Chapter_09_particle_removal - Chapter 9 Summary of Other...

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Chapter 9 – Summary of Other Air Cleaners to Remove Particles 9.2.3 Sampling Issues U = U 0 Q c = c 0 c = c 0 U = U 0 U = U 0 U = U 0 (a) isokinetic and isoaxial U < U 0 Q c = c 0 c > c 0 (b) subisokinetic and isoaxial U > U 0 Q c = c 0 c < c 0 (c) superisokinetic and isoaxial U = U 0 U = U 0 Q c = c 0 c c 0 (d) isokinetic but not isoaxial Figure 9.9 Particle trajectories (dashed) and streamlines (solid) for (a) isokinetic, isoaxial sampling, (b) subisokinetic, isoaxial sampling, (c) superisokinetic, isoaxial sampling, (d) isokinetic, but non- isoaxial sampling (misaligned sampling probe); dividing streamlines in (a), (b), and (c) are bold. 653
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9.3 Impaction between Moving Particles We let r 1 be the radius of particles of diameter D p that just barely get intercepted. This defines an upstream area, π r 1 2 , within which all particles of diameter D p or larger get collected . collector particle D c = 2R c U 0 , c 0 impacted particle intercepted particle r 1 R c r 1 uncollected particle Figure 9.14 Illustration of sphere-on-sphere particle collection; solid lines are air streamlines, dashed lines are particle pathlines. Particles within radius r 1 upstream of the collecting particle impact the collecting particle, particles outside of radius r 1 pass by uncollected, and particles at radius r 1 intercept the collecting particle. Contaminant particles initially within the stream tube defined by radius r 1 collide with ( impact ) the collector, while particles initially outside this stream tube miss the collector altogether, even for cases in which r 1 < R c , as shown in Figure 9.14. For the limiting case of particles initially at radius r 1 , their surfaces just barely collide with ( intercept ) the collector, as also sketched. Not shown in Figure 9.14 is the removal of very small particles that diffuse to the surface of the collector. The single drop, sphere-on-sphere removal efficiency ( η d ) is defined as the fraction of particles in the stream tube defined by the collector that are removed by the processes of impaction, interception, and diffusion: 2 2 01 0 1 d 2 c 0c0 crU r R cRU  π η= =  π  (9-12) Similar expressions can be defined for impaction of spheres on cylinders or for any pair of impacting bodies. 9.3.1 Single Drop Collection Efficiency The single drop collection efficiency ( η d ) of spheres impacting on spheres may be written as a function of Stokes number (Stk), as defined in Chapter 8: pr c v Stk D τ = G (9-13) where τ p is the relaxation time constant for the particle, also defined in Chapter 8 as 2 pp p D 18 ρ τ= µ (9-14) and is the velocity of the particle relative to the collector, r v G rp vvv c = G GG (9-15) G where is the velocity of the particle and p v G c v is the velocity of the collector. If gravimetric settling is neglected, the particle travels at a velocity equal to the gas velocity, p vU = o G G . A graph of the single drop
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collection efficiency for spheres impacting on spheres shows that η d is zero at Stokes number Stk = 0.083, and asymptotically approaches unity for large values of Stk. Calvert and Englund (1984) recommend that for flows in which the Stokes number exceeds 0.2, the single drop collection efficiency of spheres impacting on spheres
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This note was uploaded on 07/23/2008 for the course ME 521 taught by Professor Cimbala during the Fall '07 term at Pennsylvania State University, University Park.

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Chapter_09_particle_removal - Chapter 9 Summary of Other...

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