Study on the distribution law of airflow velocity in rectangular and semicircular roadway sections

Reliable ventilation is the cornerstone of safe production in coal mines, and accurate monitoring of ventilation parameters is the fundamental guarantee of ventilation technology decision‐making. To improve the accuracy of airflow velocity monitoring in coal mine roadways, theoretical analysis, numerical simulation, and field tests were utilized to study the distribution law of airflow velocity in typical roadway sections. First, the calculation model of position of mean airflow velocity line in rectangular and semicircular arch roadway is established based on Boussinesq theory and Pelant turbulence theory. Then, to verify the correctness of the theoretical model, 25 groups of numerical simulation tests were conducted by using COMSOL‐Multiphysics 3.5a software. The errors between theoretical analysis and numerical simulation are all less than 4%. In addition, the numerical results also show that the contour line of airflow velocity in roadway section is consistent with the shape of roadway section, and the isoline of airflow velocity is basically parallel to the roadway wall. In addition, the closer to the roadway wall, the denser the airflow velocity isoline, indicating that the airflow velocity gradient near the wall is larger. And the thickness of the boundary layer decreases with the increase of airflow inlet velocity. Finally, field tests have been conducted in Chongqing Research Institute and Sima Coal Mine to further verify the correctness of the calculation model and numerical simulation results. The measured distribution law of airflow velocity is consistent with the numerical simulation. And the errors between theoretical analysis and field tests are all less than 4%.


| INTRODUCTION
Coal mine safety has always been one of the most important parts in coal mine production. [1][2][3] With the gradual increase of mining depth, the possibility of coal mine disasters increases, which seriously threatens the production safety of coal mines. [4][5][6] A reasonable and reliable ventilation system is the guarantee of underground safety production. [7][8][9] In the actual ventilation situation in the coal mine, the air flow is turbulent. 10 The time-averaged air velocity distribution in the roadway section is uneven, that is, the airflow velocity at a point in the roadway section is related to the spatial position, so the airflow velocity sensor arranged at different positions may have different monitoring data. To accurately obtain the mean airflow velocity of the roadway according to the airflow velocity monitoring value of a certain point in the roadway, the field experiments or simulation research must be carried out to analyze and determine the reasonable suspension position of the airflow velocity sensor and the correction formula of the average airflow velocity monitoring. 11 Therefore, the accurate value of the mean airflow velocity in the roadway can be obtained through studying the velocity distribution of the air flow in the roadway, which is of great significance for the accurate calculation of the air volume and the reasonable distribution of the air volume for the coal mine. 12,13 According to the field test results, Luo et al. 14,15 studied the distribution of airflow in four rectangular section roadways with different supporting methods, and the results show that low airflow velocity region increases with surface roughness of the roof and wall. The high airflow velocity region was located around the floor of the roadway with rough roof and wall. However, in the roadways with smooth roof and wall, the high airflow velocity region was located around the center of section. To improve the accuracy of simulation results of mine ventilation, Janus and Krawczyk 16 applied the simultaneous multi-point measurements method in the field measuring airflow velocity distribution of tunnel cross-section, and introduced the SAS turbulence model into numerical modeling. Hu et al. 17 utilized the numerical modeling study the influence of wall surface roughness on the cross-sectional airflow distribution in roadway, and the results show that the influence of wall roughness on airflow velocity distribution can be reduced when the wall roughness value is less than 0.1 m. The noncontact Laser Doppler Velocimeter (LDA) is used to carry out experimental tests, and combined with numerical simulation, the stable flow of straight roadways and the air flow state after sudden expansion of sections are studied by Liu et al. [18][19][20] The results show that the airflow velocity in roadway shows turbulent characteristics, and the velocity vector and its direction display a normal Gaussian distribution. And a large eddy can be formed in the sudden enlarged area with highly irregular airflow fluctuating around 0.1-0.2 m/s. Li et al. 21 pointed out that the relation between the airflow velocity at any point (except viscous bottom) of the tube section and mean airflow velocity is nonlinear when the air flow is fully developed turbulent. However, when the mean air velocity is within a range of 0.78-6.2 m/s, and the former is proportional to the latter. Field tests carried out by Zhang 22 demonstrated that the logarithmic distribution formula can ideally describe the variation law of the airflow velocity field of the roadway section. Experiments conducted by Li et al. 23 indicated that the trend of airflow variation in the same roadway crosssection had nothing to do with the airflow velocity, and the airflow velocity decreased gradually along the central line of the roadway to the roadway wall. Wei et al. 24 put forward a method for accurate monitoring the tunnel airflow velocity by large-span ultrasonic linear airflow velocity sensor based on the method of the time difference, and studied the distribution rules of section airflow velocity in rectangular tunnel with various support forms. Ligeza et al. 25 established a threedimensional modeling of the structure of flow parameter fields in mine drifts, and obtained a set of data describing the parameters of flow in real transverse sections. To calibrate different types of anemometers in a low-speed range (0.2-1.25 m/s), Pezzotti et al. 26 built and characterized a wind tunnel. The wind tunnel calibration was performed by means of comparison of airspeed at the test cross-section (low-speed) and at the reference crosssection (high-speed). Based on the experimental and numerical results, combined with previous studies, Luo and Zhao 27 obtained the equation which can describe the airflow velocity distribution for the three types of coal mine tunnels taking into account the influence of central airflow velocity. Zhou et al. 28 studied the correction factors which is employed to convert a measured centerline air velocity to the mean air velocity using three measuring methods including single-point reading, moving traverse, and fixed-point traverse.
At present, there are few theoretical studies on the location of the mean airflow velocity in the roadway section. Through the combination of various research methods, it is only concluded that the mean airflow velocity line is a fixed position in the section, but the specific location has not been theoretically deduced. The installation position of airflow velocity monitoring sensor lacks theoretical basis in the roadway section, and the monitoring data is difficult to truly reflect the real airflow velocity of the sensor installation site, resulting in low monitoring effectiveness.
In this paper, the distribution law of airflow velocity in typical roadway sections is studied by different research methods. First, a mathematical model of the relationship between the mean airflow velocity line and the distance between the two sides of the roadway or the roof and floor in different types of roadway sections was established. And the numerical simulation, field test and other methods are used to verify the correctness of the model. The technical roadmap of this study is shown in Figure 1. This study is of great significance to improve the accuracy and access speed of ventilation parameters such as airflow velocity and air volume.

| THE MODEL OF THE RELATIONSHIP BETWEEN THE MEAN AIRFLOW VELOCITY LINE AND THE DISTANCE OF ROADWAY WALLS
Currently, airflow velocity monitoring is based primarily on point monitoring, and the layout of monitoring points in roadway section mainly relies on experience, which lacks theoretical basis. In this section, the theoretical model of the position of the mean airflow velocity line in the cross section of the rectangular and semicircular arch roadway is established, and the position relationship between the mean airflow velocity line and the roadway wall is obtained, which provides a theoretical basis for the accurate and rapid determination of the mean airflow velocity.

| Analysis of airflow movement characteristics in roadway
The flow state of airflow in shaft and roadway can be divided into two kinds, namely laminar flow and turbulent flow.
In coal mine ventilation, a dimensionless coefficient (Reynolds number) is usually used to distinguish the flow state of the fluid, and the dimensionless coefficient is expressed by Re. When the roadway section is circular, there are 29 : where v is the mean airflow velocity in the cross-section of shaft and roadway, m; υ is the coefficient of viscosity of airflow, m 2 /s; d is the pipe diameter, m.
In the case of noncircular roadway section, the Reynolds number formula is as follows 29 : where S is the cross-sectional area of roadway, m 2 ; U is the perimeter of roadway section, m. In general, laminar flow occurs when the Reynolds number Re is less than 2000, and the turbulent flow occurs when the Reynolds number Re is greater than 4000. When the Reynolds number Re ranges from 2000 to 4000, the flow may be laminar or turbulent.
The flow state of airflow in the underground roadway of can be judged according to the specific conditions. Supposing that the cross-section of a roadway is rectangular, and the size is 5 m × 3.2 m, the area is S = 16 m 2 , the perimeter of the section is U = 16.4 m, and the viscosity coefficient of air flow is υ = 14.4 × 10 −6 m 2 /s. According to Formula (2), the results are as follows 29 : By substituting the above parameters into the formula, it can be calculated that when the crosssectional area of the roadway is 16 m 2 , the mean airflow velocity of the transition from laminar flow to turbulent flow in the roadway is 0.009 m/s, that is, when the airflow velocity in the roadway is below 0.009 m/s, the airflow in the roadway is laminar flow; and when the airflow velocity is greater than 0.009 m/s, it is turbulent. The Coal Mine Safety Regulation requires that the airflow velocity in underground roadway and semi-coal-rock roadway should be not less than 0.25 m/s, and that of rock roadway should be not less than 0.15 m/s, much more than 0.009 m/s, so the airflow in most coal mines roadways is not in laminar state but in turbulent state.
This indicates that the airflow in all ventilation roadways in coal mines are normally in turbulent state.

| Main controlling factors of airflow velocity distribution in the roadway
According to the knowledge of fluid mechanics, combined with the airflow velocity distribution function and the mean airflow velocity calculation formula, it can be concluded that the airflow velocity distribution in roadway is mainly controlled by the frictional resistance coefficient of roadway α, the distance between the measuring point and the center line of the roadway r, and the shape and size of the roadway section. The frictional resistance coefficient α of the roadway is as follows 30 : where ρ is the air density, kg/m 3 ; λ is friction coefficient, and their values are measured by experiments. In the laminar flow region, λ is independent of the relative roughness ε/r, but only related to the Reynolds number Re, and λ = 64/Re; while in the resistance square region, λ is independent of the Reynolds number Re, but only related to the relative roughness. The Re value of the airflow in most ventilation roadways in coal mine is much greater than 4000 (the airflow is in a state of complete turbulence), and in this area 30 : where r is the equivalent pipe diameter of roadway, m, which is related to the shape and size of the roadway; ε is the absolute roughness of roadway wall, m, which is related to the support form and forming condition of roadway. This shows that the friction resistance coefficient is related to air density, roadway roughness, roadway section shape and roadway section size. The airflow velocity of a certain point in the roadway is related to the inlet air volume. In addition, in the field, the belt conveyor, air duct and various pipes placed in the roadway will have an impact on the airflow velocity distribution in the roadway. According to the general expression of airflow velocity at any point in roadway section obtained by Boussinesq theory and Prandtl turbulence theory, and based on the symmetrical relation of airflow velocity distribution in rectangular roadway, the calculation formula of air volume in rectangular cross-section is obtained by integral method, and the expression of the mean airflow velocity can be determined, and then the position relation function between the position of the mean airflow velocity line and the roadway wall can be obtained.
As shown in Figure 2, a calculation model of airflow velocity distribution in rectangular roadway is established.
To ensure that the calculation model is solvable, the established model is based on the following assumptions: (1) It is assumed that the airflow in the cross section of the rectangular roadway is stable and there are no sundries in the roadway. Based on the above assumptions, the two closed dashed lines in the figure are the isoline of airflow velocity and the distance is dy, and the isoline of airflow velocity is parallel to the roadway wall. Based on Boussinesq theory and Prandtl turbulence theory, the expression of airflow velocity corresponding to any point D(x,y) in the graph is as follows 31,32 : where μ is airflow velocity of arbitrary point, m/s; v is the mean airflow velocity, m/s; y is the distance from any flow layer to the roadway wall, m; α is the friction resistance coefficient; k is the mixed length coefficient; C is the integral constant. In the calculation model established in Figure 2A, to facilitate the calculation of the model, the roadway section is divided into 8 identical triangles for integral calculation according to the symmetry of the airflow velocity distribution in the rectangular roadway.
The expression of air volume corresponding to AOB in Figure 2A is calculated. It follows from the symmetry of rectangular roadway section that AOB is similar to ACD, and the corresponding edges of similar triangles are proportional. It can be obtained: In a rectangular roadway, the Q 1 integral expression of air volume corresponding to ΔAOB area is as follows: According to the symmetry of the rectangular roadway, the air volume in a cross section of the whole rectangular roadway is 8 times that of ΔAOB, then the Q expression of the rectangular cross-section air volume is as follows: By assuming f = k αv ρ 1 2 and simplifying Formula (9), the following formula can be obtained: From the relationship between the air volume and the cross-section area of the roadway, it can be concluded that the expression of the mean airflow velocity of the rectangular section in Figure 1A is The following formula can be obtained by substituting Formula (10) into Formula (11): To calculate the distance expression between the mean airflow velocity line and the roof and floor, Formula (6) and Formula (11) are solved simultaneously, and it is assumed that the airflow velocity μ at any point in the roadway is the mean airflow velocity of the roadway, then: The following formula can be obtained by simplifying Formula (13): The calculated expression of the distance from the mean airflow velocity line in the cross section of the rectangular roadway to the roof and floor is as follows: The above formula is the expression of the distance from the mean airflow velocity line to the roof and floor of the roadway.
According to the symmetry of the rectangular roadway, combined with the established geometrical model Figure 2B, the calculation expression of the distance from the mean airflow velocity line of the rectangular roadway section to the left or right side of the roadway is as follows: a ln −1.5 (16) The above formula is the expression of the distance from the right line of the mean airflow velocity line to the right side of the roadway wall.

| The position of mean airflow velocity line in semicircular arch section
The semicircular arch roadway section includes a rectangular part and a semicircular part directly above the rectangular cross section. The formula for calculating the distance from the mean airflow velocity line to the two sides of the roadway is the same as that to the roadway floor in the rectangular roadway. Therefore, it is only necessary to deduce the distance of the mean airflow velocity line to the roof of the semicircle part section. The top of the section profile of the semicircular arch roadway is a semicircular arc, and the diameter of the semicircle part is 2a, and the center of the circle coincides with the center of the top edge line of the rectangular part.
As shown in Figure 3, the calculation model of airflow velocity distribution in the cross section of semicircular arch roadway takes the arc vertex as the coordinate origin and establishes a Cartesian coordinate system. The black filling area in the figure is the area between two wind isolines.
The distance from the mean airflow velocity line to the roadway roof in the semicircle arch roadway section is set as y, and the area element (dA) surrounded by any two adjacent isolines of airflow velocity of the semicircle arch roadway section is obtained as follows: According to Boussinesq theory and Prandtl turbulence theory, the integral expression of air volume corresponding to semicircular arch roadway is established as follows: The Formula (17) is simplified and solved, and the expression of the corresponding air volume of the semicircular arch roadway can be obtained as follows: From the relationship between the air volume and the cross-section area of the roadway, it can be concluded that the mean airflow velocity of the semicircular arch section in Figure 3 is as follows: It shows that the mean airflow velocity corresponding to the semicircular arch roadway is The distance between the mean airflow velocity line in the semicircular arch roadway and the roof of the semicircular arch roadway can be calculated as follows by combining Formula (6) with Formula (21): a ln −1.5 (22) The formula for calculating the distance from the mean airflow velocity line of the semicircular arch roadway section to the roof of the semicircular arch roadway profile is y e = a ln −1.5 .
Based on the above analysis, combined with previous study, 33,34 the air volume is mainly determined by the airflow velocity and the roadway section area. The airflow velocity is mainly affected by the ventilation resistance caused by the section shape and wall roughness of roadway. In the actual underground coal mine, the environment in a whole tunnel cannot be the same everywhere, so it is impossible to obtain the mean airflow velocity in a section of tunnel. However, in the region where the roadway deformation is small and the air flow is fully developed, the change of roadway wind resistance can be ignored, and formulas (16) and (22) can be used to determine the position of the mean airflow velocity line. Therefore, for the same type of roadway and the same friction resistance, the mean airflow velocity line can be determined by the roadway size.

| Numerical model
The physical process of mine ventilation can be simply described as the continuous flow and diffusion of fresh air flow through the underground roadways. The physical models of roadway with the same size field experience are established by using COMSOL-Multiphysics 3.5a.

| Simulation scheme
According to the field measurement experience, three rectangular roadways and two semicircular arch roadways with different cross-section sizes were selected as simulation roadways. And five groups of inlet airflow velocities and two kinds of support types corresponding to roadway types are selected as initial conditions. There are a total of 25 groups of simulation tests. The simulation scheme is shown in Table 1.

| Geometric modeling
The geometric model of this numerical simulation is shown in Figures 4 and 5.
In this section, the geometric models of rectangular and semicircular arch roadways with different section sizes are established, and the basic simulation parameters of the two kinds of roadways under different airflow velocities and different support modes are given. The length of the roadway model is 100 m. When building models, the roadway length is in the X direction, the roadway height is in the Y direction, and the roadway width is in the Z direction. From the figures, the wind speed near the inlet of the roadway varies greatly, and the wind speed distribution tends to be uniform with the increase of the distance from the inlet.

| Basic parameters setting
COMSOL-Multiphysics 3.5a software is used to simulate the airflow velocity distribution in rectangular and semicircular arch roadways with different cross-section sizes under different inlet airflow velocities and different support forms.
(1) Rectangular roadway The specific scheme and parameters for the simulation of the airflow velocity distribution in rectangular roadways are shown in Table 2. Besides, in this simulation scheme, all the α value are set as 0.012, and roughness coefficient values are set as 0.5. In this table, ν is kinematic viscosity, and Re DH is the Reynolds number calculated with hydraulic diameter as the characteristic length, and I is the turbulence intensity. The specific scheme and parameters for the simulation of the airflow velocity distribution in semicircular arch roadways are shown in Table 3. Besides, in this simulation scheme, all the α value are set as 0.01, and roughness coefficient values are set as 0.5. The parameters in this table have the same meanings as those in Table 2.

| Logarithmic wall function
In COMSOL-Multiphysics, to consider the wall roughness effect, the empirical relationship between velocity and wall friction is used to replace the thin boundary layer near the wall, which is called wall function. And the logarithmic wall function was used in this simulation.
The logarithmic wall function assumes that the calculation domain begins with the distance from the wall, and that the flow is parallel to the wall, and the velocity can be described by the following formula 23 : where U is the velocity parallel to the wall; u τ is the friction velocity, uτ = τw ρ ;τ w is turbulent shear stress; k is Karman constant, and the value is about 0.42; C + is a universal constant for smooth wall, and its value is 5.5 when the wall is smooth. Since the wall of this study is rough, this value is 0. And C + can be modified by using scalar variable dialog box in the module. l* is the viscous length ratio, which is defined as The distance δ w or its equivalent δw = δw l + * must be specified in viscous units to set the logarithmic wall function; η is dynamic viscosity, Pa s; u τ is friction velocity; In this study, the roughness height is set according to different supporting methods.

| The distribution characteristics of airflow velocity in roadway sections
According to the simulation scheme, the contours of the airflow velocity distribution in different roadway sections were simulated. To facilitate the comparative analysis, the velocity contours with three airflow inlet velocity values of 0.8, 4.0, and 8.0 m/s is selected, as shown in Figures 6-10. In general, there will be a vortex in the airflow field at the entrance. To avoid the influence of vortex on the flow field, the cross-sections at the distance of 50 m from the roadway entrance were selected. And the airflow velocity field in the cross section remains basically unchanged and reaches a fully developed state.
From Figures 6 to 10, the contour line of airflow velocity in roadway section is consistent with the shape of roadway section, and the isoline of airflow velocity is basically parallel to the roadway wall, and the isoline of airflow velocity expands from the central part of roadway section to the roadway wall. Besides, the closer to the roadway wall, the denser the airflow velocity isoline, indicating that the airflow velocity gradient near the wall is larger. And the closer to the central line of the roadway section, the thinner the airflow velocity isoline is and the larger the air velocity is, indicating that the smaller the airflow velocity gradient is, that is, the airflow velocities in the central part of the roadway change little. In the same roadway, the greater the airflow inlet velocity is, the smaller the thickness of the near-wall velocity variation layer is, that is, the thickness of the boundary layer decreases with the increase of airflow inlet velocity.

| Distribution law of airflow velocity in the central axis of roadway sections
To find out the relationship between the velocity of each point on the central axis of the roadway section and the mean airflow velocity. According to the roadway type selected by the simulation scheme, the data monitoring location is selected at the central axis of X = 50 m roadway section.  roadway wall is large, and the gradient of airflow velocity in the central part of the roadway section is small. This is mainly caused by the influence of the boundary layer of the roadway wall. And the thickness of the boundary layer decreases with the increase of airflow velocity.

| Analysis of airflow velocity in the central axis of roadway sections
To find out the relationship between the airflow velocity of each measuring point and the mean airflow velocity of the roadway, the nonlinear functions of airflow velocity and average airflow velocity at each measuring point are fitted by Origin 8.0, and the results are shown in Tables 4 and 5.  Tables 4 and 5 show the relationship between the airflow velocity of each measuring point and the mean airflow velocity of the rectangular and semi-circular arch roadways with different section sizes under different airflow velocities, respectively. According to the results, it can be seen that within a certain distance from the roof, there is a logarithmic relationship between the ratio of the measuring point airflow velocity to the mean airflow velocity and the distance. When the distance from the roof increases to a certain extent, the ratio of the airflow velocity of measuring point to the mean airflow velocity is constant. In addition, the ratio of maximum airflow velocity to mean airflow velocity in the roadway section decreases with the increase of mean airflow velocity. In addition, by comparison, the roadway section shape has little influence on the ratio of the maximum airflow velocity to the mean airflow velocity, but has a great influence on the airflow velocity gradient.

| Comparative of numerical simulation results and theoretical model
In this section, the distances from mean airflow velocity to the roadway roof in different roadway from the numerical simulation and calculated from theoretical model are examined. The comparison results are shown in Tables 6  and 7. It can be seen that the errors between the theoretical  calculation results and the numerical simulation results have nothing to do with the shape of roadway section and mean airflow velocity, and they are all less than 4%. The conclusions of the two research methods are unified, which verifies the reliability of the theoretical model.

| VERIFICATION TESTS OF AIRFLOW VELOCITY DISTRIBUTION IN DIFFERENT ROADWAYS
In previous sections, a set of formulas for the position of the mean airflow velocity line in different roadway sections were obtained through theoretical research and numerical simulation. In this section, the reliability of the theoretical model is further verified by field tests.

| Preparation of experimental equipment
(1) Data monitoring equipment In this experiment, 16 CFD15 coal mine electronic airflow velocity measuring instruments (hereinafter referred to as "anemometer") and 16 YHC mine intrinsically safe data acquisition instruments were used. Ultrasonic electronic airflow velocity measuring instrument and data acquisition instrument are shown in Figure 13.
(2) Main parameters of anemometer and data acquisition instrument The main technical specifications of the anemometer are shown in Table 8.
The ventilation parameter acquisition App is independently developed and installed on the data acquisition instrument to realize the synchronous data acquisition. The main technical specifications of the data acquisition instrument are shown in Table 9.

| Calibration of experimental instruments
(1) Calibration method 16 CFD15 anemometers are calibrated in the ground wind tunnel, as shown in Figure 14 at the national firstclass wind tunnel laboratory of Chongqing Research Institute Co. Ltd., China Coal Science and Industry Group. Through the software control system, the control and adjustment of airflow velocity, the automatic collection of dynamic pressure, atmospheric pressure and temperature can be realized, and finally the standard airflow velocity can be obtained. The wind tunnel laboratory can provide the standard airflow velocity flow field with high stability and uniformity of 0.50-40.00 m/s, which can be compared with the measured anemometer.
(2) Calibration results When adjusting the anemometer, 5 standard airflow velocities were tested in the wind tunnel, and the readings of the same tested anemometer were compared with the standard airflow velocity values under the same atmospheric pressure and the same ambient temperature. If the error is within 0.1 m/s, the test passes; Otherwise, the anemometer is debugged on the spot until it is qualified. This method is used to detect and adjust 16 anemometers in turn, and the data recorded in the calibration process are shown in Table 12. It can be seen that the absolute errors of the 16 anemometers after adjustment are all within 0.1 m/s, which meets the error requirements and can be used for field testing. The anemometer calibration data is shown in Table 10.

| Brief introduction to simulation roadway
There exists a ventilation fire test roadway system in Chongqing Research Institute (as shown in Figure 15), which is equipped with airflow draught device, fan connection device, velocity measuring station, dust measuring station, air door and air resistance regulating device. The fan used is FBCDZ№12/2 × 45. After the transformation, a complete ventilation test system is formed, and the total length of the roadway is about 460 m, as shown in Figure 14.
A section of straight roadway AB with regular cross section and no debris accumulation is in the roadway. The shape of the roadway is semicircular arch, and the supporting method is Anchor jetting. The roadway is 2.82 m high, 2.89 m wide, and 50 m long, in which the length of the experimental area is 9 m, the upwind side is 12 m and the leeward side is 29 m. It meets the requirements of the measuring method of Mine Ventilation Resistance (MT/T440-2008) that the width of the roadway is three times the width of the upwind side and eight times the width of the downwind side without convergence points and air dividing points.

| Measuring method
(1) The laser rangefinder is used to accurately measure the size of the cross section, and its support form was recorded. Before testing, the obstacles in the roadway should be cleared, so that the roadway in the whole measurement range can meet the measurement requirements. (2) Since the semicircular arch roadway is symmetrical to the left and right, 1/2 cross section of the semicircular arch roadway is selected for the measurement. The position of the monitoring point of the cross-section is calculated according to the measured cross-section size: the anemometer is denser near the wall and sparse away from the wall. The specific values of the distance between measuring surfaces l, the number of measuring surfaces N, the height of measuring lines h, the length of measuring lines L and the number of anemometers n of each measuring line are determined according to the cross-section size of the roadway. Then, the installation rod of the anemometer is assembled according to the length of the measuring line L, the number of measuring surfaces N and the number of anemometers per line n. And the anemometer is fixed on the installation rod, and the installation rod of the anemometer is fixed in the roadway according to the distance between the measuring surface l and the measuring line h. The specific layout is shown in Figure 16.  mean airflow velocity measured by the six-line wind measurement method in the experimental roadway is 1.3, 2, 2.6, and 3.5 m/s, respectively. (4) A total of 16 mine intrinsically safe data collectors were used in this experiment. The ventilation parameter collector App is installed in the mine intrinsically safe data collector and connected with the monitoring anemometer one by one. To obtain the monitoring data of all anemometers at the same time, the ventilation parameter collector start time is set by modifying the built-in program of the ventilation parameter collector. All ventilation parameter collectors start up at the same time and collect the monitoring data of the anemometer. All the data acquisition instruments are opened and placed in the lower tuyere of the tested roadway, as shown in Figure 17. At the same time, another data acquisition instrument is used to take pictures and record the data, which ensures the simultaneity of the data acquisition.

| Data analysis
The measured data are fitted into a curve according to the boundary conditions by using Surfer software, and the boundary points are taken every 50 mm. The results are shown in Figure 18. It can be seen that the airflow velocity isoline of the roadway section is approximately a semicircular arch. The closer to the roadway wall, the denser the isoline of airflow velocity, indicating that the airflow velocity gradient is larger near the wall. And the closer to the center of the roadway, the thinner the isoline of airflow velocity is, indicating that the smaller the airflow velocity gradient is. The greater the inlet airflow velocity is, the smaller the thickness of the low velocity area near the wall is, that is, the thickness of the boundary layer with low airflow velocity decreases with the increase of airflow velocity To verify the theoretical model, the average distance value d 1 from the measured position of the mean airflow velocity line to the roof and the distance d 2 from the position of the theoretical mean airflow velocity line to the roof are compared, as shown in Table 11.
It can be seen that the errors of the position the mean airflow velocity line measured in the experimental roadway and calculated by the theoretical model are both less than 5%, which indicates that the theoretical model is reliable.

| Field experiment
To further verify the position of the mean airflow velocity line and the distribution law of the airflow velocity in the rectangular section, the rectangular roadway in Sima

| Introduction to the test site
The partition ventilation system is adopted in Sima Coal Mine, which consists of main vertical shaft, auxiliary vertical shaft, and new air-intake shaft, central return air shaft and new return air shaft. The total air intake volume of the mine is 19578 m 3 /min, and the total return air volume is 19200 m 3 /min.

| Experimental method
Due to the accumulation of all kinds of equipment or other obstacles in coal mines, the air flow is in an unstable state. It is difficult to measure the airflow velocity in the same section at the same time. Therefore, the mirror ladder method of is adopted to measure the airflow velocity in 100 m roadway without deformation and sundries accumulation. The specific steps for measuring airflow velocity in roadway are as follows: (1) The laser rangefinder is used to accurately measure the size of the cross section, and its support form was recorded. Before measuring, the obstacles in the roadway should be cleared, so that the roadway in the whole measurement range can meet the measurement requirements. (2) Because of the symmetry of the upper and lower, left and right sides of the rectangular roadway, 1/4 of the cross section of the rectangular roadway is selected for measurement. The specific values of the distance between measuring surfaces l, the number of measuring surfaces N, the height of measuring lines h, the length of measuring lines L and the number of anemometers n of each measuring line are determined according to the cross-section size of the roadway. Then the anemometer installation rod is assembled according to the measuring line length L, the measuring surface number N and the number of anemometers per line n. The specific anemometer layout diagram is shown in Figure 19. and placed in the position of the lower tuyere of the measured roadway, and the ventilation parameter collector installed on the data acquisition instrument automatically and uninterruptedly collects the airflow velocity values displayed on the electronic airflow velocity measuring instrument. After the data becomes stable, another data acquisition instrument is used to take pictures and record the data. The specific layout diagram is shown in Figure 20.

| Analysis of field experimental data
Four groups of experiments are conducted by using the above experimental methods, and the measured data are fitted into a curve according to the boundary conditions with Sufer software, and the boundary points are taken every 50 mm. The results are shown in Figure 21. It can be seen that the airflow velocity isoline in the roadway section is approximately rectangular. Similarly, the closer to the roadway wall, the denser the airflow velocity isoline, indicating that the airflow velocity gradient near the wall is larger; and the closer to the central part of the roadway, the sparser the airflow velocity isoline is, indicating that the smaller the airflow velocity gradient is, the less the airflow velocity variation is. In the same roadway, the lager the inlet airflow velocity is, the smaller the thickness of the nearwall velocity variation layer is, that is, the thickness of the boundary layer decreases with the increase of airflow velocity. The red line in the figure is the measured mean airflow velocity line. Under the above four experimental conditions, the average distance from the measured mean airflow velocity line to the roadway roof is 0.3946, 0.3952, 0.3437, and 0.3176 m, respectively.
To verify the theoretical model, the average distance value d 3 from the measured position of the mean airflow velocity line to the roof and the distance d 4 from the position of the theoretical mean airflow velocity line to the roof are compared, as shown in Table 12. It can be seen that the position errors of the average airflow velocity line measured in the four rectangular roadway sections selected by Sima Coal Mine and calculated by the theoretical model are all less than 5%, and the theoretical model is reliable.  In this study, the distribution law of airflow velocity in typical roadway sections (namely rectangle and semicircular arch sections) have been studied by theoretical analysis, numerical simulation and field tests. The main conclusions are as follows: (1) Based on Boussinesq theory and Pelant turbulence theory, the calculation model of position of mean airflow velocity line in rectangular and semicircular arch roadway is established, which is y e = a ln −1.5 .
The calculation model shows that the position of mean airflow velocity line is only related to roadway section size and has nothing to do with other factors. (2) A numerical simulation was conducted to study the airflow velocity distribution in rectangular and semicircular arch roadways. The contour line of airflow velocity in the roadway section is consistent with the shape of the roadway section, and the isoline of airflow velocity is basically parallel to the roadway wall. Besides, the closer to the roadway wall, the denser the airflow velocity isoline, indicating that the airflow velocity gradient near the wall is larger. And the thickness of the boundary layer