A method for defining and numerically modeling the regenerative acceleration of two-phase flow droplet breakup

Abstract

The present application relates to the technical field of fluid mechanics and chemical two-phase flow, and provides a two-phase flow droplet breaking reunion acceleration definition and numerical modeling method, which comprises the following steps: S1, establishing a two-phase flow control model family with specific surface area as an internal variable; S2, constructing a specific surface area source term evolution model and initializing a flow field; S3, obtaining a convergent specific surface area distribution from the specific surface area distribution; S4, iteratively solving the flow field, reunion force and specific surface area until convergence is obtained, and a convergent specific surface area field is obtained; and S5, coupling heat and mass transfer whole process simulation. The present application changes the existing kinematics description of the liquid breaking process into an energy description, avoids complex interface shape tracking and too many empirical parameters, and can more simply and clearly describe the breaking, atomization and accompanying heat and mass transfer process of the gas-liquid two-phase flow in a physical essence.

Description

Technical Field

[0001] This invention relates to the fields of fluid mechanics and chemical engineering two-phase flow technology, and in particular, establishes a definition and numerical modeling method for the recoil acceleration of two-phase flow droplet breakup. Background Technology

[0002] Two-phase flow breakup and heat and mass transfer are key issues in chemical multiphase flow processes and engine fuel injection atomization. In two-phase flow computational fluid dynamics (CFD) simulations, breakup theory and models determine the accuracy and cost of numerical calculations. Two-phase flow processes involve changes in the physical properties of the system, energy conversion, and reaction rates. Since they are not homogeneous systems, and there are processes such as temperature changes, pressure changes, phase changes, and chemical changes, consistent numerical simulation of multiphase flow processes is a challenge. Currently, models describing multiphase flow breakup and atomization include the TAB model (reference [1]), the Wave model (reference [2]), the KH-RT model (references [3] and [4]), the VOF model (reference [5]), the Mixture model (reference [6]), the DPM model (reference [7]), and the diffusion interface method (references [8] and [9]). These models mostly use physical analogies (such as TAB) and tracking of particle interfaces (such as VOF) to describe interface changes and droplet breakup. The diffusion interface method introduces additional pressure from the surface tension beneath the curved surface, and introduces the so-called capillary force into the momentum equation, incorporating it into the energy equation via a dot product with the velocity. However, this energy term is zero under conditions such as flat liquid surfaces and spherical droplets. Due to the difficulties in liquid tracking and droplet shape description, two-phase flow and secondary breakup models suffer from problems such as numerous empirical parameters and high computational costs. Establishing new governing equations based on fundamental scientific principles and developing new methods for gas-liquid two-phase flow breakup and heat and mass transfer is of great scientific and practical significance.

[0003] Existing technology 1

[0004] One existing technology is a breakup model based on empirical analogy and discrete phase tracking. This type of method typically discretizes the liquid phase into droplets with specific diameters, velocities, and positions, and uses the Lagrangian method to track their motion in the gas phase flow field. When a droplet meets a preset breakup criterion, smaller sub-droplets are generated based on an empirical model to simulate a secondary breakup process. Representative models include the TAB model, the KH model, and the KH-RT model.

[0005] For example, the TAB model analogizes the droplet deformation process to a spring-mass-damped system, determining breakup by solving the droplet oscillation deformation equation; the KH model, on the other hand, predicts the growth of surface waves and the peeling breakup process of droplets or liquid columns based on the Kelvin-Helmholtz instability induced by the relative motion of gas and liquid. Figure 1The diagram shown illustrates the development of turbulent jet structures under the KH model.

[0006] The existing technology has at least the following shortcomings:

[0007] 1. It relies on empirical parameters such as critical Weber number, breakup time constant, and droplet size distribution, resulting in poor parameter universality;

[0008] 2. The complex interfacial deformation, stretching, filamentation and fracture processes are usually simplified to the replacement of spherical droplets, which makes it difficult to reflect the real crushing mechanism;

[0009] 3. The study mainly focuses on droplet size evolution, but lacks sufficient description of the increase in interfacial energy during the breakup process and its coupling relationship with heat and mass transfer.

[0010] Existing technology 2

[0011] Existing technology two is the VOF method based on geometric interface reconstruction and flux transport. This method defines the liquid phase volume fraction in an Eulerian grid, determines the local interface position and normal in the interface cells through an interface reconstruction algorithm, and then combines it with an interface flux transport algorithm to achieve dynamic tracking of the gas-liquid interface. Surface tension is usually introduced into the momentum equation through a continuous surface force model. For example... Figure 2 The diagram shown illustrates the interface reconstruction and flux calculation in the VOF method.

[0012] The prior art has at least the following shortcomings:

[0013] Geometric reconstruction and flux calculation are required in the interface unit. In the three-dimensional case, the algorithm is complex and the computational cost is high.

[0014] To analyze the tiny droplets and filaments generated by breakage, a very high mesh resolution is usually required, which consumes huge computational resources on an engineering scale.

[0015] Once the flow enters the fully atomized stage, the number of interfaces increases dramatically and the scale decreases significantly, making explicit interface tracking methods difficult to apply efficiently.

[0016] Furthermore, while diffusion interface or phase field methods avoid explicit reconstruction of sharp interfaces by introducing diffusion transition regions and can introduce capillary force-related terms into the momentum and energy equations, they still rely on interface geometry information such as interface thickness, curvature, or phase field distribution to describe interface effects. In cases such as flat liquid surfaces and spherical droplets, existing capillary work terms are insufficient to directly characterize the energy conversion corresponding to the increase in specific surface area during droplet breakup.

[0017] Therefore, existing technologies still lack a gas-liquid two-phase flow breakup and heat and mass transfer method that can avoid the need for precise tracking of complex gas-liquid interfaces, reduce dependence on empirical parameters, and directly describe the evolution of specific surface area and its heat and mass transfer effects during droplet breakup from the perspective of energy conversion.

[0018] Existing technology three

[0019] The diffusion interface method, based on capillary work, is a numerical method for simulating the gas-liquid interface in two-phase flow. Its core lies in treating the traditionally "sharp" interface as a "diffused" transition region with a certain thickness, introducing a continuous phase field variable (such as phase separation) to describe the interface evolution. The momentum equation incorporates the additional pressure beneath the curved surface, i.e., capillary force, and the dot product of capillary force and velocity is introduced as a work term into the energy equation. This method is based on thermodynamic equilibrium, using a mean-field approximation to describe the Gibbs free energy and mixing energy of the flow field, establishing the equilibrium equations for the two-phase flow, and reconstructing the phase interface. This method effectively captures the heat and mass transfer processes at the interface and is suitable for simulating small-scale flows such as microchannels. Its simulation process typically includes:

[0020] 1. Model establishment: Based on the phase field method, the gas-liquid interface is regarded as a diffusion transition zone of a certain thickness. The governing equations containing the conservation of mass, momentum and energy are established. A capillary force term is introduced into the momentum equation, and a capillary work term is introduced into the energy equation.

[0021] 2. Numerical solution: The equations are discretized using methods such as the finite element method, and the distributions of the flow field, concentration field, and temperature field are obtained by iterative solution.

[0022] 3. Results Analysis: Extract data on interface morphology, velocity field, and concentration field to analyze the interface evolution patterns and their impact on the process.

[0023] The disadvantages of existing technology three are as follows:

[0024] 1. The introduction of fine-grained treatment of interface thickness increases the computational load. Capillary work requires analytical analysis of parameters such as interface curvature, which presents numerical challenges. When planar liquid surfaces and spherical droplets exist within the control volume, the additional pressure caused by surface tension is either zero or cancels out, rendering the introduction of capillary force meaningless.

[0025] 2. It is still necessary to track the phase interface, which presents the same difficulties as methods such as VOF.

[0026] The list of references is as follows:

[0027] [1] Suryaprakash R., Tomar G., J. Indian Inst. Sci., 2019, 99,1,77–91.

[0028] [2] Reitz R. D., Atomization Spray Tech. 1987, 3, 309–337.

[0029] [3] Patterson M. A., Reitz R. D., SAE Transactions, 1998,107,27-43.

[0030] [4] Beale J. C., Reitz R. D., Atomization Sprays,1999, 9(6),623-650.

[0031] [5] Hirt C. W., Nichols B. D., J. Comput. Phys,1981, 39, 201-225.

[0032] [6] Manninen M., Taivassalo V., Kallio S., On the Mixture Model forMultiphase Flow. Espoo,1996, Technical Research Centre of Finland, VTTPublications 288,1-67.

[0033] [7] Crowe C. T., Sharma M. P., Stock D. E., J. Fluid Eng., 1977, 99,325-332.

[0034] [8] Jain S. S., Mani A., Moin P., J. Comput. Phys. 2020, 418, 109606.

[0035] [9] Mostafavi, A., Ranjbar M., Yurkiv V, et al., Phys. Fluids 2025,37,072125. Summary of the Invention

[0036] To address the problems of numerous empirical parameters, high computational cost, and difficulty in interface tracking in existing two-phase flow computational fluid dynamics breakup models, this invention aims to provide a method for defining and numerically modeling the recoil acceleration of droplet breakup in gas-liquid two-phase flow. Starting from the energy essence of droplet breakup, the breakup process is viewed as an energy conversion process where mechanical energy overcomes surface tension to do work. The core lies in tracking the change in (specific) surface area caused by the conversion of liquid kinetic energy into surface free energy (also known as surface energy or surface work), establishing kinetic energy and momentum equations, and directly solving for the liquid's specific surface area through governing equations to describe the degree of liquid dispersion. Simultaneously, the specific surface area is used to correlate heat and mass transfer problems in the breakup-atomization process. Based on this method, the simulation of two-phase flow breakup, atomization, and heat and mass transfer no longer requires tracking droplets and interfaces, thus significantly reducing computational costs. This method transforms the existing kinematic description of liquid breakup processes into an energy-based description, avoiding complex interface morphology tracking and excessive empirical parameters. It can more concisely and clearly describe the breakup, atomization, and accompanying heat and mass transfer processes of gas-liquid two-phase flow, providing a more accurate and computationally cost-effective solution for numerical simulation in fields such as chemical multiphase flow processes and engine fuel injection atomization.

[0037] This invention provides the following technical solution:

[0038] A method for defining and numerically modeling the recoalescing acceleration of two-phase flow droplet breakup, comprising the following steps:

[0039] S1. Establish a family of two-phase flow control models with specific surface area as an internal variable.

[0040] Two-phase flow control equations are established, with a cohesive force term introduced into the momentum equation and a surface power term introduced into the kinetic energy equation. Specific surface area is used as the core variable, and the gas-liquid interface is not tracked.

[0041] S2. Construct a specific surface area source term evolution model and initialize the flow field.

[0042] An evolution model of specific surface area along the injection distance is constructed, and the model parameters are determined by nozzle parameters, liquid properties and breakup distance;

[0043] S3. Calculate the cohesive force field from the specific surface area distribution, and couple and update the flow field velocity to obtain a converged specific surface area distribution.

[0044] S4. Iteratively solve for the flow field, cohesion, and specific surface area until convergence, and obtain the converged specific surface area field.

[0045] S5. Coupled simulation of the entire heat and mass transfer process: Based on the convergent specific surface area field, the evaporation rate and heat transfer rate are coupled and calculated to obtain a simulation model of the entire process of two-phase flow breakup-atomization-heat and mass transfer.

[0046] Preferably, the specific steps of step S1 are as follows:

[0047] Continuity equation: in standard form, see formula (1): (1)

[0048] In the above equation, the two phases on the left-hand side are the mass time-varying rate and the convection term, respectively. For the density of the medium, Let t be the velocity vector, and t be time.

[0049] Momentum Equation: Based on the traditional Navier-Stokes equation, a cohesive force term L is introduced to characterize the resistance generated by the increase in surface energy during droplet breakup, as shown below:

[0050] (7)

[0051] In the above formula, For pressure, For viscous stress tensor, For droplet density, The relative velocity between the gas and liquid phases, and the cohesive force L, are functions of the specific surface area gradient, defined by the following equation:

[0052] (6)

[0053] In the above formula, For surface tension, The droplet phase fraction, The density of the droplets;

[0054] Kinetic energy equation: Under the framework of energy conservation, a surface power term is introduced to describe the rate at which fluid mechanical energy is converted into liquid surface free energy. Its equivalent form is shown in equation (11):

[0055] (11)

[0056] In the above formula: The volume fraction of the i-th phase The density of the i-th phase. : The kinetic energy of the i-th phase : velocity of phase i, p: pressure, τ: viscous stress tensor, v: velocity vector, γ: surface tension : Droplet phase fraction, Droplet density, : Rate of change of specific surface area;

[0057] Formulas (1), (7), and (11) above constitute the family of two-phase flow control models, which are used to compare surface area A. s Solve the problem.

[0058] In the above implementation, the purpose of step S1 is to construct a set of control equations that do not require tracking the gas-liquid interface, but instead use "specific surface area" as the core variable.

[0059] Preferably, step S2 includes the following steps:

[0060] S2.1 Establish a specific surface area evolution model:

[0061] Assume that the evolution of the specific surface area along the injection distance x follows a two-parameter exponential distribution, as shown in Equation (12):

[0062] (12)

[0063] in, This is the limiting specific surface area. A represents the characteristic fragmentation distance corresponding to the maximum increase in specific surface area. S (x) represents the increase in the liquid specific surface area from the nozzle exit to point x;

[0064] S2.2 Determination of Model Parameters:

[0065] Limiting specific surface area :

[0066] The average diameter d of Sauter 32 The empirical or semi-empirical correlation calculations use correlations based on Kolmogorov's turbulence theory:

[0067] (18)

[0068] In the above formula, We is the Weber number, describing the relative magnitude of inertial force and surface tension, and the Sauter mean diameter is... It is the core parameter characterizing the average particle size of spray droplets, and the particle size is... Determine the nozzle diameter;

[0069] The limiting specific surface area can then be calculated using formula (16):

[0070] (16)

[0071] In the above formula, For specific surface area increment, It is the core parameter characterizing the average particle size of spray droplets;

[0072] Feature breakage distance Distance completed by breaking Confirmed, see the following formula:

[0073] (28)

[0074] in, Calculate using formula (27):

[0075] (27)

[0076] In the above formula, : Distance to complete the breakage, where We is the Weiber number. The relative velocity between gas and liquid. The time required for crushing to complete. For droplet density, For gas density, The diameter of the droplet;

[0077] Initialization: Calculate the initial value A of the specific surface area of ​​the entire flow field using formula (12). s Substitute (x) into formula (6) to calculate the initial value L(x) of the cohesive force field.

[0078] In the above implementation, this step requires providing the initial distribution and evolution of the specific surface area As in order to close the governing equations. This step constructs an analytical model that does not require iteration.

[0079] Preferably, step S3 is a self-consistent field iterative solution, which includes the following steps:

[0080] S3.1, Given the specific surface area increment Initial guess, calculation of initial value of specific cohesion ;

[0081] S3.2, will Substituting into the momentum equation and solving, we obtain the velocity field. ;

[0082] S3.3 Substitute the velocity field into the kinetic energy equation to calculate the surface work and power. ;

[0083] S3.4 Calculate the surface power difference :

[0084] (31)

[0085] In the above formula, For relative velocity, For surface tension, The droplet phase fraction, The density of the droplets;

[0086] S3.5, according to The updated ratio of cohesion is ;

[0087] S3.6, will Substitute the values ​​into the momentum equation to solve for the velocity field again, then substitute them into the kinetic energy equation to calculate the specific surface work and power. Repeat steps S3.4-S3.6 until... This yields a convergent specific surface area distribution.

[0088] Preferably, step S4 is a convergence determination, specifically:

[0089] Repeat the iterative process in step S3 until the surface power difference Δ approaches zero. At this point, the flow field, cohesion field, and specific surface area field reach self-consistent convergence, and the converged specific surface area field is output. .

[0090] Preferably, the simulation process of the entire coupled heat and mass transfer process in step S5 is as follows:

[0091] In obtaining a convergent specific surface area field Then, calculations are performed on phase change and heat transfer; specific surface area. It directly provides the gas-liquid contact area;

[0092] Evaporation rate calculation: The evaporation rate consists of two parts: surface evaporation and boiling evaporation, which are calculated using formulas (34) and (35) respectively:

[0093] Surface evaporation ( ):

[0094] (34)

[0095] In the above formula, For surface evaporation rate, Liquid mass within the grid, Specific surface area Mass transfer coefficient, Liquid phase partial pressure at the droplet surface The partial pressure of the liquid phase in a fluid volume;

[0096] Boiling evaporation ( ):

[0097] (35)

[0098] In the formula, For the mass of the liquid within the grid, The mass transfer coefficient is . and The partial pressure of the liquid phase at the droplet surface and in the fluid volume is the liquid phase partial pressure. The heat transfer coefficient, For molar enthalpy of vaporization, This refers to the boiling evaporation rate;

[0099] Heat transfer rate calculation: heat flux density Calculated using Newton's law of cooling, as shown in equation (36):

[0100] (36)

[0101] In the above formula, For heat flux density, Heat transfer coefficient, Gas temperature, Droplet temperature;

[0102] Phase field and temperature field updates:

[0103] The calculated total evaporation rate Substituting into the phase fraction transport equation (32), update the liquid phase volume fraction. ;

[0104] The calculated heat flux density is substituted into the energy equation to update the temperature field T; thus, a transient simulation of the entire process from droplet breakup and atomization to evaporation is achieved.

[0105] Compared with the prior art, the present invention has the following beneficial effects:

[0106] 1) The definition and numerical modeling method of the back-coalescing acceleration of two-phase flow droplet breakup provided by this invention fundamentally reveals the physical essence and defines the "drawback force" of the liquid flow breakup process. Based on energy conversion, it greatly reduces empirical parameters and significantly improves the physical self-consistency and universality of the model.

[0107] Existing technologies (such as TAB and KH-RT models) rely on physical analogies of breakup phenomena (such as spring vibration and interfacial wave instability) and a large number of empirical parameters that need to be calibrated experimentally (such as critical Weber number, breakup time constant, and droplet size distribution). These models have poor universality and require parameter readjustment under different operating conditions. This invention abandons the aforementioned phenomenological analogies and directly starts from the physical essence of the first law of thermodynamics and the conservation of energy, explicitly defining the droplet breakup process as an energy conversion process in which the system's mechanical energy overcomes surface tension and is converted into surface energy. By introducing surface energy into the energy control equation (9) of the flow system, a physical relationship (10) between mechanical energy dissipation and specific surface area increment is directly established. This method is entirely based on fundamental principles to construct the core theory, fundamentally eliminating the dependence on phenomenological analogies and empirical parameters, thus giving the model a solid physical foundation and wider applicability.

[0108] 2) By abandoning complex interface geometry reconstruction and tracing, computational efficiency is greatly improved.

[0109] Existing interface-based techniques (such as the VOF method) require costly geometric interface reconstruction and geometry-based flux calculations for each interface-containing mesh at every time step to track complex phase interface deformation, tearing, and fusion. This is not only algorithmically complex and difficult to implement, but also requires extremely fine meshes to resolve tiny droplets, leading to exponentially increasing computational costs and high computational costs for engineering numerical simulations. This invention completely bypasses the description of interface geometry. The specific surface area increment is obtained by solving the energy equation. It naturally includes the interface information added due to fragmentation, without concern for the specific shape and distribution of the interface. This method shifts the computational focus from expensive "interface geometry" to efficient "interface energy," avoiding the limitations of interface reconstruction and fine meshes, and making it possible to perform rapid and efficient numerical simulations of large-scale, high Reynolds number gas-liquid two-phase flows and fully atomized processes.

[0110] 3) It realizes the collaborative calculation of crushing and heat and mass transfer, and the prediction capability is more comprehensive and accurate.

[0111] Under the existing technological framework, the breakup model and the evaporation mass transfer model are usually decoupled or weakly coupled. The breakup model provides the droplet size distribution, which is then used as the liquid surface area input to the independent evaporation model to calculate the phase change. Generally, the phase change of the liquid is not calculated before the droplet formation is completed, which has physical defects. This invention uses the specific surface area as a core physical quantity to achieve a fundamental unification and synergistic calculation of breakup dynamics and heat and mass transfer rates. Liquid injection can then perform heat transfer and phase change calculations based on the surface area. The specific surface area increment formula (11) directly output by the energy equation is also a key input for calculating the surface evaporation rate formula (14) and the boiling evaporation rate formula (15). This means that the entire liquid injection process will realize mass and heat transfer calculations based on the evolution of specific surface area. Conversely, the changes in physical properties and mass caused by the phase change will in turn affect the changes in specific surface area. This synergistic mechanism based on energy conservation enables the model to continuously simulate the entire process from liquid jetting, primary breakup, secondary atomization to final complete evaporation, significantly improving the overall accuracy and physical consistency of the prediction.

[0112] 4) It provides a unified and concise theoretical and numerical framework for complex multiphase flow systems.

[0113] The kinetic energy equation (9) proposed in this invention is highly consistent in form with the governing equations of single-phase flow or mixing models, and only introduces a source term (surface free energy) with clear physical meaning to characterize the droplet breakup process. This approach realizes the theoretical description of two-phase flow and homogeneous flow, as well as different breakup-evaporation mechanisms, under a unified governing equation framework. Whether solving for each phase independently or using a mixing model, the energy partitioning relation (10) provides a unified criterion for the conversion of mechanical energy to surface energy. The framework is logically clear, simple to implement, and easy to integrate and extend into existing computational fluid dynamics (CFD) code (such as OpenFOAM), providing a powerful and flexible basic tool for studying multiphase flow systems that include more complex processes such as phase transitions and reactions.

[0114] In summary, this invention, by incorporating surface energy changes into the energy conservation framework, establishes a physically clear, computationally efficient, and tightly coupled method for defining and numerically modeling the recoiling acceleration of two-phase flow droplet breakup. This effectively overcomes the inherent shortcomings of existing technologies (I, II, and III)—namely, strong empirical basis, weak scientific rigor, and high computational cost. It possesses significant scientific value and promising engineering applications in fields such as engine fuel atomization, chemical process intensification, and spray combustion. This invention uses specific surface area parameters to describe the breakup process and introduces recoiling force to obtain the specific surface area change rate. The specific surface area evolution breakup model based on this invention simplifies and saves time in numerical calculations, significantly reducing the computational cost of multiphase flow breakup and atomization. Attached Figure Description

[0115] Figure 1 A schematic diagram of the development of turbulent jet structures under the KH model, which serves as the background technology of this application.

[0116] Figure 2 A schematic diagram of interface reconstruction and flux calculation in the VOF method provided in the background technology of this application.

[0117] Figure 3A This is a schematic diagram of different Weber number breakage modes in the droplet breakage mechanism provided in the embodiments of the present invention.

[0118] Figure 3B This is a schematic diagram of the free jet breakup mechanism in the droplet breakup mechanism provided in an embodiment of the present invention.

[0119] Figure 4 Dimensionless crushing time provided for embodiments of the present invention The diagram shows the segmented and unified representations, with the blue dotted lines representing the representation used in this invention.

[0120] Figure 5A This is a schematic diagram showing the distribution of the specific surface area and specific cohesion of water along the airflow direction, calculated according to reference

[17] .

[0121] Figure 5B The diagram shows the distribution of the specific surface area and specific recoagulation force of ethanol along the airflow direction, calculated according to reference

[17] .

[0122] Figure 6A The specific surface area and specific cohesion distribution of different secondary crushing models provided in the embodiments of the present invention, and the variation of the Sauter average direct spatial distribution predicted by different models (Figure 6 of reference [9]).

[0123] Figure 6B The specific surface area and specific cohesion distribution of different secondary crushing models provided in the embodiments of the present invention are shown in the spatial distribution diagram of the specific surface area corresponding to different models.

[0124] Figure 6C The specific surface area and specific cohesion distribution of different secondary crushing models provided in the embodiments of the present invention are shown in the spatial distribution diagram of specific cohesion for different models. Detailed Implementation

[0125] This invention attributes the physical essence of liquid breakup in two-phase flow to an energy conversion process of "mechanical energy being converted into surface energy," and directly embeds this process into the macroscopic governing equations of the flow system through a "surface work source term" with clear physical meaning. Based on the energy conversion of the gas-liquid collision process, this invention introduces a cohesive force term into the momentum equation and a surface power term into the energy equation, establishing a theory and numerical simulation method for droplet breakup in gas-liquid two-phase flow based on surface area evolution.

[0126] The technical principle is as follows: when simulating gas-liquid two-phase flow, the evolution of the liquid specific surface area is obtained by introducing a cohesive force term, and the heat transfer, mass transfer and phase change rate are calculated accordingly.

[0127] Droplet breakup is essentially an energy conversion process in which the mechanical energy of the system overcomes surface tension. In droplet breakup, the specific surface area of ​​the liquid is a thermodynamic state function that can be directly calculated based on energy conversion, and this quantity does not depend on the shape of the gas-liquid interface. Simultaneously, the specific surface area of ​​the liquid determines the rate of liquid evaporation and heat transfer with the surrounding environment. Therefore, this invention, based on the energy conversion of the gas-liquid collision process, introduces specific surface work into the energy equation to establish a gas-liquid two-phase flow breakup and heat and mass transfer method based on specific surface area evolution.

[0128] Example 1: Momentum and Energy Equations for Two-Phase Flow Breakup Process

[0129] When considering the overall motion, the governing equations for a homogeneous system include the continuity equation:

[0130] (1)

[0131] The two phases on the left-hand side of the equation are the mass time-varying rate and the convection term, respectively. In the equation... For the density of the medium, Let be the velocity vector, and t be time. No other source terms are considered here. The momentum conservation equation for a homogeneous system is:

[0132] (2)

[0133] In the formula For pressure, Let be the viscous stress tensor. Gravity is not considered here. The two terms on the left side of equation (2) are the time-varying rate of momentum and the momentum convection term, respectively.

[0134] Two-phase flow systems often involve atomization and fragmentation, a process widely used in engine fuel injection, chemical two-phase flow, medical and agricultural spraying, and other applications. Droplets move at a relative velocity within the gas phase flow field. During motion, work must be done to overcome surface tension, pushing the droplets to deform and break up, thus increasing the specific surface area of ​​the liquid. The surface free energy of a liquid increases. Surface tension originates from the unbalanced forces between liquid molecules. Molecules inside the liquid are uniformly attracted by surrounding molecules, while molecules on the surface are primarily attracted by molecules inside the liquid. This asymmetric force causes surface molecules to be pulled towards the interior of the liquid, thus creating surface tension, which macroscopically manifests as the tendency of the liquid surface to contract. Since the work done by surface tension originates from intermolecular forces, surface Gibbs free energy is non-volume work. Like volume work, surface work is thermodynamic work, not mechanical work. Because surface tension work does not involve macroscopic displacement but rather energy conversion through intermolecular forces, it differs from mechanical work in its physical mechanism and application. Mechanical energy, such as the kinetic energy generated by engine liquid injection and agitators, can be directly converted into surface free energy; this conversion follows the first law of thermodynamics. It is worth noting that surface work is usually considered reversible work, while mechanical work may be partially dissipated as heat energy in irreversible processes such as friction. When a liquid (droplet) breaks up and expands its surface area, work must be done to overcome intermolecular attraction; this energy is stored as potential energy on the new surface. This energy is the reversible work required for the system to increase its surface area by a unit, manifested as the additional potential energy of surface molecules compared to bulk molecules. The mechanism of surface free energy generation is the imbalance of forces acting on surface molecules (e.g., the attraction between liquid molecules and gas molecules is greater for liquid surface molecules), resulting in their potential energy being higher than that of internal molecules.

[0135] Surface work and volume work are two independent concepts that cannot be directly converted into each other. They describe the energy changes of a system during different physical processes. In practical applications, a system may experience both surface work and volume work simultaneously, but these must be calculated independently. Furthermore, the temperature rise of a system through heat absorption can change the surface free energy by altering the surface tension. Since the energy directly converted to surface energy is mechanical energy, it is possible to introduce a surface free energy term into the energy equation and calculate the surface free energy through the consumption of the system's kinetic energy.

[0136] In the liquid fragmentation process of a gas-liquid two-phase flow, the collision and fragmentation between droplets and the gas phase will slow down the droplet velocity, and the kinetic energy dissipation will be partially or completely converted into surface free energy. The surface area of ​​the liquid within the control volume is the surface area per unit mass of liquid. The surface free energy of the control volume is:

[0137] (3)

[0138] In the formula For surface tension, The droplet phase fraction, denoted as droplet density. Specific surface area is the surface area per unit mass of liquid. For a dynamic flow and breakup process, specific surface area is a function of spatial coordinates and time, i.e.:

[0139] (4)

[0140] When considering the increase in surface free energy due to gas-liquid collision, the power of the work done by surface tension during the breakup process is:

[0141] (5)

[0142] The negative sign in equation (5) indicates that the fluid motion converts kinetic energy into potential energy as the surface area increases. Note that the surface power here only considers the change in potential energy caused by the change in surface area of ​​a constant mass of liquid (surface free energy is a type of potential energy). This represents the rate of change in specific surface area.

[0143] The conversion of droplet kinetic energy into surface free energy manifests as a decrease in droplet velocity. The increase in surface free energy during droplet breakup exerts a certain force on the droplet, but this force has long remained undiscovered and unproven. Based on fundamental mechanics principles, this invention defines the droplet force during breakup, relative to the breakup process, as the droplet withdrawal force, or simply withdrawal force. According to the fundamental principles of classical mechanics, in a conservative force field, the force acting on an object is the negative gradient of its potential energy, known as the Hermann-Feynman theorem. The withdrawal force is defined as:

[0144] (6)

[0145] In the above formula, For surface tension, The droplet phase fraction, denoted as droplet density.

[0146] This theorem ensures that the force points in the direction of the fastest decrease in potential energy. Here... It is the reverse resistance in the liquid breaking process, unlike surface tension. It is the kinetic resistance experienced by the liquid during the time of directional breakage. The cohesive force generated per unit mass of liquid is... This indicates that it becomes a cohesive force. Based on the three elements of force, The magnitude is defined by equation (6), the direction is the direction in which the droplet dispersion decreases, and the point of action is at the center of mass of the liquid. The result is a reduction in the relative velocity between the droplets and the gas phase.

[0147] The last equal sign in equation (6) indicates that the breakage is only related to the liquid surface area, therefore the gradient calculation is only applicable to... conduct.

[0148] Introduction Then, the liquid phase momentum equation (2) of the system becomes:

[0149] (7)

[0150] Equation (7) does not consider gravity. Considering the breakup scenario in a liquid-phase gas flow, the kinetic energy conservation equation can be obtained by multiplying the velocity by equation (7). According to the definition in equation (6), we have:

[0151] (8)

[0152] Summing the individual phases, we only consider one liquid phase and one gas phase here. The power of the work done by the moving object (surface work in this case):

[0153] (9)

[0154] The surface power term in equation (8) is equivalent to the surface power term shown in equation (5), that is:

[0155] (10)

[0156] Therefore, equation (8) can be written in another equivalent form:

[0157] (11)

[0158] In the above formula: The volume fraction of the i-th phase The density of the i-th phase. : The kinetic energy of the i-th phase : velocity of phase i, p: pressure, τ: viscous stress tensor, v: velocity vector, γ: surface tension : Droplet phase fraction, Droplet density, : Rate of change of specific surface area.

[0159] Equation (8) shows that the complete energy equation should include the contribution of the change in surface free energy. The kinetic energy of a liquid is dissipated through different pathways, including work done against compressive stress, work done against viscous stress, work done against surface tension, and energy transfer to the gas phase.

[0160] Example 2: Calculation method for specific surface area source term in two-phase flow breakup process

[0161] To make equations (7) and (8) closed, it is necessary to introduce a specific surface area source term. Considering that when the liquid initially exits the nozzle, only the outer surface of the liquid column undergoes minor breakage and deformation due to airflow entrainment. After traveling a certain distance, as the droplet diameter decreases and the liquid collision velocity reduces, the breakage slows down or stops completely. Therefore, in the process of the liquid's specific surface area increasing at a slow to fast rate, and finally slowing down and stopping, there exists a location where the specific surface area increase rate reaches its maximum. Let's assume this location is at a distance from the nozzle... Based on the above considerations, this embodiment proposes a two-parameter equation (with the same treatment for two-dimensional and three-dimensional conditions) to describe the one-dimensional variation of specific surface area along the injection distance under steady-state injection (excluding time) conditions, namely:

[0162] (12)

[0163] (13)

[0164] In formula (12),, This is the limiting specific surface area. A represents the characteristic fragmentation distance corresponding to the maximum increase in specific surface area. S (x) represents the increase in the liquid specific surface area from the nozzle exit to point x;

[0165] In formula (13), Let x be the unit vector in the x-direction. Equations (12) and (13) require determining two parameters: 1) the maximum surface area limit. ,Right now exist The asymptotes of time need to be explained; for the sake of brevity, they will be represented by... 1) The increase in the specific surface area of ​​the liquid from the nozzle exit to point x; 2) The injection distance corresponding to the maximum increase in specific surface area. Considering the liquid jetting process, existing secondary fragmentation models define the droplet fragmentation length or fragmentation distance, which is the distance at which the liquid column terminates or the core region disappears as observed in experiments during the liquid jetting process. In this case, the increase in specific surface area can be assumed to be maximum. Take the second derivative of equation (12) and let This can be verified in The increase in specific surface area reaches its maximum value. It can be determined by existing secondary fragmentation models or experimental measurement parameters. Starting from the nozzle... The spatial distribution function relationship has not yet been reported in the literature, and specific surface area has not received much attention. The droplet breakup process is relatively complex (e.g. Figure 3A and Figure 3B As shown, during the atomization process, the topology of the liquid flow undergoes a dramatic change from a cylindrical jet to a wavy jet, sheet-like, filamentous, and other ambiguous liquid clumps commonly referred to as "clumps." Currently, various theoretical models have been established, most of which are empirical models. Numerous experiments and theoretical analyses have revealed the variation of the droplet size of the atomized liquid over time and space. Because the cohesive force affects the relative velocity of the gas and liquid phases, the conversion of fluid kinetic energy into surface work is achieved by inertial forces overcoming surface tension, leading to an increase in the free energy of the liquid surface.

[0166] To obtain the specific surface area distribution function shown in equation (12), the incremental specific surface area of ​​the limit breakage must first be determined. For the deformation and breakup of droplets in two-phase flow, the Weber number is generally used to describe the ease of liquid breakup. The Weber number is defined as:

[0167] (14)

[0168] In the formula, For fluid density, The characteristic length is denoted as . It is a dimensionless number that describes the relative magnitude of inertial force and surface tension. When the flow is small (such as capillary action or soap bubbles), surface tension dominates, and the fluid tends to remain intact and is difficult to break. When... At larger volumes (e.g., spraying, droplet breakup), inertial forces dominate, making the fluid prone to breakup. Solving for two-phase flow requires a reasonable initial guess of the source term. Various discrete phase models, such as the TAB model and the KH model, have established relationships between characteristics like droplet diameter distribution, droplet deformation, and breakup time and the Weber number. Breakup time and sub-droplet diameter can be obtained using nozzle inlet parameters. If the Sauter diameter is used, the relationship between the liquid specific surface area and the Sauter diameter can be directly obtained. (Sauter mean diameter) It is the core parameter characterizing the average particle size of spray droplets, defined as six times the ratio of droplet volume to surface area, that is:

[0169] (15)

[0170] here Summing over particles of all sizes. Liquid from particle size... (Generally taken as the nozzle diameter) to the average diameter of Sauter's bursting. When small droplets, Corresponding distance The increase in specific surface area at (hereinafter referred to as the breaking distance):

[0171] (16)

[0172] In the above formula, For specific surface area increment, It is the core parameter characterizing the average particle size of spray droplets.

[0173] set up The measurement distance of the droplet is When the nozzle is large or the liquid is sufficiently broken up, Therefore, use To replace specific surface area increment It will not introduce significant errors. The determination of equation (12) can consider two factors: the breakdown of a certain inviscid fluid... The following empirical formula exists:

[0174] (17)

[0175] By assuming fully turbulent flow and low viscosity, the following expression for liquid / liquid two-phase disruption can be obtained corresponding to Kolmogorov's fully turbulent flow theory, as reference

[10] :

[0176] (18)

[0177] In the above formula, We is the Weber number, describing the relative magnitude of inertial force and surface tension, and the Sauter mean diameter is... It is the core parameter characterizing the average particle size of spray droplets, and the particle size is... Take the nozzle diameter. Reference

[10] gives B=0.82. Some literature also uses the Arithmetic average diameter. To describe the degree of liquid dispersion: (and provide reference

[11] )

[0178] (19)

[0179] (20)

[0180] There is a large body of literature discussing this. For empirical correlations with dimensionless numbers such as Weber number and Reynolds number, refer to reference

[12] . As a methodological description, this embodiment uses the relatively simple correlation shown in equation (17) to determine the correlation in equation (12). If a more reliable correlation formula is desired, it can be selected according to the situation. Substituting equation (18) into equation (16) yields:

[0181] (twenty one)

[0182] Equation (18) can be replaced by other empirical correlations.

[0183] The second parameter to be determined is This embodiment uses the breakup distance or breakup length from the existing secondary breakup model instead. The liquid crossflow trajectory, penetration depth, and breakup length have been discussed extensively in the literature. For example, Broumand reference

[12] summarizes the correlation formulas for the column breakup distance established by different literatures under shear flow conditions. According to the secondary breakup model, the droplet breakup distance is measured. distance Can be adopted Estimate the reference

[13] . To obtain the liquid breakage distance, the following characteristic time can be defined (references [13-15]):

[0184] (twenty two)

[0185] Define dimensionless fragmentation completion time . The current literature generally gives the critical Weber number as the representation. The segmented representation is as follows, as shown in reference

[13] :

[0186] (twenty three)

[0187] Some literature also uses the full Weber number range, see references [14,16]:

[0188] (twenty four)

[0189] Comparison of equations (23) and (24) Figure 4 As shown, equation (24) yields a higher result than the segmented empirical equation in the low to medium Weber number range. According to equation (24), the atomization completion time may be overestimated. This invention adopts equation (23) in the full Weber number range. The empirical correlation formula for intervals is:

[0190] (25)

[0191] Combining equations (22) and (25), the crushing time is completed. The following estimates can be made:

[0192] (26)

[0193] Reference

[13] according to initial velocity and A simple product is used to estimate the distance to complete the crushing process, i.e.:

[0194] (27)

[0195] In the above formula, : Distance to complete the breakage, where We is the Weiber number. The relative velocity between gas and liquid. The time required for crushing to complete. For droplet density, For gas density, denoted as the droplet diameter.

[0196] achieve At that time, the relative velocity between gas and liquid is already very small, and equation (27) may overestimate the distance to complete the crushing. However, this invention still adopts equation (27) and sets:

[0197] (28)

[0198] As can be seen from the analysis below, Different values ​​will affect the distribution of cohesion and specific surface area within the distance from the nozzle exit to complete atomization (breakup), but will not affect the total amount of liquid kinetic energy converted into surface energy at the end of breakup. The value of will not introduce substantial error. Based on the above processing, the value of equation (12) can be determined. :

[0199] (29)

[0200] Substituting equations (21), (27), and (28), we get:

[0201] (30)

[0202] Thus, the two-parameter form of the specific surface area source term shown in equation (12) is established. In equation (12), if and If the measurement results are reliable, then it can be guaranteed. The conservation of surface work conversion between them, and The value of and Distribution, but does not affect Total surface work conversion.

[0203] It should be noted that equation (12) holds true in the cases of free jet, shear flow, and collision flow. In the case of shear flow, the liquid velocity is decomposed into two components: the velocity in the direction of the airflow and the velocity perpendicular to the airflow direction. The initial velocity of the liquid perpendicular to the airflow direction is 0. Under the action of the airflow, it undergoes accelerated motion, while the relative velocity gradually decreases. The distribution of the specific surface area still follows equation (12).

[0204] Example 3: Iterative solution of droplet specific surface area in a two-phase flow breakup process

[0205] If the kinetic energy equation (11) is calculated accurately, the surface work power and the cohesive force term in the momentum equation can be solved iteratively, ultimately achieving a reasonable specific surface area distribution. Assuming an initial guess of the surface work power of a control volume, this value will determine the rate of increase in specific surface area. If the rate of increase is too fast, it will lead to an increase in the cohesive force within the control volume, thereby reducing the droplet velocity. The decrease in droplet velocity leads to a decrease in surface work power. This self-consistent field iterative approach between liquid kinetic energy and cohesive force can potentially establish a reasonable dynamic equilibrium for breakup. The steps for solving the self-consistent field iteratively are as follows.

[0206] (a) Given a specific surface area increment Initial guess, calculation of initial value of specific cohesion ;

[0207] (b) will Substituting into the momentum equation and solving, we obtain the velocity field. ;

[0208] (c) Substitute the velocity field into the kinetic energy equation to calculate the surface work power. ;

[0209] (d) Calculate the surface power difference:

[0210] (31)

[0211] In the above formula, For relative velocity, For surface tension, The droplet phase fraction, denoted as droplet density.

[0212] (e) According to The updated ratio of cohesion is ;

[0213] (f) will Substitute the values ​​into the momentum equation to solve for the velocity field again, then substitute them into the kinetic energy equation to calculate the specific surface work and power. Repeat steps (d)-(f) until... This yields a convergent specific surface area distribution. However, the exact method for this iterative convergence is not yet fully understood.

[0214] Example 4: Heat and Mass Transfer Coupling Calculation

[0215] To ensure the completeness of the theory, this invention describes the specific surface area obtained. evaporation rate Introducing the phase fraction transport equation:

[0216] (32)

[0217] The phase change rate consists of two parts: surface evaporation rate and surface evaporation rate. and bulk evaporation rate :

[0218] (33)

[0219] Surface evaporation ( ):

[0220] (34)

[0221] In the above formula, For surface evaporation rate, Liquid mass within the grid, Specific surface area Mass transfer coefficient, Liquid phase partial pressure at the droplet surface The partial pressure of the liquid phase in a fluid volume.

[0222] Boiling evaporation ( ):

[0223] (35)

[0224] In the formula, For the mass of the liquid within the grid, The mass transfer coefficient is . and The partial pressure of the liquid phase at the droplet surface and in the fluid volume is the liquid phase partial pressure. The heat transfer coefficient, This is the molar enthalpy of vaporization. Heat flux density. Based on heat transfer coefficient Decide.

[0225] (36)

[0226] In the above formula, For heat flux density, Heat transfer coefficient, Gas temperature, Droplet temperature. This represents the gas-liquid temperature difference at the liquid surface. The specific surface area calculation based on this invention will facilitate calculations for droplet evaporation (or condensation) and heat transfer.

[0227] Two examples of cohesion are given below.

[0228] Example 1

[0229] Anand discussed a series of droplet deformation problems in two-phase flow systems with secondary breakup in reference

[17] , namely, droplets in high-speed airflow (density 1.2 kg / m³). 2 The deformation problem in the liquid is addressed. Based on its experimental parameters, the specific surface area distribution of liquid fragmentation is constructed using the method of this invention, and the cohesion force is determined. The case where the liquid medium is distilled water and ethanol is discussed here, and its operating parameters are shown in Table 1.

[0230] Table 1. Working parameters of the secondary crushing model (1)

[0231] liquid phase (mN / m) <![CDATA[ kg / m 2 )]]> (mm) (m / s) We water 72 1000 1.74 833 34 34 ethanol 22 788 1.61 657 19.5 33

[0232] Table 1) References

[17] .

[0233] Applying the aforementioned theoretical processing, the modeling parameters required for this invention can be obtained as shown in Table 2, and the spatial distributions of specific surface area and specific cohesion are as follows: Figure 5A and Figure 5B .

[0234] Table 2 Parameters for Modeling Specific Surface Area Distribution

[0235] liquid phase / ms <![CDATA[ / mm 1) ]]> / (m2 / kg) / mm / mm / (m2 / kg) water 1.48 1.13 0.17 31.5 19 56.8 61.4 ethanol 1.37 1.14 0.16 42.3 10.2 30.4 82.4

[0236] Table 1) uses the correlation formula from reference

[10] , with B valued at 0.82.

[0237] Example 2

[0238] Based on the experimental results and the processing method of the empirical model, in 2003, Moin measured the average diameter of the Sauter atomization of diesel injection in reference

[18] , and the initial diameter mm, using

[19] , 66mm, take =800kg / m 3 Surface tension =0.032N / m.

[0239] According to formula (15), we can obtain m 2 / kg. Combining equation (29), we obtain the model prediction results given by different authors. As shown in Table 3. According to Table 3, the predicted specific surface area increment and cohesion according to this invention are as follows: Figures 6A-6C As shown in the figure. The smaller, There are larger peaks, but The total area under the curve remains constant, meaning the surface free energy remains constant.

[0240] Table 3. Determined based on calculation results of secondary fragmentation models from different authors.

[0241] Model Apte'03 Reitz'87 Diwakar'87 O'Rouke'87 Tanner'98 8 3 10 4 18 ) 233 200 248 206 316

[0242] The following is a list of references for the specific implementation method:

[0243]

[10] Legrand J., Morancais P., Carnelle G., Trans IChemE, 2001,79,Part A, 949-956.

[0244]

[11] Damle N., Mudawar I., Hartwig J., Therm. Sci. Eng. Prog., 2026, 69, 104384.

[0245]

[12] Broumand M., Birouk M., Prog Energ. Combust., 2016, 57,1–29.

[0246]

[13] Wang W., Yang M., Hu Z., Zhang P., Aerosp. Sci. Technol., 2024, 151, 109271.

[0247]

[14] Duke-Walker V., Musick BJ, McFarland JA, Int. J. MultiphaseFlow,2023, 161,104389.

[0248]

[15] Pilch M., Erdman CA, Int. J. Multiphase Flow,1987, 13, 741-757.

[0249]

[16] WERT KL, Int. J. Multiphase Flow, 1995, 21, 1063-1071.

[0250]

[17] Joshi S., Anand TNC, Int. J. Multiphase Flow, 2022, 146,103850.

[0251]

[18] Apte SV, Gorokhovski M., Moin P., Int. J. Multiphase Flow,2003, 29. 1503–1522.

[0252]

[19] Hiroyasu M., Kadota T., SAE Paper, 1974,74071.

[0253] The above embodiments are merely preferred embodiments of the present invention, and the scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A method for defining and numerically modeling the recoiling acceleration of two-phase flow droplet breakup, characterized in that, Includes the following steps: S1. Establish a family of two-phase flow control models with specific surface area as an internal variable. Two-phase flow control equations are established, with a cohesive force term introduced into the momentum equation and a surface power term introduced into the kinetic energy equation. Specific surface area is used as the core variable, and the gas-liquid interface is not tracked. S2. Construct a specific surface area source term evolution model and initialize the flow field. An evolution model of specific surface area along the injection distance is constructed, and the model parameters are determined by nozzle parameters, liquid properties and breakup distance; S3. Calculate the cohesive force field from the specific surface area distribution, and couple and update the flow field velocity to obtain a converged specific surface area distribution. S4. Iteratively solve for the flow field, cohesion, and specific surface area until convergence, and obtain the converged specific surface area field. S5. Coupled simulation of the entire heat and mass transfer process: Based on the convergent specific surface area field, the evaporation rate and heat transfer rate are coupled and calculated to obtain a simulation model of the entire process of two-phase flow breakup-atomization-heat and mass transfer.

2. The method for defining and numerically modeling the recoiling acceleration of two-phase flow droplet breakup according to claim 1, characterized in that, The specific steps of step S1 are as follows: Continuity equation: in standard form, see formula (1): (1) In the above equation, the two phases on the left side are the mass time-varying rate and the convection term, respectively. For the density of the medium, Let t be the velocity vector, and t be time. Momentum Equation: Based on the traditional Navier-Stokes equation, a cohesive force term L is introduced to characterize the resistance generated by the increase in surface energy during droplet breakup, as shown below: (7) In the above formula, For pressure, For viscous stress tensor, For droplet density, The relative velocity between the gas and liquid phases, and the cohesive force L, are functions of the specific surface area gradient, defined by the following equation: (6) In the above formula, For surface tension, The droplet phase fraction, The density of the droplets; Kinetic energy equation: Under the framework of energy conservation, a surface power term is introduced to describe the rate at which fluid mechanical energy is converted into liquid surface free energy. Its equivalent form is shown in equation (11): (11) In the above formula: Volume fraction of phase i The density of the i-th phase. : The kinetic energy of the i-th phase : velocity of phase i, p: pressure, τ: viscous stress tensor, v: velocity vector, γ: surface tension : Droplet phase fraction, Droplet density, : Rate of change of specific surface area; Formulas (1), (7), and (11) above constitute the family of two-phase flow control models, which are used to compare surface area A. s Solve the problem.

3. The method for defining and numerically modeling the recoiling acceleration of two-phase flow droplet breakup according to claim 2, characterized in that, Step S2 includes the following steps: S2.1 Establish a specific surface area evolution model: Assume that the evolution of the specific surface area along the injection distance x follows a two-parameter exponential distribution, as shown in Equation (12): (12) in, This is the limiting specific surface area. A represents the characteristic fragmentation distance corresponding to the maximum increase in specific surface area. S (x) represents the increase in the liquid specific surface area from the nozzle exit to point x; S2.2 Determination of Model Parameters: Limiting specific surface area : The average diameter d of Sauter 32 The empirical or semi-empirical correlation calculations use correlations based on Kolmogorov's turbulence theory: (18) In the above formula, We is the Weber number, describing the relative magnitude of inertial force and surface tension, and the Sauter mean diameter is... It is the core parameter characterizing the average particle size of spray droplets, and the particle size is... Determine the nozzle diameter; The limiting specific surface area can then be calculated using formula (16): (16) In the above formula, For specific surface area increment, It is the core parameter characterizing the average particle size of spray droplets; Feature breakage distance Distance completed by breaking Confirmed, see the following formula: (28) in, Calculate using formula (27): (27) In the above formula, : Distance to complete the breakage, where We is the Weiber number. The relative velocity between gas and liquid. The time required for crushing to complete. For droplet density, For gas density, The diameter of the droplet; Initialization: Calculate the initial value A of the specific surface area of ​​the entire flow field using formula (12). s Substitute (x) into formula (6) to calculate the initial value L(x) of the cohesive force field.

4. The method for defining and numerically modeling the recoiling acceleration of two-phase flow droplet breakup according to claim 3, characterized in that, Step S3 is the iterative solution of the self-consistent field, which includes the following steps: S3.1, Given the specific surface area increment Initial guess, calculation of initial value of specific cohesion ; S3.2, will Substituting into the momentum equation and solving, we obtain the velocity field. ; S3.3 Substitute the velocity field into the kinetic energy equation to calculate the surface work and power. ; S3.4 Calculate the surface power difference : (31) In the above formula, For relative velocity, For surface tension, The droplet phase fraction, The density of the droplets; S3.5, according to The updated ratio of cohesion is ; S3.6, will Substitute the values ​​into the momentum equation to solve for the velocity field again, then substitute them into the kinetic energy equation to calculate the specific surface work and power. Repeat steps S3.4-S3.6 until... This yields a convergent specific surface area distribution.

5. The method for defining and numerically modeling the recoalescing acceleration of two-phase flow droplet breakup according to claim 4, characterized in that, Step S4 is the convergence test, specifically: Repeat the iterative process in step S3 until the surface power difference Δ approaches zero. At this point, the flow field, cohesion field, and specific surface area field reach self-consistent convergence, and the converged specific surface area field is output. .

6. The method for defining and numerically modeling the recoiling acceleration of two-phase flow droplet breakup according to claim 5, characterized in that, The simulation process of the entire coupled heat and mass transfer process in step S5 is as follows: In obtaining a convergent specific surface area field Then, calculations are performed on phase change and heat transfer; specific surface area. It directly provides the gas-liquid contact area; Evaporation rate calculation: The evaporation rate consists of two parts: surface evaporation and boiling evaporation, which are calculated using formulas (34) and (35) respectively: Surface evaporation ( ): (34) In the above formula, For surface evaporation rate, Liquid mass within the grid, Specific surface area Mass transfer coefficient, Liquid phase partial pressure at the droplet surface The partial pressure of the liquid phase in a fluid volume; Boiling evaporation ( ): (35) In the formula, For the mass of the liquid within the grid, The mass transfer coefficient is . and The partial pressure of the liquid phase at the droplet surface and in the fluid volume is the liquid phase partial pressure. The heat transfer coefficient, For molar enthalpy of vaporization, This refers to the boiling evaporation rate; Heat transfer rate calculation: heat flux density The result is calculated using Newton's law of cooling, as shown in equation (36): (36) In the above formula, For heat flux density, Heat transfer coefficient, Gas temperature, Droplet temperature; Phase field and temperature field updates: The calculated total evaporation rate Substituting into the phase fraction transport equation (32), update the liquid phase volume fraction. ; Substitute the calculated heat flux density into the energy equation to update the temperature field T; This enables transient simulation of the entire process from droplet breakup and atomization to evaporation.

Images