Volume-of-fluid-based implementation for the spatiotemporal variation of viscosity in grouting process: transport time tracking approach

Due to the spatiotemporal variation of viscosity, the simulation of grouting processes is quite challenging. In this work, based on the volume-of-fluid method, the transport time tracking approach is developed to model the spatiotemporal variation of viscosity in grouting processes. Firstly, a partial differential equation of transport time is proposed and applied to obtain the resided time of fluid clusters in the domain. Meanwhile, in order to address the variable viscosity of the slurry phase, the dependence of viscosity on transport time is associated. Secondly, an artificial convection term is introduced in the equation of transport time to capture a sharp interface. This algorithm is implemented using the open-source CFD code OpenFOAM. Subsequently, three different test cases are launched to verify our algorithm and implementation. By using the combination of these numerical treatments, the transport time can be solved in the slurry phase with limited numerical diffusion. Finally, the approach is further compared with the previous experiment. The results show that not only can our algorithm solve the transport time correctly, but also the pressure data agree well with the experiment. It can be seen that this approach could be further applied to the simulation of other fields such as thrombosis, ventilation, and radionuclide migration problems.