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A distributed hot-wire anemometer based on Brillouin optical time-domain analysis is presented. The anemometer is created by passing a current through a stainless steel tube fibre bundle and monitoring Brillouin frequency changes in the presence of airflow. A wind tunnel is used to provide laminar airflow while the device response is calibrated against theoretical models. The sensitivity equation for this anemometer is derived and discussed. Airspeeds from 0 to 10 are examined, and the results show that a Brillouin scattering based distributed hot-wire anemometer is feasible.
© 2012 Optical Society of America
1. Introduction
Distributed temperature and strain measurements based on Brillouin scattering have been studied for over 20 years [1]. The first systems were based on time-domain reflectometry and time-domain analysis, while the latter systems were designed using frequency and correlation domain analysis [2–5]. Hot-wire anemometry has been studied for well over 50 years and is the topic of many textbooks [6], but recently hot-wire anemometers based on fibre technologies have been investigated. Some of these new anemometers obtain a quasi-distributed measurement of the airspeed since they rely on fibre Bragg gratings as their sensing mechanism [7–9]. The Bragg-grating based sensors measure a temperature change, at a single point, induced through forced-convective heat-transfer by monitoring the reflected wavelength of the grating. The difference between most of these sensors is the heat delivery method; some use external power supplies coupled to a fibre monitored cavity while others use lasers and specially designed gratings that absorb energy to generate the required heat. Even more recently, a distributed flow sensor based on in-fibre Rayleigh scattering was developed which boasts a sub-millimeter spatial resolution and a 0.1°C temperature resolution, however, the total sensing length is limited to 70 m [10]. In mining airflow applications a truly distributed measurement is desirable since it would allow mapping the airflow, and possibly the air resistance; a Brillouin scattering based anemometer with 10’s of km range would be an ideal sensing solution for this application, however, it should be noted that the amount of power to heat an anemometer that is 10’s of km long could be significant.
2. Background
Brillouin optical time-domain analysis (BOTDA) makes possible the distributed measurement of temperature and/or strain of an optical fibre [1]. By interrogating a fibre with a light source and monitoring the Doppler shift of the scattered light one of these parameters can be determined. This relationship is described in Eq. (1) where fB(z) is the Brillouin frequency, fB0 is the stain free Brillouin frequency at a known temperature, CT is the temperature coefficient, Cε is the strain coefficient, ΔT is the temperature change, and ε is the strain. In some cases it is possible to determine both quantities at a cost of accuracy for any one quantity [11].
By using a two laser stimulated scattering interrogation system where one of the lasers is pulsed, the local Brillouin frequency can be determined for every section of the fibre, and a strain or temperature map can be created. The relationship governing the hot-wire anemometer response to flow is shown in Eq. (2) where I is the wire current, Rw is the wire resistance, h is the heat transfer coefficient, Aw is the surface area of the wire, Tw is the wire temperature, and Tf is the fluid temperature [6]. The heat transfer coefficient varies with airspeed, and if the fluid temperature is known then the speed can be deduced. Typically, the anemometer is constructed and its response is calibrated. The calibration equation has been derived for this anemometer as [6] where A, B, and n are calibration constants, U is the air velocity, fw is the wire Brillouin frequency associated with the wire temperature, and ff is the fluid Brillouin frequency associated with the fluid temperature. Note, the Brillouin temperature coefficient has been absorbed into the A and B constants so that only the Brillouin frequencies are needed for calibration. The response is calibrated by taking Brillouin frequency measurements while the sensor is driven by a constant current and exposed to known velocities. The results are fitted to Eq. (3) and the values of A, B, and n are determined.3. Experimental setup
The dark pulse based BOTDA system of Fig. 1 was used for this experiment [12]. Two fibre lasers operating at 1532.68 nm were used to create the 30 mW continuous wave and 150 mW pulse signals. A “no chirp” electrooptic modulator and an Avtech pulse generator were used to create 1 ns pulses, resulting in a spatial resolution of 10 cm. Polarization control was achieved using a General Photonics Polaswitch and the photodetectors (D1 & D2) were made by Discovery Semiconductors. Frequency locking was achieved using a custom designed Optical Phase Locked Loop (OPLL) circuit and the optical components were made by Novawave. Samples were taken with a LeCroy digitizing oscilloscope at a rate of 2 Gsps, resulting in a spatial sample period of approximately 5 cm. Lastly, all the data was gathered and processed using custom designed software.
Fig. 1 The University of New Brunswick custom designed Dark-Pulse based BOTDA system used for measurement of temperature and/or strain. (EOM - electro-optic modulator, D1 & D2 - photodetectors).
A Brillouin scattering based hot-wire anemometer model is shown in Fig. 2. The stainless steel jacketed fibre is a loose-tube configuration filled with flooding gel and eight strands of fibre. A power supply is used to heat the jacket and create the hot-wire portion of the anemometer. The fibre’s Brillouin frequency will be influenced by airflow, and therefore, by comparing measurements made before heating without airflow, ff, and after heating with airflow, fw, results in a measurement that is a function of the airflow experienced by the fibre. Note, the measurement without heating before airflow, results in an ambient temperature measurement, and the heating with airflow, results in a wire temperature measurement.
Fig. 2 Stainless steel jacketed fibre used as a hot-wire anemometer. To heat the tubing a current is passed through it using an external power supply.
A potential concern with this anemometer is the absolute position of the fibre inside the tube and whether or not the stainless steel tube will be isothermal in the presence of convection. If the tube cannot be considered isothermal, then there will be a temperature dependence upon the position of the fibre. To determine if thermal gradients will be present across the tube the Biot number for this sensor can be calculated as follows
where h is the heat transfer coefficient, Lc is the characteristic length, and k is the thermal conductivity of the steel tube (16.2 ). The characteristic length for a cylinder is r/2 where r is the radius of the cylinder. The average heat transfer coefficient over the surface of the tube was determined to be 132 , and the Biot number is and since the Biot number is less than 0.1, the steel can be considered isothermal in the presence of convection [13]. This analysis assumes a solid cylinder, but letting the characteristic length approach half the conduction path around the tube still gives a Biot number less than 0.1.A wind tunnel was used to provide laminar airflow over the range of speeds for investigation of the anemometer. Figure 3 shows how the anemometer was placed across the wind tunnel. The diagonal portion of the tunnel was used to maximize the length of sensor exposed to airflow, which measured approximately 77 cm. The source of the airflow was a fan coupled to a DC motor and the airspeed was monitored indirectly using the pressure difference across the wind tunnel (pressure transducer). The fibre jacket material used in this experiment was an American Fujikura Limited stainless steel (SS304) tube with an outside diameter of 2.39 mm, and a wall thickness of 0.2 ±0.005 mm. Two of the fibres in the bundle were spliced together such that with one acquisition two fibres were interrogated. The reason for this is twofold: access to only one end of the fibre bundle is needed (both connectors are on the same end), and the results from both fibres can be compared for consistency.
Fig. 3 The wind tunnel cross section. A stainless steel tube fibre bundle was secured across the diagonal of the UNB wind tunnel so that approximately 77 cm of the sensor was exposed to laminar airflow. One end of the sensor has two fibres spliced together and the other end has two fibre connectors which are attached to the BOTDA system.
4. Experimental results
An acquisition was taken before heating to determine the Brillouin frequencies along the 77 cm exposed section at room temperature for calibration purposes. For the first set of measurements a current of 4.5 A was passed through the stainless steel tube. The room temperature fluctuated between 23.2°C and 24.0°C during all acquisitions. Figure 4 shows the Brillouin frequency fit data from one of the fibres in the bundle exposed to airflow. The Brillouin frequencies presented in this figure, as with all the figures in this paper, have been normalized to the measurement taken before heating. This makes all the presented frequency data of the form, Δf = fw − ff. Seven data points centred in the wind tunnel were selected to allow for any overshoot between heated and cooled sections [12]. Note that the heated portion is larger than the exposed section, so that the section exposed to airflow could be easy identified when examining the data. Also, the effects of thermal conduction are minimized by keeping the current connections away from the region of interest. The sensor was attached to the end of the wind tunnel using cable ties, and although there is some turbulence outside the tunnel the airflow is laminar across the sensor. It is apparent for airflows 0 , 1 , and 1.5 that the Brillouin frequency is decreasing as the airflow is increasing. To examine the response in more detail an average of the Brillouin frequency for each velocity was taken across the seven data points shown in Fig. 4 and an average was taken of the same data points for the second fibre. Then each fibre was examined separately by performing a curve fit to the expected response (Eq. (3)), and the results are plotted in Fig. 5. The coefficients of Eq. (3) are determined for the 4.5 A case by minimizing the sum of the squared residuals using the Nelder-Mead method (MatLab toolbox “ezfit”). The calibration is conducted on the gathered data and the resulting coefficients are shown in Table 1. This response shows a fractional power law relationship, which is expected when compared to theory [6, 9]. Also, the shape of this response shows that the anemometer is more sensitive to low airflow velocities. There is some error when setting airspeeds lower than 1 because the readings from the pressure transducer fluctuated on the same order as the values used to set these speeds. It would have been ideal to acquire more data points in the range 0 to 1 .
Fig. 4 Brillouin frequency response of the first fibre in the anemometer for a jacket current of 4.5 A. The seven points shown are used to determine the airspeed across the exposed portion of the sensor. Note, mps = meters per second.
Fig. 5 Calculated anemometer response from the results of the 4.5 A jacket current. Seven sequential measurements were averaged across each fibre and the results show good agreement between both curves. The error bars show ± 1 standard deviation, and the inset graph is a zoomed portion of the larger graph.
Table 1. Curve Fit Parameters for 4.5 A
To prevent overheating and damage to the wind tunnel the current had to be limited to 6 A. The next set of curves are, therefore, for a jacket current of 6 A. Figure 6 shows the Brillouin frequency data and Fig. 7 shows the curve fit results with the experimental data. The results were processed in the same manner as the 4.5 A jacket current results. The curve fitting results are summarized in Table 2 and the R2 parameter shows that these results are better than the 4.5 A results. This is not surprising because the measurements at the higher airspeeds become more accurate as the no flow wire temperature is increased. Since it is more difficult to set the lower airspeeds with this wind tunnel, increasing the wire current will allow more data points on the rapidly decreasing part of the graph to be acquired. Therefore, increasing the wire current will allow a better curve fit, and subsequently better results.
Fig. 6 Brillouin frequency response of the first fibre in the anemometer for a jacket current of 6 A. The seven points shown are used to determine the airspeed across the exposed portion of the sensor. Note, mps = meters per second.
Fig. 7 Calculated anemometer response from the results obtained in Fig. 4. Seven sequential measurements were averaged across the exposed sensor section to determine the Brillouin frequency. The error bars show ± 1 standard deviation, and the inset graph is a zoomed portion of the larger graph.
Table 2. Curve Fit Parameters for 6 A
With the calibration successfully completed for the 6 A jacket current, the distributed airspeed was determined for the 2 and 3.5 wind tunnel measurements and plotted in Fig. 8. The results show that the airspeed is correctly determined for the portion of the anemometer on the end of the wind tunnel, and for the portion outside of the tunnel the airspeed is nearly 0 . The portion between 19.25 m and 19.4 m is the egress of the wind tunnel to the ambient. Since, the transition occurs over a 15 cm segment it can be reasoned that the resolution of this anemometer is at least 15 cm, however, the flange where the transition occurs is between 5 and 10 cm. Therefore, it is plausible that the spatial resolution of this anemometer is determined solely by the BOTDA system resolution.
Fig. 8 Distributed airspeed measurements taken across the heated portion of the Brillouin hot-wire anemometer for two airspeeds, 2 and 3.5 . The portion between 19.25 m and 19.4 m shows where the transition between the wind tunnel and the still air occurs. Note, mps = meters per second.
The sensitivity of this anemometer is defined as the rate of change of the change in Brillouin frequency of Figs. 5 and 7, or alternatively the rate of change of Δf = fw − ff with respect the air velocity, U. This mathematical relation has been derived and is presented in Eq. (4),
where Δf = fw − ff, P is the power of the anemometer portion exposed to the airflow, A, B, and n are constants determined from calibration, and U is the airspeed. This relationship has also been plotted in Fig. 9 for both the 4.5 A and 6 A anemometer currents. The results show that as the current is increased the anemometer will become more sensitive to higher airspeeds, which is consistent with theory [6].Fig. 9 Sensitivity of the Brillouin hot-wire anemometer. The results are calculated from experimentally measured values.
5. Conclusion
This paper shows how a hot-wire anemometer can be created using a BOTDA system and a stainless steel jacketed fibre bundle. The stainless steel tubing of a fibre bundle was heated by passing current through it and distributed Brillouin frequency measurements were taken. Since the airflow is laminar, an average of seven data points was taken for each airspeed. The sensor was then calibrated against known airspeeds, and a set of calibration constants were determined. These constants were then used to calculate the theoretical response of the sensor. Two jacket currents were used, 4.5 A and 6 A, and the results were compared. The sensitivity of the anemometer was derived, and the results for each jacket current were examined. The results show that distributed anemometry using BOTDA systems is feasible.
Acknowledgment
The authors would like to thank the Natural Science and Engineering Research Council, the Atlantic Innovation Fund, the New Brunswick Innovation Fund, the Canadian Foundation for Innovation, and Springboard Atlantic for their financial contributions to this work. The authors would also like to thank UNB Mechanical Engineering Professor Dr. Gordon L. Holloway and his research assistant Kevin Wilcox for allowing and assisting in the use of their wind tunnel. Also, the authors would like to thank Professor Gordon Holloway for the counsel he provided with respect to thermal gradients in the stainless steel tube.
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