流体力学特別セミナー
主催：日本流体力学会中部支部
Prof. Mikhael Gorokhovski（LMFA, Ecole Centrale de Lyon, Ecully, France)
日時：3 月 10 日（金） 15:00～17:00
会場：名古屋工業大学 2 号館 B 棟６階 611B 室
https://www.nitech.ac.jp/access/index.html
乱流および乱流噴霧で国際的に著名な Gorokhovski 教授が名古屋に 3 月 6 日から 1 週間滞在されます．この機会に、乱流中における水滴の分裂や粒径分布に関する理論、その LES におけるモデリングについて講演をしていただくことになりました．
多数の方々のご参加を歓迎いたします．

Fragmentation, stochastic models of drop breakup and raindrop size distributions.
Mikhael Gorokhovski
LMFA, Ecole Centrale de Lyon, Ecully, France
Fragmentation, which is the production of random fragments (or particles) by continuous
breakup of clusters, plays a key role in a variety of physical, chemical and geological processes,
including turbulence, spray atomization, clouds fragmentation, solid particle decomposition,rock crushing, polymer degradation and network branching. Usually, each individual event offragmentation is a complex microphysical process, with fluctuations and uncertainties, and thefrequency of such events is high. Then it is natural to abstract an ‘effective’ fragmentation
scenario, and either to search analytically its statistical universalities, or to simulate thisscenario as stochastic process. In both approaches, the mechanism of fragmentation may berepresented by effective parameters. In this talk we will discuss such a framework in the caseof drop breakup in the turbulent conditions.
The ‘effective’ fragmentation scenario in the firstpart of this talk is the drop breakup under thescaling symmetry. Considering the kinetic
equation of fragmentation in the continuity form,
we will illustrate two types of its self-similarsolutions: (i) the evolution of the size-distribution
when the fragmentation frequency is constant, and (ii) the evolution of this distribution when
the fragmentation frequency is decreasing with the size of proliferating droplets. The bothsolutions are very interesting. In the first case, the size-distribution evolves through its
intermediate lognormal shape towards the power distribution (fractals), and when two first
logarithmic moments of size are equal to each other, the latter is the Pareto distribution, whichis often suggested for the exhalations of mucosalivary fluid. In the second case, the well-known
Nukiyama–Tanasawa distribution appears to be the self-similar solution of the fragmentation
equation. Such type of distribution immerges very often in the measurements of droplet size inthe spray atomization process. On the other hand, at larger sizes, the Nukiyama–Tanasawa
distribution approaches the Marshall-Palmer distribution, which is also well-known but as abroadly confirmed representative of raindrop size-distribution. This motivates to discuss on theorigins of Marshall-Palmer’s law in the representation of raindrops’ polydispersity in terms offragmentation under scaling symmetry. The evolution of Nukiyama–Tanasawa distribution fordifferent rates of rainfall and for different dissipation rates of the turbulent kinetic energy will
be displayed.
In the second part of our talk we will discuss the stochastic simulation of drop breakup on
residual scales in LES of flows with sprays. One of the models is based on the stochastic
mother-to-daughter relaxation of droplets. The relaxation is controlled by the viscous
dissipation rate “seen” by the droplet along its trajectory, and simulated as the lognormal
stochastic process. In the numerical applications, this model is discussed in comparison withother breakup stochastic models based on fragmentation under scaling symmetry.

連絡先：渡邊威，後藤俊幸