The steady one-dimensional flow of a monatomic vapor condensing onto a planar surface kept at constant and uniform temperature has been the subject of a number of investigations based on the kinetic theory of gases. It has been shown that, depending on the upstream value of the Mach number normal to the surface, a steady solution exists only when the problem parameters lie on a surface in the parameters spaces (upstream subsonic flow), or when the problem parameters lie in a proper subregion of the whole parameters space (upstream supersonic flow). Similar detailed studies do not exist for a polyatomic vapor, in spite of their potential relevance for many applications. The present paper aims at describing the effects of internal degrees of freedom on the relationships which determine the existence of steady one-dimensional condensation flows. The study is based on the numerical solution of the Boltzmann equation for a gas with rotational degrees of freedom. Inelastic collision are described by the Borgnakke-Larsen model. A few cases also have been computed by a finite difference discretization of Holway’s model kinetic equation. The role of boundary conditions is also briefly discussed.
REFERENCES
1.
C.
Cercignani
, The Boltzmann Equation and Its Applications
(Springer-Verlag
, Berlin
, 1988
).2.
Y.
Sone
, “Kinetic theoretical studies of the half-space problem of evaporation and condensation
,” Transp. Theory Stat. Phys.
29
, 227
(2000
).3.
C.
Cercignani
, “Strong evaporation of a polyatomic gas
,” in Rarefied Gas Dynamics
, edited by S. S.
Fisher
, Prog. Astronaut. Aeronaut.
Vol. 74
, Part I (AIAA
, New York, 1981
), pp. 305
–320
.4.
T.
Soga
, “A kinetic theory analysis of evaporation and condensation of a diatomic gas
,” Phys. Fluids
28
, 1280
(1985
).5.
P. A.
Skovorodko
, “Semi-empirical boundary conditions for strong evaporation of a polyatomic gas
,” in Rarefied Gas Dynamics
, edited by T. J.
Bartel
and M. A.
Gallis
, AIP Conference Proceedings
, Vol. 585
(American Institute of Physics
, Melville, NY
, 2001
), p. 588
.6.
N. A.
Zharov
, I. A.
Kudnetsova
, and A. A.
Yushkanov
, “Intense evaporation of molecular gas
” High Temp.
36
, 109
(1998
).7.
A.
Frezzotti
, “A numerical investigation of the steady evaporation of a polyatomic gas
,” Technical Report No. 648/P, Dipartimento di Matematica-Politecnico di Milano
, 2005
.8.
S.
Fujikawa
, T.
Yano
, K.
Kobajashi
, K.
Iwanami
, and M.
Ichijo
, “Molecular gas dynamics applied to phase change processes at a vapor-liquid interface: Shock-tube experiment and MGD computation for methanol
,” Exp. Fluids
37
, 80
(2004
).9.
K.
Aoki
, Y.
Sone
, and T.
Yamada
, “Numerical analysis of gas flows condensing on its plane condensed phase on the basis of kinetic theory
,” Phys. Fluids A
2
, 1867
(1990
).10.
K.
Aoki
, K.
Nishino
, Y.
Sone
, and H.
Sugimoto
, “Numerical analysis of steady flows of a gas condensing on or evaporating from its plane condensed phase on the basis of kinetic theory: effect of gas motion along the condensed phase
,” Phys. Fluids A
3
, 2260
(1991
).11.
M. N.
Kogan
and A. A.
Abramov
, “Direct Simulation Solution of the Strong Evaporation and Condensation Problem
,” in Rarefied Gas Dynamics
, edited by A. E.
Beylich
(VCH
, Weinheim
, 1991
), pp. 1278
–1284
.12.
Y.
Sone
, F.
Golse
, T.
Ohwada
, and T.
Doi
, “Analytical study of transonic flows of a gas condensing onto its plane condensed phase on the basis of kinetic theory
,” Eur. J. Mech. B/Fluids
, 17
, 277
(1998
).13.
C.
Borgnakke
and P. S.
Larsen
, “Statistical collision model for Monte Carlo simulation of polyatomic gas hixtures
,” J. Comput. Phys.
18
, 405
(1975
).14.
I.
Kuščer
, “A model for rotational energy exchange in polyatomic gases
,” Physica A
158
, 784
(1989
).15.
G. A.
Bird
, Molecular Gas Dynamics and the Direct Simulation of Gas Flows
(Clarendon
, Oxford
, 1994
).16.
P. L.
Bhatnagar
, E. P.
Gross
, and M.
Krook
, “A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems
,” Phys. Rev.
94
, 511525
(1954
).17.
L. H.
Holway
, “New statistical models for kinetic theory
,” Phys. Fluids
9
, 1658
(1966
).18.
S.
Chapman
and T. G.
Cowling
, The Mathematical Theory of Non-Uniform Gases
(Cambridge University Press
, Cambridge
, 1990
).19.
I. J.
Wysong
and D. C.
Wadsworth
, “Assessment of direct simulation Monte Carlo phenomenological rotational relaxation models
,” Phys. Fluids
10
, 2983
(1998
).20.
R.
Meland
, A.
Frezzotti
, T.
Ytrehus
, and B.
Hafskjold
, “Nonequilibrium molecular-dynamics simulation of net evaporation and net condensation, and evaluation of the gas-kinetic boundary condition at the interphase
,” Phys. Fluids
16
, 223
(2004
).21.
M.
Marek
and J.
Straub
, “Analysis of the evaporation coefficient and the condensation coefficient of water
,” Int. J. Heat Mass Transfer
44
, 39
(2001
).22.
T.
Tsuruta
, H.
Tanaka
, and T.
Masuoka
, “Condensation/evaporation coefficient and velocity distribution at liquid-vapor interface
,” Int. J. Heat Mass Transfer
42
, 4107
(1999
).23.
S. I.
Anisimov
, D. O.
Dunikov
, V. V.
Zhakhovskii
, and S. P.
Malyshenko
, “Properties of a liquid-gas interface at high-rate evaporation
,” J. Chem. Phys.
110
, 8722
(1999
).24.
T.
Ishiyama
, T.
Yano
, and S.
Fujikawa
, “Molecular dynamics study of kinetic boundary condition at an interface between argon vapor and its condensed phase
,” Phys. Fluids
16
, 2899
(2004
).25.
A.
Frezzotti
and L.
Gibelli
, “A kinetic model for equilibrium and non-equilibrium structure of the vapor-liquid interface
,” in Rarefied Gas Dynamics
, edited by A. D.
Ketsdever
and E. P.
Muntz
, AIP Conference Proceedings
, Vol. 663
(American Institute of Physics
, Melville, NY
, 2003
), pp. 980
–987
.26.
A.
Frezzotti
, L.
Gibelli
, and S.
Lorenzani
, “Mean field kinetic theory description of evaporation of a fluid into vacuum
,” Phys. Fluids
17
, 012102
(2005
).27.
T.
Ishiyama
, T.
Yano
, and S.
Fujikawa
, “Molecular dynamics study of kinetic boundary condition at an interface between a polyatomic vapor and its condensed phase
,” Phys. Fluids
16
, 4713
(2004
).28.
A. V.
Rodionov
, J. F.
Crifo
, K.
Szego
, J.
Lagerros
, and M.
Fulle
, “An advanced physical model of cometary activity
,” Planet. Space Sci.
50
, 983
(2002
).29.
C. K.
Chu
, “Kinetic-theoretic description of the formation of a shock wave
,” Phys. Fluids
8
, 12
(1965
).30.
A.
Frezzotti
, “Numerical investigation of the strong evaporation of a polyatomic gas
,” in Rarefied Gas Dynamics
, edited by A. E.
Beylich
(VCH
, Weinheim
, 1991
), pp. 12431250
.© 2006 American Institute of Physics.
2006
American Institute of Physics
You do not currently have access to this content.
