A population balance model for large eddy simulation of polydisperse droplet evolution
A population balance model for large eddy simulation of polydisperse droplet evolution
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DOI：
10.1017/jfm.2019.649
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发表时间：
2019-11-10
影响因子：
3.7
通讯作者：
Meneveau, C.
中科院分区：
文献类型：
--
作者：
Aiyer, A. K.;Yang, D.;Meneveau, C.
在湍流多相流的许多应用中，了解分散相尺寸分布及其演变对于预测重要的宏观特征至关重要。我们开发了一个大涡模拟（LES）模型，可以预测湍流传输和尺寸分布的演变，适用于特定的应用子集，其中分散相可以假设由球形液滴组成，并且发生在低体积分数下。我们使用专门适用于 LES 框架的多分散液滴分布的群体动力学模型，包括由于湍流而导致液滴破裂的模型，忽略与假设的小分散相体积分数一致的聚结。我们使用欧拉方法对离散液滴尺寸分布的每个箱的数密度场进行建模。遵循雷诺平均纳维-斯托克斯框架中使用的早期方法，通过像气体动力学理论中那样处理液滴-涡流碰撞来模拟由于湍流波动而导致的液滴破裂。现有模型假设液滴-涡流碰撞的规模处于湍流的惯性范围内。为了模拟与柯尔莫哥洛夫尺度相当或小于柯尔莫哥洛夫尺度的较小液滴，我们使用结构函数模型扩展了破碎内核，该模型可以从惯性范围平滑地过渡到粘性范围。该模型包括一个无量纲系数，该系数是通过将模型的一维版本的预测与破碎波下油滴破碎的实验室实验进行比较来拟合的。将一维模型与轴对称射流中的油滴测量进行初步比较后，将其应用于横流射流的三维 LES 中，并在射流源头释放单一尺寸的大油滴。我们使用离散液滴尺寸的容器对浓度场进行建模，并求解每个容器的标量传输方程。将所得液滴尺寸分布与已发表的实验数据进行比较，并且获得了相对尺寸分布的良好一致性。 LES 结果还使我们能够量化尺寸分布的变异性。我们发现油滴的总表面积和索特平均直径等关键量的概率分布函数变化很大，有些表现出强烈的非高斯间歇行为。
In the context of many applications of turbulent multi-phase flows, knowledge of the dispersed phase size distribution and its evolution is critical to predicting important macroscopic features. We develop a large eddy simulation (LES) model that can predict the turbulent transport and evolution of size distributions, for a specific subset of applications in which the dispersed phase can be assumed to consist of spherical droplets, and occurring at low volume fraction. We use a population dynamics model for polydisperse droplet distributions specifically adapted to a LES framework including a model for droplet breakup due to turbulence, neglecting coalescence consistent with the assumed small dispersed phase volume fractions. We model the number density fields using an Eulerian approach for each bin of the discretized droplet size distribution. Following earlier methods used in the Reynolds-averaged Navier-Stokes framework, the droplet breakup due to turbulent fluctuations is modelled by treating droplet-eddy collisions as in kinetic theory of gases. Existing models assume the scale of droplet-eddy collision to be in the inertial range of turbulence. In order to also model smaller droplets comparable to or smaller than the Kolmogorov scale we extend the breakup kernels using a structure function model that smoothly transitions from the inertial to the viscous range. The model includes a dimensionless coefficient that is fitted by comparing predictions in a one-dimensional version of the model with a laboratory experiment of oil droplet breakup below breaking waves. After initial comparisons of the one-dimensional model to measurements of oil droplets in an axisymmetric jet, it is then applied in a three-dimensional LES of a jet in cross-flow with large oil droplets of a single size being released at the source of the jet. We model the concentration fields using bins of discrete droplet sizes and solve scalar transport equations for each bin. The resulting droplet size distributions are compared with published experimental data, and good agreement for the relative size distribution is obtained. The LES results also enable us to quantify size distribution variability. We find that the probability distribution functions of key quantities such as the total surface area and the Sauter mean diameter of oil droplets are highly variable, some displaying strong non-Gaussian intermittent behaviour.