Derrick O. Njobuenwu

Simulation of inertial fibre orientation in turbulent flow

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.

Particle-Interaction Effects in Turbulent Channel Flow

Large eddy simulation and a discrete element method are applied to study the flow, particle dispersion and agglomeration in a horizontal channel. The particle-particle interaction model is based on the Hertz-Mindlin approach with Johnson-Kendall-Roberts cohesion to allow the simulation of Van der Waals forces in a dry air flow. The influence of different particle surface energies on agglomeration, and the impact of fluid turbulence, are investigated. The agglomeration rate is found to be strongly influenced by the particle surface energy, with most of the particle-particle interactions taking place at locations close to the channel walls, aided by the higher concentration of particles in these regions.

Simulation of deterministic energy-balance particle agglomeration in turbulent liquid-solid flows

An efficient technique to simulate turbulent particle-laden flow at high mass loadings within the four-way coupled simulation regime is presented. The technique implements large-eddy simulation, discrete particle simulation, a deterministic treatment of inter-particle collisions, and an energy-balanced particle agglomeration model. The algorithm to detect inter-particle collisions is such that the computational costs scale linearly with the number of particles present in the computational domain. On detection of a collision, particle agglomeration is tested based on the pre-collision kinetic energy, restitution coefficient, and van der Waals’ interactions. The performance of the technique developed is tested by performing parametric studies on the influence of the restitution coefficient (en = 0.2, 0.4, 0.6, and 0.8), particle size (dp = 60, 120, 200, and 316 μm), Reynolds number (Reτ = 150, 300, and 590), and particle concentration (αp = 5.0 × 10−4, 1.0 × 10−3, and 5.0 × 10−3) on particle-particle interaction events (collision and agglomeration). The results demonstrate that the collision frequency shows a linear dependency on the restitution coefficient, while the agglomeration rate shows an inverse dependence. Collisions among smaller particles are more frequent and efficient in forming agglomerates than those of coarser particles. The particle-particle interaction events show a strong dependency on the shear Reynolds number Reτ, while increasing the particle concentration effectively enhances particle collision and agglomeration whilst having only a minor influence on the agglomeration rate. Overall, the sensitivity of the particle-particle interaction events to the selected simulation parameters is found to influence the population and distribution of the primary particles and agglomerates formed.

Development of a real-time acoustic backscatter system for solids concentration measurement during nuclear waste cleanup

The measurement of the concentration of solid particles in suspension without physical sampling is a necessary tool for the nuclear industry involved with cleanup of a significant quantity of legacy waste in the form of sludge. This paper presents the work of a project to develop acoustic instrumentation for the in-situ characterization of such sludge. The measurement principle and signal processing employed is presented along with the design of a custom acoustic instrument for deployment in nuclear and industrial environments. The paper presents experimental results demonstrating the ability of the technique for the online measurement of mass concentration in a suspension of glass power in water.

Reynolds number effects on particle agglomeration in turbulent channel flow

The work described in this paper employs large eddy simulation and a discrete element method to study particle-laden flows, including particle dispersion and agglomeration, in a horizontal channel. The particle-particle interaction model is based on the Hertz- Mindlin approach with Johnson-Kendall-Roberts cohesion to allow the simulation of Van der Waals forces in a dry air flow. The influence of different flow Reynolds numbers, and therefore the impact of turbulence, on particle agglomeration is investigated. The agglomeration rate is found to be strongly influenced by the flow Reynolds number, with most of the particle-particle interactions taking place at locations close to the channel walls, aided by the higher turbulence and concentration of particles in these regions.

Inertial Particle Behaviour in Turbulent Fluid Flow

Abstract The influence of particle inertia, shape and orientation, and fluid turbulence intensity on the behaviour of particles in a channel flow is investigated using large eddy simulation coupled to a Lagrangian particle tracking technique that solves the Newton-Euler equations of rigid particle motion. The statistical moments of the particle velocity, the probability density function of the hydrodynamic acceleration and particle distributions within the flows are all used to characterise the particle-turbulence behaviour in these flows.

Non-spherical particle translation and orientation in wall-bounded turbulence

The translational and orientational dynamics of non-spherical particles in a turbulent channel flow at shear Reynolds number Reτ=300 is studied using an Eulerian-Lagrangian method coupled to an Eulerian rotational equation. Results show that particle dispersion to and away from the wall differs with shape, while the particle orientation exhibits several distinctive states depending on the particle shape andinitial position and orientation. There is a transition from one state to another with simulation time.

Simulation of Turbulent Particulate Flows for Nuclear Waste Management: Agglomeration in Vertical Flows

Results from large eddy simulations of relevance to the transport of nuclear waste flows are analysed to elucidate the interaction between the turbulent flow and calcite particles (a nuclear waste test material) in vertical flows. Agglomeration of particles is modelled based on the hard-sphere collision approach coupled to van der Waals’ interaction in a Lagrangian framework. The number density of particle collision frequency, efficiency and agglomeration rate reveal the importance of gravity, lift and buoyancy forces in the simulations. The number of collisions increases in the order of upward, no gravity and downward flows, whereas the reverse occurs for the number of agglomerations. The upward flow shows a higher agglomeration rate than the other flows due to the depletion of particles in the near-wall region under the action of the lift force.

Large Eddy Simulation of Non-spherical Particle Deposition in a Vertical Turbulent Channel Flow

Abstract Non-spherical particle deposition in a vertical turbulent channel flow is studied using large eddy simulation and a stochastic Markov model that represent the effect of unresolved sub-grid scale fluctuations on particle dispersion. A Lagrangian particle tracking algorithm, accounting for drag, lift, gravity and Brownian forces, as well as particle shape, orientation and rotation, is developed and used to predict particle deposition. Results show good agreement with measurements, demonstrating that the characteristics of the flow and particle force balance are well captured, and the effects of particle shape and orientation are demonstrated.

Large eddy simulation of particle agglomeration with shear breakup in turbulent channel flow

A systematic technique is developed for studying particle dynamics as induced by a turbulent liquid flow, in which transport, agglomeration, and breakup are considered. An Eulerian description of the carrier phase obtained using large eddy simulation is adopted and fully coupled to a Lagrangian definition of the particle phase using a pointwise discrete particle simulation. An efficient hard-sphere interaction model with deterministic collision detection enhanced with an energy-balance agglomeration model was implemented in an existing computational fluid dynamic code for turbulent multiphase flow. The breakup model adopted allows instantaneous breakup to occur once the transmitted hydrodynamic stress within an agglomerate exceeds a critical value, characterised by a fractal dimension and the size of the agglomerate. The results from the developed technique support the conclusion that the local turbulence kinetic energy, its dissipation rate, and the agglomerate fractal dimension control the kinetics of the agglomeration and de-agglomeration processes, and as well as defining with time the morphology of the particles and their resultant transport. Overall, the results are credible and consistent with the expected physical behavior and with known theories.