A constant-temperature hot-wire anemometer bandwidth evaluation method based on in-situ open-loop frequency characteristics

Abstract

This invention relates to a method for bandwidth evaluation of a constant-temperature hot-wire anemometer based on in-situ open-loop frequency characteristics, belonging to the field of fluid measurement and automatic control technology. The method disclosed in this invention includes the following steps: S1. Connecting an ultra-low frequency low-pass filter to the closed-loop circuit to form an in-situ open-loop system with a DC closed loop and an AC open loop; S2. Injecting a sweep frequency excitation signal E at the bias circuit. stimu And measure the output response E of the hot wire voltage. w By comparing the amplitude ratio and phase difference of the two, the frequency characteristic G is obtained. * gain (jω); S3. Based on the frequency characteristic G * gain The amplitude-frequency response curve of (jω) is used to determine the corner frequency f when its gain drops to -3dB below the DC gain. * c With this transition frequency f * c This invention serves as an estimate of the bandwidth of the constant-temperature hot-wire anemometer. It enables direct measurement and evaluation of the dynamic performance of the constant-temperature hot-wire anemometer in the frequency domain, allowing testing to be completed without changing the bias voltage and DC operating point. This accurately and conveniently reflects the system bandwidth of the hot wire under actual operating conditions.

Description

Technical Field

[0001] This invention relates to a method for evaluating the bandwidth of a constant-temperature hot-wire anemometer based on in-situ open-loop frequency characteristics, belonging to the field of fluid measurement and automatic control technology. Background Technology

[0002] The constant-temperature hot-wire anemometer is a core tool for measuring flow velocity and turbulence in fluid mechanics experiments. Its basic principle is based on the theory of hot-wire convection heat transfer: a thin metal wire (hot wire) heated by electricity is placed in the flow field. Changes in flow velocity cause changes in the heat transfer of the hot wire through convection, which in turn causes changes in its resistance.

[0003] A typical isothermal hot-wire anemometer system constitutes a high-gain closed-loop negative feedback loop. This loop dynamically adjusts the heating power of the hot wire to maintain its temperature (i.e., resistance) constant, and converts flow velocity fluctuations into a voltage signal output. In this operating mode, the system's dynamic response performance, especially its measurement bandwidth, directly determines the highest frequency of flow velocity pulsations that the instrument can accurately measure, and is a key indicator for evaluating its performance, especially its application value in high-speed turbulence measurement.

[0004] The evaluation of a system's dynamic performance is essentially a measurement of its response to wind speed excitation. However, directly generating high-frequency, controllable wind speed excitation signals with known amplitudes in the laboratory is extremely difficult in engineering, prompting researchers to seek various indirect evaluation methods.

[0005] Currently, the square wave testing method is commonly used for bandwidth estimation in engineering practice. This method involves superimposing a square wave signal onto a bias voltage, observing the system's time-domain response (such as rise time), and indirectly calculating the bandwidth using empirical formulas. However, the step excitation of this method strongly disturbs the system's DC operating point, causing the hot wire to briefly leave the isothermal state, thus failing to accurately reflect the system's dynamic performance under actual continuous measurement conditions. Furthermore, its results heavily rely on the operator's experience and lack objective and precise quantitative standards. To overcome the limitations of square wave excitation, the laser excitation method has been proposed. It simulates a thermal pulse through laser heating, providing a more realistic reflection of the wind speed excitation response. However, this method requires complex laser modulation equipment and precise optical paths, resulting in high system construction costs and poor engineering applicability.

[0006] Further analysis of existing research reveals that academic research primarily focuses on system performance optimization or response improvement under specific conditions, lacking in-depth exploration and innovation of bandwidth evaluation methods themselves. For example:

[0007] In their paper "Dynamic Characteristics Analysis and Experimental Verification of Constant Temperature Hot-Wire Anemometer System" (Journal of Instrumentation, 2015, 36(10): 2267-2272), Wei Qingyan et al. conducted an in-depth analysis of the influence of system parameters on dynamic characteristics and proposed an adjustment method based on bias voltage. However, their research was still based on traditional square wave testing, with the core objective being to optimize the frequency response. They did not provide a novel measurement method that could directly evaluate bandwidth under operating conditions.

[0008] Du Hai et al. successfully developed a low-cost hot-wire anemometer in their paper "Prototype and Experimental Verification of Constant Temperature Hot-Wire Anemometer" (Journal of Xihua University (Natural Science Edition), 2023, 42(6): 26-33) and verified its overall performance. However, their research focused on system implementation and calibration. For the evaluation method of bandwidth, a key dynamic indicator, they still used the conventional method with inherent defects mentioned above and did not conduct in-depth exploration and improvement.

[0009] Brunier-Coulin et al. (Thermal response of a nanoscale hot-wire in subsonic and supersonic flows, Experiments in Fluids, 2023, 64:8) optimized the inherent thermal response of the hot-wire from the perspective of probe design and materials science, using nanoscale structures and gold plating. This research focused on optimizing the hot-wire itself to enhance the system's bandwidth potential, rather than addressing the downstream problem of measuring and evaluating the bandwidth of existing systems in the engineering field.

[0010] In conclusion, how to conveniently and effectively evaluate the measurement bandwidth of constant temperature hot-wire anemometers in engineering practice remains a key issue that urgently needs to be addressed. Summary of the Invention

[0011] This invention enables direct measurement and evaluation of the dynamic performance of a constant-temperature hot-wire anemometer in the frequency domain. The test can be completed without changing the system bias voltage and DC operating point, and can accurately and conveniently reflect the system bandwidth of the hot wire under actual working conditions.

[0012] To achieve the above objectives, the present invention provides the following technical solution:

[0013] A method for bandwidth evaluation of a constant-temperature hot-wire anemometer based on in-situ open-loop frequency characteristics includes the following steps: S1. Connecting an ultra-low frequency low-pass filter to the closed-loop circuit to form an in-situ open-loop system with DC closed loop and AC open loop; S2. Injecting a sweep frequency excitation signal E at the bias circuit. stimu And measure the output response E of the hot wire voltage. w By comparing the amplitude ratio and phase difference of the two, the frequency characteristic G is obtained. *gain (jω); S3. Based on the frequency characteristic G * gain The amplitude-frequency response curve of (jω) is used to determine the corner frequency f when its gain drops to -3dB below the DC gain. * c With this transition frequency f * c This serves as an estimate of the bandwidth of the constant-temperature hot-wire anemometer.

[0014] The closed-loop transfer function of the constant-temperature hot-wire anemometer during normal operation can be expressed by the following formula:

[0015]

[0016] Where U is the wind speed, E is the output voltage at the top of the Wheatstone bridge, and G is the wind speed. gain (s) is the forward gain transfer function, G open (s) is the open-loop transfer function; G gain (s) reflects the system's dynamic response capability to flow velocity signals, and its cutoff frequency f c This directly determines the system's measurement bandwidth;

[0017] The frequency characteristic G * gain (jω), the corner frequency f corresponding to its gain dropping to -3dB below the DC gain. * c It can be used to estimate the forward gain transfer function G. gain The cutoff frequency f of (s) c That is, f * c ≈f c ;

[0018] The ultra-low frequency low-pass filter used to block AC signals should be able to reliably filter out all AC signals within the frequency range of the swept excitation signal. Its specific cutoff frequency and roll-off factor should be determined through the following steps:

[0019] S41. Inject a sweep frequency excitation signal into the bias circuit and set its frequency to the lowest value within the test frequency range;

[0020] S42. Use an oscilloscope to detect the output waveform of the low-pass filter;

[0021] S43. If the detected output waveform has obvious fluctuations, the cutoff frequency of the low-pass filter should be reduced or its roll-off factor should be increased until the output waveform fluctuation is less than 1mV, which can be approximated as DC.

[0022] Compared with the prior art, the advantages of this invention are: by using a frequency domain testing method, an in-situ open-loop system is constructed by connecting an ultra-low frequency filter and injecting a small amplitude sweep frequency signal, the frequency characteristics of the hot-wire anemometer can be obtained directly, accurately and conveniently without disturbing the DC operating point of the system, thereby achieving an objective and quantitative assessment of the system bandwidth, overcoming the shortcomings of the traditional square wave testing method, which is prone to operating point deviation and results rely on experience judgment. Attached Figure Description

[0023] Figure 1 This is a block diagram of the constant temperature hot wire anemometer system of the present invention.

[0024] Figure 2 G is the constant temperature hot wire anemometer of the present invention. * gain (jω) Frequency response diagram.

[0025] Figure 3 The image shows the square wave response waveform of the constant temperature hot-wire anemometer of the present invention. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] Please see Figure 1 In this embodiment of the invention, the method for stability analysis of a constant-temperature hot-wire anemometer based on in-situ open-loop frequency characteristics includes the following steps: S1. Connecting an ultra-low frequency low-pass filter to the closed-loop circuit to form an in-situ open-loop system with a DC closed loop and an AC open loop; S2. Injecting a sweep frequency excitation signal E at the bias circuit. stimu And measure the output response E of the hot wire voltage. w By comparing the amplitude ratio and phase difference of the two, the frequency characteristic G is obtained. * gain (jω); S3. Based on the frequency characteristic G * gain The amplitude-frequency response curve of (jω) is used to determine the corner frequency f when its gain drops to -3dB below the DC gain. * c With this transition frequency f * c This serves as an estimate of the bandwidth of the constant-temperature hot-wire anemometer.

[0028] Please see Figure 2In this embodiment of the invention, the closed-loop transfer function of the constant-temperature hot-wire anemometer during normal operation can be expressed by the following formula:

[0029]

[0030] Where U is the wind speed, E is the output voltage at the top of the Wheatstone bridge, and G is the wind speed. gain (s) is the forward gain transfer function, G open (s) is the open-loop transfer function; G gain (s) reflects the system's dynamic response capability to flow velocity signals, and its cutoff frequency f c This directly determines the system's measurement bandwidth;

[0031] The frequency characteristic G * gain (jω), by Figure 2 It can be determined that the corner frequency f corresponds to the gain dropping to -3dB below the DC gain. * c =32kHz, therefore the forward gain transfer function G gain The cutoff frequency f of (s) c ≈f * c =32kHz, which means the system bandwidth is around 32kHz;

[0032] Please see Figure 3 In this embodiment of the invention, the square wave testing method is used to compare and verify the bandwidth estimation method of the present invention. It requires adjusting a constant bias voltage E. bias So that E o The maximum overshoot in the time domain response is 13% of the peak response; in E stimu A square wave with an amplitude of 200mV, a duty cycle of 50%, and a frequency of 1kHz is injected into the terminal. Figure 3 Curve 2 in the figure represents E after adjustment to meet this condition. o Time domain response, at this time E bias =2.61; Let t be the time corresponding to the drop of curve 2 from its peak to 3%. n =18.7us, from which the bandwidth of the constant temperature hot wire anemometer can be calculated as:

[0033]

[0034] As can be seen, the bandwidth f of the constant temperature hot-wire anemometer obtained by the square wave testing method is... * n The bandwidth f obtained by the method of this invention * c The results are roughly similar. This fully verifies the effectiveness of the method of the present invention in evaluating the measurement bandwidth of a constant-temperature hot-wire anemometer.

[0035] This invention is not limited to the above embodiments. Based on the technical solutions disclosed in this invention, those skilled in the art can make some simple modifications, equivalent changes and alterations to some of the technical features without creative effort, all of which fall within the scope of the technical solutions of this invention.

Claims

1. A method for bandwidth evaluation of a constant-temperature hot-wire anemometer based on in-situ open-loop frequency characteristics, comprising the following steps: S1. Connecting an ultra-low frequency low-pass filter into the closed-loop circuit to form an in-situ open-loop system with DC closed loop and AC open loop; S2. Injecting a sweep frequency excitation signal E at the bias circuit. stimu And measure the output response E of the hot wire voltage. w By comparing the amplitude ratio and phase difference of the two, the frequency characteristic G is obtained. * gain (jω); S3. Based on the frequency characteristic G * gain The amplitude-frequency response curve of (jω) is used to determine the corner frequency f when its gain drops to -3dB below the DC gain. * c With this transition frequency f * c This serves as an estimate of the bandwidth of the constant-temperature hot-wire anemometer.

2. The method for evaluating the bandwidth of a constant-temperature hot-wire anemometer based on in-situ open-loop frequency characteristics as described in claim 1, characterized in that, The closed-loop transfer function of the constant-temperature hot-wire anemometer during normal operation can be expressed by the following formula: Where U is the wind speed, E is the output voltage at the top of the Wheatstone bridge, and G is the wind speed. gain (s) is the forward gain transfer function, G open (s) is the open-loop transfer function; G gain (s) reflects the system's dynamic response capability to flow velocity signals, and its cutoff frequency f c This directly determines the system's measurement bandwidth.

3. The bandwidth estimation method for a constant-temperature hot-wire anemometer based on in-situ open-loop frequency characteristics as described in claim 1, characterized in that, The frequency characteristic G * gain (jω), the corner frequency f corresponding to its gain dropping to -3dB below the DC gain. * c It can be used to estimate the forward gain transfer function G. gain The cutoff frequency f of (s) c That is, f * c ≈f c。 4. The bandwidth estimation method for a constant-temperature hot-wire anemometer based on in-situ open-loop frequency characteristics as described in claim 1, characterized in that, The ultra-low frequency low-pass filter used to block AC signals should be able to reliably filter out all AC signals within the frequency range of the swept excitation signal. Its specific cutoff frequency and roll-off factor should be determined through the following steps: S41. Inject a sweep frequency excitation signal into the bias circuit and set its frequency to the lowest value within the test frequency range; S42. Use an oscilloscope to detect the output waveform of the low-pass filter; S43. If the detected output waveform has obvious fluctuations, the cutoff frequency of the low-pass filter should be reduced or its roll-off factor should be increased until the output waveform fluctuation is less than 1mV, which can be approximated as DC.

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