Droplet evaporation characteristic numerical simulation method under high-temperature turbulence condition
By conducting single-droplet evaporation experiments in a constant-volume combustion chamber, analyzing droplet evaporation characteristics, and establishing a one-dimensional droplet evaporation model, the problem of difficulty in numerically simulating single-droplet evaporation in existing technologies is solved. This enables the prediction of droplet evaporation characteristics under high-temperature turbulent conditions and improves spray combustion efficiency.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HEFEI UNIV OF TECH
- Filing Date
- 2026-01-19
- Publication Date
- 2026-05-01
AI Technical Summary
In existing technologies, research on the evaporation characteristics of single droplets mainly relies on experiments, making it difficult to conduct numerical simulation analysis under complex operating conditions, which limits the improvement of spray combustion efficiency.
A single-droplet evaporation experiment was conducted in a constant-volume combustion chamber. The wet-bulb temperature and average evaporation rate constant were analyzed, droplet physical parameters were calculated, a normalized evaporation rate expression was fitted, a one-dimensional droplet evaporation model was established, conservation equations and boundary conditions were constructed, expressions for the Sh number and Nu number were generated, the droplet surface evaporation rate and heat transfer were calculated, and the evolution of droplet surface temperature and diameter was iteratively calculated.
A droplet evaporation model under high-temperature turbulent conditions was established, which can predict the evaporation characteristics of droplets under different turbulence intensities and fuel types, providing a theoretical basis for spray combustion models and improving combustion efficiency.
Smart Images
Figure CN121960282A_ABST
Abstract
Description
A numerical simulation method for droplet evaporation characteristics under high-temperature turbulent conditions Technical Field
[0001] This invention belongs to the field of spray combustion technology, and particularly relates to a numerical simulation method for droplet evaporation characteristics under high-temperature turbulent conditions. Background Technology
[0002] While the current use of fossil fuels has greatly boosted economic development, it has also led to increasingly serious air pollution and environmental problems. These include hydrocarbons (HC) emitted from incomplete combustion in internal combustion engines and nitrogen oxides (NOx) produced by high-temperature combustion. x As is well known, these factors are closely related to the combustion efficiency of the spray. However, droplet evaporation plays a crucial role in internal combustion engines, spray combustion, and propulsion devices, and is a key link in the coupling process of gas-liquid mass transfer and heat transfer.
[0003] Understanding the evaporation behavior of a single droplet is crucial for comprehending spray combustion efficiency. Spray combustion involves the clustering behavior of a large number of droplets, influenced by initial droplet diameter, turbulence intensity within the combustion chamber, ambient pressure, ambient temperature, and interactions between droplets. Therefore, a thorough understanding of the evaporation behavior of a single droplet in a high-temperature turbulent environment is fundamental to accurately establishing spray combustion models and improving combustion efficiency.
[0004] In the existing technology, most studies on the evaporation characteristics of single droplets are conducted through experiments, and there are few examples of numerical simulation analysis to study the evaporation characteristics of single droplets. It is difficult to carry out experimental studies under some complex working conditions. Summary of the Invention
[0005] The purpose of this invention is to provide a numerical simulation method for droplet evaporation characteristics under high-temperature turbulent conditions, aiming to solve the problems mentioned in the background art.
[0006] To achieve the above objectives, the present invention provides the following technical solution: a numerical simulation method for droplet evaporation characteristics under high-temperature turbulent conditions, the method specifically including the following steps: conducting single-droplet evaporation experiments under different ambient temperatures, turbulence intensities, and fuel types in a constant-volume combustion chamber with zero average velocity and isotropic and homogeneous properties; analyzing the wet-bulb temperature and average evaporation rate constant of the droplet evaporation, calculating the droplet's physical property parameters, and fitting a normalized evaporation rate expression; establishing a one-dimensional droplet evaporation model, constructing conservation equations and boundary conditions, and generating expressions for the Sh number and Nu number; calculating the surface evaporation rate and heat transfer of the droplet based on the expressions for the Sh number and Nu number, and iteratively calculating the evolution of the droplet surface temperature and droplet diameter.
[0007] As a further limitation of the technical solution of the present invention, in the single droplet evaporation experiment conducted in a constant volume combustion chamber with zero average velocity and isotropic and homogeneous properties, under different ambient temperatures, turbulence intensities and fuel types: the turbulence fields generated by the two sets of fans are calibrated by a particle image velocimeter (PIV), and a linear relationship between fan speed and turbulence intensity is established, with turbulence intensities of 0-0.490 m / s and 0-0.869 m / s, respectively.
[0008] As a further limitation of the technical solution of this invention, in the analysis of the wet-bulb temperature and average evaporation rate constant of the droplet evaporation, the calculation of the droplet's physical properties, and the fitting of the normalized evaporation rate expression, the droplet evaporation is divided into three stages: an initial heating stage, a stable evaporation stage, and a rapid rise stage. Specifically, when the droplet's temperature growth rate decreases to 5% of the initial value, the droplet evaporation is determined to have entered the stable evaporation stage from the initial heating stage. When the droplet has almost completely evaporated, the thermocouple node is exposed to a high-temperature atmosphere, and the evaporation temperature rises sharply, thus entering the rapid rise stage. The average temperature in the stable evaporation stage is the wet-bulb temperature; the droplet's evaporation rate constant is (D / D0). 2 =The average value within the range of 0.9-0.2.
[0009] As a further limitation of the technical solution of the present invention, the physical property parameters include: binary diffusion coefficient, gas phase dynamic viscosity, gas phase density, liquid phase thermal conductivity, gas phase isobaric specific heat capacity, liquid phase isobaric specific heat capacity, gas phase thermal conductivity, saturated vapor pressure, latent heat of vaporization and liquid phase density.
[0010] As a further limitation of the technical solution of this embodiment of the invention, the formula for calculating the binary diffusion coefficient is as follows: ; where D AB M is the binary diffusion coefficient. AB It is the average molar mass, σ AB It is the characteristic length scale of the mixture, Ω D It is a dimensionless temperature function, T ref Here, P is the reference temperature and P is the ambient pressure; the formula for calculating the gas phase dynamic viscosity is: Where η is the gas phase dynamic viscosity, and M ref It is the reference molar mass, F c It is a correction factor, V c It is the critical volume of fuel, Ω v It is a dimensionless temperature function; the formula for calculating the gas phase density is: ; where ρ g V is the gas phase density. max It is the root with the largest real part among the three roots of the van der Waals equation; the formula for calculating the thermal conductivity of the liquid phase is: ; where λ lLet λ be the thermal conductivity of the liquid phase. b It is the thermal conductivity at the standard boiling point, a=0.16, m=1-(1-T) r ) / (1-T br The formula for calculating the isobaric specific heat capacity of the gas phase is as follows: Among them, C p,g This refers to the isobaric specific heat capacity of the gas phase, where a0, a1, a2, a3, and a4 are thermodynamic coefficients, and R is the universal gas constant. The formula for calculating the isobaric specific heat capacity of the liquid phase is as follows: Among them, C p,l It is the specific heat capacity of the liquid phase at constant pressure, ω is the eccentricity factor, and T r This is the comparison temperature; the formula for calculating the gas phase thermal conductivity is: ; where λ g C is the gas phase thermal conductivity, η is the gas phase dynamic viscosity, and C is the gas phase kinetic viscosity. p,g It is the specific heat capacity of the gas phase; the formula for calculating the saturated vapor pressure is: Among them, P sat It is the saturated vapor pressure, T r It is a comparison temperature, P c It is the critical pressure, A + =-35Q, B + =-36Q,C + =42Q+α c D + =-Q, Q=K(3.758-α) c K=0.0838, α c It is a critical parameter; the formula for calculating the latent heat of vaporization is: ; where ΔH eva It is the latent heat of vaporization, M is the molar mass of fuel, R is the universal gas constant, and T is the latent heat of vaporization. c This is the critical temperature of the fuel; the formula for calculating the liquid phase density is: ; ; where ρ l It is the liquid phase density, V sat It is the saturated volume of the liquid phase, P c T c and Z c These are the critical pressure, critical temperature, and critical compressibility factor of the fuel, respectively, and T is the surface temperature of the droplet.
[0011] As a further limitation of the technical solution of this embodiment of the invention, the expression for the fitted normalized evaporation rate is: ; ; ; Where K and K0 are the evaporation rates of the droplets under turbulent and static conditions, respectively, and q 0.5 aveIt is the turbulence intensity, L lon The longitudinal integral length scale is given by v, where v is the kinematic viscosity of the fuel vapor, x is the fan speed, Sc is the Schmitt number, and v and D are also mentioned. v These are the kinematic viscosity of fuel vapor and the binary diffusion coefficient between fuel and air, Re, respectively. turb It is the turbulent Reynolds number, R s It is the droplet radius.
[0012] As a further limitation of the technical solution of this embodiment of the invention, the conservation equation is: ; ;in, R is the rate of change of droplet mass, t is time, and R is the droplet mass change rate. dro Where r is the droplet radius, r is the radial distance, and T is the droplet radius. dro It is the surface temperature of the droplet, ρ liq It is the liquid phase density, c p,liq It is the specific heat capacity of the liquid phase at constant pressure, λ liq It is the thermal conductivity of the liquid phase.
[0013] As a further limitation of the technical solution of this embodiment of the invention, the boundary conditions include the boundary conditions of the energy conservation equation and the boundary conditions of the mass conservation equation, and the expression of the boundary conditions of the energy conservation equation is: ; ; ; ; among which, L eva It is the latent heat of vaporization. It is the heat transferred from the surface of the droplet to the interior of the droplet, A dro Represents the surface area of the droplet. It is the heat transferred from the surrounding environment to the surface of the droplet, h is the heat transfer coefficient, T dro It is the surface temperature of the droplet, T ∞ The ambient temperature is given; the expression for the boundary conditions of the mass conservation equation is: Among them, A dro It is the surface area of the droplet, h m It is the mass transfer coefficient, Y dro,s and Y ∞ It is the mass fraction of vapor at the surface of the droplet and at infinity.
[0014] As a further limitation of the technical solution of this embodiment of the invention, the expression for the Sh number is: ; where h m It is the mass transfer factor, D g Y is the binary diffusion coefficient of fuel vapor and air. s It is the mass fraction of vapor on the surface of the droplet, ρ l It is the liquid phase density of fuel, ρ totalIt is the density of the mixture of fuel vapor and air, K 0,exp K is the evaporation rate of a droplet under static conditions. exp It is the evaporation rate of droplets under turbulent conditions.
[0015] As a further limitation of the technical solution of this embodiment of the invention, the expression for the Nu number is: Where β is a function of wet-bulb temperature, L eva It is the latent heat of vaporization of fuel, λ g It is the vapor phase thermal conductivity of fuel, T s It is the surface temperature of the droplet.
[0016] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention involves conducting single-droplet evaporation experiments; calculating the droplet's physical properties and fitting a normalized evaporation rate expression; establishing a one-dimensional droplet evaporation model; constructing conservation equations and boundary conditions; generating expressions for the Sh number and Nu number; calculating the droplet's surface evaporation rate and heat transfer; and iteratively calculating the evolution of the droplet surface temperature and droplet diameter. It can establish a one-dimensional droplet evaporation model and establish the relationship between K / K0 and the Sh and Nu numbers. By iteratively calculating the mass evaporation rate and heat transfer of the droplet surface using the Sh and Nu numbers, it obtains data on the droplet diameter and evaporation temperature. Under different turbulence intensities, fuel types, and ambient temperatures, it can effectively predict the droplet's evaporation characteristics. This can be directly applied to CFD simulations to predict the droplet's evaporation characteristics under different operating conditions and provide a theoretical basis for establishing an effective spray combustion model. Attached Figure Description
[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention.
[0018] Figure 1 shows a schematic diagram of the relationship between fan speed and turbulence intensity in the method provided by an embodiment of the present invention.
[0019] Figure 2 shows a schematic diagram illustrating the evolution of droplet diameter and evaporation temperature in the experiment of the method provided in the embodiment of the present invention.
[0020] Figure 3 shows a schematic diagram of the normalized evaporation rate at an ambient temperature of 373.15-473.15 K in the method provided by the embodiment of the present invention.
[0021] Figure 4 shows a schematic diagram comparing the predicted data with the experimental results in the method provided by the embodiment of the present invention. Detailed Implementation
[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.
[0023] Understandably, understanding the evaporation behavior of a single droplet is crucial for comprehending spray combustion efficiency. Spray combustion involves the clustering behavior of a large number of droplets, influenced by initial droplet diameter, turbulence intensity within the combustion chamber, ambient pressure, ambient temperature, and interactions between droplets. Therefore, a deep understanding of the evaporation behavior of a single droplet in a high-temperature turbulent environment is fundamental to accurately establishing spray combustion models and improving combustion efficiency. Currently, most studies on the evaporation characteristics of single droplets are conducted experimentally, with limited examples of numerical simulation analysis. Furthermore, conducting experimental studies under complex operating conditions is often impractical.
[0024] To address the aforementioned issues, this invention conducts single-droplet evaporation experiments under varying ambient temperatures, turbulence intensities, and fuel types within a constant-volume combustion chamber with zero average velocity and isotropic and homogeneous properties. The wet-bulb temperature and average evaporation rate constant of the droplet evaporation are analyzed, droplet physical properties are calculated, and a normalized evaporation rate expression is fitted. A one-dimensional droplet evaporation model is established, conservation equations and boundary conditions are constructed, and expressions for the Sh number and Nu number are generated. Based on these expressions, the surface evaporation rate and heat transfer of the droplet are calculated, and the evolution of the droplet surface temperature and droplet diameter is iteratively calculated. This invention enables the establishment of a one-dimensional droplet evaporation model and the establishment of the relationship between K / K0 and the Sh and Nu numbers. By iteratively calculating the mass evaporation rate and heat transfer of the droplet surface using the Sh and Nu numbers, data on the droplet diameter and evaporation temperature are obtained. Under different turbulence intensities, fuel types, and ambient temperatures, the evaporation characteristics of droplets can be accurately predicted. This model can be directly applied to CFD simulations to predict the evaporation characteristics of droplets under different operating conditions and provides a theoretical basis for establishing effective spray combustion models.
[0025] In a preferred embodiment of the present invention, a numerical simulation method for droplet evaporation characteristics under high-temperature turbulent conditions is provided. The method specifically includes the following steps: Step 1: In a constant-volume combustion chamber with zero average velocity and isotropic and homogeneous properties, single droplet evaporation experiments are conducted under different ambient temperatures, turbulence intensities, and fuel types.
[0026] In this embodiment of the invention, the turbulent fields generated by two sets of fans are calibrated using a particle image velocimeter (PIV) to establish a linear relationship between fan speed and turbulence intensity. Figure 1 shows a schematic diagram of the relationship between fan speed and turbulence intensity in the method provided in this embodiment of the invention. The turbulence intensities are 0-0.490 m / s and 0-0.869 m / s, respectively. The calibration results show that the center of the turbulent field has zero average velocity and good uniformity and isotropy.
[0027] Step 2: Analyze the wet-bulb temperature and average evaporation rate constant of the droplet evaporation, calculate the droplet's physical properties, and fit a normalized evaporation rate expression.
[0028] In this embodiment of the invention, Figure 2 illustrates the evolution of droplet diameter and evaporation temperature during the experiment using the method provided in this embodiment. Droplet evaporation is divided into three stages: an initial heating stage, a stable evaporation stage, and a rapid rise stage. Specifically, when the droplet temperature growth rate decreases to 5% of the initial value, the droplet evaporation transitions from the initial heating stage to the stable evaporation stage. When the droplet has almost completely evaporated, the thermocouple node is exposed to a high-temperature atmosphere, and the evaporation temperature rises sharply, thus entering the rapid rise stage. The average temperature in the stable evaporation stage is the wet-bulb temperature; the droplet evaporation rate constant is (D / D0). 2 =The average value within the range of 0.9-0.2; then, the physical properties are calculated based on the wet-bulb temperature obtained experimentally. Since the droplet temperature gradually increases during evaporation, and the vapor mass fraction continuously decreases from the droplet surface to the surrounding environment, the gas phase physical properties are calculated using the 1 / 3 law. The subscripts ∞ and s represent the position at infinity and on the surface of the droplet, respectively. The physical properties include the binary diffusion coefficient, gas phase dynamic viscosity, gas phase density, liquid phase thermal conductivity, gas phase isobaric specific heat capacity, liquid phase isobaric specific heat capacity, gas phase thermal conductivity, saturated vapor pressure, latent heat of vaporization, and liquid phase density. Specifically, the formula for calculating the binary diffusion coefficient is: ; where D AB M is the binary diffusion coefficient. AB It is the average molar mass, σ AB It is the characteristic length scale of the mixture, Ω D It is a dimensionless temperature function, T ref Here, P is the reference temperature and P is the ambient pressure; the formula for calculating the dynamic viscosity of the gas phase is: Where η is the gas phase dynamic viscosity, and M ref It is the reference molar mass, F c It is a correction factor, V c It is the critical volume of fuel, Ω v It is a dimensionless temperature function; the formula for calculating the gas phase density is: ; where ρ g V is the gas phase density. maxIt is the root with the largest real part among the three roots of the van der Waals equation; the formula for calculating the thermal conductivity of the liquid phase is: ; where λ l Let λ be the thermal conductivity of the liquid phase. b It is the thermal conductivity at the standard boiling point, a=0.16, m=1-(1-T) r ) / (1-T br The formula for calculating the specific heat capacity of a gas phase at constant pressure is: Among them, C p,g This refers to the isobaric specific heat capacity of the gas phase, where a0, a1, a2, a3, and a4 are thermodynamic coefficients, and R is the universal gas constant. The formula for calculating the isobaric specific heat capacity of the liquid phase is: Among them, C p,l It is the specific heat capacity of the liquid phase at constant pressure, ω is the eccentricity factor, and T r This is the comparison temperature; the formula for calculating the thermal conductivity of the gas phase is: ; where λ g C is the gas phase thermal conductivity, η is the gas phase dynamic viscosity, and C is the gas phase kinetic viscosity. p,g This refers to the specific heat capacity of the gas phase; the formula for calculating saturated vapor pressure is: Among them, P sat It is the saturated vapor pressure, T r It is a comparison temperature, P c It is the critical pressure, A + =-35Q, B + =-36Q,C + =42Q+α c D + =-Q, Q=K(3.758-α) c K=0.0838, α c It is a critical parameter; the formula for calculating the latent heat of vaporization is: ; where ΔH eva It is the latent heat of vaporization, M is the molar mass of fuel, R is the universal gas constant, and T is the latent heat of vaporization. c This is the critical temperature of the fuel; the formula for calculating the liquid phase density is: ; ; where ρ l It is the liquid phase density, V sat It is the saturated volume of the liquid phase, P c T c and Z c These are the critical pressure, critical temperature, and critical compressibility factor of the fuel, respectively, and T is the droplet surface temperature. Figure 3 shows a schematic diagram of the normalized evaporation rate for an ambient temperature of 373.15-473.15 K in the method provided by this embodiment of the invention. The fitted normalized evaporation rate expression is: ; ; ; Where K and K0 are the evaporation rates of the droplets under turbulent and static conditions, respectively, and q 0.5 ave It is the turbulence intensity, L lon The longitudinal integral length scale is given by v, where v is the kinematic viscosity of the fuel vapor, x is the fan speed, Sc is the Schmitt number, and v and D are also mentioned. v These are the kinematic viscosity of fuel vapor and the binary diffusion coefficient between fuel and air, Re, respectively. turb It is the turbulent Reynolds number, R s It is the droplet radius.
[0029] Step 3: Establish a one-dimensional droplet evaporation model, construct conservation equations and boundary conditions, and generate expressions for the Sh number and Nu number.
[0030] In this embodiment of the invention, the conservation equation is: ; ;in, R is the rate of change of droplet mass, t is time, and R is the droplet mass change rate. dro Where r is the droplet radius, r is the radial distance, and T is the droplet radius. dro It is the surface temperature of the droplet, ρ liq It is the liquid phase density, c p,liq It is the specific heat capacity of the liquid phase at constant pressure, λ liq This refers to the thermal conductivity of the liquid phase; the boundary conditions include the boundary conditions for the energy conservation equation and the mass conservation equation; the expression for the boundary conditions of the energy conservation equation is: ; ; ; ; among which, L eva It is the latent heat of vaporization. It is the heat transferred from the surface of the droplet to the interior of the droplet, A dro Represents the surface area of the droplet. It is the heat transferred from the surrounding environment to the surface of the droplet, h is the heat transfer coefficient, T dro It is the surface temperature of the droplet, T ∞ The ambient temperature is given; the expression for the boundary conditions of the mass conservation equation is: Among them, A dro It is the surface area of the droplet, h m It is the mass transfer coefficient, Y dro,s and Y ∞ It is the mass fraction of vapor at the surface of the droplet and at infinity.
[0031] Step 4: Calculate the surface evaporation rate and heat transfer of the droplet based on the expressions for the Sh number and Nu number, and iteratively calculate the evolution of the droplet surface temperature and droplet diameter.
[0032] In this embodiment of the invention, by establishing the relationship between K / K0 and Sh, assuming that the liquid phase density remains constant, the expression for the Sh number is: ; where h m It is the mass transfer factor, D g Y is the binary diffusion coefficient of fuel vapor and air. s It is the mass fraction of vapor on the surface of the droplet, ρ l It is the liquid phase density of fuel, ρ total It is the density of the mixture of fuel vapor and air, K 0,exp K is the evaporation rate of a droplet under static conditions. exp This represents the evaporation rate of the droplet under turbulent conditions; when the droplet enters the steady evaporation phase, the expression for the Nu number is: Where β is a function of wet-bulb temperature, L eva It is the latent heat of vaporization of fuel, λ g It is the vapor phase thermal conductivity of fuel, T s It is the surface temperature of the droplet; Figure 4 shows a schematic diagram comparing the predicted data and experimental results in the method provided by the embodiment of the present invention, showing that the simulation method can predict the evaporation characteristics of the droplet very well.
[0033] It should be understood that although the steps in the flowcharts of the various embodiments of the present invention are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the various embodiments may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least a portion of the sub-steps or stages of other steps.
[0034] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.
[0035] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0036] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.
[0037] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A numerical simulation method for droplet evaporation characteristics under high-temperature turbulent conditions, characterized in that, The method specifically includes the following steps: conducting single-droplet evaporation experiments under different ambient temperatures, turbulence intensities, and fuel types in a constant-volume combustion chamber with zero average velocity and isotropic and homogeneous properties; analyzing the wet-bulb temperature and average evaporation rate constant of the droplet evaporation, calculating the droplet's physical properties, and fitting a normalized evaporation rate expression; establishing a one-dimensional droplet evaporation model, constructing conservation equations and boundary conditions, and generating expressions for the Sh number and Nu number; calculating the droplet's surface evaporation rate and heat transfer based on the expressions for the Sh number and Nu number, and iteratively calculating the evolution of the droplet surface temperature and droplet diameter.
2. The numerical simulation method for droplet evaporation characteristics under high-temperature turbulent conditions according to claim 1, characterized in that, In the single-droplet evaporation experiment conducted in a constant-volume combustion chamber with zero average velocity, isotropic and homogeneous properties, under different ambient temperatures, turbulence intensities and fuel types: the turbulence fields generated by two sets of fans were calibrated using a particle image velocimeter (PIV), and a linear relationship between fan speed and turbulence intensity was established, with turbulence intensities of 0-0.490 m / s and 0-0.869 m / s, respectively.
3. The numerical simulation method for droplet evaporation characteristics under high-temperature turbulent conditions according to claim 1, characterized in that, The analysis analyzes the wet-bulb temperature and average evaporation rate constant of the evaporating droplet, calculates the droplet's physical properties, and fits a normalized evaporation rate expression. The droplet evaporation is divided into three stages: an initial heating stage, a stable evaporation stage, and a rapid rise stage. When the droplet's temperature growth rate decreases to 5% of its initial value, the droplet evaporation transitions from the initial heating stage to the stable evaporation stage. When the droplet has almost completely evaporated, the thermocouple node is exposed to a high-temperature atmosphere, and the evaporation temperature rises sharply, indicating the entry into the rapid rise stage. The average temperature in the stable evaporation stage is the wet-bulb temperature. The droplet's evaporation rate constant is (D / D0). 2 =The average value within the range of 0.9-0.
2.
4. The numerical simulation method for droplet evaporation characteristics under high-temperature turbulent conditions according to claim 3, characterized in that, The physical properties include: binary diffusion coefficient, gas phase dynamic viscosity, gas phase density, liquid phase thermal conductivity, gas phase isobaric specific heat capacity, liquid phase isobaric specific heat capacity, gas phase thermal conductivity, saturated vapor pressure, latent heat of vaporization, and liquid phase density.
5. The numerical simulation method for droplet evaporation characteristics under high-temperature turbulent conditions according to claim 4, characterized in that, The formula for calculating the binary diffusion coefficient is as follows: ; where D AB M is the binary diffusion coefficient. AB It is the average molar mass, σ AB It is the characteristic length scale of the mixture, Ω D It is a dimensionless temperature function, T ref Here, P is the reference temperature and P is the ambient pressure; the formula for calculating the gas phase dynamic viscosity is: Where η is the gas phase dynamic viscosity, and M ref It is the reference molar mass, F c It is a correction factor, V c It is the critical volume of fuel, Ω v It is a dimensionless temperature function; the formula for calculating the gas phase density is: ; where ρ g V is the gas phase density. max It is the root with the largest real part among the three roots of the van der Waals equation; the formula for calculating the thermal conductivity of the liquid phase is: ; where λ l Let λ be the thermal conductivity of the liquid phase. b It is the thermal conductivity at the standard boiling point, a=0.16, m=1-(1-T) r ) / (1-T br The formula for calculating the isobaric specific heat capacity of the gas phase is as follows: Among them, C p,g This refers to the specific heat capacity of the gas phase, where a0, a1, a2, a3, and a4 are thermodynamic coefficients, and R is the universal gas constant. The formula for calculating the specific heat capacity of the liquid phase at constant pressure is as follows: Among them, C p,l It is the specific heat capacity of the liquid phase at constant pressure, ω is the eccentricity factor, and T r This is the comparison temperature; the formula for calculating the gas phase thermal conductivity is: ; where λ g η is the gas phase thermal conductivity, η is the gas phase dynamic viscosity, and C is the gas phase thermal conductivity. p,g It is the specific heat capacity of the gas phase; the formula for calculating the saturated vapor pressure is: Among them, P sat It is the saturated vapor pressure, T r It is a comparison temperature, P c It is the critical pressure, A + =-35Q, B + =-36Q,C + =42Q+α c D + =-Q, Q=K(3.758-α) c K=0.0838, α c It is a critical parameter; the formula for calculating the latent heat of vaporization is: ; where ΔH eva It is the latent heat of vaporization, M is the molar mass of fuel, R is the universal gas constant, and T is the latent heat of vaporization. c This is the critical temperature of the fuel; the formula for calculating the liquid phase density is: ； ; where ρ l It is the liquid phase density, V sat It is the saturated volume of the liquid phase, P c T c and Z c These are the critical pressure, critical temperature, and critical compressibility factor of the fuel, respectively, and T is the droplet surface temperature.
6. The numerical simulation method for droplet evaporation characteristics under high-temperature turbulent conditions according to claim 5, characterized in that, The fitted normalized evaporation rate expression is as follows: ； ； ； Where K and K0 are the evaporation rates of the droplets under turbulent and static conditions, respectively, and q 0.5 ave It is the turbulence intensity, L lon The longitudinal integral length scale is given by v, where v is the kinematic viscosity of the fuel vapor, x is the fan speed, Sc is the Schmitt number, and v and D are also mentioned. v These are the kinematic viscosity of fuel vapor and the binary diffusion coefficient between fuel and air, Re, respectively. turb It is the turbulent Reynolds number, R s It is the droplet radius.
7. The numerical simulation method for droplet evaporation characteristics under high-temperature turbulent conditions according to claim 6, characterized in that, The conservation equation is: ； ;in, t is time, R dro Where r is the droplet radius, r is the radial distance, and T is the droplet radius. dro It is the surface temperature of the droplet, ρ liq It is the liquid phase density, c p,liq It is the specific heat capacity of the liquid phase at constant pressure, λ liq It is the thermal conductivity of the liquid phase.
8. The numerical simulation method for droplet evaporation characteristics under high-temperature turbulent conditions according to claim 7, characterized in that, The boundary conditions include the boundary conditions of the energy conservation equation and the boundary conditions of the mass conservation equation. The expression for the boundary conditions of the energy conservation equation is as follows: ； ； ； ; among which, L eva It is the latent heat of vaporization. It is the heat transferred from the surface of the droplet to the interior of the droplet, A dro Represents the surface area of the droplet. The heat transferred from the surrounding environment to the droplet surface is denoted by h, where h is the heat transfer coefficient, Tdro is the droplet surface temperature, and T∞ is the ambient temperature. The boundary conditions of the mass conservation equation are expressed as follows: Among them, A dro It is the surface area of the droplet, h m It is the mass transfer coefficient, Y dro,s and Y ∞ It is the mass fraction of vapor at the surface of the droplet and at infinity.
9. The numerical simulation method for droplet evaporation characteristics under high-temperature turbulent conditions according to claim 8, characterized in that, The expression for the Sh number is: ; where h m It is the mass transfer factor, D g Y is the binary diffusion coefficient of fuel vapor and air. s It is the mass fraction of vapor on the surface of the droplet, ρ l It is the liquid phase density of fuel, ρ total It is the density of the mixture of fuel vapor and air, K 0,exp K is the evaporation rate of a droplet under static conditions. exp It is the evaporation rate of droplets under turbulent conditions.
10. The numerical simulation method for droplet evaporation characteristics under high-temperature turbulent conditions according to claim 9, characterized in that, The expression for the Nu number is: Where β is a function of wet-bulb temperature, L eva It is the latent heat of vaporization of fuel, λ g It is the vapor phase thermal conductivity of fuel, T s It is the surface temperature of the droplet.