Method for predicting average atomization particle size of gas-liquid coaxial nozzle

Abstract

The invention discloses a method for predicting the average atomization particle size of a gas-liquid coaxial nozzle by considering fluid physical properties. The method comprises the following steps: S1, acquiring experimental data; s2, calculating an unstable wave number interval; s3, discretizing an unstable wave number interval; s4, calculating a real nozzle coefficient C; and S5, predicting the average atomization particle size of the gas-liquid coaxial nozzle. According to the method, a theoretical prediction model of the average atomization particle size of the gas-liquid coaxial nozzle with physical significance can be more simply and accurately provided, and the atomization process can be more deeply understood and understood. According to the method, the average atomization particle size of the gas-liquid coaxial nozzle can be predicted according to the physical property parameters and the flowing parameters of the fluid, the appropriate working condition can be efficiently found to obtain the ideal atomization effect, the efficiency of nozzle design optimization work is improved, the design period of the nozzle can be effectively shortened, and the practical value is large.

Description

Technical Field

[0001] The invention relates to the field of atomizing jets, and in particular to a method for predicting average atomizing particle diameter of a gas-liquid coaxial nozzle. Background Art

[0002] Liquid jet breakup is widely present in people's daily life and engineering practice, including aviation propulsion technology, biopharmaceutical technology, atomization cooling technology, inkjet printing technology, fire extinguishing technology, etc. In the combustion chamber of an aircraft engine, liquid fuel first needs to be atomized into fine droplets, and then fully mixed with air to form a combustible mixed gas before a combustion reaction can occur. The atomization characteristics of the fuel nozzle are directly related to the combustion efficiency, combustion stability and the emission of nitrogen oxide pollutants. Since the gas-liquid interaction can significantly enhance the atomization performance of the fuel nozzle, this type of engine generally uses a gas-liquid coaxial nozzle.

[0003] The atomization effect of the gas-liquid coaxial nozzle is better, mainly because the speed difference between the gas and the liquid makes the liquid surface unstable, which accelerates the droplets to peel off from the liquid surface, thereby significantly improving the atomization performance of the nozzle. One of the most important criteria for measuring the atomization effect of the nozzle is the droplet size. The larger the droplet size, the longer it takes for the spray to burn completely, which may even affect the combustion efficiency and increase the fuel consumption of the engine. The size of the droplet is affected by multiple parameters. In order to obtain the ideal atomization effect and effectively control the droplet size, a method that can predict the atomization effect of the gas-liquid coaxial nozzle by the physical parameters and flow parameters of the fluid and is easy to use has always been a hot topic in the industry. Summary of the invention

[0004] In order to solve the problems existing in the prior art, the present invention provides a method for predicting the average atomized particle size of a gas-liquid coaxial nozzle by clearly establishing a prediction model.

[0005] To this end, the present invention adopts the following technical solutions:

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

[0007] S1, obtain experimental data:

[0008] The experimental data include 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 the gas velocity U g Experimental atomized particle size SMD under working conditions;

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

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

[0011]

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

[0013] S22, using the relationship between unstable wavenumber and complex frequency in S21, the result of unstable wavenumber k when ω = 0 is taken as the upper limit of unstable wavenumber k max ;

[0014] S23, calculate the lower limit of the unstable wave number k min =π / a;

[0015] S24, get the unstable wave number interval (k min , k max );

[0016] S3, unstable wavenumber interval discretization: Use the same discrete interval width Δk to discretize the unstable wavenumber interval (k min , k max ) is discretized to obtain the unstable wave number discrete interval data set [(k1, k2), (k2, k3)…(k p , k q )], where p and q are the numbers of the boundary values ​​of the discrete interval of unstable wave numbers;

[0017] The relationship between the unstable wave number and the complex frequency in step S21 is used to calculate the K of a point in each unstable wave number discrete interval in the unstable wave number discrete interval data set. j The corresponding discrete complex frequency ω (j) , take the discrete complex frequency ω (j) The real part of the discrete unstable growth rate j is the number of the discrete complex frequency, j∈[1,n], n is the total number of discrete intervals of the unstable wave number;

[0018] S4, calculating the actual nozzle coefficient C, includes the following steps:

[0019] S41, calculate the initial atomized particle size,

[0020] The experimental data obtained by S1, the unstable wave number interval obtained by S2, and the discrete unstable growth rate obtained by S3 are Substituting into the following formula and setting the initial nozzle coefficient C′=1, we can obtain the initial atomized particle size SMD′;

[0021]

[0022] S42, calculate the actual nozzle coefficient C of nozzle A,

[0023] C = SMD / SMD′;

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

[0025] The average atomized particle size of the droplets of the substance to be tested sprayed by the 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 data set to be tested and the corresponding point data set of the discrete unstable wave number interval to be tested are calculated through steps S2 and S3, and the predicted value D of the atomized particle size SMD is calculated by the following formula;

[0026]

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

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

[0029] Preferably, the discrete unstable growth rate data set to be tested in S5 changes with the change of the substance to be tested.

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

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

[0032] 1. Compared with the empirical formula or semi-empirical formula obtained through a large amount of experimental data in engineering, this method can more simply and accurately give a theoretical prediction model of the average atomized particle size of the gas-liquid coaxial nozzle with physical significance, which helps to have a deeper understanding and knowledge of the atomization process.

[0033] 2. The model in this method only contains a coefficient C related to the nozzle structure. The average atomization particle size of the gas-liquid coaxial nozzle can be predicted based on the physical parameters and flow parameters of the fluid, which is conducive to efficiently finding the appropriate 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 amount of experiments under the premise of the atomization particle size and working conditions required by the experiment, and can obtain a complete prediction model, thereby improving the efficiency of nozzle design optimization work and having great practical value. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0036] Figure 2 It is the comparison curve between the SMD prediction result and the experimental result under the first working condition;

[0037] Figure 3 It is the comparison curve between the SMD prediction result and the experimental result under the second working condition;

[0038] Figure 4 It is the comparison curve between the SMD prediction results and the experimental results under the third working condition. DETAILED DESCRIPTION

[0039] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

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

[0041] S1, obtain experimental data.

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

[0043] S2, calculate the unstable wavenumber interval.

[0044] Under any given jet condition, solving the dispersion equation can obtain the corresponding relationship between the unstable wave number and the unstable growth rate. Among them, the maximum value of the unstable growth rate is called the maximum disturbance growth rate, which characterizes the degree of jet instability. The larger the value, the more unstable the jet. The unstable wave number corresponding to the maximum disturbance growth rate is the dominant wave number. The larger the value, the shorter the wavelength of the most unstable surface wave and the smaller the fragmentation scale. At the same time, the average atomized particle size of the gas-liquid coaxial nozzle can be predicted through the corresponding relationship between the unstable wave number and the unstable growth rate and the calculation formula of SMD.

[0045] The calculation of unstable wave number interval specifically 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 is the dimensionless complex frequency; m = ka, is the dimensionless unstable wave number; I0(x) and I1(x) are the first-order modified Bessel functions of the 0th and 1st order, respectively; K0(x) and K1(x) are the second-order modified Bessel functions of the 0th and 1st order, respectively; ρ = ρ g / ρ l ; is the Weber number of the liquid; Oh=μ l / (ρ l aσ) 1 / 2 , is the Ohnesorg number;

[0049] S22, using the relationship between unstable wavenumber and unstable complex frequency in S21, the result of unstable wavenumber k when ω = 0 is taken as the upper limit of unstable wavenumber k max ;

[0050] S23, calculate the lower limit of the unstable wave number k min , there are: k min =π / a;

[0051] S24, the range of unstable wave number k is obtained from S22 and S23 (k min , k max );

[0052] S3, using the same discrete interval width Δk for the unstable wave number k value interval (k min , k max) is discretized, and the discrete complex frequency ω corresponding to the midpoint K of each unstable wave number discrete interval is obtained through the relationship between the unstable wave number and the unstable complex frequency in step S21, and the real number part of the discrete complex frequency ω is taken as the discrete unstable growth rate ω R ;

[0053] S4, calculating the actual nozzle coefficient C, includes the following steps:

[0054] S41, calculate the initial atomized particle size,

[0055] The experimental data obtained by S1, the extreme value of the unstable wave number obtained by S2, and the discrete unstable growth rate ω obtained by S3 are R Substituting into the following formula and setting the initial nozzle coefficient C′=1, we can obtain the initial atomized particle size SMD′;

[0056]

[0057] S42, calculate the actual nozzle coefficient C of nozzle A,

[0058] C = SMD / SMD′;

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

[0060] Predict the average atomized particle size of the droplets of the substance to be tested sprayed out by nozzle A to obtain the liquid density ρ of the substance to be tested l ′, gas density ρ g ', Liquid viscosity μ l and surface tension σ′, determine the liquid velocity U l ′ and gas velocity U g ′, use steps S2 and S3 to calculate the element ω in the discrete unstable growth rate data set R The element K in the midpoint data set of the unstable wave number discrete interval is obtained by the following formula: l ′ and gas velocity U g 'The predicted value D of the atomized particle size SMD under the working condition;

[0061]

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

[0063] By introducing the dispersion equation of gas-liquid coaxial jet atomization in S21, the influence of liquid surface tension and viscosity on the jet atomization process is taken into account, so that the nozzle coefficient C in the following theoretical model is independent of the physical parameters of the fluid and is only related to the structure of the nozzle.

[0064] The SMD theoretical model used in this method is as follows:

[0065]

[0066]

[0067] Where: l is the liquid density; ρ g is the gas density, U l is the liquid velocity, U g is the gas velocity, μ l is the liquid viscosity, σ is the surface tension, a is the jet diameter of the nozzle, and i is the imaginary unit; S = ω(ρ l a 3 / σ) 1 / 2 is the dimensionless complex frequency, ω is the complex frequency; m = ka is the dimensionless unstable wave number; I0(x) and I1(x) are the first-order modified Bessel functions of the 0th and 1st order, respectively; K0(x) and K1(x) are the second-order modified Bessel functions of the 0th and 1st order, respectively; ρ = ρ g / ρ l ; is the Weber number of the liquid; Oh=μ l / (ρ l aσ) 1 / 2 is the Ohnesorg 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 above theoretical model needs to be calculated through experimental data, but for the same nozzle, even if the liquid type and flow velocity change, the nozzle coefficient C remains a constant, making the theoretical model have great practical value. Before using the theoretical model to predict the average atomized particle size of the gas-liquid coaxial nozzle, the physical parameters of the fluid, the flow parameters, the nozzle diameter and the experimental atomized particle size SMD are used as the input values ​​of the model, and the theoretical model is solved by numerical methods to obtain the value of the nozzle coefficient C.

[0069] Substituting the nozzle coefficient C into the theoretical prediction model can obtain a complete prediction model for the average atomized particle size of the gas-liquid coaxial nozzle for the current nozzle. Then, substituting the physical properties, flow parameters, and nozzle diameter of the actual working conditions into the theoretical prediction model can predict the atomized particle size SMD under the current nozzle.

[0070] For a variety of nozzles, a theoretical model can be used to determine the different nozzle coefficients for each nozzle with a small amount of experiments; then the physical properties, flow parameters, and nozzle diameter of the actual working conditions are substituted into the theoretical prediction model to obtain the corresponding atomization particle size SMD of different nozzles, and then the nozzle corresponding to the ideal atomization effect can be found.

[0071] For different working conditions of the same nozzle, first determine the theoretical model of this nozzle; then substitute the physical parameters and flow parameters of different working conditions into the theoretical prediction model to obtain different atomization particle sizes SMD of this nozzle, and then find the working conditions corresponding to the ideal atomization effect.

[0072] The steps of selecting a nozzle or working condition that meets the requirements using this method are simpler; the workload is less than when the above theoretical model is not used, and the experimental time period is shorter.

[0073] Example

[0074] The effectiveness of the present invention is illustrated below with reference to 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. The liquid density, gas density, liquid viscosity, and surface tension are known. The experimental atomization particle size of this working condition is obtained under certain liquid velocity and gas velocity.

[0076] After calculating the extreme value of the unstable wave number k, the unstable wave number interval is discretized and the discrete unstable growth rate is obtained.

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

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

[0079]

[0080]

[0081] It can be seen from Table 1 that the coefficient C does not change much under different fluid types. We take the average value of the coefficient C as the coefficient of the theoretical model to obtain a complete theoretical prediction model:

[0082]

[0083]

[0084] pass Figure 2 , Figure 3 and Figure 4 The curve chart shows the comparison between the results of the prediction model and the actual experimental results:

[0085] Figure 2 The liquid type is water and the liquid speed is U l=5m / s, the comparison curve between the predicted results of SMD theoretical calculation and the experimental results at different air speeds;

[0086] Figure 3 The liquid type is water and the liquid speed is U l =16.6m / s, the comparison curve between the predicted results of SMD theoretical calculation and the experimental results at different air speeds;

[0087] Figure 4 When the liquid type is alcohol and the liquid speed is U l =5m / s, comparison curve of the predicted results of SMD theoretical calculation and experimental results at different air velocities.

[0088] pass Figure 2 , Figure 3 and Figure 4 It can be seen that the theoretical calculation results of the model are in good agreement with the experimental results, and can well 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: The following steps are involved: S1, obtain experimental data: The experimental data include 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 the gas velocity U g Experimental atomized particle size SMD under working conditions; S2, calculates the unstable wavenumber interval, including the following steps: S21, determine the relationship between the unstable wave number and the complex frequency, as shown below: Where i is the imaginary unit; S = ω(ρ l a 3 / σ) 1 / 2 is the dimensionless complex frequency, ω is the complex frequency; m = ka is the dimensionless unstable wave number; I0(x) and I1(x) are the first-order modified Bessel functions of the 0th and 1st order, respectively; K0(x) and K1(x) are the second-order modified Bessel functions of the 0th and 1st order, respectively; ρ = ρ g / ρ l ; is the Weber number of the liquid; Oh=μ l / (ρ l aρ) 1 / 2 is the Ohnesorg number; S22, using the relationship between unstable wavenumber and complex frequency in S21, the result of unstable wavenumber k when ω = 0 is taken as the upper limit of unstable wavenumber k max ; S23, calculate the lower limit of the unstable wave number k min =π / a; S24, get the unstable wave number interval (k min , k max ); S3, unstable wavenumber interval discretization: Use the same discrete interval width Δk to discretize the unstable wavenumber interval (k min , k max ) is discretized to obtain the unstable wave number discrete interval data set [(k1, k2), (k2, k3)…(k p , k q )], where p and q are the numbers of the boundary values ​​of the discrete interval of unstable wave numbers; The relationship between the unstable wave number and the complex frequency in step S21 is used to calculate the K of a point in each unstable wave number discrete interval in the unstable wave number discrete interval data set. j The corresponding discrete complex frequency ω (j) , take the discrete complex frequency ω (j) The real part of the discrete unstable growth rate j is the number of the discrete complex frequency, j∈[1,n], n is the total number of discrete intervals of the unstable wave number; S4, calculating the actual nozzle coefficient C, includes the following steps: S41, calculate the initial atomized particle size, The experimental data obtained by S1, the unstable wave number interval obtained by S2, and the discrete unstable growth rate obtained by S3 are Substituting into the following formula and setting the initial nozzle coefficient C′=1, we can obtain the initial atomized particle size SMD′; S42, calculate the actual nozzle coefficient C of nozzle A, C = SMD / SMD′; S5, predict the average atomized particle size of the gas-liquid coaxial nozzle: The average atomized particle size of the droplets of the substance to be tested sprayed by the 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 data set to be tested and the corresponding point data set of the discrete unstable wave number interval to be tested are calculated through steps S2 and S3, and 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: In the experimental data in S1, the liquid 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 unstable wavenumbers.

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 data set to be tested in S5 changes with the change of the substance to be tested.

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

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