A method for calculating water vapor sublimation phase change products
By calculating the size and number of ice crystals generated by water vapor sublimation in rocket engine exhaust using a method based on molecular thermal motion, the complexity of ice crystal distribution simulation in existing technologies has been solved, accurate calculations have been achieved in low-temperature and rarefied environments, and the reliability of flow field distribution has been improved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- BEIJING AEROSPACE INST FOR METROLOGY & MEASUREMENT TECH
- Filing Date
- 2025-11-27
- Publication Date
- 2026-06-02
AI Technical Summary
Existing technologies struggle to accurately calculate the size and quantity distribution of ice crystals formed by water vapor sublimation in rocket engine exhaust, especially in low-temperature, thin environments where the ice crystal formation process is complex and subject to discontinuous influences, making it difficult to accurately simulate the phase transition process.
Using a molecular thermal motion-based method, the phase transition trend of water vapor is quantified by calculating the difference between the Gibbs free energy of water vapor and the Gibbs free energy of ice. Combined with the thermal motion characteristics of water vapor molecules, the formation and growth rate of ice crystals are calculated. The growth process of existing ice crystals is considered, and the phase transition consumption at each moment is recorded until the phase transition is stable.
It provides an accurate calculation method for the size and quantity distribution of ice crystals in a low-temperature and rarefied environment, ensuring the reliability of the engine exhaust flow field distribution, improving the numerical calculation of the exhaust flow field distribution, and solving the calculation problem of plume phase change products under low-temperature conditions.
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Figure CN122135803A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of phase change technology, specifically relating to a method for calculating water vapor sublimation phase change products. Background Technology
[0002] The study of the flow field distribution in rocket engine wakes is of great significance for improving engine performance. Due to the low-temperature environment, water vapor in the engine wake undergoes a phase change, resulting in sublimation and the formation of numerous ice crystals. This significantly affects the flow field characteristics of the wake, including its radiation signal and the environment surrounding instruments within it. Therefore, accurate calculation of the ice crystal size and quantity distribution is crucial for the accurate study of engine performance.
[0003] Water vapor in engine exhaust forms ice crystals at low temperatures. The discontinuity caused by the rarefied environment alters the phase transition process of water vapor, a point rarely addressed in previous studies. Furthermore, new ice crystals are generated at different times during the actual phase transition, while existing ice crystals participate in the growth process at those moments. This results in a complex relationship between the size and quantity of phase transition products. Previous studies often fix the initial ice crystal size and then examine a single ice crystal growth process. Therefore, proposing a method for calculating water vapor sublimation phase transition products is of paramount importance. Summary of the Invention
[0004] To calculate the size and quantity distribution of sublimation products, previous studies have often used methods based on classical nucleation formulas and traditional growth formulas to calculate the formation and growth of ice crystals of a single size. However, actual phase transition processes are affected by discontinuity, and the size and quantity distribution of phase transition products are complex. To address this issue, this invention provides a method for calculating water vapor sublimation phase transition products based on molecular thermal motion, providing a foundation for accurately calculating the size and quantity distribution of ice crystals in high-altitude, low-temperature, and rarefied environments.
[0005] Specifically, the present invention provides the following technical solutions: A method for calculating water vapor sublimation phase transition products includes the following steps: Step 1: Obtain local operating conditions, calculate the Gibbs free energy of water vapor and ice, and determine the phase change trend of water vapor in the local area; Step 2: Based on the local thermal motion characteristics of water vapor molecules, the discontinuity of water vapor is quantitatively calculated, and the influence of the discontinuity on the phase transition process is obtained; Step 3: Based on the operating conditions at each moment, calculate the formation rate and growth rate of newly formed ice crystals at that moment; Step 4: Calculate the growth rate of the existing ice crystals that have been generated at each moment based on the operating conditions at that moment. Step 5: Record the water vapor content consumed during the phase transition at each moment until the water vapor content no longer changes and the phase transition reaches stability. Calculate the variation law of the number and size of ice crystals under rarefied gas conditions using the methods described in Steps 3 and 4.
[0006] Preferably, in step one, the local operating conditions include local temperature and water vapor number density; The formula for calculating the Gibbs free energy of water vapor is as follows:
[0007] in, Gibbs free energy of water vapor molecules, expressed in J / kg; It is the temperature of water vapor, measured in Kelvin (K). enthalpy of water vapor The calculation formula is as follows:
[0008] In the formula, u g This is the specific internal energy of water vapor, expressed in J / kg. P g,c This represents the actual static pressure caused by water vapor, measured in Pa. On the scale of molecular thermal motion, this factor affects the volume work done by water vapor, which is the fundamental reason for the altered phase transition conditions caused by the rarefied gas effect. m g Let the mass of a single H2O molecule be . ; n g The gas number density of water vapor molecules, in m³. -3 ; T 0 is the triple point temperature, which is 273.16 K for water; Entropy of water vapor The calculation formula is as follows:
[0009] In the formula, Let be the entropy of liquid water under triple point conditions, which is set to 0 in the calculation. ; The latent heat of vaporization of liquid water under triple point conditions is expressed in J / kg. The triple point temperature is 273.16 K; The specific heat at constant volume of water vapor, in units of ; Boltzmann's constant, ; Let the mass of a single H2O molecule be . ; This represents the actual static pressure caused by water vapor, expressed in Pa. This refers to the number density of water vapor molecules under triple point conditions, expressed in m³. -3 ; The formula for calculating the Gibbs free energy of ice is as follows:
[0010] in, Enthalpy of ice The entropy of ice is given by J / kg. ; It is the temperature of ice, measured in Kelvin (K). The driving force of phase change from water vapor to ice The calculation formula is as follows:
[0011] Its unit is J / kg.
[0012] When the Gibbs free energy of ice is less than that of water vapor, the local water vapor has a tendency to sublimate and form ice crystals.
[0013] The operating conditions in step one specifically include the local water vapor number density and local temperature, which allow for the calculation of the local thermal properties of water vapor, and subsequently, the quantitative calculation of the local water vapor phase transition trend. Quantifying the water vapor phase transition trend includes thermal property parameters such as the enthalpy, entropy, and Gibbs free energy of water vapor. The magnitude of the Gibbs free energy difference between water vapor and ice reflects the magnitude of the water vapor phase transition trend.
[0014] Preferably, in step two, the thermal motion characteristics of the local water vapor molecules include the molecular thermal motion velocity and the average molecular free path.
[0015] Preferably, in step two, the distinction between continuous and discontinuous water vapor molecules lies in the ratio of the amplitude of their molecular thermal motion to the characteristic length of their thermal motion space. The molecular thermal motion velocity that distinguishes continuous molecules from free molecules is defined as... Based on Maxwell's velocity distribution, the formula for calculating the average molecular thermal velocity of continuous water vapor molecules is as follows:
[0016] The formula for calculating the average molecular thermal motion rate of discontinuous water vapor molecules is as follows:
[0017] The formula for calculating the average thermal velocity of all water vapor molecules is as follows:
[0018] The formula for calculating the amplitude of the thermal motion of continuous water vapor molecules is as follows:
[0019] At this point, the continuous water vapor molecules satisfy the following: ; Only continuous molecules generate pressure with the object of study, while free molecules bypass the object through their large thermal motion, thus avoiding the process of generating pressure through collisions. In this case, the actual static pressure caused by water vapor... The calculation formula is as follows:
[0020] The number density of gas molecules in continuous molecules The calculation formula is as follows:
[0021] In the above formula, The unit is m / s; It is the average thermal velocity of gas molecules, and its unit is m / s; It is the continuous thermal motion speed of water vapor molecules, measured in m / s; It is the velocity of discontinuous water vapor molecules in thermal motion, measured in m / s; It is the number density of gas molecules in water vapor, with units of m. -3 ; It is the mass of a single H2O molecule, which is ; It is the diameter of a single H2O molecule, which is ; It is the temperature of water vapor, measured in Kelvin (K). It is Boltzmann's constant, which is ; It is the local characteristic length, in meters, which is the size of the object that affects the thermal motion and diffusion process of gas molecules in the local area, such as diameter and length (for a wall of length L, if the thermal motion of gas molecules cannot bypass the wall, the characteristic length is taken as L).
[0022] The thermal motion characteristics of water vapor molecules in step two of this invention mainly consist of molecular thermal motion velocity and mean molecular free path. These characteristics exhibit different discontinuities depending on the characteristic length of the studied object. Changes in discontinuity alter important thermophysical parameters such as the Gibbs free energy of water vapor, thereby affecting the phase transition process. The ratio of the water vapor molecule's free path to its characteristic length quantifies the local water vapor discontinuity. Increased water vapor discontinuity reduces the collision frequency between water vapor molecules, thus decreasing the tendency for water vapor phase transition. The discontinuity of water molecules is affected by the content of other gas components. Increased content of other gas components reduces the amplitude of water vapor molecule thermal motion, decreasing discontinuity and thus increasing the tendency for water vapor phase transition. The actual static pressure caused by water vapor calculated in step two... This will affect the enthalpy and entropy of water vapor, thus influencing its Gibbs free energy, and consequently the driving force of the phase change. This has an impact.
[0023] Preferably, in step three, the formation rate of newly formed ice crystals is... The calculation formula is as follows:
[0024] Its unit is s -1 .in, g 1 and g 2 corresponds to the number of H2O molecules in the new phase particles when the influence of surface tension is offset during the formation of the new phase nucleus.
[0025]
[0026]
[0027] It is the volume of the new phase particles when the surface tension is canceled out; It is the mass of a single H2O molecule, which is ; The number of new phase particles that aggregate m H2O molecules during the H2O molecule aggregation process is calculated using the following formula:
[0028] in, It is the contact area between the new phase particles and water vapor during the formation process, measured in m². 2 ; It is surface tension, N / m; It is the volume of new phase particles during the formation process, in meters (m). 3 Discontinuity affects the driving force of phase transition. Regarding This has a direct impact, which in turn affects the aggregation rate of gas molecules.
[0029] The aggregation rate of H2O molecules is calculated using the following formula:
[0030] The formula for calculating the growth rate of each newly formed ice crystal is as follows:
[0031] The growth rate is the mass growth rate, measured in kg / s; discontinuity is directly affected by influencing the number density of continuous gas molecules and the speed of thermal motion. n g,s This is the local water vapor temperature. T g The saturation number density of gas molecules at the specified depth is expressed in m³. -3 .
[0032] In step three of this invention, the ice crystal formation rate and growth rate are not calculated using traditional methods based on classical nucleation and growth formulas, but rather directly through the thermal motion of water vapor molecules. At low temperatures, the condensation nuclei generated by the phase change of water vapor essentially transform into ice crystals instantaneously, thus making the nucleus formation rate and ice crystal formation rate completely equal at low temperatures. The ice crystal formation rate is obtained through integral calculation of the thermal motion of water vapor molecules; the ice crystal growth rate is obtained directly through calculation of the mass transfer rate based on the difference between the local number density of water vapor molecules and the number density around the ice crystal.
[0033] In step four of this invention, ice crystals are generated at different times. Furthermore, ice crystals generated at previous times participate in the growth process at that time, increasing the complexity of calculating phase transition products. The quantity and size of ice crystals generated at different times vary with the operating conditions at that time, and the growth processes of existing ice crystals generated at different times are different in subsequent times. Consequently, the existing ice crystals at the studied time have different sizes, and the content of ice crystals of different sizes varies.
[0034] Specifically, in step four, at each moment, the phase transition process consumes water vapor, thereby increasing the number density of water vapor molecules. The temperature gradually decreases. Simultaneously, at every moment, ice crystals with a diameter equal to the critical radius are generated. The critical radius is:
[0035] At this time The calculation method is the same as that in step two, but due to the water vapor molecule number density... It keeps decreasing, therefore, at different times The calculation results differ until the number density of water vapor molecules decreases to a saturation value, at which point the phase transition process stops.
[0036] At each moment, the ice crystals formed in the previous moment are still growing, and the formula for calculating their growth rate is the same as in step three. However, due to the consumption of water vapor over time and the gradual increase in the contact area between the existing ice crystals and water vapor, the calculated growth rate at different moments will also change until the water vapor molecule number density decreases to the saturation value, at which point the phase transition process stops.
[0037] The beneficial effects of this invention are at least as follows: (1) The present invention provides a method for calculating water vapor sublimation phase change products. The method calculates the water vapor consumed in the phase change, including the consumption of ice crystal formation and growth at that moment, as well as the consumption of existing ice crystal growth. The larger the content of existing ice crystals, the greater the rate of water vapor consumption for ice crystal growth. When the water vapor content no longer decreases with time, the phase change process reaches a stable state, and the ice crystal content and size distribution no longer change. After the phase change process reaches a stable state, water vapor generates a large number of ice crystal particles of different sizes, and the content of ice crystal particles of different sizes is different. At this time, the distribution law of the content of ice crystals of different sizes should be similar to a normal distribution. (2) The method for calculating water vapor sublimation phase change products provided by the present invention takes into account the influence of rarefied gas effect on the formation and growth process of ice crystals, and also takes into account the influence of existing phase change product particles on the phase change process, thereby providing a reliable method for calculating the distribution of phase change products, ensuring the reliability of the calculation method for the distribution of two-phase flow field under low temperature environment, further improving the numerical calculation method for the distribution of tail jet flow field during phase change process, and having important significance for the study of solid particle distribution of engine tail jet flow; (3) The method for calculating water vapor sublimation phase change products provided by the present invention will directly solve the problem of calculating the content and size of plume phase change products under low temperature conditions in space. Attached Figure Description
[0038] Figure 1 This is a flowchart of a method for calculating water vapor phase change conditions applicable to high-altitude rarefied gas environments, according to the present invention.
[0039] Figure 2 This is a schematic diagram of the influence of discontinuity on the phase change process; among them, curve 1 is the water vapor-ice saturation line under traditional continuous conditions; curve 2 is the water vapor-ice saturation line under discontinuous conditions; and point set 3 represents the operating conditions in a certain region of a plume.
[0040] Figure 3 This is a schematic diagram illustrating the effect of discontinuity on the time it takes for a phase transition to reach steady state; where curve 1 represents the water vapor number density at a temperature of 100K. The time required for the phase transition of pure water vapor to stabilize under certain conditions; Curve 2 represents the time required for the phase transition of pure water vapor to stabilize at 100 K and water vapor number density. The time required for the phase transition of pure water vapor to stabilize under certain conditions; Curve 3 represents the time required for the phase transition of pure water vapor to stabilize at 100 K and water vapor number density. The time required for the phase transition of pure water vapor to stabilize under certain conditions; Curve 4 represents the time required for the phase transition of pure water vapor to stabilize at 100 K and water vapor number density. The time required for phase transition stabilization under the influence of other component gases under the conditions; Curve 5 represents the time required for phase transition stabilization at 100 K and water vapor number density. The time required for phase transition stabilization under the influence of other gas components under certain conditions; Curve 6 represents the time required for phase transition stabilization at 100 K and water vapor number density. The time required for phase transition stabilization under the influence of other gas components.
[0041] Figure 4 This is a schematic diagram illustrating the effect of discontinuity on the number of homogeneous ice crystals formed during phase transition; curve 1 represents the water vapor number density at a temperature of 100K. The number of homogeneous ice crystals formed by the phase transition of pure water vapor under certain conditions; Curve 2 represents the water vapor number density at 100 K. The number of homogeneous ice crystals formed by the phase transition of pure water vapor under certain conditions; Curve 3 represents the water vapor number density at 100 K. The number of homogeneous ice crystals formed by the phase transition of pure water vapor under certain conditions; Curve 4 represents the water vapor number density at 100 K. The number of homogeneous ice crystals formed under the influence of other component gases under the condition of phase transition stability; Curve 5 represents the water vapor number density at a temperature of 100K. The number of homogeneous ice crystals formed under the influence of other gas components during phase transition stability; Curve 6 represents the water vapor number density at 100 K. The number of homogeneous ice crystals generated under the influence of other gas components under certain conditions and phase transition stability.
[0042] Figure 5 This is a schematic diagram illustrating the effect of discontinuity on the radius of homogeneous ice crystals formed during phase transition; where curve 1 represents the water vapor number density at a temperature of 100K. The radius of pure water vapor in the stable phase transition formation of homogeneous ice crystals under certain conditions; Curve 2 represents the water vapor number density at 100K. The radius of pure water vapor in the stable phase transition formation of homogeneous ice crystals under certain conditions; Curve 3 represents the water vapor number density at 100 K. The radius of pure water vapor in the stable phase transition formation of homogeneous ice crystals under certain conditions; Curve 4 represents the water vapor number density at 100 K. Under the influence of other component gases under certain conditions, the phase transition stabilizes and homogeneous ice crystals are formed; curve 5 represents the water vapor number density at 100 K. Under the influence of other gas components, the phase transition stabilizes and homogeneous ice crystals are formed; curve 6 represents the water vapor number density at 100 K. Under the influence of other gas components, the phase transition stabilizes and homogeneous ice crystals are formed with a radius of radius.
[0043] Figure 6 This is a schematic diagram illustrating the effect of discontinuity on the radius of heterogeneous ice crystals generated by phase transition; where curve 1 represents the water vapor number density at a temperature of 100K. The radius of pure water vapor in the stable phase transition formation of heterogeneous ice crystals under certain conditions; Curve 2 represents the water vapor number density at 100K. The radius of pure water vapor in the stable phase transition formation of heterogeneous ice crystals under certain conditions; Curve 3 represents the water vapor number density at 100K. The radius of pure water vapor in the stable phase transition formation of heterogeneous ice crystals under certain conditions; Curve 4 represents the water vapor number density at 100 K. Under the influence of other component gases under certain conditions, phase transition stability is achieved, forming heterogeneous ice crystal radii; Curve 5 represents the water vapor number density at 100 K. Under the influence of other gas components, phase transition stability is achieved, forming heterogeneous ice crystal radii; Curve 6 represents the water vapor number density at 100 K. Under the influence of other gas components, the phase transition stability is affected, resulting in heterogeneous ice crystal radius. Detailed Implementation
[0044] This invention provides a method for calculating water vapor sublimation phase change products, the specific implementation of which is as follows: Figure 1 The process is divided into 5 steps: S1: Determine the local temperature and water vapor number density to calculate the Gibbs free energy of local water vapor and ice based on the operating conditions, providing a basis for subsequent calculations. If the Gibbs free energy of ice is less than that of water vapor, the local water vapor has a tendency to sublimate and form ice crystals. At this time, the sublimation process begins, and the local ice crystals begin to form and grow.
[0045] S2: Calculate the effect of discontinuity on the phase transition process. In a rarefied environment, the free path of water vapor molecules is on the same order of magnitude as the characteristic length of the studied object. This allows water vapor molecules to complete flow around or spatial mass transfer processes through their own thermal motion, thus avoiding collisions and reducing the tendency for phase transition. The effect of discontinuity on the sublimation process is as follows: Figure 2 As shown. When the free path of water vapor molecules is on the same order of magnitude as that of the object under study, the Gibbs free energy of water vapor will decrease, and the range of ice phase region coverage conditions will decrease. At this time, the wake region that was originally in the ice phase region is entirely in the gas phase region, and no phase transition will occur in the wake. Conversely, when the characteristic length of the object under study suddenly increases, such as near the instrument as a fluid in the plume, the continuity of water vapor suddenly increases, thus causing the local area to suddenly be in the ice phase region, and ice crystals will suddenly begin to appear.
[0046] S3: Calculate the generation and growth rate of newly formed ice crystals at each time step, thereby calculating the number of ice crystals generated within a time step, and also calculating the size increase of newly formed ice crystals with the same radius within this time step. If heterogeneous hydrophilic particles exist locally, the particle surface will be occupied by ice crystals, resulting in the formation of heterogeneous ice crystals. Since the generation rate of hydrophilic heterogeneous particles is often much greater than that of homogeneous ice crystals, all heterogeneous particles are completely occupied by heterogeneous ice crystals at the very beginning of the phase transition process, thus only the growth process occurs in the subsequent phase transition process.
[0047] S4: Calculate the growth rate of existing ice crystals at each time step, record the number of ice crystals of all sizes generated in previous time steps within a time step, and calculate the growth rate of each ice crystal to obtain the size increase of all existing ice crystals within that time step.
[0048] S5: In the calculation of ice crystal formation and growth at each moment, record the amount of water vapor consumed until the water vapor content no longer decreases further with time, at which point the phase transition reaches stability.
[0049] After completing the calculation steps, the calculation result should be as follows: Figure 3 The figure shows the time required to reach phase transition stability under different operating conditions. The calculated time required for phase transition stability gradually decreases with increasing continuity. At the same time, the time required for phase transition decreases under the influence of other gas components. Increased continuity is beneficial to the sublimation process.
[0050] Figure 4 The figure shows the time required to reach phase transition stability under different operating conditions. The calculated number of homogeneous ice crystals generated when the phase transition reaches stability generally increases with the increase of continuity. At the same time, under the influence of other gas components, after a certain continuity is reached, the number of homogeneous ice crystals generated no longer changes with the increase of continuity. At this time, the phase transition process is the same as that under traditional continuous conditions.
[0051] Figure 5 The figure shows the radius of homogeneous ice crystals generated when the phase transition reaches stability under different operating conditions. The calculated radius of homogeneous ice crystals generated when the phase transition reaches stability generally decreases with increasing continuity. At the same time, under the influence of other gas components, after a certain continuity is reached, the radius of homogeneous ice crystals no longer changes with increasing continuity. At this point, the phase transition process is the same as that under traditional continuous conditions.
[0052] Figure 6The figure shows the radii of heterogeneous ice crystals that reach phase transition stability under different operating conditions. The calculated radii of heterogeneous ice crystals that reach phase transition stability generally decrease with increasing continuity. However, under the influence of other gas components, after reaching a certain level of continuity, the radii of heterogeneous ice crystals no longer change with increasing continuity; at this point, the phase transition process is the same as under traditional continuous conditions. Since heterogeneous ice crystals cease formation after initially occupying all heterogeneous particles, they only grow in subsequent time intervals. Therefore, under the same operating conditions, the radii of heterogeneous ice crystals are larger than those of homogeneous ice crystals.
[0053] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims
1. A method for calculating water vapor sublimation phase change products, characterized in that, Includes the following steps: Step 1: Obtain local operating conditions, calculate the Gibbs free energy of water vapor and ice, and determine the phase change trend of water vapor in the local area; Step 2: Based on the local thermal motion characteristics of water vapor molecules, the discontinuity of water vapor is quantitatively calculated, and the influence of the discontinuity on the phase transition process is obtained; Step 3: Based on the operating conditions at each moment, calculate the formation rate and growth rate of newly formed ice crystals at that moment; Step 4: Calculate the growth rate of the existing ice crystals that have been generated at each moment based on the operating conditions at that moment. Step 5: Record the water vapor content consumed during the phase transition at each moment until the water vapor content no longer changes and the phase transition reaches stability. Calculate the variation law of the number and size of ice crystals under rarefied gas conditions using the methods described in Steps 3 and 4.
2. The method for calculating water vapor sublimation phase change products according to claim 1, characterized in that, In step one, the local operating conditions include local temperature and water vapor number density; The formula for calculating the Gibbs free energy of water vapor is as follows: in, Gibbs free energy of water vapor, expressed in J / kg; It is the temperature of water vapor, measured in Kelvin (K). enthalpy of water vapor The calculation formula is as follows: In the formula, u g This is the specific internal energy of water vapor, expressed in J / kg. P g,c This represents the actual static pressure caused by water vapor, expressed in Pa. m g Let the mass of a single H2O molecule be . ; n g The gas number density of water vapor molecules, in m³. -3 ; T 0 is the triple point temperature, which is 273.16 K for water; Entropy of water vapor The calculation formula is as follows: In the formula, Let be the entropy of liquid water under triple point conditions, which is set to 0 in the calculation. ; The latent heat of vaporization of liquid water under triple point conditions is expressed in J / kg. The triple point temperature is 273.16 K; The specific heat at constant volume of water vapor, in units of ; Boltzmann's constant, ; Let the mass of a single H2O molecule be . ; This represents the actual static pressure caused by water vapor, expressed in Pa. This refers to the number density of water vapor molecules under triple point conditions, expressed in m³. -3 ; The formula for calculating the Gibbs free energy of ice is as follows: in, Enthalpy of ice The entropy of ice is given by J / kg. ; It is the temperature of ice, measured in Kelvin (K). The driving force of phase change from water vapor to ice The calculation formula is as follows: Its unit is J / kg.
3. The method for calculating water vapor sublimation phase change products according to claim 1 or 2, characterized in that, In step two, the thermal motion characteristics of the local water vapor molecules include the molecular thermal motion velocity and the average molecular free path.
4. The method for calculating water vapor sublimation phase change products according to claim 1 or 2, characterized in that, In step two, the molecular thermal motion velocity that distinguishes between continuous and discontinuous water vapor molecules is defined as... Based on Maxwell's velocity distribution, the average molecular thermal motion velocity of continuous water vapor molecules The calculation formula is as follows: Average molecular thermal motion rate of discontinuous water vapor molecules The calculation formula is as follows: The average thermal motion speed of all water vapor molecules The calculation formula is as follows: The amplitude of thermal motion of continuous water vapor molecules The calculation formula is as follows: Continuous water vapor molecules satisfy: ; Actual static pressure caused by water vapor The calculation formula is as follows: The number density of gas molecules in continuous molecules The calculation formula is as follows: In the above formula, The unit is m / s; , , The units are all m / s; It is the number density of gas molecules in water vapor, with units of m. -3 ; It is the mass of a single H2O molecule, which is ; It is the diameter of a single H2O molecule, which is ; It is the temperature of water vapor, measured in Kelvin (K). It is Boltzmann's constant, which is ; It is the local characteristic length, in meters.
5. A method for calculating water vapor sublimation phase change products according to claim 1 or 2, characterized in that, In step three, the rate of formation of newly formed ice crystals The calculation formula is as follows: Its unit is s -1 ; In the above formula, in, It is the volume of the new phase particles when the surface tension is canceled out; It is the mass of a single H2O molecule, which is ; The calculation formula is as follows: in, It is the contact area between the new phase particles and water vapor during the formation process, measured in m². 2 ; It is surface tension, N / m; It is the volume of new phase particles during the formation process, in meters (m). 3 ; The aggregation rate of H2O molecules is calculated using the following formula: The formula for calculating the growth rate of each newly formed ice crystal is as follows: Its unit is kg / s; In the above formula, , The calculation formula is the same as that in claim 4. n g,s Local water vapor temperature T g The saturation number density of gas molecules at the specified depth is expressed in m³. -3 , n g The gas number density of water vapor molecules, in m³. -3 ; It is the temperature of water vapor, measured in Kelvin (K).