Aerosol Particle Trajectories near a Flanged Round Opening The circular pipe with flanged round opening described in Section 10.3.1 is mounted with its face parallel to the horizon (pipe axis aligned vertically). It is used as a snorkel fume extractor, similar to the one shown in Figure 1.26. Unit

Question

Aerosol Particle Trajectories near a Flanged Round Opening
The circular pipe with flanged round opening described in Section 10.3.1 is mounted with its face parallel to the horizon (pipe axis aligned vertically). It is used as a snorkel fume extractor, similar to the one shown in Figure 1.26. Unit density spherical particles of various diameters [latex](D_p)[/latex] are generated at a point located at x = 0.10 m (axial distance one pipe radius from the face), and y = 0.10 m (radial distance one pipe radius from the axis), as illustrated in Figure E10.3a. The particles are injected into the flow in all directions with a maximum initial speed of about 14. m/s.
To do: Plot the trajectories of unit density spherical particles of various diameters, and determine the maximum particle diameter that can successfully be sucked into the snorkel inlet.

Accepted Answer

Only the worst-case scenario is considered, i.e. when the aerosol particles have an initial velocity in a direction opposite to the air flow. From Figure 10.8c, it is seen that at the specified initial particle location, the direction of the air flow is approximately 45° from the pipe axis. It is therefore assumed that the initial particle velocity is approximately 14. m/s opposite to this direction, as indicated in Figure E10.3a. Rounding off on the conservative side, particle velocity [latex]\vec{v}[/latex] is set to

[latex]\vec{v} =(10.0\vec{i} +10.0\vec{j} )\frac{m}{s}[/latex]

The air flow field is already known from the CFD simulation described in Section 10.3.1. This flow field is assumed to be "frozen", which means that particle motion does not affect air flow. Particles of the following diameters are injected: [latex]D_p[/latex] = 10, 25, 50, 60, 70, 80, 90, 100, and 200 μm. Their calculated trajectories are shown in Figure E10.3b. While each particle starts at the same location and moves at the same initial velocity, their trajectories are vastly different. All the particle trajectories curve towards the axis due to aerodynamic drag in that direction, but the larger particles are less affected by the surrounding air flow because of their larger inertia (and weight - gravity is in the x-direction here). It is hard to distinguish the trajectories of 10 and 25 μm particles; after quickly turning around, they follow the air streamlines almost exactly, and get sucked into the opening. Particles of diameters 50, 60, 70, and 80 μm are flung progressively further out from the starting point, but they too eventually turn around and get captured by the snorkel. It is clear from the figure that particles of diameter 90 μm and larger do not get sucked into the opening. Instead, these heavy particles eventually fall straight down due to gravity.

Discussion: The worst-case scenario is modeled, in which the particles are injected in a direction opposite that of the air. If particles were to be injected at an angle other than the one simulated, they would have a much better chance of being captured. One can conclude with some confidence, therefore, that all unit density spherical particles of diameter less than about 80 or 90 microns will be captured by the snorkel. If heavier particles, such as welding fume, were to be captured, new trajectories would need to be calculated. Since gravity acts against the suction flow of air in the present configuration, the cut-off diameter for liquid metal particles would potentially be much smaller than the 80 or 90 microns calculated here. Finally, workers and machinery near the particle injection location would certainly interfere with the air flow field. If the geometry were known, a more complex three-dimensional grid could be generated to account for such disturbances.

Question 10.3: Aerosol Particle Trajectories near a Flanged Round Opening T...

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