Relaxation in Shock Waves

Stupochenko, Ye. V.; Лосев, С. А.; Осипов, А. И.

doi:10.1007/978-3-642-48246-5

Cited by 87 publications

(19 citation statements)

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“…However, six recombination reactions involving atoms only cannot be described by the present model, which is consistent with the hypothesis, usually assumed, of the independence of these reactions on vibrational distribution of the recombined molecules. Arrhenius rate constants K s are taken from [15] and TV and VV relaxation times from [16,17]. Rather than directly calculating the transport terms, they are written as functions of the viscosity of the mixture and of the nondimensional numbers, namely, frozen Prandtl, Lewis, and vibrational numbers, quantities weakly sensitive to the nonequilibrium [18].…”

Section: Modeling and Numerical Simulation Nonequilibrium Physical Modelmentioning

confidence: 99%

Shock Detachment Distance on Blunt Bodies in Nonequilibrium Flow

et al. 2007

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Nomenclature A = chemical symbol e = total energy per mass unit e A , e D = activation, dissociation energy e Vp = vibrational energy of species p _ e Vp = vibrational energy production of species p due to TV and VV collisions e Vps = vibrational energy gained (lost) by species p due to reaction s f = distribution function J = collisional term in Boltzmann equation K = rate constant k = Boltzmann constant p = pressure Q = quantity Q at equilibrium q = total heat flux q v = vibrational heat flux R = hemispherical body radius T = translation-rotation temperature T V = vibration temperature V = mean velocity (components u and v) V p = mean velocity of component p _ w p = mass production of species p due to chemical reactions _ w Vp = vibrational energy production due to chemical reactions X = longitudinal coordinate in the nozzle x, y = coordinates in the physical plane Y = transverse coordinate in the nozzle = shock standoff distance =R = normalized shock standoff distance = density Subscripts a, b = upstream, downstream from the detached shock b = backward reaction C = chemical f = forward reaction i = internal level p, q = species p, q R = rotation s = reaction s T = translation TV = translation-vibration exchange V = vibration VV = vibration-vibration exchange 0 , 00 = stoichiometric coefficients 1, 2, 3, 4, 5 = associated to species N 2 , O 2 , NO, N, O

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Section: Modeling and Numerical Simulation Nonequilibrium Physical Modelmentioning

confidence: 99%

Shock Detachment Distance on Blunt Bodies in Nonequilibrium Flow

et al. 2007

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“…20 for O 2 and O) and do not show the well known effect of a delay of free atoms formation in a thin layer near a shock which is found experimentally (see [13]) and is described in the detailed state-to-state calculations. Such a delay appears as a consequence of a lack of the vibrational energy of molecules for their dissociation in the beginning of the relaxation zone.…”

Section: Comparison Of the State-to-state And Simplified Flow Descripmentioning

confidence: 63%

“…It is known from experimental data [13,14] that in high-temperature flows relaxation times for different kinetic processes satisfy the following relations:…”

Section: Governing Equationsmentioning

confidence: 99%

“…where D c is the dissociation energy, the coefficients A and b for air components are available in a number of works [33,13,41,42,14]. The comparison of the state-specific N 2 dissociation rate coefficients obtained using the expression (34) for different U c values for various temperature intervals and accurate quasi-classical trajectory calculations [43] is discussed in [31], whereas the influence of different dissociation models on (N 2 , N) mixture parameters behind a shock waves is studied in [30].…”

Section: Reaction Rate Coefficientsmentioning

confidence: 99%

“…Experimental data show that under wide conditions in hightemperature gases excluding light molecules like hydrogen, translational and rotational degrees of freedom equilibrate much faster compared to vibrational and chemical relaxation [13][14][15]. Therefore the vibrational and chemical non-equilibrium kinetics in the air components is often studied allowing the assumption about equilibrium or weakly non-equilibrium distributions over velocities and rotational energies.…”

Section: Introductionmentioning

confidence: 99%

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This article presents gas kinetic calculation methods for the energy transport in hydrogen/ air and methane/air mixtures. The total molecular heat conductivity as well as its various shares are calculated and discussed for a temperature range of 400 to 3500 K and for a pressure of lo5 Pa. The variation of the air/fuel ratio under the conditions of chemical equilibrium is also investigated. As opposed to our previous article, an extension of the ChapmanEnskog method which goes beyond the classical 1st approximation for elastic collisions is applied for the evaluation of suitable calculation methods. This is carried out following the method for strong relaxing thermal nonequilibrium according to Brun. The equations applied in this work are simplified formulations for the proximity to equilibrium. The method for the evaluation of the parameters of the inelastic collision and some chosen results are presented. A discussion of the various shares of the molecular heat conductivity emphasizes the considerable influence of the diffusion and the thermal diffusion processes in fuel/air mixtures compared to the Fourier heat conductivity.

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Relaxation in Shock Waves

Cited by 87 publications

References 0 publications

Shock Detachment Distance on Blunt Bodies in Nonequilibrium Flow

Shock Detachment Distance on Blunt Bodies in Nonequilibrium Flow

State-to-state description of reacting air flows behind shock waves

Energy transfer in hydrogen/air and methane/air mixtures

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