Powder Flow

Executive Summary

Project ARR-98 focused on mixing rules for powder mixing in rotating drum flows. The first phase of the project explored the viability of PEPT measurements to yield the desired measurements for validating and complimenting a granular flow model of rotating drum flows. In this regard, coarse graining strategies proved integral to the success of the project. A useful outcome was the observation of the reverse Brazil nut effect observed for a binary mixture (by size).

Phase two built upon the serendipitous finding of a Peclet-based rheology that underpinned most of the granular flow phase space. ~200 DEM simulations across a wide range of flow configurations was used to successfully validate the new rheology.

Abstract

In this report, we quantitatively assess the effectiveness of discrete element method (DEM) calibration methods utilised by 8 industrial DEM practitioners for a number of differing experimental geometries, particulate media, and combinations thereof. The accuracy of the methods is assessed by comparing the outputs of simulations performed following the procedures of the 8 participants with detailed experimental data produced using Positron Emission Particle Tracking (PEPT), a technique which allows the dynamics of particulate systems to be imaged, in three dimensions, with sub-millimetre spatial resolution and sub-millisecond temporal resolution. Strikingly, of all the participants surveyed, no two institutions adopted the same practices, highlighting the need for a more standardised approach and best practice. Our results show that while most contemporary calibration methods are able to successfully capture the dynamics of simple, free-flowing, spherical particles under low-shear conditions, the vast majority of procedures tested were unable to correctly reproduce the behaviours of smaller, more cohesive particles, or higher-shear environments. For the latter case, though qualitative agreement and visual similarity between simulated and experimental systems could be observed, deeper and more quantitative analysis using PEPT revealed significant disparities. A number of methodologies were able to successfully capture the dynamics of aspherical, highly-angular particles, but no advantage was observed in the implementation of complex and computationally-intensive geometric models over the simpler and more efficient rolling-friction method for the materials and systems explored. Of the calibration methods examined, the most effective – indeed the only one to consistently reproduce the experimentally-measured dynamics of the cohesive systems tested – involved the combination of both static and dynamic powder characterisation tests, suggesting this to be the best practice for multi-parameter DEM calibration.

Executive Summary

Project ARR-98 focused on mixing rules for powder mixing in rotating drum flows. The first phase of the project explored the viability of PEPT measurements to yield the desired measurements for validating and complimenting a granular flow model of rotating drum flows. In this regard, coarse graining strategies proved integral to the success of the project. A useful outcome was the observation of the reverse Brazil nut effect observed for a binary mixture (by size).

Phase two built upon the serendipitous finding of a Peclet-based rheology that underpinned most of the granular flow phase space. ~200 DEM simulations across a wide range of flow configurations was used to successfully validate the new rheology.

EXECUTIVE SUMMARY

2

geometry, where faster flows will be possible.

Behringer hopper for use in future experiments to test these observations in a very different

fluctuations emanating from the outer wall. Finally we have repaired and modified the IFPRIfunded

not only the roughness/smoothness of the wall (as expected), but also to the magnitude of force

this to be true. We have further observed that we can associate different amounts of wall slip to

conditions. After resolving some issues with sensitivity to changes in humidity, we have found

given set of particles, and test whether they were constant across use under different boundary

boundaries. This allowed us to measure the 3 nonlocal constitutive parameters (A; b; s) for a

both particle-dynamics and stress fields under controlled conditions for six different-roughness

As Year 6 comes to a close, we have used fully-developed experimental protocols to measure

properties.

on separating which flow properties are set by the particle properties, versus those set by the wall

and (2) use these parameters to predict flows in other geometries. Thus, our current work focuses

can we (1) make flow measurements in one geometry which determine the constitutive parameters

and apply NLR to real granular systems. We aim to establish that, for a given set of particles,

In Years 4-6 of this project, we aim to address current shortcomings in how to calibrate

(A; b; s), but that we must know the amount of slip at the wall from geometry-dependent measurements.

packing densities, particle sizes and shapes, and shear rates, using just 3 constitutive properties

In Years 1-3, we established that NLR successfully models granular flows across different

particle properties, and the boundary conditions at the walls.

particles). Doing this requires a quantitative understanding of which properties are set by both the

determine the constitutive parameters for use in predicting flows in other geometries (for the same

the aim is to make a set of flow measurements for a set of particles in one geometry, and then

intermittent, creeping, quasi-static, and intermediate flows. In order for these models to be useful,

set of particles, which then can be used to predict flow fields and stresses over a large range of

promise of permitting the determination of a small number of empirical parameters for a particular

been the development of various nonlocal rheologies [1–7]. These constitutive models hold the

In the field of granular rheology, one of the most promising advances of the past decade has

Executive Summary

transport equations in order to supply quantitative prediction of segregation at process scale.

many of these segregation models and have set the stage for these models to be used in device-level

are applicable to density, size, shape, and cohesive segregation. We have experimentally validated

inherently-scalable, theoretical models based on rheologically-relevant dimensionless groups that

may be considered state-of-the-art, but, more importantly, we development several novel

than any models previously reported. Thus far we have demonstrated which models from the literature

a new way of structuring segregation rate models that make them inherently more scalable

novel view of the interplay between granular rheology and segregation, we aim to continue to develop

ultimately deduce the segregation rate (and validate the expressions). Moreover, by exploring a

model expressions that we are interested in testing with dramatically simplified experiments to

this balance between the rate of segregation and the perturbation rate, we can combine the

free surface granular flows in order to alter the steady-state distribution of particles. By achieving

is that we use flow perturbations to establish an “equilibrium” between segregation and mixing in

combined theoretical, computational, and experimental program. One unique aspect of our work

In this project, we seek to alleviate these two shortcomings of segregation research through a

• for validation purposes
• the significant dearth of validated scale-up studies for these models.

are (1) the inherent difficulty in measuring segregation rates (especially in an experimental setting)

practice. Two significant issues that hamper the applicability of models in industry, however,

Segregation model development holds promise for translation of academic research into industrial

Abstract

e.ects of various key DEM parameters – and map our course for the remainder of the project.

software for the comparison of PEPT and DEM data, and preliminary results regarding the main

this Report, we outline the progress made so far – including the development of novel analysis

of Birmingham, will provide the central pillar of the aforementioned Best Practice document. In

This comparative analysis, supplemented by additional data provided by the team at the University

which the simulations methods employed are capable of recreating the systems’ true dynamics.

Particle Tracking (PEPT) facility, allowing a rigorous, quantitative assessment of the degree to

to detailed experimental data produced using the University of Birmingham’s Positron Emission

industrial relevance, under a variety of conditions. The simulations produced will be compared

a set of simulations modelling two distinct experimental set-ups, each chosen due to its direct

of particulate systems. Each company involved in the project has been charged with producing

several industrial sectors with a shared interest in modelling and thus predicting the dynamics

order to develop such a Best Practice, we are working alongside a number of companies spanning

the application of discrete element method (DEM) simulations to industrial process equipment. In

The ultimate goal of the IFPRI Round Robin is to develop an industry standard Best Practice for

will be measured to test the accuracy of their measurements.

measurements of both instruments at low stresses. The flow condition out of the hopper

not agree. A small hopper has been designed for gypsum powder based on the flow

the FT4 Powder Rheometer, however the measured values of unconfined yield stress do

cell and for the ball indentation method by sieve filling using an indentation attachment to

The reproducibility of flow measurement at low stresses is similar for the RST-XS.s shear

stresses as low as 100 Pa, however the variability increases for more free-flowing powders.

measurements with a coefficient of variation < 3% for the very cohesive titania at pre-shear

measurement in this range. The Schulze RST-XS.s provides unconfined yield stress

the intended applied stresses for titania DT51, and therefore does not provide a reliable

cell agree at moderate stresses, however below 2 kPa the FT4 shear cell does not achieve

Shear cell measurements using the FT4 shear cell and Schulze RST-XS.s low stress shear

than that of ball indentation and some shear cells.

the minimum consolidation stress that can yield a measurement with this method is greater

stresses the uniaxial compression test underestimates the unconfined yield stress, whilst

unconfined yield stress to be inferred from indentation measurements. However, at lower

moderate stresses, allowing constraint factor to be determined and ultimately for

Uniaxial compression measurements correlate with ball indentation measurements at

is followed.

packing state can be achieved by vertical consolidation when this bed preparation method

consistent across the radial direction of the powder bed. This indicates that a reproducible

excess powder heap away with an inclined blade, the flow resistance is found to be

consolidation stresses. Furthermore, by completely filling the powder bed and scraping the

indentation, whereas sieve-filling is able to produce a coefficient of variation < 3% at low

is found to provide a large coefficient of variation in the bed hardness measurement by

scraping away excess powder) prior to vertical consolidation. At low stresses, pre-shearing

and by blade conditioning, wire conditioning and sieve filling (with and without

approaches does not achieve this alone. Ball indentation measurements are assessed by preshearing

however the vertical consolidation applied in indentation and uniaxial compression

Shear cells pre-shear the sample in an effort to ensure a reproducible packing state,

shear cell methods.

measurement at low stresses is assessed here by ball indentation, uniaxial compression and

force measurement and (ii) the reproducibity of the loose packing state. Powder flow

measurement at low stresses is more challenging due to (i) the required resolution of the

the reliability and reproducibility of the measurement decreases. Powder flow

using shear cell measurements. As the consolidation stress applied to the powder is reduced,

with procedures developed for designing hoppers based on mass or funnel flow behaviour

The most widely established method for measuring powder flow is by shear cell analysis,

Measurement of powder flow behaviour is important for many powder handling operations.

xecutive Summary

systems.

in the rolling mode to fully cascading ows consistent with industrial comminution

successfully scales up mixing con gurations spanning slowly rotated drums operated

Mixing Mechanisms

three mixing mechanisms are then achieved via the Entrainment number. The theory

dominated, and (iii) intermediate (both shear and advection). Scale-up rules of the

that classify mixing into three categories: (i) shear dominated, (ii) advective

Focussing on shear and advective mixing, we isolate the corresponding energy signatures

forced-to-free entrainment|The Entrainment Number.

the governing equations yields a set of dimensionless numbers, including the ratio of

and basal interface) and full velocity eld. Subsequent non-dimensionalisation of

(PEPT) measurements con rms the successful recovery of bed geometry (free surface

transient and non-uniform ow conditions. Positron Emission Particle Tracking

free surface e z(x), basal interface z e (x), and depth-averaged velocity u(x) under arbitrary

subsequent balance of mass, momentum and energy yields di erential equations to the

dense, viscoplastic granular rheology of (da Cruz et al., 2005; GDR MiDi, 2004), a

spanning rolling-to-fully-cascading ow regimes. Starting with the linearised form of

of rotating drum ows that facilitates scale-up of the dominant mixing mechanisms

The Entrainment Number (^ !)|from a fundamentally-derived granular ow model

In our third phase of the project we identify a suitable dimensionless number|

Executive Summary

EXECUTIVE SUMMARY

2 conditions for the first time, and address the main Aims.

Rheology (I). This will allow us to separately determine constitutive parameters and boundary data of the type collected here, we will soon be fully able to calculate the fluidity g(r) and the elucidate the nontrivial connection between these observations, which so far is confounding. Using techniques, are similarly affected by the roughness and compliance of the wall. Future work will of the flow, allowing us to observe that the pressure P and shear stress, measured by photoelastic of the flow most sensitive to nonlocal effects. Photoelastic techniques provide us full stress profile v(r) and shear rate profile _ (r), particularly as measured at the outer wall. This is also the region boundaries. We have observed that boundary roughness strongly controls both the flow profile both particle-dynamics and stress fields under controlled conditions for six different-roughness.

As Year 5 comes to a close, we have used fully-developed experimental protocols to measure properties.

On separating which flow properties are set by the particle properties, versus those set by the wall and (2) use these parameters to predict flows in other geometries. Thus, our current work focuses can we (1) make flow measurements in one geometry which determine the constitutive parameters and apply NLR to real granular systems. We aim to establish that, for a given set of particles, in Years 4-6 of this project, we aim to address current shortcomings in how to calibrate (A; b; s), but that we must know the amount of slip at the wall from geometry-dependent measurements.

Packing densities, particle sizes and shapes, and shear rates, using just 3 constitutive properties. In Years 1-3, we established that NLR successfully models granular flows across different both the particle properties, and the boundary conditions at the walls. The same particles). Doing this requires a quantitative understanding of which properties are set by and then determine the constitutive parameters for use in predicting flows in other geometries (for to be useful, the aim is to make a set of flow measurements for a set of particles in one geometry, large range of intermittent, creeping, quasi-static, and intermediate flows. In order for these models for a particular set of particles, which then can be used to predict flow fields and stresses over a models hold the promise of permitting the determination of a small number of empirical parameters been the development of various nonlocal rheologies [2, 4, 5, 11, 13, 15, 25]. These constitutive.

In the field of granular rheology, one of the most promising advances of the past decade has.

Executive Summary

detailed flow, and motivate further refinement in our modelling efforts.

experimental screw feeder assembly to test our model predictions, provide insight into the

constitutive model for the stress that accounts for dilatancy. We have recently built an

request of several IFPRI members at the GBM. For this, we are implementing a non-local

fluctuations in the inlet flow or spontaneous fluctuations within the screw – this was the

Our ongoing work is to model dynamical changes in the feed rate, due to

of gravity and friction at the screw surface.

volumetric discharge rate on the geometry of the feeder is not altered by the introduction

value of p/d at which the feed rate is maximum. Thus, the qualitative dependence of the

find that the discharge rate exhibits the same qualitative trend, in that there is an optimum

conditions of no friction at the screw surface and no gravity, employed in the model. We

frictionless screw in the absence of gravity. We then assess the effect of relaxing the

model to be in excellent agreement with the results of the DEM simulations for a

motion, in agreement with the assumption of the model. We find the prediction of the

simulations show that a significant fraction of the material does indeed exhibit solid body

by particle dynamics simulations using the discrete element method (DEM). Our

We then studied the detailed flow within the screw feeder for non-cohesive particles

yields a non-trivial result that could be useful in the design of screw feeders.

to a specific value. Thus, despite the assumptions that simplify the analysis, the model

discharge can be maximized by setting the ratio of the screw pitch p to barrel diameter d

the discharge rate for a given angular velocity and screw geometry. We show that the

and barrel, and neglecting the effects of gravity and friction on the screw surface, we obtain

that the granular medium moves as a rigid body that slips along the surfaces of the screw

and angular momentum on a suitably chosen continuum element. With the assumptions

We first constructed a mechanics-based model by enforcing the balances of linear

flow in a twin-screw feeder.

we have studied powder flow in a single-screw feeder, as the first step towards modelling

model. Such a model would assist in optimal design of screw feeders. In this investigation,

particulate materials, there has been no attempt to derive a detailed, mechanics-based

Despite the widespread use of screw feeders in industry for the transport of