A Method for Predicting the Head Wave Position of the Water Hammer Effect Caused by Fragment Impact on a Liquid-Filled Container

Abstract

The present invention provides a method for predicting the head wave position of the water hammer effect caused by fragments impacting a liquid-filled container, comprising: step S100, using a pressure sensor to obtain 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 in the liquid, the stress wave transmitted to the back surface of the target plate forming an initial shock wave, and the stress wave transmitted to the edge of the target plate forming a head wave; step S200, obtaining time domain characteristics, frequency domain characteristics and spatial characteristics through pressure data; step S300, screening head waves through time characteristics to obtain candidate head waves, and verifying the candidate head waves through frequency characteristics; step S400, obtaining the head wave position of the verified head wave through spatial characteristics.

Description

Technical Field

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

[0002] Fuel tanks are important and vulnerable components of aircraft. Damage to them often leads to the destruction and disintegration of the entire aircraft. The water hammer effect is the dominant factor in structural damage to aircraft fuel tanks. The presence of the water hammer effect can intensify the structural damage to the tank wall caused by high-speed objects. In the study of the pressure field of the water hammer effect, the initial shock wave, as the initial large pressure signal, is often the focus of research. The pressure signal mainly studies the pressure peak and the pressure rise time, where the rise time is often defined as the time it takes to rise from 10% to 90% of the pressure peak. In the water hammer effect test on impact with a liquid-filled container, it was found that the head wave formed when hitting the front target plate would 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 object of the present invention is to provide a method for predicting the head wave position of the water hammer effect caused by fragments impacting a liquid-filled container, comprising:

[0004] 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;

[0005] Step S200, obtaining time domain features, frequency domain features and spatial features through pressure data;

[0006] Step S300, filtering head waves by time characteristics to obtain candidate head waves, and verifying the candidate head waves by frequency characteristics;

[0007] Step S400: obtaining the head wave position through spatial features of the verified head wave.

[0008] Furthermore, 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 spatial features include {movement distance}.

[0009] Furthermore, the time domain feature acquisition process in step S200 includes:

[0010] Step S210: obtaining time domain features through the time signal. The specific process includes:

[0011] Step S211, normalizing the collected pressure signal to [-1, 1];

[0012] 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 value to 90% peak value, and the rising edge slope is the slope of the signal curve during the rise time.

[0013] Furthermore, the frequency domain feature acquisition process in step S200 includes:

[0014] Step S221, performing Fourier transform on the pressure signal to obtain a frequency spectrum and calculating the power spectrum density;

[0015] 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 characteristics.

[0016] Furthermore, the spatial feature acquisition process in step S200 includes:

[0017] 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;

[0018]

[0019] Where, h is the target plate thickness, C 0 is the wave velocity of the target material;

[0020] Step S232, calculate the movement distance characteristics of the stress wave transmitted to the edge of the target plate in the target plate D y ;

[0021]

[0022] in, t is the stress wave transmission time in the time domain characteristics;

[0023] Step S233, calculate the motion distance characteristics of the head wave formed in the liquid at the initial impact moment D x

[0024]

[0025] Where C is the liquid sound velocity.

[0026] Furthermore, step S300 specifically includes:

[0027] Step S301: Set 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:

[0028] (1) The stress wave arrival time criterion is ,in is the stress wave arrival time, is the arrival time of the peak with the maximum pressure value;

[0029] (2) The amplitude criterion is ,in is the stress wave amplitude, A 0 is the predicted amplitude of the initial shock wave;

[0030] (3) The rise time criterion is , is the rise time, is the predicted value of rise time;

[0031] (4) The rising edge slope criterion is , 、 、 Respectively i +1 time window and i The slope of the rising edge of the 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;

[0032] 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;

[0033] Step S302: set verification conditions and perform verification and screening on 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

[0034] (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;

[0035] (6) The frequency band energy criterion is R low < λ low , λ low is the low-frequency energy threshold, R lowis the low-frequency energy ratio of the head wave.

[0036] Furthermore, in step S400, the head wave curve expression is determined according to the spatial characteristics. y h , get the head wave position

[0037]

[0038] in .

[0039] Based on stress wave theory, the present invention establishes a motion model of the initial shock wave and head wave formed by the target plate before the fragment hits the liquid-filled container, thereby solving the technical problem that the signal of the pressure sensor in the process of collecting the initial shock wave is affected by the head wave signal during the test. The head wave and shock wave position results obtained by numerical simulation technology are compared and analyzed with the calculation results, reflecting that the prediction and calculation method of the head wave position of the water hammer effect of the fragment hitting the liquid-filled container provided by the present invention is reasonable and feasible.

[0040] The present invention will be further described below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 Schematic diagram of the method of the present invention.

[0042] Figure 2 This is a coordinate system diagram for calculating the head wave curve during the head wave position prediction process implemented in the present invention.

[0043] Figure 3 Simulating fragment impacts on liquid-filled containers t =Pressure cloud at the moment of 15μs.

[0044] Figure 4 This is the pressure curve of the separation of the head wave and the initial shock wave captured by the sensor in the experiment.

[0045] Figure 5 This is the pressure curve of the coupling between the head wave and the initial shock wave in the numerical simulation. DETAILED DESCRIPTION

[0046] Combine Figure 1 A method for predicting the head wave position of water hammer effect caused by fragments impacting a liquid-filled container, comprising:

[0047] 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;

[0048] Step S200, obtaining time domain features, frequency domain features and spatial features through pressure data;

[0049] Step S300, filtering head waves by time characteristics to obtain candidate head waves, and verifying the candidate head waves by frequency characteristics;

[0050] Step S400: obtaining the head wave position through spatial features of the verified head wave.

[0051] In step S100, after the fragments impact and penetrate the target plate of the liquid-filled container, two types of stress waves are generated: stress waves propagating toward the back of the target plate and stress waves propagating toward the edge of the target plate. The stress wave propagating toward the back of the target plate first enters the liquid. There, when the kinetic energy of the fragments is transferred to the liquid, a high-pressure shock wave is generated in the liquid. This shock wave is the initial shock wave, characterized by a high pressure peak, a short duration (microseconds), a short rise time (sharp pulse wave), and a spherical wave. The stress wave propagating toward the edge of the target plate propagates spherically toward the edge of the target plate. During this propagation, the target plate disturbs the liquid behind the target, creating a pressure gradient in the liquid that generates a head wave. Compared to the initial shock wave, the head wave has a lower peak value and a flatter waveform. Given the different characteristics of the initial shock wave and the head wave, time domain analysis and frequency domain analysis can be used to distinguish between them, and the location of the head wave can be determined through spatial characteristics.

[0052] In step S200, time-domain features include {stress wave transmission time, amplitude, and rise time}; frequency-domain features include {power spectrum density and frequency band energy}; and spatial features include {movement distance}. These features are obtained by post-processing the pressure sensor signal. The specific process is as follows.

[0053] Step S210: obtaining time domain features through the time signal. The specific process includes:

[0054] Step S211, normalizing the collected pressure signal to [-1, 1];

[0055] Step S212: Using a sliding window, extract time domain features of the waveform, such as stress transmission time features, amplitude features, and rise time features.

[0056] In step S212, the stress wave transmission time characteristic is the time point at which the stress wave propagates through the liquid; the amplitude characteristic is the amplitude of each wave peak; and the rise time characteristic is the time required for each wave peak to rise from 10% to 90% of its peak value. A significant rise in pressure over consecutive time windows indicates the arrival of a stress wave, and the arrival time is recorded. Starting from the arrival time, if the pressure value within a time window is greater than the pressure value within the adjacent time window, the pressure value within that time window is the amplitude. The rise time is the time from 10% to 90% of the amplitude. The obtained time characteristics are analyzed as follows: In terms of the amplitude characteristic, the initial shock wave amplitude is the highest; the head wave amplitude is lower than the initial shock wave amplitude. 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 oil, and the sensor is 36 cm 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 peak of the head wave is 1-2 μs.

[0057] like Figure 4 、 Figure 5 As shown in the time series, the peak pressure value of the initial shock wave is the largest. At a position farther away from the target plate, the head wave is as follows Figure 4 As shown in the middle circle, it reaches the sensor position before the initial shock wave. However, in the initial stage of the stress wave propagation in the liquid, the head wave and the initial shock wave are coupled. After measurement and processing, the sensor can only obtain a peak, such as Figure 5 As shown. Observe Figure 5 It can be concluded that the rising edge slope of the peak appears different, such as Figure 5 As shown in the circle, the rising edge with a small slope is the head wave, but according to Figure 5 The figure shows that the specific amplitude of the head wave cannot be determined. Therefore, for sensors far from the target plate, if no other peaks can be detected before the highest peak after data processing, the time domain features are further configured to 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 shock wave arrival time is greater than the threshold, it can be confirmed that the stress wave before the increase in the rising edge slope contains a head wave.

[0058] Step S220, the process of obtaining frequency domain features is as follows:

[0059] Step S221, performing Fourier transform on the pressure signal to obtain a frequency spectrum and calculating the power spectrum density;

[0060] Step S222 , performing short-time Fourier transform on the pressure signal to generate a time-frequency diagram, and calculating the low-frequency energy ratio and the high-frequency energy ratio to obtain the frequency band energy characteristics.

[0061] In step S221, the head wave is formed by the initial shock wave propagating to the target plate edge and the solid-liquid interface before being refracted. This long propagation path and partial energy dissipation result in a high retention of low-frequency components. The initial shock wave, generated instantaneously by the high-speed impact of fragments on the liquid, has a steep rise and a short duration. This results in a spectrum rich in high-frequency components (e.g., >100 kHz), with energy concentrated in a wide frequency band. The clutter energy generated by disturbances and refraction is also distributed over a wide frequency band.

[0062] In step S222, the high-frequency energy ratio is the ratio of the energy within a high-frequency band to the total signal energy, and the low-frequency energy ratio is the ratio of the energy within a low-frequency band to the total signal energy. The low-frequency energy ratio of the head wave is set to less than 0.5. In step S222, the low-frequency energy of the early stress wave (0-50 μs) is concentrated, while the high-frequency energy of the later stress wave (50-500 μs) is enhanced.

[0063] Step S230, spatial feature acquisition includes the following process:

[0064] 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

[0065]

[0066] Where, h is the target plate thickness, C 0 is the wave velocity of the target material;

[0067] Step S232, calculate the movement distance characteristics of the stress wave transmitted to the edge of the target plate in the target plate D y

[0068]

[0069] in, t is the stress wave transmission time in the time domain characteristics;

[0070] Step S233, calculate the motion distance characteristics of the head wave formed in the liquid at the initial impact moment D x The initial head wave will gradually overlap with the subsequent shock wave, but the mathematical position of the head wave can still be used D x It means that after the head wave reaches the back of the target plate, it enters the liquid and continues to move into the liquid at the speed of sound. The specific relationship between movement and time is:

[0071]

[0072] Where C is the liquid sound velocity.

[0073] When obtaining time-domain features to distinguish head waves from initial shock waves, some clutter due to refraction and disturbance may be counted as head waves, resulting in inaccurate judgment. Analysis shows that head waves and clutter differ in power spectrum density and frequency band energy. Based on the above principles, the design uses time-domain features to obtain candidate head waves, and then uses frequency-domain features to verify the candidate head waves, further distinguishing head waves from clutter. The specific process of step S300 includes:

[0074] Step S301, setting criteria to determine the head wave candidate, the head wave candidate criteria include stress wave arrival time criterion, amplitude criterion, rise time criterion, and the stress wave that meets all three conditions is determined to be a candidate head wave.

[0075] (1) The stress wave arrival time criterion is ,in is the stress wave arrival time, is the arrival time of the peak with the maximum pressure value;

[0076] (2) The amplitude criterion is ,in is the stress wave amplitude, A 0 is the predicted amplitude of the initial shock wave, if Infrasound reflections or noise may occur, It may be a superimposed wave or a secondary shock;

[0077] (3) The rise time criterion is , is the rise time, is the predicted value of the rise time, which is obtained based on the initial velocity of the fragments and the liquid density;

[0078] Step S302: set verification conditions and perform verification and screening on 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

[0079] (4) 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;

[0080] (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;

[0081] Step S400 obtains the head wave position based on the spatial features of the verified head wave. The specific process is as follows:

[0082] 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 located at the impact point. The curve expression can be specifically expressed as:

[0083]

[0084] Step S402: Determine the curve expression of the head wave. As the radius of the initial shock wave continues to expand, the linear impact area of the head wave also continues to decrease. The curve expression can be specifically expressed as:

[0085]

[0086] in .

[0087] When it appears Figure 5 In this case, after step S301, it may not be possible to obtain a head wave candidate, and it may not pass the verification of step S302. It is necessary to set an additional rising edge slope criterion (6). When criteria (1), (2), (3) or criteria (1) (6) are met at the same time, it can be identified as a candidate head wave. Criterion (6) is

[0088] (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 increases is the candidate head wave.

[0089]

[0090] in, For the i +1 time window and i The slope of the rising edge of the time window; if the slope of the i-th rising edge changes relatively slowly, that is , the initial shock wave has not arrived; if the slope is much larger than the slope of the previous calculation at a certain point, it means that the initial shock wave has arrived.

[0091] Furthermore, in order to accurately place the pressure sensor and avoid the head wave and the initial shock wave being captured at the same time, the time interval Δ between the head wave and the initial shock wave can be predetermined. t ; For any point in the liquid ( xn , yn ), the head wave arrives first, followed by the initial shock wave. The corresponding arrival time can be obtained from the curve, and the time interval can be specifically expressed as:

[0092] .

[0093] For the expression of the sensor installation position for avoiding the influence of the head wave on the initial shock wave measurement ( x , ya ), it is specifically expressed as:

[0094]

[0095] In the formula, t resp represents the response time of the sensor.

[0096] 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 moment of 15 μs, 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 uses 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 uses water, the sound speed C = 1500 m / s, and the time t = 15 μs.

[0097] Calculate the time for the shock wave to propagate to the back of the target plate t 1 = 0.47 μs, calculate the moving distance of the stress wave propagating towards the edge of the target plate in the target plate D y = 79.3 mm, calculate the moving distance of the head wave formed in the liquid at the initial shock moment D x = 21.8 mm; 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.

[0098] To verify the accuracy of the calculation method, extract the curve expression of the head wave in the simulation. 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, 8 mm < x < 20 mm. 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 79.3 mm, between the two intercepts (68, 84) obtained from the numerical simulation. xThe range error is 9%. It can be seen that the calculation results are in good agreement with the simulation results 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 fragments 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 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 by using the spatial features of the verified head wave; 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, 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 time it takes for the stress wave to propagate in the liquid, the amplitude feature is the amplitude of each wave peak, the rise time feature is the time it takes for each wave peak to reach 90% of its peak value, and the rising edge slope is the slope of the signal curve during the rise time. 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 calculating 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; The spatial feature acquisition process in step S200 includes: Step S231, calculating the time t1 for the stress wave transmitted to the back of the target plate to propagate into the liquid; Where h is the target plate thickness, C0 is the target plate material wave velocity; Step S232, calculate the motion distance characteristic D of the stress wave transmitted to the edge of the target plate in the target plate y ; D y =C0×t Where t is the stress wave transmission time in the time domain characteristics; Step S233, calculate the motion distance characteristic D of the head wave formed in the liquid at the initial impact moment x D x =C×(t-t1) Where C is the liquid sound velocity.

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 spatial features include {movement distance}.

3. The method according to claim 2, characterized in that Step S300 specifically includes: Step S301: Set 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 stress wave arrival time criterion is t c <t peak , where t c is the stress wave arrival time, t peak is the arrival time of the peak with the maximum pressure value; (2) The amplitude criterion is A head ∈[0.1A0,0.5A0], where A head is the stress wave amplitude, A0 is the predicted amplitude of the initial shock wave; (3) The rise time criterion is t rise ∈[t min,rise ,t max,rise ], t rise is the rise time, [t min,rise ,t max,rise ] is the predicted value of rise time; (4) The rising edge slope criterion is: G t,t+1 , G t,t+2 , G t,t+3 They are respectively the slope of the rising edge of the i+1th time window and the i-th time window, the slope of the rising edge of the i+2th time window and the i+1th time window, and the slope of the rising edge of the i+3th time window and the i+2th time window; 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: set verification conditions and perform verification and screening on 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 P c <P low , where P c is the power spectral density of the candidate head wave, P low 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.

4. The method according to claim 3, characterized in that In step S400, the head wave curve expression y is determined according to the spatial characteristics. h , get the head wave position in

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