# Modeling of Linear Die Filling Based on Dimensional Analysis Using DEM-CFD Methods

## TL;DR

This paper develops a model for powder die filling using dimensional analysis and simulations to improve industrial processes.

## Contribution

A novel semi-empirical model for linear die filling is proposed using dimensionless parameters derived from DEM-CFD simulations.

## Key findings

- Filling ratio increases with dphD−1 and ρpρg−1 due to higher drag force.
- Filling ratio decreases with vρgLDμ−1 due to reduced effective filling time.
- A semi-empirical model was developed using (dphD−1)90 as a critical value.

## Abstract

Linear die filling is currently widely employed in industries. However, there is no comprehensive and systematic model to describe the powder die filling process. This paper utilizes dimensional analysis to extract and analyze various factors that affect the flow characteristics of powder based on DEM-CFD simulations. Several dimensionless parameters including the ratio of particle size to die depth (dphD−1), solid density number (ρpρg−1), shoe speed number (vρgLDμ−1), and force number (GpFDrag−1) were proposed based on the Pi theorem. The results showed that the filling ratio δ increased with the increase in dphD−1 and ρpρg−1 due to GpFDrag−1 rising. But it decreased with the increase in vρgLDμ−1 due to the shortening of effective filling time. Finally, a semi-empirical modeling of linear die filling was developed, taking the critical value (dphD−1)90 as the dependent variable and the solid density number (ρpρg−1) and shoe speed number (vρgLDμ−1) as independent variables. Hence, this model provides a new approach to computing the smallest shoe speed and designing the sizes of dies based on measurable material properties under complete die filling.