Calibration system and calibration method for near wall surface of hot-wire anemometer
Through the hot wire anemometer near wall calibration system, the calibration coefficient is calculated using polynomial fitting, which solves the problem of insufficient measurement accuracy of the hot wire anemometer near the wall and realizes efficient wind speed calibration.
Patent Information
- Application Number
- CN202510658755.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-21
- Publication Date
- 2025-09-30
AI Technical Summary
The existing hot wire anemometer has insufficient measurement accuracy near the wall, and the conventional calibration method leads to excessively large wind speed values and low test efficiency.
A hot wire anemometer near-wall calibration system is used, which includes a hot wire anemometer, a mobile control system, a flat panel and a host computer. The mobile control system changes the height of the hot wire from the wall, the signal acquisition system collects the voltage signal, and the host computer calculates the polynomial fitting to obtain the calibration coefficient, thereby realizing the relationship between wind speed and voltage.
The accuracy and test efficiency of wind speed measurement in the near-wall area are improved, and the wind speed can be accurately calibrated near the wall.
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Figure CN120722013A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to a hot wire anemometer near-wall surface calibration system and calibration method, belonging to the technical field of fluid measurement. Background Art
[0002] The hot wire anemometer is a commonly used test device for measuring fluid movement velocity. Its principle is to place a heated metal filament probe at a certain point in the flow field and apply voltage at both ends to maintain thermal equilibrium. That is, the input heat of electric heating and the heat output by fluid convection heat exchange are balanced with each other, keeping the temperature of the hot wire constant (constant temperature hot wire anemometer). Through calibration, the functional relationship between the voltage applied at both ends of the hot wire and the wind speed can be obtained, thereby realizing wind speed measurement.
[0003] Conventional hot wire calibration utilizes known wind speeds at the calibrator outlet or in the wind tunnel test section. However, this approach presents challenges when applied to wind speed measurements near walls. When the hot wire approaches a wall, the thermal effects of the wall can affect the hot wire measurement. Due to the significant temperature difference between the hot wire and the wall, the wall continuously absorbs heat from the surrounding thermal fluid, increasing convection losses. This results in a higher output voltage. Consequently, conventional hot wire calibration methods result in higher wind speed values near walls. Summary of the Invention
[0004] The technical problem solved by the present invention is to provide a hot wire anemometer near-wall surface calibration system and calibration method, so as to improve the measurement accuracy of the wind speed in the near-wall area and improve the test efficiency.
[0005] The technical solutions of the present invention are as follows:
[0006] A near-wall surface calibration method for a hot-wire anemometer is implemented using a near-wall surface calibration system for a hot-wire anemometer. The near-wall surface calibration system for a hot-wire anemometer includes a hot-wire anemometer, a mobile control system, a tablet, and a host computer. The hot-wire anemometer includes a hot wire, a probe, and a signal acquisition system, wherein the hot wire is fixed to the probe. The specific method includes:
[0007] S1. Set the probe and hot wire of the hot wire anemometer above the flat plate, and set the incoming wind speed sequence U1, U2, ..., U on the host computer. N and the height sequence h1,h2,…,h M ;
[0008] S2. The mobile control system receives the control command sent by the host computer and controls the movement of the probe of the hot wire anemometer so that the height position of the hot wire from the upper wall of the flat plate changes according to the height sequence;
[0009] S3, the signal acquisition system collects each incoming wind speed U in the incoming wind speed sequence. i At each height position hj The corresponding voltage signal of the hot wire is output to the host computer, where i = 1, 2, ..., N; j = 1, 2, ..., M; N and M are both positive integers;
[0010] S4. The host computer calculates each incoming wind speed U i At each height position h j Corresponding local theoretical wind speed value Expressed as: Get each height position h j The calibration relationship between wind speed and voltage is calculated, and the first calibration coefficient is obtained by polynomial fitting;
[0011] S5. The host computer calculates a second calibration coefficient based on the first calibration coefficient. During actual measurement, at any height h from the upper wall of the flat plate, the wind speed value U| is calculated based on the second calibration coefficient. h .
[0012] In the above-mentioned hot wire anemometer near-wall calibration method, in step S4, the host computer uses a quartic polynomial to perform fitting to obtain a first calibration coefficient, which is expressed as:
[0013] U| hj =C 4j E 4 +C 3j E 3 +C 2j E 2 +C 1j E+C 0j
[0014] Among them, C 0j 、C 1j 、C 2j 、C 3j 、C 4j is the first calibration coefficient; E is the voltage.
[0015] In the above-mentioned hot wire anemometer near-wall calibration method, in step S5, the host computer calculates the second calibration coefficient based on the first calibration coefficient, including:
[0016]
[0017] Among them, C s is the second calibration coefficient, h j With h j+1 are the height values of the two calibration sequences adjacent to h;
[0018] According to the second calibration coefficient C s Calculate the wind speed value U| h ,include:
[0019] U| h =C4E 4 +C3E 3 +C2E 2 +C1E+C0.
[0020] In the above-mentioned hot wire anemometer near-wall calibration method, the hot wire anemometer also includes a monitoring device, which is a camera for monitoring the relative position of the hot wire and the upper wall of the flat plate, and outputting a real-time image to a host computer for the host computer to calculate the distance h between the hot wire and the upper wall of the flat plate.
[0021] In the hot wire anemometer near wall calibration method, the signal acquisition system collects each incoming wind speed U in the incoming wind speed sequence. i At each height position h j The corresponding voltage signal output by the hot wire is conditioned and amplified before being output to the host computer.
[0022] In the above-mentioned hot wire anemometer near-wall calibration method, the mobile control system includes a slide and a controller; the slide is connected to the probe rod, controlling the probe rod to move along the normal direction of the upper wall of the flat plate, thereby changing the distance from the hot wire to the upper wall of the flat plate; the controller is used to receive movement instructions from the host computer and control the slide to move.
[0023] In the above-mentioned hot wire anemometer near-wall calibration method, the leading edge of the flat plate on the side facing the incoming flow direction is wedge-shaped.
[0024] In the above-mentioned hot wire anemometer near-wall calibration method, the hot wire is placed at a flow direction distance Δx=10mm-100mm from the leading edge of the flat plate.
[0025] In the above-mentioned hot wire anemometer near-wall calibration method, the wind speed sequence set by the host computer is arranged from small to large, and the wind speed range is the wind speed range during actual measurement; the height sequence is arranged from small to large, and the height range is the height range during actual measurement;
[0026] A near-wall calibration system for a hot-wire anemometer, comprising:
[0027] The hot wire anemometer includes a hot wire, a probe, and a signal acquisition system. The hot wire is fixed to the probe and is used to measure the wind speed of the fluid. The probe is connected to a motion control system, which changes the height of the hot wire from the upper wall of the plate under the control of the motion control system. The signal acquisition system is used to collect the voltage signal output by the hot wire, condition it, amplify it, and output it to the host computer.
[0028] The mobile control system includes a controller and a slide. The slide is connected to the probe rod. The controller is used to receive movement instructions from the host computer and control the slide to move, thereby driving the movement of the probe rod.
[0029] A monitoring device is used to monitor the relative position of the hot wire and the upper wall of the plate and output real-time images to the host computer;
[0030] The flat plate provides a wall surface for hot wire anemometer calibration, with the probe and hot wire of the hot wire anemometer arranged on top;
[0031] Host computer, set the incoming wind speed sequence U1, U2, ..., U N and the height sequence h1,h2,…,h M Receive the real-time image output by the monitoring device, calculate the distance h between the hot wire and the wall of the plate; send a movement instruction to the controller; receive the signal acquisition system sent by the incoming wind speed sequence of each incoming wind speed U i At each height position h j The corresponding voltage signal of the hot wire output is used to calculate the wind speed U of each incoming flow. i At each height position h j Corresponding local theoretical wind speed value Get each height position h j The calibration relationship between wind speed and voltage is obtained by polynomial fitting, and the second calibration coefficient is obtained based on the first calibration coefficient; in actual measurement, at any height h from the upper wall of the flat plate, the wind speed value U| is calculated based on the second calibration coefficient. h ; Wherein, i=1,2,…,N; j=1,2,…,M; N and M are both positive integers.
[0032] In the hot wire anemometer near-wall calibration system, the leading edge of the flat plate facing the incoming flow direction is wedge-shaped; the hot wire is placed at a flow direction distance Δx = 10 mm to 100 mm from the leading edge of the flat plate.
[0033] In the hot wire anemometer near-wall calibration system, the host computer uses a quartic polynomial to perform fitting to obtain the first calibration coefficient, which is expressed as:
[0034]
[0035] Among them, C 0j 、C 1j 、C 2j 、C 3j 、C 4j is the first calibration coefficient; E is the voltage;
[0036] Calculating a second calibration coefficient according to the first calibration coefficient includes:
[0037]
[0038] Among them, C s is the second calibration coefficient, h jWith h j+1 are the height values of the two calibration sequences adjacent to h.
[0039] In the hot wire anemometer near wall surface calibration system, the host computer calculates the value of the second calibration coefficient C according to the second calibration coefficient C. s Calculate the wind speed value U| h ,include:
[0040] U| h =C4E 4 +C3E 3 +C2E 2 +C1E+C0.
[0041] Compared with the prior art, the present invention has at least the following beneficial effects:
[0042] The embodiment of the present invention adopts a specially designed hot wire anemometer near-wall calibration system to calibrate the hot wire near the wall. The system includes a hot wire anemometer, a mobile control system, a monitoring device, a flat plate and a host computer. The mobile control system controls the movement of the probe rod of the hot wire anemometer according to the control instructions sent by the host computer, so that the height position of the hot wire from the wall on the flat plate changes according to a set height sequence; the signal acquisition system collects the required voltage signal and outputs it to the host computer. The host computer calculates the local theoretical wind speed values at different incoming wind speeds and different height positions, and obtains the calibration relationship between wind speed and voltage. The first calibration coefficient is obtained by polynomial fitting, and the second calibration coefficient is obtained according to the first calibration coefficient. Therefore, the wind speed value of the hot wire at any height from the flat plate can be obtained by simple calculation. The present invention can provide a calibration method for the hot wire near the wall, improve the measurement accuracy of the wind speed in the near-wall area, and improve the test efficiency. BRIEF DESCRIPTION OF THE DRAWINGS
[0043] Figure 1 A schematic diagram of the principle of a hot wire anemometer near-wall calibration system provided by an embodiment of the present invention;
[0044] Hot wire 1-1, probe rod 1-2, signal acquisition system 1-3, controller 2-1, slide 2-2, monitoring device 3, flat plate 4, host computer 5. DETAILED DESCRIPTION
[0045] The present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments:
[0046] like Figure 1 As shown, the hot wire anemometer near wall surface calibration system of the present invention includes a hot wire anemometer, a mobile control system, a monitoring device 3, a tablet 4 and a host computer 5, wherein:
[0047] The hot wire anemometer includes a hot wire 1-1, a probe 1-2, and a signal acquisition system 1-3. Hot wire 1-1 is a thermosensitive element used to measure the wind speed of a fluid. Hot wire 1-1 is fixed to probe 1-2, which is connected to a slide 2-2 of a motion control system. Signal acquisition system 1-3 is used to condition and amplify the voltage signal output by hot wire 1-1 and output it to a host computer 5.
[0048] The mobile control system includes a slide 2-2 and a controller 2-1. The slide 2-2 is connected to the probe 1-2 of the hot wire anemometer, and controls the probe 1-2 to move in the y direction (such as Figure 1 , i.e., the wall normal) moves to change the distance between the hot wire 1-1 and the upper wall of the plate 4. The controller 2-1 is used to receive the movement instruction of the host computer 5 and control the slide 2-2 to move.
[0049] The monitoring device 3 is a monitoring camera that monitors the relative position of the hot wire 1 - 1 and the upper wall of the plate 4 and outputs a real-time image to the host computer 5 for calculating the distance h between the hot wire 1 - 1 and the upper wall of the plate 4 .
[0050] Plate 4 provides the surface for hot-wire anemometer calibration. Its material is consistent with the surface used for actual hot-wire anemometer measurements. In this embodiment, the leading edge of plate 4 (i.e., the side facing the incoming flow) is wedge-shaped to minimize flow separation at the leading edge. In this embodiment, hot wire 1-1 is placed at a flow-wise distance Δx = 10 mm from the leading edge of plate 4. The boundary layer at this location is laminar. The Blasius solution is used to obtain velocity values at different heights above the wall, which are used to calibrate the hot wire.
[0051] Host computer 5, set the incoming wind speed sequence: U1, U2, ..., U N , the wind speed sequence is arranged from small to large, and the wind speed range should include the wind speed range during actual measurement. Set the height sequence: h1, h2, ..., h M , the height sequence is arranged from small to large, and the height range should include the height range during actual measurement.
[0052] The real-time image output by the monitoring device 3 is received, and the distance h between the hot wire 1 - 1 and the upper wall of the flat plate 4 is calculated.
[0053] A movement instruction is sent to the controller 2-1, and the controller 2-1 controls the slide 2-2 to move.
[0054] The voltage signal of the hot wire anemometer is collected and the data is analyzed and processed to obtain the calibration relationship between voltage and wind speed, specifically:
[0055] Each incoming wind speed U in the incoming wind speed sequence sent by the receiving signal acquisition system 1-3 i At each height position h jThe corresponding voltage signal output by the hot wire 1-1, where i=1, 2, ..., N; j=1, 2, ..., M; N and M are both positive integers, is used to calculate the wind speed U for each incoming flow. i At each height position h j Corresponding local theoretical wind speed value Expressed as:
[0056] Get each height position h j At , the calibration relationship between wind speed and voltage is obtained by fitting a fourth-order polynomial to obtain the first calibration coefficient, which is expressed as:
[0057]
[0058] Among them, C 0j 、C 1j 、C 2j 、C 3j 、C 4j is the first calibration coefficient; E is the voltage.
[0059] Obtaining a second calibration coefficient according to the first calibration coefficient includes:
[0060]
[0061] Among them, C s is the second calibration coefficient, h j With h j+1 are the height values of the two calibration sequences adjacent to h;
[0062] During actual measurement, at any height h from the upper wall of the plate 4, the wind speed value U| is calculated based on the second calibration coefficient. h ,include:
[0063] U| h =C4E 4 +C3E 3 +C2E 2 +C1E+C0.
[0064] The second calibration coefficients C0-C4 mentioned above include the influence of the wall thermal effect on the hot line, that is, the calibration relationship can obtain the accurate wind speed near the wall.
[0065] The present invention also provides a near-wall calibration method for a hot wire anemometer, which is implemented using the above-mentioned calibration system and specifically includes the following steps:
[0066] S1. Reference Figure 1Install the calibration system. The plane of plate 4 is parallel to the incoming flow direction. Probe 1-2 and hot wire 1-1 are positioned above plate 4, with probe 1-2 perpendicular to the plane of plate 4. Ensure that slide 2-2 moves along the normal to the surface of plate 4, and that hot wire 1-1 is 10 mm from the leading edge of plate 4 in the direction of the flow. Monitor camera 3 is positioned to the side for recording, ensuring that images of the hot wire are captured at any position within the given height sequence.
[0067] S2, host computer 5 sets the incoming wind speed sequence: U1, U2, ..., U N , the wind speed sequence is arranged from small to large, and the wind speed range should include the wind speed range during actual measurement. Set the height sequence: h1, h2, ..., h M , the height sequence is arranged from small to large, and the height range should include the height range during actual measurement.
[0068] S3, the mobile control system receives the control command sent by the host computer 5, controls the probe rod 1-2 of the hot wire anemometer to move along the y direction (such as Figure 1 , i.e., the wall normal) moves so that the height position of the hot wire 1-1 from the upper wall of the flat plate 4 changes according to the height sequence;
[0069] S4, the monitoring device 3 monitors the relative position of the hot wire 1-1 and the upper wall of the plate 4, outputs a real-time image to the host computer 5, and the host computer 5 calculates the distance h between the hot wire 1-1 and the upper wall of the plate 4;
[0070] S5, the signal acquisition system 1-3 collects each incoming wind speed U in the incoming wind speed sequence. i At each height position h j The voltage signal output by the corresponding hot wire 1-1 is conditioned, amplified, and output to the host computer 5, where i=1, 2, ..., N; j=1, 2, ..., M; N and M are both positive integers;
[0071] S6, the host computer 5 calculates each incoming wind speed U i At each height position h j Corresponding local theoretical wind speed value Expressed as: Get each height position h j The calibration relationship between wind speed and voltage is obtained by fitting a fourth-order polynomial, which is expressed as:
[0072]
[0073] Among them, C 0j 、C 1j 、C 2j 、C 3j 、C 4j is the first calibration coefficient; E is the voltage.
[0074] S7. The host computer 5 calculates the second calibration coefficient based on the first calibration coefficient. The specific method is:
[0075]
[0076] Among them, C s is the second calibration coefficient, h j With h j+1 are the height values of the two calibration sequences adjacent to h;
[0077] S8. During actual measurement, the host computer 5 calculates the wind speed value U| at any height h from the upper wall of the flat plate 4 according to the second calibration coefficient. h ,include:
[0078] U| h =C4E 4 +C3E 3 +C2E 2 +C1E+C0.
[0079] The above description is only the best specific implementation method of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or replacements that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.
[0080] The contents not described in detail in the specification of the present invention belong to the common knowledge of professionals in this field.
Claims
1. A method for calibrating a hot wire anemometer near a wall, characterized in that: The method is implemented by using a hot wire anemometer near-wall surface calibration system, the hot wire anemometer near-wall surface calibration system comprising a hot wire anemometer, a mobile control system, a flat panel (4) and a host computer (5), the hot wire anemometer comprising a hot wire (1-1), a probe (1-2) and a signal acquisition system (1-3), wherein the hot wire (1-1) is fixed on the probe (1-2), and the specific method comprises: S1. The probe rod (1-2) and the hot wire (1-1) of the hot wire anemometer are set above the flat plate (4). The host computer (5) sets the incoming wind speed sequence U1, U2, ..., U N and the height sequence h1,h2,…,h M ; S2, the mobile control system receives the control instruction sent by the host computer (5), controls the movement of the probe (1-2) of the hot wire anemometer, and changes the height position of the hot wire (1-1) from the upper wall of the flat plate (4) according to the height sequence; S3, the signal acquisition system (1-3) collects the incoming wind speed U of each incoming wind speed in the incoming wind speed sequence. i At each height position h j The corresponding hot wire (1-1) outputs a voltage signal, which is then output to the host computer (5), wherein i=1, 2, ..., N; j=1, 2, ..., M; N and M are both positive integers; S4, host computer (5) calculates each incoming wind speed U i At each height position h j Corresponding local theoretical wind speed value Expressed as: Get each height position h j The calibration relationship between wind speed and voltage is calculated, and the first calibration coefficient is obtained by polynomial fitting; S5, the host computer (5) calculates a second calibration coefficient based on the first calibration coefficient. During actual measurement, at any height h from the upper wall of the flat plate (4), the wind speed value U| is calculated based on the second calibration coefficient. h .
2. A hot wire anemometer near wall calibration method according to claim 1, characterized in that: In step S4, the host computer (5) uses a quartic polynomial to perform fitting to obtain a first calibration coefficient, which is expressed as: Among them, C 0j 、C 1j 、C 2j 、C 3j 、C 4j is the first calibration coefficient; E is the voltage.
3. A hot wire anemometer near wall calibration method according to claim 2, characterized in that: In step S5, the host computer (5) calculates the second calibration coefficient based on the first calibration coefficient, including: Among them, C s is the second calibration coefficient, h j With h j+1 are the height values of the two calibration sequences adjacent to h; According to the second calibration coefficient C s Calculate the wind speed value U| h ,include: The| h =C4E 4 +C3E 3 +C2E 2 +C1E+C0.
4. A hot wire anemometer near wall calibration method according to claim 1, characterized in that: The hot wire anemometer further comprises a monitoring device (3), which is a camera for monitoring the relative position of the hot wire (1-1) and the upper wall surface of the flat plate (4), and outputting a real-time image to a host computer (5) for the host computer (5) to calculate the distance h between the hot wire (1-1) and the upper wall surface of the flat plate (4).
5. The method for calibrating a hot wire anemometer near a wall according to claim 1, characterized in that: The signal acquisition system (1-3) acquires each incoming wind speed U in the incoming wind speed sequence. i At each height position h j The voltage signal output by the corresponding hot wire (1-1) is conditioned and amplified before being output to the host computer (5).
6. A hot wire anemometer near wall calibration method according to claim 1, characterized in that: The mobile control system includes a slide (2-2) and a controller (2-1); The slide (2-2) is connected to the probe rod (1-2), and controls the probe rod (1-2) to move along the normal direction of the upper wall of the flat plate (4), thereby changing the distance between the hot wire (1-1) and the upper wall of the flat plate (4); The controller (2-1) is used to receive movement instructions from a host computer (5) and control the slide (2-2) to move.
7. A hot wire anemometer near wall calibration method according to claim 1, characterized in that: The front edge of the flat plate (4) on the side facing the incoming flow direction is wedge-shaped.
8. The method for calibrating a hot wire anemometer near a wall according to claim 5, characterized in that: The hot wire (1-1) is placed at a flow direction distance Δx=10mm to 100mm from the front edge of the flat plate (4).
9. The method for calibrating a hot wire anemometer near a wall according to claim 1, characterized in that: The wind speed sequence set by the host computer (5) is arranged from small to large, and the wind speed range is the wind speed range during actual measurement; the height sequence is arranged from small to large, and the height range is the height range during actual measurement.
10. A hot wire anemometer near wall calibration system, characterized in that: include: A hot wire anemometer comprises a hot wire (1-1), a probe (1-2) and a signal acquisition system (1-3), wherein the hot wire (1-1) is fixed on the probe (1-2) and is used to measure the wind speed of a fluid; the probe (1-2) is connected to a mobile control system, and the height position of the hot wire (1-1) from the upper wall of a flat plate (4) is changed under the control of the mobile control system; the signal acquisition system (1-3) is used to collect the voltage signal output by the hot wire (1-1), and output it to a host computer (5) after conditioning and amplification; The mobile control system includes a controller (2-1) and a slide (2-2), wherein the slide (2-2) is connected to the probe (1-2), and the controller (2-1) is used to receive a movement instruction from a host computer (5) and control the slide (2-2) to move, thereby driving the movement of the probe (1-2); A monitoring device (3) is used to monitor the relative position of the hot wire (1-1) and the upper wall surface of the flat plate (4), and output a real-time image to a host computer (5); A flat plate (4) provides a wall surface for hot wire anemometer calibration, with a probe (1-2) and a hot wire (1-1) of the hot wire anemometer arranged on the flat plate; The host computer (5) sets the incoming wind speed sequence U1, U2, ..., U N and the height sequence h1,h2,…,h M Receive the real-time image output by the monitoring device (3), calculate the distance h between the hot wire (1-1) and the upper wall of the flat plate (4); send a movement instruction to the controller (2-1); receive the incoming wind speed U of each incoming wind speed in the incoming wind speed sequence sent by the signal acquisition system (1-3) i At each height position h j The corresponding hot wire (1-1) outputs a voltage signal and calculates each incoming wind speed U i At each height position h j Corresponding local theoretical wind speed value Get each height position h j The calibration relationship between wind speed and voltage is obtained by polynomial fitting, and a first calibration coefficient is obtained based on the first calibration coefficient; in actual measurement, at any height h from the upper wall of the plate (4), the wind speed value U| is calculated based on the second calibration coefficient. h ; Wherein, i=1,2,…,N; j=1,2,…,M; N and M are both positive integers.
11. A hot wire anemometer near-wall surface calibration system according to claim 10, characterized in that: The front edge of the flat plate (4) facing the incoming flow direction is wedge-shaped; the hot wire (1-1) is placed at a flow direction distance Δx=10mm-100mm from the front edge of the flat plate (4).
12. The hot wire anemometer near-wall calibration system according to claim 10, characterized in that: The host computer (5) uses a quartic polynomial to perform fitting to obtain a first calibration coefficient, which is expressed as: Among them, C 0j 、C 1j 、C 2j 、C 3j 、C 4j is the first calibration coefficient; E is the voltage; Calculating a second calibration coefficient according to the first calibration coefficient includes: Among them, C s is the second calibration coefficient, h j With h j+1 are the height values of the two calibration sequences adjacent to h.
13. A hot wire anemometer near-wall calibration system according to claim 12, characterized in that: The host computer (5) is based on the second calibration coefficient C s Calculate the wind speed value U| h ,include: The| h =C4E 4 +C3E 3 +C2E 2 +C1E+C0.
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