Revisiting the methodological approach to some application oriented unipolar corona investigations focusing interfacial properties of the ionised region

New insight on filamentary charge‐loaded flows originated by pulsating glow‐type unipolar coronas in atmospheric air

“…On-plane detections lead to figure out that the spherical sector with angle 2⋅γ m = 4⋅θ m can indeed change with the rod inclination; in this respect, see further details in Section 3. More in keeping with [14], it can be incidentally argued that only the hemispherical portion of the actual spherical sector mentioned above delivers most of the current with higher density on the distanced plane (see, later, Equation ( 32)).…”

“…Since each of the above curvilinear conduits are expected to approach at once an isobar and an isofield line (see, again, Section 2.4), then w c represents the mechanic pressure imparted by momentum transfer to the rounded surface A enclosing the IR. That quantity reaches 40 N/m 2 [14] and is therefore of four orders of magnitude less than that of still air, a result that will provide a simplifying effect on the present theoretical approach (see below, by extension, about the negligible changes of ρ c and related parameters). As regards the unphysical corona‐free case while V > V o , it is tacitly understood that the total charge Q would be uniformly distributed on the surface A because h ≫ r .…”

“…Subscript (‐) m is for maximum, as appropriate also for further parameters reported later on. As captured in Figure 3, h denotes elevation of the active tip, intended as an ideal spot of charge [14, 17], of the rod and θ m is proper to P–P coronas (see, for example, [18]). The referential axis of rotational symmetry in Figure 2 corresponds in Figure 3 to that aligned with the physical rod.…”

“…This steady, macro-scale behaviour of the ponderable real flow is reflected conveniently on assigning to the IR a time-averaged configuration in a consistent manner. More specifically, the IR with enclosing surface A is allowed to usually appear as a rounded-nearly spherical or cylindrical-and stable enlargement of the active electrode [14]. With special reference to the typical point-plane (P-P) setup-in which case a one-ended rod is positioned perpendicular to the facing passive plane-it should be added that the rod itself at the back of the glowing tip is influential in the following restricted sense: whether the rod extension back of the tip is gone into corona or not, depending on the applied voltage, the rounded edge of the IR can be represented as a confined spherical sector whose obtuse angle is close to 120 • (see further details in Section 2.6).…”

“…Note that the output current I is allowed to circulate in a simplified non-dissipative loop, which is evocative of, and fully consistent with, a convective flow of charges. According to fundamentals of circuit design, the current function I = F(V) supplied by the above class of sources can be conveniently expressed using a polynomial which can become F(V) = k·V 2 − k'·V, with k' = k·V o being constant as is k. The subtractive component k'·V offers additional insights into the current independent character of the glow discharge's dimension and shape claimed in [14]. In sum, the steady electrical current results in an ion convection acted upon by a pumping mechanism of power d dt W 𝛼 = V·F(V), whereas a residual electrostatic energy W β , linearly dependent on V, is separately stored.…”