3. 4. 5.
G . I . Shlikhteng, Boundary Layer Theory [in Russian], Nauka, Moscow (1974). L . L . Boshnyak and V. M. Solosovskii, Prib. Sist. Upr., No. 9 (1972). G . N . Bobrovnikov et al., Izv. Vyssh. Uchebn. Zaved., Mashinostr., No. ii (1969).
METHODS OF DRY CALIBRATION FOR ELECTROMAGNETIC FLOWMETERS UDC 681.121.89.082.74.089.6
I. D. Vel't
Electromagnetic flowmeters are based on one of the accurate laws of physics, the law of electromagnetic induction, and therefore their calibration characteristics can be calculated. In the nineteen sixties, the Thermal Instrument Research Institute together with the Arzamasskii Instrument Factory developed equipment type UGIR which was successfully employed for the direct calibration of electromagnetic flowmeters with uniform magnetic field
[1]. Since then, the electromagnetic method of measuring flow rates has become more widespread [2]; small flowmeters with nonuniform magnetic fields which are largely insensitive to profile velocity are widely used; the accuracy of flowmeters has increased and their range of measurements has expanded; miniature electromagnetic instruments for measuring speeds of flow have appeared which consist of a streamlined body with electrodes on its surface and a built-in inductor to create the magnetic field. Electromagnetic speed-of-flow instruments are used for measuring liquids in open channels and tubes of very large diameter. Electromagnetic flowmeters and speed-of-flow instruments are not generally calibrated and checked by direct methods, by testing "in the stream," due to the limitations on existing flowmeters, their complexity, low capacity, and high cost. The Thermal Instrument Research Institute has carried out work on creating methods of dry calibration and checking of rates of flow. This takes into consideration the fact that indirect calibration of electromagnetic flowmeters (or speed-of-flow meters) is based on two operations that are self-consistant and different in principle from each other: the elementby-element checking of the transducer and its electrical simulation. By checking and calculating the individual elements of the transducer by means of its physical equation, we establish the output quality of the transducer expressed in units of speed or rate of flow of liquid; we are then able to reproduce this with the aid of an electrical model built up out of standard elements. To compile the flow diagram of the electrical model, the transducer itself can be treated as a system into which we feed the energy of flow of the liquid and the energy of the supply to the inductor, and out of which we obtain electrical energy. This flow diagram can also be represented in the form of an active fourpole (with an internal source of energy), the input parameters of which are characterized by the energy supplied to the inductor. Under these circumstances, there exists a definite analogy between the converter and its electrical model. The fourpole representing an electromagnetic flowmeter and speed-of-flow meter has an asymmetrical matrix and is classified as nonreversible and nonautonomous, i.e., there is a dependent source of energy within the transducer whose physical essence is clear, namely the energy of the liquid [3] :
U~= Z~ 01. l~I U,~
[Z21 Z ~
(i)
12 9
Only one of the parameters of the fourpole is connected with measurement of the flow rate of the liquid, namely its transfer impedance Z2, which equals the ratio of the voltage Uz excited between the electrodes to the current I~ following through the inductor. Transfer impedance Z2~ is complex for existing types of flowmeters and speed meters and is characterized by modulus IZ2~I and argument @, the phase displacement between voltage U2 and current I~. The modulus of the transfer impedance for speed and flow rate meters with nominal diameters up to 300 mm varies within the range 0-0.001 ~ depending on the flow rate, Translated from Izmeritel'naya Tekhnika, No. i, pp. 68-70, January, 1979.
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0543-1972/79/2201-0098507.50
9 1979 Plenum Publishing Corporation
o
p.
-~/? Fig. 1 while for flowmeters with nominal diameter in excess of 400 mm, it lies within the range 00.01 ~. As a rule, argument ~ does not depend upon the rate of flow; its value lies close to zero for the transducers of speed meters and flowmeters of small diameter, while it increases up to 20-30 ~ as the channel diameter becomes larger. Measurement of the electrical conductivity a of the liquid being measured is connected solely with the value of impedance Zaa, which is inversely proportional to the product of the electrical conductivity and the diameter of the contact surface of the electrode, and for o = 0.i S/m it comprises 3.0-20 k~, depending upon the dimensions of the electrodes. Since the measuring systems of the flowmeters have a high input impedance and draw practically no current, we do not have to take special steps to ensure that the electrical model is nonreversible. This enables us to treat the active fourpole as a passive fourpole. The model of the transducer can take the form of a passive electrical circuit with a low input impedance made out of standard electrical elements and connected in the supply circuit to the inductor. If the parameters Z2~ and Zaa of the model are equal to the corresponding parameters of the transducer, then the voltage at the output of the model will be equivalent in amplitude, phase, frequency, and waveform to the voltage on the electrodes of the transducer when liquid flows past them. The Thermal Instrument Research Institute used this type of scheme as the basis for its "Istok" calibrator, which is intended for simulating the output signal from flowmeter transducers. The scheme of this calibrator comprises a matching standard current transformer, phase shifter, and voltage divider made up from precision resistors and capacitors. The basic error in reproducing the modulus of the transfer impedance of the calibrator does not exceed 0.3%, while ~ does not exceed 0.004. The transfer impedance Za~ varies over the range 0-200 kR, which enables us to model a flow with an electrical conductivity of from i0-' to i0 -~ S/m. When using the calibrator as an electrical model for element-by-element tests on a transducer, we have to include a definite value of transfer impedance Za~. As we can see from [4], this problem can be solved by representing the transfer impedance Zal by means of the inductance over a given surface area, such as the internal surface area of the flowmeter channel, and the so-called "surface weighing" function, which depends upon the physical shape of the channel, the coordinate of the electrodes, and the distribution characteristics of the speed of flow. By converting the volume integral into the integral over a given surface by mathematical means, we obtain the expression
Z~t= i ~ BnWndS,
(2)
where Bn is the component of the induction S that is normal to the surface; Wn is the surface weighing function. Further investigations show that there are considerable advantages in measuring the magnetic field of the flowmeter transducer at the surface rather than throughout the volume of the transducer channel. 99
! J
Fig. 2 Figure 1 shows the lines of equal surface weighing functions calculated for a planar profile of flow velocity (in which only the velocity component Vz = c o n s t exists) for the internal surface of a flowmeter channel and for the surface of a speed meter, respectively. If the sections of the system of induction coils are arranged in a definite manner, then the emf E induced into them will be proportional to the transfer impedance Z21. Under these circumstances, the expression for Z2~ will take the form:
z,1- 2vavV>-
E
where m is the angular velocity of the variation in the magnetic field; N is the summed area of the turns in the winding system; F is the sectional area of the flowmeter channel. The ratio of the emf E to the supply current I~fed to the inductor is measured by an ac potentiometer type R56 or K-509. The area F for large-diameter instruments can be found from the standardized dimensions of the instruments. For instruments of small diameters, the area F can be found by the hydrostatic method [i] with an error not exceeding 0.15-0.20%. This method leads to a considerable irregularity in the surface of the insulating lining of the instruments. The flow rate of the liquid Q or the average velocity Vav can be taken as being predetermined for a particular transfer impedance. In view of the complexity of the analytical relationships of the surface weighing functions, the calculation was carried out on a computer and from the results we established the law of distribution for the turns on the measuring winding. The winding was manufactured by photochemical means out of glass fiber foil. The phototemplates for the windings were made by an automated method with the aid of a coordinatograph type KPA-1200 or EM-703. The errors in routing the turns of the winding did not exceed 20-25 ~. A computing method of manufacturing the phototemplate has been developed which enables the winding to be designed on the basis of a single constant with an error not greater than • without the need to check each winding. Using the "Isto~' calibrator as an electrical model is not the only solution to our problem. This calibrator was developed for large-diameter flowmeters energized by sinusoidal current at mains frequency. If the transducer is fed by pulsed current, then an error will arise when the ratio of E/I~ is measured by an ac potentiometer. Tn this case, the highest degree of accuracy can be achieved by means of the electrical model shown in Fig. 2, which comprises three basic elements: the transducer i, the system of induction windings 2 for converting the induction of the magnetic field into an electrical signal, and an electrical converter 3 for converting the signal of the induction windings into a voltage equivalent to the difference in potentials induced between the measuring electrodes of the transducer. Such a Scheme for an electrical model is free from the need to use an ac potentiometer and to measure the magnetic field. The "Potok" equipment developed by the Thermal Instrument Research Institute for dry calibration is based on the scheme of Fig. 2. The "Potok" equipment can be used for instruments fed by sinusoidal or pulsed current. It has been studied on flowmeters type "Induktsiya" with nominal diameters of i00, 400, 600, and 800 n~ and nonuniform magnetic fields. The tests on the schemes using the ,Istok" calibrator and the "Potok" equipment have produced promising results. The maximum divergences between the readings of the instruments calibrated by the indirect method and tested on a standard flowmeter did not exceed the errors of the standard speed-of-flow instrument. These methods of indirect testing of flowmeters and speed of flow instruments enable us to study the effect of the speed-of-flow profile within a pipe on the measurement error. According to the algorithm and program developed by the Thermal Instrument Research Institute, it is possible to manufacture a winding appropriate to any given flow conditions.
i00
In view of the complexity and difficulty of conducting tests on real currents at the present time, data on the influence of distortions in the speed of flow on the readings of flowmeters and flow-speed instruments are extremely scarce. The methods we have discussed can be used to study the effects of variations in the speed profile, which greatly simplifies the tests needed to compile material for standardizing the instrument errors due to variations in the conditions of flow, and further improve the design of flowmeters and speedof-flow instruments. The currents measured by electromagnetic flowmeters are not steady-state in the majority of cases. Pulsations of speed caused by local hydraulic resistances, variations in static pressure, turbulance of flow, and other factors can under certain conditions affect the accuracy of electromagnetic flowmeters and flow-speed instruments. Experimental investigations of dynamic characteristics "in the current" are not carried out in practice, due to the lack of the appropriate standard equipment. Therefore the problem of creating indirect methods of experimentally investigating the dynamic characteristics of electromagnetic instruments is a very real one. As we know, when pulsating currents are being measured by means of a transducer with an alternating magnetic field, the signal is amplitude modulated, as a result of which the voltage between the electrodes has a frequency spectrum containing the frequency at which the magnetic field is varying (the carrier) ~ and the sidebands ~(~ + ~p) and pE(~ --
~p),
where ~p is the frequency of pulsations in the speed of flow. The voltage at the carrier frequency corresponds to the constant component of the speed of flow while the sideband voltages represent the components that are affected by the flow pulsations. Amplification, detection, and other signal conversion processes are carried out in the measuring equipment of the flowmeters and flow speed instruments. During these operations, the measuring equipment can introduce its own dynamic errors into the speed and flow-rate measurements 9 whereas the errors connected with the compressibility of the liquid do not arise [5]. In view of this, the dynamic characteristics of electromagnetic flowmeters and flow-speed instruments can be experimentally determined with the aid of an electric model of the transducer built in the form of equipment that is in widespread use in radio engineering which amplitude modulates the signal. LITERATURE CITED !. 2.
3. 4. 5.
O . S . Vavilov et al., Izmer. Tekh., No. 3 (1970). I . D . Vel't et al., in: Material from the Seminar "Modern Methods and Instruments for Automatic Testing and Regulation of Manufacturing Processes" [in Russian], MDNTP, Moscow (1976). I . D . Vel't, Magn. Gidrodin., No. I (1966). I . D . Vel't et al., Magn. Gidrodin., No. 3 (1976). I . D . Vel't and Yu. V. Mikhailova, Metrologiya, No. i (1978).
i01
