The present study completes the development of a model for predicting the effect of wall impacts on agglomerates in turbulent flows. Relying on an Euler-Lagrange hard-sphere approach this physical phenomenon is described in an efficient manner allowing practically relevant multiphase flow simulations at high mass loadings. In a recent study (Khalifa and Breuer, 2020) conditions for the onset of breakage and the resulting fragment size distribution were derived. In the present investigation a data-driven description of the post-breakage kinetics of the fragments is developed based on extensive DEM simulations taking a variety of impact conditions (impact velocity, impact angle, agglomerate size) into account. The description relates the velocity vectors of the fragments after breakage to three parameters: The reflection angle, the spreading angle and a velocity ratio of the magnitude of the fragment velocity to the impact velocity of the agglomerate. Relying on the DEM results Weibull distribution functions are used to describe the parameters of the wall-impact model. The shape and scale parameters of the Weibull distributions are found to mainly depend on the impact angle of the agglomerate. Consequently, relationships between the shape and the scale parameters and the impact angle are established for each of the three parameters based on a fourth-order regression. This allows to determine the velocity vectors of the fragments randomly based on the corresponding Weibull distributions of the reflection angle, the spreading angle and the fragment velocity ratio.

The devised model is evaluated in a turbulent duct flow at five Reynolds numbers and three agglomerate strengths given by powders consisting of primary particles of different size. The analysis first concentrates on the pure wall-impact breakage but then also includes agglomerate breakup due to turbulence, drag forces and rotation allowing to determine the shares of the different physical phenomena. It is found that with increasing Stokes number the wall-impact breakage occurs less effectively due to the reduced responsiveness of the agglomerates to the secondary flow motions in the duct. However, in the very high range of ${\mathrm{St}}^{+}$ other mechanisms such as the turbophoresis and the lift force augment the breakage at walls. Comparing the contributions of the different breakage mechanism reveals that the wall impact is dominant at the lowest Reynolds numbers, whereas the drag stress prevails at high Re.

本研究完成了一个模型的开发，用于预测壁面冲击对湍流中团聚体的影响。依靠欧拉-拉格朗日硬球方法，这种物理现象以有效的方式描述，允许在高质量载荷下进行实际相关的多相流模拟。在最近的一项研究（Khalifa 和 Breuer，2020 年）中，推导出了断裂开始的条件和由此产生的碎片大小分布。在本研究中，基于广泛的 DEM 模拟，考虑了各种冲击条件（冲击速度、冲击角度、团块尺寸），对碎片的破碎后动力学进行了数据驱动的描述。描述将破碎后碎片的速度矢量与三个参数相关联：反射角、散布角和碎片速度大小与团块撞击速度的速度比。依靠 DEM 结果威布尔分布函数来描述墙体冲击模型的参数。发现威布尔分布的形状和尺度参数主要取决于团聚体的撞击角度。因此，基于四阶回归，为三个参数中的每一个建立了形状和尺度参数以及撞击角度之间的关系。这允许根据反射角、扩散角和碎片速度比的相应威布尔分布随机确定碎片的速度矢量。依靠 DEM 结果威布尔分布函数来描述墙体冲击模型的参数。发现威布尔分布的形状和尺度参数主要取决于团聚体的撞击角度。因此，基于四阶回归，为三个参数中的每一个建立了形状和尺度参数以及撞击角度之间的关系。这允许根据反射角、扩散角和碎片速度比的相应威布尔分布随机确定碎片的速度矢量。依靠 DEM 结果威布尔分布函数来描述墙体冲击模型的参数。发现威布尔分布的形状和尺度参数主要取决于团聚体的撞击角度。因此，基于四阶回归，为三个参数中的每一个建立了形状和尺度参数以及撞击角度之间的关系。这允许根据反射角、扩散角和碎片速度比的相应威布尔分布随机确定碎片的速度矢量。发现威布尔分布的形状和尺度参数主要取决于团聚体的撞击角度。因此，基于四阶回归，为三个参数中的每一个建立了形状和尺度参数以及撞击角度之间的关系。这允许根据反射角、扩散角和碎片速度比的相应威布尔分布随机确定碎片的速度矢量。发现威布尔分布的形状和尺度参数主要取决于团聚体的撞击角度。因此，基于四阶回归，为三个参数中的每一个建立了形状和尺度参数以及撞击角度之间的关系。这允许根据反射角、扩散角和碎片速度比的相应威布尔分布随机确定碎片的速度矢量。

设计的模型在由不同尺寸的初级颗粒组成的粉末给出的五个雷诺数和三个团聚强度下的湍流管道流动中进行评估。分析首先集中在纯粹的壁面撞击破裂，但随后还包括由于湍流、阻力和旋转引起的团块破裂，从而可以确定不同物理现象的份额。发现随着斯托克斯数的增加，由于团聚体对管道中二次流动的响应性降低，壁面撞击破裂的发生效果较差。然而，在非常高的范围内${\mathrm{英石}}^{+}$其他机制，例如涡轮电泳和升力，会增加墙壁的破损。比较不同断裂机制的贡献表明，壁面冲击在雷诺数最低时占主导地位，而阻力应力在高 Re 时占主导地位。