Head wave position prediction method for water hammer effect of fragment impact liquid-filled container

Abstract

The invention provides a head wave position prediction method for a water hammer effect of a fragment impacting liquid-filled container, and the method comprises the steps: S100, obtaining data of stress waves transmitted to the back surface of a target plate and stress waves transmitted to the edge of the target plate at different positions of liquid through a pressure sensor, enabling the stress waves transmitted to the back surface of the target plate to form initial impact waves, and carrying out the prediction of the initial impact waves; the stress waves transmitted to the edge of the target plate form head waves; step S200, obtaining a time domain feature, a frequency domain feature and a spatial feature through the pressure data; s300, screening the head waves through the time characteristics to obtain candidate head waves, and verifying the candidate head waves through the frequency characteristics; and step S400, obtaining the position of the head wave for the verified head wave through spatial features.

Description

Technical Field

[0001] The present invention relates to a stress wave analysis method, in particular to a method for predicting the head wave position of the water hammer effect caused by fragment impact on a liquid-filled container. Background Art

[0002] As an important vulnerable component of an aircraft, the damage of the fuel tank often leads to the damage and disintegration of the entire airframe. The water hammer effect is the main factor causing structural damage to the aircraft fuel tank. The existence of the water hammer effect can enhance the structural damage of high-speed objects to the fuel tank wall. In the study of the water hammer effect pressure field, the initial shock wave, as the initial large pressure signal, is often the key research object. For the pressure signal, the main research focuses on the pressure peak and the pressure rise time, where the rise time is often defined as the time from 10% of the pressure peak to 90% of the pressure peak. In the experiment on the water hammer effect of fragment impact on a liquid-filled container, it is found that when the front target plate is impacted, the formed head wave will interfere with the pressure signal of the initial shock wave, making it impossible to accurately analyze the test results. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for predicting the head wave position of the water hammer effect caused by fragment impact on a liquid-filled container, including: Step S100: Use a pressure sensor to obtain data of the stress wave transmitted to the back of the target plate and the stress wave transmitted to the edge of the target plate at different positions in the liquid. The stress wave transmitted to the back of the target plate forms the initial shock wave, and the stress wave transmitted to the edge of the target plate forms the head wave; Step S200: Obtain time-domain characteristics, frequency-domain characteristics, and spatial characteristics through the pressure data; Step S300: Screen the head wave through the time characteristics to obtain candidate head waves, and verify the candidate head waves through the frequency characteristics; Step S400: Obtain the head wave position through the spatial characteristics of the verified head wave.

[0004] Further, the time-domain characteristics in step S200 include {stress wave transmission time, amplitude, rise time, rise edge slope}, the frequency-domain characteristics include {power spectral density, frequency band energy}, and the spatial characteristics include {moving distance}.

[0005] Further, the process of obtaining the time-domain characteristics in step S200 includes: Step S210: Obtain the time-domain characteristics through the time signal, and the specific process includes: Step S211: Normalize the collected pressure signal to [-1, 1]; Step S212: Use a sliding window to extract the stress wave transmission time feature, amplitude feature, rise time feature, and rising edge slope feature of the waveform. The stress wave transmission time feature is the propagation time of the stress wave in the liquid. The amplitude feature is the amplitude of each wave peak. The rise time feature is the time required for each wave peak to reach from 10% of the peak value to 90% of the peak value. The rising edge slope is the slope of the signal curve during the rise time.

[0006] Furthermore, the process of obtaining frequency domain features in step S200 includes: Step S221: Perform Fourier transform on the pressure signal to obtain a spectrogram and calculate the power spectral density. Step S222: Perform short-time Fourier transform on the pressure signal to generate a time-frequency diagram and calculate the low-frequency energy ratio to obtain the frequency band energy feature.

[0007] Furthermore, the process of obtaining spatial features in step S200 includes: Step S231: Calculate the time when the stress wave propagating towards the back of the target plate reaches the liquid t 1;

[0008] In the formula, h is the thickness of the target plate, C 0 is the wave speed of the target plate material; Step S232: Calculate the motion distance feature of the stress wave propagating towards the edge of the target plate in the target plate D y ;

[0009] Among them, t is the stress wave transmission time in the time domain feature; Step S233: Calculate the motion distance feature of the head wave formed in the liquid at the initial impact moment D x

[0010] In the formula, C is the sound speed of the liquid.

[0011] Furthermore, step S300 specifically includes Step S301: Set criteria to determine candidate head waves. The candidate head wave criteria include stress wave arrival time criterion, amplitude criterion, rise time criterion, and rising edge slope criterion: (1) The stress wave arrival time criterion is where is the stress wave arrival time, is the arrival time of the wave peak with the maximum pressure value; (2) The amplitude criterion is , where is the stress wave amplitude, A 0 is the predicted amplitude of the initial shock wave; (3) The rise time criterion is , is the rise time, is the predicted value of the rise time; (4) The rise edge slope criterion is , , , are respectively the slopes of the rise edges of the i +1th time window and the i th time window, the slopes of the rise edges of the i +2th time window and the i +1th time window, the slopes of the rise edges of the i +3th time window and the i +2th time window; If the stress wave that simultaneously satisfies conditions (1), (2), and (3) or simultaneously satisfies conditions (1) and (4) is recorded as a candidate head wave; Step S302, set verification conditions to verify and screen the candidate head waves; the verification conditions include the power spectral density criterion and the frequency band energy criterion, and the candidate head waves that meet both conditions are the verified head waves, where (5) The power spectral density criterion is , where is the power spectral density of the candidate head wave, is the low-frequency band threshold of the head wave; (6) The frequency band energy criterion is R low < λ low , λ low is the low-frequency energy threshold, R low is the low-frequency energy ratio of the head wave.

[0012] Furthermore, in step S400, the head wave curve expression is determined according to the spatial characteristics y h , and the head wave position

[0013] where .

[0014] Based on the stress wave theory, the present invention establishes a motion model of the initial shock wave and the head wave formed by the fragment impacting the front target plate of the liquid-filled container, thus solving the technical problem that the signal is affected by the head wave signal during the acquisition of the initial shock wave by the pressure sensor in the test process. Moreover, by comparing and analyzing the position results of the head wave and the shock wave obtained by the numerical simulation technology with the calculation results, it is reflected that the prediction calculation method of the head wave position of the water hammer effect of the fragment impacting the liquid-filled container provided by the present invention is reasonable and feasible.

[0015] The present invention will be further described below in conjunction with the accompanying drawings of the specification. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a schematic flow chart of the method of the present invention.

[0017] Figure 2 It is a coordinate system diagram in the calculation of the head wave curve during the prediction process of the head wave position implemented by the present invention.

[0018] Figure 3 It is a simulation of the fragment impacting the liquid-filled container t = The pressure contour map at the moment of 15 μs.

[0019] Figure 4 It is a pressure curve diagram of the separation of the head wave and the initial shock wave captured by the sensor in the test.

[0020] Figure 5 It is a pressure curve diagram of the coupling of the head wave and the initial shock wave in the numerical simulation. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0021] Combined with Figure 1 , a method for predicting the head wave position of the water hammer effect of a fragment impacting a liquid-filled container includes: Step S100: Use a pressure sensor to obtain data of the stress wave transmitted to the back of the target plate and the stress wave transmitted to the edge of the target plate at different positions in the liquid. The stress wave transmitted to the back of the target plate forms an initial shock wave, and the stress wave transmitted to the edge of the target plate forms a head wave; Step S200: Obtain time-domain characteristics, frequency-domain characteristics, and spatial characteristics through the pressure data; Step S300: Screen the head wave through the time characteristics to obtain a candidate head wave, and verify the candidate head wave through the frequency characteristics; Step S400: Obtain the head wave position of the verified head wave through the spatial characteristics.

[0022] In step S100, after the fragment impacts and penetrates the target plate of the liquid-filled container, two types of stress waves are generated: the stress wave propagating towards the back of the target plate and the stress wave propagating towards the edge of the target plate. The stress wave propagating towards the back of the target plate first enters the liquid. On the back of the target plate, when the kinetic energy of the fragment is transferred to the liquid, a high-pressure shock wave will be generated in the liquid. This shock wave is the initial shock wave, which has the characteristics of a high-pressure peak value, a short duration (in the microsecond range), a short rise time (a sharp pulse wave), and a spherical wave. The stress wave propagating towards the edge of the target plate will propagate towards the edge of the target plate in a spherical shape. During the propagation process, the target plate forms a head wave by disturbing the liquid behind the target plate, and the pressure gradient generated in the liquid. The head wave has the characteristics of a low peak value and a relatively gentle waveform compared to the initial shock wave. Given the different characteristics of the initial shock wave and the head wave, time-domain analysis and frequency-domain analysis can be used to judge the differences between the two, and the position of the head wave can be judged through spatial characteristics.

[0023] In step S200, the time-domain characteristics include {stress wave transmission time, amplitude, rise time}; the frequency-domain characteristics include {power spectral density, frequency band energy}; the spatial characteristics include {moving distance}. The above characteristics are obtained through signal post-processing by a pressure sensor, and the specific process is as follows.

[0024] Step S210, obtaining time-domain characteristics from the time signal, the specific process includes: Step S211, performing normalization processing on the collected pressure signal to normalize the signal to [-1, 1]; Step S212, using a sliding window to extract time-domain characteristics such as the stress transmission time characteristic, amplitude characteristic, and rise time characteristic of the waveform.

[0025] In step S212, the stress wave transmission time characteristic is the time node when the stress wave propagates in the liquid; the amplitude characteristic is the amplitude of each wave peak; the rise time characteristic is the time required for each wave peak to rise from 10% of the peak value to 90% of the peak value. For continuous time windows, if the pressure value shows an obvious upward trend all the time, it proves that the stress wave has arrived, and record this arrival time. Starting from the arrival time, when the pressure value in a certain time window is greater than the pressure value in the adjacent time window, then the pressure value in this time window is the amplitude. The rise time is the time from 10% of the amplitude to 90% of the amplitude. Analyze the obtained time characteristics, and the analysis process is as follows: the amplitude of the initial shock wave is the highest in terms of the amplitude characteristic; the amplitude of the head wave is lower than that of the initial shock wave. The rise time characteristic is affected by the initial velocity of the fragment, the liquid density, and the sensor position. For example, when the initial velocity of the fragment is 1200 m / s, the liquid is an oil body, and the sensor is 36 cm away from the impact point, the rise time of the initial shock wave is 2 - 5 μs; under the same conditions, the rise time of the first wave peak of the head wave is 1 - 2 μs.

[0026] Such as Figure 4 、 Figure 5As shown, in the time series, the peak pressure value of the initial shock wave is the largest. At positions farther from the target plate, the head wave, as shown in the middle circle, arrives at the sensor position before the initial shock wave. However, in the initial stage of the stress wave propagating in the liquid, there is a coupling situation between the head wave and the initial shock wave, and the sensor can only obtain one peak after measurement and processing, as shown in Figure 5 . By observing Figure 5 , it can be concluded that the rising edge slopes of the peaks are different. As shown in the circle in Figure 5 , the one with a smaller rising edge slope is the head wave. However, according to Figure 5 , the specific magnitude of the head wave amplitude cannot be determined. Therefore, for sensors far from the target plate, when no other peaks can be obtained before the highest peak after processing the acquired data, the further set time domain features also include {rising edge slope}. The rising edge slope is calculated based on the pressure values in adjacent time windows. If the rising edge slope suddenly increases at a certain moment and the arrival time of the shock wave is greater than the threshold, it can indicate that the stress wave before the increase in the rising edge slope contains the head wave. Figure 4 As shown in the middle circle, it arrives at the sensor position before the initial shock wave. But in the initial stage of the stress wave propagating in the liquid, there is a coupling situation between the head wave and the initial shock wave, and the sensor can only obtain one peak after measurement and processing, as shown in Figure 5 . Figure 5 Shown Figure 5 It can be concluded that the rising edge slopes of the peaks are different. As shown in the circle in Figure 5 , the one with a smaller rising edge slope is the head wave. But according to Figure 5 , the specific magnitude of the head wave amplitude cannot be determined. Figure 5 As shown in the circle, the one with a smaller rising edge slope is the head wave. But according to Figure 5 , the specific magnitude of the head wave amplitude cannot be determined. Figure 5 Shown

[0027] Step S220, the process of obtaining frequency domain features is as follows: Step S221, perform Fourier transform on the pressure signal to obtain the frequency spectrum diagram and calculate the power spectral density; Step S222, perform short-time Fourier transform on the pressure signal to generate the time-frequency diagram and calculate the low-frequency energy ratio and high-frequency energy ratio to obtain the frequency band energy features.

[0028] In step S221, the head wave is formed by the refraction of the initial shock wave after propagating to the edge of the target plate and the solid-liquid interface. The propagation path is long and part of the energy is dissipated, resulting in more low-frequency components being retained. The initial shock wave is generated instantaneously when the fragment hits the liquid at high speed, with a steep rising edge and a short duration, resulting in rich high-frequency components (such as >100 kHz) in its frequency spectrum and the energy being concentrated in a wide frequency band. And the energy of the clutter formed under the influence of perturbation and refraction is also distributed in a relatively wide frequency band.

[0029] In step S222, the high-frequency energy ratio is the ratio of the energy in a high-frequency band to the total energy of the signal, and the low-frequency energy ratio is the ratio of the energy in a low-frequency band to the total energy of the signal. The low-frequency energy ratio of the head wave is set to be less than 0.5. In step S222, the low-frequency energy of the early stress wave (0 - 50 μs) is concentrated, and the high-frequency energy of the later stress wave (50 - 500 μs) is enhanced.

[0030] Step S230, the acquisition of spatial features includes the following process: Step S231, calculate the time when the stress wave propagating towards the back of the target plate reaches the liquid t 1

[0031] In the formula, h is the thickness of the target plate, C 0 is the wave velocity of the target plate material; Step S232: Calculate the motion distance characteristic of the stress wave propagating towards the edge of the target plate in the target plate D y

[0032] Among them, t is the stress wave transmission time in the time domain characteristic; Step S233: Calculate the motion distance characteristic of the head wave formed in the liquid at the initial impact moment D x ; The initial head wave will gradually coincide with the subsequent shock wave, but the mathematical position of the head wave can still be represented by D x After the head wave reaches the back of the target plate, it enters the liquid and continues to move in the liquid at the liquid sound speed. The specific relationship between the motion and time is:

[0033] In the formula, C is the liquid sound speed.

[0034] When obtaining the time domain characteristic to distinguish the head wave and the initial shock wave, some clutter waves caused by refraction and perturbation may be counted into the head wave together, resulting in inaccurate judgment. Through analysis, the head wave and the clutter wave are different in both power spectral density and band energy. Based on the above principle, it is designed to obtain the candidate head wave using the time domain characteristic, and then use the frequency domain characteristic to verify the candidate head wave to further distinguish the head wave and the clutter wave. The specific process of step S300 includes: Step S301: Set criteria to determine the head wave candidate. The head wave candidate criteria include the stress wave arrival time criterion, the amplitude criterion, and the rise time criterion. The stress wave that satisfies all three conditions is determined as the candidate head wave.

[0035] (1) The stress wave arrival time criterion is where is the stress wave arrival time, is the arrival time of the wave crest with the maximum pressure value; (2) The amplitude criterion is where is the stress wave amplitude, A 0 is the predicted amplitude of the initial shock wave. If infrasound reflection or noise may occur, may be a superimposed wave or a secondary impact; (3) The rise time criterion is , is the rise time, is the predicted value of the rise time, which is predicted based on the initial velocity of the fragment and the liquid density; Step S302: Set verification conditions to verify and screen the candidate head waves; the verification conditions include the power spectral density criterion and the frequency band energy criterion. The candidate head waves that meet both conditions are the verified head waves, where (4) The power spectral density criterion is where is the power spectral density of the candidate head wave, is the threshold of the low-frequency band of the head wave; (5) The frequency band energy criterion is R low < λ low , λ low is the low-frequency energy threshold, R low is the low-frequency energy ratio of the head wave; Step S400: Obtain the head wave position based on the spatial characteristics of the verified head wave. The specific process is as follows: Step S401: Calculate the curve expression of the initial shock wave in the liquid; the initial shock wave propagates in the liquid in a hemispherical shape with the center of the sphere at the impact point. The curve expression can be specifically expressed as:

[0036] Step S402: Determine the curve expression of the head wave; as the radius of the initial shock wave continues to expand, the linear influence area of the head wave continues to decrease. The curve expression can be specifically expressed as:

[0037] where .

[0038] When Figure 5 occurs, it may not be possible to obtain head wave candidates after Step S301, or it may not be possible to pass the verification in Step S302. It is necessary to set an additional rising edge slope criterion (6). When both criterion (1) (2) (3) are satisfied or both criterion (1) (6) are satisfied, they can all be recognized as candidate head waves. Criterion (6) is (6) The rising edge slope criterion is that if the rising edge slope suddenly increases at a certain moment, the shock wave before the slope increase is the candidate head wave

[0039] where is the i +1th time window and the slope of the rising edge of the i th time window; if the slope change of the i-th rising edge is relatively gentle, that is , the initial shock wave has not arrived; if the slope is much greater than the previously calculated slope at a certain slope, it indicates that the initial shock wave has arrived.

[0040] Furthermore, in order to accurately place the pressure sensor and avoid capturing the head wave and the initial shock wave simultaneously, the time interval Δ between the propagation of the head wave and the initial shock wave can be determined in advance. t ; For any point in the liquid ( xn , yn ), the head wave arrives first, and then the initial shock wave arrives. The corresponding arrival times can be obtained through the curve, and the time interval expression can be specifically represented as: .

[0041] The expression for the sensor installation position ( xa , ya ) to avoid the influence of the head wave on the measurement of the initial shock wave is specifically:

[0042] In the formula, t resp represents the response time of the sensor.

[0043] In order to compare the calculation results proposed in this embodiment with the numerical simulation results, a coordinate system as Figure 2 is established. By determining the curve expression of the head wave and comparing it with the numerical simulation head wave curve. Combining Figure 3 , after the fragment impacts the liquid-filled container, at the 15 μs moment, the initial shock wave and the head wave pressure formed in the liquid. The numerical simulation results establish a coordinate system as Figure 3 . By studying the curve expression of the head wave in the first quadrant (x > 0, y > 0) for comparison. In the numerical simulation, the front target plate of the liquid-filled container is made of 2A12-T4 aluminum alloy, the sound speed of the material is C0 = 5286 m / s, the thickness of the target plate h = 2.5 mm, the liquid is water, the sound speed C = 1500 m / s, and the time t = 15 μs.

[0044] Calculate the time t 1 = 0.47 μs for the shock wave to propagate to the back of the target plate, calculate the moving distance D y = 79.3 mm of the stress wave propagating towards the edge of the target plate in the target plate, calculate the moving distance D x = 21.8 mm of the head wave formed in the liquid at the initial shock moment; calculate the curve expression of the initial shock wave in the liquid; ; Determine the head wave curve expression: y = -3.64x + 79.3, where x < 21.8 mm.

[0045] To verify the accuracy of the calculation method, the curve expression of the head wave in the simulation is extracted. Since the shock wave has a certain thickness, two curves at the edge are extracted. The coordinates of two points on curve 1 are (0, 68) and (8, 32) respectively, and the coordinates of two points on curve 2 are (0, 84) and (20, 32) respectively. The expressions of the two curves extracted accordingly are y 1 = -4.25x + 68, where; y 2 = -2.6x + 84, 8mm < x < 20mm. It can be seen that the slope of the curve obtained from the calculation result is -3.64, between the two slopes (-4.25, -2.6) of the numerical simulation; the intercept is 79.3mm, between the two intercepts (68, 84) obtained from the numerical simulation, x and the range error is 9%. It can be seen that the calculation result is in good agreement with the simulation result and can estimate the approximate range of the head wave position.

Claims

1. A method for predicting the head wave position of the water hammer effect caused by a fragment impacting a liquid-filled container, characterized in that: include: Step S100, using a pressure sensor to obtain data of stress waves transmitted to the back of the target plate and stress waves transmitted to the edge of the target plate at different positions in the liquid, wherein the stress wave transmitted to the back of the target plate forms an initial shock wave, and the stress wave transmitted to the edge of the target plate forms a head wave; Step S200, obtaining time domain features, frequency domain features and spatial features through pressure data; Step S300, filtering the head waves by time characteristics to obtain candidate head waves, and verifying the candidate head waves by frequency characteristics; Step S400, obtaining the head wave position through spatial features of the verified head wave.

2. The method according to claim 1, characterized in that The time domain features described in step S200 include {stress wave transmission time, amplitude, rise time, rising edge slope}, the frequency domain features include {power spectrum density, frequency band energy}, and the space features include {movement distance}.

3. The method according to claim 2, characterized in that The time domain feature acquisition process in step S200 includes: Step S210, obtaining time domain features through the time signal, the specific process includes: Step S211, normalizing the collected pressure signal to [-1, 1]; Step S212, using a sliding window to extract the stress wave transmission time characteristics, amplitude characteristics, rise time characteristics, and rising edge slope characteristics of the waveform; the stress wave transmission time characteristics are the propagation time of the stress wave in the liquid, the amplitude characteristics are the amplitude of each peak, the rise time characteristics are the time required for each peak to go from 10% peak to 90% peak, and the rising edge slope is the slope of the signal curve during the rise time.

4. The method according to claim 2, characterized in that: The frequency domain feature acquisition process in step S200 includes: Step S221, performing Fourier transform on the pressure signal to obtain a frequency spectrum and calculate the power spectrum density; Step S222, performing short-time Fourier transform on the pressure signal to generate a time-frequency diagram, and calculating the low-frequency energy ratio to obtain the frequency band energy characteristics.

5. The method according to claim 4, characterized in that The spatial feature acquisition process in step S200 includes: Step S231, calculate the time it takes for the stress wave transmitted to the back of the target plate to propagate into the liquid t 1; In the formula, h is the target plate thickness, C 0 is the wave velocity of the target material; Step S232, calculating the movement distance characteristic of the stress wave transmitted to the edge of the target plate in the target plate D y ; in, t is the stress wave transmission time in the time domain characteristics; Step S233, calculating the movement distance characteristic of the head wave formed in the liquid at the initial impact moment D x Where C is the liquid sound velocity.

6. The method according to claim 2, characterized in that Step S300 specifically includes: Step S301, setting criteria to determine candidate head waves, the candidate head wave criteria include stress wave arrival time criteria, amplitude criteria, rise time criteria and rising edge slope criteria: (1) The criterion for stress wave arrival time is: ,in is the stress wave arrival time, is the peak arrival time of the maximum pressure value; (2) The amplitude criterion is ,in is the stress wave amplitude, A 0 is the predicted amplitude of the initial shock wave; (3) The rise time criterion is , is the rise time, is the predicted value of rise time; (4) The criterion for the rising edge slope is , , , Respectively i +1 time window and i The slope of the rising edge of the first time window, i +2 time windows and i +1 time window rising edge slope, i +3 time windows and i +2 slopes of rising edges of time windows; If the stress wave satisfies conditions (1), (2), (3) or conditions (1) (4) at the same time, it is recorded as a candidate head wave; Step S302, setting verification conditions, verifying and screening the candidate head waves; the verification conditions include power spectrum density criterion and frequency band energy criterion, and the candidate head waves that meet the two conditions are the verified head waves, where (5) The power spectrum density criterion is ,in is the power spectral density of the candidate head wave, is the low-frequency threshold of the head wave; (6) The frequency band energy criterion is R low < λ low , λ low is the low frequency energy threshold, R low is the low-frequency energy ratio of the candidate head wave.

7. The method according to claim 6, characterized in that In step S400, the head wave curve expression is determined according to the spatial characteristics. y h , get the head wave position in .

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