Similarity of flows in strongly underexpanded jets of viscous gas

Gusev, V. N.; Klimova, T. V.; Ryabov, V. V.

doi:10.1007/bf01050964

Cited by 8 publications

(14 citation statements)

References 4 publications

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“…Historically, the first approaches were based on theoretical considerations [95][96][97]29,67,33,136,72,141,137,[99][100][101]208,140,42,127,103,43,204,105,210,46,47,13,107,211,246,108,[255][256][257][258][259][260][261]129,178,179,53,165,180,181]. Generally, these studies used the method of characteristics, whose principle is to decompose the partial differential equations describing the flow into ordinary differential equations which are easily integrated along particular directions.…”

Section: Modeling Approachesmentioning

confidence: 99%

Free underexpanded jets in a quiescent medium: A review

Franquet

Perrier

Gibout

et al. 2015

Progress in Aerospace Sciences

255

113

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Section: Modeling Approachesmentioning

confidence: 99%

Free underexpanded jets in a quiescent medium: A review

Franquet

Perrier

Gibout

et al. 2015

Progress in Aerospace Sciences

255

113

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“…The Knudsen number Kn ∞ based on the length scale parameter at infinity l = (Qa ∞ /4πγp ∞ ) ½ is the major similarity parameter in the second region. Another important similarity factor K 2 = Re * (p ∞ /p 0* ) ½ ≈ Re ∞l can be used to study the flow structure in this region [5,12]. Correlations between Kn * , Kn ∞ , and Kn + , are given in Ref.…”

Section: Expansion Of a Gas Mixture Into A Flooded Spacementioning

confidence: 99%

“…In the present study, diffusion effects in the spherical expanding flows of argon-helium mixtures have been studied using the DSMC technique [9,10] at the Knudsen numbers from 0.0015 to 0.03 and pressure ratios from 100 to 10,000. The similarity analysis [11,12] and analytical asymptotic techniques [5,6] were used to study the flow structure.…”

Section: Introductionmentioning

confidence: 99%

Kinetic Effects in Spherical Expanding Flows of Binary-Gas Mixtures

Riabov¹

2003

AIP Conference Proceedings

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Diffusion effects in the spherical expanding flows of argon-helium mixtures have been studied using the direct simulation Monte Carlo technique at the Knudsen numbers from 0.0015 to 0.03 and various pressure ratios. The similarity analysis was used to analyze the flow structure. Kinetic effects influence the shock-wave thickness, parallel and transverse species' temperatures, diffusive velocities, the effectiveness of species separation, and ambient gas penetration. A comparison of the DSMC and Navier-Stokes solutions indicates areas of the continuum-concept applicability for studying diffusive effects in low-density flows.

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“…After the change and the transition to f -> 0, we obtain the solution of the Navier-Stokes equations 8 …”

Section: Viscous Gas Jetsmentioning

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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Similarity of flows in strongly underexpanded jets of viscous gas

Cited by 8 publications

References 4 publications

Free underexpanded jets in a quiescent medium: A review

Free underexpanded jets in a quiescent medium: A review

Kinetic Effects in Spherical Expanding Flows of Binary-Gas Mixtures

Aerodynamic applications of underexpanded hypersonic viscous jets

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