,搜索用时 15 毫秒
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L. A. Pal'tsev 《Journal of Applied Mechanics and Technical Physics》1972,13(4):437-445
We derive the gas-dynamic equations in the Navier-Stokes approximation for weak excitation of molecular vibrational states. We determine the distribution function for the density of the numbers determining occupancy of the vibrational states of the molecules. We show that the relaxational pressure is proportional to the deviation of the vibrational energy density from its local-equilibrium value for the temperature of the translational and rotational degrees of freedom of the molecules.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 8–17, July–August, 1972.In conclusion, the author thanks V. N. Zhigulev and V. S. Galkin for a discussion of his results. 相似文献
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I. I. Ryzhkov I. V. Stepanova 《Journal of Applied Mechanics and Technical Physics》2011,52(4):560-570
A model of vibrational convection of a binary mixture with the thermodiffusion effect is considered. The symmetries of model
equations are found, depending on the values of physical parameters. A partially invariant solution, which describes separation
of the binary mixture in a thermodiffusion column, is constructed and studied. The influence of streamwise vibrations on the
flow regime and separation of the mixture is investigated. 相似文献
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V. A. Kronrod V. V. Shchennikov 《Journal of Applied Mechanics and Technical Physics》1973,14(4):476-482
An exact solution of the Navier-Stokes equations is presented for the flow of a viscous heat-conducting chemically reacting mixture of gases in a two-dimensional expanding channel. The conditions for the existence of an exact solution of the source type are: the chemical reactions must be equimolecular in an equilibrium mixture of gases, and they must be second order forward and backward in a nonequilibrium mixture. Numerical results are obtained for the flow of a four-component equilibrium mixture of gases in a two-dimensional nozzle for various Mach numbers (M) and Reynolds numbers (Re).Translated from Zhurnal Prikladnoi Mekhanika i Tekhnicheskoi Fiziki, No. 4, pp. 49–56, July–August, 1973. 相似文献
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V. S. Galkin 《Fluid Dynamics》1966,1(5):29-34
An extension is given of the class of exact solutions of the kinetic-moment equations for a monatomic gas in the absence of external forces [1] to the case of a mixture of monatomic Maxwellian gases with account for external forces. Very simple solutions of this class are obtained which are examples of the normal solutions of the Boltzmann equations in the Chapman-Enskog sense [2]. Conclusions are summarized concerning the applicability of the various methods of solving the Boltzmann equations and their properties, obtained on the basis of an analysis of the indicated exact solutions.The author wishes to thank M. N. Kogan and A. A. Nikol'skii for their interest in the study. 相似文献
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Yu. A. Nagel' 《Fluid Dynamics》1980,15(3):419-425
A model of a gas mixture is studied in which one of the components can carry electric charge and undergo phase transitions. Under a number of assumptions, Boltzmann kinetic equations are written down and the form of the collision integral determined. Conservation equations for the components of the mixture are found. The conservation equations for a charged mixture of gases in the absence of phase transitions have been discussed earlier [1]. Collision integrals for a reacting gas mixture in the case of chemical reactions of bimolecular type and when the mixture is described by Boltzmann kinetic equations are derived in [2].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No, 3, pp. 118–127, May–June, 1980. 相似文献
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The aim of this article is to construct a BGK-type model for polyatomic gases which gives in the hydrodynamic limit the proper
transport coefficient. Its construction relies upon a systematic procedure: minimizing Boltzmann entropy under suitable moments
constraints (Levermore in J Stat Phys 83:1021–1065, 1996; Brull and Schneider in Cont Mech Thermodyn 20(2):63–74, 2008). The
obtained model corresponds to the ellipsoidal statistical model introduced in Andries et al. (Eur J Mech B Fluids 19:813–830,
2000). We also study the return to equilibrium of its solutions in the homogeneous case.
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Summary The aim of the paper is the presentation of results obtained by the direct numerical solution of the Boltzmann equation in the case of a binary mixture of hard sphere gases. The system of two coupled Boltzmann equations is solved by a techique combining finite differences with the Monte Carlo evaluation of the Boltzmann collision integrals. It is shown how the technique proposed by Aristov and Tcheremissine for a single gas can be extended to a mixture. The resulting algorithm can be very well vectorized and the results of a few test calculations on the vector computer CRAY-XMP 48 are presented.
Sommario Il presente articolo si propone la descrizione di alcuni risultati relativi ai fenomeni di rilassamento omogeneo in una miscela binaria di sfere rigide. Il sistema di equazioni di Boltzmann che regge l'evoluzione temporale delle funzioni di distribuzione dei gas componenti viene risolto numericamente con un metodo che combina l'uso di differenze finite con la valutazione dell'integrale di collisione mediante un inetodo di Monte Carlo. La tecnica presentata costituisce per alcuni aspetti la generalizzazione di quella proposta da Aristov e Tcheremissine per un singolo gas. Si evidenzia inoltre come l'algoritmo sia di per sè in massima parte vettorizzabile e si presentano alcuni risultati ottenuti sull'elaboratore vettoriale CRAY-XMP48.相似文献
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Summary In recent years there has been developed a general thermodynamics of materials for which the stress, temperature, and energy depend on the histories of the strain and another variable, such as the entropy. Here we discuss the compatibility of that thermodynamical theory with a special theory of mechanical dissipation which has been successfully used in physical gas dynamics: the theory of gases with vibrational relaxation. Granting, without detailed study, certain technical points involving the uniqueness and stability of solutions of a class of non-linear integral equations, we observe that the theory of relaxing gases can be imbedded in the framework of the thermodynamics of materials with memory, provided only that we identify the temperature of the thermodynamical theory with the translational or (activemode) temperature of the internal-relaxation theory.We conclude our discussion with a report of a calculation we have made of the isentropic, pressure-volume, relaxation function exhibited by a gas with vibrational relaxation when regarded as a linearly viscoelastic material.
This research was supported in part by the U. S. Air Force Office of Scientific Research and the U. S. Office of Naval Research. 相似文献
Sommario Si è ultimamente sviluppata una termodinamica generale dei materiali per i quali la tensione, la temperatura e l'energia dipendono dalla storia passata dello strain e da un'altra variabile, come l'entropia.Studiamo qui la compatibilità di questa teoria termodinamica con una teoria speciale di dissipazione meccanica, che è stata applicata con successo nella dinamica dei gas reali: la teoria dei gas con rilassamento vibrazionale.Accettati, senza un esame dettagliato, certi punti tecnici che comportano l'unicità e la stabilità delle soluzioni di una classe di equazioni integrali non lineari, osserviamo che la teoria dei gas con rilassamento vibrazionale può essere inquadrata nella struttura della termodinamica dei materiali con memoria, a patto che la temperatura della teoria termodinamica venga identificata con la temperatura di traslazione o di modo attivo della teoria del rilassamento interno.Concludiamo la nostra discussione riportando i risultati ottenuti nella derivazione della funzione che descrive il rilassamento isoentropico di pressione che segue una variazione di volume rivelata da un gas con rilassamento vibrazionale quando è considerato come materiale visco-elastico lineare.
This research was supported in part by the U. S. Air Force Office of Scientific Research and the U. S. Office of Naval Research. 相似文献
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The aim of the present paper is to construct an approximate kinetic equation that, first, takes into account correctly the possibility of excitation of both rotational and vibrational degrees of freedom of the molecules and, second, is valid for any law of intermolecular interaction.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 183–187, March–April, 1982.We thank M, Ya. Alievskio for helpful consultations. 相似文献
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Takashi Arima Shigeru Taniguchi Tommaso Ruggeri Masaru Sugiyama 《Continuum Mechanics and Thermodynamics》2013,25(6):727-737
We study the dispersion relation for sound in rarefied polyatomic gases (hydrogen, deuterium and hydrogen deuteride gases) basing on the recently developed theory of extended thermodynamics (ET) of dense gases. We compare the relation with those obtained in experiments and by the classical Navier–Stokes Fourier (NSF) theory. The applicable frequency range of the ET theory is proved to be much wider than that of the NSF theory. We evaluate the values of the bulk viscosity and the relaxation times involved in nonequilibrium processes. The relaxation time related to the dynamic pressure has a possibility to become much larger than the other relaxation times related to the shear stress and the heat flux. 相似文献
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A numerical solution is obtained for the problem of air flow past a sphere under conditions when nonequilibrium excitation of the vibrational degrees of freedom of the molecular components takes place in the shock layer. The problem is solved using the method of [1]. In calculating the relaxation rates account was taken of two processes: 1) transition of the molecular translational energy into vibrational energy during collision; 2) exchange of vibrational energy between the air components. Expressions for the relaxation rates were computed in [2]. The solution indicates that in the state far from equilibrium a relaxation layer is formed near the sphere surface. A comparison is made of the calculated values of the shock standoff with the experimental data of [3].Notation uVmax, vVmax
velocity components normal and tangential to the sphere surface
- Vmax
maximal velocity
- P
V
max
2
pressure
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density
- TT
temperature
- eviRT
vibrational energy of the i-th component per mole (i=–O2, N2)
- =rb–1
shock wave shape
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a
f
the frozen speed of sound
- HRT/m
gas total enthalpy 相似文献
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Shock wave structure was studied in [1] using Struminskii's model [2] with the assumption that viscosity and thermal conductivity exist only as interactions between components. The present study will obtain asymptotic solutions of the problem of shock wave structure in the Navier-Stokes approximation.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 48–54, September–October, 1984. 相似文献
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