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Inclusion (particle) removal by interception and gravity in ceramic foam filters

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Abstract

An analytical model regarding the ceramic foam filter (CFF) as a network of branches (cylinders) has been developed to describe inclusion removal in CFFs used for aluminium filtration. The model based on measurements of filters with 30 pores per inch, should also predict behaviour of commercial filters with finer pores. Filtration efficiency is a function of particle size, metal velocity, particle settling velocity, and filter properties—the branch diameter, filter thickness, porosity, and specific surface area. The model takes into account interception with cylinders and settling on branch surfaces. The velocities are calculated from the Forchheimer and Ergun’s equation. There is good agreement between the model and plant experiments. Removal by interception increases strongly with decreasing cylinder diameter. There is indication that Al2O3 and SiC filters differ in their capture of inclusions.

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Notes

  1. The confidence lines give the range where the true value for a given measurement is likely to be given that the fitted curve is of correct form. Approximately 68 % of values drawn from a normal (or Gaussian) distribution are within one standard deviation away from the average.

Abbreviations

a :

Factor in Eq. (41)

A :

The cross-sectional area of the control volume in direction z (m2)

A :

Factor in Eq. (18)

a s :

The specific surface area: the surface area per unit volume of melt (m−1)

A x :

The filter cross-sectional area (m2)

b :

Ratio between projected area in the flow direction and the surface area

b :

Factor in Eq. (41)

C :

The drag coefficient in Eq. (28)

c or c(z):

The particle concentration (at z direction) (#/m3)

c in :

The inclusion concentrations at the inlet (#/m3)

c out :

The inclusion concentrations at the outlet (#/m3)

d pore :

The filter pore diameter (m)

d s :

The strut (cylinder) diameter in the models (m)

E :

The filtration efficiency

f :

The effective fraction of the surface in a gravity direction

F d :

The drag force on the particle (N)

F g :

The gravity force acting on the particle (N)

f 1 , f 3 , f 5 , f 7 …:

The function of λ or y, see Appendix A in [1]

g :

The acceleration due to gravity, 9.18 (m/s2)

k 1 :

Darcian permeability (m2)

k 2 :

Non-Darcian permeability (m)

L :

The filter thickness (m)

L c :

The length of the cylinder (m)

n :

Factor in Eq. (18)

ΔP :

The pressure drop across the filter (Pa)

q :

The adhesion efficiency

Q :

The volumetric flow rate (m3/s)

Q m :

The mass flow rate (ton/h)

R :

The cylinder radius (m)

R 2 :

The correlation coefficient of the curve fitting

R′:

The cylinder radius considering the coating, R = R′ + 2.5 × 10−3 m in Palmer’s case [2] (m)

Re :

Reynolds number

Re c :

Reynolds number for a cylinder

Re c′:

The Reynolds number for a cylinder considering the coating

Re p :

The Reynolds number of a particle

Re pore :

Reynolds number of a pore

R p :

The particle/inclusion radius (m)

U s :

The settling velocity of a particle relative to the metal (m/s)

U 1,U 3, U 5, U 7…:

The fluid flux coefficients, depend only on the shape of the body

U ∞ :

The approach or superficial velocity of the fluid (m/s)

x :

The distance along cylinder measured from stagnation point and x = Rθ (m)

y :

The normal distance from the cylinder surface (m)

z :

The starting point of a control volume (m)

Δz :

The length of the control volume (m)

β:

The angle made by the cylinder with the normal to the flow (°)

γ:

The angle between the normal to the surface and gravity (°)

ε:

Filter porosity (%)

η:

The collision efficiency defined as the number of inclusions that collide with the collector divided by the number moving towards the collector (%)

ηi :

The collision efficiency due to interception

ηi-avg :

Average collision efficiency due to interception

ηg :

The collision efficiency due to gravity

θ:

The polar coordinate (°)

θ:

The collection angle (°)

θc :

The maximum collection angle (°)

μ:

The fluid dynamic viscosity [kg/(m s)]

λ:

The dimensionless distance of a particle from the cylinder surface

λc :

The dimensionless distance of a particle from the cylinder surface when the particle collides with the cylinder: \( R_{\text{p}} /R\sqrt {\text{Re}_{\text{c}} } \)

ν:

The kinematic viscosity (m2/s)

ρ:

The density (kg/m3)

ρl :

The density of the liquid metal (kg/m3)

ρp :

The density of the particle (kg/m3)

Δρ:

Density difference between inclusion and melt (kg/m3)

ψ:

The fluid flux

ξ:

The dimensionless surface vorticity at the collection angle

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Acknowledgements

This research was carried out as part of the Norwegian Research Council (NRC)-funded BIP Project (No. 179947/I40) Remelting and Inclusion Refining of Aluminium (RIRA). It includes the following partners: Hydro Aluminium AS, SAPA Heat Transfer AB, NTNU and SINTEF. Fundings by the industrial partners and NRC are acknowledged gratefully. Thanks are also owed to Dr. Bjørn Rasch from Hydro Sunndalsøra and Arne Nordmark from SINTEF, for support and help in arranging the industrial experiments.

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Authors and Affiliations

  1. Norwegian University of Science and Technology, 7491, Trondheim, Norway

    Sarina Bao, Thorvald Abel Engh & Merete Tangstad

  2. SINTEF Materials and Chemistry, 7465, Trondheim, Norway

    Martin Syvertsen & Anne Kvithyld

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  1. Sarina Bao
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  2. Thorvald Abel Engh
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  3. Martin Syvertsen
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  4. Anne Kvithyld
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  5. Merete Tangstad
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Correspondence to Sarina Bao.

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Bao, S., Engh, T.A., Syvertsen, M. et al. Inclusion (particle) removal by interception and gravity in ceramic foam filters. J Mater Sci 47, 7986–7998 (2012). https://doi.org/10.1007/s10853-012-6688-4

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