- Email: [email protected]
Inspection of the hydrogen gas pressure with metal shield by cold neutron radiography at CMRR
Nuclear Instruments and Methods in Physics Research A 851 (2017) 10–14
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Inspection of the hydrogen gas pressure with metal shield by cold neutron radiography at CMRR
MARK
⁎
Hang Lia,b, Chao Caoa,b, Heyong Huoa,b, Sheng Wanga,b, , Yang Wua,b, Wei Yina,b, Yong Suna,b, Bin Liua,b, Bin Tanga,b a b
Institute of Nuclear Physics and Chemistry, Chinese Academy of Engineering Physics, Mianyang, China Key Laboratory of Neutron Physics, Chinese Academy of Engineering Physics, Mianyang, China
A R T I C L E I N F O
A BS T RAC T
Keywords: Cold neutron radiography Gas pressure Quantitative measurement
The inspection of the process of gas pressure change is important for some applications (e.g. gas tank stockpile or two phase fluid model) which need quantitative and non-touchable measurement. Neutron radiography provides a suitable tool for such investigations with nice resolution. The quantitative cold neutron radiography (CNR) is developed at China Mianyang Research Reactor (CMRR) to measure the hydrogen gas pressure with metal shield. Because of the high sensitivity to hydrogen, even small change of the hydrogen pressure can be inspected by CNR. The dark background and scattering neutron effect are both corrected to promote measurement precision. The results show that CNR can measure the hydrogen gas pressure exactly and the pressure value average relative error between CNR and barometer is almost 1.9%.
1. Introduction Cold neutron radiography (CNR) is a non destructive testing technology using cold neutron as probe to display the inner structure of sample. Different from X & γ ray radiography, CNR can penetrate metal block and show more sensitivity to light elements such as H, 6Li which can be a complementarity to existing non-destructive technology. Earlier neutron radiography was a qualitative detection [1,2] and used the gray level distribution of the imaging picture to show the region structure of interested which couldn’t obtain quantitative information. Now neutron radiography focus on the quantitative measurement such as soil water retention [3], wood firmness enhancement [4], water penetration in concrete [5], water movement in porous material [6] and so on. The hydrogenous material (e.g. water, resin) content in the sample can be confirmed by neutron radiography. Gas pressure need to be measured in gas tank stockpile and fuel cell to inspect the statement of equipment. An untouchable way to obtain gas pressure information is needed to reduce equipment scale which is better than barometer. A cold neutron imaging facility (CNRF) has been successfully commissioned at China Mianyang Research Reactor (CMRR) in China Academy of Engineering and Physics which showed in Fig. 1. The most probable neutron wavelength for this facility is 2.7 Å. The 50 µm/100 µm thickness 6LiF/Zns-scintillator screen in conjunction with a Andor iKon CCD-camera(2048×2048 pixel) are used to record
⁎
the neutron images. With different commercial lens, the field of view can be 5 cm×5–20 cm×20 cm. Based CNRF, the method of gas pressure quantitative measurement is investigated and some experiments are carried out to verify the method. The correction method is also used to improve the measurement precision. 2. Method The method of untouchable gas pressure quantitative measurement needs two conditions. One is the connection between gas pressure and neutron imaging results, another is the measurement precision. Based the state equation of ideal gas, the pressure of hydrogen gas p can be expressed as
p = ng kT
(1)
Where k is the Boltzman constant, T is the thermodynamic temperature, ng is the gas molecule number per unit volume which is proportional to gas density ρ . So if temperature is constant, the pressure of gas is proportional to ng . When neutron penetrates the gas, the exponential attenuation law is coincident as below:
I = I0 exp(−Σg dg ) = I0 exp(−ng σg dg )
(2)
Where I0 is the incident neutron flux, I is the penetrable neutron flux, Σg is the gas macro cross section, σg is the gas micro cross section, dg is the thickness of gas. The Eq. (2) is a simplification as averaged over the
Corresponding author at: Institute of Nuclear Physics and Chemistry, Chinese Academy of Engineering Physics, Mianyang, China.
http://dx.doi.org/10.1016/j.nima.2017.01.031 Received 23 October 2016; Received in revised form 15 January 2017; Accepted 16 January 2017 Available online 17 January 2017 0168-9002/ © 2017 Elsevier B.V. All rights reserved.
Nuclear Instruments and Methods in Physics Research A 851 (2017) 10–14
H. Li et al.
Fig. 1. the cold neutron imaging facility at CMRR. a). Photo of the cold neutron imaging facility. b). Open beam image at the cold beam line(FOV:20 cm×20 cm).
Fig. 2. Sketch map of the quantitative measurement hydrogen gas pressure.
I1 (x, y) = I (x, y) − Ib (x, y) = I0 (x, y)exp(−(Σg dg (x, y) + Σo do (x , y)))
full spectrum. The neutron imaging results which is converted from the penetrable neutron flux is relative to the gas density and can be used to measure the gas pressure quantitatively. So the connection between gas pressure and neutron imaging results is clear. When hydrogen gas is stored in the metal tank, cold neutron can penetrate the metal tank and show the inner gas information (Fig. 2). How to reveal the pressure from the image results and reduce the error are the key parameters. The neutron flux I (x, y) at the imaging plate which the coordinate is (x, y) can be expressed as
I (x, y) = I0 (x, y)exp(−(Σg dg (x, y) + Σo do (x, y))) + Ib (x, y)
(4)
Q1 = I1 (x, y)/ I0 (x, y) = exp(−(Σg dg (x, y) + Σo do (x, y)))
(5)
If the metal tank is empty, then
Q2 = I1 (x, y)/ I0 (x, y) = exp(−Σo do (x, y))
(6)
So the ideal relationship between the imaging results and pressure can be expressed as
L = log(Q1) − log(Q2 ) = −Σg dg (x, y)
(3)
(7)
As previously described, the pressure of gas is proportional to Σg , so L can be expressed as below at certain gas thickness which accords with linear relation.
Where I0 (x, y) is the incident neutron flux, Σg is the gas macro cross section, Σo is the metal shield macro cross section, dg (x, y) and do (x, y) is the thickness of gas and metal shield which the coordinate is (x, y), Ib (x, y) is the background distribution at the imaging plate which can be expressed as the sum of scattering background Is (x, y), environment background Ie (x, y) and dark noise Id (x, y) from CCD. I0 (x, y) can be measured by no sample exposing, Ie (x, y) can be measured by a thick and big B4C sample exposing, Id (x, y) can be measured by shutter close exposing and scattering background Is (x, y) can be calculated by the point scattered function[7]. So the background distribution can be modified as below.
L = −Σg dg (x, y) = Ap
(8)
A is a constant which need to be calibrated. But the background noise can’t be modified completely, some correctional parameters should be considered as below.
L f = Ap + Bp 2 + C
Bp 2
(9)
means the departure of linear relation and C means the departure of origin. B and C should be close to zero. So the method of untouchable gas pressure quantitative measurement consists of calibration process and measurement process.
11
Nuclear Instruments and Methods in Physics Research A 851 (2017) 10–14
H. Li et al.
Barometer
Valve1
Valve2
Gas buffer Metal gas stored tank a. Sketch map of the hydrogen gas system
Imaging system
a. Empty tank imaging result Barometer
Valve1
Valve2 1.0
Gray level ratio
Metal gas stored tank b. Photo of the hydrogen gas system in operation during imaging
0.8
0.6
0.4
Fig. 3. Hydrogen gas system. a). Sketch map of the hydrogen gas system. b). Photo of the hydrogen gas system in operation during imaging.
0.2 0
Calibration process is used to obtain the parameters of function (9) by different known gas pressure imaging results, and then an unknown gas pressure can be revealed from its imaging result by the function (9).
2
4
6
8
10
12
14
Pressure/MPa Fig. 4. Different imaging results in calibration process. a. Empty tank imaging result. b. Different pressure imaging gray level ratio to empty tank(using the average gray level in the red box of (a)).
3. Sample The hydrogen gas system consists of a metal gas stored tank, a barometer, a gas buffer and two valves which show in Fig. 3. The middle of the tank is columniform and both ends are hemisphereical. Barometer is used to obtain the real gas pressure in the metal gas stored tank. At first, high pressure gas has been bumped to metal gas stored tank, and then valve 1 & 2 is closed. Imaging with the tank, the result of p1 is obtained. Then keeping valve2 closed, and opening valve1, a bit of gas will leak to gas buffer. After that, closing valve1and opening valve2, the gas will leak from buffer to atmosphere. Imaging with the tank now, the result of p2 is obtained. Repeating the process, various pressure imaging results will be collected.
The distance to midline is 15mm The distance to midline is 10mm The distance to midline is 5mm Midline
Fig. 5. The position sketch map of four functions.
which have same distance to midline are same. The same gas thickness positions imaging results obey one function and can be used to average to reduce error. In our experiments, four functions have been obtained for different distances to midline which shown in Fig. 5. The relationship of imaging results Lf and pressures are shown in Fig. 6 and four functions parameters are shown in Table 1. The gas thickness increase when close to midline, so the absolute value of parameter A is increase, and parameter B,C are all nearly zero which is according with the method. Without scattering correction, the departure of linear relation is more serious which means the scattering correction is effective.
4. Experiment results and discussion The experiments have been carried out at the CNRF of CMRR. A 50 µm thickness 6LiF/Zns-scintillator screen is used to convert neutron to light. A 85 mm lens and Andor iKon CCD-camera(2048×2048 pixel) are used to record the images. The FOV is 100 mm×100 mm and the L/ D is 450. The exposure time is 20 s for each pressure. The distance between sample and detector is 1 cm. 4.1. Calibration process
4.2. Same FOV measurement process
Some imaging results of calibration process are shown in Fig. 4. High pressure means high Σg , which represents as low gray level ratio to empty tank in Fig. 4(b). Because the middle of the tank is columniform, the gas thicknesses
At same FOV, some unknown pressure tanks have been imaged and the pressures have been revealed. Using average value of four
12
Nuclear Instruments and Methods in Physics Research A 851 (2017) 10–14
H. Li et al.
Fig. 6. The relationship of imaging results and pressures.
Table 1 Function parameters (with scattering correction). Lf= Ap+Bp2+C
Position
Midline The distance to midline is 5 mm The distance to midline is 10 mm The distance to midline is 15 mm
A
B
C
−0.18094 −0.17927 −0.16419 −0.14074
4.63714E−5 5.88275E−4 9.9765E−4 1.34E−3
−0.00827 0.00107 −0.01002 0.00256
Table 2 The contrasts of measurement results and real values at same FOV. Measurement result /MPa
Real value/ MPa
Relative error
Measurement result /MPa
Real value/ MPa
Relative error
Measurement result /MPa
Real value/ MPa
Relative error
0.462 0.975 1.398 1.804 2.142 2.599 2.995 3.372 3.814 4.267 4.598 5.161
0.507 1.018 1.433 1.833 2.220 2.630 3.070 3.443 3.865 4.259 4.691 5.073
0.098 0.044 0.024 0.016 0.037 0.013 0.025 0.021 0.013 0.002 0.020 0.017
5.524 5.795 6.127 6.519 6.876 7.086 7.495 7.722 8.048 8.438 8.570 8.921
5.375 5.691 6.023 6.373 6.747 7.015 7.293 7.578 7.875 8.184 8.512 8.845
0.027 0.018 0.016 0.022 0.018 0.009 0.026 0.018 0.021 0.030 0.006 0.008
9.237 9.647 10.050 10.200 10.534 10.720 10.997 11.015 11.194 11.377
9.195 9.557 9.855 10.244 10.453 10.666 10.871 11.092 11.317 11.547
0.004 0.009 0.019 0.004 0.007 0.005 0.011 0.007 0.011 0.014
4.3. Large FOV measurement process
functions revealed results as measurement results, and barometer value as real value, the contrasts are shown in Table 2. The relative errors are all very small and the average relative error is 1.9% which means the measurement method is appropriate.
Another measurement is done at large FOV (20 cm×20 cm) to ensure the reliability. The imaging results are shown in Fig. 7. The
13
Nuclear Instruments and Methods in Physics Research A 851 (2017) 10–14
H. Li et al.
relative error is higher than small FOV because resizing process may increase the error. 5. Conclusions The quantitative cold neutron radiography (CNR) measurement to gas pressure is carried out at China Mianyang Research Reactor (CMRR). The measurement method is development and the corrections of background noises are considered. The results show that CNR can measure the hydrogen gas pressure exactly and the pressure value average relative error between CNR and barometer is almost 1.9%. This method is suitable for different FOV. Some corrections should be considered to reduce the measurement error like energy spectrum hardening effect in the future.
a. Empty tank imaging result 1.0
Gray level ratio
0.8
Acknowledgements This work was financially supported by the Development Found of Science and Technology of China Academy of Engineering (Grant no. 2014B0103007), Fund of the National Natural Science Foundation of China (Grant no. 11375156), Young Scientist Fund of the National Natural Science Foundation of China (Grant no. 11405153).
0.6
0.4
0.2
References 0
2
4
6
8
10
12
[1] N. Kardjilov, A. Hilger, I. Manke, et al., Industrial applications at the new cold neutron radiography and tomography facility of the HMI, Nucl. Instrum. Methods Phys. Res. A 542 (2005) 16–21. [2] M. Schulz, et al., Energy-dependent neutron imaging with a double crystal monochromator at the ANTARES facility at FRM II, Nucl. Instrum. Methods Phys. Res. A 605 (2009) 33–35. [3] M. Kang, et al., Multiple pixel-scale soil water retention curves quantified by neutron radiography, Adv. Water Resour. 65 (2014) 1–8. [4] E. Lehmann, et al., Neutron radiography as visualization and quantification method for conservation measures of wood firmness enhancement, Nucl. Instrum. Methods Phys. Res. A 542 (2005) 87–94. [5] M. Kanematsu, et al., Quantification of water penetration into concrete through cracks by neutron radiography, Nucl. Instrum. Methods Phys. Res. A 605 (2009) 154–158. [6] ZHANG Peng, et al., Visualization and quantification of water movement in porous cement-based materials by real time thermal neutron radiography: theoretical analysis and experimental study, Sci. China Tech. Sci. 53 (5) (2010) 1198–1207.
Pressure/MPa
b. Different pressure imaging gray level ratio to empty tank(using the average gray level in the red box of (a)) Fig. 7. Different imaging results at large FOV. a). Empty tank imaging result. b). Different pressure imaging gray level ratio to empty tank(using the average gray level in the red box of (a)).
large FOV results are resized to obtain the same pixel size of tank area to small FOV. Then using the same gas thickness data at large FOV imaging results, the pressure can be revealed according to the parameters in Table 1 and the average relative error is 2.8%. The
14
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Inspection of the hydrogen gas pressure with metal shield by cold neutron radiography at CMRR
MARK
⁎
Hang Lia,b, Chao Caoa,b, Heyong Huoa,b, Sheng Wanga,b, , Yang Wua,b, Wei Yina,b, Yong Suna,b, Bin Liua,b, Bin Tanga,b a b
Institute of Nuclear Physics and Chemistry, Chinese Academy of Engineering Physics, Mianyang, China Key Laboratory of Neutron Physics, Chinese Academy of Engineering Physics, Mianyang, China
A R T I C L E I N F O
A BS T RAC T
Keywords: Cold neutron radiography Gas pressure Quantitative measurement
The inspection of the process of gas pressure change is important for some applications (e.g. gas tank stockpile or two phase fluid model) which need quantitative and non-touchable measurement. Neutron radiography provides a suitable tool for such investigations with nice resolution. The quantitative cold neutron radiography (CNR) is developed at China Mianyang Research Reactor (CMRR) to measure the hydrogen gas pressure with metal shield. Because of the high sensitivity to hydrogen, even small change of the hydrogen pressure can be inspected by CNR. The dark background and scattering neutron effect are both corrected to promote measurement precision. The results show that CNR can measure the hydrogen gas pressure exactly and the pressure value average relative error between CNR and barometer is almost 1.9%.
1. Introduction Cold neutron radiography (CNR) is a non destructive testing technology using cold neutron as probe to display the inner structure of sample. Different from X & γ ray radiography, CNR can penetrate metal block and show more sensitivity to light elements such as H, 6Li which can be a complementarity to existing non-destructive technology. Earlier neutron radiography was a qualitative detection [1,2] and used the gray level distribution of the imaging picture to show the region structure of interested which couldn’t obtain quantitative information. Now neutron radiography focus on the quantitative measurement such as soil water retention [3], wood firmness enhancement [4], water penetration in concrete [5], water movement in porous material [6] and so on. The hydrogenous material (e.g. water, resin) content in the sample can be confirmed by neutron radiography. Gas pressure need to be measured in gas tank stockpile and fuel cell to inspect the statement of equipment. An untouchable way to obtain gas pressure information is needed to reduce equipment scale which is better than barometer. A cold neutron imaging facility (CNRF) has been successfully commissioned at China Mianyang Research Reactor (CMRR) in China Academy of Engineering and Physics which showed in Fig. 1. The most probable neutron wavelength for this facility is 2.7 Å. The 50 µm/100 µm thickness 6LiF/Zns-scintillator screen in conjunction with a Andor iKon CCD-camera(2048×2048 pixel) are used to record
⁎
the neutron images. With different commercial lens, the field of view can be 5 cm×5–20 cm×20 cm. Based CNRF, the method of gas pressure quantitative measurement is investigated and some experiments are carried out to verify the method. The correction method is also used to improve the measurement precision. 2. Method The method of untouchable gas pressure quantitative measurement needs two conditions. One is the connection between gas pressure and neutron imaging results, another is the measurement precision. Based the state equation of ideal gas, the pressure of hydrogen gas p can be expressed as
p = ng kT
(1)
Where k is the Boltzman constant, T is the thermodynamic temperature, ng is the gas molecule number per unit volume which is proportional to gas density ρ . So if temperature is constant, the pressure of gas is proportional to ng . When neutron penetrates the gas, the exponential attenuation law is coincident as below:
I = I0 exp(−Σg dg ) = I0 exp(−ng σg dg )
(2)
Where I0 is the incident neutron flux, I is the penetrable neutron flux, Σg is the gas macro cross section, σg is the gas micro cross section, dg is the thickness of gas. The Eq. (2) is a simplification as averaged over the
Corresponding author at: Institute of Nuclear Physics and Chemistry, Chinese Academy of Engineering Physics, Mianyang, China.
http://dx.doi.org/10.1016/j.nima.2017.01.031 Received 23 October 2016; Received in revised form 15 January 2017; Accepted 16 January 2017 Available online 17 January 2017 0168-9002/ © 2017 Elsevier B.V. All rights reserved.
Nuclear Instruments and Methods in Physics Research A 851 (2017) 10–14
H. Li et al.
Fig. 1. the cold neutron imaging facility at CMRR. a). Photo of the cold neutron imaging facility. b). Open beam image at the cold beam line(FOV:20 cm×20 cm).
Fig. 2. Sketch map of the quantitative measurement hydrogen gas pressure.
I1 (x, y) = I (x, y) − Ib (x, y) = I0 (x, y)exp(−(Σg dg (x, y) + Σo do (x , y)))
full spectrum. The neutron imaging results which is converted from the penetrable neutron flux is relative to the gas density and can be used to measure the gas pressure quantitatively. So the connection between gas pressure and neutron imaging results is clear. When hydrogen gas is stored in the metal tank, cold neutron can penetrate the metal tank and show the inner gas information (Fig. 2). How to reveal the pressure from the image results and reduce the error are the key parameters. The neutron flux I (x, y) at the imaging plate which the coordinate is (x, y) can be expressed as
I (x, y) = I0 (x, y)exp(−(Σg dg (x, y) + Σo do (x, y))) + Ib (x, y)
(4)
Q1 = I1 (x, y)/ I0 (x, y) = exp(−(Σg dg (x, y) + Σo do (x, y)))
(5)
If the metal tank is empty, then
Q2 = I1 (x, y)/ I0 (x, y) = exp(−Σo do (x, y))
(6)
So the ideal relationship between the imaging results and pressure can be expressed as
L = log(Q1) − log(Q2 ) = −Σg dg (x, y)
(3)
(7)
As previously described, the pressure of gas is proportional to Σg , so L can be expressed as below at certain gas thickness which accords with linear relation.
Where I0 (x, y) is the incident neutron flux, Σg is the gas macro cross section, Σo is the metal shield macro cross section, dg (x, y) and do (x, y) is the thickness of gas and metal shield which the coordinate is (x, y), Ib (x, y) is the background distribution at the imaging plate which can be expressed as the sum of scattering background Is (x, y), environment background Ie (x, y) and dark noise Id (x, y) from CCD. I0 (x, y) can be measured by no sample exposing, Ie (x, y) can be measured by a thick and big B4C sample exposing, Id (x, y) can be measured by shutter close exposing and scattering background Is (x, y) can be calculated by the point scattered function[7]. So the background distribution can be modified as below.
L = −Σg dg (x, y) = Ap
(8)
A is a constant which need to be calibrated. But the background noise can’t be modified completely, some correctional parameters should be considered as below.
L f = Ap + Bp 2 + C
Bp 2
(9)
means the departure of linear relation and C means the departure of origin. B and C should be close to zero. So the method of untouchable gas pressure quantitative measurement consists of calibration process and measurement process.
11
Nuclear Instruments and Methods in Physics Research A 851 (2017) 10–14
H. Li et al.
Barometer
Valve1
Valve2
Gas buffer Metal gas stored tank a. Sketch map of the hydrogen gas system
Imaging system
a. Empty tank imaging result Barometer
Valve1
Valve2 1.0
Gray level ratio
Metal gas stored tank b. Photo of the hydrogen gas system in operation during imaging
0.8
0.6
0.4
Fig. 3. Hydrogen gas system. a). Sketch map of the hydrogen gas system. b). Photo of the hydrogen gas system in operation during imaging.
0.2 0
Calibration process is used to obtain the parameters of function (9) by different known gas pressure imaging results, and then an unknown gas pressure can be revealed from its imaging result by the function (9).
2
4
6
8
10
12
14
Pressure/MPa Fig. 4. Different imaging results in calibration process. a. Empty tank imaging result. b. Different pressure imaging gray level ratio to empty tank(using the average gray level in the red box of (a)).
3. Sample The hydrogen gas system consists of a metal gas stored tank, a barometer, a gas buffer and two valves which show in Fig. 3. The middle of the tank is columniform and both ends are hemisphereical. Barometer is used to obtain the real gas pressure in the metal gas stored tank. At first, high pressure gas has been bumped to metal gas stored tank, and then valve 1 & 2 is closed. Imaging with the tank, the result of p1 is obtained. Then keeping valve2 closed, and opening valve1, a bit of gas will leak to gas buffer. After that, closing valve1and opening valve2, the gas will leak from buffer to atmosphere. Imaging with the tank now, the result of p2 is obtained. Repeating the process, various pressure imaging results will be collected.
The distance to midline is 15mm The distance to midline is 10mm The distance to midline is 5mm Midline
Fig. 5. The position sketch map of four functions.
which have same distance to midline are same. The same gas thickness positions imaging results obey one function and can be used to average to reduce error. In our experiments, four functions have been obtained for different distances to midline which shown in Fig. 5. The relationship of imaging results Lf and pressures are shown in Fig. 6 and four functions parameters are shown in Table 1. The gas thickness increase when close to midline, so the absolute value of parameter A is increase, and parameter B,C are all nearly zero which is according with the method. Without scattering correction, the departure of linear relation is more serious which means the scattering correction is effective.
4. Experiment results and discussion The experiments have been carried out at the CNRF of CMRR. A 50 µm thickness 6LiF/Zns-scintillator screen is used to convert neutron to light. A 85 mm lens and Andor iKon CCD-camera(2048×2048 pixel) are used to record the images. The FOV is 100 mm×100 mm and the L/ D is 450. The exposure time is 20 s for each pressure. The distance between sample and detector is 1 cm. 4.1. Calibration process
4.2. Same FOV measurement process
Some imaging results of calibration process are shown in Fig. 4. High pressure means high Σg , which represents as low gray level ratio to empty tank in Fig. 4(b). Because the middle of the tank is columniform, the gas thicknesses
At same FOV, some unknown pressure tanks have been imaged and the pressures have been revealed. Using average value of four
12
Nuclear Instruments and Methods in Physics Research A 851 (2017) 10–14
H. Li et al.
Fig. 6. The relationship of imaging results and pressures.
Table 1 Function parameters (with scattering correction). Lf= Ap+Bp2+C
Position
Midline The distance to midline is 5 mm The distance to midline is 10 mm The distance to midline is 15 mm
A
B
C
−0.18094 −0.17927 −0.16419 −0.14074
4.63714E−5 5.88275E−4 9.9765E−4 1.34E−3
−0.00827 0.00107 −0.01002 0.00256
Table 2 The contrasts of measurement results and real values at same FOV. Measurement result /MPa
Real value/ MPa
Relative error
Measurement result /MPa
Real value/ MPa
Relative error
Measurement result /MPa
Real value/ MPa
Relative error
0.462 0.975 1.398 1.804 2.142 2.599 2.995 3.372 3.814 4.267 4.598 5.161
0.507 1.018 1.433 1.833 2.220 2.630 3.070 3.443 3.865 4.259 4.691 5.073
0.098 0.044 0.024 0.016 0.037 0.013 0.025 0.021 0.013 0.002 0.020 0.017
5.524 5.795 6.127 6.519 6.876 7.086 7.495 7.722 8.048 8.438 8.570 8.921
5.375 5.691 6.023 6.373 6.747 7.015 7.293 7.578 7.875 8.184 8.512 8.845
0.027 0.018 0.016 0.022 0.018 0.009 0.026 0.018 0.021 0.030 0.006 0.008
9.237 9.647 10.050 10.200 10.534 10.720 10.997 11.015 11.194 11.377
9.195 9.557 9.855 10.244 10.453 10.666 10.871 11.092 11.317 11.547
0.004 0.009 0.019 0.004 0.007 0.005 0.011 0.007 0.011 0.014
4.3. Large FOV measurement process
functions revealed results as measurement results, and barometer value as real value, the contrasts are shown in Table 2. The relative errors are all very small and the average relative error is 1.9% which means the measurement method is appropriate.
Another measurement is done at large FOV (20 cm×20 cm) to ensure the reliability. The imaging results are shown in Fig. 7. The
13
Nuclear Instruments and Methods in Physics Research A 851 (2017) 10–14
H. Li et al.
relative error is higher than small FOV because resizing process may increase the error. 5. Conclusions The quantitative cold neutron radiography (CNR) measurement to gas pressure is carried out at China Mianyang Research Reactor (CMRR). The measurement method is development and the corrections of background noises are considered. The results show that CNR can measure the hydrogen gas pressure exactly and the pressure value average relative error between CNR and barometer is almost 1.9%. This method is suitable for different FOV. Some corrections should be considered to reduce the measurement error like energy spectrum hardening effect in the future.
a. Empty tank imaging result 1.0
Gray level ratio
0.8
Acknowledgements This work was financially supported by the Development Found of Science and Technology of China Academy of Engineering (Grant no. 2014B0103007), Fund of the National Natural Science Foundation of China (Grant no. 11375156), Young Scientist Fund of the National Natural Science Foundation of China (Grant no. 11405153).
0.6
0.4
0.2
References 0
2
4
6
8
10
12
[1] N. Kardjilov, A. Hilger, I. Manke, et al., Industrial applications at the new cold neutron radiography and tomography facility of the HMI, Nucl. Instrum. Methods Phys. Res. A 542 (2005) 16–21. [2] M. Schulz, et al., Energy-dependent neutron imaging with a double crystal monochromator at the ANTARES facility at FRM II, Nucl. Instrum. Methods Phys. Res. A 605 (2009) 33–35. [3] M. Kang, et al., Multiple pixel-scale soil water retention curves quantified by neutron radiography, Adv. Water Resour. 65 (2014) 1–8. [4] E. Lehmann, et al., Neutron radiography as visualization and quantification method for conservation measures of wood firmness enhancement, Nucl. Instrum. Methods Phys. Res. A 542 (2005) 87–94. [5] M. Kanematsu, et al., Quantification of water penetration into concrete through cracks by neutron radiography, Nucl. Instrum. Methods Phys. Res. A 605 (2009) 154–158. [6] ZHANG Peng, et al., Visualization and quantification of water movement in porous cement-based materials by real time thermal neutron radiography: theoretical analysis and experimental study, Sci. China Tech. Sci. 53 (5) (2010) 1198–1207.
Pressure/MPa
b. Different pressure imaging gray level ratio to empty tank(using the average gray level in the red box of (a)) Fig. 7. Different imaging results at large FOV. a). Empty tank imaging result. b). Different pressure imaging gray level ratio to empty tank(using the average gray level in the red box of (a)).
large FOV results are resized to obtain the same pixel size of tank area to small FOV. Then using the same gas thickness data at large FOV imaging results, the pressure can be revealed according to the parameters in Table 1 and the average relative error is 2.8%. The
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