Orpe A V, Khakhar D V
Department of Chemical Engineering, Indian Institute of Technology-Bombay, Powai, Mumbai 400076, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Sep;64(3 Pt 1):031302. doi: 10.1103/PhysRevE.64.031302. Epub 2001 Aug 27.
An experimental study of the flow of different materials (steel balls, glass beads, and sand) in quasi-two-dimensional rotating cylinders is carried out using flow visualization. The flow in the rotating cylinder comprises of a thin-flowing surface layer with the remaining particles rotating as a fixed bed. Experimental results indicate that the scaled layer thickness increases with increasing Froude number (Fr=omega(2)R/g, where omega is the angular speed, R is the cylinder radius, and g the acceleration due to gravity) and with increase in size ratio (s=d/R, where d is the particle diameter). The free surface profile, is nearly flat at low Fr and becomes increasingly S shaped with increasing Fr. The layer thickness profiles, which are symmetric at low Fr become skewed at high values of Fr and small s. The dynamic angles of repose for all the materials studied show a near-linear increase with rotational speed (omega). Scaling analysis of the experimental data shows that the shape of the scaled surface profiles and the scaled layer thickness profiles are nearly identical when Froude number and size ratio are held constant, for each material. The surface profiles and layer thickness profiles are also found to be nearly independent of the material used. The dynamic angle of repose (beta), however, does not scale with Fr and s and depends on the particle properties. The experimental results are compared to continuum models for flow in the layer. The models of Elperin and Vikhansky [Europhys. Lett. 42, 619 (1998)] and Makse [Phys. Rev. Lett. 83, 3186 (1999)] show good agreement at low Fr while that of Khakhar et al. [Phys. Fluids, 9, 31 (1997)] gives good predictions over the entire range of parameters considered. An analysis of the data indicate that the velocity gradient (gamma;) is nearly constant along the layer at low Fr, and the value calculated at the layer midpoint varies as gamma;(0)~g sin(beta(0)-beta(s))/d cos beta(s) for all the experimental data, where beta(s) is the static angle of repose and beta(0) is the interface angle at the layer midpoint. An extension of "heap" models (BCRE, BRdG) is used to predict the interface angle profiles, which are in reasonable agreement with experimental measurements.
利用流动可视化技术，对不同材料（钢球、玻璃珠和沙子）在准二维旋转圆柱体内的流动进行了实验研究。旋转圆柱体内的流动由一个薄流动表面层组成，其余颗粒作为固定床旋转。实验结果表明，缩放后的层厚度随着弗劳德数（Fr = ω²R/g，其中ω是角速度，R是圆柱半径，g是重力加速度）的增加以及尺寸比（s = d/R，其中d是颗粒直径）的增加而增大。自由表面轮廓在低弗劳德数时几乎是平的，随着弗劳德数的增加逐渐变成S形。层厚度轮廓在低弗劳德数时是对称的，在高弗劳德数和小尺寸比时会变得倾斜。所有研究材料的动态休止角都随转速（ω）呈近似线性增加。对实验数据的缩放分析表明，对于每种材料，当弗劳德数和尺寸比保持恒定时，缩放后的表面轮廓形状和缩放后的层厚度轮廓几乎相同。还发现表面轮廓和层厚度轮廓几乎与所使用的材料无关。然而，动态休止角（β）并不随弗劳德数和尺寸比缩放，而是取决于颗粒特性。将实验结果与层内流动的连续介质模型进行了比较。Elperin和Vikhansky [《欧洲物理快报》42, 619 (1998)] 以及Makse [《物理评论快报》83, 3186 (1999)] 的模型在低弗劳德数时显示出良好的一致性，而Khakhar等人 [《物理流体》9, 31 (1997)] 的模型在所考虑的整个参数范围内都给出了良好的预测。对数据的分析表明，在低弗劳德数时，沿层的速度梯度（γ）几乎是恒定的，并且对于所有实验数据，在层中点处计算的值随γ(0)~[g sin(β(0) - β(s))/d cos β(s)]^(1/2) 变化，其中β(s) 是静态休止角，β(0) 是层中点处的界面角。使用 “堆” 模型（BCRE、BRdG）的扩展来预测界面角轮廓，其与实验测量结果合理吻合。
