Multi-fluid modelling of laminar polydisperse spray flames: origin, assumptions and comparison of sectional and sampling methods
Multi-fluid modelling of laminar polydisperse spray flames: origin, assumptions and comparison of sectional and sampling methods
复制标题
层流多分散喷雾火焰的多流体建模：起源、假设以及截面法和取样法的比较
DOI：
10.1088/1364-7830/5/4/303
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发表时间：
2001
影响因子：
1.3
通讯作者：
M. Massot
中科院分区：
文献类型：
--
作者：
F. Laurent;M. Massot
第一次尝试推导一个多分散蒸发喷雾的完全欧拉模型是由Tamnesi等人用所谓的分段方法开发的。然而，从玻尔兹曼型喷雾方程的截面“多流体”守恒方程的完整推导从未提供，既不是一套基本假设，也不是与经典拉格朗日模型的比较：采样方法。在本文中，我们澄清了一组必要的假设，以推导出多流体截面模型从喷雾方程在“动力学水平”，并提供了整个一套守恒方程描述的分散液相的推导。而前面的推导是在任何空间维度进行的，我们限制自己的一维静止流的液滴不回头，并得出一个欧拉采样模型，这是在这种情况下，通常的拉格朗日粒子的方法是等效的。然后，我们确定了一些情况下，即使在这个限制性的框架内，其中分区的方法未能再现喷雾的蒸发和动力学的耦合，然后需要的采样方法。在区域的适用性的截面方法，这两种方法进行了数值比较，在逆流喷雾扩散火焰的配置。这两种方法，如果足够精细，给相当相似的结果，除了一些小的差异，其中的起源是确定的。证明了采样方法是更精确的，即使它产生振荡，由于Dirac δ函数的连续函数的内在表示。因此，我们提供了一个全面的分析，从建模和数值的角度来看，分段的方法。
A first attempt at deriving a fully Eulerian model for polydisperse evaporating sprays was developed by Tambour et al with the so-called sectional approach. However, the complete derivation of the sectional ‘multi-fluid’ conservation equations from the Boltzmann-type spray equation was never provided, neither was the set of underlying assumptions nor the comparison with the classical Lagrangian model: the sampling method. In this paper, we clarify the set of assumptions necessary in order to derive the multi-fluid sectional model from the spray equation at the ‘kinetic level’ and provide the derivation of the whole set of conservation equations describing the dispersed liquid phase. Whereas the previous derivation is conducted in any space dimension, we restrict ourselves to one-dimensional stationary flows where the droplets do not turn back and derive a Eulerian sampling model which is equivalent in this context to the usual Lagrangian particle approach. We then identify some situations, even within this restrictive framework, where the sectional approach fails to reproduce the coupling of the vaporization and dynamics of the spray, the sampling method then being required. In the domain of applicability of the sectional approach, the two methods are then compared numerically in the configuration of counterflow spray diffusion flames. The two methods, if refined enough, give quite similar results, except for some small differences, the origin of which is identified. It is proved that the sampling method is more precise even if it generates oscillations due to the intrinsic representation of a continuous function by Dirac delta functions. We thus provide a comprehensive analysis of the sectional approach from both the modelling and numerical points of view.