Andrea Mammoli

Migration of particles undergoing pressure-driven flow in a circular conduit

This study focuses on the demixing of neutrally buoyant suspensions of spheres during slow, pressure driven flows in circular conduits. Distributions of the solid fraction of particles, φ, and the suspension velocity, ν, are measured at different lengths from a static in-line mixer. Experiments were conducted over a range of volume average solids fractions, φbulk (0.10⩽φ⩽0.50), and at two different ratios of the particle radius, a, to the radius of the circular conduit, R (a/R=0.0256 and a/R=0.0625). At φbulk⩾0.20, the particles rapidly migrate to the low-shear-rate region in the center of the conduit. This migration results in a blunting of the ν profile, relative to the parabolic profile observed in homogeneous Newtonian fluids. For the flow geometry with the smaller ratio of a/R, the φ profile builds to a sharp maximum or cusp in the center. Particle structures are observed in the experiments with the higher a/R. The entrance lengths for the development of the φ and ν fields, Lφ and Lν, respectively, a...

Effective slip on textured superhydrophobic surfaces

We study fluid flow in the vicinity of textured and superhydrophobically coated surfaces with characteristic texture sizes on the order of 10μm. Both for droplets moving down an inclined surface and for an external flow near the surface (hydrofoil), there is evidence of appreciable drag reduction in the presence of surface texture combined with superhydrophobic coating. On textured inclined surfaces, the drops roll faster than on a coated untextured surface at the same angle. The highest drop velocities are achieved on surfaces with irregular textures with characteristic feature size ∼8μm. Application of the same texture and coating to the surface of a hydrofoil in a water tunnel results in drag reduction on the order of 10% or higher. This behavior is explained by the reduction of the contact area between the surface and the fluid, which can be interpreted in terms of changing the macroscopic boundary condition to allow nonzero slip velocity.

Flow-aligned tensor models for suspension flows

Abstract Models to describe the transport of particles in suspension flows have progressed considerably during the last decade. In one class of models, designated as suspension balance models, the stress in the particle phase is described by a constitutive equation, and particle transport is driven by gradients in this stress. In another class of models, designated as diffusive flux models, the motion of particles within the suspension is described through a diffusion equation based on shear rate and effective viscosity gradients. Original implementations of both classes of models lacked a complete description of the anisotropy of the particle interactions. Because of this, the prediction of particle concentration in torsional flows in parallel plate and cone-and-plate geometries did not match experimental data for either class of models. In this work, the normal stress differences for the suspension balance formulation are modeled using a frame-invariant flow-aligned tensor. By analogy, the diffusive flux model is reformulated using the same flow-aligned tensor, which allows separate scaling arguments for the magnitude of the diffusive flux to be implemented in the three principal directions of flow. Using these flow-aligned tensor formulations, the main shortcomings of the original models are eliminated in a unified manner. Steady-state and transient simulations are performed on various one-dimensional and two-dimensional flows for which experimental data are available, using finite-difference and finite-element schemes, respectively. The results obtained are in good agreement with experimental data for consistent sets of empirical constants, without the need for ad hoc additional terms.

Stokes flow around cylinders in a bounded two-dimensional domain using multipole-accelerated boundary element methods

The multipole technique has recently received attention in the field of boundary element analysis as a means of reducing the order of data storage and calculation time requirements from O(N2) (iterative solvers) or O(N3) (gaussian elimination) to O(N log N) or O(N), where N is the number of nodes in the discretized system. Such a reduction in the growth of the calculation time and data storage is crucial in applications where N is large, such as when modelling the macroscopic behaviour of suspensions of particles. In such cases, a minimum of 1000 particles is needed to obtain statistically meaningful results, leading to systems with N of the order of 10 000 for the smallest problems. When only boundary velocities are known, the indirect boundary element formulation for Stokes flow results in Fredholm equations of the second kind, which generally produce a well-posed set of equations when discretized, a necessary requirement for iterative solution methods. The direct boundary element formulation, on the other hand, results in Fredholm equations of the first kind, which, upon discretization, produce ill-conditioned systems of equations. The model system here is a two-dimensional wide-gap couette viscometer, where particles are suspended in the fluid between the cylinders. This is a typical system that is efficiently modelled using boundary element method simulations. The multipolar technique is applied to both direct and indirect formulations. It is found that the indirect approach is sufficiently well-conditioned to allow the use of fast multipole methods. The direct approach results in severe ill-conditioning, to a point where application of the multipole method leads to non-convergence of the solution iteration. Copyright

Finite element modelling of deformation in particulate reinforced metal matrix composites with random local microstructure variation

Abstract Deformation in particulate reinforced metal matrix composites (PR MMCs) with locally varying reinforcement volume fraction has been modelled using a two-scale finite element approach. The responses of axisymmetric unit cell models were used to define the constitutive response of mesoscale regions possessing varying volume fractions. Macroscale response was then investigated using two- and three-dimensional “random arrays” of finite elements, in which element properties were randomly assigned in line with a Gaussian distribution. Two-dimensional random arrays developed non-uniform strain fields, severe strain localization ensuing as straining proceeded. Two-dimensional random arrays are, however, inappropriate for modelling the three-dimensional microstructure of PR MMCs. Three-dimensional random arrays also developed non-uniform strain fields, but severe strain localization did not arise. Reinforcement clustering was simulated by varying the standard deviation in element volume fraction. Yield stress, strain hardening and elastic modulus were all found to increase as the severity of clustering increased.

Stochastic Analysis of Cascading-Failure Dynamics in Power Grids

A scalable and analytically tractable probabilistic model for the cascading failure dynamics in power grids is constructed while retaining key physical attributes and operating characteristics of the power grid. The approach is based upon extracting a reduced abstraction of large-scale power grids using a small number of aggregate state variables while modeling the system dynamics using a continuous-time Markov chain. The aggregate state variables represent critical power-grid attributes, which have been shown, from prior simulation-based and historical-data-based analysis, to strongly influence the cascading behavior. The transition rates among states are formulated in terms of certain parameters that capture grids operating characteristics comprising loading level, error in transmission-capacity estimation, and constraints in performing load shedding. The model allows the prediction of the evolution of blackout probability in time. Moreover, the asymptotic analysis of the blackout probability enables the calculation of the probability mass function of the blackout size. A key benefit of the model is that it enables the characterization of the severity of cascading failures in terms of the operating characteristics of the power grid..

The effect of flaws on the propagation of cracks at bi-materials inferfaces

This study uses the boundary element method to investigate the effects of interfacial flaws on the propagation of a crack at or near an interface between two elastic, isotropic materials. These calculations reveal that flaws tend to deflect cracks approaching the interface from their original trajectory if the distance between the flaw and crack tip is small in relation to the flaw size. It is found that the higher the elastic mismatch parameter, the more crack trajectories are attracted to flaws. Other calculations show that materials with interfacial flaws have a significantly increased tendency to deflect cracks along the interface as compared to defect-free materials.

Analysis of battery storage utilization for load shifting and peak smoothing on a distribution feeder in New Mexico

A Smart Grid demonstration project is currently underway at Public Service Company of New Mexico (PNM). The project combines both residential and commercial loads on a dedicated feeder, with high PV penetration ratio, equipped with a 0.5MW substation-sited photovoltaic (PV) system and large-scale utility storage. The unique aspect of the battery storage system being used, is that both slow (load-shifting) and fast (intermittency-mitigation) power discharge modes are possible. Smart meters and customer Demand Response (DR) management, along with some customer-owned storage will all be implemented. This program targets a minimum of 15% peak-load reduction at a specific feeder through a combination of these the devices and measures. In this paper, we present goals, future plans and current results of modeling for the existing and future infrastructure of this Smart Grid project.

Parallel multipole BEM simulation of two-dimensional suspension flows

Abstract The motion of a large number of cylinders of circular cross-section in various two-dimensional flows is studied using a completed double-layer indirect boundary integral formulation. This type of formulation, with specified velocity boundary conditions, results in a Fredholm integral equation of the second kind. Discretization of this type of equation produces linear systems which are generally well-conditioned and suitable for iterative solution. However, the equilibrium and rigid body motion equations necessary to close the system disrupt the diagonal dominance of the matrix, resulting in high condition numbers. A preconditioner based on the known structure of the matrix is used to significantly reduce the condition number, to a point where the number of iterations to achieve a solution is independent of the number of particles in the system. Under these conditions, the solution of a highly populated N×N matrix is proportional to N2. The computational cost quickly becomes excessive as the number of particles in the system increases. This has been the main drawback in using the Boundary Element Method for studying suspension flows. The operation count required to solve an N×N linear system can be drastically reduced to O (N log N) by using a first-shift multipole formulation, in conjunction with a matrix-free iterative linear equation solver. Even with such a reduction in the operation count, dynamic simulation of systems involving large numbers of particles can still only be solved using large-scale parallelization. It is therefore important to establish the multipole technique is suitable for parallelization. It is shown here that this is the case, provided that the implementation of the multipole method is appropriate. Having established that large scale dynamic simulations can be performed in acceptable times, the results of several such simulations are presented. Analysis is performed on the simulation results, to illustrate the usefulness of the particle-level simulation approach in the investigation of suspension flow.

Effects of reinforcement geometry on the elastic and plastic behaviour of metal matrix composites

Abstract The mechanical properties of an AlSiC composite system are modelled using the Boundary Element Method. A unit cell approach, in three dimensions, is used to model the composites. The metal matrix is allowed to deform plastically, while the ceramic reinforcement is assumed to remain perfectly elastic. Several types of reinforcement are modelled, at various volume fractions, and with different degrees of clustering. The effects of thermal residual stresses, resulting from thermal processing, are also modelled. It is found that, even at relatively low volume fractions, the shape and orientation of the reinforcement phase has significant effects, both in the elastic and plastic domains. Orientation of the reinforcement is particularly critical if the aspect ratio of the reinforcement is high. The stress field within the reinforcement particle is also analysed.