Fluid temperature and pressure partitioning and heat transfer prediction method under supercritical pressure

Abstract

The invention discloses a fluid temperature and pressure partitioning and heat transfer prediction method under supercritical pressure, which comprises the following steps: firstly, constructing a dimensionless criterion SEN to quantitatively evaluate a fluid expansion effect, and then dividing heat transfer into a plurality of temperature and pressure intervals based on Nuexp / Nufc; for each partition and the constructed dimensionless criterion, a temperature interval of a dominant mechanism and characteristic parameters representing the dominant mechanism are extracted, and particularly, the reasonability of a single-phase fluid hypothesis and a two-phase fluid hypothesis can be rapidly judged through the constructed dimensionless criterion; and establishing a partition prediction model by adopting a mechanism and data dual-drive framework. And finally, calling the corresponding sub-model according to the working condition and processing the cross-region continuity to realize high-precision heat transfer prediction in the full working condition range. The method solves the problem that a traditional method is difficult to predict full-temperature pressure interval heat transfer at high precision, and can be used for precise thermal design of the supercritical working medium in thermal equipment such as boilers, heat regenerators and coolers.

Description

Technical Field

[0001] This invention belongs to the field of supercritical fluid heat transfer and heat exchanger design, and relates to the mechanism identification and high-precision prediction of fluid flow heat transfer under supercritical pressure. Specifically, it relates to a fluid temperature and pressure zoning method and heat transfer prediction method under supercritical pressure. Background Technology

[0002] Supercritical fluids (such as supercritical CO2, water, and organic working fluids) are widely used in advanced power systems due to their high circulation efficiency, compact heat exchanger size, and stable operation under high temperature and pressure. Accurately predicting heat transfer across the entire temperature range is crucial for the thermal design of heat exchange equipment. However, compared to conventional single-phase forced convection heat transfer, fluid flow heat transfer under supercritical pressure exhibits high dimensionality and strong nonlinearity. In particular, the non-equilibrium processes occurring across the quasi-critical point cause drastic changes in thermophysical parameters such as density, specific heat capacity, thermal conductivity, and viscosity within a narrow temperature range, making the flow heat transfer process highly complex and difficult to predict accurately.

[0003] Currently, methods for treating supercritical fluid heat transfer can be broadly categorized into two types. One approach ignores the special characteristics of the quasi-critical point, treating it as a single-phase fluid with drastically changing properties. It considers buoyancy and flow acceleration effects as the main reasons for deviations from single-phase forced convection heat transfer. However, the single-phase fluid perspective cannot fully explain all heat transfer processes. For heat transfer prediction, new heat transfer correlations can be developed by adding correction terms such as density, specific heat, viscosity, thermal conductivity, and considering buoyancy and acceleration effects to the heat transfer correlations developed from single-phase forced convection heat transfer theory. The other approach analogizes the fluid crossing the quasi-critical point as a two-phase flow and supercritical fluid heat transfer as subcritical boiling, proposing heat transfer correlations that consider boiling-like processes based on experimental data. However, most of these correlations only have good predictive accuracy within their respective research scopes and cannot be extrapolated to other parameters. Furthermore, traditional methods for developing heat transfer correlations based on fitting experimental data have significant limitations: on the one hand, acquiring experimental data is costly and time-consuming; on the other hand, due to the numerous and interdependent influencing factors, it is difficult to cover all operating conditions with limited experimental data. More importantly, existing methods lack a unified criterion that can comprehensively reflect the effects of changes in physical properties and boundary conditions. They cannot effectively determine when the influence of fluid expansion effects needs to be considered, nor can they clearly distinguish the effective range of different heat transfer mechanisms.

[0004] To address the aforementioned issues, existing technologies have attempted to improve prediction using data-driven methods, but their applicability remains insufficient. For example, Chinese invention CN117150896A proposes a method for predicting the heat transfer coefficient of supercritical fluids based on interpretable machine learning. While this method improves prediction accuracy under specific operating conditions by introducing a large number of dimensionless numbers and optimizing neural networks, it is essentially still a global black-box model. It fails to effectively divide the heat transfer region from a physical mechanism perspective, and its high model complexity limits its universality and ease of engineering use. Another Chinese invention, CN120748527A, focuses on the local field reconstruction of S-CO2 within microchannel heat exchangers. Although its method based on intrinsic orthogonal decomposition and neural networks can quickly predict the flow field, it is limited to specific microchannel geometry and preset operating conditions, making it difficult to extrapolate to the full-scale operating range of engineering systems.

[0005] In summary, it is difficult to accurately quantify the complex thermo-mechanical coupling process within a single-phase fluid or boiling-like hypothesis. In addition, the heat transfer law of supercritical fluids is very complex, and traditional methods based on experimental data to develop heat transfer correlations are difficult to predict heat transfer with high accuracy across the entire temperature range. Therefore, how to establish a criterion system that can comprehensively reflect the influence of changes in physical properties and boundary conditions, how to accurately distinguish the effective range of different heat transfer mechanisms, and how to accurately predict heat transfer of fluids across the entire temperature and pressure range under supercritical pressure have become key requirements in the design and operation of supercritical fluid dynamic systems. Summary of the Invention

[0006] (a) Purpose of the invention To address the aforementioned technical problems, this invention aims to provide a method for predicting the temperature and pressure zones and heat transfer of fluids under supercritical pressure. By introducing a dimensionless criterion that comprehensively considers the fluid expansion effect, the method quantitatively delineates the temperature and pressure zones of supercritical fluids. Furthermore, for the dominant heat transfer mechanisms in different regions, key dimensionless feature parameter sets are selected, and an ensemble learning algorithm is used to construct a zoned heat transfer prediction model. This combines the guidance of physical mechanisms with the data-driven nonlinear fitting capability, achieving high-precision heat transfer prediction of fluids under supercritical pressure across the entire temperature and pressure range. This provides a solid and reliable technical basis for the efficient design, optimized operation, and safety assessment of supercritical fluid heat exchange equipment.

[0007] (II) Technical Solution To achieve the objective of this invention and solve its technical problems, the present invention adopts the following technical solution: A method for predicting the temperature and pressure zones and heat transfer of supercritical fluids, used to achieve high-precision heat transfer prediction of supercritical fluids across the entire temperature and pressure range, includes at least the following steps: S100. Constructing a dimensionless fluid expansion criterion: Based on the physical property parameters of supercritical fluids, construct a dimensionless criterion to comprehensively reflect the fluid expansion effect caused by changes in physical properties and boundary conditions. At least consider the change in fluid density along the flow direction, the density gradient between the mainstream region and the near-wall region, and the temperature distribution characteristics within the boundary layer. By analyzing the numerical value of the dimensionless criterion, quantitatively assess the degree of influence of fluid expansion effect on the heat transfer process. S200. Delineate the boundaries of temperature and pressure zones: Obtain experimental data on fluid flow and heat transfer within the channel under supercritical pressure, and calculate the experimental Nusselt number. Now exp Nusselt number with single-phase forced convection Now fc The ratio, in Now exp / Now fc With volume expansion coefficient β and temperature T product β · T Based on the correlation spectrum, the critical value X of the physical property criterion is determined. cr Then based on the critical value X cr Under different pressures β · T Follow T The temperature and pressure zoning process is performed on the change curves of single-phase and two-phase-like regions. S300. Determine the characteristics of the dominant heat transfer mechanism: For the two-phase region determined after partitioning under different pressures, based on the dimensionless criterion critical value of the fluid expansion effect determined by statistical analysis of flow heat transfer experimental data, dimensionless characteristic parameters characterizing the dominant heat transfer mechanism are extracted for two operating conditions, one above the critical value and the other below the critical value. These include parameters used to characterize the effects of buoyancy and flow acceleration under the single-phase flow assumption and the boiling-like effect under the two-phase flow assumption, thereby forming the typical heat transfer behavior mechanism identifiers corresponding to the two operating conditions. S400. Establish regional heat transfer prediction models: For the single-phase region and two-phase-like region determined after partitioning, and combined with the dominant heat transfer mechanism identifier further determined in the two-phase-like region, a mechanism- and data-driven dual-drive framework is adopted to establish regional heat transfer prediction sub-models with dimensionless characteristic parameters as input. The mechanism model is used to describe the basic heat transfer laws and physical effects in the single-phase region, and the data-driven model is based on machine learning algorithms and trained with experimental and / or numerical data covering the target operating conditions to capture and learn the nonlinear mapping relationship between dimensionless characteristics and heat transfer coefficient in the two-phase-like region. S500. Achieve full-temperature and pressure range heat transfer prediction: Based on the supercritical fluid condition to be predicted, first determine the temperature and pressure range to which it belongs, then call the corresponding zone heat transfer prediction sub-model to calculate the corresponding predicted heat transfer coefficient value; when the condition is located in the neighborhood of the zone boundary, perform continuity processing of cross-zone results to ensure the continuity and consistency of the prediction results at the zone switching point, and finally achieve high-precision heat transfer prediction of fluid under supercritical pressure in the full temperature and pressure range.

[0008] Preferably, in step S100, the dimensionless fluid expansion criterion is the supercritical expansion number. LATE Its mathematical expression is ,in q w The wall heat flux density, G For mass flow rate, d i The hydraulic diameter of the channel. c P and λ These are the specific heat capacity at constant pressure and the thermal conductivity, respectively. β The coefficient of volume expansion and , ρ For fluid density, T For temperature, P For pressure, LATE In q w 2 ·d i / G This term characterizes the magnitude of temperature rise during the heating process of the fluid within the channel. β 2 / (c P ·λ) This term characterizes the sensitivity of fluid properties to temperature changes.

[0009] Preferably, in step S200, with Now exp / Now fc With volume expansion coefficient β and temperature T product β · T Based on the correlation map, and using Now exp / Now fc =0.5 β · T The value is used as the critical value X for physical property criteria. cr ; Plotting under different pressures β · T With temperatureT The change curve, and for the change curve under each pressure, determine β · T The maximum value ( β · T ) max The relative magnitude with the critical value x: If ( β · T ) max ≤X cr It is determined that no boiling-like heat transfer occurs under this pressure, and the entire pressure is classified as a single-phase region; if ( β · T ) max >X cr Based on the determination that boiling-like heat transfer may occur under this pressure, the working conditions with temperatures below the low-temperature critical and those with temperatures above the high-temperature critical are both classified as single-phase regions, and the working condition region with temperatures between the low-temperature critical and the high-temperature critical is classified as a two-phase-like region.

[0010] Further, in step S200, for those satisfying ( β · T ) max >X cr The supercritical pressure condition, and its β · T and T Find the change curve β · T =X cr The two characteristic temperature values ​​corresponding to the time are defined as the low temperature boundary. T - and high temperature boundary T + And partition accordingly: when T < T - At that time, it is divided into a liquid-like region, and its heat transfer characteristics are similar to forced convection of the liquid phase under subcritical pressure. T > T + When the temperature is high, it is classified as a gas-like region, whose heat transfer characteristics are similar to forced convection in the gas phase under subcritical pressure, and the liquid-like region and the gas-like region are uniformly classified into the single-phase region; when T - ≤ T ≤ T + At that time, it is divided into a two-phase-like region, and its heat transfer process is strongly affected by the expansion effect and accompanied by a boiling-like phenomenon.

[0011] Preferably, step S200 includes at least the following sub-steps when dividing the temperature and pressure ranges: S201. Calculation Now exp and Now fc : Obtain experimental data on fluid flow and heat transfer in a channel under supercritical pressure, and calculate the experimental Nusselt number. Now exp = h · d i / λ ,in h The convective heat transfer coefficient is... d i The hydraulic diameter of the channel. λ The fluid thermal conductivity is used, and a single-phase forced convection heat transfer correlation is employed for calculation. Now fc ; S202. Establishment Now exp / Now fc and β · T Correlation graph: Calculating the Nusselt number ratio Now exp / Now fc and the product of volumetric expansion coefficient and temperature β · T After that Now exp / Now fc For the ordinate, β · T Using the x-axis as the horizontal axis, plot the distribution of data points under different pressure and heat flux density conditions to form a correlation graph between the two, and then... Now exp / Now fc =0.5 β · T The value is used as the critical value x for physical property criterion; S203. Define the boundaries of temperature and pressure ranges: plot the boundaries under different pressures. β · T With temperature T The change curve, and for the change curve under each pressure, if it satisfies ( β · T ) max ≤X cr If this pressure is classified as a single-phase region, then if the following conditions are met ( β · T ) max >X cr Then find β · T =X cr The corresponding low temperature boundary T- and high temperature boundary T + ,Will T < T - The corresponding liquid-like region and T > T + The corresponding gas-like regions are uniformly classified into the single-phase region, and T - ≤ T ≤ T + The region between them is divided into a biphasic region.

[0012] Preferably, in step S300, for the two-phase-like regions determined after partitioning under different pressures, the critical criterion value of the supercritical expansion number is first determined through statistical analysis of flow heat transfer experimental data. LATE cr (Preferred) LATE cr =0.15), serving as the boundary for quantitatively judging the transition from the single-phase fluid hypothesis to the two-phase flow hypothesis: when LATE ≤ LATE cr At supercritical pressure, the main mechanism of fluid heat transfer is single-phase convective heat transfer, with buoyancy or flow acceleration as the primary influencing factors; when LATE > LATE cr At that time, the main mechanism of fluid heat transfer under supercritical pressure gradually transitioned to boiling-like oscillation as the main influencing factor, and eventually became the main heat transfer mechanism.

[0013] Furthermore, in step S300, in LATE ≤ LATE cr For the two-phase region, dimensionless characteristic parameters are selected. Boo and Kv To measure the impact of buoyancy and flow acceleration on heat transfer, among which and , Re=G · d i / μ Let Reynolds number be 1. μ For dynamic viscosity, g It is the acceleration due to gravity. ρ For fluid density, T w The wall temperature, T b Mainstream temperature, q w The wall heat flux density, d i The hydraulic diameter of the channel. cP This is the specific heat capacity at constant pressure.

[0014] Furthermore, in step S300, in LATE > LATE cr The two-phase region was further selected from the supercritical region. Characterizing the competitive relationship between inertial forces and expansion forces in fluid flow, where q w The wall heat flux density, G For mass flow rate, i w The enthalpy of the fluid at the wall temperature. ρ w The fluid density is determined by the wall temperature. ρ b The fluid density is determined by the fluid temperature.

[0015] Preferably, in step S400, the heat transfer coefficient in the single-phase region is predicted using a single-phase forced convection heat transfer correlation mechanism model; the heat transfer coefficient in the two-phase-like region is predicted using a data-driven model. LATE < LATE cr When, select Re , Pr , Boo and Kv As input variables, Now As output labels, when LATE > LATE cr When, select Re , Pr , Stay , Kv and K As input variables, Now As a label, the data-driven sub-model employs an ensemble learning algorithm and divides the experimental data and / or numerical simulation data into training, validation, and test sets. The model is trained based on the training set, hyperparameters are tuned and the model is optimized using the test set, and the generalization ability of the model is evaluated through the validation set.

[0016] Preferably, in step S400, the ensemble learning algorithm is selected from at least one of Gradient Boosting Decision Tree (GBDT), Extreme Gradient Boosting (XGBoost), Lightweight Gradient Boosting Machine (LightGBM), Adaptive Boosting (AdaBoost), and Random Forest. It captures the nonlinear mapping relationship between dimensionless feature parameters and Nusselt numbers by constructing multiple weak learners and combining them into a strong learner. During model training, grid search or Bayesian optimization methods are used to fine-tune hyperparameters including learning rate, tree depth, number of leaf nodes, and feature sampling rate, using root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²). 2 As a performance evaluation indicator for the model, it ensures that the prediction model achieves high-precision prediction requirements in all temperature and pressure ranges.

[0017] Preferably, in step S500, when the calculated... LATE ≤ LATE cr When the effect of fluid expansion on heat transfer is determined to be weak, a single-phase forced convection heat transfer correlation is used for rapid prediction of the heat transfer coefficient; when LATE > LATE cr When it is determined that the fluid expansion effect has a significant impact on heat transfer, the corresponding zoned heat transfer prediction sub-model established in step SS4 is called to perform high-precision prediction based on the temperature and pressure range of the fluid.

[0018] Preferably, in step S500, the continuity processing of cross-regional results includes: setting a transition zone in the neighborhood of the temperature and pressure interval boundary, the width of which is adaptively determined according to the gradient of the change in physical property parameters; when the operating condition to be predicted is located within the transition zone, simultaneously calling the partitioned heat transfer prediction sub-models of the two adjacent intervals to calculate the predicted values ​​of the heat transfer coefficients respectively. Now 1 and Now 2. Calculate the final predicted value using a weighted average or linear interpolation method. Now = w 1· Now 1+ w 2. Now 2. Weighting coefficients w 1 and w 2. Determined based on the distance between the operating point and the interval boundary, satisfying... w 1+ w 2=1 and the closer to the center of a certain interval, the greater the weight of that interval; through continuous processing, a smooth transition of the prediction results at the interval switching point is ensured, and abrupt changes in the predicted value are avoided.

[0019] Preferably, the supercritical expansion number LATE It is also used as a criterion for heat transfer degradation: by analyzing experimental data of heat transfer degradation conditions, it is determined... Now exp / Now fc The critical value of the supercritical expansion number corresponding to the occurrence of heat transfer deterioration <0.5 LATE th When the working condition to be predicted LATE > LATE th If the system determines that there is a risk of heat transfer deterioration or that heat transfer deterioration has already occurred under the operating condition, it issues a risk warning and switches to a two-phase region model that considers boiling-like contributions and a calculation process with a tightened safety margin.

[0020] (III) Technical Effects Compared with the prior art, the fluid temperature and pressure zoning and heat transfer prediction method under supercritical pressure of the present invention has the following beneficial and significant technical effects: (1) This invention proposes a supercritical expansion number that comprehensively reflects the fluid expansion effect. LATE This enables rapid assessment of the impact of expansion on heat transfer in supercritical pressure fluids, allowing for the selection of appropriate prediction methods to forecast heat transfer in supercritical pressure fluids. This significantly improves the thermal design efficiency of related heat exchange equipment and can be used to develop criteria for determining whether heat transfer in supercritical fluids deteriorates, thereby avoiding the risk of tube rupture accidents caused by excessive metal wall temperature. (2) Based on the relationship between the degree of deviation from single-phase forced convection heat transfer and the expansion effect, this invention proposes a temperature and pressure zoning method for fluids under supercritical pressure, and determines the boiling-like range that must be considered, providing a basis for improving the heat exchange performance of heat exchange equipment in supercritical fluid circulation systems. (3) The mechanism and data dual-drive method proposed in this invention realizes high-precision heat transfer prediction in the entire temperature and pressure range, and solves the problem that traditional methods based on experimental data to develop heat transfer correlations are difficult to predict fluid heat transfer under supercritical pressure with high precision. Attached Figure Description

[0021] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 A flowchart illustrating the implementation of a method for predicting fluid temperature and pressure zones and heat transfer under supercritical pressure. Figure 2 for Now exp / Now fc andβ · T Distribution diagram; Figure 3 For different pressures β · T and T Distribution diagram; Figure 4 This is a temperature and pressure zoning diagram under supercritical pressure. Figure 5 for LATE and I Distribution relationship (a) and Now exp / Now fc and I Distribution relationship (b) diagram; Figure 6 A basic flowchart for predicting S-CO2 heat transfer using a dual-driven approach of mechanism and data. Figure 7 This diagram illustrates a comparison of error analysis results between the model trained using the ensemble learning algorithm of this invention and the traditional heat transfer correlation prediction method. Detailed Implementation

[0023] This invention aims to provide a method for predicting the temperature and pressure zoning and heat transfer of supercritical fluids, enabling high-precision heat transfer prediction across the entire temperature and pressure range. To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions in the embodiments of this invention will be described in more detail below with reference to the accompanying drawings. The described embodiments are only some, not all, of the embodiments of this invention, and are exemplary and used to explain the invention, not to limit it. This embodiment uses the heat transfer prediction of supercritical carbon dioxide (S-CO2) in a boiler cooling wall as an example to illustrate the implementation process of this method in detail.

[0024] Supercritical CO2 (S-CO2) cycle systems have significant potential applications in efficient and flexible coal-fired power, solar energy, next-generation nuclear power, waste heat recovery, and high-temperature fuel cells due to their advantages in efficiency, equipment size, and the selection of materials for high-temperature and high-pressure applications. Supercritical CO2 cycle systems include heat exchange equipment such as boilers or heat exchangers, regenerators, and preheaters. Accurately predicting heat transfer across the entire temperature range is crucial for the thermal design of heat exchange equipment and for system control strategies under varying operating conditions. However, under supercritical pressure, CO2 flow heat transfer exhibits high dimensionality and strong nonlinearity, particularly the non-equilibrium processes occurring across the quasi-critical point, making the flow heat transfer process highly complex and difficult to predict accurately.

[0025] like Figure 1As shown, this embodiment discloses a method for predicting fluid temperature and pressure zoning and heat transfer under supercritical pressure, which is used for heat transfer design and variable operating condition performance prediction of the cooling wall of a supercritical CO2 boiler. It mainly includes: S100. Constructing a dimensionless fluid expansion criterion: Based on the physical properties of supercritical fluids, a dimensionless criterion is constructed to comprehensively reflect the fluid expansion effect caused by changes in physical properties and boundary conditions. This criterion considers at least the change in fluid density along the flow direction, the density gradient between the mainstream region and the near-wall region, and the temperature distribution characteristics within the boundary layer. By analyzing the numerical value of the dimensionless criterion, the degree of influence of fluid expansion on the heat transfer process is quantitatively assessed.

[0026] This invention attributes the deviation of fluid heat transfer from single-phase forced convection under supercritical pressure to the fluid expansion effect. Due to the existence of fluid expansion, coupled with the effects of buoyancy, flow acceleration, and boiling-like processes, neither a single-phase fluid nor a boiling-like hypothesis can accurately quantify the complex internal thermodynamic coupling processes. This invention proposes a supercritical expansion coefficient... LATE This study comprehensively reflects the fluid expansion effect caused by changes in physical properties and boundary conditions, thereby quantifying the degree of influence of the expansion effect on fluid heat transfer under supercritical pressure. (1) In the formula ρ and β For the fluid density and expansion coefficient, Δ T Let Δ represent the temperature change of the fluid. Here, we only consider the Δ along the flow direction and perpendicular to the flow direction. T Change, Δ T It is related to the rate of change of energy of the fluid along the flow direction and radial direction. According to the law of conservation of energy and Fourier's law of heat conduction, LATE The expression is: (2) In the formula c P and λ These are specific heat and thermal conductivity, respectively. q w and G These are heat flux density and mass flow rate, respectively. d i Let be the inner diameter of the channel. Dimensional analysis of equation (2) yields: (3) Equation (3) can be expressed using the basic length. L ,quality M ,time θ and temperature T To represent by dimensions: (4) We can obtain a system of equations: (5) Solving the equation yields a =2, b =-1, c =1, d =-1, e =-1, f =2, substituting into equation (3) yields LATE The form of expression: (6) LATE It quantifies the relative change in fluid volume caused by fluid expansion, characterizes the extent of the influence of fluid expansion on flow heat transfer, and can be used as a criterion for judging the degree of influence of expansion on heat transfer when combined with experimental data.

[0027] S200. Define the boundaries of temperature and pressure zones: Obtain experimental data on fluid flow and heat transfer in a channel under supercritical pressure, and calculate the experimental Nusselt number. Now exp Nusselt number with single-phase forced convection Now fc The ratio, in Now exp / Now fc With volume expansion coefficient β and temperature T product β · T Based on the correlation spectrum, the critical value X of the physical property criterion is determined. cr Then based on the critical value X cr Under different pressures β · T Follow T The change curves are used to divide the region into single-phase and two-phase-like regions.

[0028] Preferably, step S200 includes the following sub-steps when dividing the temperature and pressure ranges: S201. Calculation Now exp and Now fc : Obtain experimental data on fluid flow and heat transfer in a channel under supercritical pressure, and calculate the experimental Nusselt number. Now exp = h · d i / λ ,in h The convective heat transfer coefficient is... di The hydraulic diameter of the channel. λ The fluid thermal conductivity is used, and a single-phase forced convection heat transfer correlation is employed for calculation. Now fc ; S202. Establishment Now exp / Now fc and β · T Correlation graph: Calculating the Nusselt number ratio Now exp / Now fc and the product of volumetric expansion coefficient and temperature β · T After that Now exp / Now fc For the ordinate, β · T Using the x-axis as the horizontal axis, plot the distribution of data points under different pressure and heat flux density conditions to form a correlation graph between the two, and then... Now exp / Now fc =0.5 β · T The value is used as the critical value X for physical property criteria. cr ; S203. Define the boundaries of temperature and pressure ranges: plot the boundaries under different pressures. β · T With temperature T The change curve, and for the change curve under each pressure, if it satisfies ( β · T ) max ≤X cr If this pressure is classified as a single-phase region, then if the following conditions are met ( β · T ) max >X cr Then find β · T =X cr The corresponding low temperature boundary T - and high temperature boundary T + ,Will T < T - The corresponding liquid-like region and T > T + The corresponding gas-like regions are uniformly classified into the single-phase region, and T- ≤ T ≤ T + The region between them is divided into a biphasic region.

[0029] In this embodiment, heat transfer data of the cooling wall of a supercritical CO2 boiler was first obtained through experiments, and the factors affecting heat transfer were identified. For example... Figure 2 As shown, the experiment yielded the Nusselt number. Now exp The correlation obtained by single-phase forced convection heat transfer is calculated. Now fc Ratio and fluid volume expansion coefficient β and temperature T The product ( β · T The distribution relationship is expressed on a graph. Now fc Calculated by the following formula: .

[0030] Through analysis Figure 2 middle Now exp / Now fc and β · T The relationship, when Now exp / Now fc When this ratio is below 0.5, the heat transfer of supercritical pressure fluid deviates from single-phase forced convection heat transfer, and the boiling-like phenomenon caused by fluid expansion becomes the dominant heat transfer mechanism. This invention defines... Now exp / Now fc When the value is less than 0.5, it is considered a two-phase heat transfer quasi-flow, with the main heat transfer mechanism being a boiling-like process. This means that fluid expansion causes a gas film to cover the near-wall surface, creating significant thermal resistance, thus causing the heat transfer to deviate severely from single-phase forced convection heat transfer. Now exp / Now fc When the value is ≥0.5, it is considered as single-phase fluid heat transfer. Changes in physical properties, buoyancy, or flow acceleration effects are the reasons why the heat transfer deviates significantly from single-phase forced convection heat transfer.

[0031] exist Now exp / Now fc and β · T On the correlation graph, with Now exp / Now fc=0.5 β · T The value is used as the critical value X for physical property criteria. cr .according to Figure 2 Given Now exp / Now fc and β · T From the distribution relationship, it can be seen that when Now exp / Now fc When =0.5, the corresponding β · T The value is 2.4. For example... Figure 3 As shown, different pressures will be used to... β · T and T The distribution relationship is expressed on a graph to identify the distribution under different pressures. β · T When it is 2.4, the corresponding temperature T .

[0032] from Figure 3 It can be seen that under different pressures, with T The increase, β · T First increase then decrease β · T There exists a maximum value ( β · T ) max When the pressure is less than 30 MPa, assuming a given pressure, β · T When the value is 2.4, there are two corresponding temperatures, one of which is the low-temperature boundary. T - The other is the high-temperature boundary. T + When the pressure is ≥30 MPa, then β · T When the value is 2.4, it corresponds to 1 or 0 temperatures. At this pressure, boiling-like conditions will not occur. Therefore, pressures below this level are called two-phase regions, and pressures equal to or higher than this level are called single-phase regions.

[0033] like Figure 4 As shown, the temperature and pressure ranges for boiling-like processes under different pressures were determined. The supercritical region was divided into a two-phase-like region and a single-phase region based on pressure: when the pressure... P When the pressure is ≥30 MPa, it is directly classified as a single-phase region; while at pressure... P When <30 MPa, the interval is divided based on the relationship between the mainstream temperature and the high and low temperature boundaries. T< T - At that time, the fluid is in the liquid-like region, when T>T + At this time, the fluid is in the gas-like region, and the liquid-like region and the gas-like region are uniformly classified into the single-phase region; when T - ≤ i ≤ T + At this point, the fluid is in a two-phase-like region. This partitioning method reflects both the influence of pressure on the critical characteristics of the fluid and the regulatory effect of temperature on changes in physical properties, laying the foundation for the subsequent establishment of a partitioned heat transfer prediction model.

[0034] S300. Determine the characteristics of the dominant heat transfer mechanism: For the two-phase-like regions determined after partitioning under different pressures, based on the dimensionless criterion critical value of fluid expansion effect determined by statistical analysis of flow heat transfer experimental data, dimensionless characteristic parameters characterizing the dominant heat transfer mechanism are extracted for two operating conditions: one above the critical value and the other below the critical value. These parameters include those used to characterize the effects of buoyancy and flow acceleration under the single-phase flow assumption, and the effects of boiling-like flow under the two-phase flow assumption. This forms the typical heat transfer behavior mechanism identifiers corresponding to the two operating conditions.

[0035] Preferably, in step S300, for the two-phase-like regions determined after partitioning under different pressures, the critical criterion value of the supercritical expansion number is first determined through statistical analysis of experimental data. LATE cr (Preferred value 0.15), serving as the boundary for quantitatively determining the transition from the single-phase fluid hypothesis to the two-phase flow hypothesis: when LATE ≤ LATE cr At supercritical pressure, the main mechanism of fluid heat transfer is single-phase convective heat transfer, with buoyancy or flow acceleration as the primary influencing factors; when LATE > LATE cr At that time, the main mechanism of fluid heat transfer under supercritical pressure gradually transitioned to boiling-like oscillation as the main influencing factor, and eventually became the main heat transfer mechanism.

[0036] In this embodiment of the invention, the supercritical expansion number is used. This study comprehensively reflects the fluid expansion effect caused by changes in physical properties and boundary conditions, quantifying its impact on fluid heat transfer under supercritical pressure. For example... Figure 5 As shown, all experimental conditions are given. Now exp / Now fc and LATE Distribution relationship within different dimensionless enthalpy ranges, dimensionless enthalpy values I The expression is In the formulai The enthalpy value corresponding to the mainstream temperature. i - and i + They are respectively T - and T + The corresponding enthalpy value. When I When <0, the fluid is in the liquid-like region; when I> When 1, the fluid is in a gas-like region; when 0 ≤ I When ≤1, the fluid is in a two-phase-like region.

[0037] from Figure 5 It can be seen that, Now exp / Now fc and LATE The table shows a strong negative correlation, that is LATE The larger, Now exp / Now fc The further it deviates from 1. As the enthalpy value moves away from the two-phase-like region, LATE As the flow decreases, heat transfer gradually approaches single-phase forced convection heat transfer. LATE When the error is small, the relative error between the heat transfer prediction results and experimental data using traditional single-phase forced convection heat transfer correlation is relatively small. Therefore, when high prediction accuracy is not required, single-phase forced convection heat transfer correlation calculation can be selected.

[0038] For higher precision, the expansion effect must be considered. Based on the temperature and pressure range division under supercritical pressure, the heat transfer process within different temperature and pressure ranges is further quantified. Figure 5 It can be seen that when LATE When ≤0.15, the heat transfer mechanism can be considered to be mainly single-phase convective heat transfer. LATE When <2, boiling-like processes begin to have a significant impact on heat transfer, while when LATE At ≥2, boiling-like heat transfer dominates. In the liquid-like or gas-like regions, the main heat transfer mechanism of supercritical pressure fluids is single-phase convective heat transfer, with buoyancy or flow acceleration being the main influencing factors. Boo and Kv To measure the impact of buoyancy and flow acceleration on heat transfer, their expressions are as follows: and In the formula Re Let be the Reynolds number, and its expression is: Re=G · d i / μ , μ For dynamic viscosity, g It is the acceleration due to gravity.T w Let be the wall temperature. In the two-phase-like region, heat transfer in supercritical pressure fluids may be simultaneously affected by buoyancy, flow acceleration, and boiling-like conditions. In this case, the supercritical number is selected. To measure the impact of boiling-like processes on heat transfer, among which q w The wall heat flux density, G For mass flow rate, i w The enthalpy of the fluid at the wall temperature. ρ w The fluid density is determined by the wall temperature. ρ b The fluid density is determined by the fluid temperature.

[0039] S400. Establish a regional heat transfer prediction model: For the single-phase region and two-phase-like region determined after partitioning, and combined with the dominant heat transfer mechanism identifier of the two-phase-like region, a dual-driven framework of mechanism and data is adopted to establish partitioned heat transfer prediction sub-models with dimensionless characteristic parameters as input. The mechanism model is used to describe the basic heat transfer laws and physical effects in the single-phase region, while the data-driven model is based on machine learning algorithms and trained with experimental and / or numerical data covering the target operating conditions to capture and learn the nonlinear mapping relationship between dimensionless characteristics and heat transfer coefficient in the two-phase-like region.

[0040] Preferably, in step S400, for the single-phase region, a single-phase forced convection heat transfer correlation mechanism model based on the Dittus-Boelter or Gnielinski correlation is used to quickly predict the heat transfer coefficient; for the two-phase quasi-region, a data-driven model is used to predict the heat transfer coefficient; when LATE < LATE cr When, select Re , Pr , Boo and Kv As input variables, Now As output labels, when LATE > LATE cr When, select Re , Pr , Boo , Kv and K As input variables, Now As a label, the data-driven sub-model employs an ensemble learning algorithm and divides the experimental data and / or numerical simulation data into training, validation, and test sets. The model is trained based on the training set, hyperparameters are tuned and the model is optimized using the test set, and the generalization ability of the model is evaluated through the validation set.

[0041] Specifically, in the embodiments of the present invention, such as Figure 6 As shown, based on the analysis of the heat transfer mechanism of supercritical pressure fluids, combined with experimental data, high-precision prediction of heat transfer can be further achieved. In liquid-like or gas-like regions, the Nusselt number... Now Determined by pressure P Mass flow rate G Heat flux density q w Pipe diameter d i mainstream temperature T b and wall temperature T w ,in P Influence Nusel numbers through physical properties Now Since the main mechanism in the single-phase region is single-phase convective heat transfer, [the following is selected]: Re , Pr , Boo and Kv As input variables, Now As a label, among Pr Let be a Prandtl number, expressed as: Pr=μ · c P / λ After processing and analyzing the experimental data, the data was randomly divided into training, testing, and validation sets according to a set ratio. An ensemble learning algorithm was selected to train the model using the data in the training set. Then, the trained model was further adjusted by inputting variables from the testing set to determine the final model, which was used to achieve high-precision prediction of heat transfer in supercritical pressure fluids.

[0042] In the biphasic region, the same Nusselt number Now Determined by pressure P Mass flow rate G Heat flux density q w Pipe diameter d i mainstream temperature T b and wall temperature T w ,in P Influence through physical properties Now Since heat transfer in the two-phase-like region may require simultaneous consideration of single-phase convective heat transfer and boiling-like processes, a selection is made... Re , Pr , Boo , Kv and K As input variables, NowAs labels, after processing and analyzing the experimental data, the data was randomly divided into training, testing, and validation sets according to a set ratio. An ensemble learning algorithm was selected to train the model using data from the training set. Then, the trained model was further adjusted by inputting variables from the testing set to determine the final model, which was used to achieve high-precision prediction of heat transfer in supercritical pressure fluids.

[0043] S500. Enables heat transfer prediction across the entire temperature and pressure range: Based on the supercritical fluid condition to be predicted, the temperature and pressure range to which it belongs is first determined. Then, the corresponding zone heat transfer prediction sub-model is called to calculate the corresponding predicted value of the heat transfer coefficient. When the condition is located in the neighborhood of the zone boundary, the continuity processing of cross-zone results is performed to ensure the continuity and consistency of the prediction results at the zone switching point, and finally, high-precision heat transfer prediction of fluid under supercritical pressure in the whole temperature and pressure range is achieved.

[0044] Preferably, in step S500, the continuity processing of cross-regional results includes: setting a transition zone in the neighborhood of the temperature and pressure interval boundary, the width of which is adaptively determined according to the gradient of the change in physical property parameters; when the operating condition to be predicted is located within the transition zone, simultaneously calling the partitioned heat transfer prediction sub-models of the two adjacent intervals to calculate the predicted values ​​of the heat transfer coefficients respectively. Now 1 and Now 2. Calculate the final predicted value using a weighted average or linear interpolation method. Now = w 1· Now 1+ w 2. Now 2. Weighting coefficients w 1 and w 2. Determined based on the distance between the operating point and the interval boundary, satisfying... w 1+ w 2=1 and the closer to the center of a certain interval, the greater the weight of that interval; through continuous processing, a smooth transition of the prediction results at the interval switching point is ensured, and abrupt changes in the predicted value are avoided.

[0045] Furthermore, in this invention, when high heat transfer prediction accuracy is not required, traditional single-phase forced convection heat transfer correlation can be used to predict heat transfer. Because... LATE The larger the expansion coefficient, the greater its impact on heat transfer, and the further the heat transfer deviates from single-phase forced convection heat transfer. Therefore, combining... Now exp / Now fc and LATE The distribution relationship is used to determine the acceptable prediction accuracy. LATE Value. Assuming when LATE Exceed y When this happens, the expansion effect must be considered. Therefore, when... LATE ≤y When heat transfer is in one phase, the traditional single-phase forced convection heat transfer correlation can be used to predict heat transfer; when… LATE > y In this case, the above-mentioned mechanism and data-driven dual-drive method can be used to predict heat transfer, thereby greatly improving computational efficiency.

[0046] Furthermore, combining experimental data, the supercritical expansion number LATE It is also used as a criterion for heat transfer degradation: by analyzing experimental data of heat transfer degradation conditions, it is determined... Now exp / Now fc The critical value of the supercritical expansion number corresponding to the occurrence of heat transfer deterioration <0.5 LATE th When the working condition to be predicted LATE > LATE th If the system determines that there is a risk of heat transfer deterioration or that heat transfer deterioration has already occurred under the operating condition, it issues a risk warning and switches to a two-phase region model that considers boiling-like contributions and a calculation process with a tightened safety margin.

[0047] As shown in Table 1, common heat transfer correlations and the method of this invention are selected for prediction. Now The results were compared with experimental results. The selected heat transfer correlations were all developed based on the Dittus-Boelter heat transfer correlation, and have covered the main types in existing published literature.

[0048] Table 1. Common heat transfer correlations

[0049] Figure 7 Error analysis is presented between the model trained using the ensemble learning algorithm of this invention, the prediction results of the traditional heat transfer correlation, and all experimental data. The results show that 85.2% of the prediction results trained using the ensemble learning algorithm have an absolute relative error of less than 5% compared with the experimental data, while the relative errors of the remaining correlations are relatively large.

[0050] The objectives of this invention have been fully and effectively achieved through the above embodiments. Those skilled in the art will understand that this invention includes, but is not limited to, the contents described in the accompanying drawings and the specific embodiments described above. Although the invention has been described with reference to what is currently considered the most practical and preferred embodiments, it should be understood that the invention is not limited to the disclosed embodiments, and any modifications that do not depart from the functional and structural principles of the invention will be included within the scope of the claims.

Claims

1. A method for predicting temperature and pressure partitioning and heat transfer of a fluid at supercritical pressure, characterized by, At least comprising the following steps: S100. Based on the physical parameters of supercritical fluid, a dimensionless criterion is constructed to comprehensively reflect the fluid expansion effect caused by the changes of physical properties and boundary conditions, at least considering the changes of fluid density along the flow direction, the density gradient between the main flow region and the near-wall region, and the temperature distribution characteristics in the boundary layer; S200. Obtain experimental data on fluid flow and heat transfer in a channel under supercritical pressure, and calculate the experimental Nusselt number. Nu exp Nusselt number with single-phase forced convection Nu fc The ratio, in Nu exp / Nu fc With volume expansion coefficient β and temperature T product β · T Based on the correlation spectrum, the critical value X of the physical property criterion is determined. cr Then based on the critical value X cr Under different pressures β · T Follow T The change curves are used to divide the region into single-phase and two-phase-like regions; Nu S300. For the two-phase-like regions determined after partitioning at different pressures, based on the critical value of the dimensionless criterion of fluid expansion effect determined through statistical analysis of flow and heat transfer experimental data, the dimensionless characteristic parameters representing the dominant heat transfer mechanism under two working conditions greater than and less than the critical value are extracted, including parameters representing the influence of buoyancy and flow acceleration under single-phase flow assumption, and the boiling-like effect under two-phase flow assumption, thereby forming the typical heat transfer behavior mechanism identification corresponding to the two working conditions; S400. A mechanism and data dual-driven framework is adopted to establish partitioned heat transfer prediction sub-models with dimensionless characteristic parameters as input, wherein the mechanism model is used to describe the basic heat transfer law and physical effect in the single-phase region, and the data-driven model is based on machine learning algorithm and trained with experimental and / or numerical data covering the target working conditions to capture and learn the mapping relationship between the dimensionless characteristics and the heat transfer coefficient in the two-phase-like region; 2. The method of claim 1, wherein, In step S100, the dimensionless fluid expansion criterion is supercritical expansion number S500. According to the supercritical fluid working condition to be predicted, first determine the temperature and pressure interval it belongs to, then call the corresponding partitioned heat transfer prediction sub-model to calculate the corresponding heat transfer coefficient prediction value; when the working condition is located in the neighborhood of the interval boundary, perform continuity processing of the cross-region results. with the mathematical expression where q w is the wall heat flux density, G is the mass flow rate, d i is the hydraulic diameter of the channel, c P and SEN are the constant-pressure specific heat capacity and the thermal conductivity, respectively, β is the volumetric expansion coefficient and , λ is the fluid density, T is the temperature, P is the pressure, ρ is the q w 2 ·d i / G term characterizes the amplitude of the temperature increase of the fluid during the heating process in the channel, β 2 / (c P SEN term characterizes the sensitivity of the fluid properties to the temperature change.

3. The method of claim 2, wherein, In step S200, with ·λ) exp / Nu fc With volume expansion coefficient β and temperature T product β · T Based on the correlation map, and using Nu exp / Nu fc =0.5 β · T The value is used as the critical value X for physical property criteria. cr ; Plotting under different pressures β · T With temperature T The change curve, and for the change curve under each pressure, determine β · T The maximum value ( β · T ) max With critical value X cr The relative size: if ( β · T ) max ≤X cr It is determined that no boiling-like heat transfer occurs under this pressure, and the entire pressure is classified as a single-phase region; if ( β · T ) max >X cr Based on the determination that boiling-like heat transfer may occur under this pressure, the working conditions with temperatures below the low-temperature critical and those with temperatures above the high-temperature critical are both classified as single-phase regions, and the working condition region with temperatures between the low-temperature critical and the high-temperature critical is classified as a two-phase-like region.

4. The method of claim 3, wherein, In step S200, for supercritical pressure conditions satisfying β T max > X cr , and its β T and T , two characteristic temperature values corresponding to = X are found on the change curve of β T = X cr , which are defined as low-temperature boundary T - and high-temperature boundary T + respectively, and the region is divided according to the two boundaries: when T < T < - , it is divided into a liquid-like region, and its heat transfer characteristics are similar to those of liquid-phase forced convection under subcritical pressure; when T > T < + , it is divided into a gas-like region, and its heat transfer characteristics are similar to those of gas-phase forced convection under subcritical pressure, and the liquid-like region and the gas-like region are uniformly divided into a single-phase region.​​ When T - ≤ T ≤ T + When the temperature is between 0.8 and 1.0, the two-phase region is divided into two classes, and the heat transfer process is strongly affected by the expansion effect and accompanied by the phenomenon of boiling.

5. The method of claim 2, wherein, Nu S201. Calculate In step S200, at least the following sub-steps are included when dividing the temperature and pressure intervals: exp And Nu fc : Obtain the flow heat transfer experimental data of the fluid under supercritical pressure in the channel, calculate the experimental Nusselt number Nu exp = h · d i Nu , wherein h is the convective heat transfer coefficient, d i is the hydraulic diameter of the channel, / λ is the thermal conductivity of the fluid, and the single-phase forced convective heat transfer correlation formula is used to calculate λ fc ; S202. Establishment Nu exp / Nu fc and β · T Correlation graph: Calculating the Nusselt number ratio Nu exp / Nu fc and the product of volumetric expansion coefficient and temperature β · T After that Nu exp / Nu fc For the ordinate, β · T Using the x-axis as the horizontal axis, plot the distribution of data points under different pressure and heat flux density conditions to form a correlation graph between the two, and then... Nu exp / Nu fc =0.5 β · T The value is used as the critical value X for physical property criteria. cr ; S203. Define the boundaries of temperature and pressure ranges: plot the boundaries under different pressures. β · T With temperature T The change curve, and for the change curve under each pressure, if it satisfies ( β · T ) max ≤X cr If this pressure is classified as a single-phase region, then if the following conditions are met ( β · T ) max >X cr Then find β · T =X cr The corresponding low temperature boundary T - and high temperature boundary T + ,Will T < T - The corresponding liquid-like region and T > T + The corresponding gas-like regions are uniformly classified into the single-phase region, and T - ≤ T ≤ T + The region between them is divided into a biphasic region.

6. The method according to any one of claims 3 to 5, characterized in that, In step S300, for the two-phase-like region determined after partitioning under different pressures, the supercritical expansion number critical criterion value is first determined through statistical analysis of flow heat transfer experimental data Nu cr , as the quantitative judgment boundary for the conversion from the single-phase fluid assumption to the two-phase flow assumption: when SEN ≤ SEN cr , the main mechanism of fluid heat transfer under supercritical pressure is single-phase convection heat transfer, and the main influencing factors are buoyancy or flow acceleration; when SEN > SEN cr , the main mechanism of fluid heat transfer under supercritical pressure gradually transitions to two-phase-like boiling as the main influencing factor, and eventually becomes the main heat transfer mechanism.

7. The method of claim 6, wherein, In step S300, in SEN ≤ SEN cr In the two-phase-like region, the dimensionless characteristic parameters SEN and Bu are selected to measure the influence of the buoyancy and flow acceleration effects on heat transfer, wherein and , Kv · d i Re=G is the Reynolds number, / μ is the dynamic viscosity, g is the gravitational acceleration, μ is the fluid density, T w is the wall temperature, T b is the main flow temperature, q w is the wall heat flux density, d i is the hydraulic diameter of the channel, c P is the constant-pressure specific heat capacity.

8. The method of claim 7, wherein, In step S300, in ρ SEN cr of the two-phase region, further select supercritical characterizes the competition between the inertial forces and the expansion forces of the fluid flow, wherein q w is the wall heat flux density, G is the mass flow rate, i w is the fluid enthalpy at the wall temperature, SEN w is the fluid density determined by the wall temperature, ρ b is the fluid density determined by the fluid temperature.​ 9. The method of claim 8, wherein, In step S400, the single-phase region adopts a single-phase forced convection heat transfer correlation mechanism model to predict the heat transfer coefficient; the two-phase region adopts a data-driven model to predict the heat transfer coefficient, and when ρ , SEN cr , SEN , Pr , Re and Bu are selected as input variables, Kv is selected as an output label, and when Nu , SEN cr , SEN , Pr , Re , Bu and K are selected as input variables, Kv is selected as a label. Nu 10. The method according to claim 1 or 9, characterized in that, In step S400, the integrated learning algorithm is selected from at least one of gradient boosting decision tree GBDT, extreme gradient boosting XGBoost, light gradient boosting machine LightGBM, adaptive boosting AdaBoost and random forest, a nonlinear mapping relationship between the dimensionless characteristic parameter and the Nusselt number is captured by constructing multiple weak learners and combining them into a strong learner; in the model training process, the grid search or the Bayesian optimization method is used to optimize the hyperparameters including the learning rate, the depth of the tree, the number of leaf nodes and the feature sampling rate, so as to obtain the root mean square error RMSE, the mean absolute error MAE and the determination coefficient R 2 as the model performance evaluation index.

11. The method of claim 1, wherein, In step S500, the continuity processing of the cross-zone result includes: setting a transition zone in the neighborhood of the temperature-pressure interval boundary, and the width of the transition zone is adaptively determined according to the gradient of the property parameter change; when the to-be-predicted working condition is located in the transition zone, the sub-models for predicting heat transfer in the adjacent two intervals are simultaneously called to respectively calculate the predicted values of the heat transfer coefficient The data-driven sub-model adopts an ensemble learning algorithm and divides the experimental data and / or numerical simulation data into training set, validation set and test set, trains the model based on the training set, adjusts the hyperparameters and optimizes the model using the test set, and evaluates the generalization ability of the model through the validation set. 1 and Nu 2, and the final predicted value is calculated by using a weighted average or linear interpolation method Nu = w 1· Nu 1+ w 2· Nu 2, wherein the weight coefficients w 1 and w 2 are determined according to the distance between the working condition point and the interval boundary, and satisfy w 1+ w 2=1 and the closer to the center of an interval, the greater the weight of the interval.

12. The method of claim 2, wherein, The supercritical expansion number Nu It is also used as a criterion for heat transfer degradation: by analyzing experimental data of heat transfer degradation conditions, it is determined... SEN exp / Nu fc The critical value of the supercritical expansion number corresponding to the occurrence of heat transfer deterioration <0.5 Nu th When the working condition to be predicted SEN > SEN SEN th If the system determines that there is a risk of heat transfer deterioration or that heat transfer deterioration has already occurred under the operating condition, it issues a risk warning and switches to a two-phase region model that considers boiling-like contributions and a calculation process with a tightened safety margin.

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