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Atomization and Sprays

Impact factor: 1.235

ISSN Print: 1044-5110
ISSN Online: 1936-2684

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Atomization and Sprays

DOI: 10.1615/AtomizSpr.v7.i1.10
pages 1-32

THEORY OF DROPLETS (II): STATES, STRUCTURES, AND LAWS OF INTERACTING DROPLETS

Huei-Huang Chiu
Institute of Aeronautics and Astronautics, National Cheng Kung University, Tainan, Taiwan,70101, ROC
S. P. Su
Institute of Aeronautics and Astronautics, National Cheng Kung University, Tainan, Taiwan

ABSTRACT

A theory of interacting droplets featuring laminar, hydrodynamically modulated, collisionless drop-drop interactions is developed through the extension of canonical and re normalization techniques to aid in the examination of structures, states, and laws of interphase phenomena in nonreactive environments. Parametric sensitivities of interphase processes and droplet behavior are investigated in wide ranges of Reynolds numbers, transfer numbers, and two renormalization numbers for gasification and aerodynamic drag, respectively. The laws of vaporization and aerodynamic drag of an interacting droplet in a nondilute droplet system agree with the results of Godsave, Spalding, and Stokes, in appropriate limiting cases of isolated droplets in a dilute system. Interacting droplets in nonreactive environments assume one of three allowed states: the normal state, featuring a finite gasification rate and aerodynamic drag; the "aerodynamically masked state," featuring vanishing aerodynamic drag and a finite gasification rate; and the frozen state, with vanishingly small drag and gasification rate. The structure of an interacting droplet environment exhibits a nonuniform concentration with temperature stratification, induced by the gasification of cellular-shaped ring clusters in the environment of each droplet. Laws and correlation functions for vaporization and aerodynamic drag are established to aid in the spray calculation in selected ranges of the principal parameters.