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The movement of millimeter-sized granular materials in fluids can be found in many industrial processes, such as blast furnaces, kilns, boilers, reactors, spray dryers, pipelines of granular materials, mills, classifiers, plastics forming machines, fluidized bed processes, etc.
Fig. 1 is a typical example of such motions, an initial model for studying the dumping motion of granular material that is dumped down the opening of a slider in the center of the storage room (hopper) bottom.
The motion of a millimeter-sized granular material can be quite different from that of a micrometer-sized granular material.
On the other hand, the latter is supported by the computational fluid dynamics software including ANSYS FLUENT, but the former does not.
The modeling methods of granular material transport can be classified into two categories: the Euler-Lagrangian approach and the Euler-Euler one.
We have proposed a new Euler-Euler approach to model the motion of large Stokes (mm-sized particles) particles in a fluid flow.
Our approach belongs to the combination of Euler and Lagrangian approaches.
In the approach, we first introduce a unilateral compressibility assumption for granular flow.
The friction viscosity is modeled with Schaeffer's model, the impact viscosity is modeled in a manner similar to the method for the molecular viscosity of the fluid, and the Lagrangian DiFelice model for a single particle is extended to fit the Euler view.
The pressure term of the Euler equation is discretized by the Lagrangian-like smooth particle hydraulics (SPH) method.
The discretization equation satisfying unilateral compressibility is reduced to an unconditional optimization problem.
The solid pressure field is calculated by the gradient method to solve the optimization problem.
To improve the efficiency of the approach, ANSYS FLUENT was taken as the main solver in multiphase fluid flow and our approach for granular media was compiled into ANSYS FLUENT's solver based on the user-defined functions.
Validation of the model was carried out through comparison with the results of the calculations of the three experimental and Lagrangian approaches.
A typical example is the simulation results of the spillage of granular material in a hopper, introduced in Fig. 1 (Fig. 2).
The work was published in the "International Journal of Multiphase Flow"(92 (2017) 140-149) by Elsevier Publishers under the title of "An Eulerian model for the motion of the granular material with a large Stokes number in fluid flow" (http://dx.doi.org/10.1016/j.ijmultiphaseflow 2017.03.009).