XIX Sympozjum Srodowiskowe PTZE - materialy.pdf

XIX Sympozjum PTZE, Worliny 2009
the charge cumulated in analyzed electrified material is contained in this material (Taylor and
Secker). So it can be used for assessment of charge decay time only for vessels, reactors,
pipes etc. completely filled with the analyzed material. In opposite case, if the container is
filled partially, the relaxation time constant is a complex function of the relaxation time
constant and geometry of the system and always is longer that the material time constant.
This problem was investigated earlier for some researchers (eg. Johns and Chan), who
computed time dependence of the surface charge in grounded metallic vessels or silos
partially filled or with bulk materials electrified in whole volume.
This problem was analyzed in the paper using the simplified model of the cylindrical pipe (or
vessel) of unlimited length, partially filled with the lossy dielectric uniformly electrified in
whole volume (close to the bulk material, e.g. dielectric powder). The model was shown in
Fig. 1.
Figure 1. Model of charge relaxation in partially filled metallic container
In the model there is air gap around the dielectric material, but it can be replaced by dielectric
lining also.
There made simplifying assumption as follow:
− the volume conductivity and dielectric constant of the lossy dielectric is uniform in the
whole volume,
− the analysis is begun at the moment t = 0, when the accumulated charge distribution is
uniform,
− the length L of the vessel is infinite.
The charge is dissipated by the current I0 flowing through the material to the grounded
metallic cord in the center of the vessel. The charge dissipation rate can be described with the
relation:
dQ/dt = - I0 = S j0 = 2πr0 L γ E0 (2)
The current is forced by the electric field E of the cumulated charge Q. At surface of the core
(r = r0) the field intensity E0 is the function of the electric charge Qi 0 induced in the core by
the volume charge of material.
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