A calculation method for droplet condensation on a smooth surface

Abstract

This invention relates to a calculation method for droplet condensation on a smooth surface. Condensation experiments are conducted on surfaces with different wettability. A mathematical model is established to show the dependence of the condensation rate on surface wettability. Calculation assumptions are established to obtain the relationship between the volume change of a single droplet and the change in the droplet radius within a region. A condensation system is established to track changes in condensed droplet parameters and parameter changes after droplet merging. Results are output based on the condensation system and compared with actual implementation data for verification. The beneficial effects are: this invention studies the change in relative humidity after condensation stabilization, obtaining numerical simulation results that agree well with experimental results. It can effectively predict the changes in the state parameters of condensed droplets during condensation. This numerical simulation scheme facilitates the design of condensation systems for air conditioners, electric vehicles, etc., and saves experimental costs in theoretical research.

Description

Technical Field

[0001] This invention relates to the field of droplet condensation calculation, and more particularly to a method for calculating droplet condensation on a smooth surface. Background Technology

[0002] Condensation is a common phenomenon in nature and industry. When water vapor encounters a wall surface with a temperature lower than its dew point, it undergoes a phase change to form liquid water. Condensation is divided into film condensation and droplet condensation. When the wall surface has strong wettability, the condensate can form a continuous liquid film on the wall surface. This type of condensation is called film condensation. If the wall surface has weak wettability, the condensate will form small droplets on the wetted wall surface. This type of condensation is called droplet condensation. Droplet condensation can have a heat transfer efficiency that is an order of magnitude higher than that of film condensation. Condensation has wide applications in thermal management, refrigeration and other fields. At the same time, the equipment blockage and circuit corrosion caused by condensation are also negative impacts that cannot be ignored. Therefore, the study of condensation has important practical application value.

[0003] Existing methods for studying condensation typically involve experimental methods and numerical simulations. Experimental methods, in particular, have stringent requirements and are time-consuming. For example, while there are many studies on the condensation mechanism of water vapor, the theoretical models primarily use the stable relative humidity value reached before condensation. However, in reality, the relative humidity around the condensation wall changes after condensation begins. Currently, there is a lack of research on correcting for relative humidity during the condensation process, and therefore, existing numerical simulations do not take parameter changes into account. Summary of the Invention

[0004] This invention provides a calculation method for droplet condensation on a smooth surface, primarily used to calculate the changes in various parameters during the formation of a single droplet and droplet merging, obtain the nucleation density under different relative humidities, obtain the condensation rate after stabilization based on experiments and theory, simulate the condensation process under different relative humidities, and provide a simulation method for the growth of a single droplet and droplet merging during condensation. The calculation method for droplet condensation on a smooth surface includes:

[0005] Step S1: Conduct condensation experiments on surfaces with different wettability to establish a mathematical model of the dependence of condensation rate on surface wettability, specifically as follows:

[0006] S11. Place the condensing wall on the condenser, and use a mass flow meter and a wide-mouth bottle to adjust the flow rate of nitrogen and water vapor to control the relative humidity of the condensing environment. When the relative humidity is stable, adjust the temperature of the condenser to the target temperature to prepare and obtain surfaces with different wettability.

[0007] S12. Capture the condensation process at a speed of 0.1 s / frame and record the changes in humidity;

[0008] S13. Using C++ language to process images, within the resolution range of the shot, based on the distribution of condensed droplets in the initial stage of condensation, obtain the nucleation density of droplets on surfaces with different wettability, obtain the radius value of a single droplet frame by frame, and record the radius value of each frame, wherein the radius value of the fitted circle is obtained by performing circle fitting on the droplet contour.

[0009] S14. Based on the experimental results obtained from image processing, the volume change of a single condensation droplet over time is obtained. Regression analysis is performed on it to obtain the condensation rate c [m3 / s] of a single condensation droplet on a surface with different wettability after condensation stabilization. A mathematical model is then established to describe the dependence of the condensation rate on the surface wettability.

[0010] Step S2: Establish calculation hypotheses to obtain the relationship between the volume change of a single droplet and the relationship between the radius change of the droplet within a region, specifically:

[0011] S21. Ignore the influence of gravity during the condensation process, that is, the radius of the condensate droplet is smaller than the capillary length. For a water droplet, its capillary length is about 2.7 mm.

[0012] S22. Because the condensate droplets form a spherical crown shape on a smooth surface and advance at an angle... The formula for calculating the volume of a droplet as it grows is: ,in, Let be the lateral radius of the condensate droplet.

[0013] make The formula for calculating the droplet volume is as follows: To and Related functions;

[0014] S23, the change in condensed droplets conforms to... The change in lateral radius was obtained from the experiment.

[0015] (1)

[0016] in for The lateral radius of the droplet at any given moment. This refers to the time step in numerical computation. for For details on the change in the lateral radius of the droplet at any given time and the changes in the droplet growth process, please refer to [link / reference needed]. Figure 1 ;

[0017] S24. Obtain any two droplets. , The distance between the centroids in the two-dimensional plane Calculation formula

[0018] (2)

[0019] in, If the radii of the two droplets are smaller than the sum of their radii, droplet merging will occur.

[0020] S25. Based on the law of conservation of mass and the morphological assumptions of the droplets, obtain the radius of the merged droplets. Relationship

[0021] = (3)

[0022] Assuming the center of mass of the droplets remains unchanged in the two-dimensional plane after merging. ,Right now

[0023] = (4)

[0024] =

[0025] in, , , , ..., The radius of the droplets just before they merged;

[0026] Step S3: Establish a condensation system to track changes in condensate droplet parameters and changes in parameters after droplet merging, specifically as follows:

[0027] Write a program in C++ to determine the requirements. and Two-dimensional computational domain in a plane ,in h and h represent the width and height of the computation region, respectively;

[0028] Based on the mathematical model describing the relationship between nucleation density and surface wettability, the nucleation density is determined, and then the droplet distribution at the initial moment of condensation is realized based on a random function.

[0029] Mark the initial droplet It is used to track parameter changes of a single condensed droplet;

[0030] Step S4: Output the results based on the condensation system and compare them with the actual implementation data for verification. Specifically:

[0031] Simulations are performed as needed to obtain the changes in the radius, volume, and surface coverage of any single droplet over time, as well as the changes in the overall volume and surface coverage of condensed droplets within the calculation area over time.

[0032] Experimental data were obtained for individual droplets and the overall condensation of droplets within a region, and then compared and analyzed with the data mentioned above. Beneficial effects

[0033] 1. The change in relative humidity after condensation stabilization was studied. Based on the results, a corrected droplet condensation rate was adopted. The numerical simulation results obtained are in good agreement with the experimental results, with the radius error of a single droplet being less than 2% and the volume error being less than 6%.

[0034] 2. For the overall condensation, the area coverage rate index yielded numerical simulation results that matched the experimental results. When condensation reached equilibrium, the error was less than 5%.

[0035] 3. The calculation method provided by this invention can effectively predict the changes in the state parameters of condensate droplets during the condensation process. This numerical simulation scheme can facilitate the design of condensation systems for air conditioners, electric vehicles, etc., and can save experimental costs in theoretical research. Attached Figure Description

[0036] Figure 1 This is a diagram illustrating the growth process of condensed droplets, which is a computational method for droplet condensation on a smooth surface.

[0037] Figure 2 This is a flowchart illustrating the calculation of droplet parameter changes in a method for calculating droplet condensation on a smooth surface.

[0038] Figure 3 This is a graph showing the relationship between the radius and time in simulation and experimental data of a computational method for droplet condensation on a smooth surface.

[0039] Figure 4 This is a graph showing the relationship between volume change over time in simulation and experimental data of a computational method for droplet condensation on a smooth surface.

[0040] Figure 5 This is a graph showing the changes in experimental and simulated data for an interface with a 120° contact angle in a calculation method for droplet condensation on a smooth surface.

[0041] Figure 6 This is a graph showing the changes in experimental and simulated data in the case of an interface with a 90° contact angle, used in a calculation method for droplet condensation on a smooth surface. Detailed Implementation

[0042] It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0043] like Figure 1-6 The method for calculating droplet condensation on a smooth surface, as shown, includes:

[0044] Step S1: Conduct condensation experiments on surfaces with different wettability to establish a mathematical model of the dependence of condensation rate on surface wettability, specifically as follows:

[0045] S11. Place the condensing wall on the condenser, and use a mass flow meter and a wide-mouth bottle to adjust the flow rate of nitrogen and water vapor to control the relative humidity of the condensing environment. When the relative humidity is stable, adjust the temperature of the condenser to the target temperature to prepare and obtain surfaces with different wettability.

[0046] S12. Capture the condensation process at a speed of 0.1 s / frame and record the changes in humidity;

[0047] S13. Using C++ language to process images, within the resolution range of the shot, based on the distribution of condensed droplets in the initial stage of condensation, obtain the nucleation density of droplets on surfaces with different wettability, obtain the radius value of a single droplet frame by frame, and record the radius value of each frame, wherein the radius value of the fitted circle is obtained by performing circle fitting on the droplet contour.

[0048] S14. Based on the experimental results obtained from image processing, the volume change of a single condensation droplet over time is obtained. Regression analysis is performed on it to obtain the condensation rate c [m3 / s] of a single condensation droplet on a surface with different wettability after condensation stabilization. A mathematical model is then established to describe the dependence of the condensation rate on the surface wettability.

[0049] Step S2: Establish calculation hypotheses to obtain the relationship between the volume change of a single droplet and the relationship between the radius change of the droplet within a region, specifically:

[0050] S21. Ignore the influence of gravity during the condensation process, that is, the radius of the condensate droplet is smaller than the capillary length. For a water droplet, its capillary length is about 2.7 mm.

[0051] S22. Because the condensate droplets form a spherical crown shape on a smooth surface and advance at an angle... The formula for calculating the volume of a droplet as it grows is: ,in, Let be the lateral radius of the condensate droplet.

[0052] make The formula for calculating the droplet volume is as follows: To and Related functions;

[0053] S23, the change in condensed droplets conforms to... The change in lateral radius was obtained from the experiment.

[0054] (1)

[0055] in for The lateral radius of the droplet at any given moment. This refers to the time step in numerical computation. for For details on the change in the lateral radius of the droplet at any given time and the changes in the droplet growth process, please refer to [link / reference needed]. Figure 1 ;

[0056] S24. Obtain any two droplets. , The distance between the centroids in the two-dimensional plane Calculation formula

[0057] (2)

[0058] in, If the radii of the two droplets are smaller than the sum of their radii, droplet merging will occur.

[0059] S25. Based on the law of conservation of mass and the morphological assumptions of the droplets, obtain the radius of the merged droplets. Relationship

[0060] = (3)

[0061] Assuming the center of mass of the droplets remains unchanged in the two-dimensional plane after merging. ,Right now

[0062] = (4)

[0063] =

[0064] in, , , , ..., The radius of the droplets just before they merged;

[0065] Step S3: Establish a condensation system to track changes in condensate droplet parameters and changes in parameters after droplet merging, specifically as follows:

[0066] Write a program in C++ to determine the requirements.

[0067] and

[0068] Two-dimensional computational domain in a plane

[0069] ,in

[0070] and

[0071] These are the width and height of the calculation area, respectively;

[0072] Based on the mathematical model describing the relationship between nucleation density and surface wettability, the nucleation density is determined, and then the droplet distribution at the initial moment of condensation is realized based on a random function.

[0073] Mark the initial droplet , used to track the parameter changes of a single condensed droplet, realize the growth process of the condensed droplet through formula (1) and given condensation time, realize the merging of droplets during condensation according to formula (2), and after merging, the change of the droplet still follows formula (1).

[0074] Step S4: Output the results based on the condensation system and compare them with the actual implementation data for verification. Specifically:

[0075] Simulations are performed as needed to obtain the changes in the radius, volume, and surface area of ​​any single droplet over time, as well as the changes in the overall volume and surface area of ​​the condensed droplets within the calculation region over time. The specific calculation process is described in the following reference. Figure 2 , where T represents the time of the change node;

[0076] The experimental data on the realization of individual droplets and the overall condensation droplets in the region were obtained and compared with the above data.

[0077] In this embodiment, by analyzing a single droplet, the changes in its radius and volume over time are obtained, its growth rate is calculated, and the rate parameters are input into a simulation program for execution. The program outputs the changes in radius and volume over time and compares them with experimental data to obtain... Figure 3 Comparison of the change of median radius over time and Figure 4 Comparison of volume changes over time;

[0078] By processing and analyzing the overall condensate droplets, experimental data were analyzed to determine the increase in area coverage over time. The data from three experiments were averaged to obtain a graph showing the change in area coverage. The simulation was then repeated one hundred times, and the average was taken to obtain simulated area coverage changes at contact angles of 90 degrees and 120 degrees. (See reference for details.) Figure 5-6 In the graph, the horizontal axis represents time, and the vertical axis represents area coverage, i.e., the area of ​​the condensation region. The length of the error bar represents the standard deviation of the three experiments, which is calculated as follows: Standard Deviation ,in Let be the radius measured in the i-th experiment. The average radius is the radius measured in the experiment, and n is the number of experiments. The simulated data in the figure is within the allowable error range.

[0079] The above are merely preferred embodiments of the present invention and do not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made using the present invention’s specification and content, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method of calculating condensation of a liquid droplet on a smooth surface, characterized by, Specifically comprising: Step S1, performing condensation experiments on different wettable surfaces, establishing a mathematical model of the dependence of condensation rate on surface wettability, specifically comprising, S11, placing the condensing wall on the condenser, combining the mass flow meter and the wide-mouth bottle to adjust the flow rate of nitrogen and water vapor to control the relative humidity of the condensation environment, and then adjusting the temperature of the condenser to the target temperature when the relative humidity is stable, thereby preparing and obtaining different wettable surfaces; S12, using a speed of 0.1 s / frame to shoot the condensation process and record the change of humidity; S13, according to the distribution of condensate droplets in the initial stage of condensation, obtaining the nucleation density of liquid droplets on different wettable surfaces, obtaining the radius value of single droplet frame by frame, and recording the radius value of each frame; S14, based on the experimental results obtained by image processing, obtaining the change of the volume of single condensate droplet with time, and performing regression analysis to obtain the condensation rate of single condensate droplet on different wettable surfaces after condensation stabilization and establish a mathematical model to describe the dependence of condensation rate on surface wettability; Step S2, establishing calculation assumptions, obtaining the change relationship of single droplet volume and the change relationship of droplet radius in the region, specifically comprising, S21, ignoring the effect of gravity in the condensation process, i.e. the radius of condensate droplet is less than the capillary length; S22, the calculation formula of the droplet volume is , and the calculation formula of the droplet volume after replacement is , wherein, is the advancing angle, is the lateral radius of the condensate droplet;​ S23, obtaining a change amount of the transverse radius, wherein the change of the condensate droplets complies with is a time step in the numerical calculation; S24, obtaining the center of mass of any two droplets , the distance between the center of mass of any two droplets in a two-dimensional plane the calculation formula, wherein, Droplet coalescence will occur if the sum of the radii of two droplets is less than two. S25, obtaining the radius of the merged droplet Relationship: = ， Assuming that the centroid of the merged droplet does not change in a two-dimensional plane , we obtain: = , = ， wherein , , , is the radius of the droplet one instant before merging; Step S3, establishing a condensation system for tracking the change of condensate droplet parameters and the change of parameters after droplet merging; Step S4, outputting the results according to the condensation system and comparing and verifying with the actual implementation data.

2. A method of calculating condensation of a liquid droplet on a smooth surface as claimed in claim 1, characterized in that, The step S3 specifically comprises: According to the need, it is determined that in and a two-dimensional computing area of a plane ; According to the mathematical model describing the relationship between nucleation density and surface wettability, the nucleation density is determined, and then the droplet distribution at the initial moment of condensation is realized based on the random function; Labeling the initial droplet for tracking changes in parameters of individual condensed droplets.

3. The method of claim 1, wherein, The step S4 specifically comprises: According to the need, the simulation calculation is performed to obtain the change of radius, volume and surface coverage area of any single droplet with time and obtain the change of overall volume and surface coverage area of condensate droplets in the calculation region with time; Through experiments, the implementation data of corresponding single droplets and overall condensate droplets in the region are obtained, and the simulation calculation data are compared and analyzed.

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