The present paper deals with the Taylor-Couette flow of shear-thinning fluids. It focuses on the first principles understanding the influence of the viscosity stratification and the nonlinear variation of the effective viscosity µ with the shear rateγ on the flow structure in the Taylor vortex flow regime. A wide gap configuration (η = 0.4) is mainly considered. A weakly nonlinear analysis, using the amplitude expansion method at high order is adopted as a first approach to study nonlinear effects. For the numerical computation, the shear-thinning behavior is described by the Carreau model. The rheological parameters are varied in a wide range. The results indicate that the flow field undergoes a significant change as shear-thinning effects increase. First, vortices are squeezed against the inner wall and the center of the patterns are shifted axially towards the radial outflow boundaries (z = 0, z/λ z = 1). This axial shift leads to increasing concentration of vorticity at these positions. The outflow becomes more stronger than the inflow and the inflow zone, where the vorticity is low, increases accordingly. Nevertheless, the strength of the vortices relative to the velocity of the inner cylinder is weaker. Second, the pseudo-Nusselt number, ratio of the torque to that obtained in the laminar flow, decreases. Third, higher harmonics become more relevant and grow faster with Reynolds number. Finally, the modification of the viscosity field is described.

No abstract

This work deals with the effect of the contact location distribution on the crushing of granular materials. At first, a simple drop weight experiment was designed in order to study the effect of the location of three contact edges on the fracture pattern and the strength of a model cylindrical particle. The sample was placed on two bottom contact edges symmetrically distributed with reference to the vertical symmetry plane of the particle and subjected to an impact at the top. Angle α between the plane connecting a bottom contact edge to the centerline of the cylinder and a vertical plane was varied. The energy required to fracture the particle was shown to be an increasing function of angle α. Peculiar crack patterns were also observed. Then, we present a discrete model of grain fracture based on the work of Neveu et al. (2016) and employ it for a numerical analysis of the problem. The cylindrical particle is discretized by means of a space filling Voronoï tessellation, and submitted to a compression test for different values of angle α. In agreement with experiments, simulations predict a strong effect of the contact orientation on the strength of the particle as well as similar fracture patterns. The effect of the number of contacts is also explored and the importance of a potential pre-load is emphasized. We show that the fracture pattern: (i) is diametrical in case of diametrically opposed edges, (ii) has an inverted Y-shape in the case of three or four edges. Interestingly, in the latter case, if one of the lateral edges is slightly shifted, the fracture initiates and even propagates diametrically. Furthermore, the particle strength increases with the number of contacts.

No abstract