JP2010038410A - Combustion analysis method, combustion analyzer and computer program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To prevent deterioration of calculation accuracy in a nonequilibrium combustion state while using the chemical equilibrium method. <P>SOLUTION: A combustion analysis method for numerical analysis of combustion includes: a first step of calculating generation amount of one or a plurality of first chemical species which is part of chemical species related to combustion of an analysis target in accordance with the algorithm based on the chemical equilibrium method; a second step of calculating reaction velocity by the combustion of one or plurality of second chemical species which is the other part of the chemical species related to the combustion in accordance with the algorithm based on the reaction kinetics; and a third step of calculating generation amount of the second chemical species by substituting the reaction velocity calculated in the second step to the conservation formula of the second chemical species. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a method for performing numerical analysis on combustion, a combustion analysis apparatus, and a computer program.

There is an algorithm based on the chemical equilibrium method for calculating the combustion phenomenon at high speed and concisely (see, for example, Non-Patent Document 1).
In combustion, oxygen and fuel are mixed by turbulent flow or diffusion, and this becomes a raw material for the combustion reaction. Among the chemical equilibrium methods, for example, in the Gibbs free energy minimization method, the number of elements contained in these raw materials (four elements of C, H, O, and N in a general combustion field) is before and after the combustion. By solving n + 1 (n is the number of elements contained in the raw material) multi-dimensional simultaneous nonlinear equations derived from the condition that the free energy of Gibbs of the system is minimized and the condition that the Gibbs free energy of the system is minimized, Calculated.

Masayuki Ogawa, Yoshifumi Okami, Combustion analysis by discrete vortex method, Proceedings of the 82nd Regular Meeting of the Japan Society of Mechanical Engineers Kansai Branch, No.074-1 (2007), p.3-23

The chemical equilibrium method has an advantage that any product can be predicted without requiring a chemical reaction formula if the amount of elements (for example, H, C, O, N) contained in the raw material is known.
However, the algorithm based on the chemical equilibrium method deteriorates the calculation accuracy for a phenomenon that is not in equilibrium. In other words, the algorithm based on the chemical equilibrium method assumes that the reaction rate is infinite, that is, the reaction time is infinitesimal, and the reaction rate cannot be controlled. Therefore, the calculation accuracy is lowered for a reaction product having a slow reaction rate.

  Therefore, an object of the present invention is to prevent deterioration in calculation accuracy in a non-equilibrium combustion state while using a chemical equilibrium method.

  The present invention is a combustion analysis method for numerically analyzing combustion, and an algorithm based on a chemical equilibrium method is used to determine the amount of one or more first chemical species that are a part of chemical species related to combustion to be analyzed. And a second step of calculating a reaction rate of the one or more second chemical species that are another part of the chemical species involved in the combustion according to an algorithm based on a reaction kinetics. And a third step of calculating a production amount of the second chemical species by substituting the reaction rate obtained in the second step into a conservation equation for the second chemical species. This is a combustion analysis method.

  From another viewpoint, the present invention provides means for calculating the amount of one or more first chemical species that are part of chemical species related to combustion to be analyzed according to an algorithm based on a chemical equilibrium method, Means for calculating the reaction rate of the one or more second chemical species that are another part of the chemical species involved in combustion according to the algorithm based on the reaction kinetics, and the reaction obtained by the second step A combustion analysis apparatus comprising: means for calculating a generation amount of the second chemical species by substituting the speed into a conservation equation of the second chemical species.

  According to still another aspect of the present invention, the present invention provides a first step of calculating a generation amount of one or more first chemical species that are a part of chemical species related to combustion to be analyzed according to an algorithm based on a chemical equilibrium method. A second step of calculating a reaction rate due to the combustion of one or more second chemical species that are another part of the chemical species related to the combustion according to an algorithm based on a reaction kinetics; A computer program for causing a computer to execute a third step of calculating a production amount of the second chemical species by substituting the reaction rate obtained by the step into a conservation equation of the second chemical species.

According to each of the above inventions, the generation amount of some of the chemical species related to combustion (first chemical species) can be determined quickly and simply by an algorithm based on the chemical equilibrium method.
On the other hand, for some other chemical species (second chemical species), the reaction rate is determined by calculating the reaction rate by an algorithm based on the reaction kinetics, and the production amount is calculated from the reaction rate, The generation amount can be calculated. As a result, it is possible to calculate with high accuracy by setting the second chemical species as a chemical species having a slow reaction rate that deteriorates the calculation accuracy when calculated by the chemical equilibrium method.

Therefore, for example, the main chemical species (the first chemical species) among the chemical species related to combustion are calculated quickly and simply by the chemical equilibrium method, but the reaction rate is slow and the chemical equilibrium method has a high calculation accuracy. For chemical species (second chemical species) that need to be calculated but reduced, it is possible to prevent a decrease in calculation accuracy by partially using reaction kinetics.
In addition, since the reaction kinetics with a large amount of calculation is not used for all chemical species, high-speed calculation is possible.

  Therefore, according to the present invention, it is possible to prevent deterioration in calculation accuracy in a non-equilibrium combustion state while using the chemical equilibrium method.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings.

[1. Overall configuration of combustion analyzer]
FIG. 1 is a flowchart illustrating a procedure of combustion analysis processing by the combustion analysis apparatus according to the embodiment. This combustion analyzer is constituted by a computer on which a computer program for executing each step of the flowchart of FIG. 1 is mounted.
2 and 3 show functional blocks of the combustion analysis apparatus realized by the computer program.

This combustion analyzer can calculate the amount of each of a plurality of chemical species related to the combustion to be analyzed (turbulent diffusion combustion). The combustion analysis apparatus performs calculation according to an algorithm based on a chemical equilibrium method for one or a plurality of main chemical species among a plurality of chemical species related to combustion to be analyzed.
On the other hand, the remaining one or more chemical species are calculated according to an algorithm based on reaction kinetics (chemical kinetics).

For this reason, as shown in FIG. 2, the combustion analysis apparatus sets one or a plurality of chemical species that are calculated according to the chemical equilibrium method as a “first chemical species” among a plurality of chemical species related to combustion to be analyzed. A first chemical species setting unit 11 for setting, and a second chemical species setting unit 21 for setting one or a plurality of chemical species to be calculated according to reaction kinetics as a “second chemical species” ing.
Therefore, the user of the combustion analyzer can freely set the chemical species (second chemical species) to be calculated by the reaction kinetics instead of the chemical equilibrium method by the setting unit 21.

  In addition, the combustion analysis apparatus calculates the mass fraction of the first chemical species (combustion generation amount) for each of the set (selected) first chemical species according to an algorithm based on the chemical equilibrium method. A fraction calculation unit 12 is provided. In the present embodiment, the mass fraction calculation unit 12 of the first chemical species performs an operation for obtaining a combustion product by a Gibbs free energy minimization method, which is a type of chemical equilibria (CE).

The Gibbs free energy minimization method directly obtains the chemical potential of an element from the condition that the Gibbs free energy has a minimum value in an equilibrium state when obtaining combustion products.
In addition to the Gibbs free energy minimization method, there is a method to determine the concentration ratio of each component from the equilibrium constant with pressure storage and atomic number storage as constraints. For example, when solving a combustion field consisting of 100 components, it is necessary to solve a 100-element simultaneous equation.
On the other hand, in the Gibbs free energy minimization method, it is only necessary to solve a multiple simultaneous equation of the number of elements to be considered +1, and in a general combustion field, four elements of H, C, O, and N may be considered.

Further, the combustion analysis apparatus includes a reaction rate calculation b22 for each second chemical species that calculates a reaction rate of the second chemical species for each set (selected) second chemical species according to an algorithm based on the reaction kinetics. ing. In the present embodiment, the reaction rate calculation unit 22 of the second chemical type performs an operation for obtaining the reaction rate according to an eddy dissipation concept (EDC) model that is a combustion model based on reaction kinetics.
The vortex dissipation concept model (EDC model) is a vortex dissipation model that can calculate the reaction rate of a one-stage or two-stage overall reaction so that a multistage chemical reaction equation can be solved.

The combustion analyzer calculates the mass fraction (combustion generation amount) of each second chemical species based on the reaction rates of the second chemical species obtained by the reaction rate calculation unit 22. A fraction calculation unit 23 is provided.
The mass fraction calculation unit 23 of the second chemical species obtains the combustion product by substituting the reaction rate into the conservation formula of the second chemical species.

  The eddy dissipation concept model (EDC model) also includes a file-scale volume fraction calculation unit 24, a time scale calculation unit 25, and an atom generation / annihilation rate calculation unit 26, which can calculate each value. .

  As described above, in this embodiment, the combustion model is configured by the chemical equilibrium theory (CE) and the vortex dissipation concept model (EDC model). Hereinafter, the combustion model of the present embodiment is referred to as an “EDC / CE model”.

Further, as shown in FIG. 3, the combustion analysis apparatus includes a control unit 30 that performs other calculations for combustion analysis. The controller 30 is provided with the calculated mass fractions of the first chemical species and the second chemical species, and calculates various parameters for combustion analysis. Various parameters calculated by the control unit 30 are used for calculating mass fractions of the first chemical species and the second chemical species.
The control unit 30 includes a convergence determination unit 31 for ending the processing loop, a speed / pressure calculation unit 32 for calculating speed and pressure, a temperature calculation unit 33 for calculating temperature, and a Reynolds stress for calculating Reynolds stress / turbulent viscosity coefficient. A turbulent viscosity coefficient calculating unit 34, an atomic mass fraction calculating unit 35 for obtaining the mass fraction of atom I, and a density calculating unit 36 for obtaining the density are provided.

  The mathematical formulas described later with reference to the flowchart of FIG. 1 and the block diagrams of FIGS. 2 and 3 are based on data (corresponding to the values (parameters) of each term in the mathematical formula) stored in the storage unit of the computer. The calculation unit of the computer calculates the calculation result, and the calculation result is stored in the storage unit.

[2. Combustion analysis method]
The combustion analysis apparatus according to this embodiment is realized by incorporating the function of the present invention as a user-defined function into the general-purpose fluid analysis software FLUENT (version 6.3.26) manufactured by ANSYS. However, software to which the present invention is applied is not limited to FLUENT.

[2.1 Governing equation]
The equations governing the combustion to be analyzed include the equation of motion, the Reynolds stress model, the chemical species J conservation equation, the energy equation, the gas state equation, and the temperature calculation equation, and are specifically as follows. The following governing equation is calculated in the numerical analysis of combustion.

[2.1.1 Equation of motion]
The equation of motion is as follows. In the above FLUENT, the following continuous equation and Naviestoke's equation are solved by the SIMPLE method [see Suhas V Patanka. Numerical Heat Transfer and Fluid Flow. Hemisphere Publishing Corporation, 1980].

[2.1.2 Reynolds stress model]
Since the combustion to be analyzed in the present embodiment is turbulent, a Reynolds stress model represented by the following equation was used as the turbulent flow model.

Here, the recommended value of σ _k is 0.82.

θij, is given by the following equation.

Here, θ _{ij, 1} and θ _{ij, 2} are referred to as sloterm and rapid term, respectively, and are modeled as follows.
Here, C ₁ and C ₂ are model constants, and recommended values are 1.8 and 0.60, respectively, and P = (1/2) × P _kk and C = (1/2) × C _kk is there.

ε _ij is given by the following equation.
Here, the recommended value of Cμ is 0.09.
Note that μ is a viscosity coefficient, which is a specific physical property value of the fluid. On the other hand, μ _t is an index (diffusivity due to turbulent flow) indicating the intensity of diffusion caused by turbulent flow, and is obtained by a turbulent flow model.

[2.1.3 Conservation formula of chemical species J]
The formula for the mass fraction of the chemical species J involved in combustion is calculated by the following formula using FLUENT.

[2.1.4 Energy equation]
Enthalpy is calculated by the user-defined scalar (UDS) of FLUENT. The energy equation is as follows.

[2.1.5 Equation of state of gas]
The density of the gas is calculated by the following formula.

[2.1.6 How to obtain temperature]
The temperature is calculated by the FLUENT UDS as:
Here, T ₀ is a reference temperature, 298.15 K, C _pmJ is the average constant pressure specific heat of chemical species J, and h _J0 is the standard production enthalpy of chemical species J.

[2.2 Explanation of EDC / CE model]
The EDC / CE model (vortex dissipation concept / equilibrium method model) of this embodiment is as follows. In the following description, an analysis target is an H ₂ -air turbulent diffusion flame, and H ₂ is calculated using an EDC model.

a. The reaction rate of the fuel (here, a mixture of H2 and N2) is calculated by EDC Dell.
b. Assuming that the fuel after the reaction has reached chemical equilibrium, the equilibrium is calculated using this as a reactant.

The reaction rate is calculated by an EDC (vortex dissipation concept) model equation. The EDC model assumes that combustion occurs in a turbulent microstructure, ie, fine scale. The fine scale volume fraction is defined by the following equation (IR Gran and BF Magnussen. A numerical study of a bluff-body stabilized diffusion flame .part2. Influence of combustion modeling and finite-rate chemistry. Combustion Science Technology, Vol. 119, pp. 191_217, 1998.).

Further, the reaction proceeds on a time scale represented by the following formula.

Furthermore, assuming that the reaction takes place in a constant-pressure reactor on the time scale of τ ^* , the current chemical species and temperature in the lattice are the initial conditions, and the following ordinary differential equation is numerically integrated at t = 0 to τ ^*. To do. The “inside of the lattice” refers to a small space obtained by dividing the target space for numerical analysis into a lattice shape. In Computational Fluid Dynamics, equations such as equations of motion and stresses are solved for each divided space (grid). This lattice is also called a cell.
Here, Y ^* _J and R ^* _J indicate the mass fraction and reaction rate of the chemical species J in the fine scale, respectively, and v ^′ _JK and ν ^″ _JK indicate positive values in the chemical reaction formula K of the chemical species J, respectively. And X _J is the molar concentration of species J, k _K is the reaction rate constant of chemical reaction equation K, and K _MAX is the number of reaction rate equations to be considered. A is a frequency factor, E is an activation energy, β is an index of temperature, and is an experimental parameter. Equation (26) is called Arrhenius' equation, and ordinary differential equations including this equation are generally known to be stiff. In this embodiment, CVODE [refer to SD Cohen and AC Hindmarsh. CVODE User Guide, llnl report edition, 1994. UCRL-MA-118618.] Is used to numerically integrate the ordinary differential equation.

The reaction rate appearing in the conservation equation (14) of the actual chemical species J is modeled by the following equation.

Further, the reaction rate of the N ₂ in the fuel, and assumed to be proportional to H _2, based on the mass fraction and the mass fraction of H ₂ N ₂ in the fuel, is calculated by the following equation. That is, the reaction rate calculation unit 22 for the second chemical species in the present embodiment calculates N _{2 in} the fuel by the equation (28), and for the chemical species other than N ₂ in the fuel, the equation (27). Calculate the reaction rate with.

The above formula (27) is a case where a detailed chemical reaction formula is adopted. However, if the chemical reaction equation is not taken in and the reaction is assumed to be rate-limited by turbulent mixing, the chemical reaction equation is expressed as a general reaction. Taking H ₂ -air as an example, H ₂ + 1 / 2O _2- > H ₂ O, and the reaction rate of H ₂ as a fuel at this time can be calculated by the following vortex dissipation model.
Here, Y _fuel , Y _ox , and Y _p indicate the mass fractions of fuel, oxidant, and combustion products, respectively, and A _mix and B _mix are experimental parameters of the vortex dissipation model, 4.0 and 0.5, respectively. It is. st refers to the stoichiometric oxygen fuel mass ratio.

The generation or annihilation rate of atom I is calculated by the following equation.
Furthermore, a _IJ represents a matrix of the number of atoms I for the chemical species J. For example, the number of atoms H for the chemical species H2 is _{aH, H2} = 2, the number of atoms H for the chemical species OH is _{aH, OH} = 1, and the number of atoms O is _{aO, OH} = 1. .

The conservation formula of atom I is represented by the following formula.

The enthalpy at this time is approximated by the following equation.
I _MAX is the number of atoms involved in combustion. In a normal combustion field, only H, C, O, and N are required. That is, I _MAX = 4.

The EDC / CE model of this embodiment further has a parameter for adjusting N.
By changing the value of NCTRL, the calculation result by the equilibrium calculation can be adjusted.
The program for equilibrium calculation is the NASA CEA [S Gordon and B Mc Bride. Computer program for calculations of the Gibbs free energy minimization method [JSME, editor. JSME Combustion Handbook. This was created based on NASA Reference Publication, No. 1311, 1994. This was incorporated into FLUENT as UDF.

[2.3 Processing procedure]
Returning to FIG. 1, the processing procedure of combustion analysis will be described. Here, the processing procedure will be described in accordance with an example of “Case 3” in FIG. In the flowchart of FIG. 1, the parts of steps a, b, d, e, and g are EDC / CE models. Step a is a part of the EDC model, b is a part of CE, and d, e, and g are parts other than the above, where chemical species conservation formulas and temperature calculations are performed. The other steps c, f, h, and i utilized functions provided by FLUENT.

Chemical species considered in this EDC / CE model are H ₂ , O ₂ , H ₂ O, OH, H, O, HO ₂ , N, and N ₂ . In the first chemical species setting unit 11, it is assumed that H ₂ O, O ₂ , HO ₂ , N, and N ₂ are set (selected) as the first chemical species among these chemical species. In the second chemical species setting unit 21, the remaining chemical species H ₂ , H, O, and OH are set (selected) as the second chemical species.

Step a:
In step a, the reaction rate calculation unit 22 of the EDC model obtains the reaction rate R _J of H ₂ , H, O, and OH (J = H ₂ , H, O, and OH) as the second chemical species. This calculation is performed based on the equations (24) to (29).
Also, the atom generation / annihilation rate calculation unit 26 of the EDC model obtains the generation or extinction rate of the atom I based on the equation (30) from the above reaction rate.
In the EDC model, the fine scale volume fraction calculating unit 24 calculates the volume fraction based on the equation (22), and the time scale calculating unit 25 calculates the time scale based on the equation (23).

Step b:
In step b, the equilibrium calculation for the first chemical species H ₂ O, O ₂ , HO ₂ , N, and N ₂ is performed by the mass fraction calculation unit 12 of CE (Gibbs free energy minimization method). In this equilibrium calculation, the first chemistry is assumed on the condition that the mass fraction d _I of the atom I (I = C, H, O, N) is a combustion reaction product and the enthalpy of the equation (32) does not change before and after combustion. Mass fractions (production amounts) Y _H2O , Y _O2 , Y _HO2 , Y _N , Y _N2 of the seeds H ₂ O, O ₂ , HO ₂ , N, N ₂ are determined.

Step c:
In step c, the speed / pressure calculation unit 32 obtains the speed and pressure based on the SIMPLE method (Equations (1) to (2)).

Step d:
In step d, the temperature calculation unit 33 solves the energy equation (formula (17)), and obtains the temperature based on the formula (21) from the enthalpy obtained from this.

Step e:
In step e, the mass fraction calculating unit 23 of the second chemical species uses the reaction rate R _J of the second chemical species obtained in step a as a corresponding conservation formula of the second chemical species J (formula (14)). of substituting the R _J, a second species H _2, H, O, the mass fraction of OH (generation _{amount) Y H2, Y H, Y} O, obtains the Y _OH.

Step f:
In step f, the Reynolds stress / turbulent viscosity coefficient calculator 34 obtains the Reynolds stress and the turbulent viscosity coefficient based on the Reynolds stress model (equations (3) to (13)). Reynolds stress appears in the equation of motion. Further, the turbulent viscosity coefficient appears in the energy equation, the conservation equation of the chemical species J, and the conservation equation of the atom I.

Step g:
In step g, the atomic mass fraction calculation unit 35 sets the generation / annihilation rate R _{I of} the atom I (I = C, H, O, N) obtained in step a to the corresponding atom I conservation formula (formula (31)) and determine the mass fraction d _I of atom I.

Step h:
In step h, the density calculation unit 36 obtains the density from the mass fraction Y _J of the chemical species _J and the pressure based on the equation (20).

Step i:
In step i, the convergence determination unit 31 performs convergence determination in order to end the processing loop of steps a to h in FIG.
The convergence determination is an error determination for determining whether the equation of motion, the Reynolds stress model, the energy equation, the conservation equation of the chemical species J, and the mass fraction equation of the atom I have reached a correct solution.
This convergence determination is automatically executed by a function inherent to FLUENT. In the SIMPLE method based on the finite volume method adopted by FLUENT, after discretization, a storage equation for an arbitrary variable in the cell P is expressed as the following equation.
Here, a _p is a center coefficient, a _nb is each influence coefficient of an adjacent cell, and b is a constant part S _c in the expression S = S _c + S _Pφ . In the equation (34), the following equation is established.

Furthermore, the residual of φ at this time is expressed by the following equation.
In FLUENT, the calculation is continued for each variable φ until the residual becomes a certain value or less (typically, 1.0 × 10 ^{−3 to} 1.0 × 10 ⁻⁶ ).

[3. Calculation conditions of examples and comparative examples]
In order to confirm the calculation accuracy by the EDC / CE model of this embodiment, the hydrogen jet flame was calculated (Example and Comparative Example). FIG. 4 shows calculation areas and boundary conditions. Calculation conditions are experiments of hydrogen jet flames in Takagi and Koto [Toshimi Takagi and Satoru Kotou. A prediction of flow and combustion in turbulent diffusion flame in japanese. Transactions of the Japan Society of Mechanical Engineers, Series B, Vol. 48, No. 436, 1981.].
A fuel having a hydrogen / nitrogen molar ratio of 0.4: 0.6 was ejected from a cylindrical nozzle having a radius of 2.45 mm at a rate of 55.4 m / s, and the ambient flow was air. It is assumed that air is in an equilibrium state from the beginning, and a molar ratio of dO: dN = 0.21: 0.79 is given as an inlet condition.

  Furthermore, the temperature of the fuel and the ambient flow were both 300 K, and the places where the calculation results were compared were on the central axis and on the cross sections at 60 mm and 160 mm from the nozzle. A quadratic accuracy upwind difference was applied to all equations to obtain an axial flow with the center line of FIG. 4 as an axis, and a Reynolds stress model was used as a turbulent flow model.

FIG. 5 shows typical simulation conditions (Case 1, 3, 4) of the calculations (examples and comparative examples) executed this time. Case 2 is a missing number.
FIG. 6 shows the chemical reaction formula used in the above calculation.
Chemical species considered in this EDC / CE model are H ₂ , O ₂ , H ₂ O, OH, H, O, HO ₂ , N, and N ₂ .

In Case 1 of FIG. 5 (comparative example), a conventional EDC model is employed as a combustion model.
In the Case 1 ED model, the chemical reaction formula shown in FIG. 6 was used.
In Case 3 (Example), only the chemical species (second chemical species) of H ₂ , H, O, and OH were considered, the remaining chemical species were the first chemical species, and the calculation was performed by the equilibrium method.
In Case 4 (Example), the chemical reaction formulas 1 to 8, 11 and 13 in FIG. 6 relating to OH were considered, and further, H ₂ was evaluated by formula (29) assuming mixing rate limiting.

[4. Comparison of Calculation Results and Experimental Values of Examples and Comparative Examples]
[4.0.1 Comparison of turbulent energy k, average velocity U, and main chemical species on the central axis]
7 shows the distribution of the turbulent energy k and the average flow velocity U on the center line (center axis) of FIG. 4, and FIG. 8 shows the distribution of the chemical species and the temperature T.
In FIG. 7, when turbulent energy k is seen, the experimental value (EXP) slowly increases to around L = 180, whereas in Cases 1 and 3, it rapidly increases toward L = 100. It is decreasing at the border. Past Calculation Examples [Toshimi Takagi and Satoru Kotou. A prediction of flow and combustion in turbulent diffusion flame in japanese. Transactions of the Japan Society of Mechanical Engineers, Series B, Vol. 48, No. 436, 1981.] [Kimio Iino , Shinji Murakami, and Hoshitaka Kikkawa. Numerical simulation of high pressure methane-oxygen coaxial turbulent nonpremixed flames. Journal of High Temperature Society, Vol. 31, pp. 112_121, 2005. It is reported that the simulation value is overestimated for k. In order to improve the overestimation of k of this turbulent diffusion flame, it is necessary to select a more accurate LES model of the turbulent flow model or to improve the Reynolds stress model.

Here, the parameters of the RSM in FIG. 5 are selected so that the position of the maximum temperature value on the central axis matches in all cases. In the experiment, the temperature takes a maximum value of about 1600 K around 150 mm from the nozzle. The maximum value of between H ₂ O and the temperature of Case3 is 18.9 percent, respectively, has a 1556K, approximately 18.35% of between H ₂ O and the maximum value of the temperature in the experimental value (EXP), is about 1600K Yes.

[4.0.2 Comparison of turbulent energy, average velocity, main chemical species, and temperature at L = 60]
9 shows k and U in the radial direction at L = 60, and FIG. 10 shows the distribution of chemical species and temperature T. The U of Case 3 and Case 1 in FIG. 9 agrees well with the U in the experimental value (EXP). However, k is different from the experimental value (EXP) as in the distribution on the central axis. When FIG. 10 is seen, the error with EXP is large for both Case 3 and Case 1 with respect to a temperature around R = 6 mm and H ₂ O. This is because the error with EXP of T and H ₂ O is large in the vicinity of R = 6 mm, but the agreement with EXP is good in other regions.
In addition, since Cases 1 and 3 were not able to correctly predict temperatures around R = 6 mm, and both showed similar prediction values, the T error in the vicinity was not an error caused by the combustion model. I can guess.

[4.0.3 Comparison of turbulent energy, average velocity, main chemical species, temperature at L = 160]
FIG. 11 shows k and U in the radial direction at L = 160, and FIG. 12 shows the distribution of chemical species and temperature T.
Referring to FIG. 11, as R increases, the difference between the predicted value of U for Cases 1 and 3 and U in the experiment increases. If diffusion is greatly evaluated in a portion where this difference exists, U is diffused, so it can be predicted that U due to Cases 1 and 3 in FIG. From this, the difference in this part is presumed to be caused by estimating turbulent diffusion smaller than the experiment. In order to further improve this difference, it is only necessary to select a more accurate LES model of a turbulent flow model or to improve the Reynolds stress model. Referring to FIG. 812, when the temperature of Case 1 and 3 is compared with EPX, the difference between the predicted value of T for Case 1 and 3 and the experimental T is increased as R increases (goes to the outside of the flame). growing. This is considered to be caused by the fact that the diffusion is estimated as small as U, and further that H ₂ O has been flowed because U is large.

[4.1 Comparison with EDC model of radicals]
[4.1.1 On central axis]
13 and 14 show the OH and H EDC / CE models on the central axis and the predicted values based on the EDC model. As summarized in FIG. 5, Case 1 in FIG. 5 represents a calculated value in an EDC model (comparative example), and Cases 3 and 4 represent a calculated value in an EDC / CE model (example). The difference between Cases 3 and 4 is the difference in the number of chemical species considered in the EDC model. Case 3 considers the reaction rate of H ₂ , H, O, and OH in the EDC model, whereas Case 4 considers only OH.
As shown in FIG. 13, when looking at the predicted value of OH, when comparing the calculation results with Cases 1, 3, and 4, there is a difference between L = 50 and L = 200, but in other regions, consistency is observed. is good.
This is because OH is calculated by the EDC model theory expressed by the equations (22) to (27) in both cases 3 and 4.

As shown in FIG. 14, in the predicted value of H, Case 1 and Case 3 are in good agreement until L = 150. However, after L = 150, there is a difference that the predicted value of H of Case 3 is estimated to be smaller than the predicted value of Case 1. This difference is considered due to the fact that the reaction rates of H ₂ O, O ₂ , and HO ₂ were not considered in the EDC model. Comparing Case1 and Case4, Case4 estimates H lower than Case1.

[4.1.2 L = 60]
FIGS. 16 and 15 show prediction values based on the EDC / CE model of OH and H and the EDC model of Case 1 at L60.
Looking at the predicted values of OH shown in FIG. 16, when the calculation results of Case 1 and Cases 3 and 4 are compared, they agree well up to around R = 7, but thereafter, the predicted values of the EDC / CE model and the EDC model are the same. There are some differences. It can be said that Cases 1, 3, and 4 have almost the same predicted values. This is because the reaction rate was considered for OH in both Cases 3 and 4.
In the predicted value of H shown in FIG. 15, when Case 1 and Case 3 are compared, some errors are observed near R = 0 and after R = 6. However, the agreement between the two is generally good.
The predicted value of H of Case 4 is estimated more in the vicinity of R = 0 than in Case 1, and is estimated to be lower than the predicted value of Case 1 in the vicinity of R = 8.

[4.1.3 L = 160]
18 and 17 show the OH and H EDC / CE model at L = 160 and the predicted values based on the EDC model.
Comparing the calculation results of Cases 1, 3, and 4 with the predicted values of OH in FIG. 18, it can be said that the three show similar graph slopes.
In the predicted value of H in FIG. 17, Cases 1 and 3 are in good agreement. The predicted value of H of Case 4 is estimated more in the vicinity of R = 0 than in Case 1, and is estimated to be lower than the predicted value of Case 1 with R = 13 as a trap. H is completely consumed around R = 17.

[5 Discussion]
[5.1 Comparison of Combustion Model of Example and Conventional Combustion Model]
The conventional EDC model can consider a detailed chemical reaction formula in a turbulent diffusion flame, and can handle a multi-component reaction. On the other hand, the EDC / CE model according to the example handles multi-component reactions using both chemical reaction equations and chemical equilibrium methods. Here, the calculated values of the EDC model and the model of this embodiment are compared, and the characteristics of both are discussed.

In the EDC model, in order to adjust the generation amount of a specific chemical species, the number of chemical reaction formulas is increased, or experimental parameters in the chemical reaction formulas and parameters such as C _τ and C _{ξ of the} EDC model are adjusted. However, there are many combinations of these parameters, and the number of parameters increases as the number of chemical reaction equations increases. On the other hand, since the model of the embodiment only needs to consider the parameters of the EDC model and an arbitrary chemical reaction formula, the adjustment is simpler than the EDC Dell.

In the EDC / CE model, the chemical reaction formula to be considered follows the calculation accuracy required by the person who performs the simulation.
For example, if calculation accuracy is required for an arbitrary chemical species (in this case, OH) such as Case, the chemical species is considered in the reaction rate. If calculation accuracy is required for other chemical species such as Case 3, the chemical reaction formula is also considered for other chemical species. By doing so, the calculation result of the EDC / CE model can be brought close to the calculation result of the EDC model. The EDC / CE model is the same as the EDC model if all chemical species are considered in the EDC model without considering any chemical species in the equilibrium method. The radicals calculated by Case 4 showed good agreement with OH when compared with the calculation results of the EDC model. However, there was no quantitative agreement for H.

However, when looking at FIGS. 15 and 17, it is considered that the tendency of occurrence and disappearance of H is captured. For this reason, in the first stage of numerical analysis, the EDC / CE model must be applied to only the necessary chemical species such as Case 4, and then the other chemical species must be accurate. If so, the chemical species considered in the EDC model, such as Case 3, may be increased. As an application of the EDC / CE model, for example, when calculating thermal NO _x with the extended Zeldovich mechanism expressed by the following chemical reaction formula, H, O, OH are considered by the equilibrium method, and NO _x is It can be used in consideration of the EDC model.

  As an application of other EDC / CE models, it is also useful for constructing detailed chemical reaction equations for turbulent diffusion flames. That is, the EDC model is applied only to the fuel reaction rate, as in Case 4, and the equilibrium method is applied to other chemical species. After that, chemical reaction formulas will be added for chemical species that are estimated to contribute significantly to the combustion field. The magnitude of the contribution to the combustion field can be estimated by referring to the predicted value obtained by the equilibrium method.

[5.1.1 Calculation time]
In the EDC / CE model, the equilibrium method solves a nonlinear simultaneous equation with the number of elements to be considered + 1 being an unknown. In a normal combustion field, C, H, O, and N + 1 are 5 elements. On the other hand, the EDC model solves simultaneous differential equations with the number of chemical species to be considered as unknowns. As the number of chemical reaction equations increases and the number of chemical species to consider increases, the calculation time for solving simultaneous differential simultaneous equations also increases. On the other hand, the equilibrium method is always 5 yuan, and although there is a difference in the time to convergence depending on the concentration of the reactants, the increase or decrease in calculation time is not significant compared to the EDC model. In the EDC / CE model, it is not necessary to calculate the conservation formula (14) of the chemical species J for the chemical species considered in the equilibrium method. In the EDC model, it is necessary to solve the conservation formula of the chemical species J for all the chemical species considered. For this reason, in the EDC model, as the number of chemical species to be considered increases, the number of chemical species conservation equations to be solved also increases, so that the calculation time increases. For this reason, it can be said that the larger the number of chemical species considered in the calculation, the faster the EDC / CE model is than the EDC model.

[5.1.2 EDC / CE application range]
A combustion field to which the EDC / CE model can be applied is, for example, a turbulent diffusion flame. That is, the flow field is turbulent and the fuel and oxidant flow from separate locations. Further, since the EDC model is used for calculating the reaction rate, the prediction accuracy of the chemical species is the same as that of the EDC model even at the best accuracy. If the equilibrium method is applied to chemical species with strong non-equilibrium such as NO _x , the prediction system is lowered. Therefore, for these chemical species, the reaction rate must be calculated using an EDC model.

In addition, final products such as H ₂ O and CO ₂ are considered in the equilibrium method. This is to stabilize the calculation of the equilibrium method by determining the chemical species mainly generated by combustion. In other words, it is preferable to calculate the majority of the chemical species of the combustion product by the equilibrium method and to incorporate the EDC model only for chemical species that require accuracy. The EDC / CE model uses the Arrhenius equation, and the Arrhenius equation often depends on temperature, so that extinction often occurs. This problem can be avoided by using equation (29) that does not consider the Arrhenius equation for the fuel reaction rate.

[6 Conclusion]
As a conclusion, the characteristics of the EDC / CE model according to the embodiment and its comparison / examination are summarized.
(1) The generation amount of all chemical species can be predicted without requiring a detailed chemical reaction formula, and calculation can be performed with the same degree of accuracy as the EDC model by incorporating the chemical reaction formula for any chemical species.
(2) Not only final products such as H ₂ O but also intermediate products such as OH, O, and H can be predicted, and combined with existing models such as the Zeldvich mechanism to generate NO _{x and the} like Applications such as quantity prediction are possible.
(3) Since the turbulent mixing / combustion is evaluated by the EDC model, the influence of turbulent flow and temperature can be taken into the chemical reaction in consideration of the chemical reaction formula.

Furthermore, comparison and examination of experimental values (EXP) and predicted values based on the conventional EDC model will be summarized.
(1) For H ₂ , O ₂ , and H ₂ O, the predicted values based on the EDC / CE model agree with the experimental values and the predicted values based on the EDC model.
(2) For OH and H, which are radicals, the reaction rate is taken into consideration, and a good agreement with the predicted value of the EDC model is exhibited.
(3) Considering the reaction rate for many chemical species, it approaches the predicted value by the EDC model.

  In addition, this invention is not limited to the said embodiment and Example, A various deformation | transformation is possible.

It is a flowchart of a combustion analysis process. It is a functional block diagram of a combustion analyzer. It is a functional block diagram of a combustion analyzer. It is a figure which shows the calculation area | region and boundary condition of a hydrogen jet flame. 4 is a table showing rate coefficients associated with H2-O2 chemical reaction mechanisms. It is a table | surface which shows simulation conditions. It is a graph which shows the turbulent energy and average velocity in the position along a centerline. It is a graph which shows the mole fraction and temperature of the chemical species in the position along a center line. It is a graph which shows the turbulent energy and average velocity in the position of L = 60. It is a graph which shows the mole fraction and temperature of the chemical species in the position of L = 60. It is a graph which shows the turbulent energy and average speed in the position of L = 160. It is a graph which shows the mole fraction and temperature of a chemical species in the position of L = 160. It is a graph which shows the molar fraction of OH in the position along a centerline in an EDC model and an EDC / CE model. It is a graph which shows the mole fraction of H in the position along a centerline in an EDC model and an EDC / CE model. It is a graph which shows the mole fraction of H in the position of L = 60 in an EDC model and an EDC / CE model. It is a graph which shows the mole fraction of OH in the position of L = 60 in an EDC model and an EDC / CE model. It is a graph which shows the mole fraction of H in the position of L = 160 in an EDC model and an EDC / CE model. It is a graph which shows the molar fraction of OH in the position of L = 160 in an EDC model and an EDC / CE model.

Explanation of symbols

11 First Chemical Species Setting Unit 12 First Chemical Species Mass Fraction Calculation Unit 21 Second Chemical Species Setting Unit 22 Second Chemical Species Reaction Rate Calculation Unit 23 Second Chemical Species Mass Fraction Calculation Unit

Claims (3)

A combustion analysis method for numerically analyzing combustion,
A first step of calculating the amount of one or more first chemical species that are part of the chemical species related to combustion to be analyzed according to an algorithm based on a chemical equilibrium method;
A second step of calculating a reaction rate of the one or more second chemical species that are another part of the chemical species involved in the combustion according to the combustion according to an algorithm based on a reaction kinetics;
A third step of calculating the production amount of the second chemical species by substituting the reaction rate obtained in the second step into the conservation equation of the second chemical species;
The combustion analysis method characterized by including. Means for calculating the amount of one or more first chemical species that are part of the chemical species related to combustion to be analyzed according to an algorithm based on a chemical equilibrium method;
Means for calculating a reaction rate due to the combustion of one or more second chemical species that are another part of the chemical species involved in the combustion according to an algorithm based on reaction kinetics;
Means for calculating the production amount of the second chemical species by substituting the reaction rate obtained in the second step into the conservation equation of the second chemical species;
A combustion analysis apparatus comprising: A first step of calculating the amount of one or more first chemical species that are part of the chemical species related to combustion to be analyzed according to an algorithm based on a chemical equilibrium method;
A second step of calculating a reaction rate of the one or more second chemical species that are another part of the chemical species involved in the combustion according to the combustion according to an algorithm based on a reaction kinetics;
A third step of calculating the production amount of the second chemical species by substituting the reaction rate obtained in the second step into the conservation equation of the second chemical species;
A computer program for causing a computer to execute.