·Table of Contents ·Methods and Instrumentation | Electromagnetic Invariant and its Application for Non-Destructive Testing of Moisture ContentPetro Zakharchenko,Anatoliy Syrtsov,Borys NevzlinEast-Ukrainian State University kv. Molodezhniy, 20A 91034 Lugansk UKRAINE E-mail: bnevz@vugu.lugansk.ua , Mykhaylo Zagirnyak E-mail: mzagirn@vugu.lugansk.ua, Yuriy Dyachenko E-mail: dyach@vugu.lugansk.ua Contact |
Fig 1: (a) Particles in the primary transducer; (b) particle equivalent circuit; (c) four element two-terminal network with local parameters; (d) two-terminal network with integral parameters. |
(1) |
where g_{1}=1/R_{1}, g_{2}=1/R_{2} - the active conductance of the resistors R_{1}, R_{2};
w - electric field angular frequency.
Having taken the derivatives from C and g by w, there can be found
(2) | |
From (2) it is evident that | |
(3) |
that is in four-element two-terminal network the partial derivative from the conductance of one type by the conductance of another type (reactive by active and other way round) equals to the ratio of sums of conductances of corresponding types.
It is to be noted, that the second derivative and all subsequent ones have just the same expression (3), that is,
(4) |
Thus, the expression (4) represents invariant not only by frequency in the frequency-dependable circuit, but order of the derivative..
Fig 2: (a) Particle division into parallel zones ; (b) equivalent circuit with local parameters; (c) equivalent circuit with integral parameters. |
Analogically with R-C network we find (Fig.2)
(5) |
Having taken the derivatives from L and R by w, their ratio is determined.
(6) |
All this gives the following determination of the electromagnetic invariant: partial derivative from the parameter of one type of four-element two-terminal network by the parameter of the other type equals to minus ratio of the sum of parameters of corresponding types. In the case of degeneration of four-element two-terminal network into two-element one, partial derivative is changed by the ratio of certain integrals.
Fig 3: Equivalent circuit of dielectric: C_{4} - capacity relevant to geometrical capacity and electronic polarization; g_{3}, C_{3} - active conductance and capacity from dipole-relaxational polarization; g_{4} - through conductance. |
For calculation of equivalent circuit in Fig.3 active conductance g_{O1} and g_{O2} and capacity C_{O1} and C_{O2} IT with GM on two frequencies of electric field is measured.
Value C_{3} is discovered analytically solving the equation
(7) |
where
The transition to the circuit in Fig.3 is executed under the following formulae:)
(8) | |
(9) | |
(10) |
In the further calculation we use value of invariantÕ:.(11)
(11) |
Value g_{2} is obtained analytically solving (12) with the account (11):.)
(12) |
The final transition to equivalent circuit in Fig.1(c) is realized under the formulae (13)-(15):
(13) | |
(14) | |
(15) |
Thus, with the help of electromagnetic invariant the analytical expressions permitting to calculate physical properties of particles and interparticle space of GM on integrated parameters of GM volume are obtained.
Fig 4: Dependence of logarithm of particle body capacity on moisture coal. | ||
Fig 5: Dependencies of coefficients a and b of linear function, approximating dependence of logarithm of particle body capacity on moisture from interparticle space capacity for different densities of coal. |
Fig 6: Dependence of capacity of interparticle space on moisture. |
(16) |
The calculation of coal moisture on the above-stated algorithm has allowed to increase measurement accuracy of GM moisture in 3.7 times only at the expense of handling observed data, without addition of essential changes to device construction.
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