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The normal and oblique impact of three types of wet granules

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Abstract

Impact tests against a hardened steel plate have been carried out to obtain the coefficient of restitution of three types of spherical granules. The dominant elastic γ-Al2O3, the elastic-plastic zeolite 4A and the dominant plastic sodium benzoate have been chosen as granule samples. An electromagnetic canon has been constructed to accelerate the granules and to measure the normal coefficient of restitution. The moisture content of the granules has been varied so that the pore saturation ranges between of S = 0–1. Thereby, the influence of the moisture content on the normal coefficient of restitution could be determined. A free fall apparatus, on which the impact angle is changeable in the range of ΘA = 0–80°, has been used to investigate the tangential coefficient of restitution. A high speed digital camera has been used to record the events of impact and rebound. The record frequency of the camera has been varied between 4,000 and 8,000 frames per second.

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Abbreviations

Eabs :

Energy absorption during impact [J]

dm :

Mean diameter [m]

e:

Coefficient of restitution [–]

en, et :

Normal and tangential coefficient of restitution [–]

Fn :

Normal force [N]

Fr :

Friction force [N]

G:

Elastic shear modulus [Pa]

J:

Mass moment of inertia [kg · m2]

K:

Non-dimensional radius of gyration [–]

m:

Mass [kg]

mF :

Mass of the wet granule [kg]

mTS :

Mass of the dry granule [kg]

R:

Radius [m]

S:

Pore saturation [–]

vA, vR :

Impact and rebound velocity [m/s]

vn,A, vn,R, vt,A, vt,R :

Normal and tangential component of the impact and rebound velocity [m/s]

vn,KA, vn,KR, vt,KA, vt,KR :

Normal and tangential component of the impact and rebound velocity of the contact patch [m/s]

Wkin,A, Wkin,R :

Kinetic energy of the impact and rebound [J]

XW :

Moisture content [kgWater/kgTS]

\({\varepsilon}\) :

Porosity [–]

θ A, θ R :

Impact and rebound angle [°]

θ KR :

Rebound angle of the contact patch [°]

κ :

Ratio of tangential to normal stiffness [–]

μ :

Coefficient of Coulomb friction [–]

ν :

Poisson’s ratio [–]

ρ g :

Granule density [kg/m3]

ρ s :

Solid density [kg/m3]

\({\varphi_{\rm w}}\) :

Wall friction angle [°]

χ :

Non-dimensional parameter [–]

ΨA :

Non-dimensional impact angle [–]

ΨKR :

Non-dimensional rebound angle of the contact patch [–]

ω R :

Angular velocity after impact [ rad/s]

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Authors and Affiliations

  1. Institute Process Engineering, Mechanical Process Engineering, Otto-von Guericke University Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Peter Mueller & Jürgen Tomas

  2. Institute of Solids Process Engineering and Particle Technology, Hamburg University of Technology, Denickestraße 15, 21073, Hamburg, Germany

    Sergiy Antonyuk & Stefan Heinrich

  3. Institute of Agrophysics, Polish Academy of Science in Lublin, ul. Doswiadczalna 4, 20-290, Lublin 27, Poland

    Mateusz Stasiak

Authors
  1. Peter Mueller
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  2. Sergiy Antonyuk
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  3. Mateusz Stasiak
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  4. Jürgen Tomas
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  5. Stefan Heinrich
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Correspondence to Peter Mueller.

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Mueller, P., Antonyuk, S., Stasiak, M. et al. The normal and oblique impact of three types of wet granules. Granular Matter 13, 455–463 (2011). https://doi.org/10.1007/s10035-011-0256-5

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