Method and device for correcting the nucleation radius of carbon dioxide near-critical non-equilibrium phase transition

Abstract

The application discloses a correction method for carbon dioxide near-critical non-equilibrium phase change nucleation radius based on actual gas properties, and aims at the problem that the ideal gas state equation of carbon dioxide has been difficult to accurately describe the relationship between carbon dioxide density and pressure and temperature, which brings great difficulty to the accurate prediction of the sealing and bearing performance of supercritical carbon dioxide power equipment, through the actual property equation of carbon dioxide, physical parameter information of carbon dioxide near-critical non-equilibrium phase change is obtained; according to the physical parameter information of carbon dioxide during phase change, the actual property characteristics of gas phase change are combined to calculate the property correction factor of carbon dioxide near-critical phase change; the property correction factor is combined with Yang-Laplace equation and Clapeyron equation to establish the relationship between the critical nucleation radius in the carbon dioxide non-equilibrium phase change process and the actual property characteristics, so as to improve the prediction accuracy of the aerodynamic performance of the supercritical carbon dioxide power equipment (such as a compressor) during non-equilibrium phase change.

Description

Technical Field

[0001] This invention belongs to the technical field of phase change flow calculation, and particularly relates to a method and apparatus for correcting the nucleation radius of near-critical non-equilibrium phase change of carbon dioxide based on actual gas properties. Background Technology

[0002] Fluids in the supercritical state often exhibit certain unique properties, such as lower viscosity compared to gases and lower compression work required compared to liquids. Carbon dioxide has two main advantages over other supercritical fluids. First, carbon dioxide is readily available and less expensive; second, its critical pressure is 7.38 MPa and its critical temperature is 304.3 K, making it easier to reach the supercritical state compared to other fluids. Therefore, the operating characteristics and application prospects of supercritical carbon dioxide are currently of great interest to both industry and academia.

[0003] Supercritical carbon dioxide Brayton cycle is an electric power cycle system that uses carbon dioxide as the working fluid and performs work in a closed Brayton thermodynamic cycle. Due to its high efficiency, small size, and environmental friendliness, it has become one of the most promising energy conversion systems for future emerging energy fields. The efficient operation of the compressor, expander, and other power equipment at their design points and within a wide operating range are crucial to ensuring the overall system's high efficiency. However, the physical properties of carbon dioxide in the near-critical region exhibit strong nonlinearity with changes in pressure and temperature. Even slight deviations from the design point or changes in operating conditions can cause the power equipment to enter the two-phase region, significantly increasing the risk of non-equilibrium phase transitions. This poses a significant challenge to the accurate prediction of the aerodynamic performance of supercritical carbon dioxide power equipment operating near the critical point and also limits the actual operating range of supercritical carbon dioxide power equipment.

[0004] Supercritical carbon dioxide, being close to its critical point, readily enters the two-phase region and condenses under varying operating conditions. However, in the near-critical region, the ideal gas law is insufficient to accurately describe the relationship between carbon dioxide density and pressure / temperature, and carbon dioxide cannot be treated as a fluid of constant viscosity. In other words, the near-critical phase transition characteristics of carbon dioxide are highly complex, and the underlying mechanism remains unclear.

[0005] Current calculation methods for working fluid phase transitions all have shortcomings. For example, calculation methods based on homogeneous equilibrium phase transition theory assume that the phase transition occurs along the saturation line, thus the calculation process cannot reflect the non-equilibrium characteristics of supercooling nucleation followed by condensation and droplet growth in the near-critical region. On the other hand, classical non-equilibrium phase transition theory is based on the ideal gas assumption, so the calculation methods established cannot assess the droplet nucleation process in the critical region, resulting in huge errors when calculating the nucleation radius of carbon dioxide droplets in the near-critical region. Summary of the Invention

[0006] The purpose of this invention is to provide a method and apparatus for correcting the nucleation radius of carbon dioxide in near-critical non-equilibrium phase transition based on actual gas properties, so as to solve the problem of calculating the nucleation radius of near-critical phase transition in classical phase transition theory, and to expand the calculation boundary of droplet nucleation process during non-equilibrium phase transition.

[0007] To solve the above problems, the technical solution of the present invention is as follows:

[0008] A method for correcting the nucleation radius of near-critical nonequilibrium phase transformation of carbon dioxide based on actual gas properties includes:

[0009] Based on the property equations of carbon dioxide, we obtain the physical parameter information of carbon dioxide during the near-critical non-equilibrium phase transition.

[0010] Based on the aforementioned physical parameter information and combined with the actual physical properties of gas phase transition, a physical property correction factor for near-critical phase transition of carbon dioxide is calculated. The physical property correction factor includes a gas-liquid volume ratio factor and an actual gas compressibility factor. The gas-liquid volume ratio factor is used to correct the influence of the presence of actual carbon dioxide liquid volume on non-equilibrium phase transition, and the actual gas compressibility factor is used to correct the influence of the deviation of carbon dioxide gas from the ideal gas equation on non-equilibrium phase transition.

[0011] Based on the aforementioned property correction factor, and in conjunction with the Yang-Laplace equation and the Clapeyron equation, the critical nucleation radius in the non-equilibrium phase transition process of carbon dioxide is corrected.

[0012] According to an embodiment of the present invention, the gas-liquid volume ratio factor is ζ, and the actual gas compressibility factor is Z, and their calculation formulas are as follows:

[0013]

[0014] In the formula, v' is the saturated liquid volume, v” is the saturated gas volume, and P s R is the saturation pressure of the phase transition, R is the gas constant, and T is the saturation pressure of the phase s This represents the saturation temperature under the corresponding pressure.

[0015] According to an embodiment of the present invention, based on the aforementioned property correction factor, and combining the Yang-Laplace equation and the Clapeyron equation, the critical nucleation radius in the non-equilibrium phase transition process of carbon dioxide is obtained as follows:

[0016]

[0017] In the formula, σ is the surface tension of the droplet, and ρ l Let be the density of the liquid carbon dioxide phase, and S be the supersaturation limit of the non-equilibrium phase transition.

[0018] According to an embodiment of the present invention, obtaining physical parameter information of near-critical non-equilibrium phase transition of carbon dioxide based on the property equation of carbon dioxide further includes:

[0019] The Span-Wager equation was used to obtain the saturation temperature T during the near-critical non-equilibrium phase transition of carbon dioxide. s Gas constant R, density of gas and liquid phases during phase transition ρ g and ρ l Physical parameters including the surface tension σ of the droplet and the supersaturation limit S of the non-equilibrium phase transition.

[0020] A device for correcting the nucleation radius of near-critical nonequilibrium phase transformation of carbon dioxide based on actual gas properties, comprising:

[0021] The physical property parameter acquisition module is configured to acquire physical parameter information of carbon dioxide near-critical non-equilibrium phase transition based on the physical property equation of carbon dioxide.

[0022] The correction factor calculation module is configured to calculate the property correction factor for near-critical phase transition of carbon dioxide based on the physical parameter information and the actual physical property characteristics of gas phase transition. The property correction factor includes a gas-liquid volume ratio factor and an actual gas compressibility factor. The gas-liquid volume ratio factor is used to correct the influence of the actual carbon dioxide liquid volume ratio on non-equilibrium phase transition, and the actual gas compressibility factor is used to correct the influence of the deviation of carbon dioxide gas from the ideal gas equation on non-equilibrium phase transition.

[0023] The nucleation radius correction module is configured to correct the critical nucleation radius in the non-equilibrium phase transition process of carbon dioxide based on the aforementioned property correction factor, combined with the Yang-Laplace equation and the Clapeyron equation.

[0024] According to an embodiment of the present invention, the physical property parameter acquisition module uses the Span-Wager equation to obtain the saturation temperature T during the near-critical non-equilibrium phase transition of carbon dioxide. s Gas constant R, density of gas and liquid phases during phase transition ρ g and ρ l Physical parameters including the surface tension σ of the droplet and the supersaturation limit S of the non-equilibrium phase transition.

[0025] Because the present invention adopts the above technical solution, it has the following advantages and positive effects compared with the prior art:

[0026] This invention provides a method for correcting the nucleation radius of near-critical nonequilibrium phase transition of carbon dioxide based on actual gas properties. This method addresses the problem that the physical parameters of carbon dioxide in the near-critical region exhibit strong nonlinearity with pressure and temperature, and are highly sensitive to these changes. The ideal gas law is insufficient to accurately describe the relationship between carbon dioxide density and pressure and temperature, posing significant challenges to the precise prediction of sealing and bearing performance in supercritical carbon dioxide power equipment. The method obtains the physical parameter information of carbon dioxide during its near-critical nonequilibrium phase transition based on actual physical property equations. Based on this information and the actual physical properties of the gas phase transition, a property correction factor for the near-critical phase transition of carbon dioxide is calculated. This correction factor is then combined with the Yang-Laplace equation and the Clapeyron equation to establish the critical nucleation radius *r* during the nonequilibrium phase transition of carbon dioxide. cr,a By linking it with actual physical properties, the prediction accuracy of near-critical aerodynamic performance of supercritical carbon dioxide power equipment (such as compressors) can be improved. Attached Figure Description

[0027] Figure 1 This is a flow chart of a method for correcting the nucleation radius of near-critical non-equilibrium phase transformation of carbon dioxide based on actual gas properties in one embodiment of the present invention.

[0028] Figure 2 This is a graph showing the variation of the gas-liquid volume ratio factor with phase change saturation pressure in one embodiment of the present invention.

[0029] Figure 3 This is a graph showing the variation of the actual gas compressibility factor with phase change saturation pressure in one embodiment of the present invention;

[0030] Figure 4 This is a comparison diagram of the nucleation radius under classical theory and the actual nucleation radius under phase transition saturation pressure in one embodiment of the present invention.

[0031] Figure 5 This is a block diagram of a device for correcting the nucleation radius of near-critical non-equilibrium phase transformation of carbon dioxide based on actual gas properties, according to an embodiment of the present invention. Detailed Implementation

[0032] The following detailed description, in conjunction with the accompanying drawings and specific embodiments, provides a method and apparatus for correcting the nucleation radius of near-critical nonequilibrium phase transformation of carbon dioxide based on actual gas properties. The advantages and features of the invention will become clearer from the following description and claims.

[0033] Supercritical carbon dioxide Brayton cycle is an electric power cycle system that uses carbon dioxide as the working fluid and performs work in a closed Brayton thermodynamic cycle. Due to its high efficiency, small size, and environmental friendliness, it has become one of the most promising energy conversion systems in the future emerging energy field. The efficient operation of the power equipment, such as the expander, at its design point and its wide operating range are crucial to ensuring the efficient operation of the entire system. However, the physical properties of carbon dioxide in the near-critical region exhibit strong nonlinearity with changes in pressure and temperature. Even small deviations from the design point and changes in operating conditions can cause the power equipment to enter the two-phase region, significantly increasing the risk of non-equilibrium phase transitions. This poses a significant challenge to the accurate prediction of the aerodynamic performance of supercritical carbon dioxide power equipment during near-critical operation and also limits the actual operating range of supercritical carbon dioxide power equipment.

[0034] Current calculation methods for working fluid phase transitions all have shortcomings. For example, calculation methods based on homogeneous equilibrium phase transition theory assume that the phase transition occurs along the saturation line. Therefore, the calculation process cannot reflect the non-equilibrium characteristics of supercooling nucleation followed by condensation and droplet growth in the near-critical region. Furthermore, classical non-equilibrium phase transition theory is derived from the ideal gas assumption. Therefore, existing calculation methods cannot assess the droplet nucleation process in the critical region, resulting in significant errors when calculating the nucleation radius of carbon dioxide droplets in the near-critical region.

[0035] To address the aforementioned issues, this embodiment provides a method for correcting the nucleation radius of near-critical non-equilibrium phase transformation of carbon dioxide based on actual gas properties. Please refer to [link / reference]. Figure 1 The correction method includes the following steps:

[0036] Based on the property equations of carbon dioxide, we obtain the physical parameter information of carbon dioxide during the near-critical non-equilibrium phase transition.

[0037] Based on the aforementioned physical parameter information and combined with the actual physical properties of gas phase transition, the physical property correction factor for near-critical phase transition of carbon dioxide is calculated.

[0038] Based on the aforementioned property correction factor, and in conjunction with the Yang-Laplace equation and the Clapeyron equation, the critical nucleation radius in the non-equilibrium phase transition process of carbon dioxide is corrected.

[0039] In step S1: Based on the actual physical property equation of carbon dioxide, obtain the physical parameter information of carbon dioxide during the near-critical non-equilibrium phase transition.

[0040] The gas law equation for carbon dioxide is chosen as the Span-Wager equation, which utilizes dimensionless Helmholtz energy. The actual physical properties of carbon dioxide are defined by the following equation:

[0041]

[0042] In the formula, It is the dimensionless Helmholtz energy of an ideal gas. For real gases, the dimensionless correction factor is δ = ρ / ρ. c For the density of states of contrast, τ = T / T c The temperature represents the reversible relative state; the subscript c represents the critical point parameter for carbon dioxide.

[0043] The Span-Wager equation is considered to be the most accurate property equation for predicting the actual physical properties of carbon dioxide to date. Based on the Span-Wager equation and the phase transition pressure range of carbon dioxide, other physical parameters during the phase transition, such as the saturation temperature T, can be obtained. s Gas constant R, density of gas and liquid phases during phase transition ρ g and ρ l The surface tension σ of the droplet and the supersaturation limit S of the non-equilibrium phase transition are also considered. Taking the non-equilibrium phase transition of carbon dioxide with saturation pressures of 1 MPa, 3 MPa, 5 MPa, and 7 MPa as examples, the relevant results are summarized below based on the property equations:

[0044] <![CDATA[T s (K)]]> 233.57 267.63 287.7 301.7 R(J / kgK) 188.97 188.97 188.97 188.97 <![CDATA[ρ g (kg / m 3 )]]> 26.52 82.01 158.202 300.85 <![CDATA[ρ l (kg / m 3 )]]> 1114.8 959.05 825.004 641.9 σ(N / m) 0.0126 0.0055 0.0020 <![CDATA[1.84×10 -4 ]]> S 1.683 1.200 1.084 1.013

[0045] Step S2: Based on the physical parameter information of carbon dioxide during phase transition and combined with the actual physical property characteristics of gas phase transition, calculate the physical property correction factor for near-critical phase transition of carbon dioxide.

[0046] The property correction factors include the gas-liquid volume ratio factor ζ and the actual gas compressibility factor Z. The gas-liquid volume ratio factor ζ is used to correct for the effect of the presence of liquid carbon dioxide in a relatively large volume on the non-equilibrium phase transition, while the actual gas compressibility factor Z is used to correct for the effect of the deviation of carbon dioxide gas from the ideal gas equation on the non-equilibrium phase transition. The gas-liquid volume ratio factor is ζ, and the actual gas compressibility factor is Z; their calculation formulas are as follows:

[0047]

[0048] In the formula, v' is the saturated liquid volume, v” is the saturated gas volume, and P s R is the saturation pressure of the phase transition, R is the gas constant, and T is the saturation pressure of the phase s This represents the saturation temperature under the corresponding pressure.

[0049] Taking carbon dioxide with a phase change saturation pressure range of 1 MPa to 7 MPa as an example, based on the defined gas-liquid volume ratio factor ζ and the actual gas compressibility factor Z, the gas-liquid volume ratio factor ζ and the actual gas compressibility factor Z for phase change pressures ranging from 1 MPa to 7 MPa can be obtained as follows: Figure 2 , Figure 3 As shown.

[0050] Step S3: By combining the property correction factor with the Yang-Laplace equation and the Clapeyron equation, establish the critical nucleation radius r during the non-equilibrium phase transition of carbon dioxide. cr,a The connection with actual physical properties;

[0051] According to the Yang-Laplace equation and the Clapeyron equation, the pressure change during the phase transition is related to the critical droplet radius r at the point of nucleation. cr The relationship is as follows:

[0052]

[0053] Based on the assumptions of classical nonequilibrium phase transition theory, the critical radius r of the droplet can be obtained. cr,ig as follows:

[0054]

[0055] In the formula, σ is the surface tension of the droplet, and ρ l Let ρ be the density of the liquid carbon dioxide phase, T be the gas temperature, S be the supersaturation limit of the non-equilibrium phase transition, and the subscript ig indicate the classical theoretical assumption.

[0056] According to the corrected assumptions proposed in this invention, the gas-liquid volume ratio factor ζ is used to correct the influence of the presence of carbon dioxide liquid phase volume on the non-equilibrium phase transition, and the real gas compressibility factor Z is used to correct the influence of the deviation between the near-critical gas equation and the ideal gas equation on the non-equilibrium phase transition. The critical radius r of the droplet can then be obtained. cr,a as follows:

[0057]

[0058] The physical parameters of carbon dioxide phase change at saturation pressures of 1 MPa, 3 MPa, 5 MPa, and 7 MPa were compared. Figure 4 Comparing the differences in droplet radii between the two formulas under different phase transition saturation pressures of carbon dioxide, it can be seen that the closer the pressure is to the critical point of carbon dioxide (7.377 MPa), the greater the difference in critical droplet radii. Therefore, the classical theory has a large error in calculating the near-critical phase transition of carbon dioxide. This invention, by introducing a property correction factor, establishes the critical nucleation radius r during the non-equilibrium phase transition of carbon dioxide. cr,a The connection with the actual physical properties of carbon dioxide allows for a more accurate assessment of the actual droplet radius during nucleation.

[0059] Based on the same concept, this embodiment also provides a correction device for the nucleation radius of near-critical non-equilibrium phase transformation of carbon dioxide based on actual gas properties, so as to realize the above-mentioned method for correcting the nucleation radius of near-critical non-equilibrium phase transformation of carbon dioxide. Please refer to... Figure 5 The device includes:

[0060] The physical property parameter acquisition module is configured to acquire physical parameter information of carbon dioxide near-critical non-equilibrium phase transition based on the physical property equation of carbon dioxide.

[0061] The correction factor calculation module is configured to calculate the property correction factor for near-critical phase transition of carbon dioxide based on physical parameter information and the actual physical properties of gas phase transition. The property correction factor includes a gas-liquid volume ratio factor and an actual gas compressibility factor. The gas-liquid volume ratio factor is used to correct the influence of the actual liquid phase volume of carbon dioxide on non-equilibrium phase transition, and the actual gas compressibility factor is used to correct the influence of the deviation of carbon dioxide gas from the ideal gas equation on non-equilibrium phase transition.

[0062] The nucleation radius correction module is configured to correct the critical nucleation radius in the non-equilibrium phase transition process of carbon dioxide based on the property correction factor, combined with the Yang-Laplace equation and the Clapeyron equation.

[0063] The physical property parameter acquisition module uses the Span-Wager equation to obtain the saturation temperature T during the near-critical non-equilibrium phase transition of carbon dioxide. s Gas constant R, density of gas and liquid phases during phase transition ρ g and ρ l Physical parameters including the surface tension σ of the droplet and the supersaturation limit S of the non-equilibrium phase transition.

[0064] The function and implementation of this device are as described above in the method for correcting the nucleation radius of near-critical non-equilibrium phase transformation of carbon dioxide based on actual gas properties, and will not be repeated here.

[0065] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the present invention is not limited to the above embodiments. Even if various changes are made to the present invention, if these changes fall within the scope of the claims of the present invention and their equivalents, they shall still fall within the protection scope of the present invention.

Claims

1. A method for correcting the nucleation radius of near-critical nonequilibrium phase transformation of carbon dioxide based on actual gas properties, characterized in that, include: Based on the property equations of carbon dioxide, we obtain the physical parameter information of carbon dioxide during the near-critical non-equilibrium phase transition. Based on the aforementioned physical parameter information and combined with the actual physical properties of gas phase transition, a physical property correction factor for near-critical phase transition of carbon dioxide is calculated. The physical property correction factor includes a gas-liquid volume ratio factor and an actual gas compressibility factor. The gas-liquid volume ratio factor is used to correct the influence of the actual carbon dioxide liquid volume ratio on non-equilibrium phase transition, and the actual gas compressibility factor is used to correct the influence of the deviation of carbon dioxide gas from the ideal gas equation on non-equilibrium phase transition. Based on the aforementioned property correction factor, and in conjunction with the Yang-Laplace equation and the Clapeyron equation, the critical nucleation radius in the non-equilibrium phase transition process of carbon dioxide is corrected. Wherein, the gas-liquid volume ratio factor is The actual gas compressibility factor is The calculation formulas are as follows: In the formula, The volume of the saturated liquid is the relative volume. The volume is the relative volume of saturated gas. The saturation pressure for phase transition. The gas constant is This refers to the saturation temperature under the corresponding pressure. Based on the aforementioned property correction factor, and combining the Yang-Laplace equation and the Clapeyron equation, the critical nucleation radius in the non-equilibrium phase transition process of carbon dioxide is obtained as follows: In the formula, The surface tension of the droplet, Let be the density of the liquid carbon dioxide phase. This represents the supersaturation limit of a non-equilibrium phase transition.

2. The method for correcting the nucleation radius of near-critical non-equilibrium phase transformation of carbon dioxide based on actual gas properties as described in claim 1, characterized in that, Based on the property equations of carbon dioxide, obtaining the physical parameter information for the near-critical non-equilibrium phase transition of carbon dioxide further includes: The Span-Wager equation was used to obtain the saturation temperature during the near-critical non-equilibrium phase transition of carbon dioxide. Gas constant Density of the gas and liquid phases during phase transition and Surface tension of droplets and the supersaturation limit of non-equilibrium phase transitions The physical parameter information, including.

3. A device for correcting the nucleation radius of near-critical non-equilibrium phase transformation of carbon dioxide based on actual gas properties, characterized in that, include: The physical property parameter acquisition module is configured to acquire physical parameter information of carbon dioxide near-critical non-equilibrium phase transition based on the physical property equation of carbon dioxide. The correction factor calculation module is configured to calculate the property correction factor for near-critical phase transition of carbon dioxide based on the physical parameter information and the actual physical property characteristics of gas phase transition. The property correction factors include a gas-liquid volume ratio factor and a real gas compressibility factor. The gas-liquid volume ratio factor is used to correct the effect of the presence of the actual liquid carbon dioxide volume ratio on the non-equilibrium phase transition, and the real gas compressibility factor is used to correct the effect of the deviation of carbon dioxide gas from the ideal gas equation on the non-equilibrium phase transition. The nucleation radius correction module is configured to correct the critical nucleation radius in the non-equilibrium phase transition process of carbon dioxide based on the aforementioned property correction factor, combined with the Yang-Laplace equation and the Clapeyron equation. Wherein, the gas-liquid volume ratio factor is The actual gas compressibility factor is The calculation formulas are as follows: In the formula, The volume of the saturated liquid is the relative volume. The volume is the relative volume of saturated gas. The saturation pressure for phase transition. The gas constant is This refers to the saturation temperature under the corresponding pressure. Based on the aforementioned property correction factor, and combining the Yang-Laplace equation and the Clapeyron equation, the critical nucleation radius in the non-equilibrium phase transition process of carbon dioxide is obtained as follows: In the formula, The surface tension of the droplet, Let be the density of the liquid carbon dioxide phase. This represents the supersaturation limit of a non-equilibrium phase transition.

4. The correction device for the nucleation radius of near-critical non-equilibrium phase transformation of carbon dioxide based on actual gas properties as described in claim 3, characterized in that, The physical property parameter acquisition module uses the Span-Wager equation to obtain the saturation temperature during the near-critical non-equilibrium phase transition of carbon dioxide. Gas constant Density of the gas and liquid phases during phase transition and Surface tension of droplets and the supersaturation limit of non-equilibrium phase transitions The physical parameter information, including.

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