Permafrost block stone base layer ventilation effect detection system and method

Abstract

The invention relates to the technical field of ventilation detection, and provides a permafrost block stone base layer ventilation effect detection system and a permafrost block stone base layer ventilation effect detection method. Pushing the detection system to an air inlet side, and adjusting an adjustable pull rod structure to enable the end face of the bin body and the slope of the roadbed to be attached and sealed; starting a fan, adjusting the wind speed, and collecting multiple groups of wind speed and wind pressure data; on the basis of the acquired data, fitting and calculating permeability and an inertial resistance coefficient by adopting a least square method; and finally evaluating the ventilation effect of the block stone roadbed according to the permeability and the inertia resistance coefficient. According to the external measurement method of fan ventilation and sensor arrangement, destructive behaviors of drilling, excavation and subgrade structure dismantling do not need to be carried out on the subgrade, meanwhile, the original pore structure of the block stone base layer is not damaged, it is ensured that the mechanical stability and the service performance of the subgrade are not affected, and the construction period is shortened. The method is suitable for regular detection of projects using block stone base layers.

Description

Technical Field

[0001] This invention relates to the field of ventilation testing technology, and more specifically, to a system and method for testing the ventilation effect of boulders in permafrost areas. Background Technology

[0002] Under the influence of global warming and intensified engineering activities in cold regions, the temperature in the permafrost areas of the plateau is rising continuously. The engineering problems caused by the thawing and deformation of permafrost are becoming increasingly serious and have become one of the main factors affecting the service life of transportation infrastructure in cold regions.

[0003] To address the issue of thaw settlement in permafrost engineering projects, measures such as riprap subgrade, heat pipe subgrade, and heat-insulating board subgrade have alleviated the problem to some extent. However, they still cannot completely solve the problems of pavement cracking and subgrade deformation caused by permafrost thaw settlement. Therefore, exploring solutions to permafrost thaw settlement is crucial for the design, construction, and operation and maintenance of projects in cold regions.

[0004] Due to its low cost and ease of construction, riprap subgrade is one of the main types of subgrades in plateau regions. Its core cooling mechanism relies on its internal ventilation capacity. Utilizing the high porosity of the riprap layer and the high wind speeds and temperature differences of the plateau, air can flow within the riprap subgrade, facilitating heat exchange and thus protecting the permafrost. During the warm season, hot air rises, while the gas inside the riprap subgrade remains in a state of heat conduction, maintaining a relatively low temperature and reducing heat transfer to the foundation. During the cold season, cold air infiltrates along the pores inside the riprap subgrade, and the internal gas is in a state of thermal convection, promoting the active transfer of cold energy to the foundation, thereby lowering the subgrade temperature. Simultaneously, the prevailing winds of the plateau blow along the cross slope of the subgrade, creating "wind tunnels" through the openings in the riprap layer. This drives horizontal airflow through the middle of the subgrade, enhancing lateral ventilation and strengthening heat exchange in the lower and middle sections, further improving overall cooling efficiency.

[0005] Rockfill subgrades are widely used in cold-region engineering projects, but their ventilation capacity is easily weakened by multiple factors. First, the instability of construction quality: rockfill subgrades are often constructed using the dumping method, but due to a lack of precise control, the accumulation of rocks is relatively random, resulting in a significant deviation between the internal porosity of the subgrade and the design. Second, erosion from the external environment: frequent wind and sand activity in high-altitude areas allows fine sand and dust to seep into the subgrade and gradually fill the pores; rainwater or snowmelt carrying fine soil particles can also clog the pores. Third, disturbance from operational loads: during line operation, long-term vehicle loads can cause displacement and fragmentation of the rocks, potentially leading to overly dense accumulation in localized areas, thereby reducing porosity and the connectivity of ventilation channels. Poor ventilation of the rockfill subgrade will affect the stability of the underlying permafrost, threatening the safe operation of the line.

[0006] However, a systematic approach to evaluating the ventilation effect of riprap subgrades is still lacking. Existing monitoring methods are mostly limited to measuring temperature fields or deformation, and there are no mature standards or methods for quantitatively assessing ventilation capacity. This not only limits the optimization of subgrade design but also hinders the development of maintenance strategies. For example, in the later stages of subgrade service, if the degree of ventilation blockage cannot be assessed in a timely manner, it is difficult to take targeted repair measures, such as cleaning pores or reinforcing the structure. Summary of the Invention

[0007] In view of this, the present invention proposes a ventilation effect detection system and method for riprap subgrade in permafrost areas. Through real-time detection and data acquisition, the ventilation effect of riprap subgrade is quantified. It can provide quality control methods during the construction phase to improve construction accuracy, and can dynamically monitor performance during the operation phase to guide precise maintenance. It also has the advantages of being non-destructive, widely applicable, and data-supported, providing a scientific basis for the construction quality control and subsequent operation and maintenance of riprap subgrade.

[0008] To achieve the above objectives, this invention proposes a ventilation effect testing system for riprap foundations in permafrost areas, comprising: Fans are used to provide adjustable airflow for testing. A sealed chamber is used to move and position its rear end connected to the fan. It has a fluid channel inside and the inner wall of the sealed chamber is lined with a layer of thermal insulation material. A honeycomb rectifier is fixed inside the sealed chamber near the outlet side to convert the turbulent flow generated by the fan into a uniform laminar flow. The frame of the honeycomb rectifier is provided with sealing rubber strips around its perimeter. A slope adaptive adjustment mechanism is connected to the front end face of the silo body and includes a telescopic tie rod structure for adjusting the inclination angle of the end face of the silo body relative to the horizontal plane so that the opening end of the silo body fits tightly against the slope of the roadbed. The sensor system includes an air intake sensor group arranged on the air intake side of the rubble roadbed and an air outlet sensor group arranged on the air outlet side. Each sensor group includes a wind speed sensor and a wind pressure sensor. The control panel, located on the outer surface of the chamber, is connected to the sensor system via a low-temperature resistant circuit. It is used to set the initial wind speed, speed adjustment step size, and total detection time of the fan, and to display the wind speed and pressure distribution curves of each section in real time.

[0009] Furthermore, the air outlet sensor group includes at least three parallel measurement sections arranged laterally along the roadbed, wherein the middle section is perpendicularly corresponding to the position of the air inlet side sensor group, and the other two sections are symmetrically distributed on both sides of the middle section, and each section has multiple measurement points evenly distributed along the roadbed height direction.

[0010] Further, the sensor system is connected to the data collector through a low-temperature-resistant circuit to adapt to the low-temperature environment.

[0011] Further, the honeycomb rectifier is composed of an aluminum alloy frame wrapping a honeycomb core, and sealing rubber strips are provided around it.

[0012] Further, the periphery of the front end face of the bin body is wrapped with a compressible sealing material, which is used to achieve airtight contact with the roadbed surface under the action of the telescopic pull rod structure.

[0013] Further, universal wheels are provided at the bottom of the sealed bin body.

[0014] On the other hand, to achieve the above object, the present invention proposes a method for detecting the ventilation effect of a block stone roadbed using the above system, including the following steps: Sensors are respectively arranged on the air inlet side and the air outlet side of the block stone roadbed; Push the sealed bin body to the roadbed slope, and through adjusting the telescopic pull rod structure, make the opening end face of the bin body tightly press against the roadbed slope to form a closed air chamber; Start the fan, adjust the fan speed through the operation panel to generate at least three different gradient initial wind speeds, and use the sensor system to collect and store the wind pressure gradient and flow velocity data on the air inlet and outlet sides of the block stone roadbed under different wind speed conditions; Based on the collected wind speed / wind pressure data, construct a non-linear partial differential equation set based on the Forchheimer equation, and use the least square method for fitting inversion to solve the permeability k and inertial resistance coefficient β characterizing the ventilation characteristics of the block stone roadbed; According to the fitted permeability k and inertial resistance coefficient β, compare them with the preset standard threshold of the block stone base gradation to determine whether there is a risk of pore fouling or ventilation failure inside the roadbed.

[0015] Further, the data collection interval is once every 10 minutes, and the fan speed is adjusted during the test process to obtain data under different ventilation intensities.

[0016] Further, in the process of evaluating the ventilation effect of the block stone roadbed according to the permeability k and inertial resistance coefficient β, the Reynolds number is used to describe the air flow state. When the Reynolds number is less than 5, the linear Darcy's law is used to describe the air flow state. When 5 < Re < 100, the influence brought by the inertial force is considered. When Re > 100, the influence of the inertial force brought by the air flow is considered, and the Forchheimer equation is used for description; In the data processing link, the principle of minimizing the sum of squared residuals is used to establish an objective function, and the coefficient of determination is calculated to evaluate the degree of coincidence between the fitting curve and the measured data.

[0017] Furthermore, the calculation methods for the permeability k and the inertial drag coefficient β are as follows:

[0018] in, The dynamic viscosity of air. For fluid density, , The parameters are used to ensure that the fitted curve best matches the measured data.

[0019] Compared with the prior art, the beneficial effects of the present invention are as follows: The method of this invention uses ventilation by fans and external measurement by deploying sensors, which eliminates the need for destructive actions such as drilling, excavation, and demolition of the roadbed structure. At the same time, it does not damage the original pore structure of the riprap base, ensuring that the mechanical stability and service performance of the roadbed are not affected. It is suitable for periodic inspection of projects using riprap bases, such as the Qinghai-Tibet Railway and highways in service.

[0020] The aerodynamic system proposed in this invention can flexibly adjust the fan power and sensor array density according to the roadbed width, and is suitable for boulders roadbeds with different particle sizes, different porosities and different degrees of blockage, and has wide applicability.

[0021] This invention can provide penetration rate through sensor deployment and data acquisition system. k Inertial drag coefficient β Quantitative indicators such as wind speed and wind pressure provide a scientific basis for design optimization and precise maintenance, thereby improving the level of intelligent management of infrastructure in cold regions. Attached Figure Description

[0022] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. In the drawings: Figure 1 This is a schematic diagram of the ventilation effect detection system for permafrost block base courses proposed in this invention. Figure 2 This is a flowchart of the ventilation effect detection method for boulders base courses in permafrost areas according to an embodiment of the present invention; Figure 3 This is a rear view of the detection system in an embodiment of the present invention; Figure 4 This is a side view of the detection system in an embodiment of the present invention; Figure 5 This is the sensor layout scheme for the air inlet and air outlet sides in an embodiment of the present invention; In the diagram: 1. Stone roadbed; 2. Natural soil layer; 3. Wind speed and wind pressure sensors; 4. Low temperature resistant circuit; 5. Honeycomb rectifier; 6. Telescopic tie rod structure; 7. Chamber body; 8. Control panel; 9. Data acquisition device; 10. Fan. Detailed Implementation

[0023] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the disclosure to those skilled in the art. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0024] This embodiment proposes a system for testing the ventilation effect of boulders base courses in permafrost areas, such as... Figure 1 As shown, it includes: (1) Fan 10: As a wind source, it is connected to the back of the chamber and its blowing direction is directed towards the inside of the chamber 7. It is used to provide a stable test airflow to the rubble roadbed 1.

[0025] (2) Chamber 7: It is a rectangular sealed structure and is the core component of the device. Its inner wall is lined with thermal insulation material to reduce the influence of the external ambient temperature on the test airflow. The bottom of Chamber 7 is equipped with casters for easy movement and positioning.

[0026] (3) Operation panel 8: Fixed to the outer surface of the casing 7, including a digital display panel and operation buttons. The digital display panel is used to display information such as wind speed and wind pressure in real time; the operation buttons are used to control the start and stop of the fan, the speed, and to set the detection time. The operation panel is electrically connected to the internal controller.

[0027] (4) Data acquisition unit 9: installed on the side wall of the chamber 7, responsible for receiving and storing measurement data from various sensors.

[0028] (5) Honeycomb rectifier 5: It is fixed inside the chamber 7 by bolts and is located on the side close to the paved roadbed 1. Its function is to straighten the turbulent airflow generated by the fan into a uniform and stable direct current airflow, ensuring that the initial state of the airflow entering the paved roadbed 1 is consistent. The rectifier uses an aluminum alloy frame to wrap the honeycomb core, and the frame is equipped with sealing rubber strips around it to ensure the airtightness with the chamber 7.

[0029] (6) Telescopic tie rod structure 6: In order to adapt to the slope of the boulders roadbed 1 with different slopes, the rectangular end face of the silo 7 that contacts the boulders roadbed 1 is designed as a telescopic tie rod structure to ensure that the silo can fit tightly against the slope with different slopes.

[0030] (7) Sensor system 3: including wind speed sensor and wind pressure sensor. All sensors are connected to the data acquisition unit using low temperature resistant wiring to adapt to the cold environment such as plateau permafrost areas.

[0031] Controllable airflow is achieved through a variable frequency fan and an inlet rectifier section. The overall sealed device isolates the test from external environmental influences, ensuring test accuracy. The wind speed is adjusted by changing the frequency of the inverter, covering natural ventilation to forced ventilation. A honeycomb rectifier 5 is installed in the inlet rectifier section to provide uniform, stable, and repeatable laminar flow for the test section of the rubble roadbed 1.

[0032] Data is collected by installing sensor systems 3 on both sides of the riprap roadbed 1 and by using a multi-channel data acquisition instrument. The collected data includes wind speed, wind pressure, and wind direction.

[0033] The riprap subgrade 1, through the porous structure formed by the riprap layer, allows air to flow and exchange heat internally, stabilizing the subgrade temperature field and protecting the underlying frozen soil base. Therefore, when testing the ventilation capacity of the riprap subgrade 1, a fan 10 is used to drive air to flow inside the riprap subgrade 1. The riprap layer in the riprap subgrade 1 can be described as a porous medium with riprap as a solid skeleton and internal pores filled with air. Therefore, the relationship between the measured air pressure and seepage velocity in this test can be described using the momentum equation describing the seepage of porous media.

[0034] In the evaluation of ventilation effect of rubble roadbed 1, the Reynolds number is used to determine the flow state of air in rubble roadbed 1 (laminar flow, transitional flow, turbulent flow). Generally speaking, when the Reynolds number... When the Reynolds number is 1, Darcy's law applies to linear cases; when the Reynolds number is 2, Darcy's law applies to linear cases. When considering the influence of inertial forces, it is necessary to take into account the Reynolds number. When linear terms are negligible, the Reynolds number can be calculated as follows for flow in porous media:

[0035] in, For fluid density; The average flow velocity; It is the characteristic length, which in the test refers to the average particle size of the stone. Porosity of the medium; This refers to the dynamic viscosity of air.

[0036] when In this case, Darcy's law can be used to describe the situation linearly:

[0037] in, The seepage velocity; For penetration rate; The dynamic viscosity of air; This represents the pressure gradient.

[0038] when When considering the influence of inertial forces caused by airflow, the Forchheimer equations are used to describe this:

[0039] in, The pressure difference between two points; To be with pressure difference Corresponding distance; This is the inertial drag coefficient; For fluid density; The average flow velocity is denoted as .

[0040] The penetration rate was obtained by fitting the data collected through testing using the least squares method. and inertial drag coefficient By substituting variables, the Forchheimer equation can be rewritten as:

[0041] in, This represents the measured pressure gradient; Let these represent the linear and quadratic terms on the right-hand side of the equation, respectively; the coefficients to be determined are... .

[0042] For each set of measured data, we can write the above equation. Our goal is to find a set of parameters. This makes the values ​​calculated from this set of parameters... The fitted value and the measured value The sum of squared residuals (SSE) between values ​​is minimized.

[0043] The objective function is:

[0044] According to the least squares principle, the one that minimizes SSE is... The following system of normal equations must be satisfied:

[0045] Among them, all summation operations are performed on... arrive (i.e., all data groups) are processed.

[0046] Based on measured data ,calculate: Calculate the sum of all terms in the system of canonical equations:

[0047]

[0048]

[0049] Substitute the calculated value into the system of regular equations: Solving this system of equations, the determinant of the coefficient matrix is:

[0050] but:

[0051]

[0052] The calculation results obtained from the above steps are as follows:

[0053] Calculate the coefficient of determination This is to evaluate the degree of agreement between the fitted curve and the measured data.

[0054]

[0055]

[0056] in, It is the sum of squared residuals; It is the total sum of squares; The closer the value is to 1, the better the fit.

[0057] To achieve accurate and on-site measurement of the ventilation effect (such as permeability and inertial resistance) of the rubble roadbed 1, this invention provides a method for using the above system, as detailed below: Step 1: On-site setup and equipment placement (1) Sensor deployment: Air intake side layout: On the selected test section of the riprap roadbed 1 (i.e. the section where the detection device is to be placed), wind speed and wind pressure sensors are evenly distributed along the height direction of the roadbed.

[0058] Air outlet side layout: such as Figure 5As shown, three parallel cross-sections were selected on the other side of the roadbed (the air outlet side) for measurement. The middle cross-section corresponds perpendicularly to the air inlet side cross-section, and the other two cross-sections are located 1 meter to either side of the middle cross-section. Sensors were evenly distributed along the height of each cross-section in the same manner as on the air inlet side. This arrangement effectively assesses the flow-around effect caused by uneven distribution of pores within the boulders, thus providing a more comprehensive reflection of the overall ventilation effect. For ultra-wide cross-sections, the number of air outlet side cross-sections can be increased to five or more, and the sensor arrangement can be adjusted from a simple linear arrangement to a staggered matrix arrangement.

[0059] Sensor protection: All sensors and wiring should be placed in a sealed compartment close to the roadbed slope to prevent interference from the external environment (such as wind, rain, and snow).

[0060] (2) Device installation: Push the testing device to the air inlet side section, and adjust the retractable tie rod structure 6 at the bottom of the chamber 7 so that its end face is completely in contact with the slope of the boulders roadbed 1. Wrap a sealing rubber strip in the contact area between the end face of the chamber 7 and the roadbed to ensure that the test airflow will not leak out and will be forced to pass through the boulders layer. If the roadbed surface is extremely uneven, the sealing rubber strip can be replaced with an inflatable flexible sealing ring.

[0061] (3) Connect the data acquisition unit and measurement: All sensors on the inlet and outlet sides are connected to their corresponding data acquisition units via low-temperature resistant wiring. The precise horizontal distances between the three sections on the inlet and outlet sides are manually measured as the raw data for subsequent calculations.

[0062] Step 2: Start the test and data collection (1) Start the fan 10 through the operation panel 8 and set an initial wind speed and a total detection time.

[0063] (2) The data acquisition device 9 is set to automatically collect data from all sensors (including wind speed and wind pressure at each point) every 10 minutes. The data acquisition device 9 supports remote wireless data transmission, viewing and export.

[0064] (3) During the test, the fan speed of the fan 10 can be adjusted through the operation panel 8 to obtain data under different ventilation intensities. The data acquisition unit 9 supports remote wireless data transmission, which makes it convenient for staff to view and export data in real time.

[0065] Step 3: Data Processing and Analysis (1) Data preprocessing: The collected raw data is cleaned, and outliers caused by sensor malfunctions or other reasons are checked and removed. For individual missing data, interpolation is used to complete them.

[0066] (2) Parameter inversion calculation: The preprocessed wind pressure and wind speed data are combined with the Darcy-Fochheimer law and fitted using the least squares method to invert the two key parameters characterizing the ventilation effect of the riprap subgrade: Permeability (k): reflects the ease with which airflow passes through a rocky medium.

[0067] Inertial drag coefficient (β): reflects the inertial loss when high-speed airflow flows in a porous medium.

[0068] (3) By comparing the k and β values ​​calculated under different working conditions, the ventilation effect of the rubble roadbed can be quantitatively evaluated.

[0069] In summary, this implementation provides a complete and operable on-site testing solution. Through the design of adjustable sealed chamber, airflow rectification, and multi-section synchronous measurement, it effectively improves the adaptability, stability, and accuracy of on-site testing. Finally, through mathematical modeling, scientific and quantitative evaluation indicators are obtained.

[0070] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A system for testing the ventilation effect of riprap base courses in permafrost areas, characterized in that, include: Fans are used to provide adjustable airflow for testing. A sealed chamber is used to move and position its rear end connected to the fan. It has a fluid channel inside and the inner wall of the sealed chamber is lined with a layer of thermal insulation material. A honeycomb rectifier is fixed inside the sealed chamber near the outlet side to convert the turbulent flow generated by the fan into a uniform laminar flow. The frame of the honeycomb rectifier is provided with sealing rubber strips around its perimeter. A slope adaptive adjustment mechanism is connected to the front end face of the silo body and includes a telescopic tie rod structure for adjusting the inclination angle of the end face of the silo body relative to the horizontal plane so that the opening end of the silo body fits tightly against the slope of the roadbed. The sensor system includes an air intake sensor group arranged on the air intake side of the rubble roadbed and an air outlet sensor group arranged on the air outlet side. Each sensor group includes a wind speed sensor and a wind pressure sensor. The control panel, located on the outer surface of the chamber, is connected to the sensor system via a low-temperature resistant circuit. It is used to set the initial wind speed, speed adjustment step size, and total detection time of the fan, and to display the wind speed and pressure distribution curves of each section in real time.

2. The system according to claim 1, characterized in that, The air outlet sensor group includes at least three parallel measurement sections arranged laterally along the roadbed, wherein the middle section is perpendicularly corresponding to the position of the air inlet side sensor group, and the other two sections are symmetrically distributed on both sides of the middle section. Each section has multiple measurement points evenly distributed along the height direction of the roadbed.

3. The system according to claim 1, characterized in that, The sensor system is connected to the data acquisition unit via low-temperature resistant circuitry to adapt to low-temperature environments.

4. The system according to claim 1, characterized in that, The honeycomb rectifier consists of an aluminum alloy frame enclosing a honeycomb core, with sealing rubber strips around its perimeter.

5. The system according to claim 1, characterized in that, The periphery of the front end face of the compartment is wrapped with a compressible sealing material to achieve airtight contact with the roadbed surface under the action of the telescopic tie rod structure.

6. The system according to claim 1, characterized in that, The sealed compartment is equipped with casters at the bottom.

7. A method for detecting the ventilation effect of a riprap roadbed using the system described in any one of claims 1-6, characterized in that, Includes the following steps: Sensors were installed on the air inlet and air outlet sides of the rubble roadbed. The sealed chamber is pushed to the roadbed slope, and the opening end face of the chamber is pressed tightly against the roadbed slope by adjusting the telescopic tie rod structure to form a closed air chamber. Start the fan and adjust the fan speed through the control panel to generate at least three different initial wind speeds. Use the sensor system to collect and store the wind pressure gradient and flow velocity data of the inlet and outlet sides of the boulders roadbed under different wind speed conditions. Based on the collected wind speed / pressure data, a set of nonlinear partial differential equations based on the Forchheimer equations was constructed. The least squares method was used for fitting and inversion to solve for the permeability k and inertial drag coefficient β, which characterize the ventilation properties of the rubble roadbed. Based on the permeability k and inertial drag coefficient β obtained from the fitting, they are compared with the preset threshold of the gradation standard of the boulders to determine whether there is a risk of pore sludge or ventilation failure inside the roadbed.

8. The method according to claim 7, characterized in that, The data acquisition interval is once every 10 minutes. During the test, the fan speed is adjusted to obtain data under different ventilation intensities.

9. The method according to claim 7, characterized in that, In the process of evaluating the ventilation effect of block stone subgrade according to the permeability k and the inertial resistance coefficient β, the Reynolds number is used to describe the air flow state. When the Reynolds number is less than, the linear Darcy's law is used to describe the air flow state. When 5 < Re < 100, the influence brought by inertial force is considered. When Re > 100, the influence of inertial force brought by air flow is considered, and the Forchheimer equation is used for description; In the data processing stage, the objective function is established using the principle of minimizing the sum of squared residuals, and the coefficient of determination is calculated. To evaluate the degree of agreement between the fitted curve and the measured data.

10. The method according to claim 7, characterized in that, The calculation methods for the permeability k and the inertial drag coefficient β are as follows: ， in, The dynamic viscosity of air. For fluid density, , The parameters are used to ensure that the fitted curve best matches the measured data.

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