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Settling of spherical particles in the transitional regime
International Journal of Multiphase Flow ( IF 3.8 ) Pub Date : 2021-02-09 , DOI: 10.1016/j.ijmultiphaseflow.2021.103589
Thomas Hagemeier , Dominique Thévenin , Thomas Richter

The settling process and wall impact of large spherical particles in a stagnant, highly viscous fluid has been observed by means of high-speed shadow imaging. The particles included in this study vary in size and material properties: steel, polytetrafluorethylen (PTFE), polyoxymethylen (POM), or rubber. The corresponding terminal Reynolds numbers range from 333 to 4012, covering in principle the transitional and Newton regime for drag forces. However, most particles do not reach the terminal velocity before colliding with the impact object. Therefore, the main focus of this study is set on particle settling and collision in the transitional regime. For collision studies, the Stokes number just before impact is also relevant, and lies in the range 50<St<2250. The settling curves obtained experimentally (characterized by vertical position and vertical velocity component) are compared with numerical and analytical solutions. The latter has been derived on the basis of nominal terminal velocity and relaxation time for the Stokes and Newton regimes. The numerical model takes into account the side walls and the corresponding correction of the drag coefficient.

A deviation between experimental results and analytical solution was observed in all cases where the terminal Reynolds number is larger than 300 and smaller than 1100. It appears that, in this flow regime, the settling process of the spheres is already affected at a long distance from the impact object, leading to an early but significant deceleration. Moreover, a reduced settling velocity was observed along the whole trajectory for the PTFE particles with the lowest terminal Reynolds number. All these effects are captured in the numerical model and the corresponding results agree fairly well with the experiments. There is one exception, induced by particle rotation, which is not considered in the current model. In that case, it is not possible to correctly predict the settling process. All processed datasets are available via the Mendeley Data repository Hagemeier (2020).

Two additional effects have been observed during this study. First, a bright region was detected around all PTFE spheres. It finally was found to be due to total light reflection around the sphere, but, to the best of our knowledge, this peculiarity has never been reported before. Being purely optical, this does not effect the settling behavior for PTFE. On the other hand, partial absorption of liquid at the particle surface was observed for rubber, leading to a reduced sedimentation velocity. This property, already documented for homogeneous porous particles, is found here for a rubber particle with almost impermeable core.



中文翻译:

过渡态下球形颗粒的沉降

通过高速阴影成像,可以观察到大球形颗粒在停滞的高粘度流体中的沉降过程和壁撞击。这项研究中包括的颗粒尺寸和材料特性各不相同:钢,聚四氟乙烯(PTFE),聚氧亚甲基(POM)或橡胶。相应的末端雷诺数范围为333至4012,原则上涵盖了阻力的过渡和牛顿状态。但是,大多数粒子在与冲击物体碰撞之前不会达到最终速度。因此,本研究的主要重点放在过渡状态下的粒子沉降和碰撞上。对于碰撞研究,冲击之前的斯托克斯数也很重要,并且在范围内50<英石<2250。将实验获得的沉降曲线(由垂直位置和垂直速度分量表征)与数值和解析解进行比较。后者是根据Stokes和Newton体制的名义终极速度和松弛时间得出的。数值模型考虑了侧壁和阻力系数的相应校正。

在末端雷诺数大于300且小于1100的所有情况下,观察到实验结果与分析溶液之间存在偏差。看来,在这种流动状态下,球体的沉降过程已经受到很远的影响。撞击物体,导致早期但显着的减速。而且,对于具有最低末端雷诺数的PTFE颗粒,在整个轨迹上观察到降低的沉降速度。所有这些影响都记录在数值模型中,并且相应的结果与实验相当吻合。有一个例外是由粒子旋转引起的,当前模型中未考虑。在这种情况下,不可能正确预测沉降过程。

在这项研究中,还观察到了另外两个作用。首先,在所有PTFE球周围检测到一个亮区域。最终发现这是由于球体周围的全光反射所致,但是据我们所知,这种特殊性从未被报道过。纯粹是光学的,这不会影响PTFE的沉降行为。另一方面,观察到橡胶部分表面上液体的部分吸收,导致沉降速度降低。对于均匀的多孔颗粒,已经记录了该性能,此处发现了具有几乎不可渗透的芯的橡胶颗粒。

更新日期:2021-02-21
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