A method for characterizing uncertainty in chemical reaction rates in flow simulations

Abstract

The present invention relates to the technical field of CFD uncertainty quantification, and discloses a method for characterizing the uncertainty of chemical reaction rate in flow simulation, which characterizes the uncertainty of chemical reaction rate based on experimental data and reaction rate results of a chemical kinetic model. The present invention solves the problem that it is difficult to accurately characterize the uncertainty of chemical reaction rate in the prior art. The present invention can more scientifically and reasonably utilize the existing experimental data and classical chemical kinetic model result information, and greatly reduces the uncertainty caused by the characterization model in the process of characterizing the uncertainty of chemical reaction rate.

Description

Technical Field

[0001] The invention relates to the technical field of CFD uncertainty quantification, and in particular to a method for characterizing the uncertainty of chemical reaction rate in flow simulation. Background Art

[0002] With the continuous progress of numerical methods, high-performance computers and other disciplines, computational fluid dynamics (CFD) has been increasingly widely used in heavy equipment engineering fields such as aerospace, energy and power, and transportation. However, due to the randomness of fluid mechanics problems themselves or the limitations of current cognitive levels, there are uncertainties in CFD that cannot be ignored, which brings potential major risks to engineering predictions and decisions.

[0003] In high-speed flow, due to strong compression and viscous dissipation, the gas temperature rises sharply, and the air molecules undergo a series of complex chemical reactions such as dissociation and ionization, which changes the thermodynamic properties and flow field characteristics of the gas (called the real gas effect), seriously affecting the aerodynamic and aerodynamic thermal characteristics of high-speed aircraft. In order to predict the flow field under the influence of the real gas effect, it is necessary to introduce chemical kinetic models, such as the classic Dunn-Kang model and Park model; and the key to the chemical reaction kinetic model is to determine the rate constant of each chemical reaction. In the classical chemical kinetic model, it is usually fitted based on multiple experimental results or directly selects the measured data of a single experimenter. However, there are large differences in the chemical reaction rates obtained from different experimental measurements (up to more than one order of magnitude), so there is a large uncertainty in the chemical reaction rates obtained by different chemical kinetic models. Therefore, how to scientifically and reasonably quantify the uncertainty of the chemical reaction rate is crucial for the credibility assessment of high-speed flow simulation.

[0004] Uncertainty characterization of chemical reaction rates is a prerequisite for uncertainty quantification of chemical reaction rates. In existing studies, it is usually assumed based on subjective judgment that chemical reaction rates obey a log-normal distribution with the benchmark value of the classical chemical kinetic model as the mean. However, such an assumption does not make reasonable use of real experimental data information, nor does it consider the differences in benchmark values ​​of different classical chemical kinetic models. The reference value of the uncertainty quantification results obtained is limited. Therefore, how to comprehensively consider real experimental data and the results of different classical chemical kinetic models to reasonably mathematically characterize the uncertainty of chemical reaction rates is still an urgent problem to be solved. Summary of the invention

[0005] In order to overcome the deficiencies of the prior art, the present invention provides a method for characterizing the uncertainty of chemical reaction rate in flow simulation, which solves the problem that it is difficult to accurately characterize the uncertainty of chemical reaction rate in the prior art.

[0006] The technical solution adopted by the present invention to solve the above problems is:

[0007] A method for characterizing the uncertainty of chemical reaction rates in flow simulation is provided, which characterizes the uncertainty of chemical reaction rates based on experimental data and reaction rate results of a chemical kinetic model.

[0008] As a preferred technical solution, the following steps are included:

[0009] S1, select the reaction rate result of a certain chemical kinetic model as the reference value, calculate the ratio of the test data to the reference value at different temperatures, or calculate the ratio of the reaction rate results of different chemical kinetic models at different temperatures to the reference value, record the ratio as the chemical reaction rate proportional factor, and use the uncertainty of the chemical reaction rate proportional factor to represent the uncertainty of the chemical reaction rate;

[0010] S2, estimated kernel density function;

[0011] S3, based on the estimated kernel density function, calculate the cumulative distribution function of the chemical reaction rate proportional factor to complete the uncertainty characterization of the chemical reaction rate.

[0012] As a preferred technical solution, in step S2, a kernel density estimation method is adopted to select a kernel function and a bandwidth, and estimate a kernel density function.

[0013] As a preferred technical solution, in step S2, the kernel function is one of the following: Gaussian kernel function, triangle kernel function, Epanechnikov kernel function.

[0014] As a preferred technical solution, in step S2, the bandwidth is selected according to the kernel density estimation function in MATLAB, or the bandwidth is set by itself.

[0015] As a preferred technical solution, in step S2, the kernel density function obtained is:

[0016] ;

[0017] in, represents the kernel density function, i represents the number of random samples, n represents the number of random samples, represents the i-th random sample, h represents the bandwidth, z represents any real value, Represents the kernel function.

[0018] As a preferred technical solution, z is a value within the domain of the random sample.

[0019] As a preferred technical solution, in step S3, the cumulative distribution function is:

[0020] ;

[0021] in, represents the cumulative distribution function, t represents Any value within represents the integral of the kernel function.

[0022] As a preferred technical solution, .

[0023] As a preferred technical solution, the chemical kinetic model is one or more of the following: Dunn-Kang model, Park model, Gupta model.

[0024] Compared with the prior art, the present invention has the following beneficial effects:

[0025] (1) Compared with the subjective method of characterizing the uncertainty of chemical reaction rate by lognormal distribution, the present invention can more scientifically and reasonably utilize the existing experimental data and classical chemical kinetic model result information;

[0026] (2) Compared with the subjective assumption that the chemical reaction rate is a log-normal distribution, the present invention provides a 95% confidence interval for the chemical reaction rate that can cover all experimental and classical chemical kinetic model results, greatly reducing the uncertainty caused by the characterization model in the process of characterizing the uncertainty of the chemical reaction rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 It is a comparison chart of the 95% confidence interval of the chemical reaction rate obtained by the present invention and the 95% confidence interval of NASA's subjective assumption that the chemical reaction rate is a log-normal distribution. DETAILED DESCRIPTION

[0028] The present invention will be further described in detail below in conjunction with embodiments and drawings, but the embodiments of the present invention are not limited thereto.

[0029] Example 1

[0030] like Figure 1As shown, the present invention aims at the problem of uncertainty characterization of chemical reaction rate in CFD high-speed flow simulation, and develops a method for characterizing the uncertainty of chemical reaction rate based on kernel density estimation. The basic idea of ​​this method is: comprehensively consider the experimental data (experimental data for measuring chemical reaction rate) and the reaction rate results of the classical chemical kinetic model, select a certain model result as the reference value, calculate the ratio of different chemical kinetic model results or experimental results to the reference value at different temperatures, record it as the chemical reaction rate proportional factor, and use the uncertainty of the proportional factor to represent the uncertainty of the chemical reaction rate; use the kernel density estimation method, select the kernel function and bandwidth, and estimate the kernel density function; based on the estimated kernel density function, calculate the cumulative distribution function of the chemical reaction rate proportional factor, thereby completing the uncertainty characterization of the chemical reaction rate and providing support for the subsequent uncertainty quantification.

[0031] In order to achieve the above object, the present invention is mainly implemented through the following technical solutions:

[0032] Step S1: comprehensively considering the experimental data and the reaction rate results of the classical chemical kinetic model, selecting a model result as a reference value, calculating the ratio of different chemical kinetic model results or experimental results to the reference value at different temperatures, and recording it as a chemical reaction rate proportional factor, and using the uncertainty of the proportional factor to represent the uncertainty of the chemical reaction rate;

[0033] In step S1, the classic chemical kinetic models include Dunn-Kang model, Park model, Gupta model, etc.

[0034] Step S2: adopting the kernel density estimation method, selecting the kernel function and bandwidth, and estimating the kernel density function;

[0035] In step S2, commonly used kernel functions include Gaussian kernel, triangle kernel, Epanechnikov kernel, etc.;

[0036] In step S2, you can select the default bandwidth according to the kernel density estimation function in MATLAB (Matrix&Laboratory), or you can set the bandwidth yourself;

[0037] In step S2, the kernel density function is obtained as:

[0038] ;

[0039] in is a random sample, n is the number of samples, is the kernel function, h is the bandwidth, is the kernel density function obtained by fitting, i is the sample number, z is any real value (generally within the domain of the random sample).

[0040] Step S3: Calculate the cumulative distribution function of the chemical reaction rate proportional factor based on the estimated kernel density function to complete the uncertainty characterization of the chemical reaction rate;

[0041] In step S3, the kernel of the cumulative distribution function is estimated as:

[0042] ;

[0043] in, ,and is a random sample, n is the number of samples, is the kernel function, h is the bandwidth, is the kernel density function obtained by fitting, i is the sample number, z is any real value (usually within the domain of the random sample), t is Any value within is the calculated cumulative distribution function of the chemical reaction rate scale factor.

[0044] Example 2

[0045] like Figure 1 As shown, as a further optimization of Example 1, based on Example 1, this embodiment also includes the following technical features:

[0046] The specific steps are as follows:

[0047] Step S1: Experimental data vector based on a chemical reaction at different temperatures and the result data vectors of two classical chemical kinetic models (Dunn-Kang model and Park model) ; Select Dunn-Kang model results As the benchmark value, the ratios of the experimental data at different temperatures, the results of the two classical chemical kinetic models and the benchmark value are calculated and recorded as , then Combined into a vector X, vector X is the sample vector of chemical reaction rate proportional factor;

[0048] Step S2: Use the kernel density estimation method, use the Ksdensity function in Matlab, the default Gaussian kernel function, the default optimal bandwidth, and estimate the kernel density function of vector X ,in Take any real number in [0.4,2], the following The value range of is the same as this;

[0049] Step S3: Based on the kernel density function estimated in step S2 , calculate the cumulative distribution function of the chemical reaction rate scaling factor , get the 95% confidence interval upper and lower bounds of the chemical reaction rate proportional factor, and then use the benchmark value , get the 95% confidence interval upper and lower bounds of the chemical reaction rate at different temperatures;

[0050] Step S4: Select As the benchmark value, the chemical reaction rate was assumed to be a log-normal distribution using the NASA method, and the upper and lower bounds of the 95% confidence interval of the chemical reaction rate at different temperatures were obtained.

[0051] Figure 1 The horizontal axis represents temperature T (in K), and the vertical axis represents the chemical reaction rate (in L / (mol·s)). Figure 1 It can be seen that the 95% confidence interval of the chemical reaction rate obtained by the kernel density method of the present invention covers all the experimental data and the results of the classical chemical kinetic model, while the 95% confidence interval of the chemical reaction rate obtained by the lognormal distribution method provided by NASA only covers part of the experimental data and the results of the classical chemical kinetic model.

[0052] Compared with the subjective method of characterizing the uncertainty of chemical reaction rate with lognormal distribution, the present invention can more scientifically and reasonably utilize the existing experimental data and classical chemical kinetic model result information, greatly reducing the uncertainty caused by the characterization model in the process of characterizing the uncertainty of chemical reaction rate.

[0053] As described above, the present invention can be preferably implemented.

[0054] All features disclosed in all embodiments in this specification, or steps in all methods or processes implicitly disclosed, except for mutually exclusive features and / or steps, can be combined and / or expanded or replaced in any manner.

[0055] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. According to the technical essence of the present invention, within the spirit and principles of the present invention, any simple modification, equivalent replacement and improvement made to the above embodiment still falls within the protection scope of the technical solution of the present invention.

Claims

1. A method for characterizing the uncertainty of chemical reaction rates in flow simulation, characterized in that: Characterizing the uncertainty of chemical reaction rates based on experimental data and reaction rate results from chemical kinetic models includes the following steps: S1, select the reaction rate result of a certain chemical kinetic model as the reference value, calculate the ratio of the test data to the reference value at different temperatures, or calculate the ratio of the reaction rate results of different chemical kinetic models at different temperatures to the reference value, record the ratio as the chemical reaction rate proportional factor, and use the uncertainty of the chemical reaction rate proportional factor to represent the uncertainty of the chemical reaction rate; S2, estimated kernel density function; In step S2, the kernel density function obtained is: ； in, represents the kernel density function, i represents the number of random samples, n represents the number of random samples, represents the i-th random sample, h represents the bandwidth, z represents any real value, represents the kernel function; S3, based on the estimated kernel density function, calculate the cumulative distribution function of the chemical reaction rate proportional factor to complete the uncertainty characterization of the chemical reaction rate; In step S3, the cumulative distribution function is: ； in, represents the cumulative distribution function, t represents Any value within represents the integral of the kernel function.

2. The method for characterizing uncertainty of chemical reaction rate in flow simulation according to claim 1, characterized in that: In step S2, a kernel density estimation method is used to select a kernel function and a bandwidth, and a kernel density function is estimated.

3. The method for characterizing the uncertainty of chemical reaction rate in flow simulation according to claim 2, characterized in that: In step S2, the kernel function is one of the following: Gaussian kernel function, triangular kernel function, Epanechnikov kernel function.

4. The method for characterizing uncertainty of chemical reaction rate in flow simulation according to claim 1, characterized in that: In step S2, the bandwidth is selected according to the kernel density estimation function in MATLAB, or the bandwidth is set by oneself.

5. The method for characterizing uncertainty of chemical reaction rate in flow simulation according to claim 1, characterized in that: z is a value within the domain of the random sample.

6. The method for characterizing uncertainty of chemical reaction rate in flow simulation according to claim 1, characterized in that: 。 7. A method for characterizing uncertainty of chemical reaction rate in flow simulation according to any one of claims 1 to 6, characterized in that: The chemical kinetic model is one or more of the following: Dunn-Kang model, Park model, Gupta model.

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