Method for measuring channel synchronism of fire extinguishing agent concentration measuring device
By recording flow data at the channel entrance of the fire extinguishing agent concentration measurement device and calculating the flow time difference, the problem of difficult to measure the channel synchronization of the fire extinguishing agent concentration measurement device is solved, and the accurate evaluation of the channel synchronization is achieved, ensuring the effective performance evaluation of the fire extinguishing system.
Patent Information
- Application Number
- CN202510588751.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-08
- Publication Date
- 2025-07-25
AI Technical Summary
The prior art cannot effectively measure the channel synchronization of the fire extinguishing agent concentration measurement device, resulting in the inability to evaluate the fire extinguishing performance of the aircraft fire extinguishing system.
The flow meter is externally connected to the inlets of each channel to be measured in the fire extinguishing agent concentration measuring device, and the flow data is recorded and the difference between the maximum and minimum values of the gas flow time is calculated according to the pipe diameter and length of the sampling tube to determine the channel synchronization.
Accurate measurement of the channel synchronization of the fire extinguishing agent concentration measurement device is achieved, ensuring effective evaluation and performance verification of the fire extinguishing system.
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Figure CN120369536A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of aircraft flight test measurement, and more particularly to a method for measuring the channel synchronization of a fire extinguishing agent concentration measurement device. Background Art
[0002] Currently, in the flight test of an aircraft fire extinguishing system, it is necessary to obtain the volume concentration of the fire extinguishing agent at the measurement points in the engine compartment and the APU compartment after the fire extinguishing agent is released from the fire extinguishing system, so as to evaluate the fire extinguishing performance of the aircraft engine compartment and the APU compartment. At this time, a fire extinguishing agent concentration measurement device is often used, and the inside of the device has multiple channels for gas circulation to fully collect the gas at each measurement point and measure its concentration.
[0003] In order to ensure the fire extinguishing performance of the aircraft fire extinguishing system, there are relevant industry standards for the injection dose of the fire extinguishing agent, the injection rate of the fire extinguishing agent, the distribution of the fire extinguishing agent, the density of the fire extinguishing agent, the volume concentration of the fire extinguishing agent, and the duration of the fire extinguishing agent.
[0004] For example, regarding the volume concentration of the fire extinguishing agent and the duration of the fire extinguishing agent, in Article 5.3.2.2, Sub-item (b) of GJB3275A-2022 "Installation and Test Requirements for Aircraft Fire Extinguishing Systems", for a high-rate fixed fire extinguishing system, it is required that when using Halon1301 fire extinguishing agent, the volume concentration of the fire extinguishing agent formed in all parts of its action area after injection should be at least 6%, and the duration of this fire extinguishing agent concentration in all parts of its action area should be not less than 0.5 s.
[0005] However, up to now, when the fire extinguishing agent concentration measurement device is used normally, it is impossible to judge the channel synchronization of the fire extinguishing agent concentration measurement device from the fire extinguishing agent concentration measurement data, and moreover, no method for measuring the channel synchronization of the fire extinguishing agent concentration measurement device has been disclosed in domestic and foreign patent literatures. Summary of the Invention
[0006] The present invention is completed in view of the above technical problems, and its purpose is to provide a method for measuring the channel synchronization of a fire extinguishing agent concentration measurement device, which can measure the channel synchronization of the fire extinguishing agent concentration measurement device.
[0007] To achieve the above object, a first aspect of the present invention provides a method for measuring the channel synchronization of a fire extinguishing agent concentration measurement device, wherein the outlet of the fire extinguishing agent concentration measurement device is connected to a vacuum pump, and the method includes:
[0008] A step of powering on the fire extinguishing agent concentration measurement device and starting preheating;
[0009] Steps to detect that the fire extinguishing agent concentration measuring device reaches a preset temperature and the preheating is completed; steps to drive the vacuum pump to suck gas into the fire extinguishing agent concentration measuring device; steps to externally connect a flowmeter to the inlet of each measured channel of the fire extinguishing agent concentration measuring device; steps to record the flow data of the flowmeter and calculate the flow time of the gas in each sampling tube in combination with the pipe diameter and length of the required sampling tube; calculate the maximum value t max and the minimum value t min , and take the difference between the two as the flow time difference △t of the gas in the sampling tube; steps to judge the channel synchronization of the fire extinguishing agent concentration measuring device according to the flow time difference △t; and steps to cut off the power supply of the fire extinguishing agent concentration measuring device and evacuate.
[0010] According to the above method, by externally connecting a flowmeter to the inlet of each measured channel of the fire extinguishing agent concentration measuring device, the channel synchronization of the fire extinguishing agent concentration measuring device can be measured.
[0011] The method for measuring the channel synchronization of the fire extinguishing agent concentration measuring device in the second aspect of the present invention is based on the method for measuring the channel synchronization of the fire extinguishing agent concentration measuring device in the first aspect of the present invention. In the step of calculating the flow time of the gas in each required sampling tube, it satisfies:
[0012]
[0013] wherein, Q i (i = 1, 2,...) represents the gas flow rate at the inlet of each measured channel of the fire extinguishing agent concentration measuring device, L i (i = 1, 2,...) represents the length of the sampling tube connected to each measured channel of the fire extinguishing agent concentration measuring device or the length of the required sampling tube, φ i (i = 1, 2,...) represents the inner diameter of the sampling tube connected to each measured channel of the fire extinguishing agent concentration measuring device or the inner diameter of the required sampling tube. The length L i (i = 1, 2,...) of the sampling tube is the same, and the inner diameter φ i (i = 1, 2,...) of the sampling tube is the same.
[0014] According to the above method, the flow time of the gas in each required sampling tube can be obtained through simple calculation, and the synchronization of each measured channel can be judged intermittently based on the differences between these flow times. Description of the Drawings
[0015] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required in the embodiments will be briefly introduced below. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can be obtained based on these drawings.
[0016] Figure 1 It is a system diagram showing a method for measuring the channel synchronization of a fire extinguishing agent concentration measuring device for implementing the first embodiment of the present invention.
[0017] Figure 2 It is a flowchart showing a method for measuring the channel synchronization of a fire extinguishing agent concentration measuring device for the first embodiment of the present invention.
[0018] Figure 3 It is a system diagram showing a method for measuring the channel synchronization of a fire extinguishing agent concentration measuring device for implementing the second embodiment of the present invention.
[0019] Figure 4 It is a flowchart showing a method for measuring the channel synchronization of a fire extinguishing agent concentration measuring device for the second embodiment of the present invention.
[0020] (Symbol description)
[0021] 1 Measuring system for the channel synchronization of a fire extinguishing agent concentration measuring device;
[0022] 11 Fire extinguishing agent concentration measuring device;
[0023] 111 The first measured channel;
[0024] 112 The second measured channel;
[0025] 113 The third measured channel;
[0026] 114 The fourth measured channel;
[0027] 115 The fifth measured channel;
[0028] 116 The sixth measured channel;
[0029] 117 The seventh measured channel;
[0030] 118 The eighth measured channel;
[0031] 119 The ninth measured channel;
[0032] 11A The tenth measured channel;
[0033] 11B The eleventh measured channel;
[0034] 11C The twelfth measured channel;
[0035] 12 Vacuum pump;
[0036] 13 Fire extinguishing agent collection device;
[0037] 2 Equipment - end flowmeter;
[0038] 21 Equipment - end flowmeter for the 1st channel;
[0039] 22 Equipment - end flowmeter for the 2nd channel;
[0040] 23 Equipment - end flowmeter for the 3rd channel;
[0041] 24 Equipment - end flowmeter for the 4th channel;
[0042] 25 Equipment - end flowmeter for the 5th channel;
[0043] 26 Equipment - end flowmeter for the 6th channel;
[0044] 27 Equipment - end flowmeter for the 7th channel;
[0045] 28 Equipment - end flowmeter for the 8th channel;
[0046] 29 Equipment - end flowmeter for the 9th channel;
[0047] 2A Equipment - end flowmeter for the 10th channel;
[0048] 2B Equipment - end flowmeter for the 11th channel;
[0049] 2C Equipment - end flowmeter for the 12th channel;
[0050] 3 Sampling - tube - end flowmeter;
[0051] 31 Sampling - tube - end flowmeter for the 1st channel;
[0052] 32 Sampling - tube - end flowmeter for the 2nd channel;
[0053] 33 Sampling - tube - end flowmeter for the 3rd channel;
[0054] 34 Sampling - tube - end flowmeter for the 4th channel;
[0055] 35 Sampling - tube - end flowmeter for the 5th channel;
[0056] 36 Sampling - tube - end flowmeter for the 6th channel;
[0057] 37 Sampling - tube - end flowmeter for the 7th channel;
[0058] 38 Sampling - tube - end flowmeter for the 8th channel;
[0059] 39 Sampling - tube - end flowmeter for the 9th channel;
[0060] Flowmeter at the end of the sampling tube for Channel 10 of 3A;
[0061] Flowmeter at the end of the sampling tube for Channel 11 of 3B;
[0062] Flowmeter at the end of the sampling tube for Channel 12 of 3C;
[0063] 41 Sampling tube. Specific implementation manner
[0064] Hereinafter, with reference to Figures 1 to 4 A method for measuring the channel synchronization of the fire extinguishing agent concentration measuring device according to the first and second embodiments of the present invention will be described in detail.
[0065] (First embodiment)
[0066] In this embodiment, as Figure 1 shown, the fire extinguishing agent concentration measuring device 11 is configured in a multi-channel (for example, 12 measured channels) manner. By externally connecting the device-end flowmeters 2 (respectively, the device-end flowmeter 21 for Channel 1, the device-end flowmeter 22 for Channel 2, the device-end flowmeter 23 for Channel 3, the device-end flowmeter 24 for Channel 4, the device-end flowmeter 25 for Channel 5, the device-end flowmeter 26 for Channel 6, the device-end flowmeter 27 for Channel 7, the device-end flowmeter 28 for Channel 8, the device-end flowmeter 29 for Channel 9, the device-end flowmeter 2A for Channel 10, the device-end flowmeter 2B for Channel 11, the device-end flowmeter 2C for Channel 12) to the inlets of the 12 measured channels (respectively, the first measured channel 111, the second measured channel 112, the third measured channel 113, the fourth measured channel 114, the fifth measured channel 115, the sixth measured channel 116, the seventh measured channel 117, the eighth measured channel 118, the ninth measured channel 119, the tenth measured channel 11A, the eleventh measured channel 11B, the twelfth measured channel 11C) of the fire extinguishing agent concentration measuring device 11, the synchronization of each measured channel of the fire extinguishing agent concentration measuring device 11 is measured. However, the present invention is not limited thereto, and the following manner may also be adopted: The fire extinguishing agent concentration measuring device 11 is configured as a single channel and twelve are provided, and the above-mentioned flowmeters 2 are respectively externally connected to 12 fire extinguishing agent concentration measuring devices 11.
[0067] In this embodiment, as Figure 1As shown, the measurement system 1 for the channel synchronization of the fire extinguishing agent concentration measurement device includes: a fire extinguishing agent concentration measurement device 11, which includes 12 channels to be measured and can measure the fire extinguishing agent concentration in the channels to be measured; a vacuum pump 12, which is connected to the outlet of the fire extinguishing agent concentration measurement device 11 and sucks the gas at the measurement point into the fire extinguishing agent concentration measurement device 11; and a fire extinguishing agent collection device 13, which is connected to the outlet of the vacuum pump 12 to collect the fire extinguishing agent discharged from the vacuum pump 12.
[0068] It should be noted that, in this embodiment, it is determined whether each channel to be measured is synchronized by the flow time difference Δt of the gas flowing in each channel to be measured of the fire extinguishing agent concentration measurement device. The "flow time difference Δt of the gas flowing in each channel to be measured of the fire extinguishing agent concentration measurement device" consists of two parts. One part is the flow time difference Δt1 of the gas in each sampling tube, and the other part is the response time difference Δt2 of the gas in each channel to be measured of the fire extinguishing agent concentration measurement device. This part of the difference Δt2 includes the flow time difference of the gas in the channel to be measured and the response time difference of the data acquisition system. Since the response time difference Δt2 of the gas in each channel to be measured of the fire extinguishing agent concentration measurement device 11 is so small that it is difficult to obtain through theoretical measurement, therefore, the "flow time difference Δt of each channel to be measured of the fire extinguishing agent concentration measurement device" is approximately equal to the flow time difference Δt1 of the gas in each sampling tube. Therefore, in this embodiment, the flow time difference Δt of the gas in each channel to be measured of the fire extinguishing agent concentration measurement device is indirectly inferred by measuring the flow time difference Δt1 of the gas in each sampling tube.
[0069] Thus, according to the fire extinguishing agent concentration measurement device of this embodiment, since the sampling tube is not directly connected to the inlet of the fire extinguishing agent concentration measurement device, the gas flow rate in each sampling tube is inferred from the flow rate data of the above-mentioned device-side flow meters 2 (the first-channel device-side flow meter 21 to the 12th-channel device-side flow meter 2C). Specifically, according to the law of conservation of mass of the fluid, the flow rate of the fluid at each part of the sampling tube is conserved. Therefore, the flow rate data measured by the above-mentioned device-side flow meters 2 can also be regarded as the gas flow rate at other parts in the sampling tube. On this basis, combined with the pipe diameter and length of the required sampling tube (assuming that the inner diameters and lengths of each sampling tube are the same), the flow time of the gas in each sampling tube is calculated, and the maximum value t max and the minimum value t min are calculated, and the difference between the two is used as the flow time difference Δt of the gas in the sampling tube. The channel synchronization of the fire extinguishing agent concentration measurement device 11 is judged according to the flow time difference Δt.
[0070] The fire extinguishing agent concentration measuring device according to this embodiment can measure the channel synchronization of the measuring device by the following measuring method. Specifically, as Figure 2 shown:
[0071] Step S1: Power on the fire extinguishing agent concentration measuring device 11 and start preheating;
[0072] Step S2: Detect that the fire extinguishing agent concentration measuring device 11 reaches the preset temperature T 预设 , and the preheating is completed;
[0073] Step S3: Drive the vacuum pump 12 to suck gas into the fire extinguishing agent concentration measuring device 11;
[0074] Step S4: Connect the device-side flowmeter 2 to the inlet of each measured channel of the fire extinguishing agent concentration measuring device 11 in sequence;
[0075] Step S5: Record the flow rate data of each device-side flowmeter 2 in sequence, and calculate the flow time t of the gas in each required sampling tube in combination with the pipe diameter and length of the required sampling tube;
[0076] Step S6: Calculate the maximum value t max and the minimum value t min of the flow time t, and take the difference between the two as the flow time difference △t of the gas in the required sampling tube;
[0077] Step S7: Judge the channel synchronization of the fire extinguishing agent concentration measuring device 11 according to the flow time difference △t.
[0078] Step S8: Power off the fire extinguishing agent concentration measuring device 11 and remove it.
[0079] If △t ≤ 0.1 s, it can be judged that the channel synchronization of the fire extinguishing agent concentration measuring device 11 is qualified; if △t > 0.1 s, it can be judged that the channel synchronization of the fire extinguishing agent concentration measuring device 11 is unqualified.
[0080] In this embodiment, although the sampling tube is not actually installed, in order to calculate the flow time t of the gas in each required sampling tube, it can be assumed that the shapes and sizes of the 12 required sampling tubes are the same. If the length of each required sampling tube is set as L i (i = 1, 2,... 12), and the inner diameter is set as φ i (i = 1, 2,... 12), then the length L i and the inner diameter φ i of each required sampling tube are the same as each other.
[0081] If the gas flow rate measured by the above device-side flowmeter 2 (specifically, the device-side flowmeter 21 of the first channel to the device-side flowmeter 2C of the 12th channel) is set as Qi (where \(i = 1, 2, \ldots, 12\)), then combining with the above-mentioned length \(L\) i and inner diameter \(\varphi\) i , the flow time \(t\) of the gas flowing in the demand sampling tube can be calculated according to the following mathematical formula (1) i .
[0082]
[0083] where \(i\) is \(1, 2, \ldots, 12\).
[0084] According to the method for measuring the channel synchronization of the fire extinguishing agent concentration measuring device of the present embodiment, it is not necessary to connect sampling tubes to the inlets of the respective measured channels of the measuring device to measure the channel synchronization. Therefore, the channel synchronization of the fire extinguishing agent concentration measuring device can be measured with a simple structure. In addition, the operations of connecting the respective device-side flow meters 2 to the inlets of the respective measured channels of the fire extinguishing agent concentration measuring device 11 and obtaining the measurement data of the respective device-side flow meters 2 are both simple. Therefore, the channel synchronization of the fire extinguishing agent concentration measuring device can be measured through simple operations.
[0085] (Second Embodiment)
[0086] As described above, with reference to Figures 1 to 2 the method for measuring the channel synchronization of the fire extinguishing agent concentration measuring device of the first embodiment has been described in detail. In the above embodiment, the flow rate of the gas in each measured channel is the flow rate data measured by the flow meter externally connected to the inlet of each measured channel.
[0087] Hereinafter, with reference to Figure 3 the second embodiment will be described in detail. The structure of the fire extinguishing agent concentration measuring device of the present embodiment is the same as that of the above embodiment except that the connection method of the flow meter for measuring the flow rate of the gas flowing in the sampling tube is different from that of the above embodiment. Here, the detailed description of other structures is omitted.
[0088] In the present embodiment, as Figure 3As shown, connect 12 sampling tubes 41 to the inlets of the respective channels to be measured of the fire extinguishing agent concentration measuring device (specific illustrations of the respective channels to be measured are omitted), connect the device-side flow meters 2 (specifically, the device-side flow meter 21 of the first channel to the device-side flow meter 2C of the 12th channel) to the inlets of the 12 channels to be measured of the fire extinguishing agent concentration measuring device 11, and connect the sampling tube-side flow meters 3 (specifically, the sampling tube-side flow meter 31 of the first channel to the sampling tube-side flow meter 3C of the 12th channel) to the inlets of the 12 sampling tubes 41, and measure the gas flow data through the above-mentioned device-side flow meters 2 and sampling tube-side flow meters 3. That is to say, in this embodiment, the average value of the flow data at the inlets of the respective channels to be measured of the fire extinguishing agent concentration measuring device 11 and the flow data at the inlets of the respective sampling tubes 41 is used as the gas flow of each channel to be measured.
[0089] In this embodiment, the shapes and sizes of the 12 sampling tubes 41 are the same. Specifically, if the length of each sampling tube 41 is set to L i (i = 1, 2,... 12), and the inner diameter of each sampling tube 41 is set to φ i (i = 1, 2,... 12), then the lengths L i and inner diameters φ i of each sampling tube 41 are the same as each other.
[0090] If it is assumed that the gas flow measured by the above 12 device-side flow meters 2 is Q i (i = 1, 2,... 12), and the gas flow measured by the above 12 sampling tube-side flow meters 3 is q i (i = 1, 2,... 12), then the average gas flow P i in each sampling tube 41 is i = (Q i + q i ) / 2 (i = 1, 2,... 12). Based on the above average flow P i , the flow time t
[0091]
[0092] of the gas flowing in the sampling tube 41 is calculated by combining the following mathematical formula (2).
[0093] According to the fire extinguishing agent concentration measuring device of this embodiment, the channel synchronization of the measuring device can be measured by the following measuring method. Specifically, as Figure 4 shown:
[0094] Step S11: Power on the fire extinguishing agent concentration measuring device 11 and start preheating;
[0095] Step S12: Detect that the fire extinguishing agent concentration measuring device 11 reaches the preset temperature T 预设 , and the preheating is completed;
[0096] Step S13: Connect the 12 sampling tubes 41 to the inlets of the 12 measured channels of the fire extinguishing agent concentration measuring device 11 respectively, and drive the vacuum pump 12 to suck the gas into the fire extinguishing agent concentration measuring device 11;
[0097] Step S14: Connect the device - end flowmeter 2 to the inlets of the respective measured channels of the fire extinguishing agent concentration measuring device 11 in sequence, and connect the sampling - tube - end flowmeter 3 to the inlets of the 12 sampling tubes 41 in sequence;
[0098] Step S15: Record the flow data of each device - end flowmeter 2 and sampling - tube - end flowmeter 3 in sequence, and calculate the average flow rate P of the gas flowing in each sampling tube 41 i , based on this average flow rate P i and combined with the pipe diameters and lengths of the respective sampling tubes 41 connected correspondingly, calculate the flow time t of the gas in each sampling tube 41;
[0099] Step S16: Calculate the maximum value t max and the minimum value t min of the flow time t, and take the difference between the two as the flow time difference △t of the gas in the sampling tube 41;
[0100] Step S17: Judge the channel synchronization of the fire extinguishing agent concentration measuring device 11 according to the flow time difference △t.
[0101] Step S18: Cut off the power supply of the fire extinguishing agent concentration measuring device 11 and withdraw it.
[0102] If △t ≤ 0.1 s, it can be judged that the channel synchronization of the fire extinguishing agent concentration measuring device 11 is qualified; if △t > 0.1 s, it can be judged that the channel synchronization of the fire extinguishing agent concentration measuring device 11 is unqualified.
[0103] According to the method for measuring the channel synchronization of the fire extinguishing agent concentration measuring device according to this embodiment, since the average flow rate of the gas flow at the inlets of each measured channel and the gas flow at the inlets of each sampling tube is used as the gas flow rate of each measured channel, therefore, compared with the above - mentioned first embodiment, the gas flow rate is more accurate, and thus the flow time of the gas in each sampling tube can be measured more accurately. In this way, the channel synchronization of the fire extinguishing agent concentration measuring device can be measured more accurately.
[0104] In the present invention, the number of measurement channels of the fire extinguishing agent concentration measuring device and the number of sampling tubes connected thereto are both set to 12, but the present invention is not limited thereto, and other numbers can also be set.
[0105] As described above, the first and second embodiments of the present invention have been described in detail. However, the present invention is not limited thereto. As long as it does not deviate from the gist of the present invention, the technical solutions obtained by simply transforming, combining or replacing the elements of the first and second embodiments of the present invention are all included within the scope of the present invention.
[0106] In the above embodiment, the number of measured channels of the fire extinguishing agent concentration measuring device to be measured is set to 12, and correspondingly, the number of sampling tubes is also set to 12. However, the present invention is not limited thereto, and it can also be set to other numbers.
[0107] Although in the above second embodiment, the shapes and sizes of the respective sampling tubes are the same, the present invention is not limited thereto. In the case where the shapes and sizes of the respective sampling tubes are different in the actual application scenario, at this time, external flow meters can be connected at multiple locations such as the inlets of the sampling tubes and the inlets of the respective measured channels of the fire extinguishing agent concentration measuring device to accurately obtain the flow rate data of the gas flowing in each sampling tube.
Claims
1. A measuring method for the channel synchronization of a fire extinguishing agent concentration measuring device, wherein the outlet of the fire extinguishing agent concentration measuring device is connected to a vacuum pump. Characterized in that, It includes: A step of powering on the fire extinguishing agent concentration measuring device and starting preheating; A step of detecting that the fire extinguishing agent concentration measuring device reaches a preset temperature and the preheating is completed; A step of driving the vacuum pump to suck gas into the fire extinguishing agent concentration measuring device; A step of externally connecting a flowmeter to the inlet of each measured channel of the fire extinguishing agent concentration measuring device; A step of recording the flow data of the flowmeter and calculating the flow time of the gas in each sampling tube in combination with the pipe diameter and length of the required sampling tube; Calculate the maximum value t of the flow time max and the minimum value t min , and take the difference between the two as the flow time difference △t of the gas in the sampling tube A step of judging the channel synchronization of the fire extinguishing agent concentration measuring device according to the flow time difference △t; And A step of powering off the fire extinguishing agent concentration measuring device and withdrawing it.
2. The measuring method for the channel synchronization of a fire extinguishing agent concentration measuring device according to claim 1, characterized in that In the step of calculating the flow time of the gas in each sampling tube, it satisfies: Among them, Q i (i = 1, 2, ……) represents the gas flow rate at the inlet of each measured channel of the fire extinguishing agent concentration measuring device, L i (i = 1, 2, ……) represents the length of the sampling tube connected to each measured channel of the fire extinguishing agent concentration measuring device or the required length of the sampling tube, φ i (i = 1, 2, ……) represents the inner diameter of the sampling tube connected to each measured channel of the fire extinguishing agent concentration measuring device or the required inner diameter of the sampling tube. The length L of the sampling tube i (i = 1, 2, ……) is the same. The inner diameter φ of the sampling tube i (i = 1, 2, ……) is the same.