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Typus
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Bearbeiter
Graf Isolan
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Untersuchte Arbeit:
Seite: 11, Zeilen: 20-24, 26-36
Quelle: Fan et al 2004
Seite(n): 8, Zeilen: right col 18-36
As an alternative, McGraw (1997) developed the so-called quadrature method of moments (QMOM), which is based on the product-difference (PD) algorithm formulated by Gordon (1968). QMOM has been validated for small particles in the study of aerosols in chemical engineering. It provides a precise and efficient numerical method in order to follow the size distribution of particles, without inertia, experiencing some aggregation-breakage phenomena (Marchisio, et al., 2003b). One of the main limitations of QMOM is that since the dispersed phase is represented through the moments of the size distribution, the phase-average velocity of different solid phases must be used to solve the transport equations for the moments. Thus, in order to use this method in the context of sprays for which the inertia determines the dynamical behavior of the droplets, it is necessary to extend QMOM to handle cases where each droplet size is convected by its own velocity. In order to address these issues, the direct quadrature method of moments (DQMOM) has been formulated and validated (Marchisio and Fox, 2005).

Gordon, R.G. (1968). Error bounds in equilibrium statistical mechanics. Journal of Mathematical Physics 9, pp. 655-663.

Marchisio, D.L., R.D. Vigil and R.O. Fox (2003b). Quadrature method of moments for aggregation-breakage processes. Journal of Colloid and Interface Science 258, pp. 322-334.

Marchisio, D.L. and R.O. Fox (2005). Solution of population balance equations using the direct quadrature method of moments. J. Aerosol Sci. 36, pp. 43-73.

McGraw, R. (1997). Description of aerosol dynamics by the quadrature method of moments. Aerosol Science and Technology 27, pp. 255-265.

As an alternative, McGraw [20] developed the so-called quadrature method of moments (QMOM), which is based on the approximation of the unclosed terms by using an ad-hoc quadrature formula. The quadrature approximation (i.e., its abscissas and weights) can be determined from the lower-order moments [21] by resorting to the product-difference (PD) algorithm [22]. QMOM has been extensively validated for several problems with different internal coordinates [23–25]. One of the main limitations of QMOM is that since the solid phase is represented through the moments of the distribution, the phase-average velocity of the different solid phases must be used to solve the transport equations for the moments. Thus, in order to use this method in the context of the multiphase flows, it is necessary to extend QMOM to handle cases where each particle size is convected by its own velocity.

In order to address these issues, the direct quadrature method of moments (DQMOM) has been formulated and validated [26].


[20] R. McGraw, Description of aerosol dynamics by the quadrature method of moments, Aerosp. Sci. Technol. 27 (1997) 255.

[21] H. Dette, W.J. Studden, The Theory of Canonical Moments with Applications in Statistics, Probability and Analysis,Wiley, New York, 1997.

[22] R.G. Gordon, Error bounds in equilibrium statistical mechanics, J. Math. Phys. 9 (1968) 655.

[23] J.C. Barret, N.A. Webb, A comparison of some approximate methods for solving the aerosol general dynamic equation, J. Aerosol Sci. 29 (1998) 31.

[24] D.L. Marchisio, R.D. Vigil, R.O. Fox, Quadrature method of moments for aggregation-breakage processes, J. Colloid Interface Sci. 258 (2003) 322.

[25] D.L. Marchisio, J.T. Pikturna, R.O. Fox, R.D. Vigil, A.A. Barresi, Quadrature method of moments for population-balance equations, AIChE J. 49 (2003) 1266.

[26] D.L. Marchisio and R.O. Fox, Direct quadrature method of moments: derivation, analysis and applications, J. Comput. Phys. submitted for publication.

Anmerkungen

Though in large parts identical, nothing has been marked as a citation. Mark that Jem speaks of "dispersed phase" instead of the original "solid phase".

On page 119 this passage is repeated again (see Jem/Fragment_119_12).

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