A numerical calculation method for high-temperature and high-pressure flash process
By using the Laval nozzle model and ZGB model to correct thermodynamic non-equilibrium effects under high temperature and high pressure, the problems of interphase heat transfer and thermodynamic non-equilibrium effects in the flash evaporation process were solved, and qualitative and quantitative prediction of the high temperature and high pressure flash evaporation process was realized.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- GENERAL MASCH KEY CORE INFRASTRUCTURE INNOVATION CENT (ANHUI) CO LTD
- Filing Date
- 2025-11-28
- Publication Date
- 2026-05-12
AI Technical Summary
Existing technologies are insufficient to accurately simulate the thermodynamic non-equilibrium effects and interphase heat transfer during flash evaporation under high temperature and pressure, resulting in significant discrepancies between simulation results and actual conditions.
A Laval nozzle fluid domain model was adopted, a structured mesh was generated, and temperature-dependent physical property parameters and a compressibility model were introduced. The thermodynamic non-equilibrium effects were corrected by combining the ZGB model. The physical property changes of water and steam were described by user-defined functions, considering viscous heat and interphase heat transfer. CFD software was used for simulation calculation.
Qualitative and quantitative analysis of the high-temperature and high-pressure flash evaporation process was achieved, accurately predicting the flash evaporation initiation location and steam volume distribution. The simulation results showed good agreement with the experimental data.
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Figure CN121598615B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of fluid technology, and more specifically, to a numerical calculation method for a high-temperature and high-pressure flash evaporation process. Background Technology
[0002] Flash evaporation refers to the boiling phenomenon that occurs when a superheated liquid encounters a sudden drop in pressure. While flash evaporation and cavitation occur at different locations, they share a common mechanism: when the pressure falls below the saturated vapor pressure, bubbles are generated, ultimately leading to a phase change. For high-temperature flash evaporation in some contraction-expansion structures, these two mechanisms may coexist and interact, allowing high-temperature flash evaporation to be viewed as comprehensive cavitation at high temperatures. Flash evaporation is a thermodynamically non-equilibrium process, requiring consideration of heat exchange between water and vapor bubbles. At high temperatures, even a small increase in temperature can lead to a significant increase in the saturated vapor pressure of water, making water readily vaporized even at relatively high pressures—a phenomenon known as the thermodynamic effect of high-temperature, high-pressure water.
[0003] Water is considered an incompressible fluid at room temperature. Under high temperature and pressure, its density is highly correlated with temperature and pressure, changing with variations in both. In contrast, steam under high temperature and pressure exhibits significant compressibility, and its density varies considerably with temperature and pressure. Furthermore, during high-speed flow, viscous stress generates frictional heat, which is converted into thermal energy, leading to an increase in fluid temperature. The phase change from water to steam is an endothermic process; due to the latent heat of vaporization, the system temperature decreases, and the temperature rise caused by viscous heat is not negligible compared to the overall temperature drop. Summary of the Invention
[0004] The purpose of this application is to provide a numerical calculation method for high-temperature and high-pressure flash evaporation processes to overcome the shortcomings of existing technologies. This method can achieve qualitative and quantitative analysis of high-temperature and high-pressure flash evaporation and also provide a theoretical basis for high-temperature and high-pressure flash evaporation.
[0005] According to a first aspect of the embodiments of this application, a numerical calculation method for a high-temperature and high-pressure flash evaporation process is provided, comprising:
[0006] S1: Establish a Laval nozzle fluid domain model, and perform structured mesh generation on the model to obtain a mesh model;
[0007] S2: Import the mesh model into the simulation software and enable the energy equation; define the high-temperature and high-pressure inlet boundary conditions, pressure outlet boundary conditions, and wall conditions; write the dependence of the physical properties of water and steam on temperature into the simulation software using user-defined functions; set the solver parameters and calculate the steady-state flow field results;
[0008] S3: Using the steady-state flow field results as initial conditions, select and activate the ZGB model that considers thermodynamic non-equilibrium effects, set the transient solution parameters, and calculate the transient simulation results.
[0009] S4: Import the transient simulation results into CFD post-processing software to extract and obtain the physical quantity change curves at key locations.
[0010] Furthermore, the physical properties include viscosity, specific heat capacity, and thermal conductivity.
[0011] Furthermore, the transient solution parameters include time step size and time step.
[0012] Furthermore, the key locations include the nozzle throat and a specific downstream cross-section.
[0013] Furthermore, the changes in the physical properties of water and steam with temperature are written into the simulation software as user-defined functions, including:
[0014] The viscosity, specific heat capacity, and thermal conductivity of water and steam are considered as functions of temperature, and their changes are made with temperature.
[0015] Wherein, the viscosity of the water The functional expression for temperature variation is as follows:
[0016] ;
[0017] Among them, the specific heat capacity of water The functional expression for temperature variation is as follows:
[0018] ;
[0019] Wherein, the thermal conductivity of the water The functional expression for temperature variation is as follows:
[0020] ;
[0021] Wherein, the viscosity of the steam The functional expression for temperature variation is as follows:
[0022] ;
[0023] Wherein, the specific heat capacity of the steam The functional expression for temperature variation is as follows:
[0024] ;
[0025] Wherein, the thermal conductivity of the steam The functional expression for temperature variation is as follows:
[0026] ;
[0027] In the formula, It is the temperature of the grid;
[0028] Write the above row number expressions into the simulation software as user-defined functions.
[0029] Furthermore, the ZGB model considering thermodynamic non-equilibrium effects is obtained by modifying it in the following way:
[0030] The saturated vapor pressure of water is corrected from a constant value to a value that varies with temperature; this relates to the saturated vapor pressure of water under high temperature and pressure. With temperature The function expression for the change is as follows:
[0031] ;
[0032] Add a heat transfer term to the mass source and sink formulas of the ZGB model, as shown in the following expression:
[0033] ;
[0034] In the formula, These are the thermal conductivity, density, and specific heat capacity of water, respectively. The fraction represents the bubble radius. This represents the time it takes for bubbles to form;
[0035] Add latent heat of vaporization to the energy equation With temperature The change in is expressed by the function expression as follows:
[0036] .
[0037] Furthermore, when extracting and obtaining the physical quantity change curves at key locations, a method of taking points in the near-wall region along the flow direction is adopted.
[0038] The technical solutions provided by the embodiments of this application may include the following beneficial effects:
[0039] As can be seen from the above embodiments, this application takes into account the thermodynamic non-equilibrium effect of the high-temperature and high-pressure flash evaporation process and the interphase heat transfer between the water and steam phases, while also taking into account the compressibility of water and steam and the viscous heat generated by high-speed flow, thus providing a theoretical basis for high-temperature and high-pressure flash evaporation.
[0040] The viscosity, specific heat capacity, and thermal conductivity of water and steam are treated as functions of temperature, and their changes with temperature are written into the Fluent simulation software in the form of UDFs. The density model of water adopts a compressible liquid model, and the density model of steam adopts an ideal gas model. Viscous heat is used. The ZGB model and energy equation, which are corrected considering thermodynamic non-equilibrium effects, are used to simulate high-temperature and high-pressure flashing. The results are not significantly different from the actual situation, and the flashing initiation position and steam volume distribution can be accurately predicted, realizing the qualitative and quantitative prediction of flashing characteristics under complex working conditions.
[0041] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and do not limit this application. Attached Figure Description
[0042] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.
[0043] Figure 1 The flowchart illustrates a numerical calculation method for a high-temperature and high-pressure flash evaporation process, as provided in an embodiment of the present invention.
[0044] Figure 2 This is an overall view of the Laval nozzle model given in an embodiment of the present invention.
[0045] Figure 3 This is a schematic diagram of the overall mesh of the Laval nozzle model given in an embodiment of the present invention.
[0046] Figure 4 The following are flash evaporation results of the Laval nozzle model along the XY symmetry plane given in the embodiments of the present invention: (a) Absolute pressure cloud map under three operating conditions; (b) Velocity cloud map under three operating conditions; (c) Temperature cloud map under three operating conditions; (d) Steam volume fraction cloud map under three operating conditions.
[0047] Figure 5 The diagram below shows key location nodes in an embodiment of the present invention. C represents the starting point of the convergence segment, S represents the starting point of the straight line segment, T represents the throat, and D represents the ending point of the divergence segment.
[0048] Figure 6 The following are comparison charts of numerical calculation results and experimental data under three working conditions given in the embodiments of the present invention: (a) Comparison chart under working condition 1; (b) Comparison chart under working condition 2; (c) Comparison chart under working condition 3; C represents the starting point of the convergence segment, S represents the starting point of the straight line segment, T represents the throat, and D represents the ending point of the divergence segment.
[0049] Figure 7 This is a comparison chart of mass flow rates under three operating conditions provided in an embodiment of the present invention. Detailed Implementation
[0050] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application.
[0051] The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The singular forms “a,” “the,” and “the” used herein are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any and all possible combinations of one or more of the associated listed items.
[0052] It should be understood that although the terms first, second, third, etc., may be used in this application to describe various information, such information should not be limited to these terms. These terms are only used to distinguish information of the same type from one another. For example, without departing from the scope of this application, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the word "if" as used herein may be interpreted as "when," "when," or "in response to determination."
[0053] Figure 1 This is a flowchart illustrating a numerical calculation method for a high-temperature and high-pressure flash evaporation process according to an exemplary embodiment, such as... Figure 1 As shown, the method may include the following steps:
[0054] S1: Establish a Laval nozzle fluid domain model, and perform structured mesh generation on the model to obtain a mesh model;
[0055] Specifically, such as Figure 2 As shown, the dimensions of the Laval nozzle fluid domain model are as follows: the straight pipe section before point C is 300 mm long and 66.7 mm in diameter; the converging section is 100 mm long; the straight pipe section at the throat is 363 mm long and 20 mm in diameter; the diverging section is 400 mm long with a divergence angle of 6°57'; and the straight pipe section after point D is 600 mm long. The fluid domain model was created according to these dimensions in SolidWorks modeling software and saved as a STEP format file. It was then imported into ICEM mesh generation software, where the model was named and meshed. Blocks were created and O-shaped cuts were applied, with particular attention to refining the mesh in the throat and the expected flash development region to ensure the accuracy of numerical predictions for the flash region. The MSH file was saved for subsequent import into Fluent simulation software. Figure 3 This is a schematic diagram of the overall mesh of the Laval nozzle model described in this invention.
[0056] S2: Import the mesh model into the simulation software and enable the energy equation; define the high-temperature and high-pressure inlet boundary conditions, pressure outlet boundary conditions, and wall conditions; write the dependence of the physical properties of water and steam on temperature into the simulation software using user-defined functions; set the solver parameters and calculate the steady-state flow field results;
[0057] Specifically, the viscosity, specific heat capacity, and thermal conductivity of water and steam are considered as functions of temperature, and their changes with temperature are calculated. The changes of viscosity, specific heat capacity, and thermal conductivity of water and steam with temperature (400K~600K) are extracted from the NIST database. The physical property parameters (viscosity, specific heat capacity, and thermal conductivity of water and steam)-temperature curves are fitted to obtain the functional expressions of viscosity, specific heat capacity, and thermal conductivity of water and steam with temperature.
[0058] Wherein, the viscosity of the water The functional expression for temperature variation is as follows:
[0059]
[0060] Among them, the specific heat capacity of water The functional expression for temperature variation is as follows:
[0061]
[0062] Wherein, the thermal conductivity of the water The functional expression for temperature variation is as follows:
[0063]
[0064] Wherein, the viscosity of the steam The functional expression for temperature variation is as follows:
[0065]
[0066] Wherein, the specific heat capacity of the steam The functional expression for temperature variation is as follows:
[0067]
[0068] Wherein, the thermal conductivity of the steam The functional expression for temperature variation is as follows:
[0069]
[0070] In the formula, These are viscosity, specific heat capacity, and thermal conductivity. It is the temperature of the grid, subscript and These represent water and steam, respectively. Frictional heat generated by high-speed flow is considered, and viscous heat is employed. The changes of the above physical properties with temperature are described using functional expressions to facilitate the subsequent development of user-defined functions. Furthermore, since interphase heat transfer is involved in the flash evaporation process, and viscous heat is also considered, these macroscopic parameters are thermally correlated, better reflecting actual flash evaporation conditions, and the results obtained have practical significance.
[0071] More specifically, the Mixture model was adopted, considering the interphase slip velocity. The first phase was water, labeled liq, and the second phase was steam, labeled vap. The Realizable Ke model was selected for the turbulence model. The energy equation was enabled, and the viscosity, specific heat capacity, and thermal conductivity of water and steam as a function of temperature were written into the Fluent simulation software in the form of UDFs. In order to simulate the compressibility of water and steam under high temperature and high pressure conditions, the density model of water adopted the compressible liquid model, and the density model of steam adopted the ideal gas model. The pressure-velocity coupling adopted the SIMPLEC format and the inlet initialization was used. The inlet pressure, outlet pressure, and no-slip wall were used. The inlet pressure, temperature, and outlet pressure were set according to the experiment, with a total of 3 sets of working conditions, as shown in Table 1.
[0072] Table 1:
[0073]
[0074] S3: Using the steady-state flow field results as initial conditions, select and activate the ZGB model that considers thermodynamic non-equilibrium effects, set the transient solution parameters, and calculate the transient simulation results.
[0075] Specifically, using the steady-state flow field results as initial conditions, the ZGB model considering thermodynamic non-equilibrium effects is selected and activated. The ZGB model considering thermodynamic non-equilibrium effects is obtained by modifying it in the following way:
[0076] Saturated vapor pressure is the fundamental criterion for determining flash evaporation. Under high temperature and pressure, the saturated vapor pressure of water and steam changes continuously with temperature. By correcting the constant saturated vapor pressure of water to a temperature-dependent value, and extracting the variation of saturated vapor pressure of water with temperature (400K–600K) from the NIST database, a saturated vapor pressure-temperature curve is fitted to obtain the saturated vapor pressure of water under high temperature and pressure. With temperature The function expression for the change is as follows:
[0077]
[0078] The ZGB model is a pressure-driven phase change model, similar in mechanism to flash evaporation. The mass source terms for steam generation and condensation in the ZGB model are... and confluence as follows:
[0079]
[0080] In the formula, These are the evaporation coefficient and the condensation coefficient, respectively. It is the volume fraction of nucleation sites. These are the volume fraction and density of steam. It is the density of water. This refers to the bubble radius. Based on calculations, the bubble radius is corrected to 1×10⁻⁶. -4 m, the evaporation coefficient is corrected to 5, and the condensation coefficient is corrected to 0.001. To better predict the heat transfer between the two phases at the microscopic level, a formula is introduced to represent the heat transfer between steam bubbles and water during flash evaporation, expressed using the bubble generation rate formula. The formula is derived from the approximate solution as follows:
[0081]
[0082]
[0083] In the formula, These are the thermal conductivity, density, and specific heat capacity of water, respectively. Used to represent the boundary layer thickness of a single bubble. It is the thermal diffusivity of water. This represents the bubble generation time, and is empirically set to 10. -5 .
[0084] By incorporating the heat transfer term into the source and sink terms of the ZGB model, a modified ZGB model is obtained, which is used to calculate high-temperature, high-pressure flash evaporation. The formulas are as follows:
[0085]
[0086] More specifically, the energy equation is as follows:
[0087]
[0088] In the formula, These are density, specific heat capacity, and thermal conductivity, respectively. It's speed. It is the quality score. It is the latent heat of vaporization, subscript These represent mixtures and turbulence, respectively. The latent heat of vaporization is added to the energy equation. With temperature The latent heat of vaporization of water was extracted from the NIST database as a function of temperature (400K–600K), and a latent heat of vaporization-temperature curve was fitted to obtain the latent heat of vaporization of high-temperature and high-pressure water. The functional expression for temperature variation is as follows:
[0089]
[0090] The modified ZGB model was imported into Fluent simulation software as a user-defined function (UDF). Then, the modified latent heat of vaporization as a function of temperature was imported into Fluent simulation software as a user-defined function (UDF) to correct the energy equation, which was used to characterize the thermodynamic non-equilibrium effects in the flash evaporation process.
[0091] More specifically, the calculations are performed on the original steady-state flow field, then switched to transient; a modified ZGB model considering thermodynamic non-equilibrium effects is added; the turbulence model is switched to the LES model; an XY plane is created, and contour plots of absolute pressure, velocity, temperature, and gas volume fraction are created in the XY plane. Animations are set for the four contour plots sequentially, and the time step interval is saved at 50 intervals; the time step is set to 3000 steps, with a time step range of 1×10⁻⁶. -6 -5×10 -6 The time step is increased every 3000 steps, and the maximum number of iterations is set to 20. The inlet and outlet quality flow rates are monitored, and the calculation is stopped when the change in inlet and outlet quality flow rates is less than 1%. The case file and data file are saved.
[0092] S4: Import the transient simulation results into CFD post-processing software to extract and obtain the physical quantity change curves at key locations;
[0093] Specifically, import the aforementioned case file and data file into Tecplot post-processing software, adjust the coordinate axis scale, create an XY plane in the 3D coordinate system, check Contour, click Details, calculate and select variables, change the scale to apply to all operating conditions, and output the image as a TIFF format to obtain flash vaporization cloud maps (absolute pressure cloud map, velocity cloud map, steam volume fraction cloud map, and temperature cloud map) under high temperature and high pressure. Figure 4 As shown;
[0094] Draw a schematic diagram based on the key locations of the nozzle, such as... Figure 5 As shown; switch to a 2D coordinate system, adjust the X-axis range, click Probe, refer to the experimental operation, and take points near the wall based on the X-axis coordinates and key locations (specific sections upstream and downstream of the nozzle throat). Modify the X-axis values with point C as the origin of the X-axis, fit the modified data, and obtain the curves of absolute pressure and steam volume fraction as a function of space under three operating conditions.
[0095] The change curves are quantitatively compared with the experimental data under the corresponding working conditions to obtain a comparison graph, such as... Figure 6As shown in (a), (b), and (c) in the figure; the mass flow rates obtained from numerical calculations under the three operating conditions are compared with those obtained from experiments, as follows. Figure 7 As shown.
[0096] The solution in this embodiment is applied to a numerical calculation method for a high-temperature and high-pressure flash evaporation process, which is used to predict the flash evaporation characteristics under high temperature and high pressure, and can be analyzed for different working conditions.
[0097] As can be seen from the above embodiments, this application solves the core problems of neglecting interphase heat transfer and thermodynamic non-equilibrium effects in traditional numerical methods when simulating high-temperature and high-pressure flash vaporization by introducing temperature-dependent physical property parameters (UDF), adopting a compressible model and a viscous heat and modified thermodynamic model. The numerical results obtained from the simulation can quantitatively provide the distribution curves of absolute pressure and steam volume fraction at key locations under different operating conditions, and they agree well with the experimental data. The obtained contour maps can accurately show the changes of different physical quantities under different operating conditions, realizing the qualitative prediction of flash vaporization.
[0098] This invention comprehensively considers the thermodynamic non-equilibrium effects during high-temperature and high-pressure flash evaporation, the interphase heat transfer between the water and steam phases, the compressibility of water and steam, and the viscous heat generated by high-speed flow. The simulation results can predict the flash evaporation initiation position and the steam volume fraction distribution, realizing the qualitative and quantitative prediction of flash evaporation characteristics under complex working conditions.
[0099] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only.
[0100] It should be understood that this application is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope.
Claims
1. A numerical calculation method for a high-temperature and high-pressure flash evaporation process, characterized in that, include: S1: Establish a Laval nozzle fluid domain model, and perform structured mesh generation on the model to obtain a mesh model; S2: Import the mesh model into the simulation software and enable the energy equation; define the high-temperature and high-pressure inlet boundary conditions, pressure outlet boundary conditions, and wall conditions; write the dependence of the physical properties of water and steam on temperature into the simulation software using user-defined functions; Set the solver parameters and calculate the steady-state flow field results; S3: Using the steady-state flow field results as initial conditions, select and activate the ZGB model that considers thermodynamic non-equilibrium effects, set the transient solution parameters, and calculate the transient simulation results. S4: Import the transient simulation results into CFD post-processing software to extract and obtain the physical quantity change curves at key locations; The variation of the physical properties of water and steam with temperature is incorporated into the simulation software as a user-defined function, including: The viscosity, specific heat capacity, and thermal conductivity of water and steam are considered as functions of temperature, and their changes are made with temperature. Wherein, the viscosity of the water The functional expression for temperature variation is as follows: ； Among them, the specific heat capacity of water The functional expression for temperature variation is as follows: ； Wherein, the thermal conductivity of the water The functional expression for temperature variation is as follows: ； Wherein, the viscosity of the steam The functional expression for temperature variation is as follows: ； Wherein, the specific heat capacity of the steam The functional expression for temperature variation is as follows: ； Wherein, the thermal conductivity of the steam The functional expression for temperature variation is as follows: ； In the formula, It is the temperature of the grid; Write the above row number expression into the simulation software as a user-defined function; The ZGB model considering thermodynamic non-equilibrium effects is obtained by modifying it in the following way: The saturated vapor pressure of water is corrected from a constant value to a value that varies with temperature; this relates to the saturated vapor pressure of water under high temperature and pressure. With temperature The function expression for the change is as follows: ； Add a heat transfer term to the mass source and sink formulas of the ZGB model, as shown in the following expression: ； In the formula, These are the thermal conductivity, density, and specific heat capacity of water, respectively. The fraction represents the bubble radius. This represents the time it takes for bubbles to form; Add latent heat of vaporization to the energy equation With temperature The change in is expressed by the function expression as follows: 。 2. The numerical calculation method for a high-temperature and high-pressure flash evaporation process according to claim 1, characterized in that, The physical properties include viscosity, specific heat capacity, and thermal conductivity.
3. The numerical calculation method for a high-temperature and high-pressure flash evaporation process according to claim 1, characterized in that, The transient solution parameters include time step and time step.
4. The numerical calculation method for a high-temperature and high-pressure flash evaporation process according to claim 1, characterized in that, The key locations include the nozzle throat and a specific downstream section.
5. The numerical calculation method for a high-temperature and high-pressure flash evaporation process according to claim 1, characterized in that, When extracting and obtaining the physical quantity change curves at key locations, the method of taking points in the near-wall region along the flow direction is adopted.