Distribution of droplets in a turbulent spray

Abstract

A statistical description of droplets in turbulent spray, connected with the description of turbulent dissipation, is presented. The ideas of similarity, the cascade processes, and the infinitely divisible distributions are used in this description. Formulas for characteristic droplet sizes and corresponding probability distributions are obtained along with a simple formula for turbulent dissipation in flow near a ship.

A theoretical bubble breakup model for slurry beds or three-phase fluidized beds under high pressure

“…Historically, there have been three predominant approaches to the formulation of this term: statistical models (Novikov and Dommermuth, 1997), phenomenological models based on the change in surface energy of a breaking bubble (Prince and Blanch, 1990;Martinez-Bazan et al, 1999), and hybrid models which are based on a combination of both (Konno et al, 1980). A phenomenological model with consideration to surface energy increasing and capillary pressure constraints was formulated in this work.…”

A review of statistical models for the break-up of an immiscible fluid immersed into a fully developed turbulent flow

“…This model has no physical justification; however, it has been used as a source of comparison for many of the surface-energy models described below. More recent, purely statistical models have been proposed by Longuet-Higgins (1992) and Novikov and Dommermuth (1997). Longuet-Higgins simulated the break-up process by viewing it as a sequence of random divisions of a unit cube by a number of planes oriented parallel to the faces of the cube.…”

On the breakup of an air bubble injected into a fully developed turbulent flow. Part 2. Size PDF of the resulting daughter bubbles

“…In the past, three main approaches have been used to model f(D,Do): phenomenological models based on surface energy considerations (Tsouris & Tavlarides 1994), statistical models (Coulaloglou & Tavlarides 1977;Prince & Blanch 1990;LonguetHiggins 1992;Novikov 1997), and hybrid models based on a combination of both (Konno et al 1983;Cohén 1991). Among the most widely used phenomenological models based on surface energy considerations is the one proposed by Tsouris & Tavlarides (1994).…”

“…Purely statistical studies ha ve been performed by Longuet-Higgins (1992), Novikov (1997), and others. Longuet-Higgins proposed a simple mechanism for the breakup process by simulating it through a series of a random divisions of a cubical block of size unity by a number of planes which are parallel to the faces of the block.…”