Journal Pre-proof Ultrasensitive all-fiber inline Fabry–Perot strain sensors for aerodynamic measurements in hypersonic flows Zhendong Xie, Xiu He, Yaqin Xiao, Tingting Yang, Bin Wang, Zengling Ran, Yunjiang Rao, Fu Min, Huacheng Qiu, Yanguang Yang, Wangwei Chu, Debiao Zeng
PII: DOI: Reference:
S0019-0578(20)30083-5 https://doi.org/10.1016/j.isatra.2020.02.020 ISATRA 3500
To appear in:
ISA Transactions
Received date : 18 April 2019 Revised date : 14 February 2020 Accepted date : 15 February 2020 Please cite this article as: Z. Xie, X. He, Y. Xiao et al., Ultrasensitive all-fiber inline Fabry–Perot strain sensors for aerodynamic measurements in hypersonic flows. ISA Transactions (2020), doi: https://doi.org/10.1016/j.isatra.2020.02.020. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Ultrasensitive All-Fiber Inline Fabry–Perot Strain Sensors for Aerodynamic Measurements in Hypersonic Flows
Zhendong Xie1,2,#, Xiu He1,#, Yaqin Xiao1, Tingting Yang1, Bin Wang1, Zengling Ran1,*, Yunjiang Rao1, Fu Min2, Huacheng Qiu2, Yanguang Yang2, Wangwei Chu3, Debiao Zeng3
Fiber Optics Research Center, Key Laboratory of Optical Fiber Sensing & Communications (Ministry of Education), University of Electronic Science & Technology of China, Chengdu, Sichuan, 611731, China 2China Aerodynamics Research and Development Center, Hypervelocity Aerodynamics Institute, Mianyang, Sichuan, 621000, China 3Chengdu Aircraft Industrial Group Co., Limited, Chengdu, Sichuan, 610092, China # These authors contributed equally to this work and should be considered co-first authors *Corresponding author,
[email protected]. 1
Ultrasensitive All-Fiber Inline Fabry–Perot Strain Sensors for Aerodynamic Measurements in Hypersonic Flows
Abstract: This work proposes an ultrasensitive, temperature-insensitive, all-fiber inline Fabry–Perot (FP) strain sensor for aerodynamic coefficients
measurements of a hypervelocity ballistic correlation model 2 in a Φ1 hypersonic wind tunnel. The FP sensors fabricated using 157 nm laser
micromachining system are structurally simple, small-sized, and high-
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temperature resistance. 16 FP sensors are installed on a six-force balance,
which is mounted inside the model, to sense the aerodynamic forces and moments of the model, and then the model’s aerodynamic coefficients are calculated based on aerodynamic theory according to the test data. A new
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temperature-compensated method is proposed to improve measurement accuracy of aerodynamic coefficients via eliminating temperature-induced measurement errors. Experimental results show, at high temperatures, the FP sensors based on the balance (FP balance) exhibits a high-repeatability precision of the aerodynamic coefficients measurement of less than 1%, and
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match well with the results of the traditional method using foil-resistive
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strain sensors. This enhanced-sensitivity FP sensor is currently the most promising alternative to foil-resistive strain sensors for aerodynamic tests
among kinds of fiber-optic strain sensors to the best of our knowledge. The
FP balance satisfies the requirements of practical application of aerodynamic characteristic tests, and opens up another test system of the field.
Keywords: Aerodynamic measurement; All-fiber Fabry–Perot strain sensors; Fiber balance; Wind tunnel 1. Introduction
Balances are the most basic and important equipment in aerodynamic
characteristic tests of various aerospace, transportation, energy, and building models. A key component in balance is the strain sensor, which directly
affects its measurement accuracy, operating temperature, and environmental applicability. For decades, foil-resistive (FR) strain sensors have been
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employed in aerodynamic measurements. On the downside, however, the balance based on FR strain sensors (FR balance) has a low measurement
accuracy at high temperatures and is easily affected by interference by the surrounding electromagnetic fields. With the increasing high-accuracy
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requirement of balance measurement systems in hypersonic wind tunnel aerodynamic tests [1, 2], a technology that can solve the balance instability for aerodynamic measurements in a harsh environment is highly desirable. On this note, optical fiber strain sensors have been extensively used in many fields, such as structural health monitoring, aerospace, and nanotechnology, with their unique characteristics of electromagnetic interference resistance, 2
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high-temperature resistance, small size, and high sensitivity [3–5]. Two
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sensors of this type have been specifically applied to the balance for aerodynamics characteristic tests, namely, Fabry–Perot (FP) strain sensors [6–10] and fiber Bragg grating sensors (FBGs) [11–17]. As for FP,
Vasudevan et al [6,7] firstly demonstrated multi-component wind tunnel
balance incorporating capillary-based FP strain sensors, and indicated the fiber-optic system was at least as good as the FR sensor system. Edwards [8] demonstrated the capillary-based FP strain sensors had a better resolution and accuracy than FR strain sensors. Qiu et al [9,10] demonstrated wind
tunnel balances using micro-opto-electro-mechanical-based FP strain sensors (MOEM FPs) and all-fiber FP sensors respectively, and the former
[9] had a bad repeatability of the axial force coefficient due to no temperature compensation, the latter [10] had a large temperature-strain cross sensitivity (6.8 με/℃) resulting in a low measurement accuracy in
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temperature-changing environments. For FBGs, Pieters et al [11-14] proved
that a ‘two-groove’ FBGs internal four-component balance had a better sensitivity and resolution than FR balance. Burger [15] revealed that FBGsbased sidewall wind balance displayed a poor creep characteristic of the
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order of 0.8%. David [16] demonstrated the static calibration precision of the FBGs-based platform wind tunnel balance was within 0.868% which dissatisfied the standard value (≤0.5%). Although a large of aerodynamic characterization studies have been performed using these sensors, some disadvantages of them are detrimental as an alternative to FR sensors on wind tunnel balances. For example, the capillary-based FPs have poor 3
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sensing performance consistency, the low-sensitive all-fiber FPs have large
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temperature-strain cross-sensitivity, FBGs need to pre-tension during bonding and have a high temperature sensitivity. Therefore, there is urgent
to develop an ultrasensitive, temperature-insensitive, small-size all-fiber strain sensor for aerodynamic characteristics measurements.
This paper demonstrates ultrasensitive, temperature-insensitive, all-
fiber inline FP strain sensors applied to a six-component force balance for
aerodynamic measurements in a hypersonic wind tunnel. The FP sensor,
fabricated using a 157 nm laser machining system, is advantageously simple, small-sized, and high-temperature-resistant. A temperature-compensated
method is proposed and temperature tests of the balance based on the FP strain sensors (FP balance), show good temperature stability. In addition, a
static calibration experiment that is conducted to calibrate the output value
of the FP balance to true loads through a linear fit indicates the FP balance’s
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high-static calibration accuracy of less than 0.4%. Moreover, the FP balance is used to measure the aerodynamic coefficients of the hypervelocity
ballistic correlation model 2 (HB-2) in Mach 4 and Mach 8 hypersonic flows, with the results showing its excellent repeatability precision of less than 1%,
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for the aerodynamic coefficients measurements, which is consistent with the results for the conventional FR balance. As such, the FP strain sensors offer an extreme potential for different kinds of aerodynamic testing balances in many fields under harsh environments, including missiles, hypersonic aircraft, manned spacecraft, and automobiles, and are the most competitive alternative to the FR sensors for aerodynamic testing. The FP balance 4
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satisfies the requirements of practical application of aerodynamic
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characteristic tests, and opens up another test system of the field. 2. Material and methods
2.1. Principle of the FP strain sensor 2.1.1. Structural design
Fig. 1 shows a schematic of the FP strain sensor [18]. The FP cavity is formed by splicing a single-mode fiber (SMF, lead in fiber) and a highly
doped large-diameter fiber. The tail of this large-diameter fiber is cleaved
with an oblique angle to avoid any additional interference. The relationship between the output value of the FP sensor and strain applied to it is expressed
by [18]: Δλε=λ0(L0+L1)/L0 • ε, where λ0 and Δλε are the initial resonant
wavelength of the FP sensor and its initial resonant wavelength shifts
induced by strain, respectively; L0 and L1 are the cavity length and the gutter
depth of the FP, respectively. Compared to the conventional FP sensor [19]
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with only L0 and fiber materials, this FP possesses lager strain sensitivity due to the exist of L1. The relationship between FP air cavity length and temperature variation is expressed by [18]: ΔL0,T=[Cclad(L0+ L1)-CdopedL1]
•ΔT, ΔL0,T is the air cavity length variation of the sensor over its temperature
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changing by ΔT; Cclad and Cdoped are the thermal expansion coefficients of the fiber cladding and doped parts, respectively. The cladding expansion increases the FP air cavity length whereas the doped region expansion decreases the cavity length. Because the doped region expansion coefficient (Cdoped) is much larger than that of the pure silica cladding (Cclad) expansion
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leads to an overall decrease in cavity length. Therefore, a lower temperature
2.1.2. Fabrication
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sensitivity of the FP sensors is achieved [20].
The FP strain sensor was fabricated using a 157 nm laser micromachining
system [21], through the four steps shown in Fig. 2. In the first step [Fig. 2(a)], cleaving was performed to trim the sensor-forming surface on a
cleaved highly doped large-diameter fiber. Next, a microhole was drilled at the cleaved fiber end using a circle mask [Mask I, Fig. 2(b)]. Afterward, a
ring-shaped mask (Mask II) was used to machine a wedge gutter structure around a microhole [Fig. 2(c)]. The last phase [Fig. 2(d)] encompassed
fusion splicing of the etched and tailed fibers. These aside, the fiber tail was
cut with an oblique angle to a distance away from the FP cavity for avoiding any additional interference.
Fig. 3(a) shows a micrograph of the FP stain sensor. The cavity depth (L0)
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is approximately 27 μm, and the gutter depth (L1) corresponds to 224 μm. Fig. 3(b) shows the reflection spectrum of this sensor. 2.2. FP-sensor-based balance
A six-component force balance was used to obtain the axial (FA), normal
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(FN), and side (FZ) forces as well as the pitching (MZ), yawing (MY), and roll (MX) moments on an aircraft or spacecraft model, as schematically shown
in Fig. 4(a). Its mechanical body was designed to contains 6 different structures for measuring these 6 aerodynamic forces/moments. Each structure is sensitive to the load of corresponding measuring aerodynamic component, producing a relatively obvious deformation, but insensitive to 6
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other aerodynamic component loads, producing as little deformation as
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possible. The installation positions of the FP sensors are determined by the stress-strain distribution of each structure under corresponding aerodynamic
component load. The output signals of the FP sensors are combined based on the characteristics of the deformation, to obtain the maximum
combination output of the sensors under the measuring aerodynamic
component load, and little output under other aerodynamic component loads. 16 FP strain sensors were fixed on the balance using two-point paste technology to convert the strain of the balance, induced by applied force, to
wavelength shifts of the sensors, with their mounting positions shown in Fig. 4(b). Fig. 4(c) shows a physical drawing of the FP balance, and the
relationship between each aerodynamic component and a combination output of the sensors is shown in Table I.
2.3. Temperature-compensated method
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A large temperature variation during the hypersonic wind flow caused a
large thermal drift of the sensors in the balance, leading to a lower measurement accuracy. The heat transfer of the balance is mainly from its head to other parts during wind flow since only its head touches the
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measured model, and the heat area of the head is different at the different angles of attack (AoA), which depends on its windward surface. The temperature distributions simulations of the balance with different angles of attack are carried out, using finite element analysis method, as shown in Fig. 5. The simulation parameters, including the heat capacity at constant pressure, density, and thermal conductivity, are set to 461 J/(kg·K), 8000 7
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kg/m3, 20.9 W/(m·K), respectively. Fig. 5(a) and Fig. 5(b) respectively show
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the temperature distributions of the balance with the angle of attack of 0° and 12°, corresponding to its whole head and the windward surface of the
head being heated up to 80 ℃, respectively. Their insets show the symmetric
locations of the balance have almost the same temperature and their maximum temperature difference is within 1℃, which can be neglected since the strain-temperature cross sensitivity of the FP sensors is only 0.016 με/℃ [18].
According to the symmetric locations of the balance having the same temperature, a new temperature-compensated method is proposed to
eliminated the influence of the output value of the sensor induced by
temperature variations on the aerodynamic component measurements. The temperature-compensated theory is described as follows:
Induced by the strains and temperatures, the output value of the sensor
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can be expressed by Δλi=Δλi,ε+λi,T, i=1,2,3,…,16, where Δλi is the output value of the 𝑖th sensor in the FP balance, and Δλi,ε and Δλi,T are the output
values of the 𝑖th sensor induced by the strain and temperature variations, respectively. From the combination calculations in Table I, the outputs of the
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sensors in one of the aerodynamic components’ directions can be expressed by
FN = 1 2 3 4 (1, 1,T )+(2, 2,T ) (3, 3,T ) (4, 4,T ) (1) (1, 2, 3, 4, )+( 1,T 2,T 3,T 4,T )
where ∆𝜆
∆λ , ∆λ , is the combination output value of the sensors in the normal 8
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force direction; ∆𝜆
,
and ∆𝜆
,
are the combination output values of
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the sensors in the normal force direction induced by strain and temperature variations, respectively. In this case, the temperature part (∆𝜆
,
) should be
zero in order to eliminate the influence of temperature on the normal force measurement. Moreover, a thermal drift mainly coming from the thermal expansion of the substrate results in the same direction of the output value of all sensors. By finding temperature-compensated coefficients, or the
ratios of the temperature output values of the two symmetric sensors, in Eq. (1), the temperature part (∆𝜆
,
) can be zero. Particularly, these coefficients
can be defined by Ci,j=Δλi,T/Δλj,T, where i and j, respectively, represent the
ith and jth sensors, arranged to the symmetrical locations of the balance. Therefore, the combination output value of the sensors in the normal force direction can be modified by
FN = C3,11 C4,22 3 4
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(C3,11, C4,22, 3, 4, )+( C3,11,T C4,22,T 3,T 4,T ) (2) = C3,11, C4,22, 3, 4,
=0
From Eq. 2, the combination output of the sensors in the normal force direction is independent on temperature if the temperature-compensated
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coefficients are independent on temperatures. From temperature test of the FP balance, the temperature-compensated coefficients all are constants. Therefore, this temperature-compensated method can effectively solve the measurement deterioration caused by temperatures theoretically. Moreover, to obtain excellent temperature compensation effect. First, the two sensors should be precisely installed to symmetric positions on the balance. Second,
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their cavity length is the same (nearly 27 μm) so that their temperature characteristics
are
consistent,
namely
their
temperature-
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sensing
compensated coefficients are close to 1, and the spectrum of each sensor must have good quality to ensure good sensing characteristics. 2.4. Signal processing unit
The schematic of the FP sensors demodulated system is shown in Fig. 6.
A light from a tunable laser, with the wavelength from 1528 nm to 1568 nm and wavelength spacing of 0.008 nm, was injected into a 1×16 planar waveguide optical divider (PCL), and then reached to 16 sensors through a circulator. The reflective signals of the sensors reached to a signal
processing system through the circulator. From the reflective spectrums of the 16 sensors, their resonant wavelengths were calculated by local Lorenz fit, and they were fed into a computer via Ethernet interface. 3. Results and discussions
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3.1. Temperature tests
In order to find the temperature-compensated coefficients (in this case, eight in total), temperature tests of the FP balance were carried out 20 times as its temperature was increased from 20 to 100 °C. Fig. 7(a-d) shows temperature
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responses of parts of 16 sensors from one of the 20 test sets, namely, the 1st and 3rd sensors, the 2nd and 4th sensors, the 5th and 7th sensors, and the 6th and 8th sensors, respectively. Apparently, the single sensor (red and black line)
had a nonlinear temperature response, as the thermal expansion of the balance nonlinearly changed with the temperature. Moreover, there was a
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good linearity of 0.999 between the temperature output values of the
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symmetric sensors (blue line), which indicates a constant ratio for the two temperature output values; this can be substituted into Eq. (2) to effectively eliminate the influence of temperature on the aerodynamic component
measurements. Table II shows the eight temperature-compensated coefficients for all aerodynamic components, along with the relative
standard deviations of the corresponding temperature-compensated
coefficients from the 20 sets of temperature tests. Here, the temperature-
compensated coefficients of the symmetric sensors exhibited good stability. The main reason is the FP sensors have a low temperature sensitivity
resulting in output values of the sensors mainly comes from the thermal expansion of the balance.
3.2. Static calibration tests
The balance was statically calibrated prior to the wind tunnel tests in order
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to acquire the relationship of the output values of the FP balance and the
aerodynamic components. The calibration process, which mainly consists of two steps, was as described in [9].
Firstly, a calibration matrix of the relationship between the output values
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of the FP balance and each single component was obtained by load application to the balance in different single aerodynamic component direction, followed by recording the output values of the sensors. Each single-component load is gradually loaded from zero to its near full scale of the design and then successively loaded back to zero. Fig. 8(a-f) show load responses of the FP balance in different single load direction, namely, axial, 11
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normal, and side force, pitching, yawing, and rolling moment, respectively.
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The output values of the FP balance in the direction of aerodynamic component loading are much larger than those of others. It indicates couplings of the aerodynamic components are so small that some of them can be ignored, and the combination outputs of the sensors and corresponding loads exhibits an ultrahigh linearity of 0.9999. The FP sensor
has the advantages of smaller volume and shorter length than traditional FR
strain sensors, and it can be regarded as a rigid body using two-point paste technology in the balance.
Secondly, the static calibration accuracy of the FP balance was verified through simultaneous loading in multiple aerodynamic component
directions under different load combinations (normally 12 sets). The true
loads applied to the FP balance were compared to the loads calculated by the calibrated matrix and further evaluated to the accuracy of the calibration,
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with their deviation stated as the standard errors in percentage to the corresponding component full-scale load value. Table III provides the detailed static calibration performances of the FP balance. Apparently, its
static calibration accuracy was less than 0.4%, which reaches the technical
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level of a conventional FR balance and meets the requirements of national and military standards. 3.3. Wind tunnel test 3.3.1. Hypersonic wind tunnel setup Hypersonic wind force measurements were carried out in a Φ1 hypersonic wind tunnel at the Hypervelocity Aerodynamics Institute (HAI), China 12
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Aerodynamics Research and Development Center (CARDC). Fig. 9(a)
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shows an overview of the wind tunnel system of the pressure-vacuum type, which mainly consists of a 22 MPa gas source system, heaters, nozzles, semiopen free jet test sections, a cooler, and a vacuum pumping system. This
system can provide a simulated environment within an altitude of 20–60 km, a total pressure of 0.02–12 MPa, and a total temperature of 288–1082 K.
HB-2 of a 0.125 m forebody diameter (𝐷) was utilized to evaluate the measurement accuracy of the FP balance in the wind tunnel. This model,
which is based on the FR balance, has been widely used in the verification of hypersonic wind tunnel tests. Fig. 9(b) illustrates the configuration of the 0.125 m HB-2 in the wind tunnel test section, and the FP balance will be mount inside it.
In order to verify the temperature effect of the FP balance, two different temperature test environments (13.85 ℃ and 475.85 ℃) were tested. Table
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IV presents a detailed summary of the operation parameters under both conditions. Both HB-2 models equipped with FP and FR balances were
evaluated through a comparison of each balance’s measurement performance.
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3.3.2. Experimental results at Mach 4 and discussions HB-2 equipped with the FP balance was sent into a hypersonic flow field as soon as the flow stabilized and in a horizontal arrangement during the wind tunnel operation, resulting in the measurement of only three of the model components (FA, FN, and MZ). Normally, the aerodynamic characteristics of
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the model are represented by the aerodynamic coefficients CA,N=FA,N/(q∝S)
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and CMZ=MZ/(q∝SL), where q∝, S, and L are the dynamic pressure derived
from the wind tunnel flow conditions, model’s characteristic area, and model’s characteristic length, respectively. The forces and moments were obtained from the output signals of the FP balance through the equations of balance calibration.
Wind tunnel experiments under Condition I were performed seven times. The nominal angle of attack (AoA) was increased stepwise from −4° to 12°
at an interval of 2°. Fig. 10 shows the variations of the aerodynamic
coefficients as a function of the AoA at Mach 4, of the model measured by the FP balance, along with a comparison with the results of the FR balance.
Note that the FP balance acquired very well the magnitude and the character of the variation of the normal force and pitching moment coefficients CN and
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CMZ, respectively, and that the obtained curves were consistent with those of
the conventional FR balance. Based on the FP and FR balance measurements, the axial force coefficient (CA) of the model deviated because of its much smaller aerodynamic loading variation and larger thermal gradient on the
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axial force element, compared to other components. Moreover, Fig. 10 indicates that CN and CMZ of the model measured by the FP balance maintained good consistency, except for CA, as the small axial forces applied
to the model resulted in a poorer sensitivity of measurement. The normal force coefficient (CN) linearly increases as the AoA increases, since the
windward area of the upper surface of the model is larger than that of the 14
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lower surface when AoA<0, resulting in the normal force downward,
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namely CN <0, and vice versa. As the absolute value of AoA decreases, the windward area difference between the upper and lower surface of the model decreases, so the absolute value of normal force decreases, namely absolute
CN decreases. The pitching moment caused by AoA is equivalent to a damping moment, which prevents the change of AoA. When AoA<0, the
pitching moment attempts to make AoA close to zero, leading to the model
have the head-up trend, namely CMZ <0. The axial force is actually the resistance. The lager the AoA, the larger the windward area of the model and the greater the resistance. It can be seen that CA is distributed symmetrically along the Y-axis [22]. As shown in Table V, the accuracy of repeatability of the model’s aerodynamic coefficients measured by the FP balance, which
depends on the root-mean-square deviation of the results of the seven wind tunnel runs and the result at the maximum AoA, was less than 1%.
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3.3.3. Experimental results at Mach 8 and discussions
As in Condition I, wind tunnel experiments under Condition II were performed seven times. The nominal AoA was increased stepwise from −4° to 12° at an interval of 2°. The experimental results at Mach 8, shown in Fig.
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11, were the same as those at Mach 4. And, the FP balance acquired very well the magnitude and the character of the variation of CN and CMZ, with
the obtained curves consistent with those of the conventional FR balance. Moreover, CN and CMZ of the model measured by the FP balance maintained
good consistency, except for CA. Table VI showed the comparison of the repeatability accuracies of the aerodynamic coefficients of the model based 15
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on the FP balance and FR balance. It indicated the repeatability accuracy of
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the aerodynamic coefficients of the model based on the FP balance was almost less than 1%, and the results based on FP balance were as good as
that of FR balance, even RCA measured by the FP balance was better than that of the FR balance. Furthermore, based on the experimental results at
Mach 4 and Mach 8, the FP balance exhibits excellent measurement
characteristics of the model’s aerodynamic coefficients in harsh environments. 4. Conclusions
In this paper, we demonstrated the application of ultrasensitive, temperatureinsensitive, all-fiber FP strain sensors to a six-component balance for
aerodynamic measurements in a hypersonic wind tunnel. The experimental
results confirmed the proposed FP balance’s high-static calibration accuracy of less than 0.4%, along with good temperature stability, and the hypersonic
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wind tunnel tests verified the excellent repeatability precision of the FP balance at high temperatures, at less than 1%, due to the high-strain sensitivity and temperature insensitiveness of the FP sensors. The tests captured well the variations of the aerodynamic coefficients of the model,
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which maintained consistency with that of the conventional FR balance, under a high-temperature environment. This FP sensor is the most promising alternative to FR sensors for aerodynamic tests to our knowledge. It can be applied in harsh environments such as high temperature, high flow velocity, and small-scale space, and offers an extreme potential for different various aerodynamic testing balance in many fields, including missiles, hypersonic 16
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aircraft, manned spacecraft, and automobiles.
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Acknowledgements This work was supported by the National Natural Science Foundation of
China [grant number 51205049, 51875091, 51327806]; the state 111 Project [grant number B14039]; Major Instrument Project of Ministry of Science & Technology of China [grant number 2012YQ250002]. References
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under high temperature. Appl Opt 2017; 56:4250-7.
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http://doi.org/10.1364/AO.56.004250 [20] Simon P, Donlagic D. All-fiber, long-active-length Fabry–Perot strain sensor. Opt Express 2011; 19:15641-51. http://doi.org/10.1364/OE.19.015641
[21] Ran ZL, Rao YJ, Deng HY, Liao X. Miniature in-line photonic crystal fiber etalon fabricated by 157-nm laser micromachining. Opt Lett 2007; 32:3071-3. http://doi.org/10.1364/OL.32.003071
[22] Gray J D. Summary report on aerodynamic characteristics of standard
models HB-1 and HB-2[R]. ARNOLD ENGINEERING DEVELOPMENT
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CENTER ARNOLD AFB TN, 1964.
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Tables
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Table I. Strain sensor combinations for the six aerodynamic components. MZ FZ MY FA MX Component FN Combination -1+2+3-15-6-5-13+149+10-11output 4 2+3+4 7+8 6+7+8 15+16 12 Note. The number “1” indicates the output signal of the first sensor of the FP balance
Table II. Temperature-compensated coefficients and corresponding standard deviations of symmetric sensors Symmetric sensors 3/1 4/2 7/5 8/6 11/9 12/10 14/13 16/15 Ci,j 1.153 0.766 0.833 0.990 1.346 1.743 0.564 1.034 Relative standard deviation 0.18 0.20 0.11 0.15 0.13 0.14 0.21 0.10 (%) Note. The expression “3/1” represents the ratio of the output value of the third and first sensors of the FP balance.
Table III. Calibration performances of the FP-strain-sensor-based balance. Aerodynamic Maximum load Maximum Standard Accuracy component (kg/kg·m) output (nm) deviation (%) FN 70 8.685 0.208 0.30 FZ 50 15.979 0.056 0.16 FA 36 13.770 0.059 0.17 MX ±2.25 2.660 0.008 0.35 MY ±1.28 10.523 0.005 0.19 MZ ±4.80 19.597 0.016 0.33 Test condition Condition I Condition II
Table IV. Wind tunnel operation parameters. Mach Stagnation Stagnation number temperature (℃) pressure (MPa) 4 13.85 4 8 475.85 5
Renolds number (×107) 1.956 1.74
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Table V. Repeatability accuracy of the aerodynamic coefficients based on the FP balance at Mach 4. AoA (°) −4 −2 0 2 4 6 8 10 12 RCN (%) 0.34 0.51 0.58 0.42 0.46 0.41 0.64 0.47 0.69 RMZ (%) 0.54 0.54 0.41 0.49 0.63 0.79 0.88 0.79 0.95 RCA (%) 0.39 0.58 0.62 0.52 0.57 0.70 0.88 0.85 0.80 Note. The expressions “RCN,” “RMZ,” and “RCA” represent the repeatability accuracy of the normal force, pitching moment, and axial force coefficients, respectively.
Table VI. Comparison of repeatability accuracies of the aerodynamic coefficients based on the FP balance and FR balance at Mach 8. AoA(°)
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-4 -2 0 2 4 6 8 10 12
RCN (%) 0.37 0.41 0.45 0.58 0.34 0.34 0.70 0.93 1.29
FP balance RMZ (%) RCA (%) 0.51 0.83 0.88 0.59 0.75 0.52 0.68 0.51 0.74 0.72 0.83 0.54 0.78 0.77 0.87 0.69 0.83 0.77
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RCN (%) 0.71 0.46 0.34 0.23 0.54 0.58 1.26 0.65 0.72
FR balance RMZ (%) RCA (%) 0.67 1.07 0.63 1.03 0.48 1.09 0.47 1.11 0.77 1.10 0.93 1.18 0.99 1.22 1.09 1.18 1.59 1.11
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Figures
Fig. 1. A schematic of the FP strain sensor.
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Fig. 2. Fabrication process of the FP sensor.
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Fig. 3. FP sensor’s (a) micrograph and (b) reflection spectrum.
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Fig. 4. (a) Schematic structure of a six-component force balance. (b) Mounting positions of the 16 sensors. (c) A physical image of the FP balance.
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Fig. 5. Temperature distributions simulations of the balance with the angle of attack (AoA) of (a) 0°, (b) 12°. The two insets of each figure respectively are temperature distributions between symmetric surfaces (i) normal surfaces, (ii) axial surfaces, of the balance. The x-label “Distance” is the distance to the simulation origin.
Fig. 6. Schematic of the FP demodulated system.
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Fig. 7. Temperature responses of parts of 16 sensors from one of the 20 temperature test sets. In each figure, the black and red lines represent the temperature responses of the two sensors arranging to the symmetrical locations of the balance, the purple line is the test data (the ratios of the temperature output values of the two symmetric sensors) , and the blue line is the linear fitting of data (a) the 1st and 3rd sensors, (b) the 2nd and 4th sensors, (c) the 5th and 7th sensors, (d) the 6th and 8th sensors.
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Fig. 8. Responses of all aerodynamic components in different load direction: (a)FA, (b) FN, (c) FZ, (d) MZ, (e) MY, (f) MX
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Fig. 9. (a) Overview of the Φ1 hypersonic wind tunnel. (b) HB-2 in the test section of the Φ1 hypersonic wind tunnel.
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Fig. 10. Comparison of the aerodynamic (a) normal force, (b) pitching moment, and (c) axial force coefficients between the FP and FR balances under different angles of attack at Mach 4. The error bars show the standard deviations of the seven wind tunnel runs measured by the FP balance.
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Fig. 11. Comparison of the aerodynamic (a) normal force, (b) pitching moment, and (c) axial force coefficients under different angles of attack at Mach 8. The error bars show the standard deviations of the seven wind tunnel runs measured by the FP balance.
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Tables Table I. Strain sensor combinations for the six aerodynamic components. Table II. Temperature-compensated coefficients and corresponding standard deviations of symmetric sensors Table III. Calibration performances of the FP-strain-sensor-based balance. Table IV. Wind tunnel operation parameters. Table V. Repeatability accuracy of the aerodynamic coefficients based on the FP balance at Mach 4. Table VI. Comparison of repeatability accuracies of the aerodynamic coefficients based on the FP balance and FR balance at Mach 8.
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Figures Fig. 1. A schematic of the FP strain sensor. Fig. 2. Fabrication process of the FP sensor. Fig. 3. FP sensor’s (a) micrograph and (b) reflection spectrum. Fig. 4. (a) Schematic structure of a six-component force balance. (b) Mounting positions of the 16 sensors. (c) A physical image of the FP balance. Fig. 5. Temperature distributions simulations of the balance with the angle of attack (AoA) of (a) 0°, (b) 12°. The two insets of each figure respectively are temperature distributions between symmetric surfaces (i) normal surfaces, (ii) axial surfaces, of the balance. The x-label “Distance” is the distance to the simulation origin. Fig. 6. Schematic of the FP demodulated system. Fig. 7. Temperature responses of parts of 16 sensors from one of the 20 temperature test sets. In each figure, the black and red lines represent the temperature responses of the two sensors arranging to the symmetrical locations of the balance, the purple line is the test data (the ratios of the temperature output values of the two symmetric sensors), and the blue line is the linear fitting of data (a) the 1st and 3rd sensors, (b) the 2nd and 4th sensors, (c) the 5th and 7th sensors, (d) the 6th and 8th sensors. Fig. 8. Responses of all aerodynamic components in different load direction: (a)FA, (b)FN, (c)FZ, (d)MZ, (e)MY, (f)MX. Fig. 9. (a) Overview of the Φ1 hypersonic wind tunnel. (b) HB-2 in the test section of the Φ1 hypersonic wind tunnel. Fig. 10. Comparison of the aerodynamic (a) normal force, (b) pitching moment, and (c) axial force coefficients between the FP and FR balances under different angles of attack at Mach 4. The error bars show the standard deviations of the seven wind tunnel runs measured by the FP balance. Fig. 11. Comparison of the aerodynamic (a) normal force, (b) pitching moment, and (c) axial force coefficients under different angles of attack at Mach 8. The error bars show the standard deviations of the seven wind tunnel runs measured by the FP balance.
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All-fiber Fabry-Perot strain sensors for aerodynamic tests in wind tunnel are proposed. A new temperature-compensated method is proposed to eliminated temperature effect. The sensor based on a balance shows a high static accuracy, a temperature stability. A high repeatability precision of aerodynamic tests at high temperatures is achieved. The FP sensor is the most promising alternative to FR sensors for aerodynamic tests.
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Declaration of interests ☒ 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. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
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