Velocity gradient

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

On the Reynolds number dependence of velocity-gradient structure and dynamics

Abstract: We seek to examine the changes in velocity-gradient structure (local streamline topology) and related dynamics as a function of Reynolds number ( ). The analysis factorizes the velocity gradient ( ) into the magnitude ( ) and normalized-gradient tensor ( ). The focus is on bounded as (i) it describes small-scale structure and local streamline topology, and (ii) its dynamics is shown to determine magnitude evolution. Using direct numerical simulation (DNS) data, the moments and probability distributions of and its scalar invariants are shown to attain independence. The critical values beyond which each feature attains independence are established. We proceed to characterize the dependence of -conditioned statistics of key non-local pressure and viscous processes. Overall, the analysis provides further insight into velocity-gradient dynamics and offers an alternative framework for investigating intermittency, multifractal behaviour and for developing closure models.

A Hybrid Lattice Boltzmann and Finite-Volume Method for Melting with Convection

Abstract: A hybrid lattice Boltzmann and finite-volume model is proposed to solve the natural-convection-controlled melting problem. The lattice Boltzmann method (LBM) is applied to solve the velocity field, while the temperature field is obtained by the finite-volume method (FVM). The D2Q9 model and finite-difference velocity gradient boundary condition are used in the LBM and the SIMPLE algorithm with QUICK scheme is employed in the FVM. An interfacial tracking model based on energy balance at the interface is applied to obtain the location of the solid–liquid interface. The results from the present hybrid method are validated with experimental results, and good agreement is obtained.

Simulation of inertial fibre orientation in turbulent flow

Abstract: The spatial and orientational behaviour of fibres within a suspension influences the rheological and mechanical properties of that suspension. An Eulerian-Lagrangian framework to simulate the behaviour of fibres in turbulent flows is presented. The framework is intended for use in simulations of non-spherical particles with high Reynolds numbers, beyond the Stokesian regime, and is a computationally efficient alternative to existing Stokesian models for fibre suspensions in turbulent flow. It is based on modifying available empirical drag correlations for the translation of non-spherical particles to be orientation dependent, accounting for the departure in shape from a sphere. The orientational dynamics of a particle is based on the framework of quaternions, while its rotational dynamics is obtained from the solution of the Euler equation of rotation subject to external torques on the particle. The fluid velocity and turbulence quantities are obtained using a very high-resolution large eddy simulation with dynamic calibration of the sub-grid scale energy containing fluid motions. The simulation matrix consists of four different fibre Stokes numbers (St = 1, 5, 25, and 125) and five different fibre aspect ratios (λ = 1.001, 3, 10, 30, and 50), with results considered at four distances from a channel wall (in the viscous sub-layer, buffer, and fully turbulent regions), which are taken as a measure of the flow velocity gradient, all at a constant fibre to fluid density ratio (ρp/ρ = 760) and shear Reynolds number Reτ = 150. The simulated fibre orientation, concentration, and streakiness confirm previous experimentally observed characteristics of fibre behaviour in turbulence, and that of direct numerical simulations of fibres in Stokesian, or creeping flow, regimes. The fibres exhibit translational motion similar to spheres, where they tend to accumulate in the near-wall (viscous sub-layer and buffer) region and preferentially concentrate in regions of low-speed streaks. The current results further demonstrate that the fibres’ translational dynamics, in terms of preferential concentration, is strongly dependent on their inertia and less so on their aspect ratio. However, the contrary is the case for the fibre alignment distribution as this is strongly dependent on the fibre aspect ratio and velocity gradient, and only moderately dependent on particle inertia. The fibre alignment with the flow direction is found to be mostly anisotropic where the velocity gradient is large (i.e., viscous sub-layer and buffer regions), but is virtually non-existent and isotropic where the turbulence is near-isotropic (i.e., channel centre). The present investigation highlights that the level of fibre alignment with the flow direction reduces as a fibre’s inertia decreases, and as the shape of the fibre approaches that of a sphere. Short fibres, and especially near-spherical λ = 1.001 particles, are found to exhibit isotropic orientation with respect to all directions, whilst sufficiently long fibres align themselves parallel to the flow direction, and orthogonal to the other two co-ordinate directions, and the vorticity and flow velocity gradient directions.