Pressurized air supply characteristic simulation method for lower evacuation channel of ultra-long shield tunnel

Abstract

The invention discloses a method for simulating pressurized air supply characteristics of a lower evacuation channel of an ultra-long shield tunnel. The method comprises the following steps: 1) determining the geometric dimension of the lower evacuation channel of the ultra-long shield tunnel, the geometric dimension of an evacuation staircase, the geometric dimension of an evacuation door, the geometric dimension of an evacuation cover plate and the arrangement position of an axial flow fan; 2) obtaining flow velocity distribution and pressure distribution in the evacuation channel at the lower part of the ultra-long shield tunnel through a turbulent flow # imgabs0 # model; and (3) according to the flow velocity distribution and the pressure distribution, obtained in the step (2), of the evacuation door and the evacuation cover plate in the lower evacuation channel, whether the flow velocity and pressure conditions of the lower evacuation channel of the ultra-long shield tunnel meet personnel evacuation requirements or not is judged. According to the method, the pressurized air supply effect of the lower evacuation channel of the ultra-long shield tunnel and the working condition of the axial flow fan can be analyzed, pressurized air supply parameter design of the lower evacuation channel of the ultra-long shield tunnel and model selection of the axial flow fan are promoted, and a pressurized air supply scheme of the lower evacuation channel of the ultra-long shield tunnel is preferably selected.

Description

Technical Field

[0001] The invention relates to a method for simulating pressurized air supply characteristics of a lower evacuation passage of an ultra-long shield tunnel in fire protection engineering and civil engineering. Background Art

[0002] A tunnel is a semi-enclosed building, and accident communication and rescue are greatly restricted. Once a fire occurs in a tunnel, it is easy to cause serious structural damage, casualties and property losses. In an ultra-long shield tunnel, in addition to evacuating through the tunnel entrance and exit, people can also evacuate through the lower evacuation passage. When using the lower evacuation passage of an ultra-long shield tunnel for personnel evacuation, in order to ensure that the lower evacuation passage is not invaded by smoke, there are two standards when calculating the pressurized air supply volume: wind speed standard and pressure standard. Referring to the corresponding requirements for determining the pressurized air supply volume in general buildings, the standards for pressurized air supply in the lower evacuation passage are set as follows: (1) Wind speed standard: When the evacuation staircase (or slide) is open, the wind speed value of the door section is 0.7~1.2m / s; (2) Pressure standard: When the evacuation slide (or staircase) is closed, the positive pressure value in the evacuation passage is 25~50Pa;

[0003] At present, the structure of some super-long shield tunnels is as follows: the driving lane of the super-long shield tunnel is connected to the evacuation stairwell of the lower evacuation passage through an evacuation cover plate, and the evacuation stairwell is connected to the evacuation passage through an evacuation door. An evacuation stairwell is set at intervals in the super-long shield tunnel. The numerous evacuation stairwells and evacuation passages together form a complete super-long shield tunnel lower evacuation passage project.

[0004] This type of project faces many ventilation technical difficulties. The main ones are as follows: (1) The project needs to install axial flow fans in the lower evacuation channel of the super-long shield tunnel to ensure that there is sufficient pressure in the lower evacuation channel of the super-long shield tunnel. (2) The pressurized air supply volume in the lower evacuation channel of the super-long shield tunnel is one of the important factors affecting the smoke prevention effect. If the pressurized air supply volume is too small, it cannot effectively prevent smoke. However, if the pressurized air supply volume is too large, it will not only increase the load of the fan, but also make the positive pressure value of the pressurized area too high, making it difficult to open the evacuation door. The working condition of the axial flow fan should be reasonably adjusted to make the pressure in the evacuation channel appropriate. (3) The axial flow fan in the lower evacuation channel of the super-long shield tunnel has normal working parameters. If the actual working parameters do not match the designed working parameters of the axial flow fan, a stall will occur, thereby damaging the axial flow fan. The axial flow fan must be kept working normally at all times. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and provide a method for simulating the pressurized air supply characteristics of the lower evacuation channel of an ultra-long shield tunnel.

[0006] To solve the above technical problems, the present invention proposes a technical solution: a method for simulating the pressurized air supply characteristics of the lower evacuation channel of an ultra-long shield tunnel, comprising the following steps:

[0007] 1) Determine the geometric dimensions of the evacuation passage below the super-long shield tunnel, the geometric dimensions of the evacuation stairwell, the geometric dimensions of the evacuation door, the geometric dimensions of the evacuation cover, and the layout location of the axial flow fan;

[0008] 2) The velocity and pressure distribution in the lower evacuation channel of the ultra-long shield tunnel is obtained by using the turbulent k-ε model

[0009] 3) Based on the flow velocity distribution and pressure distribution at the evacuation door and evacuation cover in the lower evacuation channel obtained in step 2), determine whether the flow velocity and pressure conditions in the lower evacuation channel of the ultra-long shield tunnel meet the personnel evacuation requirements.

[0010] In the above-mentioned method for simulating the pressurized air supply characteristics of the lower evacuation channel of an ultra-long shield tunnel, preferably, the turbulent k-ε model includes:

[0011]

[0012] Where k is the turbulent kinetic energy, ε is the turbulent kinetic energy dissipation rate, U is the wind speed, x is the spatial coordinate, "-" means taking the average, v t is the kinematic viscosity, μ t is the turbulent viscosity, C μ is an empirical constant, usually C μ =0.09, ρ is the fluid density.

[0013] In the above-mentioned method for simulating the pressurized air supply characteristics of the lower evacuation channel of an ultra-long shield tunnel, preferably, the transport equation corresponding to the turbulent kinetic energy k and the turbulent dissipation rate ε is:

[0014]

[0015] Where t is time, u j and u i are the components of velocity in the j and i directions respectively; x j and x i is the spatial coordinate, i, j = 1, 2, 3 correspond to the x, y, z directions respectively; μ is the dynamic viscosity of the fluid, σ k is the turbulent Prandtl number of turbulent kinetic energy, which is an empirical constant and is usually taken as σ k =1.0;P k is the generation term of turbulent kinetic energy, which represents the contribution of the average flow to the turbulent kinetic energy, σ ε The turbulent Prandtl number is the turbulent kinetic energy dissipation rate, which is an empirical constant and is usually taken as σ ε =1.3; C ε1 and Cε2 is an empirical constant, usually C ε1 =1.44, C ε2 =1.92.

[0016] The above-mentioned method for simulating the pressurized air supply characteristics of the lower evacuation channel of an ultra-long shield tunnel, preferably, obtains the pressure-flow curve of the axial flow fan through the turbulent k-ε model in the step 2), and matches it with the pressure-flow curve of the actual working of the axial flow fan; if it does not match, re-enter new initial conditions and boundary conditions to simulate the turbulent k-ε model, and then match the new pressure-flow curve obtained by simulation with the pressure-flow curve of the actual working of the axial flow fan, and repeats this operation until the simulated working parameters match the PQ curve.

[0017] In the above-mentioned method for simulating the pressurized air supply characteristics of the lower evacuation channel of an ultra-long shield tunnel, preferably, the actual working pressure-flow curve of the axial flow fan is obtained by fitting the actual working pressure-flow parameter scatter plot of the axial flow fan using the least squares method.

[0018] Compared with the existing technology, the advantages of the present invention are: 1. The method for simulating the pressurized air supply characteristics of the lower evacuation channel of an ultra-long shield tunnel of the present invention can realize the analysis of the flow field and pressure characteristics of the lower evacuation channel of an ultra-long shield tunnel, improve the numerical simulation capability of the pressurized air supply of the lower evacuation channel of an ultra-long shield tunnel, and promote the process of engineering refinement.

[0019] 2. Analyze the effect of pressurized air supply in the lower evacuation channel of ultra-long shield tunnels and the working conditions of axial flow fans, promote the design of pressurized air supply parameters in the lower evacuation channel of ultra-long shield tunnels, and optimize the pressurized air supply scheme in the lower evacuation channel of ultra-long shield tunnels.

[0020] 3. Realize precise control and dynamic regulation of the design parameters of pressurized air supply in the lower evacuation channel of super-long shield tunnels, and improve the timeliness of the selection of pressurized air supply parameters in the lower evacuation channel of super-long shield tunnels.

[0021] 4. The numerical simulation method is used to analyze the pressurized air supply characteristics of the lower evacuation channel of the ultra-long shield tunnel, and the flow velocity distribution characteristics and pressure distribution characteristics of the lower evacuation channel of the ultra-long shield tunnel are analyzed. This can help select the model of the axial flow fan in the lower evacuation channel of the ultra-long shield tunnel, ensure that the lower evacuation channel is not invaded by smoke, and at the same time, the evacuation door is easy to open, thereby ensuring the safety of personnel evacuation in the lower evacuation channel. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 This is a flow chart of the method for simulating the pressurized air supply characteristics of the lower evacuation channel of the ultra-long shield tunnel in Example 1.

[0023] Figure 2This is a three-dimensional schematic diagram of the numerical model of the pressurized air supply characteristics of the lower evacuation channel of an ultra-long shield tunnel in Example 1.

[0024] Figure 3 This is the pressure distribution diagram in the evacuation channel when evacuation exits 1-13 are opened in Example 1.

[0025] Figure 4 This is the pressure distribution diagram in the evacuation channel when evacuation exits 14-26 are opened in Example 1.

[0026] Figure 5 This is the pressure distribution diagram in the evacuation channel when evacuation exits 27-39 are opened in Example 1.

[0027] Figure 6 This is a diagram of the average wind speed in the cross section of the evacuation passage when evacuation exits 1-13 are opened in Example 1.

[0028] Figure 7 This is a diagram of the average wind speed in the cross section of the evacuation passage when evacuation exits 14-26 are opened in Example 1.

[0029] Figure 8 This is a diagram of the average wind speed in the cross section of the evacuation passage when evacuation exits 27-39 are opened in Example 1.

[0030] Figure 9 This is the flow velocity diagram at the evacuation door in the evacuation passage when evacuation exits 1-13 are opened in Example 1.

[0031] Figure 10 This is the flow velocity diagram at the evacuation door in the evacuation passage when evacuation exits 14-26 are opened in Example 1.

[0032] Figure 11 This is the flow velocity diagram at the evacuation door in the evacuation passage when evacuation exits 27-39 are opened in Example 1.

[0033] Figure 12 This is the flow rate diagram of the evacuation cover plate in the stairwell of the evacuation passage when the evacuation exits 1-13 are opened in Example 1.

[0034] Figure 13 This is the flow rate diagram of the evacuation cover plate in the stairwell of the evacuation passage when the evacuation exits 14-26 are opened in Example 1.

[0035] Figure 14 This is the flow rate diagram of the evacuation cover plate in the stairwell of the evacuation passage when the evacuation exits 27-39 are opened in Example 1.

[0036] Figure 15 This is the PQ curve diagram of the axial flow fan working performance in Example 1. DETAILED DESCRIPTION

[0037] In order to facilitate understanding of the present invention, the present invention will be described more comprehensively and meticulously below in conjunction with preferred embodiments, but the protection scope of the present invention is not limited to the following specific embodiments.

[0038] It should be noted that when an element is described as being "fixed, fixed, connected or communicated with" another element, it can be directly fixed, fixed, connected or communicated with the other element, or it can be indirectly fixed, fixed, connected or communicated with the other element through other intermediate connectors.

[0039] Unless otherwise defined, all technical terms used hereinafter have the same meanings as those generally understood by those skilled in the art. The technical terms used herein are only for the purpose of describing specific embodiments and are not intended to limit the scope of protection of the present invention.

[0040] Example 1

[0041] A method for simulating the pressurized air supply characteristics of an evacuation passage below an ultra-long shield tunnel according to this embodiment includes the following steps:

[0042] 1) Determine the geometric dimensions of the evacuation passageway at the lower portion of the super-long shield tunnel, including the dimensions of the evacuation stairwell, evacuation door, evacuation cover, and the placement of the axial flow fans. The evacuation passageway is 5,000 meters long, with a maximum width of 4.2 meters and a maximum height of 3.3 meters. Two axial flow fans are installed at each end of the tunnel. The evacuation stairway is 5.8 meters wide, with one stairway every 80 meters. The evacuation door measures 0.9 meters by 2.5 meters, and the evacuation cover of the stairwell measures 3.6 meters by 1.1 meters.

[0043] 2) The velocity distribution and pressure distribution in the lower evacuation channel of the ultra-long shield tunnel are obtained through the turbulent k-ε model.

[0044] The turbulent k-ε model includes:

[0045]

[0046] Where k is the turbulent kinetic energy, ε is the turbulent kinetic energy dissipation rate, U is the wind speed, x is the spatial coordinate, "-" means taking the average, v t is the kinematic viscosity, μ t is the turbulent viscosity, C μ is an empirical constant, usually C μ =0.09, ρ is the fluid density.

[0047] The transport equation corresponding to the turbulent kinetic energy k and the turbulent dissipation rate ε is:

[0048]

[0049] Where t is time, uj and u i are the components of velocity in the j and i directions respectively; x j and x i is the spatial coordinate, i, j = 1, 2, 3 correspond to the x, y, z directions respectively; μ is the dynamic viscosity of the fluid, σ k is the turbulent Prandtl number of turbulent kinetic energy, which is an empirical constant and is usually taken as σ k =1.0;P k is the generation term of turbulent kinetic energy, which represents the contribution of the average flow to the turbulent kinetic energy, σ ε The turbulent Prandtl number is the turbulent kinetic energy dissipation rate, which is an empirical constant and is usually taken as σ ε =1.3; C ε1 and C ε2 is an empirical constant, usually C ε1 =1.44, C ε2 =1.92.

[0050] The initial conditions for the turbulent k-ε model include ambient temperature, atmospheric pressure, gauge pressure, initial velocity, turbulent kinetic energy, turbulent dissipation rate, fluid density, and fluid viscosity. Boundary conditions include inlet and outlet pressures, wind speed, and hydraulic parameters. The axial fan outlet is set as the velocity inlet with a velocity of 5.2 m / s, and the evacuation cover opening boundary condition is set as the pressure outlet.

[0051] The present invention adopts the pressure-velocity coupled SIMPLEC algorithm to iteratively calculate the pressure and wind speed in the evacuation channel, thereby solving the numerical model of the pressurized air supply characteristics of the lower evacuation channel of an ultra-long shield tunnel.

[0052] 3) Based on the flow velocity and pressure distribution at the evacuation door and evacuation cover within the lower evacuation passage obtained in step 2), determine whether the flow velocity and pressure conditions in the lower evacuation passage of the ultra-long shield tunnel meet the evacuation requirements. Specifically, the flow velocity and pressure conditions at the evacuation door and evacuation cover meet the flow velocity and pressure values specified in the regulations for safe evacuation. Only when these values meet the regulations can the flow velocity and pressure conditions in the lower evacuation passage be considered to meet the evacuation requirements.

[0053] In this embodiment, inner pile No. 0 is set deep in the evacuation channel; evacuation exits No. 1 to 13 are set at positions 0-1625 meters in the evacuation channel; evacuation exits No. 14 to 26 are set at positions 1625-3375 meters deep in the evacuation channel, and evacuation exits No. 27 to 39 are set at positions 3375-5000 meters in the evacuation channel.

[0054] The pressure distribution in the evacuation passage when the evacuation cover and evacuation door of different areas are opened is shown in Figure 2. Figure 3-Figure 5 , evacuation exit refers to the evacuation cover and evacuation door; Figure 3 It can be seen that when evacuation openings 1 to 13 are opened, the wind pressure in the passage is released from the evacuation openings. The farther away from the evacuation openings, the greater the pressure in the evacuation passage, and the greater the ventilation resistance. Since the opened evacuation openings 1 to 13 are close to the ventilation openings on one side, the pressure in the passage is distributed as "low on the left and high on the right", and the maximum pressure in the passage is about 1600Pa. Figure 4 It can be seen that when evacuation exits 14 to 26 are opened, the wind pressure in the passage is released from the evacuation openings. The farther away from the evacuation exits, the greater the pressure in the evacuation passage, and the greater the ventilation resistance. Since the opened evacuation exits 14 to 26 are close to the left side of the middle of the passage, the pressure in the passage is basically distributed in a "V" shape, with the pressure on both sides of the evacuation passage being approximately 900Pa and 1300Pa. Figure 5 It can be seen that when evacuation exits 27 to 39 are opened, the wind pressure in the passage is released through the evacuation openings. The farther away from the evacuation exits, the greater the pressure in the evacuation passage, and the greater the ventilation resistance. Because the opened evacuation exits 27 to 39 are close to the middle of the passage, the pressure in the passage is symmetrically distributed in a "V" shape, with the pressure on both sides of the passage being approximately 1200Pa.

[0055] The average wind speed distribution in the cross section of the evacuation passage when the evacuation exit opening area is different is as follows: Figure 6-Figure 8 As shown by Figure 6 It can be seen that when evacuation exits 1 to 13 are opened, the flow in the channel flows out through the opened evacuation exits. Since the evacuation stairwell in the lower evacuation channel will occupy the space in the evacuation channel, the cross-sectional area of the evacuation channel at the stairwell position will suddenly shrink. Therefore, the wind speed at the stairwell position will suddenly increase, and then suddenly decrease in the middle position between the two stairwells. The wind speed in the area where the evacuation exits are not opened in the channel is about 2m / s to 6m / s. Figure 7 It can be seen that when evacuation exits 14 to 26 are opened, the flow in the channel flows out through the opened evacuation exits, and the wind speed in the area where the evacuation exits are not opened is about 4m / s to 10m / s. Figure 8 It can be seen that when evacuation exits 27 to 39 are opened, the flow in the channel flows out through the opened evacuation exits, and the wind speed in the area of the channel where the evacuation exits are not opened is approximately in the range of 2m / s to 8m / s.

[0056] The velocity distribution at the evacuation door in the evacuation passage when the evacuation exit opening area is different is shown in Figures 9-11 ,Depend on Figure 9 It can be seen that when evacuation exits 1 to 13 are opened, the wind speed meets the specification requirements when the tunnel longitudinal evacuation channel is supplied with air in both directions. The flow velocity at each open evacuation door is approximately symmetrically distributed, showing an overall trend of "large at both ends, small in the middle, first decreasing and then increasing". Figure 10It can be seen that when evacuation exits 14 to 26 are opened, the wind speed meets the specification requirements when the tunnel longitudinal evacuation passage is supplied with air in both directions. Since the opened evacuation doors are close to the middle of the passage, the pressure and wind speed on both sides of the evacuation exits are relatively symmetrical, so the flow rate of each opened evacuation door is also relatively stable, basically maintained at 4m / s. Figure 11 It can be seen that when evacuation exits 27 to 39 are opened, the wind speed meets the requirements of the specifications when air is supplied in both directions in the tunnel's longitudinal evacuation channel. Since the opened evacuation doors are close to the middle of the channel, the pressure and wind speed on both sides of the evacuation exits are relatively symmetrical, so the flow rate of each open evacuation door is also relatively stable, basically maintained at 3m / s.

[0057] The velocity distribution of the stairwell cover in the evacuation passage when the evacuation exit opening area is different is shown in Figure 12-14 ,Depend on Figure 12 It can be seen that when evacuation exits 1 to 13 are opened, the wind speed meets the specification requirements when the tunnel longitudinal evacuation channel is supplied with air in both directions. The flow velocity at each open evacuation cover is approximately symmetrically distributed, showing an overall trend of "large at both ends, small in the middle, first decreasing and then increasing". Figure 13 It can be seen that when evacuation exits 14 to 26 are opened, the wind speed meets the specification requirements when the tunnel longitudinal evacuation channel is supplied with air in both directions. The flow rate of each opened evacuation cover is relatively stable, basically maintained at 2.5m / s to 3m / s. Figure 14 It can be seen that when evacuation exits 27 to 39 are opened, the wind speed meets the requirements of the specification when air is supplied in both directions in the tunnel's longitudinal evacuation channel. The flow velocity at each open evacuation cover is approximately symmetrically distributed, showing an overall change trend of "large at both ends, small in the middle, first decreasing and then increasing".

[0058] 4) Obtaining the pressure-flow curve of the axial flow fan through the turbulence k-ε model in step 2) and matching it with the actual working pressure-flow curve of the axial flow fan; if it does not match, re-entering the initial conditions such as the initial velocity and pressure in the evacuation channel; changing the hydraulic parameters such as the geometric dimensions of the evacuation channel and the evacuation port size, modifying the boundary conditions such as the wind speed outlet pressure and wind speed, re-simulating the turbulence ke model, and then matching the new pressure-flow curve obtained by simulation with the actual working pressure-flow curve of the axial flow fan, and repeating this operation until the simulated working parameters match the PQ curve.

[0059] The actual working pressure-flow curve of the axial flow fan in this embodiment is obtained by fitting the actual working pressure-flow parameter scatter plot of the axial flow fan using the least squares method. The least squares method is a mathematical optimization technique that seeks the best function matching the data by minimizing the sum of squared errors. The least squares method can be used for curve fitting, and the mathematical expression is:

[0060]

[0061] In the present invention, the fitting data of the PQ curve of the axial flow fan is derived from the working parameter data of the actual operation of the axial flow fan. The working pressure and flow data obtained by numerical simulation do not necessarily match the PQ curve. If they do not match, the axial flow fan will stall. Only when they match can the fan meet the demand, which is of great help to the selection of the fan.

[0062] In this embodiment, Figure 15 The working performance PQ curve is fitted according to the actual working parameters of the axial flow fan. It can be found that by using the fitting tool to fit the actual working parameter data, a complete curve formula will be obtained, and the variables of the formula are only flow Q and pressure P.

[0063] This embodiment can realize the analysis of the pressurized air supply effect and the working condition of the axial flow fan in the lower evacuation channel of the ultra-long shield tunnel, promote the design of the pressurized air supply parameters of the lower evacuation channel of the ultra-long shield tunnel and the selection of the model of the axial flow fan, and optimize the pressurized air supply scheme of the lower evacuation channel of the ultra-long shield tunnel.

Claims

1. A method for simulating the pressurized air supply characteristics of the lower evacuation channel of an ultra-long shield tunnel, characterized in that: The following steps are involved: 1) Determine the geometric dimensions of the evacuation passage below the super-long shield tunnel, the geometric dimensions of the evacuation stairwell, the geometric dimensions of the evacuation door, the geometric dimensions of the evacuation cover, and the layout location of the axial flow fan; 2) The velocity and pressure distributions in the lower evacuation channel of the ultra-long shield tunnel are obtained using the turbulent k-ε model; 3) Based on the flow velocity distribution and pressure distribution at the evacuation door and evacuation cover in the lower evacuation channel obtained in step 2), determine whether the flow velocity and pressure conditions in the lower evacuation channel of the ultra-long shield tunnel meet the personnel evacuation requirements.

2. The method for simulating pressurized air supply characteristics of the lower evacuation passage of an ultra-long shield tunnel according to claim 1 is characterized by: The turbulence k-ε model includes: Where k is the turbulent kinetic energy, ε is the turbulent kinetic energy dissipation rate, U is the wind speed, x is the spatial coordinate, "-" means taking the average, v t is the kinematic viscosity, μ t is the turbulent viscosity, C μ is an empirical constant, usually C μ =0.09, ρ is the fluid density.

3. The method for simulating pressurized air supply characteristics of the lower evacuation passage of an ultra-long shield tunnel according to claim 2 is characterized in that: The transport equation corresponding to the turbulent kinetic energy k and the turbulent dissipation rate ε is: Where t is time, u j and u i are the components of velocity in the j and i directions, respectively, x j and x i is the spatial coordinate, μ is the dynamic viscosity of the fluid, σ k is the turbulent Prandtl number of turbulent kinetic energy, P k is the generation term of turbulent kinetic energy, which represents the contribution of the average flow to the turbulent kinetic energy, σ ε is the turbulent Prandtl number for the turbulent kinetic energy dissipation rate, C ε1 and C ε2 is an empirical constant.

4. The method for simulating pressurized air supply characteristics of the lower evacuation passage of an ultra-long shield tunnel according to any one of claims 1 to 3, characterized in that: The turbulence k-ε model in step 2) is used to obtain the pressure-flow curve of the axial flow fan, and the pressure-flow curve is matched with the actual working pressure-flow curve of the axial flow fan. If there is no match, the turbulence k-ε model is re-entered with new initial conditions and boundary conditions to simulate the turbulence k-ε model, and the new pressure-flow curve obtained by simulation is matched with the actual working pressure-flow curve of the axial flow fan. This operation is repeated until the simulated working parameters match the PQ curve.

5. The method for simulating pressurized air supply characteristics of the lower evacuation passage of an ultra-long shield tunnel according to claim 4 is characterized in that: The actual working pressure-flow curve of the axial flow fan is obtained by fitting the actual working pressure-flow parameter scatter diagram of the axial flow fan using the least square method.

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