## Distributed hot-wire anemometry based on Brillouin optical time-domain analysis |

Optics Express, Vol. 20, Issue 14, pp. 15669-15678 (2012)

http://dx.doi.org/10.1364/OE.20.015669

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### Abstract

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

© 2012 OSA

## 1. Introduction

1. T. Horiguchi and M. Tateda, “Botda-nondestructive measurement of single-mode optical fiber attenuation characteristics using Brillouin interaction: theory,” J. Lightwave Technol. **7**(8), 1170–1176 (1989). [CrossRef]

7. L. J. Cashdollar and K. P. Chen, “Fiber bragg grating flow sensors powered by in–fiber light,” IEEE Sensors **5**(6), 1327–1331 (2005). [CrossRef]

*C*temperature resolution, however, the total sensing length is limited to 70 m [10

10. T. Chen, Q. Wang, B. Zhang, R. Chen, and K. P. Chen, “Distributed flow sensing using optical hot-wire grid,” Opt. Express **20**(8), 8240–8249 (2012). [CrossRef] [PubMed]

## 2. Background

1. T. Horiguchi and M. Tateda, “Botda-nondestructive measurement of single-mode optical fiber attenuation characteristics using Brillouin interaction: theory,” J. Lightwave Technol. **7**(8), 1170–1176 (1989). [CrossRef]

*f*(

_{B}*z*) is the Brillouin frequency,

*f*

_{B}_{0}is the stain free Brillouin frequency at a known temperature,

*C*is the temperature coefficient,

_{T}*C*is the strain coefficient, Δ

_{ε}*T*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

11. P. C. Wait and T. P. Newson, “Landau Placzek ratio applied to distributed fibre sensing,” Opt. Commun. **122**(4–6), 141–146 (1996). [CrossRef]

*I*is the wire current,

*R*is the wire resistance,

_{w}*h*is the heat transfer coefficient,

*A*is the surface area of the wire,

_{w}*T*is the wire temperature, and

_{w}*T*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

_{f}*A*,

*B*, and

*n*are calibration constants,

*U*is the air velocity,

*f*is the wire Brillouin frequency associated with the wire temperature, and

_{w}*f*is the fluid Brillouin frequency associated with the fluid temperature. Note, the Brillouin temperature coefficient has been absorbed into the

_{f}*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

12. A. Brown, B. Colpitts, and K. Brown, “Dark-pulse brillouin optical time-domain sensor with 20-mm spatial resolution,” J. Lightwave Technol. **25**(1), 381–386 (2007). [CrossRef]

*f*, and after heating with airflow,

_{f}*f*, 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.

_{w}*h*is the heat transfer coefficient,

*L*is the characteristic length, and k is the thermal conductivity of the steel tube (16.2

_{c}*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

## 4. Experimental results

*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, Δ

*f*=

*f*−

_{w}*f*. Seven data points centred in the wind tunnel were selected to allow for any overshoot between heated and cooled sections [12

_{f}12. A. Brown, B. Colpitts, and K. Brown, “Dark-pulse brillouin optical time-domain sensor with 20-mm spatial resolution,” J. Lightwave Technol. **25**(1), 381–386 (2007). [CrossRef]

*R*

^{2}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.

*f*=

*f*−

_{w}*f*with respect the air velocity,

_{f}*U*. This mathematical relation has been derived and is presented in Eq. (4), where Δ

*f*=

*f*−

_{w}*f*, P is the power of the anemometer portion exposed to the airflow,

_{f}*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].

## 5. Conclusion

## Acknowledgment

## References and links

1. | T. Horiguchi and M. Tateda, “Botda-nondestructive measurement of single-mode optical fiber attenuation characteristics using Brillouin interaction: theory,” J. Lightwave Technol. |

2. | T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada, “Brillouin optical-fiber time domain reflectometry,” IEICE Trans. Commun. |

3. | M. DeMerchant, A. Brown, X. Bao, and T. Bremner, “Brillouin scattering based strain sensing,” Proc. SPIE |

4. | R. Bernini, L. Crocco, A. Minardo, F. Soldovieri, and L. Zeni, “All frequency domain distributed fiber-optic brillouin sensing,” IEEE Sensors |

5. | K. Hotate and M. Tanaka, “Distributed fiber brillouin strain sensing with 1cm spatial resolution by correlation-based continuous wave technique,” Proc. SPIE |

6. | H. H. Bruun, |

7. | L. J. Cashdollar and K. P. Chen, “Fiber bragg grating flow sensors powered by in–fiber light,” IEEE Sensors |

8. | S. Gao, A. Zhang, H. Tam, L. Cho, and C. Lu, “All–optical fiber anemometer based on laser heated fiber bragg gratings,” Opt. Express |

9. | I. Latka, T. Bosselmann, W. Ecke, and M. Willsch, “Monitoring of inhomogeneous flow distributions using fibre–optic bragg grating temperature sensor arrays,” Proc. SPIE |

10. | T. Chen, Q. Wang, B. Zhang, R. Chen, and K. P. Chen, “Distributed flow sensing using optical hot-wire grid,” Opt. Express |

11. | P. C. Wait and T. P. Newson, “Landau Placzek ratio applied to distributed fibre sensing,” Opt. Commun. |

12. | A. Brown, B. Colpitts, and K. Brown, “Dark-pulse brillouin optical time-domain sensor with 20-mm spatial resolution,” J. Lightwave Technol. |

13. | F. P. Incropera and D. P DeWitt, |

**OCIS Codes**

(060.2370) Fiber optics and optical communications : Fiber optics sensors

(280.2490) Remote sensing and sensors : Flow diagnostics

**ToC Category:**

Sensors

**History**

Original Manuscript: May 10, 2012

Revised Manuscript: June 1, 2012

Manuscript Accepted: June 16, 2012

Published: June 26, 2012

**Citation**

Michael T. V. Wylie, Anthony W. Brown, and Bruce G. Colpitts, "Distributed hot-wire anemometry based on Brillouin optical time-domain analysis," Opt. Express **20**, 15669-15678 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-14-15669

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### References

- T. Horiguchi and M. Tateda, “Botda-nondestructive measurement of single-mode optical fiber attenuation characteristics using Brillouin interaction: theory,” J. Lightwave Technol.7(8), 1170–1176 (1989). [CrossRef]
- T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada, “Brillouin optical-fiber time domain reflectometry,” IEICE Trans. Commun.E76-B(4), 382–390 (1993).
- M. DeMerchant, A. Brown, X. Bao, and T. Bremner, “Brillouin scattering based strain sensing,” Proc. SPIE3670, 352–358 (1999). [CrossRef]
- R. Bernini, L. Crocco, A. Minardo, F. Soldovieri, and L. Zeni, “All frequency domain distributed fiber-optic brillouin sensing,” IEEE Sensors3(1), 36–43 (2003). [CrossRef]
- K. Hotate and M. Tanaka, “Distributed fiber brillouin strain sensing with 1cm spatial resolution by correlation-based continuous wave technique,” Proc. SPIE4185, 647–650 (2000).
- H. H. Bruun, Hot-wire Anemometry: Principles and Signal Analysis (Oxford University Press, 1995)
- L. J. Cashdollar and K. P. Chen, “Fiber bragg grating flow sensors powered by in–fiber light,” IEEE Sensors5(6), 1327–1331 (2005). [CrossRef]
- S. Gao, A. Zhang, H. Tam, L. Cho, and C. Lu, “All–optical fiber anemometer based on laser heated fiber bragg gratings,” Opt. Express19(11), 10124–10130 (2011). [CrossRef] [PubMed]
- I. Latka, T. Bosselmann, W. Ecke, and M. Willsch, “Monitoring of inhomogeneous flow distributions using fibre–optic bragg grating temperature sensor arrays,” Proc. SPIE6189, 6189G-1 (2006).
- T. Chen, Q. Wang, B. Zhang, R. Chen, and K. P. Chen, “Distributed flow sensing using optical hot-wire grid,” Opt. Express20(8), 8240–8249 (2012). [CrossRef] [PubMed]
- P. C. Wait and T. P. Newson, “Landau Placzek ratio applied to distributed fibre sensing,” Opt. Commun.122(4–6), 141–146 (1996). [CrossRef]
- A. Brown, B. Colpitts, and K. Brown, “Dark-pulse brillouin optical time-domain sensor with 20-mm spatial resolution,” J. Lightwave Technol.25(1), 381–386 (2007). [CrossRef]
- F. P. Incropera and D. P DeWitt, Fundamentals of Heat and Mass Transfer (John Wiley and Sons, 2002)

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