A method for calculating a wake vortex cloud formation process based on fluent software

Abstract

The application provides a calculation method of a wake cloud forming process based on fluent software, comprising the following steps: S1, constructing a self-defined function to correct thermodynamic parameters of water vapor in a phase change process; the self-defined function comprises a water vapor saturation temperature self-defined function and a water vapor saturation pressure self-defined function; S2, constructing a self-defined scalar equation to represent a phase change state and a transport process; the self-defined scalar equation comprises a phase change particle mass fraction transport equation and a phase change particle number density transport equation; S3, constructing a self-defined control equation source term for solving together with the self-defined scalar equation; S4, initializing a flow field and performing iterative calculation; and S5, post-processing results of the calculation to obtain a morphological feature and a distribution feature of each phase change parameter after phase change of water vapor. The calculation method provided by the application can simulate a water vapor phase change process in a wake jet flame under different atmospheric environments.

Description

Technical Field

[0001] This invention belongs to the field of fluid dynamics calculation technology, and specifically relates to a calculation method for the formation process of contrail clouds based on Fluent software. Background Technology

[0002] With the increasing number of aerospace activities, the contrails caused by exhaust gases from aircraft and rocket missile engines have gradually attracted attention. The formation of contrails involves complex phase changes of water vapor. In order to clarify the formation mechanism of rocket engine contrails and the characteristics of phase change particles, it is necessary to study the phase change process and mechanism of water vapor in the exhaust flame.

[0003] However, in existing computational models, the saturation pressure and saturation temperature of water vapor are often calculated using pre-defined formulas, which have a limited range of applicable temperatures and pressures. This makes it impossible to simulate the phase transition process of water vapor in the tailpipe plume under different atmospheric conditions. Therefore, it is urgent to adjust and correct the parameters in existing models to establish a more widely applicable model for the saturation pressure and saturation temperature of water vapor, so as to meet the requirements for simulating the phase transition process of water vapor in the tailpipe plume under different atmospheric conditions and to predict the formation of high-altitude contrails. Summary of the Invention

[0004] To address one or more technical problems existing in the prior art, this invention provides a calculation method for the formation process of contrails based on Fluent software. By adjusting and correcting the parameters in the existing model, a more widely applicable model of water vapor saturation pressure and water vapor saturation temperature is established. This method can simulate the phase change process of water vapor in the tail flame under different atmospheric conditions and predict the formation of contrails in the upper atmosphere.

[0005] This invention provides a calculation method for the contrail cloud formation process based on Fluent software, including: S1. Construct a custom function to correct the thermodynamic parameters of water vapor during the phase transition; The user-defined functions include a user-defined function for water vapor saturation temperature and a user-defined function for water vapor saturation pressure. The user-defined function for water vapor saturation temperature is a user-defined function that shows the change of water vapor saturation temperature with water vapor partial pressure. The user-defined function for water vapor saturation pressure is a user-defined function that shows the change of water vapor saturation pressure with temperature. S2. Construct custom scalar equations to characterize phase transition states and transport processes; Custom scalar equations include the phase transition particle mass fraction transport equation and the phase transition particle number density transport equation; S3. Construct custom source terms for the governing equations, which are then solved together with the custom scalar equations; S4. Initialize the flow field and perform iterative calculations; S5. Post-process the calculation results to obtain the morphological characteristics of water vapor after phase change and the distribution characteristics of each phase change parameter.

[0006] In some possible designs, the custom function for water vapor saturation pressure is a piecewise function; When the temperature is 273-647K, the user-defined function for the saturated pressure of water vapor is: Where a1=-7.77224, b1=1.45684, c1=-2.71942, d1=-1.41336; When the temperature is 213-273K, the user-defined function for the saturated pressure of water vapor is: ; When the temperature is 191-213K, the user-defined function for the saturated pressure of water vapor is: ; When the temperature is 174-191K, the user-defined function for the saturated pressure of water vapor is: ; When the temperature is 0-174K, the user-defined function for the saturated pressure of water vapor is: ; In the formula, P crit This is the critical pressure of water. beta For comparison and correction items; beta =1- T red ,in, T red For comparison temperature; T red = T / T c , T The local fluid thermodynamic temperature. T c This is the critical temperature of water.

[0007] In some possible designs, the custom function for water vapor saturation temperature is a piecewise function; When the partial pressure of water vapor is 610.38 - 22.115 × 10 6 At Pa, the user-defined function for the water vapor saturation temperature is: ;in, and A coefficient related to pressure; When the partial pressure of water vapor is 1.077-610.38 Pa, the user-defined function for water vapor saturation temperature is: ; When the partial pressure of water vapor is 0.0387-1.077 Pa, the user-defined function for the water vapor saturation temperature is: ; When the partial pressure of water vapor is 0.0016-0.0387 Pa, the user-defined function for the water vapor saturation temperature is: ; When the partial pressure of water vapor is less than 0.0016 Pa, the user-defined function for the water vapor saturation temperature is: ; in, This refers to the partial pressure of water vapor.

[0008] In some possible designs, the custom functions also include custom functions for water vapor density, water vapor dynamic viscosity, droplet surface tension, water vapor thermal conductivity, and water vapor latent heat of condensation.

[0009] In some possible designs, the custom function for water vapor density is: ,in, The gas constant of water vapor. For water vapor partial pressure, For fluid temperature; and / or The user-defined function for water vapor dynamic viscosity is: ,in, 8.022×10 -6 Pa·s, c is 961.

[0010] In some possible designs, the custom function for droplet surface tension is: , where σ ∞ Let g be the surface tension of the liquid plane, and g be the number of molecules in the droplet.

[0011] In some possible designs, the custom function for the thermal conductivity of water vapor is: =0.0261W / (m·K).

[0012] In some possible designs, the latent heat of water vapor condensation is defined as follows:

[0013] in, , The temperature of water vapor. The critical temperature is given by ω = 0.313. is the gas constant for water vapor.

[0014] In some possible designs, the phase transition particle mass fraction transport equation is: ; The phase transition particle number density transport equation is: ; in, ρ Y is the density of the mixed gas; Y is the mass fraction of phase transition particles. t For the flow of time, x j For the spatial coordinate components of a three-dimensional Cartesian coordinate system, j Take 1, 2, and 3 respectively, which correspond to x , y , z Three directions; For gaseous fluid in x j Directional gas phase velocity component; The condensation rate of water vapor; The particle number density; S N This is the particle number density source term.

[0015] In some possible designs, custom control equation source terms include: , , , ; in, This refers to the mass change in the gas phase caused by condensation. S Y For the phase transition particle mass fraction source term, The condensation rate of water vapor. This represents the change in momentum of the gas phase after condensation. Condensation leads to energy exchange between the gas and liquid phases. u j For gaseous fluid in x j Directional gas phase velocity component, Latent heat of water vapor condensation For nucleation rate, S N This is the particle number density source term.

[0016] Compared with the prior art, the present invention has at least the following beneficial effects: This invention establishes a more widely applicable model for the saturation pressure and saturation temperature of water vapor by constructing custom functions to adjust and correct the parameters in existing models. It characterizes the phase transition state and transport process by constructing phase transition particle mass fraction transport equations and phase transition particle number density transport equations. By constructing custom control equation source terms and solving them together with custom scalar equations, it obtains the morphological characteristics of water vapor after phase transition and the distribution characteristics of each phase transition parameter. This can simulate the water vapor phase transition process in tail jets under different atmospheric conditions and predict the formation of high-altitude contrails. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart illustrating a calculation method for the formation process of contrail clouds based on Fluent software provided by the present invention. Figure 2 This is a comparison chart of the calculation results of the custom function for water vapor saturation pressure provided by this invention in the temperature range of 273-647K; Figure 3 This is a fitting curve of water vapor saturation pressure in the temperature range of 213-273K according to the present invention; Figure 4 This is a fitting curve of water vapor saturation pressure in the temperature range of 174-213K according to the present invention; Figure 5 The water vapor partial pressure of this invention is 610.38-22.115×10⁻⁶. 6 Fitting curve of water vapor saturation temperature at Pa; Figure 6 This is a fitting curve of water vapor saturation temperature when the water vapor partial pressure is 1.077-610.38 Pa according to the present invention; Figure 7 This is a fitting curve of water vapor saturation temperature when the water vapor partial pressure is 0.0016-1.077 Pa according to the present invention; Figure 8 This is a comparison chart of the calculation results of the custom function for water vapor dynamic viscosity provided by this invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0020] This invention provides a calculation method for the contrail cloud formation process based on Fluent software, including: S1. Construct a custom function to correct the thermodynamic parameters of water vapor during the phase transition; The user-defined functions include a user-defined function for water vapor saturation temperature and a user-defined function for water vapor saturation pressure. The user-defined function for water vapor saturation temperature is a user-defined function that shows the change of water vapor saturation temperature with water vapor partial pressure. The user-defined function for water vapor saturation pressure is a user-defined function that shows the change of water vapor saturation pressure with temperature. S2. Construct custom scalar equations to characterize phase transition states and transport processes; Custom scalar equations include the phase transition particle mass fraction transport equation and the phase transition particle number density transport equation; S3. Construct custom source terms for the governing equations, which are then solved together with the custom scalar equations; S4. Initialize the flow field and perform iterative calculations; S5. Post-process the calculation results to obtain the morphological characteristics of water vapor after phase change and the distribution characteristics of each phase change parameter.

[0021] This invention modifies the thermodynamic parameters of water vapor during phase transition by constructing custom functions. In particular, by constructing custom functions for water vapor saturation temperature and saturation pressure, it adjusts and corrects the parameters in existing models, establishing a more widely applicable model for water vapor saturation pressure and saturation temperature. By constructing phase transition particle mass fraction transport equations and phase transition particle number density transport equations, it characterizes the phase transition state and transport process. By constructing custom control equation source terms and solving them together with custom scalar equations, it obtains the morphological characteristics of water vapor after phase transition and the distribution characteristics of each phase transition parameter. This invention can simulate the water vapor phase transition process in tail jets under different atmospheric conditions and predict the formation of high-altitude contrails.

[0022] At a certain temperature, the equilibrium pressure when water vapor and liquid water coexist is called the gas-liquid saturation pressure at that temperature, and the equilibrium pressure when water vapor and solid ice coexist is called the gas-solid saturation pressure at that temperature. However, in mature calculation software, saturation pressure and saturation temperature are often obtained from pre-defined calculation formulas, and the applicable temperature and pressure ranges are generally small. In order to simulate the water vapor phase change phenomenon in the tail flame under different atmospheric conditions, this invention introduces a custom function for water vapor saturation pressure and a custom function for water vapor saturation temperature into the model by using custom functions. The parameters in the existing model are adjusted and corrected to establish a water vapor saturation pressure and water vapor saturation temperature model with a wider range of applicability, so as to meet the simulation of water vapor phase change process in tail flame under different atmospheric conditions.

[0023] In some embodiments, the custom function for water vapor saturation pressure is a piecewise function; When the temperature is 273-647K, the user-defined function for the saturated pressure of water vapor is: (1), where a1=-7.77224, b1=1.45684, c1=-2.71942, d1=-1.41336; As can be seen from the three-phase diagram of water vapor, water exhibits phase changes between gas and liquid phases when the temperature is between 273-647K. Existing formulas commonly used to describe the relationship between water vapor saturation pressure and temperature in the temperature range of 273-647K include the Antoine equation and the Wagner equation. Antoine equations: In the formula, P is the saturated pressure of water vapor in bar, and T is the temperature of water vapor in K. , , Applicable pressure range: 0.01-16MPa; applicable temperature range: 273.20-473.20K.

[0024] Wagner equation: ; In the formula, , , , Applicable pressure range: 0.01-22.1 MPa; temperature range: 273.20-647.30 K.

[0025] By consulting the water vapor property table, we can find that the saturated pressure of water vapor at 273-647K is shown in Table 1. Table 1 273.15 611.2 373.15 101325 473.15 1.55366×106 573.15 8.58308×106 647.30 2.21×107 A comparison of the results calculated using the two equations above with the saturated pressure results in the water vapor property table. Figure 2 As shown; by comparison, it can be seen that the water vapor saturation pressure calculated by the Wagner equation is closer to the result in the water vapor property table when the water vapor temperature is close to the critical temperature. Therefore, the Wagner equation is selected to calculate the water vapor saturation pressure in the temperature range of 273-647K.

[0026] At an altitude of 2 km, the atmospheric temperature drops to 268.7 K. Existing formulas cannot accurately calculate the water vapor saturation pressure in this temperature range. In order to simulate the water vapor condensation phenomenon in the airborne tail flame, it is necessary to establish a method to calculate the water vapor saturation pressure in the temperature range of 0-273 K. Through the water vapor property table, the water vapor saturation pressure in the temperature range of 174-273 K can be obtained as shown in Table 2. Table 2 174 0.0016 194 0.0533 214 1.233 234 14.41 254 113.84 175 0.0020 195 0.0627 215 1.413 235 16.116 255 125.17 176 0.0024 196 0.0746 216 1.613 236 18.009 256 137.43 177 0.0029 197 0.0880 217 1.840 237 20.088 257 150.90 178 0.0036 198 0.1026 218 2.093 238 22.408 258 165.43 179 0.0044 199 0.1320 219 2.373 239 24.967 259 181.42 180 0.0053 200 0.1400 220 2.706 240 27.78 260 198.62 181 0.0064 201 0.1640 221 3.066 241 30.90 261 217.55 182 0.0077 202 0.1906 222 4.479 242 34.32 262 237.94 183 0.0104 203 0.2226 223 3.946 243 38.11 263 259.94 184 0.0112 204 0.2586 224 4.452 244 42.26 264 284.06 185 0.0133 205 0.2999 225 5.039 245 47.85 265 310.06 186 0.0160 206 0.3479 226 5.679 246 51.85 266 338.45 187 0.0187 207 0.4026 227 6.412 247 57.32 267 368.57 188 0.0227 208 0.4650 228 7.212 248 63.45 268 401.63 189 0.0267 209 0.5370 229 8.118 249 70.12 269 437.22 190 0.0320 210 0.7120 230 9.118 250 77.31 270 475.61 191 0.0387 211 0.8180 231 10.237 251 85.31 271 517.20 192 0.0387 212 0.9370 232 11.49 252 93.98 272 562.13 193 0.0453 213 1.077 233 12.877 253 102.11 273 610.38 As can be seen from the temperature and corresponding water vapor saturation pressure data given in the table, a single function cannot describe the relationship between water vapor saturation pressure and temperature within the temperature range of 0-273K. Therefore, a piecewise function is used to describe the relationship between water vapor saturation pressure and temperature within the temperature range of 0-273K.

[0027] When the temperature is 213-273K, the user-defined function for the saturated pressure of water vapor is: (2); When the temperature is between 213-273K, the above equation (2) is used for fitting. The fitting result is given in the water vapor property table as the curve of saturated pressure versus temperature. Figure 3 As shown, the fitting results are basically consistent with the saturated pressure results in the water vapor property table.

[0028] When the temperature is 191-213K, the user-defined function for the saturated pressure of water vapor is: (3); When the temperature is 174-191K, the user-defined function for the saturated pressure of water vapor is: (4); When the temperature is between 174-213 K, the above equations (3)-(4) are used for fitting. The fitting results are given in the water vapor property table as the curve of saturated pressure versus temperature. Figure 4 As shown, the fitting results are basically consistent with the saturated pressure results in the water vapor property table.

[0029] When the temperature is 0-174K, the user-defined function for the saturated pressure of water vapor is: (5).

[0030] Since the water vapor saturation pressure is 0.0016 Pa at a temperature of 174 K, the temperature change has little effect on the water vapor saturation pressure. Therefore, the above-mentioned custom function for water vapor saturation pressure is used for linear fitting in the range of 0-174 K.

[0031] In the above custom function for water vapor saturation pressure, in the formula, P crit The critical pressure of water is 22.115 × 10⁻⁶. 6 Pa; beta For comparison and correction items; beta =1- T red ,in, T red For comparison temperature; T red = T / T c , T The local fluid thermodynamic temperature. T c The critical temperature of water is 647.16 K.

[0032] During the flow process, condensation will only occur when the partial pressure of water vapor is greater than the saturation pressure and the temperature is less than the saturation temperature. The saturation temperature of water vapor is determined by the partial pressure of water vapor in the flow. Therefore, the relationship between the saturation temperature of water vapor and the pressure is obtained by using a piecewise fitting method.

[0033] In some embodiments, the custom function for water vapor saturation temperature is a piecewise function; it should be noted that in the following custom functions... This refers to the partial pressure of water vapor.

[0034] When the partial pressure of water vapor is 610.38 - 22.115 × 10 6 At Pa, the user-defined function for the water vapor saturation temperature is: (6); among which, and A coefficient related to pressure; It should be noted that, , , The coefficients related to pressure are given in Table 3; Table 3

[0035] The above-mentioned custom function for water vapor saturation temperature was used to calculate 610.38-22.115×10.6 The water vapor saturation temperature within the Pa range was fitted, and the fitting results were compared with the results calculated by the Wagner equation, such as... Figure 5 As shown, the fitting results are basically consistent with the results calculated by the Wagner equation.

[0036] When the partial pressure of water vapor is 1.077-610.38 Pa, the user-defined function for water vapor saturation temperature is: (7); The saturation temperature in the range of 1.077-610.38 Pa was fitted using the aforementioned user-defined function for water vapor saturation temperature. The fitting results were compared with the water vapor saturation temperature results in the water vapor property handbook. Figure 6 As shown, the fitting results are quite close to those in the water vapor property table.

[0037] When the partial pressure of water vapor is 0.0387-1.077 Pa, the user-defined function for the water vapor saturation temperature is: (8); When the partial pressure of water vapor is 0.0016-0.0387 Pa, the user-defined function for the water vapor saturation temperature is: (9); The saturation temperature in the range of 0.0016-1.077 Pa was fitted using the aforementioned custom function for water vapor saturation temperature. The fitting results were compared with the water vapor saturation temperature results in the water vapor property handbook. Figure 7 As shown, the fitting results are basically consistent with the results in the water vapor property table.

[0038] When the partial pressure of water vapor is less than 0.0016 Pa, the user-defined function for the water vapor saturation temperature is: (10); When the pressure is less than 0.0016 Pa, the change in pressure has little effect on the water vapor saturation temperature. Therefore, when the pressure is less than 0.0016 Pa, the above-mentioned custom function for water vapor saturation temperature is used for linear fitting.

[0039] In some embodiments, the custom functions also include custom functions for water vapor density, water vapor dynamic viscosity, droplet surface tension, water vapor thermal conductivity, and water vapor latent heat of condensation.

[0040] In some embodiments, the custom function for water vapor density is: (11), among which, The gas constant of water vapor. For water vapor partial pressure, For fluid temperature; In this study, water vapor is considered an ideal gas, and the ideal gas law is used to solve for the water vapor density. is the gas constant for water vapor, with a value of 461.889.

[0041] The user-defined function for water vapor dynamic viscosity is: ,in, 8.022×10 -6 Pa·s, c is 961.

[0042] Dynamic viscosity is defined as the ratio of stress to strain rate. It is calculated using existing formulas, including equation (12) proposed by Hirschfelder et al. in 1954 and the empirical formula for gas dynamic viscosity (13). The dynamic viscosity is then compared with that in the handbook of thermophysical properties of water vapor. The comparison results are as follows: Figure 8 As shown; the dynamic viscosity of water vapor calculated using Equation (13) is closer to that given in the Handbook of Thermophysical Properties of Water Vapor. Therefore, Equation (13) is chosen to calculate the dynamic viscosity of water vapor.

[0043] (12) In the formula, dynamic viscosity The unit is , Molar mass, unit , For gas temperature, The diameter of a molecule is given by the unit 1. ,Right now .

[0044] (13) Units are , 0 The dynamic viscosity of the gas, with water vapor taking a value of , For gas properties, the value is 961 for water vapor.

[0045] Surface tension appears in the exponential term of nucleation rate, and its value has a significant impact on the nucleation rate. At the same time, the surface tension in the microscopic state cannot be replaced by the surface tension in the macroscopic state. For the droplets generated by water vapor condensation in supersonic flow, the size is generally on the submicron scale, so the calculation of macroscopic surface tension needs to be corrected to obtain a calculation method suitable for the surface tension of microscopic droplets.

[0046] In some embodiments, the droplet surface tension custom function is: (14), where σ ∞Let g be the surface tension of the liquid plane, and g be the number of molecules in the droplet.

[0047] Surface tension σ of a liquid plane ∞ Calculate using equation (15); (15), among which, The water vapor saturation temperature The critical temperature for water vapor is taken as 647.16 K.

[0048] In some embodiments, the custom function for the thermal conductivity of water vapor is: =0.0261W / (m·K)(16).

[0049] Gas thermal conductivity refers to the transfer of heat from higher-temperature areas to lower-temperature areas when a temperature gradient exists within the gas. The thermal conductivity coefficient describes the amount of heat transferred per unit area when the temperature difference between the two sides of a unit thickness of gas is 1 K. The growth rate of droplet radius is related to the thermal conductivity of the gas. According to Fang Da's research, the thermal conductivity of water vapor changes relatively little; therefore, a constant value of 0.0261 is used in the calculation. .

[0050] In some embodiments, the latent heat of water vapor condensation is a user-defined function: (17), among which, , The temperature of water vapor. The critical temperature is given by ω = 0.313. is the gas constant for water vapor.

[0051] The latent heat of condensation refers to the heat released when water vapor undergoes a phase change, i.e., condenses into liquid water or solid ice. Refer to Pitzer's formula in the Gas-Liquid Property Estimation Handbook to calculate the latent heat of condensation of water vapor.

[0052] To describe the state of phase transition particles in a flow, the following assumptions are further introduced: (1) The phase change particles have small mass and size, and have little impact on the dynamics of the entire flow field; (2) The water vapor condensation process is a uniform nucleation process; (3) The phase transition particles have the same velocity as the gas phase, there is no slip, and the particles will not collide with each other.

[0053] Based on the above assumptions, the phase change particle mass fraction transport equation and the phase change particle number density transport equation are introduced into the model by using custom scalar equations to characterize the phase change state and transport process of water vapor.

[0054] In some embodiments, the phase transition particle mass fraction transport equation is: (18); among which, ρ The density of the mixed gas; Y This represents the mass fraction of phase transition particles. t For the flow of time; x j For the spatial coordinate components of a three-dimensional Cartesian coordinate system, j Take 1, 2, and 3 respectively to correspond to x , y , z Three directions; For gaseous fluid in x j Directional gas phase velocity component; The condensation rate of water vapor; It should be noted that, (19), among which, For the mass of liquid water, The mass of gaseous water; The density of a gas mixture can be expressed as the gas density. (20), among which, The density of gaseous water; Substituting equations (19)-(20) into equation (18), we get: (twenty one); make ,get (twenty two); The phase transition particle number density transport equation is: (23); among which, The particle number density; t For the flow of time; x j For the spatial coordinate components of a three-dimensional Cartesian coordinate system, j Take 1, 2, and 3 respectively to correspond to x , y , z Three directions; For gaseous fluid in x j Directional gas phase velocity component; S N This is the particle number density source term.

[0055] In some embodiments, the source terms of the governing equations include: (24), among which, This refers to the mass change in the gas phase caused by condensation. S Y For the phase transition particle mass fraction source term, The condensation rate of water vapor; (25), of which, This represents the change in momentum of the gas phase after condensation. The condensation rate of water vapor. u j For gaseous fluid in x j Directional gas phase velocity component; (26), among which, Condensation leads to energy exchange between the gas and liquid phases. The condensation rate of water vapor. Latent heat of water vapor condensation; (27); among which, S N For the particle number density source term, This represents the nucleation rate.

[0056] This invention introduces a custom control equation source term and a custom scalar equation to solve together, establishes an equation, and calculates the morphological characteristics of water vapor after phase change and the distribution characteristics of each phase change parameter under different conditions, thereby enabling the prediction of the formation of contrail clouds in the upper atmosphere.

[0057] The mass of a particle in the flow field can be expressed as Then we have: (28); among which, The critical radius of the particle. The density is the density of the liquid phase, i.e., the density of liquid water. For nucleation rate, Particle radius within the flow field The particle number density; For the particle radius growth rate, This represents the mass of the critical nucleus formed per unit time and per unit volume. It represents the mass of liquid phase condensed on existing particles per unit time and unit volume.

[0058] Particle critical radius The calculation is performed using equation (29); (29), among which, For the surface tension of the droplet, The gas constant of water vapor. The density of liquid water, It is the water vapor pressure. This is the saturated pressure of water vapor. The fluid temperature.

[0059] Nucleation rate The calculation is performed using equation (30); (30); among which, This is the solidification coefficient, usually taken as 1. For the mass of a water vapor molecule, take , For the surface tension of the droplet, The density of water vapor, The density of liquid water, Let be the Boltzmann constant, and take . , The critical radius of the particle. For fluid temperature; The non-isothermal correction factor is calculated using equation (31); (31); among which, The specific heat ratio of water vapor. For latent heat of condensation, The gas constant of water vapor. The fluid temperature.

[0060] Particle radius growth rate The calculation is performed using equation (32); (32), among which, The thermal conductivity of water vapor, Where is the droplet radius, The value is a constant, based on the droplet growth rate given by Gyarmathy. , For the droplet temperature, For fluid temperature, For droplet component density, It is the latent heat of condensation; among which, Knudsen number is calculated using equation (33); (33), among which, For fluid dynamic viscosity, Where is the droplet radius, For the mass of a water vapor molecule, take , Boltzmann's constant, This refers to the temperature of the water vapor.

[0061] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0062] 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 calculation method for the formation process of contrail clouds based on Fluent software, characterized in that, include: S1. Construct a custom function to correct the thermodynamic parameters of water vapor during the phase transition; The custom functions include a custom function for water vapor saturation temperature and a custom function for water vapor saturation pressure; the custom function for water vapor saturation temperature is a custom function that changes water vapor saturation temperature with water vapor partial pressure; the custom function for water vapor saturation pressure is a custom function that changes water vapor saturation pressure with temperature. S2. Construct custom scalar equations to characterize phase transition states and transport processes; The custom scalar equations include the phase transition particle mass fraction transport equation and the phase transition particle number density transport equation; S3. Construct custom source terms for the governing equations, which are then solved together with the custom scalar equations; S4. Initialize the flow field and perform iterative calculations; S5. Post-process the calculation results to obtain the morphological characteristics of water vapor after phase change and the distribution characteristics of each phase change parameter; The transport equation for the mass fraction of phase transition particles is as follows: ; The phase transition particle number density transport equation is as follows: ; in, ρ Y is the density of the mixed gas; Y is the mass fraction of phase transition particles. t For the flow of time; x j For the spatial coordinate components of a three-dimensional Cartesian coordinate system, j Take 1, 2, and 3 respectively to correspond to x , y , z Three directions; For gaseous fluid in x j Directional gas phase velocity components; The condensation rate of water vapor; The particle number density; S N For the particle number density source term; The source terms of the custom control equation include: ， ， ， ； in, This refers to the mass change in the gas phase caused by condensation. S Y For the phase transition particle mass fraction source term, The condensation rate of water vapor. This represents the change in momentum of the gas phase after condensation. Condensation leads to energy exchange between the gas and liquid phases. u j For gaseous fluid in x j Directional gas phase velocity component, Latent heat of water vapor condensation For nucleation rate, S N This is the particle number density source term.

2. The calculation method according to claim 1, characterized in that, The custom function for water vapor saturation pressure is a piecewise function; When the temperature is 273-647K, the custom function for the water vapor saturation pressure is: Where a1=-7.77224, b1=1.45684, c1=-2.71942, d1=-1.41336; When the temperature is 213-273K, the custom function for the water vapor saturation pressure is: ； When the temperature is 191-213K, the custom function for the water vapor saturation pressure is: ； When the temperature is 174-191K, the custom function for the water vapor saturation pressure is: ； When the temperature is 0-174K, the custom function for the water vapor saturation pressure is: ； In the formula, P crit This is the critical pressure of water. beta For comparison and correction items; beta =1- T red ,in, T red For comparison temperature; T red = T / T c , T The local fluid thermodynamic temperature. T c This is the critical temperature of water.

3. The calculation method according to claim 1, characterized in that, The custom function for water vapor saturation temperature is a piecewise function; When the partial pressure of water vapor is 610.38 - 22.115 × 10 6 At Pa, the user-defined function for the water vapor saturation temperature is: ;in, and A coefficient related to pressure; When the partial pressure of water vapor is 1.077-610.38 Pa, the user-defined function for the water vapor saturation temperature is: ； When the partial pressure of water vapor is 0.0387-1.077 Pa, the custom function for the water vapor saturation temperature is: ； When the partial pressure of water vapor is 0.0016-0.0387 Pa, the user-defined function for the water vapor saturation temperature is: ； When the partial pressure of water vapor is less than 0.0016 Pa, the user-defined function for the water vapor saturation temperature is: ； in, This refers to the partial pressure of water vapor.

4. The calculation method according to claim 1, characterized in that, The custom functions also include custom functions for water vapor density, water vapor dynamic viscosity, droplet surface tension, water vapor thermal conductivity, and water vapor latent heat of condensation.

5. The calculation method according to claim 4, characterized in that, The custom function for water vapor density is: ,in, The gas constant of water vapor. For water vapor partial pressure, For fluid temperature; and / or The custom function for water vapor dynamic viscosity is: ,in, 8.022×10 -6 Pa·s, c is 961.

6. The calculation method according to claim 4, characterized in that, The custom function for the surface tension of the droplet is: , where σ ∞ Let g be the surface tension of the liquid plane, and g be the number of molecules in the droplet.

7. The calculation method according to claim 4, characterized in that, The custom function for the thermal conductivity of water vapor is: =0.0261W / (m·K).

8. The calculation method according to claim 4, characterized in that, The custom function for the latent heat of water vapor condensation is: in, , The temperature of water vapor. The critical temperature is given by ω = 0.

313. is the gas constant for water vapor.

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