Preparation of Semi-Solid 357.0 Slurries with Different α-Al Phase Features by Solidification from Full Liquid State and Remelting

The characteristics of the solid phase, namely the volume fraction, particle size, and morphology, are dominant variables that can determine the viscosity of the semi-solid slurry. However, particle size and morphology were always being ignored and the solid fraction was simply determined using the temperature in the conventional power-law viscosity, resulting in a disagreement in the viscosity values in different researches. To make the power-law viscosity model more accurate for predicting the filling process of semi-solid die casting, it is essential to modify this viscosity model based on particle characteristics. Therefore, there is a fundamental demand to prepare semi-solid slurries with different α-Al phase features at first. This is achieved in this study by two kinds of heat history controlling methods: remelting and solidification, which can get slurries with spherical structure and dendric structure, respectively. The semi-solid 357.0 slurries with 0.11-0.43 solid fraction, 137-182μm particle size, and 0.81-0.90 shape factor were prepared in the remelting process, while dendritic structures (shape factor<0.5) with 0.1 and 0.3 solid fractions were obtained by solidification controlling from the full liquid state. Besides, the effect of parameters on the evolution of the α-Al phase has been discussed. These slurries with different solid features will be further used to quantify the influence of primary phase characteristics on rheological behavior and make the power-law viscosity model more accurate for simulation.

A phenomenological theory-based viscosity model for shear thickening fluids

A viscosity model for shear thickening fluids (STFs) based on phenomenological theory is proposed. The model considers three characteristic regions of the typical material properties of STFs: a shear thinning region at low shear rates, followed by a sharp increase in viscosity above the critical shear rate, and subsequently a significant failure region at high shear rates. The typical S-shaped characteristic of the STF viscosity curve is represented using the logistic function, and suitable constraints are applied to satisfy the continuity of the viscosity model. Then, the Levenberg–Marquardt algorithm is introduced to fit the constitutive model parameters based on experimental data. Verification against experimental data shows that the model can predict the viscosity behavior of STF systems composed of different materials with different mass concentrations and temperatures. The proposed viscosity model provides a calculation basis for the engineering applications of STFs (e.g., in increasing impact resistance and reducing vibration).

Mathematical Modelling of the Elliptical Vortex Ring in a Viscous Fluid with the Vortex Filament Method

The article deals with modelling an elliptical vortex ring in a viscous fluid using the Lagrangian vortex filament method. The novelty is that earlier only inviscid flows restricted vortex filament method application. The proposed viscosity model uses an analogue of the diffusion rate method, which is widely applied to simulate plane-parallel and axisymmetric flows of viscous fluid. A transfer of the formula of a diffusion rate from two-dimensional flows to the model of spatial vortex filament is due to assumption that swirling of vortex lines (helicity of vorticity) is unavailable. Despite the laxity of the diffusion rate model for general spatial flows, its application enables taking into account the effect of viscous diffusion of vorticity, which provides expansion of vortex tubes in space. The paper formulates the vortex filament method in which the filaments are broken into the vortex segments. Such discretization enables turning from the equation of vorticity evolution in partial derivatives to a system of ordinary differential equations with respect to the parameters of the segments. Formulas to calculate a filament system-induced flow rate as well as formulas to perform approximate calculation of an analogue of the diffusion rate are given.The objective is to propose the viscosity model as an application to the vortex filament method by the example of modelling the evolution of an elliptical vortex ring in viscous fluid. The calculation results obtained by the vortex method are compared with the existing experiment and with the calculation performed by the grid method in the OpenFOAM package. A feature of the problem is that there are zones of nonzero helicity of vorticity where the proposed model of viscosity, strictly speaking, is not correct. It is shown that the results of calculations are in good agreement with each other and are in complete agreement with experiment. This allows saying that the effects of swirling vortex lines do not significantly affect the results of modelling a specific example of the spatial flow of viscous fluid by the proposed modification of the vortex filament method.