




Stationary acoustic anemometers for mine workingsS.Z.Shkundin ABSTRACT: An evaluation of the accuracy of tachometric and hotwire anemometers in mine workings and gasmedia ducts is given. The acoustic means of gas flow rates measurement is considered with particular reference to the equations of acoustic waves propagation in aerodynamic fields. The paper defines how it is possible to minimize the error of integrating acoustic anemometers.
Measurement of gas flow rates in mine workings and industry gas media ducts demands the introduction of modern devices. Underground mining of gassy deposits introduces ventilation problems. Since all the gases emitted into the mine workings finally find their way into the earth's atmosphere, the environmental aspects of mine ventilation can be considered from two points of view: the necessity of maintaining acceptable atmospheric conditions in mine workings and the need to control gaseous emission into the general atmosphere. Coal mines are often major sources of methane emission and up to 70% of methane gets into the Earth's atmosphere. The majority of coal deposits of Russia, Ukraine and Kazakhstan are coal seams with methane content varying from several cubic meters per ton in low gassy seams, to 2628 cubic meters in seams and rocks of high gas content. The process of methane concentration control in the mine workings requires constant measuring of two parameters: methane concentration and gas flow rate. The present report is devoted to elaboration of velocity and flow rate integrating sensors. Anemometry error evaluationThe anemometers considered here are suitable for measurements in mine workings and in pipes, and may be used in different projects to control sources of atmospheric pollution. Anemometers currently used in the Russian mining industry are tachometric or thermal ones, which do not afford accurate velocity and air gas flow rate measurements, particularly in case of automatic control. An error of flow measurement in any gas media duct comprises on error of average flow rate in a controlled section measurement and an error of the section measurement. Nowadays, the average flow rate measurement across a working's cross section is usually made with a selfcontained anemometer by taking the measurement at a point, where the flow rate is assumed to be the average one across the section. In such cases, an error of the average rate measurement will comprise an anemometer error and an error in the location of the anemometer. Total error characterizing flow rate measurements cannot be calculated by summing its components. Therefore a method of the total error evaluation has been elaborated, based on the information theory of K.Shennon [1]. The process of flow rate measurement in the case of a spot sensor location is illustrated in Fig. 1.
Figure 1. The velocity measurement as an information process:  real velocity at the point of the sensor location;  measured velocity value at the same point;  measurement error of the spot velocity; Information quantity at the anemometer outlet as per 16th theorem of K.Shennon is given by:
where:  average a priori entropy of the anemometer indication;  average a priori entropy of the real velocity in the measurement point;  average entropy of an error;  average conventional entropy. It follows from (1), that average entropy of the controlled value of , left after series of measurements and determining remaining uncertainty interval , depends not only on the anemometer error, but also on the difference in and :
As per definition; the remained (after measurements) uncertainly:
where:  remaining uncertainty after getting the result of measurement of  i.e. specific conventional entropies, comprising average conventional entropy , corresponding to specific uncertainty intervals ;  probability of the ith measurement result. Further a new definition of entropy for uniformly distributed error power [1] is put into use, so that the entropy of the error dispersion with given law distribution, having entropy H value is equal to the error of any other with the following distribution law:
By using of the 15th theorem of K.Shennon, one can obtain uncertainty interval value of the flow rate measurement by a point sensor, i.e. the measurement error (detailed calculation made by S.Shkundin [2]):
where  entropy error power of the flow rate measurement. The upper limit for error may be got if we deal with normal distribution of the error (entropy coefficient . It means that for normal distribution law, with standard deviation will equal:
Total error of the spot method will equal , where s 2  square rootmean error of the sensor location in a proper place; K S  entropy error factor of the average velocity measurement spot method. An error of measurement of stream velocity in a mine tunnel crosssection or pipes, as this analysis shows, may reach 25 and more percents [2]. The main reason being that the velocity measured at a point is interpreted as the average velocity in the crosssection. Let us point out here that reliability of tachometric and thermal anemometers is not enough  the first one contains rotating parts, the second is highly vulnerable to the mine atmosphere, furthermore, the setting up of the anemometer operating in the automatic mode in a tunnel is generally impossible because of minerals transport etc. Acoustic integrating anemometers Acoustic integrating anemometers based on ultrasonic wave propagation through a tunnel crosssection are free from all the deficiencies referred to earlier. The working acoustic beam accumulates information about vectors of longitudinal velocities of the flow, which forms the aerodynamic curve, and as such is an integrating anemometer. Such an anemometer is able to determine the average velocity of air streams in crosssections with consistancy. The principle of acoustic integrating anemometry is based on the use of two pairs of electricacoustic converters. One of them works streamwise and the other in the opposite direction. In other words, acoustic signals used by the first pair of converters are accelerated by the stream and signals used by the second pair are decelerated by the stream. The value of this deceleration or acceleration is a measure of the controlled average velocity. Particular devices may consist of only two converters, each of them taking turns in working as an emitter and as a receiver. Such a system based on two pairs of converters allows a reduction in error, concerned with variation of sound velocity. Figure 2 illustrates the principle. Electric acoustic converters (if there are two of them) are switched in turn from emitting to receiving mode, so that the vector, characterizing the emitting direction, forms either an acute angle (emittance streamwise) or an obtuse angle (emittance against the stream) with the flow axis.
Figure 2. The integrating acoustic anemometry principle: 1, 2 electroacoustic transformers; D cross dimension of airduct; L the length of through sounded base; V(r) the air velocity in plan cross section.
Figure 3. Acoustic rays in aerodynamic field propagation
Figure 4. Frequencyimpulse anemometer function scheme based on a synchroring principle One more advantage of the integrating anemometers should be mentioned: its independence of the dust loading in the medium in which a device operates. This stability is explained by the fact that the informative parameter, which is either oscillation frequency or phase, does not change with dust deposition on the converters. Besides, oscillations of the emitting converter prevent dry dust deposition on its surface. When used in an airduct or a tunnel, the acoustic rays are bent due to the aerodynamic field (Figure 3). Here two kinds of problems should be considered, i.e. those related to the laminar and turbulent flow regimes. Figure 3 shows the location of an emitter, a receiver and an acoustic ray path in stationary (1, 5) and moving (2, 3, 4) streams. Kinematics of a moving material point will be determined by two forces: pressure in moving air flow and force of excess pressure in an acoustic wave. Material point motion velocity in the field of these two forces has the following projections on the coordinates axis:
where: r and x coordinates of the point considered. In laminar flow the projection is described as:
where:  velocity in the airduct axis;  half of the airduct width. The initial equation for the velocity components will be as follows:
From (9) taking into account (7), one can obtain:
Here one can obtain an equation in differentials:
Integration of this equation gives the folling result (see Figure 3):
Similarly, consideration of a more general case, when oscillations are emitted at an angle to the working axis and the stream is laminar, gives a curve described by the equation:
In the case of a turbulent flow, the projection is described as:
Integration of the corresponding equation gives the following paths of acoustic rays [2]:
Conclusion The description of the paths of acoustic rays in an aerodynamic field leads to an elimination of errors in measuring of gasair flow rates in tunnels and airducts. Figure 4 shows a block diagram of the anemometer, based on the synchroring principle. Recently a pilot integrating acoustic anemometer has been developed, intended for use in the channel of the main ventilator of the Severnaya Mine (Vorcuta deposit). References 1. Shennon C. "Theory of the information" Bell magazine, pp. 463480, 1968. 2. Shkundin, S.Z., Clebanov F.S. 1980. About the accuracy of airgas flow rate measurement in mine workings. Physical and Technical problems of mining. Novosibirsk, No. 2. 3. Shkundin S.Z. 1988. The equations of air acoustic kinematics for integrating anemometers. Mining Journal 'High School transactions', Ecaterinburg. No. 5. 



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