CN117059188B - Method and system for improving thermodynamic equilibrium energy system of chemical unbalanced gas - Google Patents
Method and system for improving thermodynamic equilibrium energy system of chemical unbalanced gas Download PDFInfo
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Abstract
The invention discloses a method and a system for improving a thermodynamic equilibrium energy system of a chemical unbalanced gas, wherein the method comprises the steps of thermodynamic energy parameter calculation sampling, piecewise fitting temperature interval repartition, piecewise fitting polynomial coefficient reconstruction, thermodynamic energy parameter calculation correction in a low-temperature area, thermodynamic equilibrium energy system improvement method application, chemical unbalanced flow field acquisition and the like, and the method is based on Chemkin fitting polynomials, and repartition is carried out on a temperature interval applicable to a first stage and a second stage of piecewise function according to thermodynamic energy parameter distribution characteristics of each air component; meanwhile, the specific heat and internal energy values calculated by a molecular dynamics theory method based on thermodynamic temperature model assumption are used as interpolation template data, and a mathematical approximation method is used for reconstructing the piecewise fitting polynomial coefficients of each air component. The invention can solve the problem of difference of the traditional method in the aspect of calculating thermodynamic equilibrium energy parameters of high-enthalpy gas components.
Description
Technical Field
The invention relates to the technical field of aerodynamics, in particular to an improved method and system for a chemical unbalanced gas thermodynamic equilibrium energy system.
Background
The use of damkohler numbers in aerodynamics is commonDaAnd judging the flow characteristics of the hyperspectral reaction.DaIs numerically equal to the ratio of the flow characteristic time (dead time of fluid infinitesimal in the flow field) to the chemical reaction characteristic time (time required for the chemical reaction to reach an equilibrium state).Da>>1, which means that the fluid element has a relatively long dead time in the flow field, the components in the mixed gas have enough time to chemically react and reach a local equilibrium state.Da<<1 is referred to as chemical freeze flow, which means that the dead time of fluid microelements in a flow field is relatively short, and each component in the mixed gas leaves the flow field before chemical reaction occurs.DaThe flow approaching 1 is called a chemical unbalanced flow, which indicates that the dead time of the fluid microelements in the flow field is in the same order of magnitude as the characteristic time of chemical reaction, and at the moment, the fluid microelements simultaneously react with the flow, but cannot reach an equilibrium state, and the chemical reaction is carried out at a limited speed. In fact, the three states exist in the real flow field at the same time, and are difficult to distinguish specifically. Thus, engineering uses chemical imbalance to describe the flow state of all computational domains, and chemical equilibrium and frozen flow can be considered as two extreme states of chemical imbalance flow.
The chemical unbalanced flow is a flow problem which is more researched by the numerical application of the super engineering model, and the calculation modes of the thermodynamic energy parameters of the high enthalpy gas mainly comprise two types, namely a molecular dynamic theory method based on thermodynamic temperature model assumption (hereinafter referred to as thermodynamic temperature model method) and an approximation method based on experimental data fitting. The former uses the Born-Oppenheimer approximation method to make the internal energy of high-temperature gas moleculee) Is decomposed into translation energye tr ) Rotation energye rot ) Vibration energye V ) And the electron potential energye E ) The equal energy distribution forms correspondingly adopt translation temperature #T tr ) Temperature of rotationT rot ) Vibration temperature%T V ) And electron temperature [ ]T E ) The isothermal modes are characterized and calculated respectively. The latter directly models the energy parameters characterized by the statistical temperature under the thermodynamic equilibrium assumption condition, and mainly adopts a piecewise fitting polynomial to calculate, and the most commonly used fitting method of Chemkin in Computational Fluid Dynamics (CFD).
The molecular dynamics theory method based on thermodynamic temperature model assumption is more accurate and strict, is more suitable for characterization of high-enthalpy gas energy distribution forms, but has complex relative forms and is time-consuming to calculate. In comparison, the approximation method based on experimental data fitting has the advantages of simple calculation form, convenient program writing, high calculation efficiency and the like, so CFD numerical value research often adopts the method to simulate the chemical unbalanced flow problem. Theoretically, for a typical hyperspectral unbalanced flow problem, the conditions of flow field energy, temperature, wall heat flow distribution and the like calculated by a thermodynamic temperature model assumption-based method (mainly adopting a temperature model method) and an experimental data fitting-based approximation method (mainly adopting a Chemkin fitting method) should be consistent.
However, at present, the key thermodynamic energy parameters such as internal energy and specific heat calculated by the two methods have significant deviation (as shown in fig. 1 and 2) between a low-temperature interval (less than 1000K) and a higher-temperature interval (greater than 6000K), so that the flow field structure (such as shock wave shape), flow field energy distribution, wall thermal environment distribution and the like obtained by final simulation are different, that is, the two methods have not realized calculation result normalization in terms of simulating chemical unbalanced flow, and cannot realize mutual verification and verification.
In summary, it is necessary to improve and correct the existing fitting approximation method, and achieve the goal of "normalizing" the calculation result when simulating chemical unbalanced flow by the two methods.
Disclosure of Invention
In order to solve the problems, the invention provides an improved method and an improved system for a thermodynamic equilibrium energy system of a chemical unbalanced gas, which can solve the problem of difference between a Chemkin fitting approximation method and a molecular motion theory method based on thermodynamic temperature model assumption in terms of calculating thermodynamic energy parameters of high-enthalpy gas components, and further realize the purposes that the simulation results of the chemical unbalanced flow CFD adopting the two methods can be normalized and can be mutually verified.
The technical scheme adopted by the invention is as follows:
a method for improving a thermodynamic equilibrium energy system of a chemically unbalanced gas, comprising:
thermodynamic energy parameter calculation sampling: calculating thermodynamic energy parameters of each air component by adopting a molecular dynamic theory method based on a thermodynamic temperature model to obtain specific heat and internal energy value distribution;
dividing the temperature interval by segment fitting: dividing temperature intervals applicable to the first-stage and second-stage classification functions of the Chemkin fitting method again according to thermodynamic energy parameter distribution characteristics of each air component, and establishing a non-uniform segmentation fitting form;
reconstructing a piecewise fitting polynomial coefficient: the specific heat and internal energy values calculated by a molecular dynamic theory method are used as interpolation template data, and a mathematical approximation method is adopted to reconstruct the piecewise fitting polynomial coefficients of each air component, so as to obtain an improved and corrected piecewise fitting polynomial model and coefficient sets thereof;
and (3) calculating and correcting thermodynamic energy parameters in a low temperature region: establishing a linear calculation formula of thermodynamic energy parameters in a low-temperature region based on complete gas setting, and obtaining a calculation correction form of the thermodynamic energy parameters in the low-temperature region outside a temperature range where a fitting polynomial is applicable;
thermodynamic equilibrium energy system improvement method application and chemical unbalanced flow field acquisition: in a thermodynamic single-temperature model solver, calculating a correction form based on the obtained piecewise fitting polynomial model and thermodynamic energy parameters of a low-temperature region, calculating thermodynamic energy parameters of mixed gas, and updating relevant parameters of a flow field in a numerical iteration process until the flow field convergence condition is met, thereby obtaining the final required chemical unbalanced steady-state flow parameter distribution.
Further, in the piecewise fitting polynomial coefficient reconstruction, first, the first 5 coefficients of the fitting polynomial are constructed by taking the specific heat calculated by a molecular dynamics theory method as a core interpolation objecta 1 ~a 5 Then the last coefficient of the fitting polynomial is determined by taking the internal energy value calculated by the molecular dynamics theory method as a referencea 6 。
Further, in the thermodynamic energy parameter calculation correction of the low temperature region, a thermodynamic energy parameter calculation form of each component is constructed by adopting a linear relation for the low temperature region lower than 50K.
Further, the thermodynamic energy parameter calculation form of each component comprises:
wherein,c v,i (T)、c p,i (T) Respectively represent air components under corresponding temperature conditionsiA constant specific heat capacity value and a constant specific heat pressure value,e i (T)、h i (T) Respectively represent air components under corresponding temperature conditionsiIs a specific internal energy value and an enthalpy value,R= 8.314J/mol is a universal gas constant,M i is an air componentiIs used for the preparation of a polymer having a molecular weight of (1),Tin order to be able to determine the temperature,T const =50k is a constant temperature,h 0,i is an air componentiIs a heat of formation of (c).
Further, in the application of the thermodynamic equilibrium energy system improvement method and the acquisition of a chemical unbalanced flow field, the LU-SGS numerical format is adopted for carrying out discrete and iterative solution aiming at a chemical unbalanced flow control equation, and when the average residual error tends to be stable or reaches the maximum iterative step number, the flow field calculation is regarded as convergence, so that the chemical unbalanced steady-state flow parameter is obtained.
A chemical non-equilibrium gas thermodynamic equilibrium energy system improvement system comprising:
the thermodynamic energy parameter calculation sampling module is configured to calculate thermodynamic energy parameters of each air component by adopting a molecular dynamic theory method based on a thermodynamic temperature model to obtain specific heat and internal energy value distribution;
the piecewise fitting temperature interval repartitioning module is configured to repartition the temperature interval applicable to the first stage and the second stage of the piecewise function of the Chemkin fitting method according to the thermodynamic energy parameter distribution characteristics of each air component, and establish a non-uniform piecewise fitting form;
the piecewise fitting polynomial coefficient reconstruction module is configured to calculate specific heat and internal energy values obtained by the sampling module according to the thermodynamic energy parameters to be interpolation template data, reconstruct piecewise fitting polynomial coefficients of each air component by adopting a mathematical approximation method, and obtain an improved and corrected piecewise fitting polynomial model and coefficient sets thereof;
the low-temperature region thermodynamic energy parameter calculation and correction module is configured to establish a linear calculation formula of the low-temperature region thermodynamic energy parameter based on complete gas setting, and obtain a low-temperature region thermodynamic energy parameter calculation form outside a fitting polynomial applicable temperature range;
the thermodynamic equilibrium energy system improvement method is applied to a thermodynamic single temperature model solver, and a chemical unbalanced flow field acquisition module is configured to calculate and correct the thermodynamic energy parameters of the mixed gas based on the piecewise fitting polynomial model obtained by the piecewise fitting polynomial coefficient reconstruction module and the thermodynamic energy parameters of the low temperature region obtained by the thermodynamic energy parameter calculation and correction module, and update the relevant parameters of the flow field in a numerical iteration process until the flow field convergence condition is met, so that the final required chemical unbalanced steady-state flow parameter distribution is obtained.
Further, the piecewise fitting polynomial coefficient reconstruction module firstly constructs the first 5 coefficients of the fitting polynomial by taking the specific heat obtained by the thermodynamic energy parameter calculation module as a core interpolation objecta 1 ~a 5 Then with the thermodynamic energy parameterDetermining the last coefficient of the fitting polynomial by taking the internal energy value obtained by the calculation module as a referencea 6 。
Further, the thermodynamic energy parameter calculation and correction module of the low temperature region adopts a linear relation to construct a thermodynamic energy parameter calculation form of each component for the low temperature region lower than 50K.
Further, the thermodynamic energy parameter calculation form of each component comprises:
wherein,c v,i (T)、c p,i (T) Respectively represent air components under corresponding temperature conditionsiA constant specific heat capacity value and a constant specific heat pressure value,e i (T)、h i (T) Respectively represent air components under corresponding temperature conditionsiIs a specific internal energy value and an enthalpy value,R= 8.314J/mol is a universal gas constant,M i is an air componentiIs used for the preparation of a polymer having a molecular weight of (1),Tin order to be able to determine the temperature,T const =50k is a constant temperature,h 0,i is an air componentiIs a heat of formation of (c).
Further, the thermodynamic equilibrium energy system improvement method is applied, and the chemical unbalanced flow field acquisition module adopts LU-SGS numerical format to carry out discrete and iterative solution aiming at a chemical unbalanced flow control equation, and when the average residual tends to be stable or reaches the maximum iterative step number, the flow field calculation is regarded as convergence, so that the chemical unbalanced steady-state flow parameter is obtained.
The invention has the beneficial effects that:
1. according to the invention, specific heat and internal energy values obtained by calculation by a molecular dynamic theory method are taken as interpolation template points, and Chemkin fitting polynomial coefficients of each air component are constructed by re-interpolation, so that consistency of the two methods in calculating thermodynamic energy parameters of high enthalpy gas is ensured, and therefore, the problem of calculation difference of the two methods in chemical unbalanced flow simulation is solved, and the normalization and mutual verification of calculation results are realized.
2. According to the thermodynamic energy parameter distribution characteristics of each air component, a more flexible temperature interval division form is adopted, so that the interpolation error of a polynomial fitting method in a low-temperature interval is smaller, and further the method has a smaller value fluctuation phenomenon when processing low-temperature near-wall area flow, and calculation is more robust and accurate.
3. The temperature interval applicable to the chemical unbalanced gas thermodynamic equilibrium energy system improvement method is 0-30000K, and the applicable temperature range is wide; meanwhile, the method is applicable to any gas type including the earth atmosphere and the Mars atmosphere, has good compatibility to the existing thermodynamic single-temperature model solver, has little code modification and is easy to program and realize.
Drawings
Fig. 1 is a graph of the change in specific heat value calculated by the original Chemkin fitting method and the molecular dynamics theory method.
Fig. 2 is a graph of the internal energy value change calculated by the original Chemkin fitting method and the molecular dynamics theory method.
FIG. 3 is a flow chart of an improved method for improving the thermodynamic equilibrium energy system of a chemically unbalanced gas in example 1.
FIG. 4 is a graph showing the comparison of the calculated specific heat value with the calculated molecular dynamics theory method in the modified method of example 2.
FIG. 5 is a graph showing the comparison between the internal energy calculated by the modified method and the calculated by the molecular dynamics theory method in example 2.
Fig. 6 is a graph showing the comparison of the wall pressure distribution calculated after the improvement of the fitting method in the HEG wind tunnel test cylinder model example of example 3.
Fig. 7 is a comparative schematic diagram of the heat flux density distribution of the wall surface calculated after the fitting method is improved in the HEG wind tunnel test cylinder model example of example 3.
Detailed Description
Specific embodiments of the present invention will now be described in order to provide a clearer understanding of the technical features, objects and effects of the present invention. It should be understood that the particular embodiments described herein are illustrative only and are not intended to limit the invention, i.e., the embodiments described are merely some, but not all, of the embodiments of the invention. All other embodiments, which can be made by a person skilled in the art without making any inventive effort, are intended to be within the scope of the present invention.
Example 1
As shown in fig. 3, the present embodiment provides a method for improving a thermodynamic equilibrium energy system of a chemically unbalanced gas, which includes:
thermodynamic energy parameter calculation sampling: calculating thermodynamic energy parameters of each air component by adopting a molecular dynamic theory method based on a thermodynamic temperature model to obtain specific heat and internal energy value distribution;
dividing the temperature interval by segment fitting: dividing temperature intervals applicable to the first-stage and second-stage classification functions of the Chemkin fitting method again according to thermodynamic energy parameter distribution characteristics of each air component, and establishing a non-uniform segmentation fitting form;
reconstructing a piecewise fitting polynomial coefficient: the specific heat and internal energy values calculated by a molecular dynamic theory method are used as interpolation template data, and a mathematical approximation method is adopted to reconstruct the piecewise fitting polynomial coefficients of each air component, so as to obtain an improved and corrected piecewise fitting polynomial model and coefficient sets thereof;
and (3) calculating and correcting thermodynamic energy parameters in a low temperature region: establishing a linear calculation formula of thermodynamic energy parameters in a low-temperature region based on complete gas setting, and obtaining a calculation correction form of the thermodynamic energy parameters in the low-temperature region outside a temperature range where a fitting polynomial is applicable;
thermodynamic equilibrium energy system improvement method application and chemical unbalanced flow field acquisition: in the thermodynamic single-temperature model solver, a correction form is calculated based on the obtained piecewise fitting polynomial model and thermodynamic energy parameters of a low-temperature region, the thermodynamic energy parameters of the mixed gas are calculated, and related parameters (such as temperature parameters and energy parameters) of a flow field are updated in a numerical iteration process until the final required chemical unbalanced steady-state flow parameter distribution is obtained when the flow field convergence condition is met.
Accordingly, the present embodiments provide a chemical non-equilibrium gas thermodynamic equilibrium energy system improvement system comprising:
the thermodynamic energy parameter calculation sampling module is configured to calculate thermodynamic energy parameters of each air component by adopting a molecular dynamic theory method based on a thermodynamic temperature model to obtain specific heat and internal energy value distribution;
the piecewise fitting temperature interval repartitioning module is configured to repartition the temperature interval applicable to the first stage and the second stage of the piecewise function of the Chemkin fitting method according to the thermodynamic energy parameter distribution characteristics of each air component, and establish a non-uniform piecewise fitting form;
the piecewise fitting polynomial coefficient reconstruction module is configured to reconstruct piecewise fitting polynomial coefficients of each air component by adopting a mathematical approximation method according to the specific heat and internal energy values obtained by the thermodynamic energy parameter calculation module as interpolation template data to obtain an improved and corrected piecewise fitting polynomial model and coefficient sets thereof;
the low-temperature region thermodynamic energy parameter calculation and correction module is configured to establish a linear calculation formula of the low-temperature region thermodynamic energy parameter based on complete gas setting, and obtain a low-temperature region thermodynamic energy parameter calculation and correction form outside a fitting polynomial applicable temperature range;
the thermodynamic equilibrium energy system improvement method is applied to a chemical unbalanced flow field acquisition module, and is configured to obtain final required chemical unbalanced steady-state flow parameter distribution in a numerical iteration process by calculating thermodynamic energy parameters of mixed gas based on a piecewise fitting polynomial model obtained by the piecewise fitting polynomial coefficient reconstruction module, a coefficient set thereof and a low-temperature region thermodynamic energy parameter calculation correction form obtained by the low-temperature region thermodynamic energy parameter calculation correction module in a thermodynamic single-temperature model solver, and updating relevant parameters (such as temperature parameters and energy parameters) of the flow field in the numerical iteration process until flow field convergence conditions are met.
Preferably, the implementation process of the improved method of this embodiment is as follows:
1. thermodynamic energy parameter calculation sampling
Step S1: and calculating thermodynamic energy parameters of each air component by adopting a molecular dynamics theory method based on thermodynamic temperature model assumption, and obtaining specific heat and internal energy value distribution.
Molecular theory method based on thermodynamic temperature model assumption is adopted, and gas molecules are obtainediIs the total specific energy content ofe i The calculation form characterized by each temperature energy mode is
(1)
In the middle ofT、T V 、T E Respectively a translation temperature, a vibration temperature and an electron temperature,e tr,i (T)、e rot,i (T) Represents the translational energy and rotational energy calculated from the translational temperature respectively,e V,i (T V ) Representing the vibration energy calculated from the vibration temperature,e E,i (T E ) Representing the electron energy calculated from the electron temperature.
Kinetic energy of translatione tr,i (T) And rotational energye rot,i (T) Respectively is calculated as
(2)
Wherein the method comprises the steps ofmonRepresenting the type of monoatomic gas molecules,M i is the molecular weight (kg/mol),R= 8.314J/(mol·k) is a universal gas constant,is the enthalpy of formation (J/kg) of the molecule.
Corresponding translational energy constant specific heatc v,tr,i And a specific heat of rotation energyc v,rot,i Respectively is
(3)
In addition, vibration energye V,i (T V ) And electron energye E,i (T E ) Is of the meter(s)The arithmetic is respectively
(4)
Wherein the method comprises the steps ofeRepresenting free electrons. In the calculation formula of the vibration energy,nmis the number of vibration modes of polyatomic molecules,g i,m is a moleculeiFirst, themThe degeneracy of the individual modes of vibration,θ V,i,m is a moleculeiFirst, themAnd the characteristic vibration temperature corresponding to each vibration mode. In the electronic energy calculation formula,g 0,i andg 1,i respectively are moleculesiThe degeneracy of the ground state and the first electron excited state,θ E,i is a moleculeiIs a temperature characteristic of electrons of (a) a (b).
Accordingly, the specific heat of vibration energy is fixedc v,V,i And electron energy constant specific heatc v,E,i Respectively is
(5)
Thus, gas moleculesiSpecific heat of (2)c v,i Represented as
(6)
In the middle ofT、T V 、T E Respectively a translation temperature, a vibration temperature and an electron temperature,c v,tr,i (T)、c v,rot,i (T)、c v,V,i (T V )、c v,E,i (T E ) The specific heat capacity corresponding to each temperature mode is respectively shown.
Under thermodynamic equilibrium assumption conditions, i.eT=T V =T E According to the method, the specific heat capacity of each air component is calculated in the temperature interval of 50-30000Kc v,i Sum of internal energy valuese i The data is output every 100K intervals for the next step to construct interpolation coefficients. Wherein the air componentThe basic thermodynamic parameters of (2) are shown in Table 1.
TABLE 1 thermodynamic parameters of commonly used components of air
Where E is an abbreviation for the index Exponent, e.g. "1.599940E-02" means 1.599940 by 10 to the power-2.
2. Piecewise fitting temperature interval repartition
Step S2: and (3) dividing the temperature interval applicable to the first stage and the second stage of the stage function of the Chemkin fitting method again according to the thermodynamic energy parameter distribution characteristics of each air component, and establishing a non-uniform sectional fitting form.
The original Chemkin fitting method adopts a unified temperature interval division form, namely all air components adopt 5-level segmentation functions, and the corresponding temperature interval applicable to each level segmentation function is 200-1000, 1000-6000, 6000-15000, 15000-25000 and 25000-30000 (unit K).
Based on Chemkin piecewise fitting polynomial method, a 5-stage fractional interpolation function calculation form is still employed, but here the interpolation temperature intervals for each air component are repartitioned in the manner described in table 2.
TABLE 2 temperature interval division form corresponding to segment interpolation function of different air components
Different from the original Chemkin fitting method, the improved method adjusts the interpolation temperature interval of the 1 st-stage and 2 nd-stage segmentation functions, but the 3 rd-5 th-stage segmentation functions still adopt the temperature interval division form of the original Chemkin fitting method.
3. Piecewise fitting polynomial coefficient reconstruction
Step S3: and reconstructing the piecewise fitting polynomial coefficients of each air component by using the specific heat and internal energy values calculated by a molecular dynamics theory method as interpolation template data and adopting a mathematical approximation method to obtain an improved and corrected piecewise fitting polynomial model and coefficient sets thereof.
Based on the interpolation template point data constructed in the step S1, according to the interpolation temperature interval division form of the step S2, a mathematical approximation method is adopted to acquire the Chemkin fitting polynomial coefficients of each air component again. Since the specific heat of constant heat cannot be negative, this basic physical condition must first be satisfied when constructing the fitting polynomial coefficients.
First, the first 5 coefficients of Chemkin fitting polynomial are built by taking specific heat capacity as interpolation core object, namelya 1 ~a 5 . Calculating the fitting polynomial of specific heat of constant capacity as
(7)
In the middle ofR= 8.314J/mol is a universal gas constant,M i is an air componentiIs used for the preparation of a polymer having a molecular weight of (1),Tin order to be able to determine the temperature,c v,i (T) Representing air components under corresponding temperature conditionsiSpecific heat value of (2).
Second, the last coefficient of the Chemkin fitting polynomial is determined for the interpolation object with the specific energy, i.ea 6 . Calculating fit polynomial of internal energy of ratio as
(8)
In the middle ofR= 8.314J/mol is a universal gas constant,M i is an air componentiIs used for the preparation of a polymer having a molecular weight of (1),Tin order to be able to determine the temperature,e i (T) Representing air components under corresponding temperature conditionsiIs a specific internal energy value of (c).
In practice, the number of the cells to be processed,e i (T) Is thatc v,i (T) In the temperature range of [0 ],T]an integral value of the above, and thus the coefficienta 1 ~a 5 First determined by constant specific heat interpolation, and last coefficienta 6 Where it is determined by the specific internal energy value.
Finally, the Chemkin fitting polynomial coefficients of each air component were retrieved by mathematical approximation, as shown in Table 3 below.
TABLE 3 piecewise fitting polynomial coefficients for common air components
Where E is an abbreviation for the index Exponent, e.g. "1.599940E-02" means 1.599940 by 10 to the power-2.
In addition, the constant pressure specific heat of the air componentc p,i (T) Sum enthalpy valueh i (T) Can be fixed by specific heatc v,i (T) Sum of specific energye i (T) Calculated according to the following formula
(9)
In the middle ofR= 8.314J/mol is a universal gas constant,M i is an air componentiIs used for the preparation of a polymer having a molecular weight of (1),Tin order to be able to determine the temperature,c v,i (T)、c p,i (T) Respectively represent air components under corresponding temperature conditionsiA constant specific heat capacity value and a constant specific heat pressure value,e i (T)、h i (T) Respectively represent air components under corresponding temperature conditionsiIs a specific internal energy value and an enthalpy value. Wherein the piecewise interpolation and interpolation coefficients are shown in Table 3.
4. Thermodynamic energy parameter calculation and correction in low temperature region
Step S4: and establishing a linear calculation formula of the thermodynamic energy parameters in the low temperature range based on the complete gas assumption, and obtaining a calculation form of the thermodynamic energy parameters in the low temperature range outside the applicable temperature range of the fitting polynomial.
In the step S3, the applicable temperature interval of the piecewise fitting polynomial is 50-30000 k, and when the temperature is not within the interval range, the energy parameter calculated by the piecewise fitting method in the step S3 will have a larger error and is not applicable any more. Because the flight environment of more than 30000K is difficult to appear in the engineering application at present, the thermodynamic energy parameter calculation problem of a high-temperature area exceeding 30000K can be temporarily ignored. However, the low temperature region below 50K cannot be ignored, and the piecewise fitting method described in S3 cannot be used, so that it is necessary to establish a new calculation method for thermodynamic energy parameters of the low temperature region below 50K because the non-physical situation of "negative specific heat" is easy to occur under this condition, and stability and accuracy of flow field simulation calculation are further affected.
Under the condition of complete gas assumption, specific heat is a constant value, and then a thermodynamic energy parameter calculation method of each component is constructed by adopting a linear relation in a low-temperature range below 50K. To ensure continuity of piecewise fitting calculation, specific heat value of constant capacityc v,i The calculation is still carried out by adopting the formula (7), but the temperature uniformly takes the constant valueT=50k, i.ec v,i (T)=const=c v,i (T const =50K)。
In addition, the specific heat of constant pressure under the corresponding temperature conditionc p,i Specific internal energye i Sum enthalpy valueh i Calculated by the following formula
(10)
In the middle ofR= 8.314J/mol is a universal gas constant,M i is an air componentiIs used for the preparation of a polymer having a molecular weight of (1),Tin order to be able to determine the temperature,T const =50k is a constant temperature,h 0,i is an air componentiIs a heat of formation (J/kg),c v,i (T)、c p,i (T) Respectively represent air components under corresponding temperature conditionsiA constant specific heat capacity value and a constant specific heat pressure value,e i (T)、h i (T) Respectively represent air components under corresponding temperature conditionsiIs a specific internal energy value and an enthalpy value.
And (3) combining the fitting approximation method in the step (S3), and finally establishing a new thermodynamic equilibrium energy system calculation method with the applicable temperature range of 0-30000K for the thermodynamic single-temperature model solver.
5. Application of thermodynamic equilibrium energy system improvement method and acquisition of chemical unbalanced flow field
Step S5: and (3) calculating thermodynamic energy parameters of the mixed gas in a thermodynamic single-temperature model solver by using the fitting approximation new method established in the steps (S3) and (S4), and updating flow field related parameters (such as temperature, energy and the like) in a numerical iteration process until the final required chemical unbalanced steady-state flow parameter distribution is obtained when the flow field convergence condition is met.
The chemical unbalanced flow control equation related to the thermodynamic single temperature solver adopts a conservation integral form as
(11)
In the middle ofRespectively represent a control body and an enclosing surface thereof,Vin order to control the volume of the body unit,sfor the area of the flow-through surface,nis the normal vector of the flow surface, +.>To the incoming flow reynolds number. In addition, in the case of the optical fiber,Qis a vector of the conservation quantity,F、F v the convection flux and the viscous flux are respectively,Wis an unbalanced source term.
Vector of conservation constantQConvection fluxFFlux of viscosityF v Unbalanced source termWThe specific expression of (2) is
(12)
Wherein the method comprises the steps ofn=(n x ,n y ,n z ) Is a circulation surfacesIs characterized by a normal vector of (c),n x 、n y 、n z respectively the normal vectornThe components in the directions of the respective coordinate axes,U=(u,v,w) nas the absolute velocity of the fluid,u、v、wat each coordinate respectively the speedComponent values in the axial direction;c i 、h i 、D i respectively is each component in the mixed gasiMass fraction of (c) a specific enthalpy value and a mass diffusion coefficient,i=1,2,…,ns（nsfor the total number of mixed gas components),ρ、p、Tthe density, the pressure and the temperature of the mixed gas are respectively,Hfor the total enthalpy of the mixed gas,κfor the heat conductivity of the mixed gas,w i is a constituent elementiIs generated by chemical reaction of (a) and (b).
In addition, in the case of the optical fiber,τ ij as a tensor of the viscous stress,τ xx 、τ yy 、τ zz 、τ xy 、τ xz 、τ yz each component value of the viscous stress tensor, respectively, andu j τ ij satisfy the following requirements
(13)
In the middle ofμIn order to achieve a coefficient of viscosity of the mixed gas,u、v、wrespectively Cartesian coordinate systemsx、y、zVelocity component values in three coordinate directions.
Unlike the molecular theory based on thermodynamic temperature model assumption, the energy system parameters of the mixed gas are calculated by adopting the improved fitting approximation method in the steps S3 and S4, and the specific correlation is that
(14)
In the middle ofu、v、wThe component values of the velocity in the directions of the respective coordinate axes,ρ、p、eandhthe density, pressure, total specific internal energy and enthalpy of the mixed gas are respectively obtained.
In addition, the total ratio internal energy of the mixed gaseSum enthalpy valuehAnd each component elementiSpecific internal energy of (2)e i And specific enthalpy valueh i The relation is that
(15)
Wherein the method comprises the steps ofc i 、e i 、h i Respectively is each component in the mixed gasiMass fraction, specific internal energy value and specific enthalpy value,i=1,2,…,ns（nstotal number of mixed gas components).e i Andh i the fitting polynomial coefficient sets described based on steps S3 and S4 are calculated using equations (8), (9) and (10), respectively.
Finally, performing discrete and iterative solution by adopting an LU-SGS numerical format aiming at a chemical unbalanced flow control equation (11), and considering flow field calculation convergence when the average residual tends to be stable or reaches the maximum iterative step number, thereby obtaining various parameters of the chemical unbalanced steady flow, such as wall pressure distribution value, wall heat flow distribution value and the like. The LU-SGS numerical iteration format may be expressed as
(16)
Middle and upper marknRespectively representing the calculation time, representing the intermediate calculation amount,Ris the right-hand end item of the pen,L、D、Uthe lower triangular matrix, the diagonal matrix and the upper triangular matrix are respectively deltaQ * For temporary conservation quantity increment, deltaQ n Is at presentnThe conservation amount calculated at the moment is increased.
Example 2
This example is based on example 1:
the embodiment provides an improved method for a thermodynamic equilibrium energy system of a chemical unbalanced gas, which is used for calculating thermodynamic equilibrium energy parameters of common air components. Specifically, the original Chemkin fitting method and related polynomial coefficient references "Gupta R N, yos J M, thompson R A, et al A Review of Reaction Rates and Thermodynamic and Transport Properties for an-Species Air Model for Chemical and Thermal Nonequilibrium Calculations to 30000K, NASA Sti/recon Technical Report N; 1990.doi: 10.1210/jc.2005-0784.", molecular dynamics theory method reference "Hao Jiaao. Modeling study of hypersonic thermochemical unbalanced coupling effect. Doctor's articles, beijing aviation aerospace university, 2018: 25-34". And respectively calculating the specific heat capacity and the specific internal energy value of the common air component by adopting the two methods in a temperature interval of 50-30000K, and outputting a group of data at each interval of 100K.
Fig. 1 shows a change curve of the specific heat value of the oxygen component calculated by the original Chemkin fitting method and the molecular dynamics theory method. It can be seen that the difference between the specific heat value calculated by the original Chemkin fitting method and the calculated value of the molecular dynamics theory method is very large in the low temperature region and the high temperature region, especially in the low temperature region of 0-300K, the calculated value distribution of the original Chemkin fitting method completely violates the real physical mechanism, so that the coefficient correction is very necessary for the original Chemkin fitting method.
Fig. 2 shows the internal energy value change curve of the oxygen component calculated by the original Chemkin fitting method and the molecular dynamics theory method. It can be seen that the internal energy value calculated by the original Chemkin fitting method has a significant difference from the molecular motion theory method calculated value, and the difference is particularly significant in low and high temperature regions, so that coefficient correction is very necessary for the original Chemkin fitting method.
The specific heat value calculated by the improved method is compared with the calculated value of the molecular dynamics theory method as shown in fig. 4. It can be seen that the specific heat value change curve calculated by the improved method provided by the invention completely coincides with the molecular dynamics theory method calculation curve, and the consistency of the improved method and the molecular dynamics theory method is proved.
The internal energy value calculated by the improved method is compared with the calculated value of the molecular dynamics theory method as shown in fig. 5. It can be seen that the internal energy value change curve calculated by the improved method provided by the invention is completely coincident with the molecular dynamics theory method calculation curve, so that the consistency of the improved method and the molecular dynamics theory method is further proved, and the effectiveness of the improved method is also shown.
Example 3
This example is based on example 1:
the embodiment provides an improved method of a thermodynamic equilibrium energy system of chemical unbalanced gas, which is applied to a thermodynamic single-temperature model solver and is used for carrying out chemical unbalanced flow simulation based on HEG shock tunnel cylindrical model experimental conditions. Specifically, computational models and experimental condition references "Hannesmann K.," High Enthalpy Flows in the HEG Shock Tunnel: experiment and Numerical Rebuilding, AIAA 2003-0978, 41st Aerospace Sciences Meeting and Exhibit 6-9 January 2003, reno, nevada, 2003:1-18". Numerical simulation using a thermodynamic single temperature 5 component Dunn-Kang chemistry model, selecting Steger format and Minmod limiter for convection flux, CFL number 200, wall boundary isothermal complete non-catalytic condition (wall temperature)T w =300K), single-core serial iteration steps 10000 steps.
FIG. 6 shows the comparison of the wall pressure distribution curves calculated after the improvement of the fitting method in the cylindrical standard model example of the HEG wind tunnel test. It can be seen that the simulation results of the chemical unbalanced flow field using the original Chemkin fitting approximation method and the simulation results using the molecular dynamics theory method are already nearly coincident, proving the effectiveness and reliability of the improved method.
Fig. 7 shows a comparison of the wall heat flux density distribution calculated after the fitting method is improved by the cylindrical standard model example of the HEG wind tunnel test. It can be seen that the simulation results of the chemical unbalanced flow field using the original Chemkin fitting approximation method and the simulation results using the molecular dynamics theory method are already nearly coincident, proving the effectiveness and reliability of the improved method.
It should be noted that, for the sake of simplicity of description, the foregoing method embodiments are expressed as a series of combinations of actions, but it should be understood by those skilled in the art that the present application is not limited by the order of actions described, as some steps may be performed in other order or simultaneously according to the present application. Further, those skilled in the art will also appreciate that the embodiments described in the specification are all preferred embodiments, and that the acts and modules referred to are not necessarily required in the present application.
Claims (6)
1. A method for improving a thermodynamic equilibrium energy system for a chemically unbalanced gas, comprising:
thermodynamic energy parameter calculation sampling: calculating thermodynamic energy parameters of each air component by adopting a molecular dynamic theory method based on a thermodynamic temperature model to obtain specific heat and internal energy value distribution;
dividing the temperature interval by segment fitting: dividing temperature intervals applicable to the first-stage and second-stage classification functions of the Chemkin fitting method again according to thermodynamic energy parameter distribution characteristics of each air component, and establishing a non-uniform segmentation fitting form;
reconstructing a piecewise fitting polynomial coefficient: the specific heat and internal energy values calculated by a molecular dynamic theory method are used as interpolation template data, and a mathematical approximation method is adopted to reconstruct the piecewise fitting polynomial coefficients of each air component, so as to obtain an improved and corrected piecewise fitting polynomial model and coefficient sets thereof;
and (3) calculating and correcting thermodynamic energy parameters in a low temperature region: establishing a linear calculation formula of thermodynamic energy parameters in a low-temperature region based on complete gas setting, and obtaining a calculation correction form of the thermodynamic energy parameters in the low-temperature region outside a temperature range where a fitting polynomial is applicable;
thermodynamic equilibrium energy system improvement method application and chemical unbalanced flow field acquisition: in a thermodynamic single-temperature model solver, calculating a correction form based on the obtained piecewise fitting polynomial model and thermodynamic energy parameters of a low-temperature region, calculating thermodynamic energy parameters of mixed gas, and updating relevant parameters of a flow field in a numerical iteration process until the flow field convergence condition is met, so as to obtain final required chemical unbalanced steady-state flow parameter distribution;
in the low-temperature region thermodynamic energy parameter calculation correction, constructing a thermodynamic energy parameter calculation form of each component by adopting a linear relation in a low-temperature region lower than 50K, wherein the thermodynamic energy parameter calculation form of each component comprises:
wherein,c v,i (T)、c p,i (T) Respectively represent air components under corresponding temperature conditionsiA constant specific heat capacity value and a constant specific heat pressure value,e i (T)、h i (T) Respectively represent air components under corresponding temperature conditionsiIs a specific internal energy value and an enthalpy value,R= 8.314J/mol is a universal gas constant,M i is an air componentiIs used for the preparation of a polymer having a molecular weight of (1),Tin order to be able to determine the temperature,T const =50k is a constant temperature,h 0,i is an air componentiIs a heat of formation of (c).
2. The method for improving a thermodynamic equilibrium energy system of a chemically unbalanced gas according to claim 1, wherein in the piecewise fitting polynomial coefficient reconstruction, first 5 coefficients of a fitting polynomial are constructed by taking specific heat calculated by a molecular dynamics theory method as a core interpolation objecta 1 ~a 5 Then the last coefficient of the fitting polynomial is determined by taking the internal energy value calculated by the molecular dynamics theory method as a referencea 6 。
3. The method for improving a thermodynamic equilibrium energy system of a chemically unbalanced gas according to claim 1, wherein in the application of the thermodynamic equilibrium energy system improving method and the acquisition of a chemically unbalanced flow field, discrete and iterative solutions are performed by adopting an LU-SGS numerical format for a chemically unbalanced flow control equation, and when an average residual tends to be stable or reaches a maximum number of iterative steps, flow field calculation is regarded as convergence, thereby obtaining a chemically unbalanced steady-state flow parameter.
4. A system for improving a thermodynamic equilibrium energy system for a chemically unbalanced gas, comprising:
the thermodynamic energy parameter calculation sampling module is configured to calculate thermodynamic energy parameters of each air component by adopting a molecular dynamic theory method based on a thermodynamic temperature model to obtain specific heat and internal energy value distribution;
the piecewise fitting temperature interval repartitioning module is configured to repartition the temperature interval applicable to the first stage and the second stage of the piecewise function of the Chemkin fitting method according to the thermodynamic energy parameter distribution characteristics of each air component, and establish a non-uniform piecewise fitting form;
the piecewise fitting polynomial coefficient reconstruction module is configured to calculate specific heat and internal energy values obtained by the sampling module according to the thermodynamic energy parameters to be interpolation template data, reconstruct piecewise fitting polynomial coefficients of each air component by adopting a mathematical approximation method, and obtain an improved and corrected piecewise fitting polynomial model and coefficient sets thereof;
the low-temperature region thermodynamic energy parameter calculation and correction module is configured to establish a linear calculation formula of the low-temperature region thermodynamic energy parameter based on complete gas setting, and obtain a low-temperature region thermodynamic energy parameter calculation form outside a fitting polynomial applicable temperature range;
the thermodynamic equilibrium energy system improvement method comprises the steps of applying and a chemical unbalanced flow field acquisition module, wherein the thermodynamic equilibrium energy system improvement method is configured to obtain final required chemical unbalanced steady-state flow parameter distribution in a thermodynamic single-temperature model solver based on a piecewise fitting polynomial model obtained by the piecewise fitting polynomial coefficient reconstruction module and a thermodynamic energy parameter calculation and correction form of a low-temperature region obtained by the thermodynamic energy parameter calculation and correction module, calculate thermodynamic energy parameters of mixed gas, and update relevant parameters of the flow field in a numerical iteration process until flow field convergence conditions are met;
the thermodynamic energy parameter calculation and correction module of the low temperature region adopts a linear relation to construct a thermodynamic energy parameter calculation form of each component for the low temperature region lower than 50K, and the thermodynamic energy parameter calculation form of each component comprises:
wherein,c v,i (T)、c p,i (T) Respectively represent air under corresponding temperature conditionsComponent elementiA constant specific heat capacity value and a constant specific heat pressure value,e i (T)、h i (T) Respectively represent air components under corresponding temperature conditionsiIs a specific internal energy value and an enthalpy value,R= 8.314J/mol is a universal gas constant,M i is an air componentiIs used for the preparation of a polymer having a molecular weight of (1),Tin order to be able to determine the temperature,T const =50k is a constant temperature,h 0,i is an air componentiIs a heat of formation of (c).
5. The system of claim 4, wherein the piecewise fitting polynomial coefficient reconstruction module constructs the first 5 coefficients of the fitting polynomial using the specific heat obtained by the thermodynamic energy parameter calculation module as a core interpolation objecta 1 ~a 5 Determining the last coefficient of the fitting polynomial by taking the internal energy value obtained by the thermodynamic energy parameter calculation module as a referencea 6 。
6. The system of claim 4, wherein the application of the thermodynamic equilibrium energy system improvement method and the chemical imbalance flow field acquisition module perform discrete and iterative solution on the chemical imbalance flow control equation in LU-SGS numerical format, and consider the flow field calculation convergence when the average residual tends to be stable or the maximum number of iterative steps is reached, thereby obtaining the chemical imbalance steady-state flow parameters.
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