Analytic expressions for interface terms in general dispersed two–phase flow laden with arbitrary–shaped dispersed elements
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Keywords
dispersed two–phase flow, arbitrary shaped elements, probability density function, indicator function
Abstract
This paper presents the methodology of the indicator function–discrete elementsprobability density function statistical average applied to Two–phaseflow modelling. This formulation allows to consider particles of arbitrary shapeand size and it can be applied to any laminar or turbulent flow. In the case ofequal sized spherical dispersed elements, the most common case found in theliterature, the final expression for the interaction terms (contributions thatdescribe the effect of the second phase on the continuous one) are obtainedwithout great difficulties due to the high isotropy of the spherical shape. Thistask, in the general case of non–spherical non–equal particles is no longerstraightforward and the derivation of the appropriate general interaction termsis presented in §4. In the case that the dispersed elements are small enough,some simplifications can be further introduced leading to a final presentation that remembers that obtained for the simplest case of spherical particles, butwhere some of the quantities must be adequately redefined.
PACS: 47.50.Cd
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References
[2] J. L. Achard and J. M. Delhaye. On the averaging operators introduced in Two–phase flow modelling. In OECD/NEA Specialists Meeting on Transient Two– Phase Flow, 1976. Toronto, Canada.
[3] Mamoru Ishii and Takashi Hibiki. Thermo–fluid dynamics of Two–phase flow. ISBN 0–387–28321–8. Springer, 2005.
[4] Richard Hercynski and Isabela Pienskowska. Toward a statistical theory of suspension. Annual Review of Fluid Mechanics, ISSN 0066–4189, 12, 237–269 (1980).
[5] D. Drew. Mathematical modelling of two phase flow. Annual Review of Fluid Mechanics, ISSN 0066–4189, 15, 261–291 (1983).
[6] W. G. Gray and S. M. Hassanizadeh. Averaging theorems and averaged equations for transport of interface properties in multiphase systems. International Journal of Multiphase Flow, ISSN 0301–9322, 151, 81–95 (1989).
[7] A. Prosperetti and D. Z. Zhang. Averaged equations for inviscid disperse Two– phase flow. Journal of Fluid Mechanics Digital Archive, ISSN 0022–1120, 267, 185–219 (1994).
[8] R. Aliod and C. Dopazo. A statistically conditioned averaging formalism for deriving Two–phase flow equations. Particle and Particle Systems Characterization ISSN 0934–0866, 7, 191–202 (1990).
[9] Santiago Laín and R. Aliod. Deduction and validation of an Eulerian–Eulerian model for turbulent dilute Two–phase flows by means of the phase indicator function–disperse elements.pdf. Chinese Journal of Chemical Engineering, ISSN 1004–9541, 8(3), 189–202 (2000).
[10] Clayton T. Crowe, Martin Sommerfeld and Yutaka Tsuji. Multiphase flows with droplets and particles, ISBN 0–8493–9469–4. CRC Press, 1998.
[11] G. F. Roach. Green’s functions, ISBN 0–521–28288–8. Cambridge University Press, 1982.