Characteristics of the Pressure-drop, Cut-size and the Fractional Collection Efficiency for Various Kinds of the Miniature Cyclones

Abstract

In general speaking, it is well known that the cut-size X_c becomes to decrease with decreasing the diameter D₁ of the cyclone dust collectors. Here the cut-size X_c is defined as a particle diameter corresponding to 50% of the fractional collection efficiency η^x (X_p). But on the traditional theoretical formulae of the cut-size of the cyclone dust collectors, the cut-sizes are estimated by the representative sizes of the cyclone, namely, the outer diameter D₁ and the inner diameter D₂ and also mean inlet velocity V₀ in the inlet pipe without the restriction of the flow pattern of the three-dimensional turbulent rotational gas flow which depends on the sizes of the large, middle, small and miniature cyclones.
Therefore it appears to be a lack of understanding that, when the size of the cyclone becomes smaller and smaller, so the cut-size X_c becomes smaller and smaller due to increasing the centrifugal effect.
On the other hand, the author showed that the flow pattern in the cyclone changes with the cyclone Reynolds number R_cy= Q₀/H_iν, where Q₀ (m³/s) means the flow rate into the cyclone, H_i (m) is the imaginary cylindrical length and ν(m²/s) is the kinetic viscosity of gas.
Then the author (Europäscher Kongrepβ “Austauschprozesse in Partikelsystemen” Nürenberg, 28-30. März, 1977) derived the theoretical formula of the cut-size X_c basing upon the flow pattern of OGAWA combined vortex model, especially, the variation of the rotational flow of gas in the cyclone dust collectors as follows:
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In this equation, n (1) is the velocity index, φ(1) is the shape factor of the solid particle, ξ(1) is the effective factor (ξ=0.333) of the inward air flow, η(Pa·s) is the viscosity of gas, A₀ (m²) is the cross-sectional area of the inlet-pipe, D₁ (m), D₂ (m) and D₀ (m) are the diameters of the outer cylinder (body), inner pipe and the inlet pipe respectively, Q₀ (m³/s) is the flow rate into the cyclone, and Q_b (m³/s) is the flow rate into the dust bunker which is a function of the diameter D₃ of the throat of the cone.
In this paper, using the experimental results of the cut-size X_c of Hochstrasser, J. M.(1976) Ph. D. “The Investigation and development of cyclone dust collector theories for application to miniature cyclone presamplers” and of Smith, W. B., Wilson, R. R., and Harris, D. B., (1979) “A Five Stage Cyclone System for in Situ Sampling” Environmental Science and Technology, Vol.13, No.11, 1979, pp.1387-1396, the author has compared the calculated cut-size X_c with the experimentally determined cut-size X_c50 of various kinds of the miniature cyclones.
Then, the calculated cut-size X_c is well coincided with the experimentally determined cut-size X_c50 And also, the author explained that even if the diameter D₁ of the cyclone becomes smaller, the cut-size X_c50 is not always decreased due to the increment of the viscous effect in the boundary layer on the wall surface of the miniature cyclones.