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Improved theoretical modeling of a cyclone separator as a diesel soot particulate emission arrester

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Abstract

Particulate matter is considered to be the most harmful pollutant emitted into air from diesel engine exhaust, and its reduction is one of the most challenging problems in modern society. Several after-treatment retrofit programs have been proposed to control such emission, but to date, they suffer from high engineering complexity, high cost, thermal cracking, and increased back pressure, which in turn deteriorates diesel engine combustion performance. This paper proposes a solution for controlling diesel soot particulate emissions by an improved theoretical model for calculating the overall collection efficiency of a cyclone. The model considers the combined effect of collection efficiencies of both outer and inner vortices by introducing a particle distribution function to account for the non-uniform distribution of soot particles across the turbulent vortex section and by including the Cunningham correction factor for molecular slip of the particles. The cut size diameter model has also been modified and proposed by introducing the Cunningham correction factor for molecular slip of the separated soot particles under investigation. The results show good agreements with the existing theoretical and experimental studies of cyclones and diesel particulate filter flow characteristics of other applications.

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Abbreviations

A :

inlet cross sectional area of cyclone flow [m2]

H :

inlet height of the cyclone [m]

B :

inlet width of the cyclone [m]

D 1 :

outer diameter of the cyclone [m]

D 2 :

diameter of the vortex finder [m]

D d :

diameter of the dust exit [m]

D p50 :

cut size diameter of the particle [µm]

D p50m :

modified cut size diameter of the particle [µm]

d p :

diameter of soot particle [µm]

F C :

centrifugal force [N]

F D :

drag force acting on the particle [N]

L 1 :

length of the cylindrical portion of the cyclone [m]

L 2 :

length of the conical portion of the cyclone [m]

L i :

inner vortex length [m]

L o :

outer vortex length [m]

V θ :

tangential velocity of the exhaust gas and particle [m]

\( V_{\theta _2 } \) :

tangential velocity of the gas at outer vortex [m/sec]

\( V_{r_2 } \) :

radial velocity of the particles at outer vortex [m/sec]

n :

vortex exponent

T :

exhaust gas temperature in K

N θ :

number of particles remain in the outer vortex at an angle of turn θ

N 0 :

number of particles at the inlet of cyclone, at θ=0

P ref :

reference pressure [pa]

ΔP :

pressure drop across cyclone [pa]

Q :

volume flow rate [m3/sec]

r 1 :

vortex finder or Inner radius of cyclone flow [m]

r 2 :

outer radius of cyclone flow [m]

t :

temperature of the exhaust gas [°C]

ρ c :

density of the exhaust gas [kg/m3]

ρ p :

density of the particle [kg/ m3]

η o :

collection efficiency of outer vortex

η i :

collection efficiency of inner vortex

η overall :

overall collection efficiency of the cyclone

μ :

dynamic viscosity of the gas [kg/m-sec]

θ :

angle of turn in traversing the cyclone [rad]

θ i :

angle of turn of the inner vortex [rad]

θ o :

angle of turn of the outer vortex [rad]

R gas :

characteristic gas constant of the exhaust gas [N-m/kg/°k]

R u :

universal gas constant, in N-m/kmolk

C p :

concentration of the particles per unit area

C p (r1,θ):

concentration of particles at inner radius r 1 & at an angular position θ

C p (r2,θ):

concentration of particles at outer radius r 2 & at an angular position θ

\( \overline {C_p (\theta )_0 } \) :

mean value of particle concentration at outer vortex

\( \overline {C_p (\theta )_i } \) :

mean value of particle concentration at inner vortex

C*:

cunningham correction factor

λ :

mean free path of the gas molecules [µm]

\( \bar u \) :

mean molecular velocity

M :

molecular weight [kg/kmol]

m :

mass of the soot particles

T in :

inlet temperature [K]

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Authors and Affiliations

  1. Department of Mechanical Engineering, Jadavpur University, Kolkata, 700032, India

    P. K. Bose

  2. Department of Mechanical Engineering, Central Calcutta Polytechnic, Kolkata, 700014, India

    K. Roy

  3. Department of Mechanical Engineering, Jalpaiguri Government Engineering College, Jalpaiguri, 735102, India

    N. Mukhopadhya

  4. Department of Mechanical Engineering, Jadavpur University, Kolkata, 700032, India

    R. K. Chakraborty

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  1. P. K. Bose
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  3. N. Mukhopadhya
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  4. R. K. Chakraborty
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Correspondence to P. K. Bose.

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Bose, P.K., Roy, K., Mukhopadhya, N. et al. Improved theoretical modeling of a cyclone separator as a diesel soot particulate emission arrester. Int.J Automot. Technol. 11, 1–10 (2010). https://doi.org/10.1007/s12239-010-0001-9

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