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Simulation of generalized Newtonian fluids with the Smoothed Particle Hydrodynamics method
Author(s) -
Simeunović Miloš,
Steeb Holger
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900494
Subject(s) - newtonian fluid , mechanics , generalized newtonian fluid , non newtonian fluid , hagen–poiseuille equation , smoothed particle hydrodynamics , rheology , shear stress , flow (mathematics) , shear thinning , boundary value problem , solver , particle (ecology) , herschel–bulkley fluid , physics , classical mechanics , mathematics , shear rate , mathematical analysis , mathematical optimization , geology , thermodynamics , oceanography
In this paper we examine Direct Numerical Simulation DNS of single phase non‐Newtonian fluids described by a generalized Newtonian rheology. Non‐Newtonian flow including large deformations and free surface flow could be observed in a wide range of industrial and environmental applications. For that reason, we choose the Lagrangian Smoothed Particle Hydrodynamics (SPH) as a simulation tool. The non‐Newtonian solver is implemented into the general purpose particle framework HOOMD‐blue [1,2], which allows for massive parallel CPU and GPU simulations. Numerical accuracy of the model is demonstrated by simulating confined Poiseuille flow between parallel plates. The validation has been done for a wide variety of shear strain–shear stress ratios where also the effect of the solid‐fluid interface boundary condition is examined. Furthermore, a comparison with the experimental results for the broken dam problem [3] showed good accuracy of the free‐surface flow prediction. Additionally, we have investigated a slump test (Abrams cone [4]), a relatively simple but in practice often performed experiment for non‐Newtonian yield‐stress fluids. Finally, we have investigated in further detail the cone diameter, height, flow time, the final shape and the influence of the rheological model parameters as well as the boundary conditions related to the stationary cone configuration.