The maximum entropy principle(MEP) is one of the first methods which have been used to predict droplet size and velocity distributions of liquid sprays. This method needs a mean droplets diameter as an input to predic...The maximum entropy principle(MEP) is one of the first methods which have been used to predict droplet size and velocity distributions of liquid sprays. This method needs a mean droplets diameter as an input to predict the droplet size distribution. This paper presents a new sub-model based on the deterministic aspects of liquid atomization process independent of the experimental data to provide the mean droplets diameter for using in the maximum entropy formulation(MEF). For this purpose, a theoretical model based on the approach of energy conservation law entitled energy-based model(EBM) is presented. Based on this approach, atomization occurs due to the kinetic energy loss. Prediction of the combined model(MEF/EBM) is in good agreement with the available experimental data. The energy-based model can be used as a fast and reliable enough model to obtain a good estimation of the mean droplets diameter of a spray and the combined model(MEF/EBM) can be used to well predict the droplet size distribution at the primary breakup.展开更多
Some researchers have suggested that scientific foundations expressed in a mathematical form are needed to thrust the success of systems engineering as a discipline on its own merit. In order to contribute the develop...Some researchers have suggested that scientific foundations expressed in a mathematical form are needed to thrust the success of systems engineering as a discipline on its own merit. In order to contribute the development of such systems science, this paper investigates from a foundational standpoint the relationships between stakeholder needs, system requirements, and sets of systems. Various theorems and corollaries are proposed and mathematically proven. The theoretical elements are presented as a foundation for the development of a science for requirements engineering. The proposed foundations are finally tested to mathematically describe, in a rigorous and precise manner, qualities of good requirements, which are otherwise traditionally defined using vague narrative. By showcasing practical examples of the theoretical aspects, the paper is intended to serve as a bridge between practitioners and theorists.展开更多
文摘The maximum entropy principle(MEP) is one of the first methods which have been used to predict droplet size and velocity distributions of liquid sprays. This method needs a mean droplets diameter as an input to predict the droplet size distribution. This paper presents a new sub-model based on the deterministic aspects of liquid atomization process independent of the experimental data to provide the mean droplets diameter for using in the maximum entropy formulation(MEF). For this purpose, a theoretical model based on the approach of energy conservation law entitled energy-based model(EBM) is presented. Based on this approach, atomization occurs due to the kinetic energy loss. Prediction of the combined model(MEF/EBM) is in good agreement with the available experimental data. The energy-based model can be used as a fast and reliable enough model to obtain a good estimation of the mean droplets diameter of a spray and the combined model(MEF/EBM) can be used to well predict the droplet size distribution at the primary breakup.
文摘Some researchers have suggested that scientific foundations expressed in a mathematical form are needed to thrust the success of systems engineering as a discipline on its own merit. In order to contribute the development of such systems science, this paper investigates from a foundational standpoint the relationships between stakeholder needs, system requirements, and sets of systems. Various theorems and corollaries are proposed and mathematically proven. The theoretical elements are presented as a foundation for the development of a science for requirements engineering. The proposed foundations are finally tested to mathematically describe, in a rigorous and precise manner, qualities of good requirements, which are otherwise traditionally defined using vague narrative. By showcasing practical examples of the theoretical aspects, the paper is intended to serve as a bridge between practitioners and theorists.
