Multi-phase hybrid chaotic feature evaluation method and system based on coordinate time series
By acquiring the three-dimensional coordinate time series of tracer particles in the stirred tank, plotting trajectory diagrams and iterating, the problem of evaluating chaotic phenomena in the stirred tank was solved, efficient mixing was achieved, and the design process of the stirred tank was simplified.
Patent Information
- Application Number
- CN202310451646.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-04-25
- Publication Date
- 2025-12-05
- Estimated Expiration
- 2043-04-25
AI Technical Summary
Existing technologies make it difficult to effectively identify and evaluate chaotic phenomena within a stirred tank, resulting in low mixing efficiency. In particular, during low-speed laminar flow mixing, a mixing isolation zone forms, making it difficult to achieve efficient mixing.
By acquiring the three-dimensional coordinate time series of tracer particles in the stirred tank, three-dimensional and two-dimensional trajectory diagrams are plotted and iterated. The number of iterations under different working conditions is determined by using the midpoint coordinate method and image processing technology to evaluate the chaotic characteristics and mixing uniformity.
This paper presents a simple and convenient method to effectively evaluate the chaotic characteristics in a mixing tank, improve mixing efficiency, and reduce the loss of manpower and resources caused by unreasonable design.
Smart Images
Figure CN116452567B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the fields of metallurgy and chemical engineering technology, specifically to a method and system for evaluating the characteristics of multiphase mixed chaos based on coordinate time series. Background Technology
[0002] Mixing operations have wide applications in chemical, metallurgical, and biological fields, and improving mixing efficiency is crucial for enhancing product quality and reducing enterprise costs. However, in practical applications, high-speed turbulent mixing, which offers better mixing results, is difficult to promote due to objective factors such as high shear forces, short mechanical lifespan, and the tendency for materials to splash. Therefore, the mainstream mixing method in industry is currently low-speed laminar flow mixing. However, low-speed laminar flow mixing is very inefficient, especially since it creates a mixing isolation zone during the mixing process. Within this zone, material exchange with the outside relies solely on basic diffusion. Therefore, the more efficient chaotic mixing is attracting increasing attention.
[0003] To meet the demand for efficient mixing under various operating conditions, mixer design has become a crucial issue. Since numerous parameters influence the flow field under forced convection, such as the number of blades, impeller speed, and impeller radius, the design must be tailored to specific circumstances. In practice, the parameters of different stirred tanks vary significantly; therefore, to quickly and efficiently induce chaos, the stirred tank needs to be highly customized. Currently, the most common technical approach is to start from the laboratory, scale up gradually, and finally promote widespread application. This process involves evaluating the chaos under various operating conditions. The chaos of the flow field exhibits significant initial value sensitivity, thus its chaotic characteristics change significantly under different operating conditions. Essentially, it aims to break the periodic disturbances in the mixing process, causing flow field traces to intersect or even perpendicularly, inducing chaos and improving mixing efficiency. However, judging or comparing chaotic phenomena within stirred tanks remains a major challenge.
[0004] Current research techniques for studying the chaotic characteristics of systems primarily rely on mathematical quantification methods based on mathematical theory, including the maximum Lyapunov number (MAXL) and the Poincaré section. The MAXL is a relatively mainstream method for determining chaos, representing the average exponential rate of convergence or divergence between adjacent trajectories in phase space. This method first requires determining an approximate solution to the ordinary differential equations of the dynamical system, then performing eigenvalue decomposition or singular value decomposition on the system's Jacobian matrix to obtain the Lyapunov number. This method presupposes the kinematic equations of the dynamical system, which is extremely difficult in practice. Although subsequent trajectory tracking methods, such as those based on the Wolf algorithm and Rosenstein's small data method, have been developed as auxiliary methods, these are based on theoretical estimations and cannot fully represent actual dynamical systems. Similar to the MAXL, the Poincaré section method requires reconstructing the phase space and also struggles to avoid solving the kinematic equations of the dynamical system. Furthermore, the Poincaré section method itself is a simplified algorithm and, in some cases, cannot fully describe the trajectory state within phase space, making it highly dependent on the algorithm itself. In summary, mathematical quantification methods based on mathematical theory heavily rely on the kinematic equations of the dynamic system, which is very difficult to implement in practice. Furthermore, the input data is often time-series data such as pressure and temperature fluctuations, which can only be collected at single points, making it difficult to represent the entire fluid domain. Moreover, the data collection points are complex to set up. Therefore, a simple and convenient method is needed that can analyze the chaotic characteristics of the entire fluid domain. Summary of the Invention
[0005] To address the technical problems mentioned above, this application focuses on judging the most fundamental initial value sensitivity and ergodicity of chaotic characteristics. Chaotic systems are formed by adding perturbations to periodic systems. This application starts with the final result, using an iterative algorithm to remove the perturbations, ultimately obtaining the initial periodic trajectory, i.e., the limit cycle. By comparing the number of iterations required to form the limit cycle, the chaotic characteristics of different mixing methods are compared. This provides a highly practical method for evaluating chaotic characteristics.
[0006] To achieve the above objectives, this application provides a method for evaluating the characteristics of multiphase mixed chaos based on coordinate time series, the steps of which include:
[0007] The three-dimensional coordinates of tracer particles in the stirring tank during the chaotic mixing process are recorded to obtain the time series of the three-dimensional coordinates of the tracer particles;
[0008] Based on the three-dimensional coordinate time series, a three-dimensional trajectory diagram and a two-dimensional trajectory diagram are drawn; the two-dimensional trajectory diagram includes: two-dimensional trajectory diagrams in the xy, xz and yz planes;
[0009] Based on the three-dimensional trajectory diagram and the two-dimensional trajectory diagram, the iteration is performed;
[0010] The uniformity and efficiency of mixing can be determined by the number of iterations under different operating conditions.
[0011] Preferably, the method for obtaining the three-dimensional coordinate time series includes: when the container is a transparent container, using a camera to capture the movement of tracer particles inside the container, identifying and recording the three-dimensional coordinates of the tracer particles in real time, and obtaining the three-dimensional coordinate time series.
[0012] Preferably, the method for obtaining the three-dimensional coordinate time series further includes: when the container is a non-transparent container, placing a multi-axis gyroscope into the tracer particle, and determining the three-dimensional coordinate time series of the tracer particle by means of velocity, acceleration and angle.
[0013] Preferably, the method for performing the iteration includes:
[0014] S1. Perform image processing on the two-dimensional trajectory graph and calculate the number of connected components;
[0015] S2. Process the three-dimensional coordinate time series using the midpoint coordinate method;
[0016] S3. Repeat S1 and S2 until the two-dimensional trajectory graph has a connected component, i.e., a stable limit cycle is formed.
[0017] Preferably, the three-dimensional trajectory diagram and the two-dimensional trajectory diagram are line graphs; and they are connected end to end.
[0018] Preferably, the method for performing the image processing includes:
[0019] The two-dimensional trajectory graph is processed to obtain a grayscale image;
[0020] The grayscale image is binarized to obtain a binary image;
[0021] The binary image is subjected to morphological processing, and the edges of the binary image are eroded to obtain the final image;
[0022] Count the number of connected components in the final image.
[0023] Preferably, the specific steps of the midpoint coordinate method include: selecting the midpoint of two adjacent coordinate points on the three-dimensional trajectory graph and connecting them sequentially to form a new spatial closed curve.
[0024] This application also provides a multiphase mixed chaotic feature evaluation system based on coordinate time series, including: an acquisition module, a plotting module, an iteration module, and a judgment module;
[0025] The acquisition module is used to acquire and record the three-dimensional coordinates of tracer particles in the stirring tank during the chaotic mixing process, and obtain the three-dimensional coordinate time series of the tracer particles.
[0026] The drawing module is used to draw a three-dimensional trajectory diagram and a two-dimensional trajectory diagram based on the three-dimensional coordinate time series; the two-dimensional trajectory diagram includes: two-dimensional trajectory diagrams in the xy, xz and yz planes;
[0027] The iteration module is used to perform iteration based on the three-dimensional trajectory map and the two-dimensional trajectory map;
[0028] The judgment module is used to determine the mixing uniformity and mixing efficiency by judging the number of iterations under different working conditions.
[0029] Compared with the prior art, the beneficial effects of this application are as follows:
[0030] This application is theoretically supported by the most basic initial value sensitivity and ergodicity characteristics of chaos, as well as the generation methods of chaos, ensuring high reliability. Furthermore, it introduces the midpoint coordinate method, effectively avoiding the situation where local chaos results in overall non-chaos. This application incorporates image processing technology, which is simple, convenient, and highly operable; in addition, it greatly facilitates the design of the mixer and reduces the loss of manpower and resources caused by unreasonable design. Attached Figure Description
[0031] To more clearly illustrate the technical solutions of this application, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0032] Figure 1 This is a schematic diagram of the method flow of an embodiment of this application;
[0033] Figure 2 This is a schematic diagram of three-dimensional coordinate acquisition according to an embodiment of this application;
[0034] Figure 3 This is a schematic diagram illustrating the operation of the point coordinate method in the embodiments of this application;
[0035] Figure 4 This is a schematic diagram comparing the chaotic features of two example operating conditions in an embodiment of this application;
[0036] Figure 5 This is a schematic diagram of the system structure according to an embodiment of this application. Detailed Implementation
[0037] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0038] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0039] Example 1
[0040] like Figure 1 and Figure 2 The figure shows the multiphase mixed chaos feature evaluation method based on coordinate time series proposed in this embodiment. The steps include:
[0041] The three-dimensional coordinates of tracer particles in a stirred tank during chaotic mixing are recorded using a camera recognition system or a multi-axis gyroscope, resulting in a time series of the tracer particles' three-dimensional coordinates. Taking the mixing effect of a common mechanical stirring process in chemical engineering as the research object, relevant techniques are used to obtain the changes in the coordinates of a single tracer particle over time during the mixing process. For comparisons of chaotic characteristics in containers of different sizes, the data can be appropriately normalized before proceeding to the next step.
[0042] In the above steps, when the container is transparent, a camera is used to capture the movement of the tracer particles inside the container, and the three-dimensional coordinates of the tracer particles are identified and recorded in real time to obtain the three-dimensional coordinate time series. When the container is non-transparent, a multi-axis gyroscope is placed inside the tracer particles, and the three-dimensional coordinate time series of the tracer particles is determined by velocity, acceleration, and angle.
[0043] Subsequently, based on the three-dimensional coordinate time series, three-dimensional trajectory diagrams and two-dimensional trajectory diagrams are drawn; among them, the two-dimensional trajectory diagrams include two-dimensional trajectory diagrams of the xy, xz and yz planes; during the drawing process, it should be noted that whether it is a three-dimensional trajectory diagram or a two-dimensional trajectory diagram, the final trajectory should be connected end to end.
[0044] Then, based on the three-dimensional trajectory map and the two-dimensional trajectory map, iterative steps are performed, including:
[0045] S1. Perform image processing on the two-dimensional trajectory graphs of the xy, xz, and yz planes, and calculate the number of connected components.
[0046] The two-dimensional trajectory graph is processed into grayscale to obtain a grayscale image; the grayscale image is binarized to obtain a binary image; the binary image is morphologically processed, and the edges of the binary image are eroded to obtain the final image; the number of connected components in the final image is counted.
[0047] S2. Processing three-dimensional coordinate time series using the midpoint coordinate method.
[0048] Select the midpoints of two adjacent coordinate points and connect them sequentially to form a new closed curve in space.
[0049] S3. Repeat S1 and S2 until the two-dimensional trajectory graphs of the xy, xz, and yz planes each have a connected component, i.e., a stable limit cycle is formed, such as... Figure 3 As shown.
[0050] Finally, the mixing uniformity and mixing efficiency are determined by the number of iterations under different operating conditions; the more iterations, the stronger the chaos, and vice versa.
[0051] Example 2
[0052] To verify the technical effectiveness of this application, this embodiment compares the chaotic effect of a set of tracer particle trajectory data over time from a certain mixing experimental platform with the three-dimensional trajectory generated by the formula. The experimental parameters are as follows: the stirring tank diameter is 25cm, the liquid level is 15cm, the material is plexiglass, and the working fluid is water; the stirring impeller is a standard two-blade impeller with a diameter of 7cm, a height from the bottom of 7.5cm, and a rotation speed of 60rpm; to reduce optical distortion, a cubic tank is used outside the stirring tank and filled with the same working fluid; a dual-camera system is arranged outside the cubic tank to collect the coordinates of the tracer particles. The tracer particles used have the same density as the working fluid to reduce errors caused by density differences. The three-dimensional trajectory generated by the formula is a schematic diagram of a tracer particle trajectory with a poor mixing effect, which is quite similar to the phenomenon in the actual mixing process, and therefore has strong persuasiveness. The same number of coordinates is used in both conditions, i.e., the same sampling rate and sampling time are used. Based on the initial value sensitivity and ergodicity of chaos, the trajectory diagrams of the two working conditions are iterated using the midpoint method. The chaos of the working conditions is judged by different iteration numbers. The more iterations, the stronger the chaos.
[0053] Reference Figure 4 As shown, the experimental condition requires 82,000 iterations, while the example condition requires 23,800 iterations. Since the sampling time and sampling rate are the same for both conditions, it can be concluded that the tracer particle trajectories in the example condition are highly overlapping. In the experimental condition, the tracer particles are distributed throughout the entire fluid domain, exhibiting better ergodicity, indicating that its chaotic nature is stronger than that of the example condition. This also proves the effectiveness and practicality of this application.
[0054] Example 3
[0055] like Figure 5 The diagram shown illustrates the system structure of this embodiment, including: an acquisition module, a drawing module, an iteration module, and a judgment module. The acquisition module records the three-dimensional coordinates of tracer particles within the stirring tank during the chaotic mixing process, obtaining a three-dimensional coordinate time series of the tracer particles. The drawing module draws a three-dimensional trajectory diagram and a two-dimensional trajectory diagram based on the three-dimensional coordinate time series. The two-dimensional trajectory diagram includes two-dimensional trajectory diagrams in the xy, xz, and yz planes. The iteration module iterates based on the three-dimensional and two-dimensional trajectory diagrams. The judgment module determines the mixing uniformity and mixing efficiency by judging the number of iterations under different operating conditions.
[0056] The following will describe in detail, with reference to this embodiment, how this application solves technical problems in real life.
[0057] In this embodiment, the acquisition module uses a camera recognition system or a multi-axis gyroscope to record the three-dimensional coordinates of tracer particles in the stirring tank during the chaotic mixing process, obtaining a time series of the three-dimensional coordinates of the tracer particles. Taking the mixing effect of a mechanical stirring process commonly used in chemical processes as the research object, relevant techniques are used to obtain the change of coordinates of a single tracer particle over time during the mixing process. For the comparison of chaotic characteristics in containers of different sizes, the data can be appropriately normalized before proceeding to the next step.
[0058] In the above workflow, when the container is transparent, a camera is used to capture the movement of tracer particles inside the container, and the three-dimensional coordinates of the tracer particles are identified and recorded in real time to obtain the three-dimensional coordinate time series. When the container is non-transparent, a multi-axis gyroscope is placed inside the tracer particles, and the three-dimensional coordinate time series of the tracer particles is determined by velocity, acceleration, and angle.
[0059] Then, the drawing module draws a three-dimensional trajectory graph and a two-dimensional trajectory graph based on the three-dimensional coordinate time series. The two-dimensional trajectory graph includes two-dimensional trajectory graphs in the xy, xz and yz planes. During the drawing process, it should be noted that whether it is a three-dimensional trajectory graph or a two-dimensional trajectory graph, the final trajectory should be connected end to end.
[0060] Subsequently, the iteration module performs iterations based on the three-dimensional trajectory map and the two-dimensional trajectory map. The process includes:
[0061] a. Perform image processing on the two-dimensional trajectory graphs of the xy, xz, and yz planes, and calculate the number of connected components.
[0062] The two-dimensional trajectory graph is processed into grayscale to obtain a grayscale image; the grayscale image is binarized to obtain a binary image; the binary image is morphologically processed, and the edges of the binary image are eroded to obtain the final image; the number of connected components in the final image is counted.
[0063] b. Processing three-dimensional coordinate time series using the midpoint coordinate method.
[0064] Select the midpoints of two adjacent coordinate points and connect them sequentially to form a new closed curve in space.
[0065] c. Repeat steps a and b until the two-dimensional trajectory graphs of the xy, xz, and yz planes each have a connected component, i.e., a stable limit cycle is formed, such as... Figure 3 As shown.
[0066] Finally, the judgment module determines the mixing uniformity and mixing efficiency by judging the number of iterations under different operating conditions.
[0067] The embodiments described above are merely preferred embodiments of this application and are not intended to limit the scope of this application. Any modifications and improvements made to the technical solutions of this application by those skilled in the art without departing from the spirit of this application shall fall within the protection scope defined by the claims of this application.
Claims
1. A multi-phase mixed chaotic feature evaluation method based on coordinate time series, characterized by the steps of The method comprises the following steps: acquiring three-dimensional coordinates of tracer particles in a stirring tank in a chaotic mixing process to record and obtain a three-dimensional coordinate time sequence of the tracer particles; based on the three-dimensional coordinate time sequence, drawing a three-dimensional trajectory graph and a two-dimensional trajectory graph; the two-dimensional trajectory graph comprises two-dimensional trajectory graphs of x-y, x-z and y-z planes; based on the three-dimensional trajectory graph and the two-dimensional trajectory graph, performing iteration; the method for performing the iteration comprises the following steps: S1. performing image processing on the two-dimensional trajectory graph to calculate the number of connected domains; the method for performing the image processing comprises the following steps: performing gray processing on the two-dimensional trajectory graph to obtain a gray image; performing binaryzation processing on the gray image to obtain a binary image; performing morphological processing on the binary image and corroding edges of the binary image to obtain a final image; and counting the number of connected domains of the final image; S2. processing the three-dimensional coordinate time sequence by using a midpoint coordinate method; the specific steps of the midpoint coordinate method comprise the following steps: selecting midpoints of adjacent two coordinate points of the three-dimensional trajectory graph and connecting the midpoints in sequence to form a new spatial closed curve; S3. repeatedly performing S1 and S2 until the two-dimensional trajectory graph has one connected domain, i.e., a stable limit cycle is formed; the three-dimensional trajectory graph and the two-dimensional trajectory graph are line graphs; and the line graphs are connected at the beginning and the end; by judging the number of iterations under different working conditions, the mixing uniformity and the mixing efficiency are judged.
2. The coordinate time series-based polyphase hybrid chaotic feature evaluation method according to claim 1, characterized in that, The method for obtaining the three-dimensional coordinate time sequence comprises the following steps: when the container is a transparent container, a camera is used to shoot the movement of the tracer particles in the container, the three-dimensional coordinates of the tracer particles are identified and recorded in real time, and the three-dimensional coordinate time sequence is obtained.
3. The method according to claim 2, wherein, The method for obtaining the three-dimensional coordinate time sequence further comprises the following steps: when the container is a non-transparent container, a multi-axis gyroscope is placed in the tracer particles, and the three-dimensional coordinate time sequence of the tracer particles is determined by using speed, acceleration and angle.
4. A multiphase hybrid chaotic feature evaluation system based on coordinate time series, the system being configured to implement the method of any one of claims 1 to 3, characterized in that, The method comprises the following steps: an acquisition module, a drawing module, an iteration module and a judgment module; the acquisition module is used to acquire three-dimensional coordinates of tracer particles in a stirring tank in a chaotic mixing process to record and obtain a three-dimensional coordinate time sequence of the tracer particles; the drawing module is used to draw a three-dimensional trajectory graph and a two-dimensional trajectory graph based on the three-dimensional coordinate time sequence; the two-dimensional trajectory graph comprises two-dimensional trajectory graphs of x-y, x-z and y-z planes; the iteration module is used to perform iteration based on the three-dimensional trajectory graph and the two-dimensional trajectory graph; the judgment module is used to judge the mixing uniformity and the mixing efficiency by judging the number of iterations under different working conditions.