Rotational relaxation time and transfer coefficients in a diatomic gas

Lebed, I. V.; Ryahov, V. V.

doi:10.1007/bf00907889

Cited by 8 publications

(32 citation statements)

References 8 publications

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“…In the present study parameters p R1 (T) and p R2 (T) are calculated for nitrogen by formulas (18)-(20) from [6]. Multifold integrals are calculated at 200 points over the range of temperatures 200 K T 10,000 K, using the Monte-Carlo technique [5], with 4000 tests at each point. The data for intermediate points are determined by means of the interpolation technique [6] using cubic splines of defect 1 with smoothing.…”

Section: Rotational Relaxation Timementioning

confidence: 99%

“…The problem of deriving the nonequilibrium gas dynamic equations from the first principles of the kinetic theory of gases was studied by Ferziger and Kaper [1] in the cases of near-equilibrium and slow-relaxation processes of the energy exchange between internal and translational degrees of molecular freedom. The case of the arbitrary energy exchange ratio was analyzed by Alekseev [2], Kogan and Makashev [3], Matsuk and Rykov [4], and Lebed and Riabov [5] for polyatomic gas mixtures.…”

Section: Introductionmentioning

confidence: 99%

“…In the present study the problem of redistribution of translational and rotational energy has been solved for diatomic gases within the framework of the Chapman-Enskog method [1], [5], [6] and the Parker model [7] in the general case of the arbitrary energy exchange ratio. The nonequilibrium gasdynamic equations, transport coefficients and relaxation time have been found for rotational-translational processes in a diatomic gas [5], [6]. The calculations of relaxation time, viscosity, thermal conductivity, and diffusion coefficients are carried out in the temperature range from 200 K to 10,000 K for nitrogen by using the technique of integral brackets [1], [4].…”

Section: Introductionmentioning

confidence: 99%

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Estimations of Rotational Relaxation Parameters in Diatomic Gases

Riabov¹

2011

AIP Conference Proceedings

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The problem of redistribution of translational and rotational energy has been solved for diatomic gases within the framework of the Chapman-Enskog method and the Parker model in the general case of the arbitrary energy exchange ratio. The nonequilibrium gasdynamic equations, transport coefficients and relaxation time have been found for rotational-translational processes in a diatomic gas. The calculations of relaxation time, viscosity, thermal conductivity, and diffusion coefficients are carried out in the temperature range from 200 K to 10,000 K for nitrogen. The calculated parameters and coefficients are compared with the values obtained by the Mason-Monchick approximate method as well as data from experiments in ultrasonic, shock-wave, and vacuum devices. The correlation of the theoretical and experimental data is satisfactory. The applicability of one-and two-temperature relaxation models is discussed. The numerical solutions of the obtained system of the Navier-Stokes equations are analyzed for the cases of nitrogen flow in underexpanded jets and supersonic rarefied gas flow near a sphere.

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Section: Rotational Relaxation Timementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Estimations of Rotational Relaxation Parameters in Diatomic Gases

Riabov¹

2011

AIP Conference Proceedings

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“…The combined effect of the rotational-translational relaxation and dissipative processes of viscosity and conductivity was analyzed by Riabov, 27 - 28 Lebed and Riabov,29 Skovorodko, 30 Rebrov and Chekmarev, 31 and Molodtsov and Riabov. 32 The full system of the Navier-Stokes equations and the relaxation equation, based on the r-approximation technique, 29 has been solved by the implicit technique utilizing the stabilization principle described by Riabov 28 in detail.…”

Section: Rotational Relaxation In Viscous Gas Flowsmentioning

confidence: 99%

“…32 The full system of the Navier-Stokes equations and the relaxation equation, based on the r-approximation technique, 29 has been solved by the implicit technique utilizing the stabilization principle described by Riabov 28 in detail.…”

Section: Rotational Relaxation In Viscous Gas Flowsmentioning

confidence: 99%

Aerodynamic applications of underexpanded hypersonic viscous jets

Riabov

1995

Journal of Aircraft

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energy G = transformed temperature function / = concentration of heavy component h -plate thickness / = Bessel function / = Bessel function K = hypersonic similarity parameter, M.^ sin a K 2 = similarity parameter, Re*(p (l lp s ) { ' 2 K ff = relaxation parameter, p*u*r*/(pT R )* I = length of model M = Mach number M, = molecular weight of / species m -relaxation parameter, Eq. (10) n = exponent in the viscosity law JUL -T" (Pr.r 2) = average transition probability per one gas-kinetic collision for y* rotational level Pr = Prandtl number p = pressure q = dynamic pressure, {p y ul_ R = asymptotic parameter, 0.75/te*,-Rej = Reynolds number calculated by flow parameters in the nozzle exit cross section, p*u*rj/fj,j Re () = Reynolds number and the main similarity parameter, p y uJ,l[L s Re* = Reynolds number calculated by flow parameters at the critical sphere, p*u*r*/iJi* r = distance from a nozzle exit along the ray r tl = location of the shock wave ("Mach disk") on the jet axis r, f = radius of spherical source Sc = Schmidt number s = exponent in the molecular interaction law T = temperature / = dimensionless temperature function, TITt w = temperature factor, TJT S u = radial velocity component V = transformed velocity function, Eqs. (4) and (6)v' = tangential velocity component, Eq. (1) v = dimensionless velocity, M/M*,-, Eqs. (6) and (8) W = transformed velocity function, Eqs. (4) and (8) X = transformed coordinate, Eqs. (4) and (6) X = drag force x = inverse dimensionless radius, r^/r Y = lift force Z = transformed coordinate, Eq. (8) a = angle of attack /3 = thermal diffusion ratio y = ratio of specific heats 8 = dimensionless plate thickness, hll e = ratio of molecular weights, M 1Ie /M Ar 77 = argument for Bessel functions, Eq. (7) 0 = transformed temperature function, Eq. (8) 0 = angle between the body generatrix and the freestream flow A = expansion parameter, 2w(y -1), Eq. (4) fji = viscosity coefficient £ = deformable coordinate, Eq. (4) p = density r = relaxation time = transformed concentration function, Eq. (6) tp = angle between the ray from a nozzle exit and symmetry axiŝ = transformed concentration function, Eq. (8) a) = expansion parameter, l/[2y -1 -2(y -l)/i], Eq. (4)Subscripts a = ambient media parameter d = "Mach disk" parameter FM = free-molecular-flow parameter / = inviscid gas parameter j = nozzle exit parameter /* = rotational quantum level R = rotational relaxation parameter s = stagnation parameter t = translational temperature parameter w = wall quantity 1 = first-order approximation 3° = freestream quantity + = coordinate, at which gas density is extreme * = critical value parameter

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Rotational-translational relaxation effects in diatomic-gas flows

Riabov

2009

Shock Waves

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Rotational relaxation time and transfer coefficients in a diatomic gas

Cited by 8 publications

References 8 publications

Estimations of Rotational Relaxation Parameters in Diatomic Gases

Estimations of Rotational Relaxation Parameters in Diatomic Gases

Aerodynamic applications of underexpanded hypersonic viscous jets

Rotational-translational relaxation effects in diatomic-gas flows

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