A dynamic calibration system and method for wall friction stress

Abstract

This invention relates to a dynamic calibration system and method for wall friction stress, belonging to the field of fluid measurement technology. Dynamic calibration is performed using a specially designed calibration system. The probe of a hot-wire anemometer is placed in the viscous sublayer of the turbulent boundary layer, above a flat plate assembly. A pressure sensor measures the fluid pressure on the plate surface, and the hot-wire anemometer measures the wall friction stress on the plate surface. The measured voltage signal is transmitted to a host computer in real time. The host computer sets a friction stress sequence, corresponding to the measured voltage values, and sets a polynomial that satisfies the relationship between the predicted friction stress value and the voltage. Fitting coefficients are obtained through static calibration, and these coefficients are substituted into the polynomial to obtain a preliminary predicted friction stress value. A corrected friction stress pulsation value is obtained through dynamic calibration. Based on the preliminary and corrected friction stress pulsation values, a higher precision dynamic friction stress measurement value can be obtained.

Description

Technical Field

[0001] This invention relates to a dynamic calibration system and method for wall friction stress, belonging to the field of fluid measurement technology. Background Technology

[0002] Hot-wire anemometers, characterized by high frequency response and high sensitivity, are important testing equipment for measuring velocity fluctuations in turbulent flow fields. When measuring wall friction stress, the hot wire is inserted into the viscous sublayer near the wall, and the friction stress value is obtained through the linear relationship between fluid velocity and wall friction stress. In the turbulent boundary layer, wall friction stress exhibits strong dynamic characteristics. When using a hot-wire anemometer to measure dynamic friction stress, two factors affect the accuracy of the dynamic value measurement. First, when measuring wall friction stress, the hot wire needs to be inserted into the viscous sublayer, at which point the hot wire is very close to the wall. Due to the temperature difference between the hot wire and the wall, the wall continuously absorbs heat from the hot wire. Influenced by the wall, the thermal inertia of the hot wire increases, and the dynamic response capability decreases, resulting in an underestimation of the dynamic measurement value. Second, the spatial resolution of the hot wire is limited; the instantaneous velocity value measured is actually the average value of the fluid velocity along the length of the hot wire itself, making the actual measured value of the dynamic signal smaller than the true value. Summary of the Invention

[0003] The technical problem solved by this invention is to provide a dynamic calibration system and method for wall friction stress. By designing a dedicated calibration system and correcting the dynamic response of the hot wire, higher accuracy dynamic friction stress measurement values ​​can be obtained.

[0004] The technical solution of the present invention is as follows:

[0005] A method for dynamically calibrating wall friction stress is implemented using a dynamic calibration system. The dynamic calibration system includes a hot-wire anemometer, a flat plate assembly, a pressure sensor, and a host computer. The hot-wire anemometer includes a probe, and the pressure sensor is mounted on the flat plate. The specific method includes:

[0006] S1. Place the probe of the hot-wire anemometer in the viscous sublayer of the turbulent boundary layer, and position it above the flat plate assembly;

[0007] S2. The host computer sets the frictional stress sequence τ0(t) on the flat plate wall. (1) ,τ0(t) (2) ,…,τ0(t) (N) The probe of the hot-wire anemometer will measure the voltage signal E(t) corresponding to the frictional stress sequence. (1) E(t) (2) E(t) (N) The data is transmitted to the host computer in real time, where t is the time.

[0008] S3, The host computer sets the predicted value of frictional stress τ p The polynomial relationship between τ0(t) and voltage E(t) is satisfied, and the relationship between τ0(t) and τ is also satisfied. p (t) is decomposed, including:

[0009]

[0010] in, Let τ0'(t) be the time average, and τ be the time average. p '(t) is the pulsation value; to make τ p (t)=τ0(t), which must satisfy: τ p '(t)=τ0'(t);

[0011] S4, Order The host computer obtains the fitting coefficients in the polynomial relationship through static calibration, and substitutes the fitting coefficients into the polynomial relationship to obtain the preliminary predicted value of frictional stress τ. p (t)';

[0012] S5, let τ p Frictional stress pulsation value '(t)=τ'0(t) is obtained by the host computer through dynamic calibration.

[0013] S6. The host computer calculates the initial frictional stress prediction value τ. p (t)' and the corrected frictional stress pulsation value The predicted value of frictional stress τ is obtained. p (t), where,

[0014] In the above-mentioned dynamic calibration method for wall friction stress, the plate assembly includes a plate, a tail plate, and a tripwire. One end of the plate is connected to the tail plate via a rotating shaft. The tail plate rotates around the rotating shaft to form an angle with the plate. The tripwire is connected to the other end of the plate to promote flow transition.

[0015] In the above-mentioned dynamic calibration method for wall friction stress, the pressure sensor includes a first pressure sensor and a second pressure sensor, which are respectively embedded inside the plate to measure the pressure on the surface of the plate. By adjusting the angle between the plate and the tail plate, the pressure measurement values ​​of the two sensors are made consistent, so that the pressure gradient of the plate flow direction is 0.

[0016] In the above-mentioned dynamic calibration method for wall friction stress, the first pressure sensor and the second pressure sensor are embedded inside the plate and installed upstream and downstream of the probe, respectively. The installation positions of the two sensors are at the same distance from the probe in the flow direction, which is 0.2m to 0.3m.

[0017] In the above-mentioned dynamic calibration method for wall friction stress, the leading edge of the plate assembly is wedge-shaped, and the probe is set at a flow distance of 2m to 3m from the leading edge of the plate.

[0018] In the above-mentioned dynamic calibration method for wall friction stress, in step S3, the host computer sets the predicted friction stress value τ. p The relationship between voltage E(t) and voltage E(t) is a fourth-degree polynomial, as follows:

[0019] τ p (t)=C4E(t) 4 +C3E(t) 3 +C2E(t) 2 +C1E(t)+C0

[0020] Where C0 to C4 are the fitting coefficients.

[0021] In the above-mentioned dynamic calibration method for wall friction stress, in step S4, let The host computer obtains the fitting coefficients in the polynomial relationship through static calibration, including:

[0022] For a quartic polynomial τ p (t)=C4E(t) 4 +C3E(t) 3 +C2E(t) 2 Averaging both sides of +C1E(t)+C0 over time, we get:

[0023]

[0024] In equation (3), the calibration coefficients C0 to C4 must satisfy the following relationship, that is, for each calibration point, the predicted value of frictional stress measured by the hot-wire anemometer (1) is equal to the true value:

[0025]

[0026] Equation (4) can be simplified as follows: The coefficient matrix C is then calculated using the following formula:

[0027]

[0028] In the above-mentioned dynamic calibration method for wall friction stress, in step S5, let τ p Frictional stress pulsation value '(t)=τ0'(t) is obtained by the host computer through dynamic calibration. include:

[0029] τ′ at any calibration point p The Fourier transform of (t) is Y pThe Fourier transform of τ′0(t) is Y0(f), where f is the frequency; Y p Y(f) and Y0(f) are decomposed into real and imaginary parts:

[0030] Y p (f)=R p (f)+I p (f)j

[0031] Y0(f)=R0(f)+I0(f)j

[0032] Solve for the transfer function H(f) = R H (f)+I H (f)j, for Y p (f) Make corrections so that:

[0033] Y p (f)H(f)=Y0(f) (6)

[0034] By Y p The power spectral density and phase frequency function are calculated from the real and imaginary parts of Y0(f), H(f), and Y0(f), respectively.

[0035]

[0036] Where, Δf p Δf0 represents the frequency resolution;

[0037] By combining equations (6) and (7), we can obtain the expressions for the real and imaginary parts of H(f):

[0038]

[0039] Equation (8) simplifies to:

[0040]

[0041] At each calibration point, the transfer function H(f) is obtained using equation (9). (1) H(f) (2) H(f) (N) The transfer function H with respect to G is obtained. p The calibration database of f;

[0042] In actual measurement, according to G p The values ​​of f are obtained by linear interpolation in the calibration database to determine H(f); after determining the transfer function H(f), the values ​​of Y are then used to determine the transfer function H(f). p Performing an inverse Fourier transform on H(f) yields the corrected frictional stress pulsation value.

[0043] .

[0044] A dynamic calibration system for wall friction stress, comprising:

[0045] A hot-wire anemometer, including a probe, is placed in the viscous sublayer of the turbulent boundary layer and located above a flat plate. It is used to measure the frictional stress on the plate wall and transmit the measured voltage signal to a host computer in real time.

[0046] The flat plate assembly includes a flat plate, a tail plate, and a tripwire. The flat plate provides a wall surface for calibration by a hot-wire anemometer. One end of the flat plate is connected to the tail plate via a pivot. The tail plate rotates around the pivot to form an angle with the flat plate. The tripwire is connected to the other end of the flat plate to facilitate flow transition.

[0047] The pressure sensor includes a first pressure sensor and a second pressure sensor. The two pressure sensors are embedded inside the plate to measure the fluid pressure on the surface of the plate and send the data to the host computer.

[0048] In the host computer, set the frictional stress sequence τ0(t) under the current calibration environment. (1) ,τ0(t) (2) ,…,τ0(t) (N) It receives the voltage signal E(t) corresponding to the frictional stress sequence sent by the hot-wire anemometer. (1) E(t) (2) E(t) (N) Where t is time; the predicted frictional stress value τ is set. p The polynomial relationship between τ0(t) and voltage E(t) is satisfied, and the relationship between τ0(t) and τ is also satisfied. p (t) is decomposed, including: in, Let τ0'(t) be the time average, and τ be the time average. p '(t) is the pulsation value; to make τ p (t)=τ0(t), which must satisfy: τ p Let '(t) = τ0'(t); The fitting coefficients in the polynomial relationship are obtained through static calibration. Substituting these fitting coefficients into the polynomial relationship yields a preliminary predicted value of frictional stress τ. p (t)';Let τ′ p (t)=τ′0(t), the corrected frictional stress pulsation value is obtained through dynamic calibration. Based on the preliminary predicted frictional stress value τ p (t)' and the corrected frictional stress pulsation value The predicted value of frictional stress τ is obtained. p (t), where,

[0049] In the above-mentioned dynamic calibration method for wall friction stress, the first pressure sensor and the second pressure sensor are embedded inside the plate and installed upstream and downstream of the probe, respectively. The installation positions of the two sensors are the same as the flow direction distance of the probe, which is 0.2 to 0.3 m. By adjusting the angle between the plate and the tail plate, the pressure measurement values ​​of the two sensors are made consistent, so that the pressure gradient in the flow direction of the plate is 0.

[0050] In the above-mentioned dynamic calibration method for wall friction stress, the host computer sets the predicted friction stress value τ. p The relationship between voltage E(t) and voltage E(t) is a fourth-degree polynomial, as follows:

[0051] τ p (t)=C4E(t) 4 +C3E(t) 3 +C2E(t) 2 +C1E(t)+C0

[0052] Where C0 to C4 are the fitting coefficients.

[0053] In the above-mentioned dynamic calibration method for wall friction stress, let The host computer obtains the fitting coefficients in the polynomial relationship through static calibration, including:

[0054] For a quartic polynomial τ p (t)=C4E(t) 4 +C3E(t) 3 +C2E(t) 2 Averaging both sides of +C1E(t)+C0 over time, we get:

[0055]

[0056] In equation (3), the calibration coefficients C0 to C4 must satisfy the following relationship, that is, for each calibration point, the predicted value of frictional stress measured by the hot-wire anemometer (1) is equal to the true value:

[0057]

[0058] Equation (4) can be simplified as follows: The coefficient matrix C is then calculated using the following formula:

[0059]

[0060] In the above method for dynamic calibration of wall friction stress, let τ p Frictional stress pulsation value '(t)=τ0'(t) is obtained by the host computer through dynamic calibration. include:

[0061] τ at any calibration point p The Fourier transform of '(t) is Y p The Fourier transform of τ0'(t) is Y0(f), where f is the frequency; Y p Y(f) and Y0(f) are decomposed into real and imaginary parts:

[0062] Y p (f)=R p (f)+I p (f)j

[0063] Y0(f)=R0(f)+I0(f)j

[0064] Solve for the transfer function H(f) = R H (f)+I H (f)j, for Y p (f) Make corrections so that:

[0065] Y p (f)H(f)=Y0(f) (6)

[0066] By Y p The power spectral density and phase frequency function are calculated from the real and imaginary parts of Y0(f), H(f), and Y0(f), respectively.

[0067]

[0068] Where, Δf p Δf0 represents the frequency resolution;

[0069] By combining equations (6) and (7), we can obtain the expressions for the real and imaginary parts of H(f):

[0070]

[0071] Equation (8) simplifies to:

[0072]

[0073] At each calibration point, the transfer function H(f) is obtained using equation (9). (1) H(f) (2) H(f) (N) The transfer function H with respect to G is obtained. p The calibration database of f;

[0074] In actual measurement, according to G p The values ​​of f are obtained by linear interpolation in the calibration database to determine H(f); after determining the transfer function H(f), the values ​​of Y are then used to determine the transfer function H(f). pPerforming an inverse Fourier transform on H(f) yields the corrected frictional stress pulsation value.

[0075] .

[0076] Compared with the prior art, the present invention has at least the following beneficial effects:

[0077] This invention relates to a dynamic calibration system and method for wall friction stress, belonging to the field of fluid measurement technology. It employs a specially designed calibration system for dynamic calibration. The system includes a hot-wire anemometer, a flat plate assembly, a pressure sensor, and a host computer. The probe of the hot-wire anemometer is placed in the viscous sublayer of the turbulent boundary layer and positioned above the flat plate assembly. The pressure sensor measures the fluid pressure on the flat plate surface to adjust the tail plate of the flat plate assembly, ensuring the flow-direction pressure gradient is zero. The hot-wire anemometer measures the wall friction stress on the flat plate surface and transmits the measured voltage signal to the host computer in real time. The calibration between friction stress and voltage is completed in the host computer. The host computer sets the known friction stress sequence under the current calibration environment, the corresponding voltage value measured by the probe, and sets the polynomial relationship between the predicted friction stress value and the voltage. The fitting coefficients are obtained through static calibration, and the fitting coefficients are substituted into the polynomial relationship to obtain the preliminary predicted friction stress value. The corrected friction stress pulsation value is obtained through dynamic calibration. Based on the preliminary predicted friction stress value and the corrected friction stress pulsation value, the predicted friction stress value is obtained. This invention can obtain a more accurate dynamic friction stress measurement value. Attached Figure Description

[0078] Figure 1 A schematic diagram of the principle of the wall friction stress dynamic calibration system provided in the real-time example of the present invention;

[0079] Hot-wire anemometer 1, probe 1-1, tripwire 2-1, tail plate 2-2, flat plate 2-3, first pressure sensor 3-1, second pressure sensor 3-2, host computer 4. Detailed Implementation

[0080] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments:

[0081] like Figure 1 As shown, the wall friction stress dynamic calibration system of the present invention includes a hot-wire anemometer 1, a flat plate assembly, a pressure sensor, and a host computer 4, wherein:

[0082] Hot-wire anemometer 1, an instrument for calibrating and measuring wall friction stress, includes probe 1-1. During calibration, probe 1-1 is ensured to be located in the viscous sublayer of the turbulent boundary layer. During measurement and calibration, the distance between probe 1-1 and the wall of plate 2-3 is kept consistent.

[0083] The flat plate assembly, providing a wall surface for hot-wire anemometer calibration, specifically includes a flat plate 2-3, a tail plate 2-2, and a tripwire 2-1. One end of the flat plate 2-3 is connected to the tail plate 2-2 via a pivot, allowing the tail plate 2-2 to rotate around the pivot and change the angle between the tail plates 2-2 to achieve a flow-direction pressure gradient of zero. The tripwire 2-1 is connected to the other end of the flat plate 2-3 to promote flow transition and achieve fully developed turbulence. In this embodiment, the leading edge of the flat plate 2-3 is wedge-shaped to minimize flow separation at the leading edge. A 5mm diameter tripwire 2-1 is placed 20mm from the leading edge of the flat plate 2-3. The probe 1-1 is placed at a flow-direction distance x = 2m from the leading edge of the flat plate 2-3, where the boundary layer is a fully developed turbulent boundary layer.

[0084] The pressure sensors include a first pressure sensor 3-1 and a second pressure sensor 3-2, both embedded inside the plate 2-3. These sensors measure the pressure on the surface of the plate 2-3 and transmit the measurements to the host computer 4. In this embodiment, the first pressure sensor 3-1 and the second pressure sensor 3-2 are respectively installed upstream and downstream of the probe 1-1, with their installation positions coinciding with the flow direction distance of the probe 1-1, located 0.25m upstream and 0.25m downstream of the hot wire, respectively. The angle of the tail plate 2-2 of the plate assembly is adjusted to ensure that the pressure measurements from the two sensors are consistent, resulting in a zero pressure gradient along the plate flow direction.

[0085] The host computer 4 collects signals from the hot-wire anemometer and pressure sensor, and performs data analysis and processing. Specifically, this includes:

[0086] 1. Set the known frictional stress sequence τ0(t) for the current calibration environment. (1) ,τ0(t) (2) ,…,τ0(t) (N) The receiver receives the voltage signal E(t) corresponding to the frictional stress sequence transmitted by the hot-wire anemometer 1. (1) E(t) (2) E(t) (N) Where t is time, the relationship between wall friction stress and voltage is calibrated in the host computer 4.

[0087] Preliminary setting of the predicted frictional stress τ of the hot wire p (t) and the hot wire voltage satisfy a fourth-order polynomial relationship:

[0088] τ p (t)=C4E(t) 4 +C3E(t) 3 +C2E(t) 2 +C1E(t)+C0 (1)

[0089] C0~C4 are the fitting coefficients, which are used to compare τ0(t) with τ p(t) is decomposed:

[0090]

[0091] in Let τ0'(t) be the time average, and τ be the time average. p '(t) represents the pulsation value. To make τ p (t)=τ0(t), which must satisfy: τ p '(t)=τ0'(t).

[0092] 2. Static calibration

[0093] Calibration hot wire Equation (1) holds true. Taking the average of both sides with respect to time, we get:

[0094]

[0095] The calibration coefficients C0 to C4 in equation (3) must satisfy the following relationship, that is, for each calibration point, the predicted value of frictional stress measured by the hot-wire anemometer is equal to the actual value:

[0096]

[0097] Equation (4) can be simplified as follows: The coefficient matrix C is then calculated using the following formula:

[0098]

[0099] The fitting coefficients C0 to C4 in the polynomial relation are obtained through static calibration. Substituting the fitting coefficients C0 to C4 into the polynomial relation (1), the preliminary predicted value of frictional stress τ is obtained. p (t)'.

[0100] 3. Dynamic calibration

[0101] A dynamic calibration method based on frequency domain correction is proposed. Due to the thermal inertia of the wall and spatial resolution, the spectrum of hot-wire anemometers suffers from amplitude loss. Therefore, this invention uses the spectrum of the true frictional stress value to correct the spectrum of the predicted value.

[0102] After completing the static calibration, the preliminary predicted value of frictional stress τ is obtained from equation (1). p (t), whose time mean satisfies The following dynamic calibration is performed to ensure that the pulsation value at each calibration point satisfies τ. p '(t)=τ0'(t).

[0103] Realizing τ in the time domain pThe problem of '(t)=τ0'(t) is quite difficult, so it is converted to the frequency domain. Let τ be the value at any calibration point. p The Fourier transform of '(t) is Y p The Fourier transform of τ0'(t) is Y0(f), where f is the frequency. p Y(f) and Y0(f) can be decomposed into real and imaginary parts: Y p (f)=R p (f)+I p (f) j Y0(f) = R0(f) + I0(f)j. The demand solution transfer function is H(f) = R H (f)+I H (f)j, for Y p (f) Make corrections so that:

[0104] Y p (f)H(f)=Y0(f) (6)

[0105] By Y p The real and imaginary parts of Y0(f), H(f) can be used to calculate the power spectral density and phase frequency function, respectively.

[0106]

[0107] Where, Δf p Let Δf0 be the frequency resolution. Combining equations (6) and (7), we obtain the expressions for the real and imaginary parts of H(f):

[0108]

[0109] Generally speaking, the phase frequency response of the hot wire is sensitive enough to ensure... Equation (8) simplifies to:

[0110]

[0111] At each calibration point, the transfer function H(f) is obtained using equation (9). (1) H(f) (2) H(f) (N) The transfer function H with respect to G is obtained. p The calibration database for f. During actual measurements, according to G... p The values ​​of f are obtained by linear interpolation in the calibration database to find H(f).

[0112] After determining the transfer function H(f), for Y p Performing an inverse Fourier transform on H(f) yields the corrected frictional stress pulsation value.

[0113]

[0114] satisfy That is, the predicted RMS value of the frictional stress pulsation is consistent with the actual value.

[0115] The expression for the final predicted frictional stress value is:

[0116]

[0117] This invention also provides a method for dynamic calibration of wall friction stress, which is implemented using the above-mentioned dynamic calibration system. The specific method includes the following steps:

[0118] S1. Inside the wind tunnel, according to Figure 1 Install the calibration device and, within the range of incoming flow velocity corresponding to the wall friction stress calibration, adjust the angle of the tail plate 2-2 to make the pressure gradient along the flow direction of the plate zero. Place the probe 1-1 at the required distance along the flow direction at the leading edge of the plate, for example, at x = 2m, and ensure that the probe 1-1 is located within the viscous sublayer.

[0119] S2. The host computer sets the incoming airflow velocity sequence and calculates the known (actual) value of the wall friction stress at each incoming airflow velocity: τ0(t). (1) ,τ0(t) (2) ,…,τ0(t) (N) The probe 1-1 of the hot-wire anemometer 1 measures the voltage signal E(t) corresponding to the frictional stress sequence. (1) E(t) (2) E(t) (N) The data is transmitted to the host computer 4 in real time, where t is time; the relationship between wall friction stress and voltage is calibrated in the host computer 4.

[0120] S3, Host computer 4 initially sets the predicted value of frictional stress τ for the hot wire. p (t) and the hot wire voltage satisfy a fourth-order polynomial relationship:

[0121] τ p (t)=C4E(t) 4 +C3E(t) 3 +C2E(t) 2 +C1E(t)+C0 (1)

[0122] C0~C4 are the fitting coefficients, which are used to compare τ0(t) with τ p (t) is decomposed:

[0123]

[0124] in Let τ0'(t) be the time average, and τ be the time average. p '(t) represents the pulsation value. To make τ p (t)=τ0(t), which must satisfy: τ p '(t)=τ0'(t).

[0125] S4, Order The host computer 4 obtains the fitting coefficients in the polynomial relationship through static calibration. Specific methods include:

[0126] Calibration hot wire Equation (1) holds true. Taking the average of both sides with respect to time, we get:

[0127]

[0128] The calibration coefficients C0 to C4 in equation (3) must satisfy the following relationship, that is, for each calibration point, the predicted value of frictional stress measured by the hot-wire anemometer is equal to the actual value:

[0129]

[0130] Equation (4) can be simplified as follows: The coefficient matrix C is then calculated using the following formula:

[0131]

[0132] Substituting the obtained fitting coefficients C0 to C4 into the polynomial relation (1), we obtain the preliminary predicted value of frictional stress τ. p (t)'.

[0133] S5, let τ p Frictional stress pulsation value is obtained by the host computer 4 through dynamic calibration, where τ'(t) = τ'0(t). Specific methods include:

[0134] Due to the thermal inertia of the wall and spatial resolution, the spectrum of the hot-wire anemometer exhibits amplitude loss. Therefore, the spectrum of the predicted value is corrected using the spectrum of the true frictional stress value.

[0135] After completing the static calibration, the preliminary predicted value of frictional stress τ is obtained from equation (1). p (t), whose time mean satisfies The following dynamic calibration is performed to ensure that the pulsation value at each calibration point satisfies τ. p '(t)=τ0'(t).

[0136] Realizing τ in the time domain p The problem of '(t)=τ0'(t) is quite difficult, so it is converted to the frequency domain. Let τ be the value at any calibration point. pThe Fourier transform of '(t) is Y p The Fourier transform of τ0'(t) is Y0(f), where f is the frequency. p Y(f) and Y0(f) can be decomposed into real and imaginary parts: Y p (f)=R p (f)+I p (f)j, Y0(f)=R0(f)+I0(f)j. Demand solution transfer function H(f)=R H (f)+I H (f)j, for Y p (f) Make corrections so that:

[0137] Y p (f)H(f)=Y0(f) (6)

[0138] By Y p The real and imaginary parts of Y0(f), H(f) can be used to calculate the power spectral density and phase frequency function, respectively.

[0139]

[0140] Where, Δf p Let Δf0 be the frequency resolution. Combining equations (6) and (7), we obtain the expressions for the real and imaginary parts of H(f):

[0141]

[0142] Generally speaking, the phase frequency response of the hot wire is sensitive enough to ensure... Equation (8) simplifies to:

[0143]

[0144] At each calibration point, the transfer function H(f) is obtained using equation (9). (1) H(f) (2) H(f) (N) The transfer function H with respect to G is obtained. p The calibration database for f. During actual measurements, according to G... p The values ​​of f are obtained by linear interpolation in the calibration database to find H(f).

[0145] After determining the transfer function H(f), for Y p Performing an inverse Fourier transform on H(f) yields the corrected frictional stress pulsation value.

[0146]

[0147] satisfy That is, the predicted RMS value of the frictional stress pulsation is consistent with the actual value.

[0148] S6, the host computer 4, based on the preliminary predicted frictional stress value τ p (t)' and the corrected frictional stress pulsation value The predicted value of frictional stress τ is obtained. p (t), the expression for the final predicted value of frictional stress is:

[0149]

[0150] The above description is only the best specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the protection scope of the present invention.

[0151] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A method for dynamic calibration of wall friction stress, characterized in that, A dynamic calibration system is used, which includes a hot-wire anemometer (1), a flat panel assembly, a pressure sensor, and a host computer (4). The hot-wire anemometer (1) includes a probe (1-1), and the pressure sensor (3) is mounted on the flat panel (2). The specific method includes: S1. Place the probe (1-1) of the hot-wire anemometer (1) in the viscous sublayer of the turbulent boundary layer and above the flat plate assembly; S2, Host computer (4) sets the friction stress sequence of the flat plate wall. , ,…, The probe (1-1) of the hot-wire anemometer (1) measures the voltage signal corresponding to the frictional stress sequence. , ,…, Real-time transmission to the host computer (4), of which t For time; S3, host computer (4) sets the predicted value of frictional stress With voltage The polynomial relation between them is satisfied, and will and Decomposition includes: in, , The average value over time. , For the pulsation value; to make It must meet the following requirements: , ; S4, Order The host computer (4) obtains the fitting coefficients in the polynomial relationship through static calibration, and substitutes the fitting coefficients into the polynomial relationship to obtain the preliminary predicted value of friction stress. ; S5, Order The host computer (4) obtains the corrected friction stress pulsation value through a dynamic calibration method based on frequency domain correction. That is, the spectrum of the predicted value is corrected by using the spectrum of the true value of frictional stress; S6, Host computer (4) Based on the preliminary predicted value of frictional stress and the corrected frictional stress pulsation value Obtain the predicted value of frictional stress ,in, = + .

2. The method for dynamic calibration of wall friction stress according to claim 1, characterized in that, The flat plate assembly (2) includes a flat plate (2-3), a tail plate (2-2), and a tripwire (2-1). One end of the flat plate (2-3) is connected to the tail plate (2-2) via a pivot. The tail plate (2-2) rotates around the pivot and forms an angle with the flat plate (2-3). The tripwire (2-1) is connected to the other end of the flat plate (2-3) to facilitate flow transition.

3. The method for dynamic calibration of wall friction stress according to claim 1, characterized in that, The pressure sensor includes a first pressure sensor (3-1) and a second pressure sensor (3-2), which are embedded inside the plate (2-3) to measure the pressure on the surface of the plate (2-3). By adjusting the angle between the plate (2-3) and the tail plate (2-2), the pressure measurement values ​​of the two sensors are made consistent, so that the pressure gradient of the plate (2-3) is 0.

4. The method for dynamic calibration of wall friction stress according to claim 3, characterized in that, The first pressure sensor (3-1) and the second pressure sensor (3-2) are embedded inside the plate and installed upstream and downstream of the probe (1-1), respectively. The installation positions of the two sensors are the same as the flow direction distance of the probe (1-1), which is 0.2m to 0.3m.

5. The method for dynamic calibration of wall friction stress according to claim 1, characterized in that, The leading edge of the plate (2-3) of the plate assembly is wedge-shaped, and the probe (1-1) is located at a flow distance of 2m to 3m from the leading edge of the plate (2-3).

6. The method for dynamic calibration of wall friction stress according to claim 1, characterized in that, In step S3, the host computer (4) sets the predicted value of frictional stress. With voltage The relationship between them satisfies a fourth-degree polynomial relation, as shown below: in, C 0~ C 4 represents the fitting coefficient.

7. The method for dynamic calibration of wall friction stress according to claim 1, characterized in that, In step S4, let The host computer (4) obtains the fitting coefficients in the polynomial relationship through static calibration, including: For quartic polynomials Taking the average of both sides with respect to time, we get: （3） The calibration coefficients in equation (3) C 0~ C 4. The following relationship must be satisfied, that is, for each calibration point, the predicted value of frictional stress measured by the hot-wire anemometer (1) is equal to the actual value: （4） Equation (4) can be simplified as follows: Then the coefficient matrix C It is calculated by the following formula: 。 8. The method for dynamic calibration of wall friction stress according to claim 1, characterized in that, In step S5, let The host computer (4) obtains the corrected frictional stress pulsation value through dynamic calibration. ,include: At any calibration point The Fourier transform is , The Fourier transform is ,in f For frequency; and Decompose into real and imaginary parts: Solving the transfer function ,right Make corrections so that: （6） Depend on , , The power spectral density and phase frequency function were calculated from the real and imaginary parts respectively: ， ， （7） in, and Frequency resolution; By combining equations (6) and (7), we can obtain the answer. The expressions for the real and imaginary parts: (8) Equation (8) simplifies to: (9) At each calibration point, the transfer function is obtained from equation (9). , … , thus obtaining the transfer function H about , f The calibration database; In actual measurement, according to , f The value is obtained by linear interpolation in the calibration database. Determine the transfer function Afterwards, Perform an inverse Fourier transform to obtain the corrected frictional stress pulsation value. : 。 9. A dynamic calibration system for wall friction stress, characterized in that, include: The hot-wire anemometer (1), including the probe (1-1), is placed in the viscous sublayer of the turbulent boundary layer and located above the plate (2) to measure the frictional stress on the plate wall and send the measured voltage signal to the host computer (4) in real time. The flat plate assembly includes a flat plate (2-3), a tail plate (2-2), and a tripwire (2-1), wherein the flat plate (2-3) provides a wall surface calibrated by a hot-wire anemometer (1), one end of the flat plate (2-3) is connected to the tail plate (2-2) via a pivot, the tail plate (2-2) rotates around the pivot to form an angle with the flat plate (2-3), and the tripwire (2-1) is connected to the other end of the flat plate (2-3) to facilitate flow transition; The pressure sensor includes a first pressure sensor (3-1) and a second pressure sensor (3-2). The two pressure sensors are embedded inside the plate (2-3) to measure the fluid pressure on the surface of the plate (2-3) and send it to the host computer (4). The host computer (4) sets the friction stress sequence under the current calibration environment. , ,…, Receive the voltage signal corresponding to the friction stress sequence sent by the hot-wire anemometer (1). , ,…, ,in t For time; set the predicted value of frictional stress. With voltage The polynomial relation between them is satisfied, and will and Decomposition includes: , ,in, , The average value over time. , For the pulsation value; to make It must meet the following requirements: , ;make By obtaining the fitting coefficients in the polynomial relationship through static calibration, and substituting these fitting coefficients into the polynomial relationship, a preliminary predicted value of frictional stress is obtained. ;make The corrected frictional stress pulsation value is obtained through dynamic calibration. Based on preliminary predicted frictional stress values and the corrected frictional stress pulsation value Obtain the predicted value of frictional stress ,in, = + .

10. A dynamic calibration system for wall friction stress according to claim 9, characterized in that, The first pressure sensor (3-1) and the second pressure sensor (3-2) are embedded inside the plate and installed upstream and downstream of the probe (1-1), respectively. The installation positions of the two sensors are the same as the flow distance of the probe (1-1), which is 0.2~0.3m. By adjusting the angle between the plate (2-3) and the tail plate (2-2), the pressure measurement values ​​of the two sensors are made consistent, so that the flow pressure gradient of the plate (2-3) is 0.

11. The wall friction stress dynamic calibration system according to claim 9, characterized in that, The host computer (4) sets the predicted value of frictional stress. With voltage The relationship between them satisfies a fourth-degree polynomial relation, as shown below: in, C 0~ C 4 represents the fitting coefficient.

12. The wall friction stress dynamic calibration system according to claim 9, characterized in that, make The host computer (4) obtains the fitting coefficients in the polynomial relationship through static calibration, including: For quartic polynomials Taking the average of both sides with respect to time, we get: （3） The calibration coefficients in equation (3) C 0~ C 4. The following relationship must be satisfied, that is, for each calibration point, the predicted value of frictional stress measured by the hot-wire anemometer (1) is equal to the actual value: （4） Equation (4) can be simplified as follows: Then the coefficient matrix C It is calculated by the following formula: 。 13. The wall friction stress dynamic calibration system according to claim 9, characterized in that, make The host computer (4) obtains the corrected frictional stress pulsation value through dynamic calibration. ,include: At any calibration point The Fourier transform is , The Fourier transform is ,in f For frequency; and Decompose into real and imaginary parts: Solving the transfer function ,right Make corrections so that: （6） Depend on , , The power spectral density and phase frequency function were calculated from the real and imaginary parts respectively: ， ， （7） in, and Frequency resolution; By combining equations (6) and (7), we can obtain the answer. The expressions for the real and imaginary parts: (8) Equation (8) simplifies to: (9) At each calibration point, the transfer function is obtained from equation (9). , … , thus obtaining the transfer function H about , f The calibration database; In actual measurement, according to , f The value is obtained by linear interpolation in the calibration database. Determine the transfer function Afterwards, Perform an inverse Fourier transform to obtain the corrected frictional stress pulsation value. : 。

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