M.Sc Student | Yonatan Schwartz |
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Subject | Development of Discrete Methods for Correcting Continuous Solutions in Multi-Size Sprays |

Department | Department of Aerospace Engineering |

Supervisor | Professor Emeritus Tambour Yoram |

Full Thesis text |

Droplet size-distribution prediction in spray combustion has been for many years an important field of research, in the attempt to improve spray injection and combustion efficiencies. Although the main concern deals with evaporation, the effect of coalescence to the physics of spray combustion problems may be significant.

It is clear that droplet coalescence in a spray is a discrete phenomenon, and thus, the most fundamental differential equations describing the evolution in drop size distributions are discrete coupled equations. Although these equations are discrete, the solutions for the equations are continuous, and hence, yield results with anomalies which stem from mixing discrete equations with continuous solutions.

The purpose of the present study is to suggest new techniques to correct the solutions in order to overcome these anomalies. We begin with Smulochowski's solution which is limited to an initial mono-size drop distribution and switch into the Tambour-Seinfeld solution which is capable of handling any arbitrary initial multi-size droplet distribution. We continue employing the Tambour-Seinfeld solution by "stopping" our computational procedure at short time intervals and restarting a "new" problem at each time interval which has a new initial multi-size droplet distribution.

The calculations lead to fractions of droplets and to an effect of "missing mass", in which non-physical mass conserves in impossible droplet sizes. New techniques are presented, with corrections to the solutions so that droplets will remain integers and no mass will be missing in the system in the solutions for the time evolution of drop sizes. The solution is finally extended to a practical problem of two chemical components coalescing, such as oxidizer and fuel droplets.