Method and system for determining particle size distribution of ice slurry containing nanofluid salt solution

Abstract

The invention discloses a method and a system for determining particle size distribution of ice slurry containing a nanofluid salt solution, and relates to the technical field of ice slurry refrigeration, the method comprises the following steps: coupling a local concentration field of nanoparticles in a solution with a driving force in a phase change process to obtain a control relationship of the ice slurry containing the nanofluid salt solution; defining the ice crystal as a discrete phase, and establishing a dynamic relationship between the nucleation rate and the growth rate; solving the control relation based on the initial parameters of the dynamic relation, extracting size information of the ice crystals from a solving result, and dividing a plurality of characterization intervals according to the size information to obtain first volume fraction distribution of the ice crystals; according to the method disclosed by the invention, a dynamic relationship between nucleation and growth of an ice crystal dispersed phase is established by coupling a nanoparticle local concentration field and a phase change process driving force, and then theoretical solution and iterative calibration of experimental data are combined, so that accurate determination of the particle size distribution of the ice slurry containing the nanofluid salt solution is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of ice slurry refrigeration, and particularly relates to a method and system for determining the particle size distribution of ice slurry containing a nanofluid salt solution. BACKGROUND

[0002] Ice slurry refrigeration technology has been widely used in central air conditioning, industrial cooling and many other fields due to its high efficiency in latent heat storage and transportation, and has become one of the most promising refrigeration technologies under the background of energy saving and emission reduction. Ice slurry is composed of ice crystal particles and carrier liquid, and its heat exchange performance and flow characteristics are directly determined by the particle size distribution of the ice crystals. A uniform and suitable particle size distribution can significantly reduce flow resistance and improve heat transfer efficiency, while an unbalanced particle size distribution can easily cause problems such as pipe deposition and ice blockage, which seriously restricts the stable operation of the system.

[0003] However, the flow and heat transfer process of ice slurry in the heat exchange pipeline is accompanied by complex micro behaviors, including the growth, fragmentation, coalescence and interphase heat and mass transfer of ice crystals. These micro phenomena are coupled with each other and directly affect the macro performance of the ice slurry, making it difficult to accurately characterize the particle size distribution. Especially in the system of ice slurry containing nanofluid salt solution, the introduction of nanoparticles further aggravates the complexity of the problem: the nanoparticles change the key physical parameters such as thermal conductivity and viscosity of the fluid, and these physical parameters change nonlinearly with temperature, breaking the stability of the physical properties of the traditional ice slurry system and bringing additional challenges to the prediction of the particle size distribution.

[0004] In the prior art, the determination of the particle size distribution of ice slurry mainly relies on two methods, but both have defects that are difficult to overcome. On the one hand, traditional experimental observation methods are limited by measurement technology and coverage of working conditions, and it is difficult to capture the transient and local details of ice crystal distribution. Whether it is sampling analysis or online detection, it is difficult to fully restore the dynamic evolution trajectory of ice crystals in the flow process. Moreover, the experimental cost is high, the cycle is long, and it is difficult to adapt to the rapid characterization requirements under multiple working conditions, which seriously limits the accurate design and optimization of the heat exchange performance of the ice slurry system.

[0005] On the other hand, although existing numerical simulation studies attempt to use multiphase flow models or population balance models for simulation, there are obvious shortcomings in practical application: most models are simplified calculations that do not fully consider key physical mechanisms such as the dynamic growth process of ice crystals, the temperature dependence of physical parameters and the interaction between phases, resulting in large deviations between simulation results and actual working conditions and insufficient precision. At the same time, mainstream commercial CFD software lacks built-in models for ice slurry systems that are accompanied by complex phase change and dynamic changes of particles, and cannot accurately describe the evolution of ice crystal particle size. Even if embedded through self-programming functions, existing solutions cannot achieve fine simulation of growth, fragmentation and other mechanisms, and cannot meet the requirements of engineering applications for simulation accuracy.

[0006] In summary, existing technologies for determining the particle size distribution of ice slurries containing nanofluid salt solutions, whether through experimental methods or numerical simulations, suffer from problems such as incomplete consideration of physical mechanisms, insufficient simulation accuracy, and poor adaptability to operating conditions. These limitations make it difficult to accurately characterize the dynamic characteristics of particle size distribution during heat transfer. Therefore, there is an urgent need to develop a numerical determination method that can balance the integrity of physical mechanisms with simulation accuracy, thereby overcoming the shortcomings of traditional methods and providing reliable simulation tools and theoretical support for the efficient design and operating condition optimization of ice slurry refrigeration systems. Summary of the Invention

[0007] This invention provides a method and system for determining the particle size distribution of ice slurry containing nanofluid salt solution, in order to solve the problems mentioned in the background art.

[0008] To achieve the above objectives, the present invention provides a method for determining the particle size distribution of ice slurry containing nanofluidic salt solution, comprising:

[0009] S1. The local concentration field of nanoparticles in solution is coupled with the driving force of the phase transition process to obtain the control relationship of ice slurry containing nanofluid salt solution; ice crystals are defined as discrete phases, and the kinetic relationship between their nucleation rate and growth rate is established.

[0010] S2. Solve the control relationship based on the initial parameters of the dynamic relationship, extract the size information of ice crystals from the solution results, and divide multiple characterization intervals according to the size information to obtain the first volume fraction distribution of ice crystals.

[0011] S3. Pass the solution into the solid heat exchange pipe and let the solution flow under the boundary conditions that satisfy the control relationship. When the flow is stable, acquire dynamic images of the slurry at the outlet to obtain a dynamic image sequence of the slurry.

[0012] S4. Statistically analyze the projected size of ice crystals in the dynamic image sequence, divide the continuous particle size intervals according to the statistical results, and determine the proportion of the ice crystal volume to the total volume of the slurry in each interval to obtain the second volume fraction distribution.

[0013] S5. Using the overall shape of the second volume fraction distribution as the calibration benchmark, synchronously iteratively adjust the nucleation and growth parameters in the kinetic relationship, and through iterative solution and comparison, make the shape of the first volume fraction distribution converge to the benchmark, thereby determining the calibrated kinetic parameters;

[0014] S6. Substitute the calibrated kinetic parameters into the control relationship, and obtain the particle size distribution of the ice slurry under different working conditions by changing the working conditions and solving again.

[0015] Preferably, the coupling of the local concentration field of nanoparticles in the solution with the driving force of the phase transition process to obtain the control relationship of the nanofluidic salt solution ice slurry includes:

[0016] Microscopic imaging analysis of the solution was performed to extract the distribution density of nanoparticles in three-dimensional space, thus obtaining the spatial distribution of nanoparticle concentration.

[0017] Based on the principles of phase transition thermodynamics, a fundamental relationship of phase transition driving force determined by temperature difference is established;

[0018] The spatial distribution of concentration is used as a modulation factor, and a scalar multiplication operation is performed with the basic relationship of the phase transition driving force to obtain the modulated phase transition driving force.

[0019] The modulated phase change driving force is used as a source term and embedded into the basic conservation relationship describing solution flow and heat transfer to form a coupled control relationship.

[0020] Preferably, defining ice crystals as a discrete phase and establishing the kinetic relationship between their nucleation rate and growth rate includes:

[0021] Statistical analysis of microscopic nucleation events in solutions under supercooled conditions yielded statistical data on the initial number of ice crystal nuclei per unit volume as a function of temperature and local nanoparticle concentration, which served as data on nucleation patterns.

[0022] The interfacial propagation velocity of ice crystals under constant supercooling conditions was measured to obtain the corresponding data between the interfacial propagation velocity and supercooling, which can be used as data on growth patterns.

[0023] Based on the heterogeneous nucleation theory, the nucleation law data were processed to obtain the nucleation rate relationship between the nucleation rate and the local nanoparticle concentration and local supercooling.

[0024] Based on the theory of interface dynamics, growth data were processed to obtain the relationship between growth rate and local supercooling.

[0025] Preferably, the control relationship is solved based on the initial parameters of the dynamic relationship, the size information of the ice crystals is extracted from the solution, and multiple characterization intervals are divided according to the size information to obtain the first volume fraction distribution of the ice crystals, including:

[0026] The initial parameters of the dynamic relationship are applied to the control relationship for numerical iteration to obtain the phase state and attribute data of each analysis location in the flow field;

[0027] Retrieve phase and property data, locate the part belonging to the ice crystal solid phase, analyze the geometric characterization parameters of this part, and form a list of ice crystal sizes;

[0028] Based on the density of values ​​in the ice crystal size list, multiple boundary points are set to define continuous size groups;

[0029] For each size group, the total volume of all ice crystal solid phase portions contained therein is summarized, and the share of this total volume in the total fluid volume in the flow field is determined to obtain the first volume fraction distribution.

[0030] Preferably, the step of dynamically acquiring images of the outlet slurry to obtain a dynamic image sequence of the slurry includes:

[0031] Backlight sources and high-speed imaging equipment are installed at the exit. The intensity and angle of the backlight sources are adjusted to create a uniform backlight environment at the exit to highlight the outline of the ice crystals.

[0032] Start the high-speed imaging device, set its acquisition frame rate and exposure time, and make it continuously capture images of the stable flow field at the outlet to obtain a set of original images arranged in chronological order.

[0033] Contrast enhancement is performed on each image in the original image set to obtain a dynamic image sequence.

[0034] Preferably, the step of statistically analyzing the projected sizes of ice crystals in the dynamic image sequence, dividing continuous particle size intervals based on the statistical results, and determining the proportion of ice crystal volume to the total slurry volume within each interval to obtain a second volume fraction distribution includes:

[0035] Contour analysis is performed on each image in the dynamic image sequence to mark the projection regions of all ice crystals and obtain the equivalent circle diameter data for each region;

[0036] The equivalent circle diameter data of all images are summarized, sorted by numerical value, and several dividing values ​​are determined based on the cumulative frequency distribution of data points to define continuous particle size intervals.

[0037] For each continuous particle size interval, the equivalent circle diameter of all ice crystal projection regions within the continuous particle size interval is selected. Based on the sphere assumption, the equivalent circle diameter is converted into the volume estimate of a single ice crystal, and the total volume estimate of the ice crystals in that interval is obtained by summing them up.

[0038] Determine the proportion of the total ice crystal volume in the total volume of the slurry sample for each interval, and construct a second volume fraction distribution based on the volume proportions of all intervals.

[0039] Preferably, the calibration benchmark based on the overall shape of the second volume fraction distribution includes:

[0040] The volume percentage values ​​of each particle size range are extracted from the second volume fraction distribution and arranged in order of particle size to form the first data sequence;

[0041] Perform morphological quantization analysis on the first data sequence to obtain at least one set of feature values ​​describing the overall morphology;

[0042] At least one set of feature values ​​is combined to establish a calibration benchmark for subsequent comparisons.

[0043] Preferably, the synchronous iterative adjustment of nucleation and growth parameters in the kinetic relationship, through iterative solution and comparison, converges the first volume fraction distribution morphology to a reference, thereby determining the calibrated kinetic parameters, including:

[0044] Based on the current nucleation and growth parameters, the control relationship is solved to obtain the current first volume fraction distribution, and the distribution is fitted with a function to obtain the current function expression;

[0045] Determine the difference between the current function expression and the benchmark, and determine the adjustment amount and direction of the nucleation and growth parameters based on the difference;

[0046] Multiple iterative adjustments are performed, and the continuous changes in the adjustment amount are recorded. When the adjustment amount approaches zero and the adjustment direction remains unchanged, the calibration is considered complete, and the parameters used in the last iteration are recorded as the calibrated kinetic parameters.

[0047] Preferably, the step of substituting the calibrated kinetic parameters into the control relationship, and obtaining the particle size distribution of the ice slurry under different operating conditions by changing the operating conditions and resolving the problem includes:

[0048] The operating condition parameters under different operating scenarios are defined and sorted to obtain a set of operating condition sequences;

[0049] Based on the sequence of operating conditions, the boundary and inlet conditions of the control relationship are updated sequentially, and the solution is completed to obtain a set of particle size distribution results corresponding to each condition.

[0050] The particle size distribution result set is correlated and mapped with the corresponding operating condition parameters to form a complete operating condition-particle size distribution prediction spectrum.

[0051] To address the aforementioned problems, the present invention also provides a system for determining the particle size distribution of ice slurry containing nanofluidic salt solution, the system comprising:

[0052] The relation construction module is used to couple the local concentration field of nanoparticles in solution with the driving force of the phase transition process to obtain the control relationship of ice slurry containing nanofluid salt solution; ice crystals are defined as discrete phases, and the kinetic relationship between their nucleation rate and growth rate is established.

[0053] The feature extraction module is used to solve the control relationship based on the initial parameters of the dynamic relationship, extract the size information of ice crystals from the solution results, and divide multiple characterization intervals according to the size information to obtain the first volume fraction distribution of ice crystals.

[0054] The experimental data acquisition module is used to introduce the solution into the solid heat exchange pipe, so that the solution flows under the boundary conditions that meet the control relationship. When the flow is stable, dynamic images of the outlet slurry are acquired to obtain a dynamic image sequence of the slurry.

[0055] The image processing module is used to statistically analyze the projected size of ice crystals in the dynamic image sequence, divide the continuous particle size intervals according to the statistical results, and determine the proportion of the ice crystal volume to the total volume of the slurry in each interval to obtain the second volume fraction distribution.

[0056] The parameter iterative calibration module is used to synchronously and iteratively adjust the nucleation and growth parameters in the kinetic relationship with the overall morphology of the second volume fraction distribution as the calibration benchmark. Through iterative solution and comparison, the morphology of the first volume fraction distribution converges to the benchmark, thereby determining the calibrated kinetic parameters.

[0057] The distribution prediction application module substitutes the calibrated kinetic parameters into the control relationship, and obtains the particle size distribution of ice slurry under different working conditions by changing the working conditions and resolving.

[0058] Compared with the prior art, the present invention has the following beneficial effects:

[0059] 1. By coupling the local concentration field of nanoparticles with the driving force of the phase transition process, the nucleation and growth kinetics of the discrete phase of ice crystals are established. Combined with theoretical solutions and iterative calibration of experimental data, the particle size distribution of ice slurry containing nanofluid salt solutions is accurately determined. This allows for the full capture of the influence of the spatial heterogeneity of nanoparticle distribution on ice crystal formation, as well as the dynamic evolution law of ice crystals under changing operating conditions. The particle size distribution characterization conforms to the logic of thermodynamic and kinetic theories and fits the actual flow heat transfer scenario, significantly improving the accuracy and reliability of particle size distribution determination under different operating conditions, and providing precise data support for the design and optimization of ice slurry systems.

[0060] 2. By using microscopic imaging analysis and scalar multiplication to achieve precise modulation of the phase transition driving force, and working in conjunction with iterative calibration logic based on distribution morphology characteristics, the calibration of dynamic parameters becomes more targeted and stable, significantly reducing the deviation between the theoretical model and actual working conditions. At the same time, the environmental optimization and contrast enhancement technology of dynamic image acquisition complements the equivalent circle diameter statistics and the sphere assumption volume conversion method, ensuring the integrity and accuracy of experimental data, providing a high-quality benchmark for theoretical model calibration, and further improving the consistency and universality of particle size distribution prediction under multiple working conditions. Attached Figure Description

[0061] Figure 1 This is a flowchart illustrating a method for determining the particle size distribution of an ice slurry containing a nanofluid salt solution according to an embodiment of the present invention.

[0062] Figure 2 This is a functional block diagram of a system for determining the particle size distribution of an ice slurry containing a nanofluid salt solution, provided in an embodiment of the present invention. Figure 3 This shows the variation in the volume fraction of ice crystal particles ranging from 0 to 0.1 mm in the invention.

[0063] Figure 4 This illustrates the volume fraction variation of 0.1-0.2 mm ice crystal particles in this invention.

[0064] Figure 5 This shows the volume fraction variation of 0.2-0.3mm ice crystal particles in this invention;

[0065] Figure 6 This shows the volume fraction variation of 0.3-0.4mm ice crystal particles in this invention;

[0066] Figure 7 This shows the volume fraction variation of 0.4-0.5mm ice crystal particles in this invention.

[0067] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0068] It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0069] This application provides a method for determining the particle size distribution of ice slurry containing nanofluid salt solution. The execution subject of this method includes, but is not limited to, at least one of the following electronic devices that can be configured to execute the method provided in this application: a server, a terminal, etc. In other words, the method for determining the particle size distribution of ice slurry containing nanofluid salt solution can be executed by software or hardware installed on a terminal device or a server device. The server includes, but is not limited to, a single server, a server cluster, a cloud server, or a cloud server cluster. The server can be an independent server or a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, content delivery networks (CDN), and big data and artificial intelligence platforms.

[0070] Example 1, referring to Figure 1 , Figures 3-7 As shown. In this embodiment, a method for determining the particle size distribution of an ice slurry containing a nanofluidic salt solution includes:

[0071] S1. The local concentration field of nanoparticles in solution is coupled with the driving force of the phase transition process to obtain the control relationship of ice slurry containing nanofluid salt solution; ice crystals are defined as discrete phases, and the kinetic relationship between their nucleation rate and growth rate is established.

[0072] S2. Solve the control relationship based on the initial parameters of the dynamic relationship, extract the size information of ice crystals from the solution results, and divide multiple characterization intervals according to the size information to obtain the first volume fraction distribution of ice crystals.

[0073] S3. Pass the solution into the solid heat exchange pipe and let the solution flow under the boundary conditions that satisfy the control relationship. When the flow is stable, acquire dynamic images of the slurry at the outlet to obtain a dynamic image sequence of the slurry.

[0074] S4. Statistically analyze the projected size of ice crystals in the dynamic image sequence, divide the continuous particle size intervals according to the statistical results, and determine the proportion of the ice crystal volume to the total volume of the slurry in each interval to obtain the second volume fraction distribution.

[0075] S5. Using the overall shape of the second volume fraction distribution as the calibration benchmark, synchronously iteratively adjust the nucleation and growth parameters in the kinetic relationship, and through iterative solution and comparison, make the shape of the first volume fraction distribution converge to the benchmark, thereby determining the calibrated kinetic parameters;

[0076] S6. Substitute the calibrated kinetic parameters into the control relationship, and obtain the particle size distribution of the ice slurry under different working conditions by changing the working conditions and solving again.

[0077] In this embodiment, the local concentration field of nanoparticles in the solution is coupled with the driving force of the phase transition process to obtain the control relationship of the nanofluidic salt solution ice slurry, including:

[0078] Microscopic imaging analysis of the solution was performed to extract the distribution density of nanoparticles in three-dimensional space, thus obtaining the spatial distribution of nanoparticle concentration.

[0079] Based on the principles of phase transition thermodynamics, a fundamental relationship of phase transition driving force determined by temperature difference is established;

[0080] The spatial distribution of concentration is used as a modulation factor, and a scalar multiplication operation is performed with the basic relationship of the phase transition driving force to obtain the modulated phase transition driving force.

[0081] The modulated phase change driving force is used as a source term and embedded into the basic conservation relationship describing solution flow and heat transfer to form a coupled control relationship.

[0082] The phase change driving force modulation is achieved through the following formula:

[0083]

[0084] In the formula, The modulated phase transition driving force, i.e., the heterogeneous nucleation energy barrier, is a spatial location. The function.

[0085] The modulation factor is the local volume fraction of nanoparticles. The function, That is, the core parameter obtained from the "concentration spatial distribution".

[0086] The fundamental relationship representing the driving force of phase transition, namely the homogeneous nucleation energy barrier, is usually related to the supercooling (ΔT), as follows:

[0087]

[0088] In practice, a high-resolution three-dimensional microscope is used to continuously and dynamically photograph the salt solution containing nanofluids to obtain three-dimensional microscopic images of the nanoparticles inside the solution.

[0089] Furthermore, by converting the image pixel size into the actual spatial scale through pixel calibration, the contours and position coordinates of nanoparticles in the image are identified frame by frame.

[0090] Furthermore, the number of nanoparticles within each fixed-volume micro-element is counted, and the total volume of nanoparticles within that micro-element is calculated by combining the volume of a single nanoparticle with that volume. This yields the volume fraction of nanoparticles per unit volume of solution, i.e., the distribution density of nanoparticles, ultimately forming a spatial distribution of concentration covering the entire solution space. The core parameter in this distribution is the local nanoparticle volume fraction corresponding to each spatial location.

[0091] It should be noted that nanoparticles include, but are not limited to, silicon dioxide, aluminum oxide, silver, copper, etc.

[0092] Furthermore, the freezing point of the salt solution was first determined using the cooling curve method: a salt solution of the same concentration without nanoparticles was placed in a temperature control device and slowly cooled, and the temperature change over time was recorded in real time. The temperature corresponding to the stage when the temperature remained constant was the freezing point of the salt solution. The freezing point of the salt solution containing nanofluids was then determined using the same measurement results. Based on the principle of energy conservation in solidification phase transition in phase transition thermodynamics, the core influencing factor of the phase transition driving force was identified as the difference between the actual temperature of the solution and the freezing point, i.e., the supercooling.

[0093] Furthermore, by analyzing the influence of supercooling on the energy barrier during phase transition, a homogeneous nucleation energy barrier relationship with supercooling as the core variable is established. It is clarified that the homogeneous nucleation energy barrier decreases with the increase of supercooling, and the two are inversely proportional. Specifically, the homogeneous nucleation energy barrier is inversely proportional to the square of supercooling. This relationship is the fundamental relationship of the phase transition driving force.

[0094] Furthermore, based on the local nanoparticle volume fraction corresponding to each spatial location in the concentration spatial distribution, multiple groups of nanofluid-containing salt solution samples with different volume fractions were designed. The actual values ​​of the phase transition driving force of each group of samples were measured through comparative experiments. The correspondence between the local nanoparticle volume fraction and the change amplitude of the phase transition driving force was analyzed, and the form of the modulation factor that can accurately reflect this law was determined. The value of the modulation factor will be adaptively adjusted with the change of the local nanoparticle volume fraction.

[0095] Furthermore, for each spatial location in the solution, the modulation factor value corresponding to that location is multiplied by the homogeneous nucleation barrier value corresponding to that location. This allows the homogeneous nucleation barrier at each location to be adaptively adjusted according to the local nanoparticle volume fraction, ultimately yielding a heterogeneous nucleation barrier specific to each spatial location. This heterogeneous nucleation barrier is the modulated phase transition driving force, and its physical meaning is the phase transition energy barrier after considering the influence of local nanoparticle concentration.

[0096] Furthermore, the momentum conservation relation describing the flow state of the solution and the energy conservation relation describing the heat transfer process are selected as the basic conservation relations. These two relations are used to quantify the flow characteristics and heat transfer laws of the solution, respectively.

[0097] Finally, the modulated phase change driving force is used as a source term reflecting the influence of the phase change process on flow and heat transfer. Through mathematical derivation, this source term is incorporated into the expressions of momentum conservation and energy conservation, so that the interaction between the flow process, heat transfer process and phase change process can be quantitatively described. Finally, a control relationship that couples the local concentration field of nanoparticles and the phase change driving force is formed. This relationship can simultaneously characterize the synergistic effect of the three.

[0098] In this embodiment, ice crystals are defined as a discrete phase, and a kinetic relationship between their nucleation rate and growth rate is established, including:

[0099] Statistical analysis of microscopic nucleation events in solutions under supercooled conditions yielded statistical data on the initial number of ice crystal nuclei per unit volume as a function of temperature and local nanoparticle concentration, which served as data on nucleation patterns.

[0100] The interfacial propagation velocity of ice crystals under constant supercooling conditions was measured to obtain the corresponding data between the interfacial propagation velocity and supercooling, which can be used as data on growth patterns.

[0101] Based on the heterogeneous nucleation theory, the nucleation law data were processed to obtain the nucleation rate relationship between the nucleation rate and the local nanoparticle concentration and local supercooling.

[0102] Based on the theory of interface dynamics, growth data were processed to obtain the relationship between growth rate and local supercooling.

[0103] The nucleation rate formula is as follows:

[0104]

[0105] In the formula, Represents the nucleation rate, which is a spatial location. The function, Indicates the kinetic precondition factor. This represents the modulated phase transition driving force. Represents the Boltzmann constant. This indicates absolute temperature.

[0106] The growth rate formula is as follows:

[0107]

[0108] In the formula, Indicates growth rate, which is spatial location. The function, Represents the growth rate constant. This indicates localized supercooling.

[0109] Specifically, the salt solution containing nanofluid is sealed and placed in a high-precision temperature control device. The temperature inside the device is gradually reduced through program control, so that the solution enters a supercooled state. At the same time, the actual temperature of the solution is monitored in real time by a temperature sensor, and the monitored Celsius temperature is converted into Kelvin temperature as the absolute temperature.

[0110] At the same time, a high-speed microscopic imaging system is used to record the microscopic changes inside the solution in real time. Image recognition technology is used to accurately capture the formation time and location of each ice crystal nucleus, ensuring that no microscopic nucleation event is missed.

[0111] Furthermore, the initial number of ice crystal nuclei appearing per unit volume of solution under different temperature conditions and different local nanoparticle concentration regions was statistically analyzed. To eliminate the interference of accidental factors, at least three parallel experiments were conducted under each experimental condition. The average value of the experimental results was taken, and the corresponding data of temperature, local nanoparticle concentration and initial number of ice crystal nuclei per unit volume were compiled. This data is the nucleation law data, which can directly reflect the correlation between the number of nuclei and key influencing factors.

[0112] Furthermore, the solution is stabilized at a fixed supercooling degree using a temperature control device, and a high-magnification microscope is used to focus on a single initial ice crystal. Image information of the ice crystal interface is acquired in real time using an image acquisition device to ensure that the image resolution meets the requirements for interface position recognition.

[0113] Furthermore, by using image analysis technology to track the spatial position changes of the interface, recording the interface coordinates at different times at fixed time intervals, calculating the straight-line distance of the interface movement between two adjacent times, and then dividing this distance by the time interval between the two times, we can obtain the movement distance of the ice crystal interface per unit time, i.e., the interface propagation speed.

[0114] Furthermore, the supercooling value was changed and the above measurement operation of the interface propagation speed was repeated. After each change, other experimental conditions were kept unchanged, and multiple sets of data on different supercooling values ​​and corresponding interface propagation speeds were obtained. This data is the growth law data, which can directly reflect the relationship between growth rate and supercooling.

[0115] Furthermore, based on the regulation mechanism of the phase transition energy barrier on the nucleation process in the heterogeneous nucleation theory, a systematic analysis of the nucleation law data was conducted to clarify the intrinsic logic that the local nanoparticle concentration affects the number of ice crystal nuclei formed by changing the size of the heterogeneous nucleation energy barrier. That is, the higher the local nanoparticle concentration, the lower the heterogeneous nucleation energy barrier, and the greater the initial number of ice crystal nuclei per unit volume.

[0116] Furthermore, based on the correspondence between temperature, local nanoparticle concentration and the initial number of ice crystal nuclei per unit volume in the nucleation law data, and combined with the correlation logic of various parameters in the heterogeneous nucleation theory, the least squares method is used to fit the data. By minimizing the deviation between the theoretical calculation value and the experimental measurement value, the specific value of the kinetic precondition factor is determined. Then, combined with the recognized physical value of the Boltzmann constant, the correlation between the nucleation rate and the local nanoparticle concentration, local supercooling and absolute temperature is established.

[0117] The local supercooling affects the nucleation rate by determining the size of the heterogeneous nucleation energy barrier, while the absolute temperature affects the thermal motion probability of the nucleation process by combining with the Boltzmann constant. Specifically, the smaller the ratio of the heterogeneous nucleation energy barrier to the product of the Boltzmann constant and the absolute temperature, the larger the value of the exponential term, and the higher the nucleation rate. Finally, a nucleation rate relationship that can accurately describe the nucleation intensity at different spatial locations is obtained.

[0118] Furthermore, based on the driving mechanism of supercooling on crystal growth in the theory of interface dynamics, the growth law data were fitted and analyzed. Based on the correspondence between supercooling and interface propagation speed in the growth law data, the least squares method was used to minimize the deviation between the theoretical value and the experimental data, and the specific value of the growth rate constant was determined.

[0119] Finally, the quantitative relationship between ice crystal growth rate and local supercooling is clarified. That is, the growth rate increases with the increase of local supercooling, and the growth rate is directly proportional to the square of the local supercooling. In specific operation, first obtain the local supercooling value at a certain spatial location, multiply the value by itself to obtain the square value of supercooling, and then multiply the square value by the growth rate constant to obtain the ice crystal growth rate at that spatial location. Finally, the growth rate relationship reflecting the dependence of ice crystal growth rate on local supercooling is obtained.

[0120] In summary, this embodiment incorporates the local concentration field as a modulation factor into the phase transition driving force, and obtains the spatially specific heterogeneous nucleation energy barrier through scalar multiplication. This enables the control relationship to accurately reflect the influence of the concentration difference of nanoparticles in different regions on the phase transition process, avoiding the error caused by the average concentration assumption. This makes the control relationship describing the coupling of solution flow, heat transfer and phase transition more consistent with the actual physical process, and significantly improves the authenticity and accuracy of the theoretical model.

[0121] In summary, this embodiment defines ice crystals as a discrete phase and establishes a correlation between nucleation rate and local nanoparticle concentration and supercooling, as well as a quantitative relationship between growth rate and local supercooling, based on heterogeneous nucleation theory and interface dynamics theory. This achieves a quantitative characterization of the ice crystal formation process. This quantitative relationship makes nucleation and growth no longer vague macroscopic phenomena, but physical processes that can be controlled by key parameters (such as local concentration and supercooling), providing a clear calculation basis for subsequent numerical solutions of ice crystal size information.

[0122] In this embodiment, the control relationship is solved based on the initial parameters of the dynamic relationship. The size information of the ice crystals is extracted from the solution results, and multiple characterization intervals are divided according to the size information to obtain the first volume fraction distribution of the ice crystals, including:

[0123] The initial parameters of the dynamic relationship are applied to the control relationship for numerical iteration to obtain the phase state and attribute data of each analysis location in the flow field;

[0124] Retrieve phase and property data, locate the part belonging to the ice crystal solid phase, analyze the geometric characterization parameters of this part, and form a list of ice crystal sizes;

[0125] Based on the density of values ​​in the ice crystal size list, multiple boundary points are set to define continuous size groups;

[0126] For each size group, the total volume of all ice crystal solid phase portions contained therein is summarized, and the share of this total volume in the total fluid volume in the flow field is determined to obtain the first volume fraction distribution.

[0127] Specifically, the initial parameters of the dynamic relationship are applied to the control relationship for numerical iteration. First, the initial parameters in the nucleation rate relationship and the growth rate relationship are substituted into the coupled control relationship. The iteration convergence condition is set, that is, the difference between the flow field data obtained by two adjacent iterations is less than a set threshold. Starting from the initial state of the flow field, the physical quantities of each analysis position at each time node are calculated sequentially according to a fixed time step. The data is continuously updated through iteration until the convergence condition is met, and finally the phase state and attribute data of each analysis position in the flow field are obtained.

[0128] Furthermore, phase and attribute data are retrieved, and different phases are distinguished by phase identification information. The part belonging to the ice crystal solid phase is located. For this part of the solid phase data, geometric characterization parameters that can characterize the geometric features of the ice crystal are extracted. All extracted geometric characterization parameters are arranged according to the analysis location to form an ice crystal size list.

[0129] Furthermore, based on the density of values ​​in the ice crystal size list, the values ​​in the list are sorted in ascending order, and the intervals between adjacent values ​​after sorting are counted. Areas with small intervals and concentrated values ​​are divided into the same preliminary range. Boundary points are determined at both ends of the preliminary range, and continuous and non-overlapping size groups are defined by multiple such boundary points.

[0130] Finally, for each size group, the volume data of all the solid phase ice crystals contained in the group are counted one by one. These volume data are accumulated to obtain the total volume of ice crystals in the group. The total volume of all fluids in the flow field is measured and determined. The total volume of ice crystals in each group is divided by the total volume of all fluids in the flow field to obtain the share of ice crystals in the total volume of fluids in the flow field in that group. The share data of all groups together constitute the first volume fraction distribution.

[0131] In summary, this embodiment, based on the control and dynamic relationships established in S1, extracts ice crystal size information through numerical iteration, overcoming the limitation of traditional methods in quantifying the global ice crystal characteristics of the flow field. The numerical iteration process strictly follows the set convergence conditions, ensuring the accuracy and reliability of phase and attribute data at each analysis location in the flow field. Furthermore, phase identification is used to locate the ice crystal solid phase and analyze geometric parameters, providing a clear theoretical basis and rigorous operational logic for extracting ice crystal size information. This effectively avoids local deviations that easily occur in direct measurements and improves the accuracy of the basic particle size data.

[0132] In summary, this embodiment divides the characterization intervals based on the density of ice crystal size values, rather than using fixed equidistant intervals, which better reflects the natural distribution pattern of ice crystal particle size. This grouping method based on the characteristics of the data itself can accurately capture concentrated and sparse regions of particle size, making subsequent volume fraction statistics more targeted and avoiding the distortion of distribution patterns caused by unreasonable interval divisions. This allows the first volume fraction distribution to truly reflect the theoretical particle size distribution characteristics.

[0133] In this embodiment, dynamic image acquisition is performed on the outlet slurry to obtain a dynamic image sequence of the slurry, including:

[0134] Backlight sources and high-speed imaging equipment are installed at the exit. The intensity and angle of the backlight sources are adjusted to create a uniform backlight environment at the exit to highlight the outline of the ice crystals.

[0135] Start the high-speed imaging device, set its acquisition frame rate and exposure time, and make it continuously capture images of the stable flow field at the outlet to obtain a set of original images arranged in chronological order.

[0136] Contrast enhancement is performed on each image in the original image set to obtain a dynamic image sequence.

[0137] In practice, the backlight source can be fixed on a bracket on one side of the flow channel outside the outlet, and the high-speed imaging device can be fixed on the other side of the flow channel opposite to the backlight source, ensuring that the central axis of both is perpendicular to and coplanar with the flow direction of the slurry in the flow channel.

[0138] Then turn on the backlight source, adjust the light source intensity by adjusting the power knob, and slowly rotate the angle adjustment bracket of the light source. Observe the preview screen of the high-speed imaging device in real time until the background brightness of the flow channel area in the preview screen is uniform and consistent, without obvious bright spots or dark areas, forming a uniform backlight environment that can produce clear light and dark contrast between the ice crystals and the background to highlight the outline of the ice crystals.

[0139] Furthermore, the control system of the high-speed imaging equipment is activated, and the acquisition frame rate of the equipment is set according to the expected flow rate of the slurry in the channel to ensure that the frame rate can capture the continuous movement of the ice crystals in the channel. At the same time, the exposure time is set so that the edges of the ice crystals in the preview image are free of ghosting and the details are clear.

[0140] Furthermore, the focal length of the lens of the high-speed imaging device is adjusted so that the stable flow field of the slurry at the outlet completely fills the field of view. After the equipment parameters stabilize, continuous shooting begins. During the shooting process, all parameters remain unchanged, and the captured images are automatically stored in chronological order to form a set of original images arranged in chronological order.

[0141] Finally, the first image in the original image set is selected, and the grayscale range of the image is determined by comparing the grayscale values ​​of the image pixels one by one. The pixels corresponding to the lowest grayscale value in the image are adjusted to the minimum grayscale level, and the pixels corresponding to the highest grayscale value are adjusted to the maximum grayscale level.

[0142] Simultaneously, the grayscale values ​​of all pixels in the image are stretched linearly to increase the grayscale difference between the ice crystal region and the background region, thus enhancing the contrast of a single image. Following the same grayscale stretching operation, each image in the original image set is processed sequentially. All processed images maintain the same temporal order as the original image set, ultimately resulting in a dynamic image sequence.

[0143] In summary, this embodiment ensures that the experimental environment is highly consistent with the theoretical model assumptions established in S1 by introducing the solution into a solid heat exchange pipe and strictly adhering to the boundary conditions of the control relationship. The solid pipe simulates the flow scenario in actual applications, avoiding the limitations of pure numerical simulation that deviates from engineering reality. At the same time, by controlling boundary conditions, such as temperature and flow rate, the solution flow state is matched with the flow field settings in the theoretical model, reducing the systematic deviation between experiment and theory, and laying a consistent foundation for subsequent comparison and calibration of experimental data and theoretical results.

[0144] In summary, the design of waiting for the flow to stabilize before data collection in this embodiment effectively eliminates interference from transient flow processes. In the initial stages of solution flow, issues such as flow velocity fluctuations and uneven temperature distribution may occur, leading to abnormal ice crystal morphology and distribution. Under stable flow conditions, the formation and movement of ice crystals more closely resemble the actual working conditions, ensuring the representativeness of the collected ice crystal information, avoiding the impact of transient errors on subsequent data processing, and improving the reliability of experimental data.

[0145] In summary, this embodiment overcomes the limitations of traditional static sampling by employing a dynamic image acquisition method. By arranging a backlight source and a high-speed imaging device to create a uniform backlight environment, the outline of the ice crystals can be clearly highlighted. Combined with high frame rate continuous shooting and contrast enhancement processing, a dynamic image sequence is formed, which can not only capture the instantaneous shape of the ice crystals but also record their continuous motion state, avoiding the accidental deviations of a single static image.

[0146] In this embodiment, the projected size of ice crystals in the dynamic image sequence is statistically analyzed. Based on the statistical results, continuous particle size intervals are divided, and the proportion of ice crystal volume to the total slurry volume in each interval is determined to obtain a second volume fraction distribution, including:

[0147] Contour analysis is performed on each image in the dynamic image sequence to mark the projection regions of all ice crystals and obtain the equivalent circle diameter data for each region;

[0148] The equivalent circle diameter data of all images are summarized, sorted by numerical value, and several dividing values ​​are determined based on the cumulative frequency distribution of data points to define continuous particle size intervals.

[0149] For each continuous particle size interval, the equivalent circle diameter of all ice crystal projection regions within the continuous particle size interval is selected. Based on the sphere assumption, the equivalent circle diameter is converted into the volume estimate of a single ice crystal, and the total volume estimate of the ice crystals in that interval is obtained by summing them up.

[0150] Determine the proportion of the total ice crystal volume in the total volume of the slurry sample for each interval, and construct a second volume fraction distribution based on the volume proportions of all intervals.

[0151] Specifically, for each image in the dynamic image sequence, the grayscale threshold for distinguishing ice crystals from the background is first determined by comparing the pixel grayscale values ​​point by point. Areas with grayscale values ​​higher than the threshold are identified as candidate regions for ice crystals. Then, the edge tracking method is used to scan point by point along the boundary of the candidate region, and the continuous boundary points are connected to form a closed contour, thereby marking the projection area of ​​all ice crystals.

[0152] Furthermore, for each marked projection area, the number of pixels in the area is counted by scanning line by line. Combined with the correspondence between image pixel size and actual spatial scale, the number of pixels is converted into the actual area of ​​the projection area. Then, according to the correspondence between the area and diameter of a circle, the diameter of a circle with the same area as the projection area is calculated, thus obtaining the equivalent circle diameter data for each projection area.

[0153] Furthermore, the equivalent circle diameter data corresponding to all images in the dynamic image sequence are extracted and integrated into the same dataset, and the equivalent circle diameter data in the dataset are arranged in ascending order of value.

[0154] Furthermore, after statistically arranging all data points, the cumulative frequency corresponding to each data point is calculated, which is the proportion of the number of the data point and all previous data points to the total number. Based on the distribution characteristics of the cumulative frequency, the equivalent circle diameter values ​​corresponding to multiple cumulative frequencies are selected as separator values. Each adjacent separator value forms a continuous and non-overlapping range, and these ranges together constitute a continuous particle size interval.

[0155] Furthermore, for each continuous particle size interval, all equivalent circle diameter data falling within that interval are filtered out from the dataset.

[0156] Based on the sphere assumption, the diameter of each selected equivalent circle is regarded as the sphere diameter of the corresponding ice crystal. By measuring the length of this diameter, the volume of the ice crystal with this diameter as the sphere diameter is calculated as the volume estimate of a single ice crystal.

[0157] The volume estimates of all individual ice crystals within the range are summed sequentially, and the cumulative result is the total volume estimate of ice crystals in that continuous particle size range.

[0158] Furthermore, by measuring the cross-sectional area of ​​the slurry flow channel corresponding to the acquisition of dynamic image sequences, and combining the acquisition time of the high-speed imaging equipment with the flow velocity of the slurry, the total volume of the slurry passing through the field of view during the acquisition period, i.e., the total volume of the slurry sample, is calculated.

[0159] Then, the estimated total ice crystal volume for each continuous particle size interval is divided by the total volume of the slurry sample to obtain the proportion of ice crystal volume to the total slurry volume in each interval.

[0160] Finally, all continuous particle size ranges and their corresponding volume fractions are arranged in ascending order of particle size to form the second volume fraction distribution.

[0161] In summary, this method extracts ice crystal sizes using contour analysis and equivalent circle diameter conversion, overcoming the limitations of traditional manual measurement or static sampling. By employing grayscale thresholding and edge tracking, the projected areas of all ice crystals in each image are precisely marked. Combined with pixel calibration and area equivalence conversion, the two-dimensional projection information is transformed into equivalent circle diameter data characterizing the actual size of the ice crystals. This effectively avoids measurement deviations caused by irregular ice crystal morphology, ensuring the objectivity and accuracy of the basic particle size data.

[0162] In summary, this approach divides continuous particle size intervals based on the cumulative frequency distribution of data, reflecting respect for the natural distribution patterns of ice crystals. Unlike mechanical division methods with fixed equidistant intervals, this method determines reasonable separation values ​​by statistically analyzing the distribution density and cumulative frequency of all equivalent circle diameter data. This ensures that the particle size intervals accurately match the concentration and sparsity characteristics of the data itself, avoiding distortion of the distribution pattern caused by improper interval division. Furthermore, it allows the second volume fraction distribution to more accurately reflect the actual ice crystal particle size distribution characteristics under real-world conditions.

[0163] In summary, this scheme achieves volume conversion and proportion statistics through the spherical assumption, completing a quantitative upgrade from a single size parameter to overall distribution characteristics. By treating the equivalent circular diameter as the diameter of the ice crystal spheres and combining the pipe cross-sectional area, flow velocity, and collection time, the total volume of the slurry is calculated. This accurately verifies the volume proportion of ice crystals in each particle size range, transforming dispersed size data into a systematic volume fraction distribution. This generates complete experimental data that can be directly compared with theoretical calculations, building a quantitative bridge between experiment and theory.

[0164] In this embodiment, the overall shape of the second volume fraction distribution is used as the calibration benchmark, including:

[0165] The volume percentage values ​​of each particle size range are extracted from the second volume fraction distribution and arranged in order of particle size to form the first data sequence;

[0166] Perform morphological quantization analysis on the first data sequence to obtain at least one set of feature values ​​describing the overall morphology;

[0167] At least one set of feature values ​​is combined to establish a calibration benchmark for subsequent comparisons.

[0168] In practice, the volume percentage values ​​corresponding to each continuous particle size interval are extracted from the second volume fraction distribution. First, all continuous particle size intervals included in the second volume fraction distribution are sorted out to clarify the particle size range and corresponding volume percentage of each interval. Then, the volume percentage values ​​of each interval are arranged in order of increasing particle size range to form the first data sequence.

[0169] Furthermore, morphological quantification analysis is performed on the first data sequence, and the peak position distribution width and cumulative percentage inflection point are selected as feature values ​​to describe the overall morphology.

[0170] When determining the peak position, each volume percentage value in the first data sequence is traversed one by one to find the particle size range corresponding to the largest volume percentage value, and the center particle size of the particle size range is used as the peak position feature value.

[0171] When calculating the distribution width, first set the minimum effective proportion, filter out all particle size intervals in the first data sequence whose volume proportion is greater than the minimum effective proportion, extract the minimum particle size boundary and the maximum particle size boundary of these intervals, and subtract the minimum particle size boundary from the maximum particle size boundary to obtain the distribution width feature value.

[0172] When determining the inflection point of the cumulative proportion, starting from the beginning of the first data sequence, the volume proportion of each interval is accumulated sequentially to obtain the cumulative proportion. The difference between two adjacent cumulative proportions is the rate of change of the cumulative proportion. The particle size value corresponding to the position with the largest rate of change is found as the characteristic value of the inflection point of the cumulative proportion.

[0173] Finally, the three sets of characteristic values ​​obtained—peak position distribution width and cumulative percentage inflection point—are combined in sequence to form a characteristic value set. This characteristic value set can completely characterize the overall shape of the second volume fraction distribution and is established as the calibration benchmark for subsequent comparisons.

[0174] In this embodiment, the nucleation and growth parameters in the kinetic relationship are adjusted synchronously and iteratively. Through cyclic solving and comparison, the first volume fraction distribution morphology converges to the benchmark, thereby determining the calibrated kinetic parameters, including:

[0175] Based on the current nucleation and growth parameters, the control relationship is solved to obtain the current first volume fraction distribution, and the distribution is fitted with a function to obtain the current function expression;

[0176] Determine the difference between the current function expression and the benchmark, and determine the adjustment amount and direction of the nucleation and growth parameters based on the difference;

[0177] Multiple iterative adjustments are performed, and the continuous changes in the adjustment amount are recorded. When the adjustment amount approaches zero and the adjustment direction remains unchanged, the calibration is considered complete, and the parameters used in the last iteration are recorded as the calibrated kinetic parameters.

[0178] In practice, the nucleation and growth parameters corresponding to the current iteration are selected as the current nucleation and growth parameters. These two sets of parameters are substituted into the coupled control relationship. According to the set iterative convergence conditions, the control relationship is solved iteratively by numerical calculation step by step to obtain the phase state and attribute data of each analysis position in the flow field. Based on these data, ice crystal size information is extracted and characterization intervals are divided to obtain the current first volume fraction distribution.

[0179] Furthermore, the current first volume fraction distribution is subjected to the same morphological quantification analysis as the first data sequence, and the corresponding peak position distribution width and cumulative percentage inflection point feature values ​​are extracted to form the current feature value sequence, which is the current function expression.

[0180] Furthermore, the current eigenvalue sequence is aligned and compared with the eigenvalue set of the calibration benchmark one by one, and the difference between the two is calculated for each corresponding eigenvalue to form a difference sequence.

[0181] Then, the adjustment amount is determined based on the sign and magnitude of each difference in the difference sequence. If the particle size corresponding to the current peak position is greater than the characteristic value of the benchmark peak position, it indicates that the number of small-diameter ice crystals generated during the nucleation process is insufficient, and the adjustment amount of the nucleation parameter needs to be increased. If the current distribution width is greater than the characteristic value of the benchmark distribution width, it indicates that the difference in ice crystal growth rate is too large, and the adjustment amount of the growth parameter needs to be reduced to narrow the particle size distribution range. If the particle size corresponding to the current cumulative percentage inflection point is less than the characteristic value of the benchmark cumulative percentage inflection point, it indicates that the volume ratio of small-diameter ice crystals is too high, and the growth parameter needs to be adjusted appropriately to promote the growth of medium-diameter ice crystals.

[0182] Furthermore, according to the determined adjustment amount and direction, the values ​​of nucleation parameters and growth parameters are updated, and the next iteration begins; after each iteration, the adjustment amount of nucleation parameters and growth parameters is recorded.

[0183] The iterative adjustment process is repeated, continuously comparing the difference between the current eigenvalue sequence obtained in each round and the calibration benchmark, and constantly correcting the adjustment amount and direction. The changing trend of the adjustment amount is tracked in real time. When the adjustment amounts of nucleation parameters and growth parameters in several consecutive rounds are infinitely close to zero, and the adjustment direction no longer changes (i.e., the adjustment direction remains consistent in several consecutive rounds and there is no more reverse adjustment), the calibration is considered complete. The nucleation parameters and growth parameters used in the last iteration are recorded as the calibrated kinetic parameters.

[0184] In summary, this scheme uses the overall morphology of the second volume fraction distribution as the calibration benchmark, overcoming the limitations of traditional single data point comparisons. By extracting the volume percentage of particle size intervals to form a data sequence, and obtaining characteristic value combinations such as peak position and distribution width through morphological quantification analysis, a calibration benchmark that comprehensively reflects the experimental distribution characteristics is constructed, rather than relying on individual particle size data. This avoids the influence of local data deviations on the calibration results and ensures the objectivity and completeness of the benchmark.

[0185] In summary, this scheme achieves synergy in parameter optimization by simultaneously iteratively adjusting the nucleation and growth parameters. Nucleation and growth parameters jointly determine the ice crystal size distribution; adjusting a single parameter can easily lead to an imbalance in the distribution morphology. Simultaneous iteration, through iteratively solving the control relationship and comparing the differences in distribution morphology, precisely determines the adjustment amount and direction of the two types of parameters, causing the first volume fraction distribution to gradually converge to the experimental baseline. This effectively avoids the one-sidedness of parameter optimization and improves the matching degree of kinetic parameters.

[0186] In summary, this scheme uses "the adjustment amount tends to zero and its direction remains unchanged" as the convergence criterion, ensuring the stability and rigor of the calibration results. This criterion avoids parameter deviations caused by local optima during the iteration process. By continuously tracking the trend of the adjustment amount, it ensures that the finally determined kinetic parameters can stably reproduce the experimental distribution characteristics, making the theoretical model highly consistent with the actual working conditions and significantly reducing the systematic error in subsequent particle size distribution prediction.

[0187] In this embodiment, the calibrated kinetic parameters are substituted into the control relationship, and the particle size distribution of the ice slurry under different working conditions is obtained by changing the operating conditions and resolving the problem, including:

[0188] The operating condition parameters under different operating scenarios are defined and sorted to obtain a set of operating condition sequences;

[0189] Based on the sequence of operating conditions, the boundary and inlet conditions of the control relationship are updated sequentially, and the solution is completed to obtain a set of particle size distribution results corresponding to each condition.

[0190] The particle size distribution result set is correlated and mapped with the corresponding operating condition parameters to form a complete operating condition-particle size distribution prediction spectrum.

[0191] In practical implementation, different operating scenarios are analyzed to identify the core operating condition parameters affecting ice slurry formation, including solution inlet temperature, inlet flow rate, and heat exchange pipe wall temperature. Based on the common variation range of each parameter in actual applications, the value of each parameter is clearly defined. The primary sorting criterion is in ascending order of inlet temperature. At the same inlet temperature, a secondary sorting is performed based on ascending inlet flow rate. The sorted operating condition parameters are then combined and arranged sequentially to obtain a set of operating condition sequences.

[0192] Furthermore, based on the first combination of operating condition parameters in the operating condition sequence, the corresponding inlet boundary conditions in the control relationship are adjusted, that is, the set values ​​of inlet temperature and inlet flow rate are updated. At the same time, the boundary conditions of heat exchange wall temperature are updated. The calibrated kinetic parameters are substituted into the adjusted control relationship, and the numerical iterative solution is completed according to the set iterative convergence conditions to obtain the first volume fraction distribution, i.e., particle size distribution result, corresponding to this operating condition.

[0193] Then, following the same operating procedure described above, each parameter combination in the sequence of operating conditions is processed sequentially, the boundary and entry conditions of the control relationship are updated one by one and the solution is completed. The particle size distribution results corresponding to all operating conditions are arranged in the order of the operating condition sequence to obtain a set of particle size distribution results corresponding to each condition.

[0194] Furthermore, a data association table is established, in which columns for operating condition parameters and particle size distribution results are set. Each parameter combination in the operating condition sequence is filled into the operating condition parameter column one by one, and the corresponding particle size distribution results in the particle size distribution result set are filled into the particle size distribution result column in the same row, so as to achieve a precise correspondence between each operating condition parameter and the corresponding particle size distribution result.

[0195] Finally, the data in the association table is checked for completeness to ensure that there are no omissions or mismatches, and a complete working condition-particle size distribution prediction spectrum is finally formed.

[0196] In summary, this scheme relies on the S5-calibrated kinetic parameters to ensure high accuracy of the prediction results. These parameters undergo closed-loop calibration through theory and experiment, incorporating the physical characteristics of actual working conditions while maintaining the rigor of the theoretical model, effectively solving the prediction bias problem caused by the disconnect between traditional parameters and reality. Substituting these parameters into the control relationship, the solution process can accurately replicate the true laws of ice crystal nucleation and growth under different working conditions, giving the particle size distribution results for each condition experimental-grade reliability and significantly enhancing the practical value of the prediction data.

[0197] In summary, this solution achieves universality across multiple scenarios by systematically changing and solving operating conditions. This step clarifies core operating parameters such as solution inlet temperature, inlet flow rate, and wall temperature. Based on common variation ranges in practical applications, an operating condition sequence is constructed, and the corresponding particle size distribution is obtained by solving each parameter. This approach overcomes the limitations of traditional single-condition measurements, comprehensively covering the needs of different operating scenarios. Whether the operating parameters are fine-tuned or significantly changed, it can quickly output accurate results, adapting to application scenarios in multiple fields such as refrigeration, energy storage, and cold chain transportation.

[0198] In summary, this approach significantly improves efficiency and reduces costs by replacing repetitive physical experiments with numerical solutions. Traditional methods require complex physical experiments for each operating condition, which is time-consuming, labor-intensive, and resource-intensive. In contrast, step S6, based on calibration parameters, can quickly complete multi-condition solutions through numerical iteration, eliminating the need to repeatedly build experimental setups and collect samples. This greatly shortens the particle size distribution acquisition cycle and reduces the consumption of experimental materials and equipment, resulting in significant economic advantages.

[0199] In summary, this scheme forms a complete operating condition-particle size distribution prediction spectrum through correlation mapping, achieving systematization and ease of use of the results. This prediction spectrum accurately matches operating condition parameters with corresponding particle size distribution results, avoiding the chaos of scattered data. It allows engineers to directly query the expected distribution characteristics under different operating conditions, providing an intuitive decision-making basis for the design optimization and operating condition control of ice slurry preparation systems. Furthermore, this prediction spectrum can expand the operating condition range according to actual needs, further extending the application boundaries of the method. This transforms the entire technical solution from theoretical research into an engineering tool with practical operational value, significantly improving the efficiency of technology transfer.

[0200] Example 2, as Figure 2 The diagram shown is a functional block diagram of a system for determining the particle size distribution of an ice slurry containing a nanofluid salt solution, provided in an embodiment of the present invention.

[0201] This invention discloses a system for determining the particle size distribution of ice slurry containing nanofluidic salt solution, which can be installed in an electronic device. Depending on the functions implemented, the system may include a relation construction module 101, a feature extraction module 102, an experimental data acquisition module 103, an image processing module 104, a parameter iteration calibration module 105, and a distribution prediction application module 106. The modules of this invention can also be referred to as units, which are a series of computer program segments that can be executed by the processor of an electronic device and perform a fixed function, stored in the memory of the electronic device.

[0202] In this embodiment, the functions of each module / unit are as follows:

[0203] The relationship construction module 101 is used to couple the local concentration field of nanoparticles in solution with the driving force of the phase transition process to obtain the control relationship of ice slurry containing nanofluid salt solution; ice crystals are defined as discrete phases, and the kinetic relationship between their nucleation rate and growth rate is established.

[0204] The feature extraction module 102 is used to solve the control relationship based on the initial parameters of the dynamic relationship, extract the size information of ice crystals from the solution results, and divide multiple characterization intervals according to the size information to obtain the first volume fraction distribution of ice crystals.

[0205] The experimental data acquisition module 103 is used to introduce the solution into the solid heat exchange pipe, so that the solution flows under the boundary conditions that satisfy the control relationship. When the flow is stable, dynamic images of the outlet slurry are acquired to obtain a dynamic image sequence of the slurry.

[0206] The image processing module 104 is used to statistically analyze the projected size of ice crystals in the dynamic image sequence, divide the continuous particle size intervals according to the statistical results, and determine the proportion of the volume of ice crystals in each interval to the total volume of the slurry, thereby obtaining the second volume fraction distribution.

[0207] The parameter iterative calibration module 105 is used to synchronously iteratively adjust the nucleation and growth parameters in the kinetic relationship with the overall shape of the second volume fraction distribution as the calibration benchmark. Through iterative solution and comparison, the shape of the first volume fraction distribution converges to the benchmark, thereby determining the calibrated kinetic parameters.

[0208] The distribution prediction application module 106 substitutes the calibrated kinetic parameters into the control relationship, and obtains the particle size distribution of ice slurry under different working conditions by changing the working conditions and resolving.

[0209] In the several embodiments provided by this invention, it should be understood that the disclosed methods and systems can be implemented in other ways. For example, the system embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and other division methods may be used in actual implementation.

[0210] The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0211] Furthermore, the functional modules in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or in the form of hardware plus software functional modules.

[0212] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the present invention.

[0213] The embodiments of this application can acquire and process relevant data based on artificial intelligence technology. Artificial intelligence is the theory, method, technology, and application system that uses digital computers or machines controlled by digital computers to simulate, extend, and expand human intelligence, perceive the environment, acquire knowledge, and use that knowledge to obtain optimal results.

[0214] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for determining the particle size distribution of ice slurry containing nanofluidic salt solution, characterized in that, The method includes: S1. The local concentration field of nanoparticles in solution is coupled with the driving force of the phase transition process to obtain the control relationship of ice slurry containing nanofluid salt solution; ice crystals are defined as discrete phases, and the kinetic relationship between their nucleation rate and growth rate is established. S2. Solve the control relationship based on the initial parameters of the dynamic relationship, extract the size information of ice crystals from the solution results, and divide multiple characterization intervals according to the size information to obtain the first volume fraction distribution of ice crystals. S3. Pass the solution into the solid heat exchange pipe and let the solution flow under the boundary conditions that satisfy the control relationship. When the flow is stable, acquire dynamic images of the slurry at the outlet to obtain a dynamic image sequence of the slurry. S4. Statistically analyze the projected size of ice crystals in the dynamic image sequence, divide the continuous particle size intervals according to the statistical results, and determine the proportion of the ice crystal volume to the total volume of the slurry in each interval to obtain the second volume fraction distribution. S5. Using the overall shape of the second volume fraction distribution as the calibration benchmark, synchronously iteratively adjust the nucleation and growth parameters in the kinetic relationship, and through iterative solution and comparison, make the shape of the first volume fraction distribution converge to the benchmark, thereby determining the calibrated kinetic parameters; S6. Substitute the calibrated kinetic parameters into the control relationship, and obtain the particle size distribution of the ice slurry under different working conditions by changing the working conditions and solving again.

2. The method for determining the particle size distribution of an ice slurry containing a nanofluidic salt solution as described in claim 1, characterized in that, The coupling of the local concentration field of nanoparticles in solution with the driving force of the phase transition process to obtain the control relationship of the nanofluidic salt solution ice slurry includes: Microscopic imaging analysis of the solution was performed to extract the distribution density of nanoparticles in three-dimensional space, thus obtaining the spatial distribution of nanoparticle concentration. Based on the principles of phase transition thermodynamics, a fundamental relationship of phase transition driving force determined by temperature difference is established; The spatial distribution of concentration is used as a modulation factor, and a scalar multiplication operation is performed with the basic relationship of the phase transition driving force to obtain the modulated phase transition driving force. The modulated phase change driving force is used as a source term and embedded into the basic conservation relationship describing solution flow and heat transfer to form a coupled control relationship.

3. The method for determining the particle size distribution of an ice slurry containing a nanofluidic salt solution as described in claim 2, characterized in that, The definition of ice crystals as a discrete phase and the establishment of a kinetic relationship between their nucleation rate and growth rate include: Statistical analysis of microscopic nucleation events in solutions under supercooled conditions yielded statistical data on the initial number of ice crystal nuclei per unit volume as a function of temperature and local nanoparticle concentration, which served as data on nucleation patterns. The interfacial propagation velocity of ice crystals under constant supercooling conditions was measured to obtain the corresponding data between the interfacial propagation velocity and supercooling, which can be used as data on growth patterns. Based on the heterogeneous nucleation theory, the nucleation law data were processed to obtain the nucleation rate relationship between the nucleation rate and the local nanoparticle concentration and local supercooling. Based on the theory of interface dynamics, growth data were processed to obtain the relationship between growth rate and local supercooling.

4. The method for determining the particle size distribution of an ice slurry containing a nanofluidic salt solution as described in claim 1, characterized in that, The initial parameters based on the dynamic relationship are used to solve the control relationship. The size information of the ice crystals is extracted from the solution results, and multiple characterization intervals are divided based on the size information to obtain the first volume fraction distribution of the ice crystals, including: The initial parameters of the dynamic relationship are applied to the control relationship for numerical iteration to obtain the phase state and attribute data of each analysis location in the flow field; Retrieve phase and property data, locate the part belonging to the ice crystal solid phase, analyze the geometric characterization parameters of this part, and form a list of ice crystal sizes; Based on the density of values ​​in the ice crystal size list, multiple boundary points are set to define continuous size groups; For each size group, the total volume of all ice crystal solid phase portions contained therein is summarized, and the share of this total volume in the total fluid volume in the flow field is determined to obtain the first volume fraction distribution.

5. The method for determining the particle size distribution of an ice slurry containing a nanofluidic salt solution as described in claim 1, characterized in that, The process of acquiring dynamic images of the outlet slurry to obtain a dynamic image sequence of the slurry includes: Backlight sources and high-speed imaging equipment are installed at the exit. The intensity and angle of the backlight sources are adjusted to create a uniform backlight environment at the exit to highlight the outline of the ice crystals. Start the high-speed imaging device, set its acquisition frame rate and exposure time, and make it continuously capture images of the stable flow field at the outlet to obtain a set of original images arranged in chronological order. Contrast enhancement is performed on each image in the original image set to obtain a dynamic image sequence.

6. The method for determining the particle size distribution of an ice slurry containing a nanofluidic salt solution as described in claim 5, characterized in that, The process of statistically analyzing the projected sizes of ice crystals in the dynamic image sequence, dividing continuous particle size intervals based on the statistical results, and determining the proportion of ice crystal volume to the total slurry volume within each interval to obtain a second volume fraction distribution includes: Contour analysis is performed on each image in the dynamic image sequence to mark the projection regions of all ice crystals and obtain the equivalent circle diameter data for each region; The equivalent circle diameter data of all images are summarized, sorted by numerical value, and several dividing values ​​are determined based on the cumulative frequency distribution of data points to define continuous particle size intervals. For each continuous particle size interval, the equivalent circle diameter of all ice crystal projection regions within the continuous particle size interval is selected. Based on the sphere assumption, the equivalent circle diameter is converted into the volume estimate of a single ice crystal, and the total volume estimate of the ice crystals in that interval is obtained by summing them up. Determine the proportion of the total ice crystal volume in the total volume of the slurry sample for each interval, and construct a second volume fraction distribution based on the volume proportions of all intervals.

7. The method for determining the particle size distribution of an ice slurry containing a nanofluidic salt solution as described in claim 1, characterized in that, The calibration benchmark based on the overall shape of the second volume fraction distribution includes: The volume percentage values ​​of each particle size range are extracted from the second volume fraction distribution and arranged in order of particle size to form the first data sequence; Perform morphological quantization analysis on the first data sequence to obtain at least one set of feature values ​​describing the overall morphology; At least one set of feature values ​​is combined to establish a calibration benchmark for subsequent comparisons.

8. The method for determining the particle size distribution of an ice slurry containing a nanofluidic salt solution as described in claim 7, characterized in that, The synchronous iterative adjustment of nucleation and growth parameters in the kinetic relationship, through iterative solution and comparison, converges the first volume fraction distribution morphology to a reference, thereby determining the calibrated kinetic parameters, including: Based on the current nucleation and growth parameters, the control relationship is solved to obtain the current first volume fraction distribution, and the distribution is fitted with a function to obtain the current function expression; Determine the difference between the current function expression and the benchmark, and determine the adjustment amount and direction of the nucleation and growth parameters based on the difference; Multiple iterative adjustments are performed, and the continuous changes in the adjustment amount are recorded. When the adjustment amount approaches zero and the adjustment direction remains unchanged, the calibration is considered complete, and the parameters used in the last iteration are recorded as the calibrated kinetic parameters.

9. The method for determining the particle size distribution of an ice slurry containing a nanofluidic salt solution as described in claim 1, characterized in that, The process involves substituting the calibrated kinetic parameters into the control relationship, changing the operating conditions, and resolving the problem to obtain the particle size distribution of the ice slurry under different operating conditions, including: The operating condition parameters under different operating scenarios are defined and sorted to obtain a set of operating condition sequences; Based on the sequence of operating conditions, the boundary and inlet conditions of the control relationship are updated sequentially, and the solution is completed to obtain a set of particle size distribution results corresponding to each condition. The particle size distribution result set is correlated and mapped with the corresponding operating condition parameters to form a complete operating condition-particle size distribution prediction spectrum.

10. A system for determining the particle size distribution of ice slurry containing nanofluidic salt solution, used to implement the method for determining the particle size distribution of ice slurry containing nanofluidic salt solution as described in any one of claims 1-9, characterized in that, The system includes: The relation construction module is used to couple the local concentration field of nanoparticles in solution with the driving force of the phase transition process to obtain the control relationship of ice slurry containing nanofluid salt solution; ice crystals are defined as discrete phases, and the kinetic relationship between their nucleation rate and growth rate is established. The feature extraction module is used to solve the control relationship based on the initial parameters of the dynamic relationship, extract the size information of ice crystals from the solution results, and divide multiple characterization intervals according to the size information to obtain the first volume fraction distribution of ice crystals. The experimental data acquisition module is used to introduce the solution into the solid heat exchange pipe, so that the solution flows under the boundary conditions that meet the control relationship. When the flow is stable, dynamic images of the outlet slurry are acquired to obtain a dynamic image sequence of the slurry. The image processing module is used to statistically analyze the projected size of ice crystals in the dynamic image sequence, divide the continuous particle size intervals according to the statistical results, and determine the proportion of the ice crystal volume to the total volume of the slurry in each interval to obtain the second volume fraction distribution. The parameter iterative calibration module is used to synchronously and iteratively adjust the nucleation and growth parameters in the kinetic relationship with the overall morphology of the second volume fraction distribution as the calibration benchmark. Through iterative solution and comparison, the morphology of the first volume fraction distribution converges to the benchmark, thereby determining the calibrated kinetic parameters. The distribution prediction application module substitutes the calibrated kinetic parameters into the control relationship, and obtains the particle size distribution of ice slurry under different working conditions by changing the working conditions and resolving.

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