A population balance model coupled with large eddy simulations (LES) is adapted and applied to study the evolution of oil droplets in an axisymmetric turbulent jet including the effects of droplet breakup. A key unknown in simulating secondary breakup in turbulent multiphase jets is the inflow size distribution generated within the primary breakup zone near the nozzle exit. A monodisperse injection inflow condition is commonly used for simplicity, but this choice is often unrealistic. In order to provide more realistic inlet conditions for LES, we develop a one-dimensional (1D) parcel model to predict the evolution of the dispersed phase along the jet centerline due to the combined effects of advection, radial turbulent transport, and droplet breakup due to turbulence in the regions closer to the jet nozzle that cannot be resolved using coarse LES. The model is validated with experimental data measured far from the nozzle. The 1D model is also used to generate an initial size distribution for use in a coarse-resolution LES of a turbulent jet. Number density fields for each bin of the discretized droplet size distribution are modeled using an Eulerian LES approach and scalar transport equations are solved for each bin. LES results are compared to published experimental data, with good agreement, and we examine the statistics of the velocity field and the concentration of the polydisperse oil droplet plumes for two droplet Weber numbers. We find that the centerline decay rate of the concentration for different droplet sizes is modified in the breakup dominated zone. Unlike Reynolds averaged approaches, LES also allows us to quantify size distribution variability due to turbulence. We quantify the radial and axial distributions and the variability of key quantities such as the Sauter mean diameter, total surface area, and droplet breakup timescale and explore their sensitivity to the Weber number.

中文翻译：

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湍流圆形射流中多分散液滴演化的种群平衡和大涡模拟耦合模型

人口平衡模型与大涡流模拟（LES）结合使用，并用于研究轴对称湍流射流中油滴的演化，包括油滴破裂的影响。在湍流多相射流中模拟二次破碎的一个关键未知因素是在喷嘴出口附近的一次破碎区内产生的流入流量分布。为了简化起见，通常使用单分散进样条件，但是这种选择通常是不现实的。为了为LES提供更逼真的入口条件，我们开发了一个一维（1D）包裹模型，以预测由于对流，径向湍流传输和液滴破裂的综合影响，沿喷射中心线的分散相的演变。在更靠近喷嘴的区域产生湍流，而使用粗LES无法解决这些问题。使用远离喷嘴测量的实验数据验证了该模型。一维模型还用于生成初始尺寸分布，以用于湍流射流的粗分辨率LES。使用欧拉LES方法对离散液滴大小分布的每个单元的数量密度场进行建模，并为每个单元求解标量传输方程。将LES结果与已发表的实验数据进行比较，结果吻合良好，我们检查了两个液滴Weber数的速度场和多分散油滴羽流浓度的统计数据。我们发现，在分裂支配区，不同液滴尺寸的浓度的中心线衰减率发生了变化。与雷诺平均法不同，LES还允许我们量化由于湍流引起的尺寸分布变异性。