Method for predicting the average atomized particle size of gas-liquid coaxial nozzles

Abstract

This invention discloses a method for predicting the average atomized particle size of a gas-liquid coaxial nozzle considering fluid properties, comprising the following steps: S1, acquiring experimental data; S2, calculating the unstable wavenumber interval; S3, discretizing the unstable wavenumber interval; S4, calculating the true nozzle coefficient C; and S5, predicting the average atomized particle size of the gas-liquid coaxial nozzle. This method can more simply and accurately provide a theoretical prediction model for the average atomized particle size of a gas-liquid coaxial nozzle with physical meaning, contributing to a deeper understanding and awareness of the atomization process. This method can predict the average atomized particle size of the gas-liquid coaxial nozzle based on the fluid's physical properties and flow parameters, facilitating the efficient identification of suitable operating conditions to achieve ideal atomization effects, improving the efficiency of nozzle design optimization, effectively shortening the nozzle design cycle, and possessing significant practical value.

Description

Technical Field

[0001] This invention relates to the field of atomized jets, and in particular to a method for predicting the average atomized particle size of a gas-liquid coaxial nozzle. Background Technology

[0002] Liquid jet breakup is a widespread phenomenon in daily life and engineering practice, including aerospace propulsion, biopharmaceuticals, atomization cooling, inkjet printing, and fire suppression. In the combustion chamber of an aero-engine, liquid fuel must first be atomized into fine droplets before being thoroughly mixed with air to form a combustible mixture for combustion. The atomization characteristics of the fuel nozzle directly affect combustion efficiency, combustion stability, and nitrogen oxide emissions. Because gas-liquid interaction significantly enhances the atomization performance of fuel nozzles, these engines commonly employ coaxial gas-liquid nozzles.

[0003] The superior atomization effect of gas-liquid coaxial nozzles is primarily due to the instability of the liquid surface caused by the velocity difference between gas and liquid, which accelerates the shedding of droplets from the liquid surface, thus significantly improving the nozzle's atomization performance. One of the most important metrics for evaluating nozzle atomization is droplet size. Larger droplet sizes require longer combustion times, potentially impacting combustion efficiency and increasing engine fuel consumption. Droplet size is influenced by multiple parameters. Therefore, developing a convenient method to predict the atomization effect of gas-liquid coaxial nozzles using fluid properties and flow parameters has been a focus of industrial research in order to achieve ideal atomization and effectively control droplet size. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a method for predicting the average atomized particle size of a gas-liquid coaxial nozzle by establishing a clear and explicit prediction model.

[0005] Therefore, the present invention adopts the following technical solution:

[0006] A method for predicting the average atomized particle size of a gas-liquid coaxial nozzle includes the following steps:

[0007] S1, Obtain experimental data:

[0008] The experimental data includes liquid density ρ l Gas density ρ g Liquid viscosity μ l Surface tension σ, jet diameter a of nozzle A, and liquid velocity U l and gas velocity U g Experimental atomized particle size (SMD) under operating conditions;

[0009] S2, Calculate the unstable wavenumber interval, including the following steps:

[0010] S21, determine the relationship between the unstable wave number and the complex frequency, as shown in the following equation:

[0011]

[0012] Where i is the imaginary unit; S = ω(ρ l a 3 / σ) 1 / 2 Let ω be the dimensionless complex frequency; m = ka be the dimensionless unstable wavenumber; I0(x) and I1(x) are the 0th and 1st order modified Bessel functions of the first kind, respectively; K0(x) and K1(x) are the 0th and 1st order modified Bessel functions of the second kind, respectively; ρ = ρ g / ρ l ; For liquid Weber number; Oh = μ l / (ρ l aσ) 1 / 2 It is an Onezoglu number;

[0013] S22, using the relationship between the unstable wavenumber and complex frequency from S21, takes the result of the unstable wavenumber k when ω=0 as the upper limit value of the unstable wavenumber k. max ;

[0014] S23, Calculate the lower limit of the instability wavenumber k min =π / a;

[0015] S24, obtaining the unstable wavenumber interval (k) min k max );

[0016] S3, Discretization of Unstable Wavenumber Intervals: Using the same discrete interval width Δk, the unstable wavenumber intervals (k) described in S24 are discretized. min k max Discretize the data to obtain the discrete interval dataset of unstable wavenumbers [(k1, k2), (k2, k3)...(k... p k q )], where p and q are the boundary values ​​of the discrete interval of the unstable wavenumber;

[0017] By using the relationship between the unstable wavenumber and the complex frequency in step S21, a point K within each unstable wavenumber discrete interval in the dataset of unstable wavenumber discrete intervals is obtained. j The corresponding discrete complex frequency ω (j) Take the discrete complex frequency ω (j) The real part of the value is used as a discrete, unstable growth rate. j is the number of the discrete complex frequency, j∈[1,n], and n is the total number of discrete intervals of the unstable wavenumber;

[0018] S4, Calculate the actual nozzle coefficient C, including the following steps:

[0019] S41, Calculate the initial atomized particle size.

[0020] The experimental data obtained in S1, the unstable wavenumber interval obtained in S2, and the discrete unstable growth rate obtained in S3 are used to... Substitute into the following formula and set the initial nozzle coefficient C′=1 to obtain the initial atomized particle size SMD′;

[0021]

[0022] S42, Calculate the true nozzle coefficient C of nozzle A.

[0023] C = SMD / SMD′;

[0024] S5, Predicted average atomized particle size of gas-liquid coaxial nozzle:

[0025] The average atomized particle size of the droplets of the substance to be tested ejected by nozzle A is predicted, the liquid density, gas density, liquid viscosity and surface tension of the substance to be tested are obtained, the liquid velocity and gas velocity of the substance to be tested are determined, and the discrete unstable growth rate dataset and the corresponding point dataset of the discrete interval of the unstable wavenumber to be tested are calculated through steps S2 and S3. The predicted value D of the atomized particle size SMD is calculated by the following formula.

[0026]

[0027] Preferably, the liquid in the experimental data in S1 is water or alcohol, and the gas is air.

[0028] Preferably, the K in S3 j is the midpoint of the discrete interval of the unstable wavenumber.

[0029] Preferably, the discrete unstable growth rate dataset to be measured in S5 varies with the substance to be measured.

[0030] Preferably, the dataset of points corresponding to the discrete interval of the unstable wavenumber to be measured in S5 changes with the substance to be measured.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] 1. Compared with empirical or semi-empirical formulas obtained through a large amount of experimental data in engineering, this method can provide a more simple and accurate theoretical prediction model for the average atomized particle size of a gas-liquid coaxial nozzle with physical meaning, which helps to gain a deeper understanding and knowledge of the atomization process.

[0033] 2. The model in this method contains only one coefficient C related to the nozzle structure. It can predict the average atomized particle size of the gas-liquid coaxial nozzle based on the fluid's physical properties and flow parameters, which is beneficial for efficiently finding suitable working conditions to obtain the ideal atomization effect.

[0034] 3. The theoretical model in this method can determine the nozzle coefficient C through a small number of experiments under the premise of atomization particle size and working conditions with experimental requirements. It can obtain a complete prediction model, improve the efficiency of nozzle design optimization, and has great practical value. Attached Figure Description

[0035] Figure 1 This is a schematic diagram of a gas-liquid coaxial nozzle atomizing jet;

[0036] Figure 2 This is a comparison curve of the SMD prediction results and experimental results under the first working condition;

[0037] Figure 3 This is a comparison curve of SMD prediction results and experimental results under the second working condition;

[0038] Figure 4 This is a comparison curve of the SMD prediction results and experimental results under the third operating condition. Detailed Implementation

[0039] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0040] like Figure 1 As shown, the method for predicting the average atomized particle size of a gas-liquid coaxial nozzle considering fluid properties according to the present invention includes the following steps:

[0041] S1, Obtain experimental data.

[0042] First, select the gas-liquid coaxial nozzle A, the experimental gas, and the experimental liquid. Then, the liquid density ρ can be determined. l Liquid viscosity μ l Gas density ρ g 1. Surface tension σ and jet diameter a of nozzle A, then determine the liquid velocity U. l and gas velocity U g Finally, the atomized particle size SMD is measured using a PDPA or laser particle size analyzer.

[0043] S2, calculate the unstable wavenumber interval.

[0044] Under any given jet operating condition, solving the dispersion equation yields the relationship between the unstable wavenumber and the unstable growth rate. The maximum value of the unstable growth rate is called the maximum disturbance growth rate, characterizing the degree of jet instability; the larger the value, the more unstable the jet. The unstable wavenumber corresponding to the maximum disturbance growth rate is the dominant wavenumber; the larger the value, the shorter the wavelength of the most unstable surface wave and the smaller the fragmentation scale. Furthermore, the relationship between the unstable wavenumber and the unstable growth rate, along with the SMD calculation formula, allows for the prediction of the average atomized particle size of a gas-liquid coaxial nozzle.

[0045] The calculation of the unstable wavenumber interval includes the following steps:

[0046] S21, the relationship between the unstable wave number k and the unstable complex frequency ω is determined by the following dispersion equation:

[0047]

[0048] Where i is the imaginary unit; S = ω(ρ l a 3 / σ) 1 / 2 ρ is the dimensionless complex frequency; m = ka is the dimensionless unstable wavenumber; I0(x) and I1(x) are the 0th and 1st order modified Bessel functions of the first kind, respectively; K0(x) and K1(x) are the 0th and 1st order modified Bessel functions of the second kind, respectively; ρ = ρ g / ρ l ; For liquid Weber number; Oh = μ l / (ρ l aσ) 1 / 2 , is an Onezoglu number;

[0049] S22, using the relationship between the unstable wavenumber and the unstable complex frequency from S21, takes the result of the unstable wavenumber k when ω=0 as the upper limit value of the unstable wavenumber k. max ;

[0050] S23, Calculate the lower limit of the instability wavenumber k min There is: k min =π / a;

[0051] S24, from S22 and S23, we obtain the range of values ​​for the unstable wavenumber k (k min k max );

[0052] S3, using the same discrete interval width Δk for the range of values ​​of the unstable wavenumber k (k min k maxThe wavenumber is discretized, and the discrete complex frequency ω corresponding to point K in each discrete interval of the unstable wavenumber is obtained through the relationship between the unstable wavenumber and the unstable complex frequency in step S21. The real part of the discrete complex frequency ω is taken as the discrete unstable growth rate ω. R ;

[0053] S4, Calculate the actual nozzle coefficient C, including the following steps:

[0054] S41, Calculate the initial atomized particle size.

[0055] The experimental data obtained in S1, the extreme values ​​of the unstable wavenumber obtained in S2, and the discrete unstable growth rate ω obtained in S3 are used to... R Substitute into the following formula and set the initial nozzle coefficient C′=1 to obtain the initial atomized particle size SMD′;

[0056]

[0057] S42, Calculate the true nozzle coefficient C of nozzle A.

[0058] C = SMD / SMD′;

[0059] S5, Predicted average atomized particle size of gas-liquid coaxial nozzle:

[0060] The average atomized particle size of the test substance droplets ejected using nozzle A is predicted to obtain the liquid density ρ of the test substance. l ′、Gas density ρ g ′、Liquid viscosity μ l And surface tension σ′, determine the liquid velocity U l ′ and gas velocity U g Using steps S2 and S3, calculate the elements ω in the discrete unstable growth rate dataset. R The element K in the dataset at the midpoint of the discrete interval of the unstable wavenumber is obtained by the following formula at the liquid velocity U. l ′ and gas velocity U g The predicted value D of the atomized particle size SMD under the operating condition;

[0061]

[0062] The implementation principle of this invention is as follows:

[0063] By introducing the dispersion equation for gas-liquid coaxial jet atomization in S21, the influence of liquid surface tension and viscosity on the jet atomization process is considered, making the nozzle coefficient C in the following theoretical model independent of the fluid's physical properties and only related to the nozzle structure.

[0064] The SMD theoretical model used in this method is shown below:

[0065]

[0066]

[0067] Where: ρ l ρ is the density of the liquid. g For gas density, U l For liquid velocity, U g For gas velocity, μ l Let ρ be the liquid viscosity, σ be the surface tension, a be the nozzle jet diameter, and i be the imaginary unit; S = ω(ρ l a 3 / σ) 1 / 2 Let ω be the dimensionless complex frequency; m = ka be the dimensionless unstable wavenumber; I0(x) and I1(x) are the 0th and 1st order modified Bessel functions of the first kind, respectively; K0(x) and K1(x) are the 0th and 1st order modified Bessel functions of the second kind, respectively; ρ = ρ g / ρ l ; For liquid Weber number; Oh = μ l / (ρ l aσ) 1 / 2 It is an Onezoglu number; C is the nozzle coefficient; the real part of ω is the unstable growth rate ω. R .

[0068] The nozzle coefficient C in the theoretical model described above needs to be calculated using experimental data. However, for the same nozzle, even if the liquid type and flow velocity change, the nozzle coefficient C remains constant, giving the theoretical model significant practical value. Before using the theoretical model to predict the average atomized particle size of a gas-liquid coaxial nozzle, the fluid's physical properties, flow parameters, nozzle diameter, and experimental atomized particle size (SMD) are used as input values ​​to the model. By solving the theoretical model using numerical methods, the value of the nozzle coefficient C can be obtained.

[0069] Substituting the nozzle coefficient C into the theoretical prediction model yields a complete prediction model for the average atomized particle size (SMD) of the gas-liquid coaxial nozzle for the current nozzle. Then, substituting the physical property parameters, flow parameters, and nozzle diameter of the actual operating conditions into the theoretical prediction model allows for the prediction of the SMD of the atomized particle size under the current nozzle.

[0070] For a variety of nozzles, a small number of experiments are sufficient to determine the different nozzle coefficients for each nozzle using a theoretical model. Then, by substituting the physical properties, flow parameters, and nozzle diameter of the actual working conditions into the theoretical prediction model, the corresponding atomized particle size (SMD) of different nozzles can be obtained. Finally, the nozzle corresponding to the ideal atomization effect can be found.

[0071] For different operating conditions of the same nozzle, first determine the theoretical model of the nozzle; then substitute the physical property parameters and flow parameters of different operating conditions into the theoretical prediction model to obtain the different atomized particle size (SMD) of the nozzle, and then find the operating condition corresponding to the ideal atomization effect.

[0072] Using this method, the steps for selecting a suitable nozzle or operating condition are simpler; the workload is less and the experimental time is shorter compared to not using the above theoretical model.

[0073] Example

[0074] The effectiveness of the present invention will be illustrated below with examples.

[0075] The nozzle used in the experiment is a gas-liquid coaxial nozzle with a jet diameter of 0.32 mm. The liquid used in the atomization experiment is water or alcohol, and the gas is air. Given the liquid density, gas density, liquid viscosity, and surface tension, the experimental atomized particle size is obtained under certain liquid and gas velocities.

[0076] After calculating the extreme values ​​of the unstable wavenumber k, the unstable wavenumber interval is discretized and the discrete unstable growth rate is obtained.

[0077] The initial nozzle coefficient is set to 1. The value of coefficient C is obtained by comparing the calculated initial atomized particle size with the experimental atomized particle size. Different theoretical model coefficients C are obtained by changing the experimental conditions, as shown in Table 1.

[0078] Table 1. Experimental conditions and calculation results of coefficient C for the gas-liquid coaxial nozzle.

[0079]

[0080]

[0081] As can be seen from Table 1, the coefficient C does not change significantly under different fluid types. We can obtain the complete theoretical prediction model by taking the average value of coefficient C as the coefficient of the theoretical model.

[0082]

[0083]

[0084] pass Figure 2 , Figure 3 and Figure 4 The graph shows the comparison between the predicted model results and the actual experimental results:

[0085] Figure 2 When the liquid type is water and the liquid velocity is U lComparison curves of SMD theoretical calculation prediction results and experimental results for different air velocities at a working condition of 5 m / s;

[0086] Figure 3 When the liquid type is water and the liquid velocity is U l Comparison curves of SMD theoretical calculation prediction results and experimental results for different air velocities at a working condition of 16.6 m / s;

[0087] Figure 4 When the liquid type is alcohol and the liquid velocity is U l Comparison curves of SMD theoretical calculation predictions and experimental results for different air velocities at a speed of 5 m / s.

[0088] pass Figure 2 , Figure 3 and Figure 4 It can be seen that the theoretical calculation results and experimental results of the model are in good agreement, and it can accurately predict the average atomized particle size of the gas-liquid coaxial nozzle.

Claims

1. A method for predicting the average atomized particle size of a gas-liquid coaxial nozzle, characterized in that, Includes the following steps: S1, Obtain experimental data: The experimental data includes liquid density ρ l Gas density ρ g Liquid viscosity μ l Surface tension σ, jet diameter a of nozzle A, and liquid velocity U l and gas velocity U g Experimental atomized particle size (SMD) under operating conditions; S2, Calculate the unstable wavenumber interval, including the following steps: S21, determine the relationship between the unstable wave number and the complex frequency, as shown in the following equation: Where i is the imaginary unit; S = ω(ρ l a 3 / σ) 1 / 2 Let ω be the dimensionless complex frequency; m = ka be the dimensionless unstable wavenumber; I0(x) and I1(x) are the 0th and 1st order modified Bessel functions of the first kind, respectively; K0(x) and K1(x) are the 0th and 1st order modified Bessel functions of the second kind, respectively; ρ = ρ g / ρ l ; For liquid Weber number; Oh = μ l / (ρ l aρ) 1 / 2 It is an Onezoglu number; S22, using the relationship between the unstable wavenumber and complex frequency from S21, takes the result of the unstable wavenumber k when ω=0 as the upper limit value of the unstable wavenumber k. max ; S23, Calculate the lower limit of the instability wavenumber k min =π / a; S24, obtaining the unstable wavenumber interval (k) min k max ); S3, Discretization of Unstable Wavenumber Intervals: Using the same discrete interval width Δk, the unstable wavenumber intervals (k) described in S24 are discretized. min , k max Discretize the data to obtain the discrete interval dataset of unstable wavenumbers [(k1, k2), (k2, k3)...(k... p , k q )], where p and q are the boundary values ​​of the discrete interval of the unstable wavenumber; By using the relationship between the unstable wavenumber and the complex frequency in step S21, a point K within each unstable wavenumber discrete interval in the dataset of unstable wavenumber discrete intervals is obtained. j The corresponding discrete complex frequency ω (j) Take the discrete complex frequency ω (j) The real part of the value is used as a discrete, unstable growth rate. j is the number of the discrete complex frequency, j∈[1,n], and n is the total number of discrete intervals of the unstable wavenumber; S4, Calculate the actual nozzle coefficient C, including the following steps: S41, Calculate the initial atomized particle size. The experimental data obtained in S1, the unstable wavenumber interval obtained in S2, and the discrete unstable growth rate obtained in S3 are used to... Substitute into the following formula and set the initial nozzle coefficient C′=1 to obtain the initial atomized particle size SMD′; S42, Calculate the true nozzle coefficient C of nozzle A. C = SMD / SMD′; S5, Predicted average atomized particle size of gas-liquid coaxial nozzle: The average atomized particle size of the droplets of the substance to be tested ejected by nozzle A is predicted, the liquid density, gas density, liquid viscosity and surface tension of the substance to be tested are obtained, the liquid velocity and gas velocity of the substance to be tested are determined, and the discrete unstable growth rate dataset and the corresponding point dataset of the discrete interval of the unstable wavenumber to be tested are calculated through steps S2 and S3. The predicted value D of the atomized particle size SMD is calculated by the following formula.

2. The method for predicting the average atomized particle size of a gas-liquid coaxial nozzle according to claim 1, characterized in that: The liquid mentioned in the experimental data in S1 is water or alcohol, and the gas is air.

3. The method for predicting the average atomized particle size of a gas-liquid coaxial nozzle according to claim 1, characterized in that: The K in S3 j is the midpoint of the discrete interval of the unstable wavenumber.

4. The method for predicting the average atomized particle size of a gas-liquid coaxial nozzle according to claim 1, characterized in that: The discrete, unstable growth rate dataset to be measured in S5 varies with the substance to be measured.

5. The method for predicting the average atomized particle size of a gas-liquid coaxial nozzle according to claim 1, characterized in that: The dataset of points corresponding to the discrete interval of the unstable wavenumber to be measured in S5 changes with the substance to be measured.

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