A method and system for rapid prediction of evaporation of droplets under high-temperature turbulent flow conditions

Abstract

The application discloses a kind of liquid drop high-temperature turbulent flow conditions under the evaporation fast prediction method and system, prediction method: obtaining ambient temperature, ambient pressure, liquid drop temperature, liquid drop boiling point temperature, to calculate the saturation vapor pressure of liquid drop evaporation, reference temperature, equivalent molecular mass, gas dynamic viscosity;Based on reference temperature, calculate binary diffusion coefficient;The gas phase density and liquid phase density of liquid drop evaporation are calculated;The evaporation rate constant of liquid drop is calculated and the influence of Stefan flow is introduced;Custom non-dimensional parameter is calculated, to carry out linear fitting to evaporation rate constant and custom non-dimensional parameter and obtain numerical relationship formula.The application can be used in the evaporation rate prediction in the field of numerical simulation simulation liquid drop evaporation, by studying the evaporation behavior of n-dodecane single liquid drop under turbulent flow conditions, it has significant meaning for improving the combustion reaction in internal combustion engine.

Description

Technical Field

[0001] This invention belongs to the field of prediction methods, and in particular relates to a rapid prediction method and system for evaporation under high-temperature turbulent conditions of droplets. Background Technology

[0002] The primary chemical reaction inside an internal combustion engine is combustion. When liquid fuel enters the combustion chamber, it undergoes atomization into single droplets, evaporation, and then combustion to release heat. The atomization effect of the fuel droplets within the combustion chamber directly affects thermal efficiency and fuel economy. Due to the multiphase flow characteristics of the spray and the complexity of the internal environment of the combustion chamber, practical research on liquid fuel atomization is very difficult. The multiphase flow of the spray can be considered as a coupling of the multiphase flow characteristics of multiple single droplets. n-Dodecane has advantages such as chemical stability, moderate volatility, and good solubility, and is often used as a standard compound in experimental research. The main flow field inside the combustion chamber is a turbulent field. Different turbulence intensities and ambient temperatures have a significant impact on the evaporation characteristics of n-dodecane droplets. Therefore, studying the evaporation behavior of n-dodecane single droplets under turbulent conditions is of significant importance for improving the combustion reaction inside an internal combustion engine. Summary of the Invention

[0003] The purpose of this invention is to overcome the above-mentioned problems in the prior art and to provide a method and system for rapid prediction of evaporation under high-temperature turbulent conditions of droplets.

[0004] To achieve the above-mentioned technical objectives and effects, the present invention is implemented through the following technical solution:

[0005] A rapid prediction method for evaporation under high-temperature turbulent droplet conditions includes:

[0006] The ambient temperature, ambient pressure, droplet temperature, and droplet boiling point temperature are obtained to calculate the saturated vapor pressure, reference temperature, converted molecular mass, and gas dynamic viscosity during droplet evaporation.

[0007] Calculate the binary diffusion coefficient based on the reference temperature;

[0008] Calculate the gas phase density and liquid phase density during droplet evaporation;

[0009] Calculate the droplet evaporation rate constant and introduce the effect of Stefan flow;

[0010] Calculate a custom dimensionless parameter to obtain a numerical relationship by linearly fitting the evaporation rate constant and the custom dimensionless parameter.

[0011] Furthermore, the formula for calculating the liquid phase density is:

[0012]

[0013] Furthermore, the formula for calculating the evaporation rate constant under the influence of Stefan flow is as follows:

[0014]

[0015] Furthermore, the custom dimensionless parameters include the evaporation Damköhler number, calculated using the following formula:

[0016]

[0017] Furthermore, linear fitting includes calculations based on the dimensionless evaporation rate constant and the evaporation Damköhler number for evaporation rate prediction. The calculation formula is as follows:

[0018]

[0019] Furthermore, the formula for calculating saturated vapor pressure is:

[0020]

[0021] Furthermore, the formula for calculating the reference temperature is:

[0022] T ref =(T ∞ +2T s ) / 3;

[0023] The formula for calculating the equivalent molecular mass is: M = M A *X1+M B *(1-X1);

[0024] The formula for calculating the dynamic viscosity of a gas is:

[0025] Furthermore, the formula for calculating the binary diffusion coefficient is:

[0026]

[0027] M AB =2[(1 / M A )+(1 / M B )] -1

[0028] σ AB =(σ A +σ B ) / 2

[0029]

[0030] The present invention also provides a rapid evaporation prediction system under high-temperature turbulent droplet conditions, comprising:

[0031] The parameter initialization module is used to obtain ambient temperature, ambient pressure, droplet temperature, and droplet boiling point temperature in order to calculate the saturated vapor pressure, reference temperature, converted molecular mass, and gas dynamic viscosity during droplet evaporation.

[0032] The coefficient analysis module is used to calculate the binary diffusion coefficient based on a reference temperature.

[0033] The density analysis module is used to calculate the gas phase density and liquid phase density during droplet evaporation.

[0034] The constant analysis module is used to calculate the droplet evaporation rate constant and incorporate the effect of Stefan flow;

[0035] The fitting analysis module is used to calculate custom dimensionless parameters to perform linear fitting between the evaporation rate constant and the custom dimensionless parameters to obtain a numerical relationship.

[0036] The present invention also provides a computer storage medium having a computer program stored thereon, wherein the computer program, when executed, implements the above-described prediction method.

[0037] The beneficial effects of this invention are:

[0038] This invention can be used to predict the evaporation rate in the field of numerical simulation of droplet evaporation. The evaporation rate constant is calculated from the physical property parameters queried by the droplet temperature. The evaporation rate constant can be obtained directly by setting the temperature of the droplet and the environment. At the same time, it can accurately predict the influence of the droplet turbulence intensity on the evaporation rate. By studying the evaporation behavior of n-dodecane single droplets under turbulent conditions, it has significant implications for improving the combustion reaction inside the internal combustion engine. Attached Figure Description

[0039] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0040] Figure 1 This is a flowchart of the method of the present invention;

[0041] Figure 2 This is a partial schematic diagram of the method flow of the present invention;

[0042] Figure 3 This is a schematic diagram of the experimental data of the present invention;

[0043] Figure 4 This is a schematic diagram of the experimental data of the present invention;

[0044] Figure 5 This is a system structure block diagram of the present invention. Detailed Implementation

[0045] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0046] like Figure 1 The method shown is a rapid prediction method for evaporation under high-temperature turbulent conditions of droplets, comprising:

[0047] Step 1: Obtain ambient temperature, ambient pressure, droplet temperature, and droplet boiling point temperature to calculate the saturated vapor pressure, reference temperature, converted molecular mass, and gas dynamic viscosity during droplet evaporation.

[0048] Saturated vapor pressure P sat The calculation formula is

[0049]

[0050] A + =-35Q

[0051] B + =-36Q

[0052] C + =42Q+α c

[0053] D + =-Q

[0054] Q = K(3.758 - α) c )

[0055]

[0056] Acids, K = -0.120 + 0.025h; Alcohols, K = 0.373 - 0.030h;

[0057] T b T is the boiling point temperature at 1 atm. c This is the critical temperature. Where A... + =-35Q, B + =-36Q,C + =42Q+α c D + =-Q, Q=K(3.758-α) c ), where K for acids and alcohols can be calculated using the following formula, T r =T s / T cT b =T b / T c Here T s It is the temperature of the droplet surface, T b T is the boiling point temperature of the component at 1 atm. c and P c These are the critical temperature and critical pressure of the components.

[0058] Reference temperature T ref The calculation formula is:

[0059] T ref =(T ∞ +2T s ) / 3

[0060] T ∞ For ambient temperature, T s It is the surface temperature of the droplet.

[0061] The formula for calculating the equivalent molecular mass M is as follows:

[0062] M = M A *X1+M B *(1-X1)

[0063] M A M is the relative molecular mass of n-dodecane. B The relative molecular mass of air, X1 is the mass fraction of n-dodecane, and the formula for calculating X1 is:

[0064]

[0065] P0 is atmospheric pressure.

[0066] The formula for calculating the dynamic viscosity η of a gas is as follows:

[0067]

[0068] M is the molar mass, g / mol; T is the characteristic temperature, K; V C The critical volume, Ω v For the viscous collision integral, Ω v The calculation formula is as follows:

[0069] Ω v =[A(T * ) -B ]+C[exp(-DT * )]+E[exp(-FT * )]

[0070] T * =1.2593T r, T s T is the temperature of the droplet surface. c The critical temperatures are given by 1 bar; A = 1.16145, B = 0.14874, C = 0.52487, D = 0.77320, E = 2.16178, F = 2.43787.

[0071] Parameter F c The calculation formula is:

[0072]

[0073] ω is the eccentricity factor, and k is the molecular polarity.

[0074] μ r The calculation formula is:

[0075]

[0076] μ r P is a dimensionless dipole moment; μ is the dipole moment; P c The critical pressure is 1 atm, and the unit is bar; T c This is the critical temperature, expressed in Kelvin (K).

[0077] Step 2: Calculate the binary diffusion coefficient based on the reference temperature.

[0078] Binary diffusion coefficient D AB The calculation formula is

[0079]

[0080] M AB =2[(1 / M A )+(1 / M B )] -1

[0081] σ AB =(σ A +σ B ) / 2

[0082]

[0083] M AB The reduced molecular weights of the two components, σ AB The characteristic Lennard-Jones lengths of the two components, Ω is the collision integral function, A = 1.06036, B = 0.15610, C = 0.19300, D = 0.47635, E = 1.03587, F = 1.52996, G = 1.76474, H = 3.89411.

[0084] Step 3: Calculate the gas phase density and liquid phase density during droplet evaporation.

[0085] The formulas for calculating gas phase density and liquid phase density are:

[0086]

[0087] ρ is the gas phase density, and R is the universal gas constant.

[0088] For a single component, the liquid density ρ i :

[0089]

[0090] T c,i ,P c,i and Z c,i Let V be the critical temperature (K) of the i-th fuel, par, and the critical compressibility factor (dimensionless). sat,i Let be the volume of the i-th saturated liquid.

[0091] For mixed components ρ l ,

[0092]

[0093] Y i ρ represents the average liquid phase mass fraction, N represents the type of fuel, and ρ represents the average liquid phase mass fraction. i Let be the liquid phase density of the i-th type of fuel.

[0094] Step 4: Calculate the droplet evaporation rate constant and introduce the effect of Stefan flow.

[0095] The formula for calculating the evaporation rate constant K is derived from the following formula:

[0096]

[0097] When Stefan flow is ignored, the evaporation rate of the droplet surface is completely controlled by vapor diffusion. According to the law of conservation of mass, the rate of droplet mass reduction is equal to the droplet surface evaporation rate. Let D be the droplet mass, r be the radial distance, and D be the distance from the droplet. AB ρ is the binary diffusion coefficient of fuel steam. g,total ρ is the density of the gas mixture. v Let Y be the steam density and Yv be the mass fraction of fuel steam. Integrating the above formula while considering the steam mass fraction at infinity as 0, we obtain...

[0098]

[0099] The radial velocity u of the fuel vapor on the droplet surface s for:

[0100]

[0101] When the influence of Stefan flow exists

[0102]

[0103] The above formula consists of a diffusion term caused by the composition gradient and a convection term caused by the Stefan flow.

[0104]

[0105] U is the Stefan velocity, calculated using equation (29), where Da is the air diffusion coefficient and ρa is the air density. Combining the above formulas, we have...

[0106]

[0107] Assume D AB Similar to Da, and with a constant total density (ρg,total=ρv+ρa=constant), and obtained by integrating from the droplet surface to infinity, we get...

[0108]

[0109] The following formula considers the radial velocity of fuel vapor on the surface of the droplets after the Stefan flow:

[0110]

[0111] thereby,

[0112]

[0113] The above equation establishes the relationship between the evaporation rate constant and the mass reduction rate. The following formula is for calculating the evaporation rate constant without Stefan flow:

[0114]

[0115] Y v,s ,Y v,∞ Let represent the surface vapor mass fraction and the vapor mass fraction at infinity, respectively. The following formula is the calculation formula for the evaporation rate constant under the influence of Stefan flow:

[0116]

[0117] Step 5: Calculate the custom dimensionless parameter to obtain a numerical relationship by linearly fitting the evaporation rate constant and the custom dimensionless parameter.

[0118] Evaporation Damcoll number Da eva The calculation formula is:

[0119]

[0120] The dimensionless evaporation rate and the evaporation Da can be expressed by the following formula. eva By replacing the radial velocity under static conditions with the radial velocity under turbulent conditions, the evaporation rate constant K under turbulent conditions can be obtained. turb .

[0121]

[0122] K turb Let be the evaporation rate constant under turbulent droplet conditions. Here is the dimensionless evaporation rate constant:

[0123]

[0124] The radial velocity under turbulent conditions is the sum of the radial velocity and velocity increment under static conditions. If Δu is replaced by the turbulence intensity u', the newly defined evaporation Damcole number Da... eva

[0125]

[0126] u′ is the turbulence intensity, r s It is the droplet radius.

[0127] Then, we can obtain based on And evaporation Damköhler number Da eva empirical formula

[0128]

[0129] This formula can be used to predict the evaporation rate in numerical simulations of droplet evaporation. The evaporation rate constant K is calculated from the physical properties of the droplet temperature. The evaporation rate constant can be obtained directly by setting the temperatures of the droplet and the environment, while accurately predicting the influence of droplet turbulence intensity on the evaporation rate.

[0130] like Figure 5 As shown, a second aspect of the present invention also provides a rapid evaporation prediction system under high-temperature turbulent droplet conditions, specifically including the following steps:

[0131] The parameter initialization module is used to obtain ambient temperature, ambient pressure, droplet temperature, and droplet boiling point temperature in order to calculate the saturated vapor pressure, reference temperature, converted molecular mass, and gas dynamic viscosity during droplet evaporation.

[0132] The coefficient analysis module is used to calculate the binary diffusion coefficient based on a reference temperature.

[0133] The density analysis module is used to calculate the gas phase density and liquid phase density during droplet evaporation.

[0134] The constant analysis module is used to calculate the droplet evaporation rate constant and incorporate the effect of Stefan flow.

[0135] The fitting analysis module is used to calculate custom dimensionless parameters to perform linear fitting between the evaporation rate constant and the custom dimensionless parameters to obtain a numerical relationship.

[0136] A third aspect of the present invention also provides a computer storage medium having a computer program stored thereon, which, when executed, implements the above-described method. The storage medium may include various media capable of storing program code, such as a USB flash drive, a portable hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0137] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0138] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention.

Claims

1. A rapid prediction method for evaporation under high-temperature turbulent droplet conditions, characterized in that, include: The ambient temperature, ambient pressure, droplet temperature, and droplet boiling point temperature are obtained to calculate the saturated vapor pressure, reference temperature, converted molecular mass, and gas dynamic viscosity during droplet evaporation. Calculate the binary diffusion coefficient based on the reference temperature; Calculate the gas phase density and liquid phase density during droplet evaporation; Calculate the droplet evaporation rate constant and introduce the effect of Stefan flow; Calculate a custom dimensionless parameter to obtain a numerical relationship by linearly fitting the evaporation rate constant and the custom dimensionless parameter; The formula for calculating liquid phase density is: ρ i Let V be the liquid phase density of the i-th component. sat,i Let T be the volume of the i-th saturated liquid, R be the universal gas constant, and T be the volume of the saturated liquid. c,i Let P be the critical temperature of the i-th component. c,i Z is the critical pressure of the i-th component. c,i Let be the critical compressibility factor of the i-th component, and T be the characteristic temperature; The formula for calculating the evaporation rate constant under the influence of Stefan flow is: K is the evaporation rate constant, ρ is the gas phase density, and D is the vapor density. AB The diffusion coefficient is the binary diffusion coefficient. Custom dimensionless parameters include the evaporation Damköhler number, calculated using the following formula: Da eva U is the evaporation Damköhler number, u' is the turbulence intensity, and r is the turbulence intensity. s Where is the droplet radius; Linear fitting includes calculations based on the dimensionless evaporation rate constant and the evaporation Damcole number, used for evaporation rate prediction. The calculation formula is as follows: The formula for calculating saturated vapor pressure is: A + =-35Q B + =-36Q C + =42Q+a c D + =-Q Q=K'(3.758-α c ) Acids, K' = -0.120 + 0.025h; Alcohols, K' = 0.373 - 0.030h; P sat It is the saturated vapor pressure. T b T is the boiling point temperature at 1 atm. s It is the temperature of the droplet surface, T c and P c These are the critical temperature and critical pressure of the components; The formula for calculating the reference temperature is: T ref =(T ∞ +2T s ) / 3; The formula for calculating the equivalent molecular mass is: M = M A *X1+M B *(1-X1); The formula for calculating the dynamic viscosity of a gas is: T ref For reference temperature, T ∞ Where M is the ambient temperature, and M is the converted molecular mass. A M is the relative molecular mass of n-dodecane. B The relative molecular mass of air, X1 is the mass fraction of n-dodecane, η is the gas dynamic viscosity, and V c For the critical volume, Ω v For viscous collision integrals; Ω v The calculation formula is as follows: Ω v =[A'(T * ) -B' ]+C'[exp(-D'T * )]+E'[exp(-F'T * )] T * =1.2593T r , T s The values ​​are: A' = 1.16145, B' = 0.14874, C' = 0.52487, D' = 0.77320, E' = 2.16178, F' = 2.43787; Parameter F c The calculation formula is: ω represents the eccentricity factor, and k represents the molecular polarity. μ r The calculation formula is: μ r μ is a dimensionless dipole moment; μ is a dipole moment. The formula for calculating the binary diffusion coefficient is: M AB =2[(1 / M A )+(1 / M B )] -1 s AB =(s A +s B ) / 2 M AB σ represents the reduced molecular weight of the two components. AB Let Ω be the characteristic Lennard-Jones length of the two components, and Ω be the collision integral function. A = 1.06036, B = 0.15610, C = 0.19300, D = 0.47635, E = 1.03587, F = 1.52996, G = 1.76474, and H = 3.89411.

2. A rapid prediction system for evaporation under high-temperature turbulent droplet conditions, utilizing the prediction method described in claim 1, characterized in that, include: The parameter initialization module is used to obtain ambient temperature, ambient pressure, droplet temperature, and droplet boiling point temperature in order to calculate the saturated vapor pressure, reference temperature, converted molecular mass, and gas dynamic viscosity during droplet evaporation. The coefficient analysis module is used to calculate the binary diffusion coefficient based on a reference temperature. The density analysis module is used to calculate the gas phase density and liquid phase density during droplet evaporation. The constant analysis module is used to calculate the droplet evaporation rate constant and incorporate the effect of Stefan flow; The fitting analysis module is used to calculate custom dimensionless parameters to perform linear fitting between the evaporation rate constant and the custom dimensionless parameters to obtain a numerical relationship.

3. A computer storage medium storing a computer program thereon, characterized in that: When the computer program is executed, it implements the prediction method of claim 1.

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