Parametric study of the $${\beta }$$-$${\sigma }$$ two-fluid model for simulating fully suspended slurry flow: effect of flow conditions

As proven in a recently published paper [Messa GV, Matousek V (2020) Analysis and discussion of two fluid modelling of pipe flow of fully suspended slurry. Powder Technol 30:747 $$-$$ 768.], the $$\beta$$ - $$\sigma$$ two-fluid model is capable of accurately reproducing the main features of turbulent, fully-suspended slurry flows in horizontal pipes provided that suitable values of the two parameters $$\beta$$ and $$\sigma$$ are chosen. At present, the case-specific nature of $$\beta$$ and $$\sigma$$ and their lack of a clear physical meaning are the main obstacles that must be overcome to give the $$\beta$$ - $$\sigma$$ two-fluid model value not only as interpretative tool, but also as a predictive one. An important preliminary step to achieve this goal is to disclose the mathematical essence of the $$\beta$$ - $$\sigma$$ two-fluid model, namely, to interpret the fluid-dynamic solution on the grounds of the structure of the differential and discretized equations. Such a methodological approach is applied here to the benchmark case of turbulent slurry flow between two infinite, horizontal, parallel plates, focusing, in particular, on the influence of the bulk-mean velocity of the slurry and the volumetric concentration of the solids in the flow. The study provides not only deeper insight into the $$\beta$$ - $$\sigma$$ model, but also indicates important implications for alternative two-fluid models.