Analysis of Granular Flows Using Stress Tensor Modified Continuum Models

Granular flows are frequently encountered in both industry and in nature. However, the complex granular flows are usually observed at the surface and the interior information of granular flow is usually difficult to be obtained. This project uses a continuum model to study granular flows and realize the information both at the flow surface and in the interior of the flow. Since some physical properties of the continuum granular flows are not measurable and await the development of suitable models to estimate the values of these properties. Here, two models are used to study the constitutive particulate flows. Firstly, the kinetic theory of collisional granular flow model for dilute continuum granular flow will be modified in order to be applied to both the dilute and dense continuum granular flows. Secondly, the frictional model of Jop-et-al (2006) is used for the stress tensor calculation. When modifying the kinetic theory of collisional granular flow, the collisional viscosity, the kinetic viscosity and the frictional viscosity are all considered in the shear viscosity. While previous works considered the frictional viscosity activation with the solid fraction of 0.5, the solid fraction for the “activation” of the frictional viscosity is considered from 0.3 to 0.6 in this work. The analogy of the constitutive granular flow behavior and the visco-plastic Bingham fluid was considered by Jop-et-al. The constitutive particulate phase begins to flow when the shear stress applying to the granular assembly exceeds some critical value. Hence, the frictional coefficient of the constitutive particulate phase is assumed to be a function of the inertial number as   1  with I the inertial number (i.e., the ratio of the deformation time  1 to the inertial time ), μs the frictional coefficient with zero inertia number and μ2 the frictional coefficient with infinite inertia number. This two-year project aims to develop the constitutive relations for the granular flows based on three steps. (1) The surface flow patterns of the granular flows in drum mixers and in V-mixers will be understood by PIV experiments. (2) A trial-and-error method will be used to determine the appropriate values for the granular viscosity and solid fraction for the frictional viscosity activation. The modified kinetic theory of collisional granular flow should be able to well predict the dense granular flows in drum mixers and in V-mixers. (3) The frictional model of Jop-et-al is adopted in the calculation of the stress tensor in the constitutive relations and the model will be validated by the PIV experimental results.

Project ID:PB10408-5739
External Project ID:MOST104-2221-E182-060-MY2