埃蒙斯问题再探讨

IF 2.3 3区 工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY
Howard R. Baum, J. G. Quintiere
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引用次数: 0

摘要

埃蒙斯问题 "是火灾科学的基础,它给出了从浸没在均匀氧化气体流中的平板表面汽化燃料燃烧的数学边界层解决方案。它近似于纳维-斯托克斯方程,假设化学反应无限快,并忽略了微分扩散和热辐射。这使得 "相似性 "解得以开发,并用经典的布拉修斯函数来表示。本文以数学形式将该解法扩展到远离边界层和前缘上游的整个域。通过引入共形抛物线坐标和使用 Howarth 变换,流函数的解可以用与 Emmons 所发现的完全相同的形式表示,并为压力扰动提供了明确的公式。通过相同的坐标变换,还可以获得全椭圆混合物分数方程的精确解,而用流函数来表示速度分量则保证了连续性方程也能得到精确满足。此外,横向动量方程的精确解也得到了显示,从而可以将横流引入所获得的结果谱中。总之,我们找到了埃蒙斯问题在整个椭圆域--上游和远场--的解析解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

The Emmons Problem Revisited

The Emmons Problem Revisited

The “Emmons Problem” is a foundation of fire science and gives a mathematical boundary layer solution to the burning of a vaporizing fuel from the surface of a flat plate immersed in a uniform flow of oxidizing gas. It approximates the Navier–Stokes equations assuming infinitely fast chemistry and ignores differential diffusion and thermal radiation. This allows “similarity” solutions to be developed and expressed in terms of the classic Blasius function. The current paper extends the solution, in mathematical form, to the entire domain far from the boundary layer and upstream of the leading edge. The introduction of conformal parabolic coordinates and use of the Howarth transformation allows the solution for the stream function to be expressed in exactly the same form as that found by Emmons and furnishes an explicit recipe for the pressure perturbation. The same coordinate transformations allow the exact solution of the full elliptic mixture fraction equation to be obtained, and the representation of the velocity components in terms of the stream function guarantees that the continuity equation is also satisfied exactly. Further, an exact solution to the transverse momentum equation is also displayed permitting the introduction of a crossflow into the spectrum of results obtained. In short, an analytic solution is found for the Emmons problem in the entire elliptic domain - upstream and in the far field.

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来源期刊
Fire Technology
Fire Technology 工程技术-材料科学:综合
CiteScore
6.60
自引率
14.70%
发文量
137
审稿时长
7.5 months
期刊介绍: Fire Technology publishes original contributions, both theoretical and empirical, that contribute to the solution of problems in fire safety science and engineering. It is the leading journal in the field, publishing applied research dealing with the full range of actual and potential fire hazards facing humans and the environment. It covers the entire domain of fire safety science and engineering problems relevant in industrial, operational, cultural, and environmental applications, including modeling, testing, detection, suppression, human behavior, wildfires, structures, and risk analysis. The aim of Fire Technology is to push forward the frontiers of knowledge and technology by encouraging interdisciplinary communication of significant technical developments in fire protection and subjects of scientific interest to the fire protection community at large. It is published in conjunction with the National Fire Protection Association (NFPA) and the Society of Fire Protection Engineers (SFPE). The mission of NFPA is to help save lives and reduce loss with information, knowledge, and passion. The mission of SFPE is advancing the science and practice of fire protection engineering internationally.
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