Numerical Investigation of Bingham Plastic Flow and Melting in Heated Rotary Kilns

Viscoplastic materials—disordered assemblies of solid particles that exhibit both solid-like and fluid-like behavior—are among the most widely used in industry and play a crucial role in processes such as cement paste and concrete production. In rotary kilns, these materials undergo complex thermo-mechanical transformations under extreme operating conditions, including high temperatures, abrasive motion, and reactive environments, which make direct experimental investigation both challenging and costly.

Over the past few decades, mathematical modeling and numerical simulations have become essential tools for studying rotary kilns and fluidized beds, helping to address phenomena such as ring accretion formation, material transport, and energy efficiency. In particular, transverse flow induced by drum rotation significantly influences heat and mass transfer, as well as the efficiency of particle mixing.

In this study, we model the viscoplastic flow behavior using a “Papanastasiou-regularized Bingham plastic model”, which captures the yield-stress-dominated response of dense particulate systems. This rheological framework enables the smooth numerical treatment of the transition from solid-like to flow behavior. The flow is governed by the momentum and continuity equations, which are coupled with the energy equation to simulate non-isothermal conditions inside the kiln.

To account for partial melting, we implement the enthalpy–porosity method, where phase change is represented via a temperature-dependent liquid fraction. Buoyancy effects arising from density variations are incorporated through the Boussinesq approximation. The full set of governing equations is solved using a stabilized finite element method developed in-house.

A comprehensive parametric study is conducted to evaluate the effects of rotational speed and fill level on key process variables, including temperature distribution and the extent of melting. The results indicate that increasing drum rotation enhances heat transfer and improves thermal uniformity, promoting more efficient processing of the viscoplastic material bed.