Method for simultaneous measurement of water droplet thickness and velocity field under plasma excitation

Abstract

The application provides a method for synchronously measuring the thickness and the moving speed field of water drops under plasma excitation, belongs to the technical field of synchronously measuring the thickness and the speed of water drops, adopts a signal generator, a high-speed camera, a nanosecond flash lamp and a projection light path to form a synchronous measurement system, controls the high-speed camera to collect a first image of a water drop illuminated by the nanosecond flash lamp and containing tracer particles at t1 by the signal generator, controls the high-speed camera to collect a second image projected by the projection light path at t1+Δt, alternately collects the images, records the images on the odd image sequence and the even image sequence of the high-speed camera respectively, respectively performs cross-correlation method analysis and projection analysis, and couples the analysis results with the continuity equation to realize the time and space synchronous measurement of the thickness field and the speed field in the same water drop.

Description

Technical Field

[0001] This invention relates to the technical field of synchronous measurement of water droplet thickness and velocity, and specifically to a method for synchronous measurement of water droplet thickness and velocity field under plasma excitation. Background Technology

[0002] When an aircraft flies over icing clouds, supercooled water droplets in the clouds collide with its windward surface and ic up. Icing during flight often poses a significant threat to flight safety, thus requiring corresponding aircraft de-icing technologies. In the past two decades, plasma excitation has been widely studied both domestically and internationally as a means of flow control. However, it generates a large amount of heat during operation, making it suitable for de-icing. Plasma exhibits both aerodynamic and thermal effects during operation. To understand in detail how and to what extent the aerodynamic effects of plasma play a role in de-icing, simultaneous non-contact measurements of water droplet thickness and velocity fields can be performed. The thickness distribution and motion information of the water droplets can then be used to quantitatively study the driving effect of plasma de-icing technology on the water droplets.

[0003] Currently, studies on the driving effect of plasma on water droplets typically rely on high-speed photography. However, this method struggles to obtain quantitative velocity and mass distributions, and even more so to analyze the internal flow of the droplet. For measuring droplet mass, existing methods include conductivity probe methods, optical interferometry, and ultrasonic measurements to determine thickness distribution. However, conductivity probe methods are invasive, which can affect the droplet's thickness and velocity distribution. Furthermore, for plasma applications, the suitability of the equipment for high-voltage environments must be considered. Optical interferometry and ultrasonic measurements require specific equipment. Therefore, a method for simultaneously and non-contactly measuring both the thickness and motion of water droplets is urgently needed. Summary of the Invention

[0004] To address the problems in existing technologies, this invention proposes a method for simultaneously measuring the thickness and velocity field of a water droplet under plasma excitation. Compared with existing research, this method utilizes Digital Image Projection (DIP) and Particle Image Velocimetry (PIV) to simultaneously and non-contactly measure the thickness and velocity field of the same water droplet in the same coordinate system, so as to quantitatively study the driving effect of plasma excitation on the water droplet.

[0005] This invention provides a method for simultaneously measuring the thickness and velocity field of a water droplet under plasma excitation, the method comprising the following steps: Step 1: A synchronous measurement system is composed of a signal generator, a high-speed camera, a nanosecond flash lamp, and a projection optical path. The plasma exciter is placed below the high-speed camera to form the measurement area. The projection optical path consists of an electromagnetic relay, an LED light source, a dot matrix image, and a lens group. Step 2: Add tracer particles to the water to be tested, and place the water droplet containing the tracer particles in the measurement area on the surface of the plasma exciter; Step 3: Control the high-speed camera to acquire a first image illuminated by the nanosecond flash lamp and containing tracer particles at time t1 using the signal generator, and control the high-speed camera to acquire a second image projected by the projection optical path at time t1+Δt. Alternately acquire images in this way, and record the first image and the second image on the odd-numbered image sequence and even-numbered image sequence of the high-speed camera, respectively. Step 4: Perform cross-correlation analysis between every two adjacent first images in the odd-numbered image sequence to obtain the velocity field inside the water droplet; perform projection analysis between each second image in the even-numbered image sequence and the reference image to obtain the measured value of the water droplet thickness. Step 5: Introduce the average continuity equation of the water droplet, and use the velocity field obtained in Step 4 as input to obtain the thickness prediction value at the corresponding subsequent time. Use the ensemble Kalman filter method to assimilate and fuse the measured thickness value and the thickness prediction value at the same time to obtain the optimal thickness field and the optimal velocity field. Step 6: Using the optimal thickness field, optimal velocity field, and average continuity equation, the synchronous thickness field at the corresponding moment of each first image in the odd-numbered image sequence is obtained through time interpolation or inversion, thereby realizing the spatiotemporal synchronous measurement of the thickness field and velocity field inside the same water droplet.

[0006] Preferably, the signal generator in step 1 is the overall timing control unit of the synchronous measurement system, used to control the high-speed camera, the nanosecond flash lamp and the projection optical path to work synchronously.

[0007] Preferably, in the projection optical path, the electromagnetic relay is connected to the signal generator and the LED light source, and the dot matrix image and the lens group are sequentially located in front of the LED light source; the signal generator controls the switching of the electromagnetic relay, thereby controlling the flashing frequency of the LED light source, and then the projection image is formed through the dot matrix image and the lens group.

[0008] Preferably, the flicker frequency of the projection optical path is ≥500Hz, and the size of the projected image is 20mm×20mm.

[0009] Preferably, the average diameter of the tracer particles in step 2 is 20µm.

[0010] Preferably, the reference image in step 4 is the image projected by the projection optical path when there are no water droplets.

[0011] Preferably, the Δt in step 3 is 0.5ms-3ms.

[0012] Preferably, in step 4, particle image velocimetry is used to process every two adjacent first images in the odd-numbered image sequence to obtain the instantaneous velocity field inside the water droplet; digital image projection is used to process every second image in the even-numbered image sequence with the reference image to obtain the measured value of the water droplet thickness.

[0013] Preferably, in step 5, the average continuity equation is: (7); Where h is the thickness of the water droplet, and u and v are the average velocity components in the x and y directions obtained from the velocity field, respectively.

[0014] Compared with the prior art, the present invention has the following beneficial effects: This invention uses the same signal generator and a high-speed camera to perform synchronous, non-contact measurement of the thickness and velocity field of a water droplet. This enables synchronous measurement of the thickness and velocity field within the same water droplet in the same coordinate system, avoiding systematic and calibration errors caused by measurements from different devices or at different times.

[0015] The projection optical path and high-speed camera set up in this invention can record the motion pattern of water droplets with high frequency and low exposure time, solving the problem that digital image projection technology and particle image velocimetry technology in the prior art cannot measure the same water droplet at the same time.

[0016] This invention enables precise quantitative research on the driving effect of plasma excitation on water droplets by simultaneously and non-contactly measuring the thickness and velocity field of water droplets. Attached Figure Description

[0017] Figure 1 This is the synchronous measurement system provided by the present invention.

[0018] Figure 2 This is a schematic diagram of the synchronization between the DIP image sequence and the PIV image sequence in the high-speed camera timing diagram provided by the present invention.

[0019] Figure 3 This is a schematic diagram of the projection optical path provided by the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of this disclosure clearer, the technical solutions of the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this disclosure. All other embodiments obtained by those skilled in the art based on the described embodiments of this disclosure without creative effort are also within the scope of protection of this disclosure.

[0021] Unless otherwise defined, all terms used herein (including technical and scientific terms) shall have the same meaning as commonly understood by one of ordinary skill in the art to which this subject matter pertains. It will be further understood that terms such as those defined in commonly used dictionaries shall be interpreted as having the meaning consistent with their meaning in the context of the specification and in the relevant art, and shall not be interpreted in an idealized or overly formal form unless otherwise explicitly defined herein.

[0022] The term "embodiment" as used herein means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of the phrase "embodiment" in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0023] In embodiments of the present invention, the strategy for measuring the internal thickness of a water droplet using DIP technology is as follows: Figure 1 As shown, for a water droplet on a plane, the portion of the LED light source projected onto point D will also be projected onto point C. When AB is parallel to the experimental plane, triangle ABC is similar to triangle EDC. The horizontal displacement s (i.e., the distance DE) from point D to point C can be obtained from two images, one with and one without the water droplet. The distance AB between the high-speed camera and the LED light source, and the height H (i.e., the distance AC) from the camera to the plane, can be measured. Therefore, the thickness h of the water droplet (i.e., the length CE) can be obtained using the similarity of triangles. (1); (2); Where h is the thickness of the water droplet, and H is the height of the high-speed camera above the plane, that is... Figure 1 The AC distance in the equation, s is Figure 1 In the distance between DE and AB, AB is Figure 1 The distance between the medium- and high-speed camera and the LED light source; Since the horizontal displacement s from point D to point C is much smaller than the distance AB between the high-speed camera and the LED light source, the thickness of the water droplet can be calculated using the following formula: (3); Where K is the ratio of the height of the high-speed camera from the plane to the distance between the high-speed camera and the LED light source.

[0024] This invention proposes a method for simultaneously measuring the thickness and velocity field of a water droplet under plasma excitation, comprising the following steps: Step 1: A synchronous measurement system is constructed using a signal generator, a high-speed camera, a nanosecond flash lamp, and a projection optical path. The plasma exciter is placed below the high-speed camera to form the measurement area. The projection optical path consists of an electromagnetic relay, an LED light source, a dot matrix image, and a lens group. The high-speed camera, the nanosecond flash lamp, and the LED light source are all connected to the signal generator. Specifically, the signal generator in step 1 is the overall timing control unit of the synchronous measurement system, used to control the high-speed camera, nanosecond flash lamp and projection optical path to work synchronously.

[0025] As an optional implementation, the nanosecond flash lamp can be the CAVILUX Smart model, with an output power of 300 W, a wavelength of 810 nm, a pulse duration of 50 µs, and a repetition frequency of 500 Hz. It forms a circular spot with a diameter of 50 mm through an optical fiber and a laser head to illuminate the tracer particles in the water droplet. The signal generator is preferably a dual-channel signal generator, such as the Rigol DG4062. The high-speed camera is the Revealer M220, equipped with a SIGMA 105mm F2.8 lens, with a sampling frequency of 1000 Hz, an exposure time of 0.9 ms, an image pixel size of 800 pixels × 600 pixels, a distance of 200 mm from the wall, an actual field of view of 17.20 mm × 13.00 mm, and a resolution of 46.15 pixels / mm.

[0026] Specifically, such as Figure 3 The projection optical path shown has an electromagnetic relay connected to a signal generator and an LED light source. The dot matrix image and lens group are located sequentially in front of the LED light source. The signal generator controls the switching of the electromagnetic relay, thereby controlling the flashing frequency and single flash duration (exposure time) of the LED light source. The projection image is then formed through the dot matrix image and lens group.

[0027] As an optional implementation method, Figure 3The LED light source shown is a 50W LED flat panel lamp, measuring 100mm × 100mm. A signal generator controls the switching of an electromagnetic relay, which in turn controls the LED light source to flash at a set frequency, and also controls the projection exposure time during the DIP measurement process. The electromagnetic relay model is TRD060, with a control voltage of 4V-32V, an output voltage of 1V-60V, and a response time of 100μs. Artificially synthesized particle images are printed on a transparent plastic film to form a dot matrix image, which is then placed in front of the LED light source to generate the specific projection pattern required for DIP measurement. The pattern is then projected onto the observation plane through a lens group, while the projected pattern is reduced to a size of 20mm × 20mm to improve the resolution of the water droplet thickness. By sequentially setting the dot matrix image and the lens group in front of the LED light source, the measurement accuracy of DIP is ensured.

[0028] Step 2: Add tracer particles to the water to be tested, and place the water droplet containing the tracer particles in the measurement area on the surface of the plasma exciter; Step 3: Control the high-speed camera to acquire the first image (PIV image) illuminated by the nanosecond flash lamp and containing tracer particles at time t1 using the signal generator; control the high-speed camera to acquire the second image (DIP image) projected by the projection optical path at time t1+Δt, and so on, and record the first image and the second image on the odd image sequence and even image sequence of the high-speed camera respectively. As an optional implementation, during the synchronous measurement of the velocity field and thickness field within the water droplet, the frequencies of both the LED light source and the nanosecond flash lamp are ≥500Hz, and both operate at the same frequency. The frequency of the signal generator is the same as that of the high-speed camera. The signal generator controls the exposure time of the high-speed camera to acquire images. The delay time Δt between the exposure and acquisition of the first and second images is preferably 0.5ms-3ms, for example, it can be 0.5ms, 1ms, 2ms, or 3ms.

[0029] Step 4: Perform coupled data assimilation processing on the odd-numbered and even-numbered image sequences to obtain spatiotemporally synchronized thickness and velocity fields, specifically: (1) Particle image velocimetry is used to process every two adjacent first images in the odd image sequence to obtain the instantaneous velocity field inside the water droplet; and the center time of the corresponding two first images is assigned, such as v(t2), v(t4), etc. (2) For each second image in the even-numbered image sequence, digital image projection technology is used to process the image with the reference image when there are no water droplets (i.e., at t=0) to obtain the initial estimate of the water droplet thickness field at the corresponding time of the second image, such as h(t2), h(t4), etc. (3) Introducing the average continuity equation from fluid mechanics as a physical constraint on the thickness and velocity fields of the water droplet (treating the water droplet as a free surface flow with extremely thin thickness), the average continuity equation is: (7); Where h is the thickness of the water droplet, and u and v are the average velocity components in the x and y directions obtained from the velocity field, respectively; The corresponding time t of the second image in an even-numbered image sequence 2k (k=1, 2, 3, etc.) are nodes, and the optimal thickness field at the corresponding time in the second image is obtained. Specifically, t is first calculated using PIV. 2k The velocity field v(t) at time t 2k Substituting this into the continuity equation, calculate the predicted thickness h at the corresponding time point of the next second image. f (t) 2k+2 ); to t 2k+2 At time t, the measured thickness h(t) at that moment is measured using a DIP. 2k+2 The measured velocity value v(t) at that moment is obtained by processing adjacent first images using PIV. 2k+2 The predicted thickness value is fused with the measured thickness value and the measured velocity value using an ensemble Kalman filter to obtain the optimal thickness field h at that moment. a (t) 2k+2 ) and optimal velocity field v a (t) 2k+2 ); As an optional implementation, the strategy of the present invention for obtaining the optimal thickness field at the corresponding moment of the second image is as follows: at the moment when the velocity is measured by PIV, the thickness field at the next even moment is predicted by the continuity equation. When the even-numbered image sequence obtains the actual thickness measurement value through DIP processing, the predicted value and the measured value are fused by the ensemble Kalman filter algorithm to obtain a time-continuous thickness field.

[0030] By using the optimal thickness field at the corresponding moment of the second image and the velocity field at adjacent moments, and through forward and backward integration (interpolation or inversion) of the continuity equation over time, the synchronous thickness field at the corresponding moment of the odd-numbered image sequence is obtained. This yields a spatiotemporally synchronized thickness field and velocity field with a temporal resolution consistent with the camera frame rate.

[0031] As an optional implementation, this invention couples PIV processing technology and DIP processing technology with the continuity equation, so that the velocity field and thickness field become co-existing variables that constrain each other and are optimized together during the data processing. This mechanism not only eliminates the time difference caused by alternating acquisition, but also significantly improves the temporal resolution and spatial consistency of thickness measurement through data assimilation.

[0032] As an optional implementation method, in the process of quantitatively studying the driving effect of plasma excitation on water droplets, based on the obtained synchronous thickness field and velocity field of the water droplets, the mass distribution information of the water droplets can be obtained, and the driving effect of plasma on water droplets can be further quantitatively obtained, as shown in formula (4), where d m d represents the mass of the water droplet corresponding to each water droplet velocity field grid. x and d y Let represent the length and width of each water droplet velocity field grid, respectively. The acceleration distribution information of the water droplet is obtained by taking the first derivative of the water droplet velocity, as shown in formula (5). After obtaining the acceleration distribution and mass distribution of the water droplet, the force distribution of the water droplet is calculated, that is, the driving effect of the plasma on the water droplet is quantitatively obtained, as shown in formula (6). (4); (5); (6); Among them, a i Represents the acceleration components, i represents x and y, u represents the acceleration components. i For the velocity component, F i For force components.

[0033] As an alternative implementation, particle image velocimetry is used to measure the velocity distribution inside a water droplet. The tracer particles added to the water droplet have an average diameter of 20µm and a concentration of 1:100. The tracer particles are illuminated using a nanosecond flash lamp, and a high-speed camera records a sequence of images at fixed time intervals. The velocity distribution inside the water droplet is then calculated using a cross-correlation method, and the thickness h of the water droplet is calculated using digital image projection technology.

[0034] Example 1 Tracer particles with an average diameter of 20 µm were added to water and dropped onto the surface of the exciter. The signal generator was activated, triggering the nanosecond lamp, LED light, and camera to operate sequentially. The recorded time sequence diagram from the high-speed camera is shown below. Figure 2 As shown, the frequency of the LED light source is 500 Hz. The even-numbered image sequences corresponding to times t2, t4, t6, etc. are the sequences of the second images, and the odd-numbered image sequences corresponding to times t1, t3, t5, etc. are the sequences of the first images. The high-speed camera captures images at a specific acquisition frequency fs=1000 Hz. Both the LED light source and the nanosecond flash lamp operate at a frequency of fs / 2=500 Hz. The exposure time of the LED light source is 0.9ms, and the exposure time of the nanosecond flash lamp is 50µs. The high-speed camera's exposure and acquisition of the second image is delayed by 1 / fs compared to the acquisition and holding of the first image, that is, Δt=1ms. Thus, the second image and the first image are recorded on the even-numbered image sequence and the odd-numbered image sequence of the high-speed camera, respectively. Cross-correlate the first two PIV images, i.e., the images corresponding to times t1 and t3, to obtain the instantaneous velocity field, which is recorded at time t2 as v(t2); cross-correlate the first and second images with the reference image to calculate the initial thickness field of the water droplet at time t2 as h(t2). To calculate the optimal thickness field at the corresponding time point of the second image in an even-numbered image sequence, the prediction from time t2 to t4 is obtained by substituting v(t2) into the average continuity equation and performing numerical integration over a time step of 1 ms. This yields the predicted thickness value h at time t4. f (t4); The second image corresponding to time t4 and the reference image are processed by DIP to obtain the measured thickness value h(t4) at that time. The first image corresponding to time t3 and the first image corresponding to time t5 are processed by PIV to obtain the measured velocity value v(t4). The predicted thickness value, the actual thickness value and the measured velocity value are fused by ensemble Kalman filtering to generate the optimal thickness field h at time t4. a (t4) and the optimal velocity field v a (t4); and so on, to complete the calculation of the entire even-numbered image sequence; By using the continuity equation back-interpolation, the thickness distribution corresponding to the first image in all odd-numbered image sequences is obtained, resulting in a spatiotemporally synchronized thickness field and velocity field with a temporal resolution consistent with the camera frame rate (1000 Hz).

[0035] The embodiments given above are preferred examples for implementing the present invention, and the present invention is not limited to the above embodiments. Any non-essential additions or substitutions made by those skilled in the art based on the technical features of the present invention are within the protection scope of the present invention.

Claims

1. A method for simultaneously measuring the thickness and velocity field of a water droplet under plasma excitation, characterized in that, The method includes the following steps: Step 1: A synchronous measurement system is composed of a signal generator, a high-speed camera, a nanosecond flash lamp, and a projection optical path. The plasma exciter is placed below the high-speed camera to form the measurement area. The projection optical path consists of an electromagnetic relay, an LED light source, a dot matrix image, and a lens group. Step 2: Add tracer particles to the water to be tested, and place the water droplet containing the tracer particles in the measurement area on the surface of the plasma exciter; Step 3: Control the high-speed camera to acquire a first image illuminated by the nanosecond flash lamp and containing tracer particles at time t1 using the signal generator, and control the high-speed camera to acquire a second image projected by the projection optical path at time t1+Δt. Alternately acquire images in this way, and record the first image and the second image on the odd-numbered image sequence and even-numbered image sequence of the high-speed camera, respectively. Step 4: Perform cross-correlation analysis between every two adjacent first images in the odd-numbered image sequence to obtain the instantaneous velocity field inside the water droplet; perform projection analysis between each second image and the reference image in the even-numbered image sequence to obtain the measured value of the water droplet thickness. Step 5: Introduce the average continuity equation of the water droplet, and use the velocity field obtained in Step 4 as input to obtain the thickness prediction value at the corresponding subsequent time. Use the ensemble Kalman filter method to assimilate and fuse the measured thickness value and the thickness prediction value at the same time to obtain the optimal thickness field and the optimal velocity field. Step 6: Using the optimal thickness field, optimal velocity field, and average continuity equation, the synchronous thickness field at the corresponding moment of each first image in the odd-numbered image sequence is obtained through time interpolation or inversion, thereby realizing the spatiotemporal synchronous measurement of the thickness field and velocity field inside the same water droplet.

2. The method for synchronously measuring the thickness and velocity field of a water droplet under plasma excitation as described in claim 1, characterized in that, The signal generator in step 1 is the overall timing control unit of the synchronous measurement system, used to control the high-speed camera, the nanosecond flash lamp and the projection optical path to work synchronously.

3. The method for synchronously measuring the thickness and velocity field of a water droplet under plasma excitation as described in claim 1, characterized in that, In the projection optical path, the electromagnetic relay is connected to the signal generator and the LED light source, and the dot matrix image and the lens group are located in front of the LED light source in sequence; the signal generator controls the switching of the electromagnetic relay, thereby controlling the flashing frequency of the LED light source, and then the dot matrix image and the lens group form a projection image.

4. The method for synchronously measuring the thickness and velocity field of a water droplet under plasma excitation according to claim 3, characterized in that, The flicker frequency of the projection optical path is ≥500Hz, and the size of the projected image is 20mm×20mm.

5. The method for synchronously measuring the thickness and velocity field of a water droplet under plasma excitation according to claim 1, characterized in that, The average diameter of the tracer particles mentioned in step 2 is 20µm.

6. The method for synchronously measuring the thickness and velocity field of a water droplet under plasma excitation according to claim 1, characterized in that, The reference image mentioned in step 4 is the image projected by the projection optical path when there are no water droplets.

7. The method for synchronously measuring the thickness and velocity field of a water droplet under plasma excitation according to claim 1, characterized in that, The Δt mentioned in step 3 is 0.5ms-3ms.

8. The method for synchronously measuring the thickness and velocity field of a water droplet under plasma excitation according to claim 1, characterized in that, In step 4, particle image velocimetry is used to process every two adjacent first images in the odd-numbered image sequence to obtain the instantaneous velocity field inside the water droplet; digital image projection is used to process every second image in the even-numbered image sequence with the reference image to obtain the measured value of the water droplet thickness.

9. The method for synchronously measuring the thickness and velocity field of a water droplet under plasma excitation according to claim 1, characterized in that, In step 5, the average continuity equation is: ； Where h is the thickness of the water droplet, and u and v are the average velocity components in the x and y directions obtained from the velocity field, respectively.

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