Archives of Mining Sciences
, Volume 59 (2) – Jun 1, 2014

/lp/de-gruyter/the-hot-wire-anemometer-anemometr-z-grzanym-w-knem-l0gbp1w5ZT

- Publisher
- de Gruyter
- Copyright
- Copyright © 2014 by the
- ISSN
- 1689-0469
- eISSN
- 1689-0469
- DOI
- 10.2478/amsc-2014-0033
- Publisher site
- See Article on Publisher Site

Arch. Min. Sci., Vol. 59 (2014), No 2, p. 467475 Electronic version (in color) of this paper is available: http://mining.archives.pl DOI 10.2478/amsc-2014-0033 JAN KIELBASA* THE HOT-WIRE ANEMOMETER ANEMOMETR Z GRZANYM WLÓKNEM This study analyses the behaviour of a hot-wire anemometer incorporated into a bridge circuit in the function of the voltage Uz supplying the bridge circuit and hence the current Iw flowing through the hot wire. The dependence of differential voltage U on Iw and the value of derivative d(U)/dIw as a function of the current supplying the hot-wire element were determined. These data enable the determination of working conditions of the constant-resistance (i.e. the constant-temperature) hot-wire anemometer. Keywords: thermal anemometer, hot-wire anemometer, constant-resistance (constant-temperature) anemometer W artykule analizowano zachowanie si grzanego wlókna wlczonego w mostek w zalenoci od napicia Uz zasilania mostka, a co za tym idzie od prdu Iw plyncego przez grzane wlókno. Wyznaczono napicie rónicowe U(Iw) oraz wielko pochodnej d(U)/dIw jako funkcje prdu zasilania wlókna. Te dane pozwalaj na wyznaczenie warunków pracy grzanego wlókna jako anemometru stalorezystancyjnego (stalotemperaturowego). Slowa kluczowe: anemometr cieplny, anemometr z grzanym wlóknem, anemometr stalorezys-tancyjny (stalotemperaturowy) 1. Introduction The hot-wire anemometer is one of the most frequently used instruments for investigation of flows. In such anemometer, a hot-wire element of several to several tens of micrometres in diameter is heated by an electric current flowing through it and the measure of the velocity of analysed flow is expressed by means of the voltage measured across the heated hot-wire element, * STRATA MECHANICS RESEARCH INSTITUTE OF THE POLISH ACADEMY OF SCIENCES, UL. REYMONTA 27, 30-059 KRAKOW, POLAND the intensity of current supplying the wire or its resistance. The system solutions vary depending on which quantity is chosen as the measure of flow velocity. This study provides an analysis of the so-called anemometric bridge circuit. It consists of two branches (Ra + Rw) and (Rb + Rc) connected in parallel and supplied by voltage Uz. Schematic diagram of the bridge circuit is presented in Fig. 1. The output voltage U is the voltage across the diagonal of the bridge which is the difference between the voltages occurring at terminals UB and UA. Fig. 1. The bridge circuit incorporating the hot-wire element Thus, the voltage across the diagonal of the bridge U equals Rc Ra Rc Rb Rw Rw U U B U A U z Uz Rb Rc Rw Ra ( Rw Ra )( Rb Rc ) (1) It is obvious, that if Uz = 0 then U = 0 irrespective of the value of the resistance of the wire Rw. When Uz increases, the current supplying the wire Iw rises and the temperature of the wire Tw also rises entailing the increase in resistance Rw, which is in the function of the supplying current Iw, what can be designated as R(Iw). Moreover, it can be noticed that the power dissipated in the heated hot-wire equal to Iw2 Rw is transferred to the medium flowing by, by means of the thermal conduction and convection. Assuming balanced situation, one gets an equation I w2 Rw [a b(v)](Tw Tg ) (2) where a -- stands for the coefficient of thermal conductivity of the flowing medium, b(v) -- analogical coefficient related to convection, v -- the velocity of medium, Tg -- the temperature of hot wire element and Tw -- the temperature of flowing medium. Linking the wire resistance with the temperature, we may write that Rw R0 [1 (Tw T0 )] and Rg R0 [1 (Tg T0 )] (4) (3) where Rw and Rg stand for the resistances of hot-wire element heated up to the temperature of Tw and at the temperature of flowing medium Tg, respectively, R0 the wire resistance at the reference temperature, at which the temperature coefficient of the resistance of wire was determined. Combining (3) and (4) we get: Rw Rg Tw Tg R0 and substitution of this relationship into (2) leads to I w2 Rw [a b(v)] Subsequently by making Rw Rg (5) R0 (6) and substituting into equation (2) we get 2 I w Rw R0 [a b(v)] (7) ( Rw Rg ) (8) Bearing in mind that the heating coefficient of the anemometer's wire N is expressed by formula N one ends up finally with 2 Iw Rw Rg 1 ) N (9) (1 (10) or 2 Iw a b (v ) 1 (1 ) R0 N (11) The equation (10) may be written in a dimensionless form as: 1 2 1 Iw N (12) which says that for Iw = 0 the wire does not heat up, which means that N = 1, and analogically for increasing Iw the heating coefficient N rises. Fig. 2 presents the relationship (12) in the case of sensor made up of tungsten wire of 5 m in diameter with resistance of Rg = 4.82 W. The boundary value for 1/N = 0 from equation (12) determines the current Iw 1 (13) 1.2 1 0.8 [1] 0.6 1/N 0.4 0.2 0 0 500 1000 1500 I w 2 [mA2} 2000 2500 3000 1/N = -0.0001908 I2 + 1 R2 = 0.9997 Fig. 2. Reciprocal dependence of heating coefficient N on the intensity of current supplying the sensor under no-flow conditions, Rg = 4.82 W at which the coefficient N becomes infinitely large. It is not equal to current flowing through the wire, as it is degraded earlier as a result of the oxidation of metal which the wire element is made of. It is thus more preferable to heat up the wire to reach N = 2. Then equation (12) gives Iw2 = 0,5 and hence 0,5 2 (14) I w( N 2) The voltage U across the diagonal of the bridge circuit is used as the input voltage of the amplifier which is in control of the voltage Uz supplying the bridge operating in classic circuit of hot-wire anemometer. 2. The dependence of voltage Uz supplying the bridge and the offset voltage U of the bridge on the current Iw heating up the wire The dependence of the voltage Uz supplying the bridge on the current flowing through the wire of the sensor is determined by equation U z I w ( Ra Rw ) and according to (12) we get Rw Rg 2 1 Iw (15) (16) Combining (15) and (16) we end up with: U z I w ( Ra Rg 2 1 Iw (17) This formula indicates that given the constant current supplying the wire, the voltage Uz will depend on parameter defined by formula (7), and hence the velocity of the medium v. By rewriting equation (1) we have U U z ( and considering that Iw we get U I w ( Ra Rw )( Rc Rw Iw ) Rb Rc Ra Rw Rb Rc Rb Rg Ra Rc 2 1 Iw (20) Uz Ra Rw (19) Rc Rw ) Rb Rc Ra Rw (18) 6 5 4 [V] 3 Uz 2 1 0 0 10 20 30 Iw 40 [mA] 50 60 70 80 Fig. 3. Dependence of the bridge supplying voltage Uz on intensity of current Iw supplying the wire The voltage U is in the function of the voltage supplying the wire Iw, the conditions of cooling of the wire (by means of ) and parameters of the bridge. If Iw = 0, the voltage U equals zero. If the current Iw increases slightly, the voltage U rises, although for Iw2 = 1/ it converges towards . Hence a conclusion can be drawn that U has an inflection point. This point can be determined equating the derivative of U with respect to Iw to zero. Differentiating the voltage U and equating the derivative to zero, an equation can be obtained for the value of Iw, at which the maximum of voltage U occurs. 2 Rb Rg 2 I w R R Rb Rg d (U ) a c 1 2 2 dI w Rb Rc Ra Rc (1 I w ) Ra Rc (1 I w ) 2 (21) Figure 4 presents the graph of U(Iw) and (d(U)/dIw) as well as Uz(Iw). The data refer to the sensor made of tungsten wire with a diameter of 5 mm and the resistance Rg = 4.82 W. The remaining resistances of the bridge circuit were Ra = 10.0 W, Rb = 1.0 kW and Rc = 1.0 kW. The value of parameter for this wire equalled 0.00019015 [1/mA2] at the temperature Tg =295.5 K. Fig. 4. Dependence of Uz(Iw), U(Iw) and d(U)/dIw on the intensity of current supplying the wire for v = 0 From Figure 4 it is obvious, that the voltage U depending on the intensity of current supplying the wire Iw initially increases, but still slower and slower to reach the maximum at approx. 35 mA. The voltage U then begins to decrease and for Iw around 52 mA becomes equal to zero. For higher intensities of current Iw, the voltage U across the diagonal of the bridge will be negative. The course of these three curves depends on conditions of hot-wire cooling. Figure 5 presents the courses of 1/N in function of the squared intensity of current supplying the wire for five selected flow velocities v. Table I summarizes the values of the (v) parameter and the coefficients of correlation R 2 given these flow velocities. TABLE 1 Values of parameters of lines 1/N = b I w2 for five different flow velocities Designation of the curve The flow velocity parameter [1/mA2] b parameter [1] R2 [1] a b c d e v = 9.54 cm/s v = 27.84 cm/s v = 50.72 cm/s v = 78.18 cm/s v = 123.9 cm/s 0.000223 0.000206 0.000189 0.000176 0.000163 Based on the table it is obvious, that the b parameter, which should theoretically be equal to unity, is very close to this value (0.98870 on average) and the R 2 parameter is close to 0.999 or even better. 0.8 1/N [1] a b c d e 0.4 0 500 1000 1500 I 2000 [mA ] Fig. 5. The reciprocal dependence of heating coefficient of the anemometer's how-wire element on squared intensity of current heating the wire Given the values of (v), the voltages U(Iw) for the above mentioned values of flow velocities were calculated according to formula (20). Obtained results are presented in Fig. 6. 80 70 60 50 [mV] 40 30 20 10 0 -10 0 -20 I w [mA] 10 20 30 40 50 60 a b c d e Fig. 6. Dependence of the voltage across the diagonal of the bridge circuit shown in Fig. 1 on the current supplying the hot-wire for different values of air flow velocity Based on Figure 6 it is obvious, that in the initial range of current supplying the wire the voltage across the diagonal of the bridge circuit changes linearly and does not depend on the velocity of flow around the wire. For current intensities above approx. 20 mA, the curves separate from each other and visible maximums show up, the positions of which depend on the velocity of air U(I w) flow. Further increase of the heating current Iw causes the voltage across the bridge diagonal to drop and, finally, with subsequent increase of current intensity Iw the voltage becomes negative. Naturally, the presented curves apply to sensors made of tungsten wires with 5 m in diameter only. The reader (should such show up) may find it weird, that the curve a (v = 9.54 cm/s) in Figure 6 finds itself to the left from the analogical curve presented in Figure 4 obtained for v equal to zero. In both cases, the position of the wire was the same (the horizontal position). This is probably caused by the "chimney draft" effect arising around the heated wire, which does not occur under conditions of existing flow. 3. Conclusion Analysing the U(Iw) curve shown in Figure 4 and analogical ones shown in Figure 6 it is clearly obvious, that if the hot-wire element is to operate in a constant-resistance (i.e. constanttemperature) anemometer circuit, its working point should find itself in the negative part of the U(Iw) characteristics, and thus must pass the maximum U(Iw) early. But especially in the initial part of this characteristic, the increase U results in increased current Iw and thus increased heating of the wire. Therefore we conclude, that should the sensor be able to operate as the CTA, it must be delivered an impulse in order to place its working point in decreasing part of the U(Iw) characteristics, and more specifically, in its negative part. This can be achieved by several means and the most simple one is by adding the voltage U by the voltage Uoff which is selected such that U(Iw) + U > approx. 60 mV, that is, such that the current Iw flowing through the hot wire exceeded the intensity of 35 mA, but this depends on selected parameters of the bridge circuit and, above all, on the value of heating coefficient. This situation is illustrated in Fig. 7. Fig. 7. The voltage U = (UB UA) is added by Uoff The voltage U will be the input voltage of balanced voltage amplifier constituting the control unit of the power amplifier supplying the bridge current with the voltage Uz. This situation is illustrated in Fig. 8. Selection of the offset voltage Uoff is hindered by the fact, that the A1 and A2 amplifiers may both have their own offsets U which may have arisen during the process of their production. These are difficult to be measured and will inevitably sum up with Uoff . Their common regulation is possible by means of the U terminal. It often may by the case, that the range of regulation of U is so wide, that the introduction of Uoff is unnecessary and redundant. This can be verified by measuring the voltage Ua across the resistor Ra, which depends on the intensity of current flowing through the hot wire element Rw. Fig. 8. The block scheme of the constant-resistance (i.e. constant temperature) hot-wire anemometer The anemometer must be set to specific operational conditions. First, the value of Rg is measured at given temperature Tg and under no-flow conditions (v = 0). Then, knowing the value of heating coefficient N at which the anemometric sensor is to be calibrated, the value of Rc at which the bridge circuit is to operate with given heating coefficient N is calculated. The value of resistor Rc is calculated according to formula Rc NRa Rg Rb (22) expressing the condition for balance within the bridge circuit. Following such setup of the bridge, the anemometer can be introduced into operation. The voltage Ua across the resistor Ra is the measure of the current supplying the hot-wire element under given operational conditions (known temperature Tg, known heating coefficient N, known diameter of the wire and its length). Following the sensor calibration for a given medium and in a specified flow velocity range, it may be used for measurement of unknown velocity of this medium. Here, it is also worth emphasizing that the courses shown in Fig. 4 and 6 depend strongly on the value of heating coefficient N. It will each time influence the intensity of current Iw (v,N). This study was performed within the framework of statutory activities of the Strata Mechanics Research Institute of the Polish Academy of Sciences. Received: 18 November 2013

Archives of Mining Sciences – de Gruyter

**Published: ** Jun 1, 2014

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