A new smoothed particle hydrodynamics (SPH) scheme is presented to simulate multi-component fluid mixing with thermally-driven buoyancy and temperature-dependent viscosities. The scheme is developed for multi-phase flows in industrial tanks used in the vitrification process in the nuclear industry for waste immobilisation before long-term storage. These multi-component flows feature a mixing of high-temperature phases composed of molten glass and highly radioactive waste, with fluid properties changing with temperature. SPH is a meshless Lagrangian discretization scheme whose major advantage is the absence of a mesh, making the method ideal for highly non-linear flows with mixing of multiple components whose properties change with time. Emphasis has been given to modelling the thermally-induced buoyancy flows from the external heating and viscous flow instabilities, which are needed to predict accurately the mixing phenomena. The numerical SPH scheme includes temperature-dependent viscosities, thermal conduction and convection using a Boussinesq approximation, and external heating. A new boundary treatment has been developed to implement adiabatic boundary conditions by extending the recently developed modified dynamic boundary condition (mDBC) to thermally-driven driven flows. The SPH scheme has been implemented to run on a graphics processing unit (GPU), showing speed-ups on the order of 50 compared to optimised code on a multi-core multi-thread central processing unit (CPU). The code is extensively validated for a range of test cases including two-phase Poiseuille flow where each phase has a different viscosity, temperature dependent Poiseuille flow, two-phase lid-driven cavity flow, and a differentially-heated cavity in 2-D and 3-D.For the two-phase Poiseuille flow, an interfacial instability is observed for certain ranges of viscosity and channel-width ratios. Both stable and unstable flow regimes are correctly predicted. The instability growth rate predicted by the new SPH model agrees with linear analytical theory, which has not been seen before. The evolution of consequent non-linear flow is straightforwardly predicted, with the interface remaining clear. A new mixing measure is proposed based on the combination of the finite time Lyapunov exponent (FTLE) and the volume fraction (VF) that enables both the degree of mixing at a point and how well-mixed the two phases are at that location to be quantified in a single value. The VF-FTLE mixing measure is applied to the two-phase lid-driven cavity flow, highlighting regions with high particle movement and where both phases are present. A new global mixing measure is established from this local measure, quantifying the change in overall mixing with time. The new model is applied to a vitrification melter for single-phase and two-phase flows with temperature-dependent viscosities. The VF-FTLE measure is applied to interpret the mixing taking place due to buoyancy-driven circulation within the heated melter. A 3-D flow instability is observed, likely related to a thin thermal boundary layer existing at high Rayleigh and Prandtl numbers, suggesting distinct flow regimes in the melter which requires further investigation.
- computational fluid dynamics
- smoothed particle hydrodynamics