Wambaugh John F, Behringer Robert P, Matthews John V, Gremaud Pierre A
Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Nov;76(5 Pt 1):051303. doi: 10.1103/PhysRevE.76.051303. Epub 2007 Nov 14.
We experimentally investigate the response to perturbations of circular symmetry for dense granular flow inside a three-dimensional right-conical hopper. These experiments consist of particle tracking velocimetry for the flow at the outer boundary of the hopper. We are able to test commonly used constitutive relations and observe granular flow phenomena that we can model numerically. Unperturbed conical hopper flow has been described as a radial velocity field with no azimuthal component. Guided by numerical models based upon continuum descriptions, we find experimental evidence for secondary, azimuthal circulation in response to perturbation of the symmetry with respect to gravity by tilting. For small perturbations we can discriminate between constitutive relations, based upon the agreement between the numerical predictions they produce and our experimental results. We find that the secondary circulation can be suppressed as wall friction is varied, also in agreement with numerical predictions. For large tilt angles we observe the abrupt onset of circulation for parameters where circulation was previously suppressed. Finally, we observe that for large tilt angles the fluctuations in velocity grow, independent of the onset of circulation.
我们通过实验研究了三维直角锥形漏斗内密集颗粒流对圆对称扰动的响应。这些实验包括对漏斗外边界处流动的粒子跟踪测速。我们能够测试常用的本构关系，并观察到可以用数值方法建模的颗粒流现象。未受扰动的锥形漏斗流被描述为一个没有方位角分量的径向速度场。在基于连续介质描述的数值模型的指导下，我们发现了实验证据，表明通过倾斜相对于重力的对称性进行扰动会产生二次方位角环流。对于小扰动，我们可以根据它们产生的数值预测与我们的实验结果之间的一致性来区分本构关系。我们发现，随着壁面摩擦力的变化，二次环流可以被抑制，这也与数值预测一致。对于大倾斜角，我们观察到在之前环流被抑制的参数下环流突然出现。最后，我们观察到对于大倾斜角，速度波动会增大，与环流的开始无关。
