Method and system for rapidly predicting evaporation of liquid drops under high-temperature turbulence condition

Abstract

The invention discloses a method and system for rapidly predicting evaporation of liquid drops under a high-temperature turbulence condition, and the method comprises the steps: obtaining environment temperature, environment pressure, liquid drop temperature and boiling point temperature of the liquid drops, and calculating saturated vapor pressure, reference temperature, reduced molecular mass and gas dynamic viscosity when the liquid drops are evaporated; calculating a binary diffusion coefficient based on the reference temperature; calculating the gas phase density and the liquid phase density when the liquid drops are evaporated; the evaporation rate constant of the liquid drops is calculated, and the influence of Stefan flow is introduced; and calculating a self-defined dimensionless parameter, and carrying out linear fitting on the evaporation rate constant and the self-defined dimensionless parameter to obtain a numerical relational expression. The method provided by the invention can be used for predicting the evaporation rate in the field of numerical simulation of droplet evaporation, and has remarkable significance for improving the combustion reaction in an internal combustion engine by researching the single-droplet evaporation behavior of the n-dodecane under the turbulent flow condition.

Description

Technical Field

[0001] The present invention belongs to the field of prediction methods, and in particular relates to a method and system for quickly predicting the evaporation of a droplet under high-temperature turbulent conditions. Background Art

[0002] The main chemical reaction inside the internal combustion engine is the combustion reaction. When the liquid fuel enters the combustion chamber, it will be atomized into single droplets, evaporate, and then burn to release heat. The atomization effect of the oil droplets in the combustion chamber directly affects the 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. It is very difficult to actually study the atomization of liquid fuels. The multiphase flow of the spray can be regarded as the coupling of the multiphase flow characteristics of multiple single droplets. n-Dodecane has the advantages of stable chemical properties, moderate volatility, and good solubility. It is often used as a standard compound for experimental research. The main flow field inside the combustion chamber is the turbulent field. Different turbulence intensities and ambient temperatures have a significant effect on the evaporation characteristics of n-dodecane droplets. Therefore, studying the evaporation behavior of single droplets of n-dodecane under turbulent conditions is of great significance for improving the combustion reaction inside the internal combustion engine. Summary of the invention

[0003] The purpose of the present invention is to overcome the above problems existing in the prior art and to provide a method and system for quickly predicting the evaporation of a droplet under high-temperature turbulent conditions.

[0004] In order to achieve the above technical objectives and the above technical effects, the present invention is implemented through the following technical solutions:

[0005] A method for quickly predicting evaporation of a droplet under high-temperature turbulent conditions, comprising:

[0006] Obtain the ambient temperature, ambient pressure, droplet temperature, and boiling point of the droplet to calculate the saturated vapor pressure, reference temperature, equivalent molecular mass, and gas dynamic viscosity when the droplet evaporates;

[0007] Based on the reference temperature, the binary diffusion coefficient is calculated;

[0008] Calculate the gas phase density and liquid phase density when the droplet evaporates;

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

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

[0011] Furthermore, the liquid density calculation formula is:

[0012]

[0013] Furthermore, the evaporation rate constant under the influence of Stefan flow is calculated as:

[0014]

[0015] Furthermore, the custom dimensionless parameters include the evaporation Damköhler number, which is calculated as:

[0016]

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

[0018]

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

[0020]

[0021] Furthermore, the reference temperature calculation formula is:

[0022] T ref =(T ∞ +2T s ) / 3;

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

[0024] The calculation formula of gas dynamic viscosity is:

[0025] Furthermore, the binary diffusion coefficient calculation formula 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 prediction system for evaporation of droplets under high-temperature turbulent conditions, comprising:

[0031] The parameter initialization module is used to obtain the ambient temperature, ambient pressure, droplet temperature, and boiling point temperature of the droplet to calculate the saturated vapor pressure, reference temperature, equivalent molecular mass, and gas dynamic viscosity when the droplet evaporates;

[0032] Coefficient analysis module, used to calculate binary diffusion coefficient based on reference temperature;

[0033] Density analysis module, used to calculate the gas phase density and liquid phase density when the droplet evaporates;

[0034] Constant analysis module, used to calculate the evaporation rate constant of droplets and introduce the influence of Stefan flow;

[0035] The fitting analysis module is used to calculate the custom dimensionless parameters so as to obtain a numerical relationship by linearly fitting the evaporation rate constant and the custom dimensionless parameters.

[0036] The present invention also provides a computer storage medium on which a computer program is stored, and the computer program implements the above prediction method when executed.

[0037] The beneficial effects of the present invention are:

[0038] The present invention can be used to predict the evaporation rate in the field of numerical simulation of droplet evaporation. The evaporation rate constant is calculated by the physical property parameters queried by the droplet temperature. The evaporation rate constant is directly obtained by setting the temperature of the droplet and the environment, and the influence of the turbulence intensity of the droplet on the evaporation rate is accurately predicted. By studying the evaporation behavior of a single droplet of n-dodecane under turbulent conditions, it has a significant significance for improving the combustion reaction inside an internal combustion engine. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of this application. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0040] Figure 1 is a flow chart of the method of the present invention;

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

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

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

[0044] Figure 5 It is a system structure block diagram of the present invention. DETAILED DESCRIPTION

[0045] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

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

[0047] Step 1: Obtain the ambient temperature, ambient pressure, droplet temperature, and boiling point of the droplet to calculate the saturated vapor pressure, reference temperature, equivalent molecular mass, and gas dynamic viscosity when the droplet evaporates.

[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 is the boiling point temperature at 1 atm, T c is the critical temperature. + =-35Q, B + =-36Q, C + =42Q+α c , D + = -Q, Q = K (3.758 - α c ), where K for acids and alcohols can be calculated by the following formula, T r =T s / T c, T b =T b / T c , here T s is the temperature of the droplet surface, T b is the boiling point temperature of the component at 1 atm, T c and P c are the critical temperature and critical pressure of the component.

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

[0059] T ref =(T ∞ +2T s ) / 3

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

[0061] The calculation formula of the equivalent molecular mass M is:

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

[0063] M A is the relative molecular mass of n-dodecane, M B The relative molecular mass of air, X 1 is the mass fraction of n-dodecane, X 1 The calculation formula is

[0064]

[0065] P 0 is the atmospheric pressure.

[0066] The calculation formula of gas dynamic viscosity η is:

[0067]

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

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

[0070] T * =1.2593T r , T s is the temperature of the droplet surface, T c is the critical temperature under 1 bar condition; 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, k is the molecular polarity.

[0074] μ r The calculation formula is:

[0075]

[0076] μ r is the dimensionless dipole moment; μ is the dipole moment; P c is the critical pressure of 1 atm, in bar; T c is the critical temperature, in K.

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

[0078] The 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 combined molecular weight of the two components, σ ABThe 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 when the droplet evaporates.

[0085] The calculation formulas for 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 are the critical temperature of the i-th fuel, K; critical pressure, par; critical compressibility factor, dimensionless; V sat,i is the volume of the i-th saturated liquid.

[0091] For the mixed component ρ l ,

[0092]

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

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

[0095] The calculation formula of the evaporation rate constant K is derived from the following formula:

[0096]

[0097] When Stefan flow is ignored, the evaporation rate on the droplet surface is completely controlled by vapor diffusion. According to the law of conservation of mass, the rate of decrease of the droplet mass is equal to the evaporation rate on the droplet surface. is the droplet mass, r is the radial distance, D AB is the binary diffusion coefficient of fuel vapor, ρ g,total is the density of the mixed gas, ρ vis the steam density, and Yv is the fuel steam mass fraction. When the steam mass fraction at infinity is considered to be 0 and the above formula is integrated, we can get

[0098]

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

[0100]

[0101] When the influence of Stefan flow exists,

[0102]

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

[0104]

[0105] U is the Stefan flow velocity, which is calculated by formula (29), where Da is the air diffusion coefficient and ρa is the air density. Combining the above formula, we have

[0106]

[0107] Assumption D AB is the same as Da, and the total density is a constant (ρg,total = ρv + ρa = constant), and is integrated from the droplet surface to infinity to obtain

[0108]

[0109] Then the following equation is the radial velocity of the fuel vapor on the droplet surface after Stefan flow:

[0110]

[0111] thereby,

[0112]

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

[0114]

[0115] Y v,s ,Y v,∞ are the surface steam mass fraction and the steam mass fraction at infinity, respectively. The following 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 Damköhler number Da eva The calculation formula is:

[0119]

[0120] The dimensionless evaporation rate can be related to the evaporation Damköhler number Da by the following formula eva In conjunction, 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 is the evaporation rate constant under droplet turbulence conditions, is the dimensionless evaporation rate constant:

[0123]

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

[0125]

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

[0127] Then, we can get the and evaporation Damköhler number Da eva The empirical formula

[0128]

[0129] This formula can be used to predict the evaporation rate in the field of numerical simulation of droplet evaporation. The evaporation rate constant K is calculated by the physical parameters queried by the droplet temperature. The evaporation rate constant can be directly obtained by setting the temperature of the droplet and the environment, and the effect of the turbulence intensity of the droplet on the evaporation rate can be accurately predicted.

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

[0131] The parameter initialization module is used to obtain the ambient temperature, ambient pressure, droplet temperature, and boiling point temperature of the droplet to calculate the saturated vapor pressure, reference temperature, equivalent molecular mass, and gas dynamic viscosity when the droplet evaporates.

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

[0133] Density analysis module, used to calculate the gas phase density and liquid phase density when the droplet evaporates.

[0134] Constant analysis module, used to calculate the evaporation rate constant of droplets and introduce the effect of Stefan flow.

[0135] The fitting analysis module is used to calculate the custom dimensionless parameters so as to obtain a numerical relationship by linearly fitting the evaporation rate constant and the custom dimensionless parameters.

[0136] The third aspect of the present invention also provides a computer storage medium on which a computer program is stored, and the computer program implements the above method when executed. The storage medium may include: a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, and other media that can store program codes.

[0137] In the description of this specification, the description with reference to the terms "one embodiment", "example", "specific example", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0138] The above shows and describes 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, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements all fall within the scope of the present invention to be protected.

Claims

1. A method for rapid prediction of evaporation of droplets under high-temperature turbulent conditions, characterized in that: include: Obtain the ambient temperature, ambient pressure, droplet temperature, and boiling point of the droplet to calculate the saturated vapor pressure, reference temperature, equivalent molecular mass, and gas dynamic viscosity when the droplet evaporates; Based on the reference temperature, the binary diffusion coefficient is calculated; Calculate the gas phase density and liquid phase density when the droplet evaporates; Calculate the evaporation rate constant of the droplet and introduce the effect of Stefan flow; Calculate the custom dimensionless parameter to obtain a numerical relationship by linearly fitting the evaporation rate constant and the custom dimensionless parameter.

2. The method for rapid prediction of evaporation of a droplet under high-temperature turbulent conditions according to claim 1, characterized in that: The formula for calculating liquid density is:

3. The method for rapid prediction of evaporation of a droplet under high-temperature turbulent conditions according to claim 1, characterized in that: The calculation formula of the evaporation rate constant under the influence of Stefan flow is:

4. The method for rapid prediction of evaporation of a droplet under high-temperature turbulent conditions according to claim 1, characterized in that: Custom dimensionless parameters include the evaporation Damköhler number, which is calculated as:

5. The method for rapid prediction of evaporation of a droplet under high-temperature turbulent conditions according to claim 4, characterized in that: Linear fitting includes: calculation based on dimensionless evaporation rate constant and evaporation Damköhler number for evaporation rate prediction, the calculation formula is:

6. The method for rapid prediction of evaporation of a droplet under high-temperature turbulent conditions according to claim 1, characterized in that: The calculation formula for saturated vapor pressure is:

7. The method for rapid prediction of evaporation of a droplet under high-temperature turbulent conditions according to claim 1, characterized in that: The reference temperature calculation formula 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 calculation formula of gas dynamic viscosity is:

8. A method for rapid prediction of evaporation of a droplet under high-temperature turbulent conditions according to claim 7, characterized in that the binary The diffusion coefficient is calculated as: M AB =2[(1 / M A )+(1 / M B )] -1 s AB =(s A +s B ) / 2 9. A rapid prediction system for evaporation of droplets under high-temperature turbulent conditions, characterized in that: include: The parameter initialization module is used to obtain the ambient temperature, ambient pressure, droplet temperature, and boiling point temperature of the droplet to calculate the saturated vapor pressure, reference temperature, equivalent molecular mass, and gas dynamic viscosity when the droplet evaporates; Coefficient analysis module, used to calculate binary diffusion coefficient based on reference temperature; Density analysis module, used to calculate the gas phase density and liquid phase density when the droplet evaporates; Constant analysis module, used to calculate the evaporation rate constant of droplets and introduce the influence of Stefan flow; The fitting analysis module is used to calculate the custom dimensionless parameters so as to obtain a numerical relationship by linearly fitting the evaporation rate constant and the custom dimensionless parameters.

10. A computer storage medium having a computer program stored thereon, characterized in that: When the computer program is executed, the prediction method according to any one of claims 1 to 8 is implemented.

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