valizadeh, mehdi (2025) Smoothed Particle Hydrodynamics (SPH) model for numerical simulation of Non-Newtonian Fluids Flows. [Tesi di dottorato]

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Abstract

Numerical simulations of mudflows are crucial in different fields of application such as environmental management and geotechnical engineering. Accurate modelling of such free-surface flows is vital for risk assessment and mitigation yet remains challenging because of their multiphase nature. They are usually described as continuous fluid with a non-Newtonian rheology, with shear-thinning or shear-thickening behaviour. Smoothed Particle Hydrodynamics (SPH), a fully Lagrangian and mesh-free method, provides an effective framework for simulating free-surface flows of both Newtonian and non-Newtonian fluids, also highly unsteady dynamics condition. In the present work, a new SPH code, PVSPH, was developed to investigate gravity-driven dam-break flows of non-Newtonian fluids describing mudflows. The study addresses the complex rheology of concentrated sediment–water mixtures by implementing a generalized power-law model for describing the fluids characteristics. The incorporation of power-law models into the SPH model represents the main original contribution of the work and it furnishes an accurate PVSPH method for reproducing mudflows. The PVSPH results are compared with the output of two Eulerian approaches: a depth-averaged model (EDAM) and a depth-resolved model (EDRM). The PVSPH code was validated through appropriate test cases considering turbulent water and non-Newtonian laminar fluid flows. The first validation is performed with the SPHERIC dam-break benchmarks (both dry and wet bed) for water. To validate the code with power-law fluids the analytical solution of the plane Poiseuille flows was adopted. All preliminary tests were used to tune numerical parameters, including particle resolution, artificial viscosity, CFL number, smoothing coefficients, time integration scheme, etc. The PVSPH code successfully reproduced benchmarks and analytical solutions with generally low errors. In the SPHERIC dry-bed tests, the model accurately matched the measured free-surface profiles, yielding an RMSE value as low as 3.4%. Although the RMSE for the wet-bed tests was slightly higher, the model still presented the height and shape of the wave, as well as the bubble formed by wave plunging. For the plane Poiseuille power-law fluid flow, the results yielded R² values greater than 0.95 and RMSE values typically below 4.5% across a wide range of rheological indices. Therefore, validation confirms the validity of the adopted PVSPH model in simulating dam-break flows of both Newtonian and non-Newtonian fluids. Laboratory experiments of dam-break simulations with non-Newtonian fluids were conducted at the University of Zaragoza using a non-Newtonian shear-thinning fluid realized with Carbopol-940. Free- iii surface measurements were obtained using an RGB-D device (Kinect v1), velocity fields were captured with Particle Image Velocimetry (PIV), and the speed of the removal gate was controlled by pressure. The experimental data, under elaboration, will provide information on the characteristics of the dam-break wave propagation and impact against a rigid obstacle. They will be subsequently used to evaluate the performance of the PVSPH code. Numerical simulation of non-Newtonian dam-break were performed to study the characteristics of the phenomenon and the performance of the numerical models. Different power-law fluids with rheological indices n =0.1 and 0.2 were considered. The geometrical scheme is a flume with an upstream reservoir closed by a moving gate (dam-break scheme) and dry-bed condition downstream. Three different configurations were assumed: horizontal open-end channel; horizontal and inverse slope closed-end channels. By calculating the Reynolds number, it was observed that the flow was laminar for n =0.1 and transitional for n =0.2. Since the SPH simulations did not include specific turbulence modelling, the cases for n =0.2 were treated with caution. For all flume configurations in the dam-break simulations at the gate section, the numerical results showed consistent agreement between PVSPH, EDAM, and EDRM for higher viscosity (n =0.1) compared to lower viscosity (n =0.2). Due to the lower viscosity and greater ease of flow, the fluid depth of the returning wave for n =0.2 was approximately 20% higher than that for n =0.1 across all models with closed-end and inverse slope configurations. This thesis provides new insights into debris-flow and mudflow behaviour by applying dam-break simulations with a novel mesh-free SPH approach. The findings are expected to serve as a foundation for future advancements in numerical techniques and risk mitigation. Moreover, the collected experimental data will provide information to study the phenomenon and will be used to verify the performance of numerical models.

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