Design and experimental study of a sensitization structure with fiber grating sensor for nonintrusive pipeline pressure detection

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Research article

Design and experimental study of a sensitization structure with fiber grating sensor for nonintrusive pipeline pressure detection ∗

Zhidan Yan a,b , , Guo Chen a , Chaoyu Xu a , Wenyi Xu a a

College of Control Science & Engineering, China University of Petroleum (East China), Changjiangxi Road 66, Qingdao, Shandong Province, 266580, China b State Key Laboratory of Precision Measuring Technology and Instruments, Tianjin University, Weijin Road 92, Tianjin, 300072, China

article

info

Article history: Received 16 July 2019 Received in revised form 28 January 2020 Accepted 29 January 2020 Available online xxxx Keywords: Fiber Bragg grating Sensitization structure Finite element modeling Fluid–solid coupling Nonintrusive pipeline pressure detection

a b s t r a c t With the extensive applications of pressure pipelines in various fields, research on pipeline pressure nonintrusive detection technology has become a promising measurement technology and development trend. In this study, taking a pressure pipeline as the research object, a wall strain sensitization structure with a nonintrusive fiber Bragg grating (FBG) pressure sensor was proposed. First, the strain characteristics of the pipeline wall under internal pressure were analyzed in detail. Then, a nonintrusive strain-amplifying structure with a rhomboid structure as the core was designed in accordance with the linear relationship between the strain of the pipeline wall and the pressure inside the pipeline. The designed structure can enlarge and transmit the pipeline wall strain to the strain beam of the rhomboid structure. Next, simulation models for the pipeline, sensitization structure, and detection system were established. Afterward, a series of structural optimization tasks were performed. Simulation results of the analysis of the sensitization structure with different sizes show that the sensitization structure of the FBG sensor can amplify the strain of the pipeline wall several times. Besides, the test results indicate that the sensitized structure with a long diagonal of approximately 2.5 times the short diagonal and the rhomboid structure material of 7075 aluminum alloy has a more stable and effective transmission and amplification effect on the wall strain. Moreover, it can effectively amplify the measurement signal and has a high application value. © 2020 ISA. Published by Elsevier Ltd. All rights reserved.

1. Introduction Pressure pipelines are widely used in various industries such as the petroleum, chemical, and gas industries because of their unique advantages of low cost and high efficiency. In practical applications, however, any accidental leakage would cause substantial economic losses and severe environmental pollution due to the danger of the transportation medium. Therefore, an efficient, accurate, and direct method for pipeline pressure detection is essential. At present, mechanical or resistance straintype pipeline pressure detecting sensors are commonly used in pipeline state detection; however, an opening on the pipeline is required in the pipeline pressure measurement, reducing the integrity and strength of the pipeline and making it difficult to ensure the safety of the system. With the development of pipeline pressure detection and sensing technology, research on nonintrusive pipeline pressure detection methods [1,2] has gradually ∗ Correspondence to: College of Control Science & Engineering, China University of Petroleum (East China), 266580 Qingdao, Shandong Province, China. E-mail addresses: [email protected] (Z. Yan), [email protected] (G. Chen), [email protected] (C. Xu), [email protected] (W. Xu).

progressed in recent years. These methods have the advantages of maintaining pipeline integrity, high accuracy, safe operation, and adaptability in various working environments. Major nonintrusive sensing technologies include ultrasonic detection and fiber grating sensing. Specifically, the ultrasonic detection method launches an ultrasonic beam through an ultrasonic probe installed on one side of a pipeline. Then, the beam crosses the pipeline wall and is collected by the receiving probe on the opposite side. Through the phase modulation of the ultrasonic signal, pressure can be calculated using the relationship between pressure and phase [3,4]. Fiber Bragg gratings (FBGs) that have the advantages of being small and lightweight are immune to electromagnetic interference, multiplexing, high sensitivity, and repeatability [5,6]. Through monitoring the shift of the Bragg wavelength, many kinds of the measurands such as temperature, strain, displacement, and pressure can be calibrated [7–9]. In the field of pressure sensing, sensitivity is an important parameter that determines the resolution and accuracy of a sensing system [10]. With the rapid development of fiber optic sensors in recent years, many new fiber optic pressure sensors were proposed; meanwhile, various configurations were designed to enhance the pressure

https://doi.org/10.1016/j.isatra.2020.01.036 0019-0578/© 2020 ISA. Published by Elsevier Ltd. All rights reserved.

Please cite this article as: Z. Yan, G. Chen, C. Xu et al., Design and experimental study of a sensitization structure with fiber grating sensor for nonintrusive pipeline pressure detection. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.01.036.

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sensitivity. For example, Gu et al. [11] proposed an optical fiber sensor for measuring hydraulic pressure. Their sensor consists of two FBGs. One FBG is clamped to the outer wall of a thin-walled cylinder along the circumferential direction to measure the deformation of the cylinder while the other FBG is used to measure the temperature and obtain the in-pipe hydraulic pressure by monitoring the wavelength difference between the two FBGs. The sensitivity of the proposed pressure sensor is 69.4 pm/MPa in the region of 0–16 MPa. Based on FBG and elastic metal film, Jiang et al. [12] presented a novel hydraulic pressure sensor, which possesses good linearity and repeatability in its large measurement range with a sensitivity of 23.8 pm/Mpa approximately. According to the double-shell cylinder with temperature compensation, a novel FBG pressure sensor was introduced by Zhang et al. [13]; a pressure sensitivity of 93.7 pm/MPa was achieved. Using 3D printing method, an FBG pressure sensor was designed and fabricated by Hong et al. [14] for the measurement of vertical pressure. The maximum measured vertical pressure of this new pressure sensor was 2 MPa with a measurement sensitivity of 75.64 pm/MPa. Zhang et al. [15] proposed a high-sensitivity pressure sensor based on FBG wavelength detection technology and used an eccentric-pushrod structure to improve the sensitivity of the sensor. The sensitivity of the sensor can reach 230.9 pm/MPa when the measured pressure is in the range of 0 to 20 MPa. Based on Mach–Zehnder interferometer, a dual-core photonic crystal fiber (DC-PCF) stress/pressure sensor with the sensitivity of 41 pm/MPa was presented by Xu et al. [16]. In this paper, a sensitization structure of an FBG sensor is designed based on existing technologies for the nonintrusive measurement of pipeline internal pressure. According to the theories of mechanical design and material mechanics, a pressure pipeline is selected as the research object. Then, high-sensitivity noninvasive measurement of pipeline pressure was realized through a series of theoretical explorations and simulation analyses. Finally, the effectiveness and practicability of the proposed method were verified by experiments. 2. Stress and strain analyses of a pipeline wall under internal pressure When a pipeline is under internal pressure, the principal stress (positive stress) in three directions would be generated at any point on the pipeline wall: axial, circumferential, and radial stresses. Fig. 1 shows the force diagram of a pipeline subjected to internal pressure. Axial stress σ z is normal stress acting parallel to the axis of the pipeline. Circumferential stress σ θ is a type of normal stress caused by internal pressure. It is perpendicular to the axial direction and parallel to the tangential direction of the circumference of the pipeline wall. Radial stress σ r is the third normal stress caused by internal pressure. It is parallel to the radial direction of the pipeline and acts on the pipeline wall. Within the elastic range of pipeline material, the pressure load acting on the pipeline will cause the pipeline to produce a corresponding strain. When the pipeline is subjected to uniform pressure P, its stress and strain analyses can be simplified to the elastic analysis of a thick-walled cylinder, i.e., the Lame˙ formula [17–19]. The radial σ r , circumferential σ θ , and axial σ z stresses (Pa) are as follows:

σr =

P K2 − 1

( 1−

R2o r2

) (1)

Fig. 1. Force diagram of pipeline caused by internal pressure.

(

P

σθ =

K2 − 1

σz =

1+

R2o

) (2)

r2

P

(3)

K2 − 1

The radial ε r , circumferential ε θ , and axial ε z strains can be directly obtained in accordance with the generalized Hooke’s law:

εr = εθ =

1 E

[(2 − v) σz − (1 + v) σr ]

(4)

[(2 − v) σz − (1 + v) σr ]

(5)

1 E

1 (6) (1 − 2v) σz E The equivalent stress σ v and equivalent elastic strain ε v of the pipeline are

εz =

√ σν = εν =

1[ 2

(σθ − σz )2 + (σz − σr )2 + (σr − σθ )2

]

(7)

σν

(8) E where Ri and Ro are the inner and outer radius of the pipeline (mm); K is the ratio of the outer radius Ro to the inner radius Ri (K = Ro /Ri ); r is the radius of any point between the inner and outer walls of the pipeline (mm), with a range from Ri to Ro ; E is the elastic modulus of the pipeline material (MPa); and ν is the Poisson’s ratio of the pipeline material. 3. Design of a sensitization structure for the circumferential strain of a pipeline 3.1. Double-beam rhomboid sensitization structure The sensitization structure of the FBG sensor is shown in Fig. 2. The structure is composed of a double-beam rhomboid structure, a two-petal hoop, and a fastener. The rhomboid structure has a flexible conversion function for pressure and tension, along with sensitization and strain amplification functions. It is a key

Please cite this article as: Z. Yan, G. Chen, C. Xu et al., Design and experimental study of a sensitization structure with fiber grating sensor for nonintrusive pipeline pressure detection. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.01.036.

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Fig. 2. Schematic diagram of the sensitization structure of the FBG sensor. (a) Sensitization structure of the FBG sensor. (b) Schematic diagram of the pressure sensor.

3.2. Mathematical modeling of the pipeline internal pressure measurement of the double-beam rhomboid sensitization structure For the structural size parameters shown in Fig. 4, the strain transmission mode of the sensitization structure that is composed of the two-petal hoop and the double-beam rhomboid structure was analyzed. The rhomboid structure exerts an amplification effect on pipeline wall strain, and the derivation process is as follows. The internal pressure of the pipeline p (Pa) causes the strain on the outer wall of the pipeline to generate a load px (N) at the two ends of the rhomboid structure through linear coupling (stress coupling coefficient kp ); then, the strain of the outer wall of the pipeline is transmitted to the strain beam of the rhomboid structure. Due to the influence of friction and other factors, there is a relationship between the pressure inside the pipeline and the load on the arm end of the rhomboid structure, as shown in Eq. (9). Fig. 3. Schematic diagram of rhomboid structure.

component of the sensitization structure. The two-petal hoop is used to connect the buckle of the rhomboid structure, and the ears are fastened by a fastening bolt to closely attach the inner side of the hoop to the pipeline wall, thereby transmitting the pipeline wall strain to the rhomboid structure between the two snap rings. The two-petal hoop can better sense the wall strain compared with the traditional clamp hoop. The double-beam rhomboid structure is the core component of the FBG sensor sensitization structure; it is primarily composed of two buckles, two arms, two grooves, a base, a temperaturecompensating beam, and a strain beam (see Fig. 3). One end of the temperature-compensating beam is disconnected from the base, ensuring that it can independently sense the effect of temperature when measuring strain. Both ends of the strain beam are connected to the base to detect stress load from the arms and the buckles. The groove design ensures that the rhomboid structure and the pipeline wall are in the noncontact state at all times; that is, the load can only come from the buckle and the arm at both ends of the rhomboid structure. The contact portion between the lower end of the arm and the pipeline wall is designed as a curved surface with the same curvature and radian as the outer wall of the pipeline to make it fit into the pipeline wall. The force at both ends of the rhomboid structure can be stabilized when force is applied.

px = kp p

(9)

Let u and h be the width and thickness of the arm of the rhomboid structure (mm); Fx is the tensile force at the arm (N). Then, Fx = px × u × h

(10)

φ is the angle between the edge of the base and the connecting line of the arm (o ). Since there is a partial strain loss at the four sides of the base and the arm during the strain transmission process, the strain compensation coefficient ks is introduced. Furthermore, the thickness of the base of the rhomboid structure is h (mm); the thickness, width, and elastic modulus of the strain beam are hy (mm), z (mm), and E (MPa); the lengths of the short and long diagonals of the base are x and y. Subsequently, the pressure Fy (Pa), stress py (Pa), and strain ε y of the strain beam are obtained as follows: y Fx × sin φ = ks × Fx × tan φ=ks × Fx × (11) Fy = ks × cos φ x py =

εy =

Fy z × hy py E

=

=

k s × px × u × h × y hy × z × x

ks × kp × p × u × h × y hy × z × E × x

(12)

(13)

From the preceding formulas, the internal pressure of the pipeline can be indirectly measured by calculating the strain value ε y of the strain beam of the rhomboid structure.

Please cite this article as: Z. Yan, G. Chen, C. Xu et al., Design and experimental study of a sensitization structure with fiber grating sensor for nonintrusive pipeline pressure detection. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.01.036.

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Fig. 4. Size parameter of rhomboid structure. (The black part on the beam is FBG.)

Particularly, the actual strain transfer amplification of the rhomboid sensitization structure can be affected by the mounting errors of the hoop, the rhomboid structure, and the measurement pipeline installation. However, this effect is determined for known overall structural dimensions. The corrected strain value ε ′ y can be obtained as follows by introducing a correction factor k:

εy′ = kεy

(14)

Two FBGs are respectively attached to the strain beam and the temperature-compensating beam of the rhomboid structure. In accordance with the measurement principle of FBG, the center wavelength shift of FBG is affected by both strain and temperature changes. Thus, the central wavelength shift ∆λB S of the FBG attached to the strain beam is

∆λ B S = kε × εy′ + (α + ξ ) × ∆T λB

(18)

Therefore, after all the part sizes and materials are determined, the linear relationship between the wavelength change and the pressure inside the pipeline is shown as follows: p=K×

∆λ B λB

(19)

where K is the linear coefficient of the strain measurement. 4. Simulation, experiment, and discussion 4.1. Analysis of pipeline wall strain under internal pressure

(16)

Therefore, the effect of temperature is eliminated by subtracting Eq. (16) from Eq. (15); the result is shown as Eq. (17).

∆λ B ∆λ B S ∆λB T = − = kε × εy′ λB λB λB

k × kε × kp × ks × p × u × h × y ∆λB = λB hy × z × E × x

(15)

where λB is the central wavelength (m), α is the thermal expansion, ξ is the thermo-optical coefficient, and kε is the linear strain coupling coefficient of strain and wavelength change. For a typical fused silica fiber, kε = 0.78. The temperature-compensating beam and the strain beam are close to each other; the temperature effects on FBGs attached to the two beams are considered to be identical. Since one end of the temperature-compensating beam is disconnected from the base, the position of the temperature-compensating beam may not produce strain. Thus, the wavelength shift ∆λB T of the FBG attached to the temperature-compensating beam is

∆λ B T = (α + ξ ) × ∆ T λB

central wavelength changes of the FBG and the measured pipeline pressure have the following mathematical model:

(17)

Eq. (17) shows that the difference between the wavelengths of the two FBGs is only related to the strain variation. Thus, the cross-sensitivity problem of FBG sensors is solved; that is, the

A thin-walled straight pipeline processed from a structural steel material was used as the model in accordance with the actual measurement requirements. The pipeline was designed to have an inner diameter of 120 mm, a wall thickness of 2 mm, and a pipeline length of 500 mm. A static pressure load of 1 MPa was applied inside the pipeline, and the external pressure load (atmospheric pressure) was 0.1 MPa. Fig. 5 presents the equivalent elastic strain distribution of the pipeline wall under a pressure of 1 MPa on the inner surface. The figure shows that the inner surface is subjected to the largest strain while the outer surface is subjected to the smallest strain. From the inside to the outside of the pipeline wall, the strain gradually decreases. The theoretical value of the pipeline strain is consistent with the finite element value obtained by ANSYS; besides, the relative errors of both values are below 0.1%. Fig. 6 shows the variation of the strain from the inner to the outer walls along the radial direction of the pipeline. Apparently, the radial strain of the pipeline has an approximately linear increase from the inner wall to the outer wall; the circumferential strain has an approximately linear decrease; the axial strain remains unchanged. Besides, the equivalent elastic strain is consistent with the circumferential strain change and has an approximately linear decrease because it is mostly affected by the circumferential stress. Through leastsquares linear fitting, the mathematical relationships of radial

Please cite this article as: Z. Yan, G. Chen, C. Xu et al., Design and experimental study of a sensitization structure with fiber grating sensor for nonintrusive pipeline pressure detection. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.01.036.

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Fig. 5. Equivalent elastic strain distribution of the pipeline wall.

Fig. 6. Simulation curve of strain along with the pipeline wall radial variation.

strain ε r , circumferential strain ε θ , axial strain ε z , and equivalent elastic strain ε v with thickness L can be expressed as Eqs. (20) to (23), with fitting degrees of 0.99983, 0.99983, 0.9995, and 0.99983, respectively.

εr = 3.243 × 10−6 × L − 7.287 × 10−5

(20)

εz = 2.212 × 10−8 × L + 2.962 × 10−5

(21)

εθ = −3.258 × 10−6 × L + 1.318 × 10−4

(22)

εν = −4.334 × 10−6 × L + 1.365 × 10−4

(23)

Fig. 7. Strain cloud map of the rhomboid structure.

4.2. Simulation analysis of the sensitization ability of the doublebeam rhomboid structure The rhomboid structure was modeled and meshed with the initial values provided in Table 1. A tensile force of 25 N was applied to the left and right end faces of the rhomboid structure simultaneously at 25 ◦ C environment temperature; then, the stress–strain transmission was observed and analyzed. The result is presented in Fig. 7. The beams of the rhomboid structure exhibit a uniform strain distribution; meanwhile, the difference in strain values is obvious, meeting the requirements for an FBG pasting package. Moreover, Fig. 8 shows the strain sensitivity of the strain beam and the temperature-compensating beam under the tensile force of 5–25 N. As the tensile force increases, the strain of the strain beam linearly increases. The temperaturecompensating beam is insensitive to the force load and can meet

Fig. 8. The strain sensitivity of the strain beam and the temperaturecompensating beam.

the requirements for an FBG to independently reflect temperature changes, thereby providing temperature compensation for strain measurement. The material selection and design dimensions were meticulously simulated to further analyze the strain amplification and sensitization ability of the rhomboid structure (see Fig. 9). Due to the sensitizing capability of the rhomboid structure, the long diagonal y is required to be larger than the short diagonal x. Considering the installation and fixing of the FBG, the three dimensions of x, z, and hy were fixed during the simulation. The

Please cite this article as: Z. Yan, G. Chen, C. Xu et al., Design and experimental study of a sensitization structure with fiber grating sensor for nonintrusive pipeline pressure detection. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.01.036.

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Fig. 9. Strain simulation effects for different sizes and materials. (a) Strain simulation data of different w; (b) Strain simulation data of different u; (c) Strain simulation data of different v; (d) Strain simulation data of different y; (e) Strain simulation data of different h; (f) Strain simulation data for different materials.

initial values of other dimensions are provided in Table 1. Forces of 5, 10, 15, 20, and 25 N were successively applied to both ends of the rhomboid structure; moreover, the influences of u, v, w, y, h, and the rhomboid structure’s metal materials on the strain of the variable beam were obtained. The strain sensitivity of each size is presented in Fig. 10. As shown in Fig. 9, the strain change of the strain beam and the force load change of the rhomboid structure composed of different sizes and materials show an acceptable linear relationship. The strain sensitivity of the rhomboid structure is affected by the elastic modulus of the material. Besides, as the elastic modulus increases, its value gradually decreases and the magnification of the rhomboid structure for measuring strain is also reduced. As shown in Fig. 10, size parameter w has no effect on the strain measurement sensitivity of the rhomboid structure. As the size parameters u and h increase, strain detection sensitivity shows an approximate linear reduction and size parameter h exhibits a relatively greater influence on sensitivity than size parameter u. As the size parameter y increases, strain sensitivity displays an approximately linear increase. Meanwhile, as size parameter v increases, strain sensitivity exponentially decreases. The preceding analysis suggests that the beam design can accurately reflect the force load applied to the two ends of the rhomboid structure; furthermore, it can be found that there is a stable and good linear relationship between the strain of the strain beam and the force load. An analysis of the simulation results shows that the values of v, u, and h are as small as possible based on the premise of meeting the strength requirements; the value of y exerts a highly stable linear influence on the sensitivity of the rhomboid structure to measure strain. Therefore, the strain magnification can be flexibly customized by the value of y.

Table 1 Initial value of the rhomboid structure. Parameter

u

v

w

x

y

z

h

hy

Material

Initial value (mm)

2

2

3

9

45

1

4

1

65 Mn steel

4.3. Sensitization characteristics of the double-beam rhomboid structure under internal pressure 4.3.1. Fluid–solid coupling theory model 4.3.1.1. Liquid flow model. The sensitization characteristics of the double-beam rhomboid structure derive from the deformation coupling among fluid motion, the pipeline, and the sensitizing component. Coupling only occurs at the two-phase interface and is reflected by the equilibrium condition on the two-phase interface. The flow process of any fluid follows the laws of conservation, including those of mass, momentum, and energy [20–24]. The mass conservation equation can be expressed as

∂ρ ∂ (ρ u) ∂ (ρv ) ∂ (ρw) + + + =0 ∂t ∂x ∂y ∂z By introducing the vector div (ρ U) = Eq. (24) can be written as

(24) ∂ (ρ u) ∂x

+

∂ (ρv ) ∂y

+

∂ (ρw ) , ∂z

∂ρ + div (ρ U) = 0 (25) ∂t where ρ is the density (ppg); t is the time (s); U is the velocity vector (m/s); and u, v, and w are the components of the velocity vector U in the x, y, and z directions (m/s). The momentum conservation equation can be expressed as follows:

∂ (ρ u) ∂P ∂ (τxx ) ∂ (τyx ) ∂ (τzx ) + div (ρ uU) = − + + + + Fx (26) ∂t ∂x ∂x ∂y ∂z

Please cite this article as: Z. Yan, G. Chen, C. Xu et al., Design and experimental study of a sensitization structure with fiber grating sensor for nonintrusive pipeline pressure detection. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.01.036.

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Fig. 10. The strain sensitivity of different sizes. (a) Strain sensitivity of different w; (b) Strain sensitivity of different u; (c) Strain sensitivity of different v; (d) Strain sensitivity of different y; (e) Strain sensitivity of different h.

∂ (ρv ) ∂P ∂ (τxy ) ∂ (τyy ) ∂ (τzy ) + div (ρv U) = − + + + + Fy (27) ∂t ∂y ∂x ∂y ∂z ∂ (ρw ) ∂P ∂ (τxz ) ∂ (τyz ) ∂ (τzz ) + div (ρw U) = − + + + + Fz (28) ∂t ∂z ∂x ∂y ∂z where P is the pressure on the fluid microcell (Pa); τ is the shear stress (Pa); and Fx , Fy , and Fz are the forces on the microcells (N). The energy conservation equation can be expressed as follows:

∂ (ρ T ) ∂ (ρ uT ) ∂ (ρv T ) ∂ (ρw T ) ∂ k ∂T + + + = ( ) ∂t ∂x ∂y ∂z ∂ x cP ∂ x ∂ k ∂T ∂ k ∂T + ( )+ ( ) + ST (29) ∂ y cP ∂ x ∂ z cP ∂ z where cp is the specific heat capacity (J/(kg×K)); T is the temperature (K); k is the heat transfer coefficient of the fluid; ST is a viscous dissipation term, namely, the internal energy of a fluid and the thermal energy converted by mechanical energy due to viscosity. 4.3.1.2. Standard k − ε model. The standard k − ε model [25], as shown in Eqs. (30) to (31), is the most widely used turbulence model in recent years.

∂ µt ∂ k ∂ (ρ k) ∂ (ρ kui ) + = [(µ+ ) ]+ Gk + Gb −ρε− YM + Sk (30) ∂t ∂ xi ∂ xj σk ∂ xj ∂ (ρε ) ∂ (ρεui ) ∂ µt ∂ε ε + = [(µ + ) ] + C1ε (Gk + C3ε Gb ) ∂t ∂ xi ∂ xj σε ∂ xj k ε2 − C2ε ρ + Sε k

(31)

where k is the kinetic energy (m2 /s2 ); ε is the dissipation rate (m2 /s3 ); ui is the velocity component (m/s); µ is the hydrodynamic viscosity (N×s/m2 ); Gk is the generic term of the turbulent

flow energy k caused by the average velocity gradient; Gb is the generation term of the turbulent flow energy k caused by buoyancy; YM is the contribution of pulsation expansion in compressible turbulence, YM = 0; C1 ε , C2 ε , and C3 ε are empirical constants equal to 1.44, 1.92, and 0; σ k and σ ε are Prandtl numbers corresponding to kinetic energy k and dissipation rate ε , which are equal to 1.0 and 1.3; and Sk and Sε are user-defined source items. 4.3.1.3. Basic conditions of the fluid–solid coupling interface. The basic conditions applied to the fluid–solid coupling interface are kinematic and dynamic conditions. Kinematic conditions are also called displacement coordination. Then, df = ds ; X ∈ Si , t ∈ [0, T ]

(32)

A dynamic condition, also called force balance, represents the stress balance of the fluid and solid domains in the direction of the vertical boundary. n · τf = n · τs ; X ∈ Si , t ∈ [0, T ]

(33)

where τ f and τ s are fluid and structural stresses (Pa); n is a unit normal vector; df and ds are displacements of fluids and structures (m); X is the geometric point coordinate; Si is a fluid– solid coupling surface; T is the total time of transient calculation (s), and t is the time (s). 4.3.2. Simulation result analysis The overall structure that consists of various components (rhomboid structure, two-petal hoop, fastener, and pipeline with pressure holes) was simulated. The dimensions of each fitting are provided in Table 2. The friction coefficients of each contact surface were set as 0.2. The environment temperature was set as 25 ◦ C. One end of the pipeline was provided with a pressure hole that was 20 mm in diameter; besides, a pressure of 0–1 MPa was

Please cite this article as: Z. Yan, G. Chen, C. Xu et al., Design and experimental study of a sensitization structure with fiber grating sensor for nonintrusive pipeline pressure detection. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.01.036.

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Z. Yan, G. Chen, C. Xu et al. / ISA Transactions xxx (xxxx) xxx Table 2 Parts size. Name

Material

Size

Pipeline Hoop Rhomboid structure

304 stainless steel 304 stainless steel 7075 aluminum alloy

Fastener

Alloy steel

Inner diameter 120 mm, wall thickness 2 mm Thickness 4 mm, width 10 mm x = 9 mm, y = 13.5 mm, 22.5 mm, 31.5 mm, 40.5 mm (the ratio of the long diagonal to the short diagonal y/x: 1.5, 2.5, 3.5, 4.5), v = 2 mm, h = 4 mm M5 × 25

Table 3 Effect of friction on strain sensitivity of sensitization structure. Pressure (MPa)

0.2 0.4 0.6 0.8 1

Strain (µε) Friction coefficient = 0.1

Friction coefficient = 0.15

Friction coefficient = 0.2

148.47 290.57 438.72 585.45 720.53

147.46 287.98 434.96 580.63 715.88

143.68 286.33 423.08 573.01 703.74

applied by water injection through the pressure hole. The strain measurement effect of the sensitization structure was simulated under different y values. Fig. 11 shows the strain of the sensitization structure (aspect ratio of 2.5) coupled to the pipeline when a water pressure of 1 MPa was applied. As shown in Fig. 11(b), the pressure gradient at the inlet is relatively dense, and the range of variation is relatively small, whereas the pressure on the fluid– solid coupling surface is relatively uniform and stable. Fig. 11(c) indicates that the strain distribution in the outer wall of the pipeline is relatively stable; moreover, the strain on the pipeline wall can be effectively transmitted to the rhomboid structure through the hoop of the sensitization structure. Furthermore, the strain distribution of the strain beam of the rhomboid structure is uniform and significantly larger than the strain value of the pipeline wall. Besides, in the rhomboid structure for different y/x, the axial direction of the outer wall of the pipeline exhibits a characteristic that the strain in the middle is less than those at both sides due to the restraining effect of the hoop on the pipeline wall. Fig. 12 shows the strain distribution in the axial direction of the outer wall of the pipeline under an internal pressure of 1 MPa. The wall strain at the hoop-restraint position is the smallest when y/x = 1.5; it gradually increases as y/x increases. The variation

in strain sensitivity of the rhomboid structure with different y/x is shown in Fig. 13. The rhomboid structure has the highest strain sensitivity when y/x = 1.5. Figs. 11 and 12 show that the smaller the ratio of the long diagonal to the short diagonal of the rhomboid structure, the stronger the restraining ability of the sensitization structure on the pipeline, the tighter the fit with the pipeline wall, and the better the transmission of strain. The strain sensitivity of the sensitization structure is optimal when the y/x of the rhomboid structure is approximately 1.5. Under different conditions, it can be found that there is a stable and good linear relationship between the pressure inside the pipeline and the strain of the rhomboid structure’s strain beam. The transmission of strain between the hoop and the outer wall of the pipeline is primarily achieved through friction. Therefore, the rhomboid structure of y/x = 1.5 is adopted for simulation on the premise that all the simulation conditions remain unchanged. The friction coefficients of the inner part of the hoop that is in contact with the pipeline wall are 0.1, 0.15, and 0.2. The results in Table 3 show that the smaller the friction coefficient, the higher the sensitivity. However, the overall variation range is extremely small. The amplification effect of the sensitization structure is provided in Table 4. The relative error between the theoretical value and the finite element value obtained through simulation is less than 0.1. Moreover, the strain value of the strain beam of the sensitization structure is considerably increased compared with the strain value of the pipeline wall. The optimal amplification effect can reach approximately five times. 4.4. Experimental test and results 4.4.1. Experimental system For the design of the rhomboid structure of 7075 aluminum alloy with y/x = 2.5, the related nonintrusive detection experiments were designed on the basis of the aforementioned theoretical

Table 4 The amplification effect of the sensitization structure. y/x

Pressure (MPa)

Theoretical value of pipeline wall strain (µε)

Simulation value of pipeline wall strain (µε)

The strain of the strain beam (µε)

Magnification

1.5

0.2 0.4 0.6 0.8 1

25.56 51.11 76.67 102.22 127.77

25.57 51.13 76.70 102.26 127.83

143.68 286.33 423.08 573.01 703.74

5.6 5.6 5.6 5.6 5.6

2.5

0.2 0.4 0.6 0.8 1

25.56 51.11 76.67 102.22 127.77

25.57 51.13 76.70 102.26 127.83

108.26 213.36 320.76 429.32 534.85

4.2 4.2 4.2 4.2 4.2

3.5

0.2 0.4 0.6 0.8 1

25.56 51.11 76.67 102.22 127.77

25.57 51.13 76.70 102.26 127.83

71.26 141.27 208.66 280.23 346.37

2.8 2.8 2.8 2.8 2.8

4.5

0.2 0.4 0.6 0.8 1

25.56 51.11 76.67 102.22 127.77

25.57 51.13 76.70 102.26 127.83

47.68 92.27 139.32 190.02 238.79

1.9 1.9 1.9 1.9 1.9

Please cite this article as: Z. Yan, G. Chen, C. Xu et al., Design and experimental study of a sensitization structure with fiber grating sensor for nonintrusive pipeline pressure detection. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.01.036.

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Fig. 11. Simulation of sensitization structure (y/x = 2.5) and pipeline coupling. (a) The sensitization structure model; (b) Fluid pressure distribution in the pipeline; (c) Strain distribution of the sensitization structure and the pipeline.

Fig. 12. Axial direction strain distribution of the outer wall of the pipeline. (It is the hoop constraint position when the abscissa is 0.)

Fig. 13. The strain sensitivity of rhomboid structures with different y/x.

analysis and simulation research. An experimental device that detects pipeline internal pressure is shown in Fig. 14. The experimental system includes a pressure pump, pressure gauge, stainless steel pipelines, a rhomboid sensitization structure, an FBG demodulator, and spectrum measuring software. Both sides of the stainless-steel pipeline (with a length of 500 mm, the

inner diameter of 120 mm, and the wall thickness of 2 mm) were fixed with flanges. A pressure pump within a range of 0–4 MPa was connected to the pipeline where a sensitizing rhomboid structure was mounted; two FBGs with center wavelengths of 1536 nm and 1539 nm were adhered to the strain beam and the temperature-compensating beam of the rhomboid structure by the epoxy resin. The two FBGs were connected to the SM125 fiber demodulator produced by Weiguang company through two Ferrule connector/angled physical contact (FC/APC) optical connectors. The standard pressure gauge was adopted in this sensing system to calibrate the proposed pressure sensor mainly consisting of sensitization rhomboid structure and FBGs. The measurement range of the standard pressure gauge was 0∼2 MPa, and its accuracy was ±0.2%. At a steady room temperature of around 25 ◦ C, the pipeline was pressurized by the pump and the pressure inside the pipeline was measured by the gauge. The pressure range is 0.1–1 MPa with each increment of 0.1 MPa. Three sets of data were acquired and their average values were calculated at each pressure point. The wall strain caused by the change in the pressure inside the pipeline is transmitted to both sides of the rhomboid structure through the two-valve hoop and the fastener, causing strain changes in the strain beam. Then, the shift of center wavelength of the FBG that is caused through the adhesive layer was observed at the user interface. The fiber demodulation device can efficiently identify the central wavelength of the reflection spectrum of the FBGs attached to the strain beam and the temperaturecompensating beam respectively. Besides, the optical channel can be flexibly selected; then, the offset of multiple spectra can be observed.

4.4.2. Analysis of the experimental data without sensitization structure First, an FBG was directly attached to the circumferential position of the pipeline wall to measure the wall strain of the nosensitized structure, as shown in Fig. 15. Considering that the FBG with a center wavelength of 1536 nm has a strain sensitivity of 1.198 pm/µε, the pressure sensor should possess a pressure sensitivity of 153.14 pm/MPa. The experimental results show that the sensitivity of the pressure measurement system is 122.6 pm/MPa, which is slightly lower than the theoretical analysis. However, this deviation is determined by introducing a calibration factor K to obtain a corrected wavelength shift. The sensitivity after correction is 153.1 pm/MPa.

Please cite this article as: Z. Yan, G. Chen, C. Xu et al., Design and experimental study of a sensitization structure with fiber grating sensor for nonintrusive pipeline pressure detection. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.01.036.

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Z. Yan, G. Chen, C. Xu et al. / ISA Transactions xxx (xxxx) xxx

Fig. 14. Pipeline internal pressure detection experimental system.

Fig. 15. Strain measurement results without sensitization structure.

Fig. 16. Strain measurement results based on sensitization structure.

4.4.3. Analysis of the experimental data with sensitization structure The measurement results with the sensitization structure are shown in Fig. 16. The rhomboid structure shows an acceptable linear relationship with the center wavelength shift and the pressure change in the pipeline. The strain value was effectively expanded through the sensitization structure; besides, the corresponding center wavelength shift was also relatively increased by sensor measurement. The theoretical sensitivity of the pressure measurement system is 640.75 pm/MPa; the experimental sensitivity is 513.11 pm/MPa; the sensitivity is 641.41 pm/MPa after the introduction of the calibration factor. The main reasons for the low sensitivity of the experimental system are as follows. (1) The strain of the strain beam was transferred to the FBG by the epoxy resin. However, the strain cannot be completely transferred to the FBG due to the toughness of the glue. Moreover, the FBG may not be tightly attached to the strain beam. Meanwhile,

a parameter deviation is available between the simulation and the actual manufacturing. (2) The artificial error was caused by manual pressurization and reading processes. 5. Conclusion This study focused on the theoretical and experimental research of the nonintrusive pipeline pressure measurement of an FBG. With the sensing advantage of the FBG, a sensitization structure consisted of a double-beam rhomboid structure, a tworing hoop with ears, and a fastener was proposed for pipeline inner pressure detection. The major conclusion can be drawn as follows. (1) The type and production principle of the stress and strain of the pipeline were analyzed. The influences of factors

Please cite this article as: Z. Yan, G. Chen, C. Xu et al., Design and experimental study of a sensitization structure with fiber grating sensor for nonintrusive pipeline pressure detection. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.01.036.

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such as pipeline material, size, and internal pressure on the strain of the pipeline wall were determined. From the theoretical and simulation analyses, a stable and favorable linear relationship between the strain of the pipeline wall and the pressure inside the pipeline was found. (2) The sensitization structure of the FBG sensor was designed with a double-beam rhomboid structure as the core and coupled with a two-petal hoop structure. The mathematical model of the sensitization structure was derived using material and elastic mechanics theory. (3) Fluid–solid coupling simulation was performed; the simulation models of the pipeline, fluid, and sensitization structure were established; then, the rationality of the pipeline pressure sensor design was verified. Moreover, the material and size of the rhomboid structure were optimized. The sensitization structure with a rhomboid structure of y/x = 1.5 and a material of 7075 aluminum alloy achieved the best sensitizing effect. The strain of the pipeline wall can be amplified 5.6 times. An FBG-based pipeline pressure verification experiment was performed several times. The experimental results indicate that the design with y/x = 2.5 and the rhomboid structure made of 7075 aluminum alloy exerted stable and effective transfer effects on wall strain. Therefore, it can be proved that the wall strain caused by the internal pressure of a pipeline can be effectively amplified without damaging the pipeline wall by using the sensitization structure proposed in this study. Lastly, nonintrusive measurement of pipeline pressure was realized. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments We would like to acknowledge the anonymous reviewers for their valuable suggestions and corrections, and thank the financial support of Key R & D project of Shandong Province (No. 2019GHY112080), State key laboratory of precision measuring technology and instruments (No. PIL1604) and Fundamental Research Funds for the Central Universities (18CX02108A, 14CX02204A). References [1] Fultz DW, Allen JS. Nonintrusive pressure measurement in microfluidic systems via backscattering interferometry. Exp Fluids 2014;55(1754):1–12. http://dx.doi.org/10.1007/s00348-014-1754-0. [2] Golyamina IP, Greshilov EM, Mironov MA, Rastorguev DL. The use of distributed pressure receivers based on elastic piezoelectric composite materials for measuring the hydrodynamic noise produced by a nearwall turbulence. Acoust Phys 2001;47:392–7. http://dx.doi.org/10.1134/1. 1385411. [3] Wang D, Song Z, Wu Y, Jiang Y. Ultrasonic wave based pressure measurement in small diameter pipe. Ultrasonics 2015;63:1–6. http://dx.doi.org/ 10.1016/j.ultras.2015.06.002.

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Please cite this article as: Z. Yan, G. Chen, C. Xu et al., Design and experimental study of a sensitization structure with fiber grating sensor for nonintrusive pipeline pressure detection. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.01.036.