SPH simulations of non-isothermal viscoplastic free-surface flows incorporating Herschel-Bulkley-Papanastasiou model

In this paper, an improved smoothed particle hydrodynamics (SPH) method is employed to accurately simulate non-isothermal viscoplastic free surface flows, wherein the viscoplastic behavior of the fluid is precisely captured through the incorporation of the Herschel-Bulkley-Papanastasiou constitutive model. To suppress the non-physical oscillation arising from the weakly compressible hypothesis within the pressure field, the density dissipation term is incorporated into the mass conservation equation. To address the tensile instability arising from the uneven distribution of particles, the particle shifting technique is incorporated as a solution. To enhance the precision and ensure numerical stability of the gradient operator, a kernel gradient correction algorithm is implemented. The improved SPH method is employed for numerically simulating the non-isothermal viscoplastic mixed convection, dam-break flow and droplet impacting the solid wall. The effectiveness of the improved SPH method in tackling the complexities of non-isothermal viscoplastic fluid is validated through a rigorous comparison of its outcomes with those derived from alternative numerical methodologies. The assessment of the numerical convergence of the improved SPH method is undertaken through the utilization of varying initial particle spacings. The numerical outcomes demonstrate that the improved SPH method adeptly and precisely delineates the heat transfer mechanisms, intricate rheological properties, as well as the dynamic variation characteristics of the free surface in non-isothermal viscoplastic free surface flows.