1. TKM College of Engineering
Kollam, Kerala, India
Experimental investigation on mass flow rate measurements using fibre Bragg grating sensors
S. R. Thekkethil1, 2, R. J. Thomas2, H. Neumann1, R. Ramalingam1
1Institute for Technical Physics, Karlsruhe Institute of Technology, Germany
2TKM College of Engineering, Kollam, Kerala

2. Contents Fibre Bragg Gratings - Introduction Introduction
Single Fibre mass flow meter
Sensor design
Results
Matrix type mass flow meter
Introducation
Design
Conclusions

3. FIBRE BRAGG GRATINGS - Introduction
A fibre Bragg grating is a strain transducer inscribed in an optical fibre. It is created by allowing two beams of UV radiation to fall on a fibre at a specific angle to each other. The constructive and destructive interference of the light creates alternate areas of higher refractive index.
Fig. 1 Fabrication of fibre Bragg grating

4. FIBRE BRAGG GRATINGS - Introduction
An FBG sensor reflects light of a certain wavelength and rest is allowed to pass through. This wavelength called Bragg wavelength can is dependent of the distance between the gratings[1].
The Bragg wavelength will vary if any strain is applied on the FBG sensor.
λb= 2 Δ ηeff
λ b - Bragg Wavelength
Δ - Grating period
ηeff - Effective Refractive Index
Fig. 2 Operation of FBG sensor

5. FIBRE BRAGG GRATINGS
Miniature size (Ø 0.2 mm, 1 cm long)
Passive operation (explosion free)
Tolerant to harsh environments
Electrical and magnetic immunity
Remote sensing
Wavelength Division Multiplexing (WDM)
>100 million cycles of strain with no degradation
Versatile system - Displacement, Temperature, Acceleration, Flow
1.2 K to 473 K Operation range
Ease and Cost of Installation

6. Flow measurement - INTRODUCTION
Measurement of cryogenic flows is in general an difficult task.
In specific, the flow through miniature channels, such as that in case of rocket engines cooling channels or heat exchangers.
These cases pose specific difficulties such as
Least pressure drop expected
Insulation of system
Cryogenic temperatures
Minimal invasive installation

7. Single fibre flow meter
The proposed design consists of a FBG sensor placed inside the pipe, such that the flow passes perpendicular to the fibre.
The drag force induced by the flow will induce a bending moment on the fibre.
The bending strain will induce a Bragg shift which can be recorded using the Bragg meter.
A unconstrained FBG is placed in contact with flow. This will only experience thermal strains, and will act as a thermal compensator.

8. Mathematical Model 𝜆 𝐵 =2𝛬 𝑛 𝑒𝑓𝑓 𝛥 𝜆 𝐵 = 𝛼+ζ 𝛥𝑇+ 1− 𝑝 𝑒 𝜀 𝜆 𝐵
The Bragg wavelength can be expressed as
𝜆 𝐵 =2𝛬 𝑛 𝑒𝑓𝑓
where 𝛬 is the grating period
𝑛 𝑒𝑓𝑓 is the effective refractive index of the FBG.
The Bragg shift is given by
𝛥 𝜆 𝐵 = 𝛼+ζ 𝛥𝑇+ 1− 𝑝 𝑒 𝜀 𝜆 𝐵
where 𝛥𝑇 and 𝜀 denote the change in temperature and strain on fibre respectively.
𝛼 is the thermal expansion coefficient,
ζ is the thermo-optic coefficient
𝑝 e is the effective strain-optic coefficient of the fibre given as
P11 and P12 are the components of strain-optic tensor,
n is the fibre core refractive index
ν is the Poisson’s ratio
Thermal
Strain
Physical
Pe = 0.5 * n2 * [P12 – ν(P11+P12)]
where C is constant based on structural properties of FBG

9. Fig. 3 Schematic of flow sensor

10. Sensor Design
For testing purposes, the dimensions and other parameters of the sensor was fixed.
Pipe diameter
Ø.018 m
Diameter of fibre
2x 10-4 m
Flow rate
0-5 g/s
Fibre parameters[11]
P11 = 0.113, P12 = 0.252, ν = 0.16 and n =
Bragg wavelength, 𝜆 𝐵 = nm
Fluid properties were taken from literature[12]

11. Experimental Result
A calibration setup was used to test the fabricated flow meter.

12. Fig. 4 Loading and Unloading of flow meter
Results
Fig. 4 Loading and Unloading of flow meter

13. Fig. 5 Regression Equation for experimental data
Results
Fig. 5 Regression Equation for experimental data

14. MATRIX TYPE FLOW METER
Based on the response from the single fibre flow meter, a new design was proposed.
The concept is to place multiple sensors across the cross-section of the pipe.
This will enable the flowmeter to sense variations within the flow, such as turbulence or change in flow domain.
Due to the multiplexing capabilities of FBG, a minimum number of fibres can be used to place all the sensors.

15. Fig. 6 Matrix layout of sensor

16. Fig. 7 Sensor disk with 1 fibre (8 FBGs)

17. Fig. 8 Final design of Matrix type flow meter

18. conclusions
The concept of using FBG sensors for the measurement of flow parameters is established.
The concept is to use the bending of the fibre placed in the flow to measure flow parameters.
Two separate designs were introduced based on the concept.
The operation of the sensors are feasible in both room temperatures and cryogenic temperatures.
Further experiments will be conducted to test and calibrated the design.
Feasibility of these designs in two-phase region will also be investigated.

19. References
Byoungho Lee, “Review of the present status of optical fiber sensors”, Optical Fiber Technology, Volume 9, Issue 2, April 2003, Pages 57-79, ISSN ,
Hill, K.O.; Fujii, Y.; Johnson, D. C.; Kawasaki, B. S. (1978). "Photosensitivity in optical fiber waveguides: application to reflection fiber fabrication". Appl. Phys. Lett. 32 (10): 647
Roths, J., Andrejevic, G., Kuttler, R., Süsser, M., "Calibration of Fiber Bragg cryogenic temperature sensors," 18th International Optical Fiber Sensors Conference, Optical Society of America, (2006).
Cashdollar, L. J., Chen, K. P.,“Fiber Bragg grating flow sensors powered by in-fiber light,” IEEE Sensors, 5(6), (2005).
Shim, J. H., et al., “Gas-flow sensor using optical fiber Bragg grating (FBG),” Journal of Navigation and Port Research International Edition, 32(9), , ISSN (2008).

20. References
J. H. Shim, et al., “Gas-flow sensor using optical fiber Bragg grating (FBG),” Journal of Navigation and Port Research International Edition, 32(9), , ISSN (2008).
J. Lim, Q. P. Yang, B. E. Jones, P. R. Jackson, “DP flow sensor using optical fiber Bragg grating,” Sensors and Actuators, A(92), (2001).
S. Takashima, H. Asanuma,H. Niitsuma, “A water flowmeter using dual fiber Bragg grating sensors and cross-correlation technique,” Sensors and Actuators, A(116), (2004).
Y. Zhao, K. Chen, J. Yang,“Novel target type flowmeter based on a differential fiber Bragg grating sensor,” Measurement, 38, (2005).
Ramalingam, R., Neumann, H., Süsser, M., “Mass flow sensor and method for determining the mass flow in a pipe,” Patent Application Publication, US A1 (2013).

21. References
Othonos, A., “Fiber Bragg gratings,” Review of Scientific Instruments, 68, , (1997)
Haefer, R. A., : Kryo-Vakuumtechnik: Grundlagen und Anwendungen, Springer-Verlag, Berlin 1981, dt. 15/09/2015.
Venkataraman Narayanan Venkatesan; K-P. Weiss; R. Ramalingam; “Strain Calibration of Substrate-Free FBG Sensors at Cryogenic Temperature” International Conference on Sensor Systems and Software, Oct 26–27, 2015

22. THANK YOU!