Velocity gradient

About: Velocity gradient is a research topic. Over the lifetime, 3013 publications have been published within this topic receiving 77120 citations.

An implicit viscosity formulation for SPH fluids

Abstract: We present a novel implicit formulation for highly viscous fluids simulated with Smoothed Particle Hydrodynamics SPH. Compared to explicit methods, our formulation is significantly more efficient and handles a larger range of viscosities. Differing from existing implicit formulations, our approach reconstructs the velocity field from a target velocity gradient. This gradient encodes a desired shear-rate damping and preserves the velocity divergence that is introduced by the SPH pressure solver to counteract density deviations. The target gradient ensures that pressure and viscosity computation do not interfere. Therefore, only one pressure projection step is required, which is in contrast to state-of-the-art implicit Eulerian formulations. While our model differs from true viscosity in that vorticity diffusion is not encoded in the target gradient, it nevertheless captures many of the qualitative behaviors of viscous liquids. Our formulation can easily be incorporated into complex scenarios with one- and two-way coupled solids and multiple fluid phases with different densities and viscosities.

Particle pressure in sheared Brownian suspensions

Abstract: The isotropic contribution of the particle phase to the bulk stress, or the particle pressure, is studied for Brownian hard sphere suspensions in computationally simulated shear flow. The particle pressure is mechanically defined as the negative mean normal stress exerted by the particles, i.e., Π=−(1∕3)[Σ11+Σ22+Σ33] for a viscometric flow where 1, 2, and 3 refer to the flow, velocity gradient, and vorticity directions, respectively. Analysis is provided to relate the particle pressure to the equilibrium osmotic pressure and to show the relation of Π to particle migration phenomena. Utilizing existing hydrodynamic functions and simulating the flow by the Stokesian Dynamics technique, the particle pressure is evaluated for particle volume fractions in the range 0.1⩽ϕ⩽0.52 for monodisperse spherical particles. The relative strength of Brownian to shearing motion is given by the Peclet number Pe=γa2∕D0, where γ is the shear rate of a simple shear flow, a is the spherical particle radius, and D0=kT∕6πηa wit...

Dual-plane stereo particle image velocimetry measurements of velocity gradient tensor fields in turbulent shear flow. II. Experimental results

Abstract: Results are presented from highly resolved dual-plane stereo particle image velocimetry (DSPIV) measurements for the structure, statistics, similarity, and scaling of all nine simultaneous components of the velocity gradient tensor fields ∂ui∕∂xj on the quasi-universal intermediate and small scales of turbulent shear flows. Measurements were obtained at three combinations of the outer-scale Reynolds number Reδ and the local mean shear rate S in the fully developed self-similar far field of a turbulent jet, and thus reflect the combined effects of the large-scale structure, spatial inhomogeneities, and anisotropies inherent in such a flow. Conditions addressed in this study correspond to local outer-scale Reynolds numbers Reδ=6,000 and 30,000 and local mean shear values Sδ∕uc=0 and 1.7, corresponding to Taylor-scale Reynolds numbers Reλ≈44 and 113 and shear rates Sk∕e=0 and 2.1. Gradient fields investigated here include the individual velocity gradient component fields, the strain rate component fields and...