The purpose of this article is the analysis and the development of Eulerian multi-fluid models to describe the evolution of the mass density of evaporating liquid sprays. First, the classical multi-fluid model developed in [Laurent and Massot, Combust. Theor. Model. 5 (2001) 537-572] is analyzed in the framework of an unsteady configuration without dynamical nor heating effects, where the evaporation process is isolated, since it is a key issue. The classical multi-fluid method consists then in a discretization of the droplet size variable into cells called sections. This analysis provides a justification of the “right” choice for this discretization to obtain a first order accurate and monotone scheme, with no restrictive CFL condition. This result leads to the development of a class of methods of arbitrary high order accuracy through the use of moments on the droplet surface in each section and a Godunov type method. Moreover, an extension of the two moments method is proposed which preserves the positivity and limits the total variation. Numerical results of the multi-fluid methods are compared to examine their capability to accurately describe the mass density in the spray with a small number of variables. This is shown to be a key point for the use of such methods in realistic flow configurations.
Keywords: spray, evaporation, multi-fluid method, kinetic schemes
@article{M2AN_2006__40_3_431_0, author = {Laurent, Fr\'ed\'erique}, title = {Numerical analysis of eulerian multi-fluid models in the context of kinetic formulations for dilute evaporating sprays}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {431--468}, publisher = {EDP-Sciences}, volume = {40}, number = {3}, year = {2006}, doi = {10.1051/m2an:2006023}, mrnumber = {2245317}, zbl = {1160.76380}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/m2an:2006023/} }
TY - JOUR AU - Laurent, Frédérique TI - Numerical analysis of eulerian multi-fluid models in the context of kinetic formulations for dilute evaporating sprays JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2006 SP - 431 EP - 468 VL - 40 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2006023/ DO - 10.1051/m2an:2006023 LA - en ID - M2AN_2006__40_3_431_0 ER -
%0 Journal Article %A Laurent, Frédérique %T Numerical analysis of eulerian multi-fluid models in the context of kinetic formulations for dilute evaporating sprays %J ESAIM: Modélisation mathématique et analyse numérique %D 2006 %P 431-468 %V 40 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2006023/ %R 10.1051/m2an:2006023 %G en %F M2AN_2006__40_3_431_0
Laurent, Frédérique. Numerical analysis of eulerian multi-fluid models in the context of kinetic formulations for dilute evaporating sprays. ESAIM: Modélisation mathématique et analyse numérique, Volume 40 (2006) no. 3, pp. 431-468. doi : 10.1051/m2an:2006023. http://archive.numdam.org/articles/10.1051/m2an:2006023/
[1] Kiva II, a computer program for chemically reactive flows with sprays. Technical Report LA-11560-MS. Los Alamos National Laboratory, Los Alamos, New Mexico (1989).
, and ,[2] A compressible model for separated two-phase flows computations, in ASME Fluids Engineering Division Summer Meeting, number 31141, Montreal (2002).
, and ,[3] The kinetic sectional approach for noncolliding evaporating sprays. Atomization Spray. 11 (2001) 291-303.
,[4] A numerical method for the computation of the dispersion of a cloud of particles by a turbulent gas flow field. J. Comput. Phys. 133 (1997) 256-278. | Zbl
and ,[5] Theory of multicomponent fluids. Applied Mathematical Sciences, Springer 135 (1999). | MR | Zbl
and ,[6] A second-order multi-fluid model for evaporating sprays. ESAIM: M2AN 39 (2005) 931-963. | Numdam | Zbl
and ,[7] A particle-fluid numerical model for liquid sprays. J. Comput. Phys. 35 (1980) 229-253. | Zbl
,[8] An opposed jet quasi-monodisperse spray diffusion flame. Combust. Sci. Technol. 50 (1986) 255-270.
, and ,[9] On the origin of spray sectional conservation equations. Combust. Flame 93 (1993) 90-96.
, and ,[10] A five equation reduced model for compressible two phase flow problems. Prepublication 4778, INRIA (2003). | Zbl
and ,[11] On finite-difference approximations and entropy conditions for shocks. Comm. Pure Appl. Math. 29 (1976) 297-322. With an appendix by B. Keyfitz. | Zbl
, and ,[12] Modélisation cinétique et simulation numérique d'un brouillard dense de gouttelettes. Application aux propulseurs à poudre. Ph.D. thesis, ENSAE (1999).
,[13] Analyse numérique d'une méthode multi-fluide Eulérienne pour la description de sprays qui s'évaporent. C. R. Math. Acad. Sci. Paris 334 (2002) 417-422. | Zbl
,[14] Modélisation mathématique et numérique de la combustion de brouillards de gouttes polydispersés. Ph.D. thesis, Université Claude Bernard, Lyon 1 (2002).
,[15] Multi-fluid modeling of laminar poly-dispersed spray flames: origin, assumptions and comparison of the sectional and sampling methods. Combust. Theor. Model. 5 (2001) 537-572.
and ,[16] Eulerian multi-fluid modeling for the numerical simulation of polydisperse dense liquid spray. J. Comput. Phys. 194 (2004) 505-543. | Zbl
, and ,[17] Accurate treatment of size distribution effects in polydispersed spray diffusion flames: multi-fluid modeling, computations and experiments. Combust. Theor. Model. 8 (2004) 385-412.
, , , , and ,[18] Numerical methods for conservation laws. Birkhäuser Verlag, Basel, second edition (1992). | MR | Zbl
,[19] Quadrature method of moments for aggregation-breakage processes. J. Colloid Interf. Sci. 258 (2003) 322-334.
, and ,[20] Modélisation multi-fluide eulérienne pour la simulation de brouillards denses polydispersés. C. R. Acad. Sci. Paris Sér. I Math. 332 (2001) 869-874. | Zbl
and ,[21] Counterflow spray diffusion flames of heptane: computations and experiments, in Proceedings of the 27th Symp. (International) on Combustion, The Comb. Institute (1998) 1975-1983.
, , and ,[22] Collective drop effects on vaporizing liquid sprays. Ph.D. thesis, University of Princeton (1981).
,[23] Population Balances: Theory and Applications to Particulate Systems in Engineering. Academic Press (2000).
and ,[24] A nonconservative hyperbolic system modeling spray dynamics. I. Solution of the Riemann problem. Math. Mod. Meth. Appl. S. 5 (1995) 297-333. | Zbl
and ,[25] Euler/Lagrange calculations of turbulent sprays : the effect of droplet collisions and coalescence. Atomization Spray. 10 (2000) 47-81.
, , and ,[26] Towards the ultimate conservative difference scheme v. a second order sequel to godunov's method. J. Comput. Phys. 32 (1979) 101-136. | Zbl
,[27] Une méthode particulaire aléatoire reposant sur une équation cinétique pour la simulation numérique des sprays denses de gouttelettes liquides. C. R. Acad. Sci. Paris Sér. I Math. 325 (1997) 323-328. | Zbl
and ,[28] Spray combustion and atomization. Phys. Fluids 1 (1958) 541-545. | Zbl
,[29] Combustion Theory (Combustion Science and Engineering Series). F.A. Williams Ed., Reading, MA: Addison-Wesley (1985).
,[30] Bivariate extension of the quadrature method of moments for modeling simultaneous coagulation and sintering of particle populations. J. Colloid Interf. Sci. 236 (2001) 242-251.
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