Potential exposure from hazardous dusts may be assessed by evaluating the dustiness of the powders being handled. Dustiness is the tendency of a powder to aerosolize with a given input of energy. We have previously used computational fluid dynamics (CFD) to numerically investigate the flow inside the European Standard (EN15051) Rotating Drum dustiness tester during its operation. The present work extends those CFD studies to the widely used Heubach Rotating Drum. Air flow characteristics are investigated within the Abe-Kondoh-Nagano k-epsilon turbulence model; the aerosol is incorporated via a Euler-Lagrangian multiphase approach. The air flow inside these drums consists of a well-defined axial jet penetrating relatively quiescent air. The spreading of the Heubach jet results in a fraction of the jet recirculating as back-flow along the drum walls; at high rotation rates, the axial jet becomes unstable. This flow behavior qualitatively differs from the stable EN15051 flow pattern. The aerodynamic instability promotes efficient mixing within the Heubach drum, resulting in higher particle capture efficiencies for particle sizes

Dust consists of fine and ultrafine solid particles (typically formed by the physical disintegration of a parent material) that may become aerodynamically suspended (

Dustiness is “the propensity of material to generate airborne dust during its handling” (

Various measures and apparatuses have been developed for dustiness measurement (

The rotating drum and continuous drop test methods are included in the European standard EN15051 (

A smaller variant of the (large EN15051) Rotating Drum dustiness tester was introduced earlier, independently in the pigment (

The Heubach drum has been incorporated into the German standard for dustiness measurement (

While we defer a detailed discussion of the Heubach architecture to _{bulk} and length _{bulk}) which tapers at the entrance (over length _{in} down to diameter _{in}) and at the exit (over length _{out} down to diameter _{out}). Air flows through each drum at a volumetric flow rate

The superficial velocities may be calculated as _{axial}
^{2}. The axial transit times are _{transit}
_{axial}. The Reynolds numbers are estimated as _{axial}
^{−5} m^{2}/s is the kinematic viscosity of air. The two drums possess comparable dynamic parameters in the bulk (comparable _{bulk}_{rot}_{transit}). However, while the EN15051 drum has laminar flow at the entrance and exit, due to the constricted entrance, the Heubach entrance flow is borderline turbulent; this necessitates the more sophisticated turbulent air flow modeling. As we shall see, the incoming axial jet becomes unstable, due to the super-imposed rotational flow, and this unstable air jet alters the instrument function.

Computational Fluid Dynamics (CFD) has been used for research of dustiness tester apparatus.

The Wypych group (Univ. of Wollongong, Australia) have conducted Discrete Element Method (DEM) simulations of the Rotating Drum (

This work represents the first modelling of the Heubach Rotating Drum dustiness test method. In this research, the flow field inside the high-speed (Heubach) rotating dustiness tester is simulated numerically. The higher volumetric flow results in turbulent air flow conditions, and the axial air jet, responsible for the transport of dust particles out of the drum (and onto the collecting media) is found to be unstable; this has consequences for the particle-size dependence of the instrument collection efficiency (the ‘instrument function’) of the Heubach drum. The dustiness, measured under this turbulent air flow, is compared with dustiness measurement under laminar flow (EN 15051 drum). The influence of the shape of inner vanes toward dust generation is also discussed.

We have used STAR-CCM+ as the CFD simulation software in this study. STAR-CCM+ can easily track massive particle trajectories. For a general discussion of modeling turbulent dilute particle-laden flows, see (

The geometry of the Heubach drum is a cylinder, tapered at both inlet and outlet. Dimension parameters of this drum are given in

Structured grids were generated within Star CCM+; cells are cubes (‘trimmed cells’) in the bulk of the domain and flattened rectangular prisms at the boundary surface; half of the grid cells are situated in the five layers adjacent to the drum wall. There was no refinement in the axial direction near the entrance and exit into/out of the Rotating Drum volume. The grid rigidly rotates, anchored to the rotating drum wall. The basic grid parameters are listed in

At _{sound} < 10^{−3}, where c_{sound} is the velocity of sound in air), the flow is incompressible. We model the turbulent air flow with the low-Re AKN k-ε turbulence formulation (Abe, Kondoh & Nagano, `994, 1005); the AKN k-ε has been evaluated by

The finite volume method (FVM) is used to discretize the governing equations. The discretization of equations and domain, as well as the iterations of discretized equations, are all conducted using commercial FVM solver STAR-CCM+. The convection terms are discretized using second-order Upwind Scheme. The transient terms are discretized by second-order Temporal Scheme. The time step is set at Δ^{−5} for each time step.

In order to simulate the experiments, the particles are initially distributed uniformly in a band at the bottom along the entire length of the drum. The number of particles in the simulations was N = 10^{4} for the dustiness simulations and N = 10^{2} for the particle track simulations. Particles are injected at ^{−6} m/s. The parcel injectors are uniformly distributed at the bottom of the drum. Tracking of massive particles is incorporated via the Lagrangian-Euler Method with two-way coupling between air continuum and dispersed particulate phase. Particle – particle interactions are neglected. For the largest particles (_{p} = 100 μm), the volume fraction of the drum occupied by the powder is ϕ ~ N × 10^{−10}; if all the particles were to accumulate in one cell (side = 1.5 mm), ϕ ~ N × 10^{−4}. Particle agglomeration and breakup are also neglected since aerodynamic shear forces are insufficient to break up agglomerates; however, particle impact on the drum walls may induce breakup, and this has been neglected. Particle – drum wall interaction is modeled as pure elastic collision (i.e. unit coefficient of restitution), so no particles stick to the drum wall.

In the Lagrangian-Euler Method, the motion of each dust particle in the Lagrangian frame is given by:
_{p} and _{p} are the mass and velocity of the particle and _{d}, and pressure force, _{p}, are given below. The drag force (in a direction opposite to the motion of the particle) is given by
_{p} = (π/2) _{p}^{2} is the particle cross-sectional area, _{p} is the particle diameter, _{r}
_{p}, where _{p} is the local particle velocity, and where _{d} is the _{p} = (π/6) _{p}^{3} is the particle volume, and ∇_{static} is the gradient of the static air pressure. There is an additional _{LS}, on each particle, due to shear near the walls.

We have used two-way coupling for these simulations. A result of our simulations is that the particles remained well-dispersed throughout the drum; the aerosol is thus sufficiently dilute so that one-way coupling is sufficient. However, we wanted to admit the possibility of particles accumulating in a localized region of the drum, in which case, the feedback of the particle motion on the fluid would become important, necessitating two-way coupling.

In two-way coupling, the rate of momentum transfer from the particles back to the continuum air phase is achieved by augmenting the Reynolds-averaged Navier-Stokes equations with a sink term
_{d}^{n} is the drag force ^{th} particle, and δt_{n}/Δt is the fraction of time that the n^{th} particle spends in the given cell during this time step.

We first discuss (

In this section, we examine the air flow in the Heubach drum. Differences in air flow will determine differences in aerosol capture efficiency and hence differences in measured dustiness. Three planes perpendicular to the axial direction are selected to study the air flow in the drums: the midplane (8.3 cm from inlet); a downstream plane (12.9 cm from the inlet), and the outlet plane.

At the axial midplane (

Similar behavior is observed on the downstream plane (

Vortex-shedding from the vanes is observed at the axial midplane for all models, similar to the vortex shedding observed from the vanes in the EN15051 drum. Presumably, the shed vortices travel towards the central jet, where their interaction induces asymmetry to the central air flow. The vortices shed in the 90° model are stronger (and the vane tips are closer to the axial centerline) compared to the 45° models. As these vortices interact with the central jet, they cause the jet to wander, which produces a large recirculating flow and destabilizes the central core flow. At the downstream plane, vortex shedding from the vanes can still be seen for the 45° models; however, for the 90° model, the wandering jet obscures any coherent vortex shedding from the vanes.

The differences in stability of the air flow between the 45° and 90° models is made explicit in a side view of the flow (

Mixing of the aerosol in the drum is determined by its radial transport. A measure of the mixing strength of the various air flows is an average of the radial velocity. Normalizing by the drum radius, gives a radial mixing rate,

We believe that the mixing rate differentiates the dustiness instrument function for the various rotating drum configurations.

^{4} monodisperse silica particles (^{3}). For the same material with same the size dust particle, the different apparatuses evince different dustiness measurement results; i.e. the dustiness measurement depends on the dustiness apparatus. This size dependent variation in the performance of the apparatus represents an instrument function for that apparatus.

For particle diameter

We verify the grid independence of our simulations, using simulations of the 90° Heubach model, rotating at 30 rpm, for 90 seconds, with three successively refined structured grids. The grid parameters are shown in ^{4} particles on each of these grids and recorded the fraction of particles collected at the outlet over the course of the 90 second simulation. The results are shown in

In order to better understand the size dependence of the Heubach drum instrument function, it is instructive to examine the behavior of particle trajectories for different sized particles. In the following simulations, the trajectories were accumulated for N = 10^{2} particles. In

Potential exposure from hazardous dusts may be assessed by evaluating the dustiness of the powders being handled. Dustiness is the tendency of a powder to aerosolize with a given input of energy. Various techniques are being used to measure dustiness. Much contemporary research attempts to relate the dustiness measurement to the physico-chemical properties of the powder. However, it is important to separate out contributions to dustiness due to materials parameters versus those due to measurement technique. The instrument function, the efficiency of a particular technique at measuring aerosolized powder of a given size, is a measure of the dynamic range of the instrument. The instrument function may be determined from a CFD simulation of noninteracting particles of that size. As such it separates out the performance of the dustiness measuring instrument from the actual dustiness measured on real powders.

We have previously used computational fluid dynamics (CFD) to simulate the flow inside the Venturi (high Re) and the European Standard (EN15051) Rotating Drum (low Re) dustiness testers during their operation. The present work extended those CFD studies to the widely used Heubach Rotating Drum. As with the larger EN15051 drum, it is found that the Heubach dustiness measurement is sensitive to particle diameter.

Since the air flows within the Heubach drum are turbulent, the CFD modeling is significantly more complicated than the previous modeling of the EN15051 Rotating Drum. Air flow was investigated within the Abe-Kondoh-Nagano k-epsilon turbulence model; the aerosol was incorporated via a Euler-Lagrangian multiphase approach. The air flow inside both the EN15051 and Heubach drums consists of a well-defined axial jet penetrating relatively quiescent air. The spreading of the Heubach jet results in a fraction of the jet recirculating as back-flow along the drum walls; at high rotation rates, the axial jet becomes unstable. This flow behavior qualitatively differs from the stable EN15051 flow pattern. Details of the aerodynamic instability in the Heubach Drum depend on details of the vane geometry and rotation orientation. The aerodynamic instability promotes efficient mixing within the Heubach drum, resulting in higher particle capture efficiencies for particle sizes

Since this work is focused on the instrument function (the particle-size dependence of the instrument collection efficiency) of the Heubach drum, the formation and breakup of agglomerates of smaller size particles were not incorporated into our simulations; similarly, particle adherence to the drum walls was also neglected. The CFD model overpredicts typical experimental dustiness measurements. Experimental powders invariably consist of agglomerates; these larger structures are not aerosolized and are not captured at the outlet—hence, they do not contribute to the measured dustiness. Clearly, agglomeration processes need to be included in simulations of the dustiness of real powder materials.

We thank Leonhard Heubach (Heubach GmbH) for helpful discussions on the architecture of the Heubach drum. This work is supported, in part, by the NIOSH Nanotechnology Research Center (NTRC).

The findings and conclusions in this paper are those of the authors and do not necessarily represent the views of the National Institute for Occupational Safety and Health. Mention of any product or company name does not constitute endorsement by the Centers for Disease Control and Prevention. None of the authors has a financial relationship with a commercial entity that has an interest in the subject of this paper.

Video Supplemental Material

Link to videos of 90° Heubach drum: i) air only—(a) ω = 15 rpm; (b) ω = 30 rpm; ii) particle trajectories—(a)

It is an unfortunate artifact of the videos that the vanes on the wall of the drum do not appear to rotate. In the particle trajectory videos, the particle tracks are shown for the previous Δt ~ 3 seconds.

45° and 90° Heubach Models

Meshes of 45° and 90° Heubach Models

Air flow tangential velocity vectors at midplane (8.3 cm) of cylindrical drum (top: 90°; bottom left: 45° anti-clockwise; bottom right: 45° clockwise); t = 30 sec.

Air flow tangential velocity vectors at midplane (8.3 cm) of cylindrical drum (top: 90°; bottom left: 45° anti-clockwise; bottom right: 45° clockwise); t = 60 sec.

Air flow tangential velocity vectors at end plane (12.9 cm) of cylindrical drum (top: 90°; bottom left: 45° anti-clockwise; bottom right: 45° clockwise); t = 30 sec.

Air flow tangential velocity vectors at end plane (12.9 cm) of cylindrical drum (top: 90°; bottom left: 45° anti-clockwise; bottom right: 45° clockwise); t = 60 sec.

Air flow velocity magnitude (cloud image) at end plane (12.9 cm) of cylindrical drum (top: 90°; bottom left: 45° anti-clockwise; bottom right: 45° clockwise); t = 30 sec.

Air flow velocity magnitude (cloud image) at end plane (12.9 cm) of cylindrical drum (top: 90°; bottom left: 45° anti-clockwise; bottom right: 45° clockwise); t = 60 sec.

Air flow velocity vectors on central horizontal plane of cylindrical drum (top: 90o; bottom left: 45o anti-clockwise, bottom right: 45o clockwise); t = 30 sec.

Air flow velocity vectors on central horizontal plane of cylindrical drum (top: 90o; bottom left: 45o anti-clockwise, bottom right: 45o clockwise); t = 60 sec.

Mixing Rate as a function of time at central plane of cylindrical drum (

Dustiness as a function of particle size for different rotating drums: Heubach 90° fins, 45° anticlockwise and clockwise fins; European Standard EN15051; small Danish drum. Particle size (absolute scale) indicated at top; log_{10}(d) at bottom, where diameter d is measured in meters.

Dustiness as a function of particle size for 90° Heubach drum; simulation results for different mesh sizes: 1.5 mm, 2.0 mm, 2.6 mm. Particle size (absolute scale) indicated at top; log_{10}(d) at bottom, where diameter d is measured in meters.

Particle Track (d = 100 nm) in Heubach models. From left to right: 45° anti-clockwise, 45° clockwise, and 90°.

Particle Track (

Particle Track (

Particle Track (

Particle Track (

Comparison of Parameters between EN15051 and Heubach Drums

units | EN15051 | Heubach | |
---|---|---|---|

Inlet Diameter _{in} | cm | 15 | 1.2 |

Bulk Drum Diameter _{bulk} | cm | 30 | 14.0 |

Outlet Diameter _{out} | cm | 8 | 2.12 |

Inlet Length _{in} | cm | 13 | 1.4 |

Bulk Drum Length _{bulk} | cm | 23 | 11.5 |

Outlet Length _{out} | cm | 6 | 5.3 |

Volumetric Flow Rate | L/min | 38 | 20 |

Angular Rotation Rate | rotations/min | 4 | 30 |

Axial transit time _{transit} | sec | 32 | 5.4 |

_{transit} | 2.2 | 2.7 | |

_{in} | 360 | 2300 | |

_{bulk} | 180 | 200 | |

_{out} | 670 | 1300 | |

_{rot} | 400 | 650 |

Dimension Parameters Table of High-Speed Rotating Drum

Item | Unit | Quantity |
---|---|---|

Inlet Diameter | m | 0.012 |

Outlet Diameter | m | 0.0212412 |

Drum Diameter | m | 0.14 |

Inlet Chamber Length | m | 0.014 |

Outlet Chamber Length | m | 0.053 |

Cylindrical Drum Chamber Length | m | 0.115 |

Vane Count | 3 | |

Vane Height | m | 0.025 |

Vane Length | m | 0.119 |

Vane Thickness | m | 0.001 |

Vane Angle | deg | 45/90 |

Rotation Rate | rpm | 30 |

Time Duration | second | 300 |

Simulation Time | second | 90 |

Mesh Parameters for High-Speed Rotating Drum Simulations

Model | Heubach-45 | Heubach-45 | Heubach-90 | Heubach-90 | Heubach-90 |
---|---|---|---|---|---|

Rotation Direction | Anti-Clockwise | Clockwise | Anti-Clockwise | Anti-Clockwise | Anti-Clockwise |

Mesh Base Size [mm] | 1.5 | 1.5 | 1.5 | 2 | 2.6 |

No. of Cells | 920071 | 920071 | 859468 | 385986 | 384609 |

No. of Faces | 2713561 | 2713561 | 2533338 | 1132683 | 1128732 |

No. of Vertices | 921540 | 921540 | 863569 | 388387 | 387772 |

Mesh parameters

Mesh Base Size [mm] | 1.5 | 2 | 2.6 |

No. of Cells | 859468 | 385986 | 384609 |

No. of Faces | 2533338 | 1132683 | 1128732 |

No. of Vertices | 863569 | 388387 | 387772 |

CFD simulations are used to characterize the Heubach dustiness drum.

The efficiency of the drum (‘instrument function’) depends on the orientation of the internal vanes.

90°-oriented vanes generate strong swirl that destabilizes the axial jet.

A destabilized axial jet (90° vane orientation) efficiently entrains small (d < 1 μm) dust particles.