A chemical nonequilibrium partitioning method based on local Damkolle numbers

Abstract

This invention discloses a chemical nonequilibrium partitioning method based on local Damcole numbers, comprising: S1. Selecting a characteristic length according to the flow field characteristics; S2. Calculating the chemical reaction rate; S3. Calculating the equilibrium components of each component under isochoric and adiabatic reaction conditions using the local thermodynamic physical density and static enthalpy of the flow field; S4. Establishing a local Damcole number that quantifies the relative size of chemical reactions and flow scales; S5. Quantifying the degree of chemical nonequilibrium at different locations in the flow field based on the local Damcole number, thereby establishing a partitioning criterion to divide the flow field into equilibrium, freezing, and nonequilibrium regions; S6. Obtaining a unified dimensionless governing equation system that includes the degree of chemical nonequilibrium based on the local Damcole number.

Description

Technical Field

[0001] This invention relates to the field of hypersonic flow analysis in the aerospace industry, and in particular to a chemical nonequilibrium partitioning method based on local Darmco numbers. Background Technology

[0002] In recent years, aircraft have transitioned from subsonic and supersonic flight to hypersonic flight, with a trend towards integrated air and space operations. Trans-domain extreme flight presents new challenges and fundamental scientific questions for mechanics, particularly regarding the impact of high temperatures on aircraft surface thermal protection under extreme environments. In addition to employing more heat-resistant surface materials, predicting surface thermal loads using theoretical or numerical simulation methods is essential in the design of hypersonic vehicles. Accurate prediction of the hypersonic thermal environment requires considering the high-temperature real gas effect of the incoming gas, i.e., correctly calculating the internal energy level distribution and composition of the gas. The excitation of vibrational energy levels within the molecular internal energy levels and the dissociation chemical reactions of gas molecules under high-temperature environments are finite-rate processes that often fail to reach equilibrium during flow; this is known as the thermochemical non-equilibrium effect, and it is a key issue in correctly considering the high-temperature real gas effect.

[0003] Currently, when conducting theoretical analysis and numerical simulations of flows considering thermochemical nonequilibrium effects, experimentally measured thermochemical finite-rate data are typically incorporated as mass and energy generation terms into the Navier-Stokes equations (hereinafter referred to as the NS equations) describing compressible flows. These mass and energy generation source terms significantly increase the complexity of the original equations. For example, in numerical calculations, in addition to calculating the source terms themselves, the rigidity problem caused by the difference between the timescale of the thermochemical finite-rate process and the flow field's time progression must be considered, greatly increasing the computational load. Simultaneously, to accurately characterize the excitation of internal energy levels and chemical reactions, the reaction models given by reaction kinetics in recent years have become increasingly complex, further increasing the difficulty of solving the NS equations considering thermochemical nonequilibrium effects. However, when there is a significant difference between the flow timescale and the thermochemical reaction timescale, the thermochemical finite-rate process can be treated as an equilibrium or frozen state. In this case, the above problems are greatly simplified, and the computational load is comparable to that of a calorimetric complete gas. Existing numerical or experimental results show that thermochemical equilibrium or frozen states do exist within the flow field, but an effective method for quantitatively describing the intensity of thermochemical nonequilibrium effects is still lacking.

[0004] The Damkohler number (Da) is a dimensionless parameter previously used to describe the relationship between flow and thermochemical finite-rate scales. It is expressed as the ratio of the flow characteristic time (tf) to the thermochemical reaction characteristic time (tc). If Da >> 1, it corresponds to a thermochemical equilibrium state; if Da << 1, it corresponds to a thermochemical frozen state; if Da is approximately on the order of 1, it corresponds to a thermochemical non-equilibrium state. It is evident that the criterion for Da to determine non-equilibrium states is fuzzy. Furthermore, a few applications of Da are only for specific model flows, such as stagnation line flows and boundary layer flows. For general flow fields, there is a lack of quantitative expressions and related criteria for determining chemical non-equilibrium states at different local locations. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art. The main technical problems to be solved are: (1) Overcoming the shortcomings of the previous definition of Da number being vague, lacking discrimination criteria and only applicable to specific flow problems, and providing a dimensionless parameter Da for quantifying the degree of chemical nonequilibrium at various local locations of the flow field. L And give the corresponding criteria for judging balanced flow, frozen flow and non-equilibrium flow. (2) According to Da L A unified dimensionless governing equation system containing the degree of chemical nonequilibrium was obtained and used for numerical simulation; (3) Overcoming the shortcomings of previous hypersonic chemical reactive flow problems that required consideration of chemical nonequilibrium effects throughout the flow field, resulting in low computational efficiency, a method based on Da L The method of partitioning the flow field, considering chemical nonequilibrium effects only in the nonequilibrium region, improves computational efficiency. This invention provides a chemical nonequilibrium partitioning method based on the local Damköhler number. It constructs a dimensionless parameter quantifying the degree of chemical nonequilibrium at various local locations in the flow field, and partitions the flow field into equilibrium, frozen, and nonequilibrium regions based on this parameter value. In the equilibrium and frozen regions, a reaction model with lower computational cost is used, thereby simplifying calculations and improving efficiency.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] A chemical nonequilibrium partitioning method based on local Damkolle numbers includes:

[0008] S1. Select the characteristic length L based on the flow field characteristics. The characteristic length L reflects the dimensions of the aircraft's shape, including the cylinder radius in a cylindrical shape and the plate length in a blunt plate shape.

[0009] S2. Calculating chemical reaction rates Given by the Arrhenius formula, as in equations (1)-(2), where M i C is the molar mass of component i. iThe concentration is expressed as a molar mass concentration. Other quantities of the reaction are given by Gupta's experimental data, including the stoichiometric coefficient v and the forward and reverse reaction coefficients k. f and k b The superscript · represents the generation rate per unit time, the subscripts i and j represent the component and reaction code, and ns is the total number of components involved in the chemical reaction.

[0010]

[0011] S3. Calculate the equilibrium composition Y of each component under isochoric and adiabatic reaction conditions using the local thermodynamic physical quantity density ρ and static enthalpy h of the flow field. i,eq ;

[0012] S4. Establish the local Darmque number Da, which relates the quantitative chemical reaction to the relative size of the flow scale. L Give the local Darmck-Köhler number Da for component i. L,i The expression, as shown in equation (3), Da L,i Preserving information about the flow characteristics over time t f With the characteristic time t of chemical reaction c The original definition of t c,i The chemical reaction characteristic time of component i is given; by splitting component i, equations (4)-(5) are obtained; where u s Let be the local velocity along the streamline direction of the analyzed flow field; in a rectangular coordinate system, u and v are the velocities in the x and y directions, respectively; m is a constant defining the equilibrium condition, when the mass fraction of the component Y... i With equilibrium component mass fraction Y i,eq When the difference is less than 5%, the reaction is considered to have reached equilibrium, that is, when Y... i <Y i,eq When m = 0.95; when Y i >Y i,eq When m = 1.05; ε is a small constant introduced to avoid singularity, and is fixed at 1e-11;

[0013]

[0014] S5. According to Da L,i The degree of chemical nonequilibrium at different locations in the flow field is quantified, and a zoning discrimination criterion is established to divide the flow field into equilibrium, freezing, and nonequilibrium regions. When defining the discrimination criterion, the oxygen atomic composition is taken as the standard, as shown in equation (6).

[0015] Da L =Da L,O (6)

[0016] According to Da LThe partitioning criteria for the chemical equilibrium zone, freezing zone, and non-equilibrium zone are obtained as shown in equation (7); the two criteria of 2500 and 0.1 make the fluid in the chemical equilibrium zone move at u s The time required for the flow rate to flow through the characteristic length L is at least 10 times the time required for the local components to reach chemical equilibrium under isochoric and adiabatic conditions; in the chemically frozen zone, the latter is at least 10 times the former.

[0017]

[0018] S6. According to Da L A unified system of dimensionless governing equations, encompassing the degree of chemical nonequilibrium, was obtained and used for numerical simulations.

[0019] Furthermore, in step S1, when defining the chemical equilibrium state, the smaller L is, the shorter the distance required for the local components of the chemical equilibrium state to achieve reaction equilibrium; when defining the frozen state, the larger L is, the longer the distance required for the local components of the chemically frozen state to remain unaffected by the chemical reaction.

[0020] Furthermore, in step S3, the equilibrium component Y i,eq The system of algebraic equations is obtained by iteratively solving the system of equations, where i is the component symbol; the iterative equations are shown in equations (8)-(14), where K eq,j The chemical equilibrium constant represents the reaction; j is the symbol for the reaction equation, given by Gupta's experimental data; r is the mass ratio of oxygen to nitrogen, which for Earth's atmosphere is approximately 0.23 / 0.77 = 0.2987. Equation (9) gives the specific expression for the equivalent isobaric specific heat of component i, where These represent the translational energy, rotational energy, vibrational energy, electronic energy, and zero-point energy density corresponding to component i, respectively. i Let Y be the molar mass of component i; given by statistical thermodynamics, where T is the local ambient temperature of the flow field; upon convergence, the equilibrium component Y under isochoric and adiabatic reaction conditions is obtained. i,eq h is the local static enthalpy of the flow field; R0 is the gas constant, taken as 8.314 J / (mol·K);

[0021]

[0022]

[0023] Furthermore, the dimensionless equations in step S6 are as shown in equations (15)-(19); equation (20) gives the specific dimensionless method, where the superscript "^" represents a dimensionless physical quantity and the subscript ∞ represents the incoming flow physical quantity; in numerical calculations, if based on Da L If the corresponding grid belongs to the chemical equilibrium region or the freezing region, then the grid containing Da is omitted. L Items;

[0024]

[0025] In the above formula, ρ is the local thermodynamic physical quantity density of the flow field, u is the velocity vector, and Y is the velocity vector. i Y represents the mass fraction of component i. i,eq To balance the mass fraction of the components, D i Let u be the diffusion coefficient of component i, D be the mass-average diffusion coefficient of the component, and u be the diffusion coefficient of component i. s Da represents the local velocity along the streamline direction in the flow field. L,i Let m be the local Darmck-Köhler number of component i, m be the constant defining the equilibrium condition, L be the characteristic length, P be the pressure, τ be the Stokes viscous stress tensor, and H be the local Darmck-Köhler number of component i. sen h i These are the sensible enthalpy density and the static enthalpy of component i, respectively, k. tr k v T represents the thermal conductivity at translational, rotational, and vibrational temperatures, respectively. tr The rotational temperature, i.e., the ambient temperature, is T. v This refers to the vibration temperature corresponding to the Park two-temperature model; both are dimensionless and similar. 0,i Let E be the zero-point energy of component i. v and e v,i These are the total vibrational energy density and the vibrational energy density corresponding to component i, respectively. v,i The characteristic time of energy transfer between the translational-rotational-vibrational energy levels is determined according to the Landau-Teller model; Re, Sr, and Pr are the Reynolds number, Schmidt number, and Prandtl number, respectively, as shown in Equation (20).

[0026] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the chemical non-equilibrium partitioning method based on local Darmquerel numbers.

[0027] The present invention also provides a computer-readable storage medium having a computer program stored thereon, characterized in that, when the computer program is executed by a processor, it implements the steps of the chemical non-equilibrium partitioning method based on the local Darmquerel number.

[0028] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0029] 1. Precise quantification of the degree of chemical nonequilibrium: The local Darmck-Köhler number (Da) proposed in this invention... L This method can accurately quantify the degree of chemical nonequilibrium at various local locations in the flow field, overcoming the shortcomings of traditional Darmck-Köhler numbers, such as vague definitions, unclear discrimination criteria, and applicability only to specific flow problems. LIt has a clear physical meaning and is applicable to different local locations in the entire flow field, thus expanding its application range.

[0030] 2. Simplify numerical simulation complexity: By explicitly introducing Da into the compressible Navier-Stokes equations L This invention establishes a unified governing equation system that incorporates the degree of chemical nonequilibrium. This method can intuitively determine the influence of chemical relaxation source terms in the equations, simplifying theoretical analysis and making the calculation of complex thermochemical nonequilibrium effects more systematic and reasonable.

[0031] 3. Partitioning improves computational efficiency: Based on Da L The chemical partitioning method divides the flow field into equilibrium, freezing, and non-equilibrium regions. Within the equilibrium and freezing regions, this invention employs a reaction model with lower computational complexity, thereby significantly reducing computational redundancy in numerical simulations of chemical non-equilibrium flow, substantially improving computational efficiency, and ensuring the accuracy of the results.

[0032] 4. Enhanced prediction capability of high-temperature gas effects: The method of this invention improves the prediction accuracy of the real effects of high-temperature gas in hypersonic flow, providing a more reliable numerical simulation tool for the design and optimization of hypersonic vehicles. In particular, under high-temperature conditions, it can more accurately predict the thermal load on the surface of the vehicle.

[0033] 5. Expanding the scope of application: This invention is not only applicable to specific model flows, such as stagnation line flows and boundary layer flows, but also to a wider range of general flow field analyses. It improves the ability to handle chemical reactions in hypersonic flow problems and has strong universality and application prospects.

[0034] These advantages make this invention valuable for applications in hypersonic flow analysis and numerical simulation, significantly improving simulation accuracy and computational efficiency. Attached Figure Description

[0035] Figure 1 This is a flowchart illustrating the method of the present invention.

[0036] Figure 2 This section describes the external shape and operating conditions used in the calculation of specific embodiments.

[0037] Figure 3 This is a schematic diagram of the computational grid, with the horizontal and vertical axes representing spatial coordinates, and the total grid size is 601*151.

[0038] Figure 4 It is the Da obtained within the computational grid. L The distribution cloud map shows that the boundaries for determining the chemically frozen zone and the equilibrium zone are 0.1 and 2500, respectively.

[0039] Figure 5a and Figure 5b The results obtained along the normal direction at position x = 1m are presented, comparing the results obtained by applying chemical partitioning and considering non-equilibrium effects only in the chemical non-equilibrium region with the results obtained by considering chemical non-equilibrium effects throughout the entire flow field without partitioning. Figure 5a The comparison is based on ambient temperature; Figure 5b The comparison is between the mass fractions of oxygen and nitrogen atoms, with the left and right vertical axes representing oxygen and nitrogen atoms, respectively.

[0040] Figure 6 This is a comparison chart of the computational models used in different regions after adopting chemical partitioning. Black represents the computational models for chemical freezing and equilibrium regions, red represents the additional computational terms required for non-equilibrium models, and blue represents the implicit special treatment for reaction source terms required to eliminate the multi-scale rigidity problem caused by flow and chemical reaction after considering the chemical non-equilibrium effect. Detailed Implementation

[0041] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the present invention and are not intended to limit the present invention.

[0042] like Figure 1 The following is a flowchart illustrating the chemical nonequilibrium partitioning method based on local Darmco numbers provided in this embodiment:

[0043] S1. Select the characteristic length L based on the flow field characteristics;

[0044] L needs to reflect the key dimensions of the aircraft's shape or the researchers' focus, such as the cylinder radius in a cylindrical shape or the plate length in a blunt plate shape. When defining a chemical equilibrium state, the smaller L is, the more stringent the requirements for the chemical equilibrium state, that is, requiring local components to achieve reaction equilibrium over a shorter distance; when defining a frozen state, the larger L is, the more stringent the requirements for the chemical frozen state, that is, requiring components to remain largely unchanged by chemical reactions over a longer distance.

[0045] S2. Calculating chemical reaction rates

[0046] The calculation formula is given by the Arrhenius formula, as shown in equations (1)-(2), where M i C is the molar mass of component i. i The concentration is expressed as a molar mass concentration. Other quantities of the reaction are given by Gupta's experimental data, including the stoichiometric coefficient v and the forward and reverse reaction coefficients k. f and k b The superscript · represents the generation rate per unit time, the subscripts i and j represent the component and reaction code, and ns is the total number of components involved in the chemical reaction.

[0047]

[0048]

[0049] S3. Calculate the equilibrium composition Y of each component under isochoric and adiabatic reaction conditions using the local thermodynamic physical quantity density ρ and static enthalpy h of the flow field. i,eq These reaction conditions represent the actual reaction environment in most areas of hypersonic flow, except for a small region within the boundary layer.

[0050] Equilibrium component Y i,eq The algebraic equations are obtained by iteratively solving the system of equations, where i is the component symbol; taking a common 5-component reaction model as an example, the iterative equations (3)-(8) are given, where K eq,j The chemical equilibrium constant represents the reaction; j is the symbol for the reaction equation, given by Gupta's experimental data; r is the mass ratio of oxygen to nitrogen, which for Earth's atmosphere is approximately 0.23 / 0.77 = 0.2987. Equation (9) gives the specific expression for the equivalent isobaric specific heat of component i, where Let represent the translational kinetic energy, rotational energy, vibrational energy, electronic energy, and zero-point energy density corresponding to component i, respectively, given by statistical thermodynamics. T is the local ambient temperature of the flow field. The iterative process requires approximately 10 steps, and upon convergence, the equilibrium component Y under isochoric and adiabatic reaction conditions is obtained. i,eq h is the local static enthalpy of the flow field; R0 is the gas constant, taken as 8.314 J / (mol·K).

[0051]

[0052] M is the molar mass of O2. O M is the molar mass of oxygen. N M is the molar mass of element N. NO The molar mass of a NO molecule is... Let N be the molar mass of N2.

[0053] S4. Establish the local Darmque number Da, which relates the quantitative chemical reaction to the relative size of the flow scale. L Give the local Darmck-Köhler number Da for component i. L,i The expression, as in equation (10), Da L,i Preserving information about the flow characteristics over time t f With the characteristic time t of chemical reaction c The original definition of t c,i The chemical reaction characteristic time of component i is given; by splitting component i, equations (11)-(12) are obtained; where u sLet be the local velocity along the streamline direction of the analyzed flow field; in a rectangular coordinate system, v and y are the velocities in the x and y directions, respectively; m is a constant defining the equilibrium condition, when the mass fraction of the component Y i With equilibrium component mass fraction Y i,eq When the difference is less than 5%, the reaction is considered to have reached equilibrium. i <Y i,eq When m = 0.95; when Y i >Y i,eq When m = 1.05; ε is a small constant introduced to avoid singularity, and is fixed at 1e-11;

[0054]

[0055] S5. According to Da L,i The degree of chemical nonequilibrium at different locations in the flow field is quantified, thereby establishing a zoning criterion to divide the flow field into equilibrium, freezing, and nonequilibrium zones. Due to the mutual influence between components in the dissociation and recombination-related reactions occurring when air is heated, the characteristic chemical reaction times t for different components are ultimately determined. c,i When defining the judgment criteria, one of the components is taken as the standard, and in practice, oxygen atoms are taken as the standard, as in equation (13).

[0056] Da L =Da L,O (13)

[0057] According to Da L The partitioning criteria for the chemical equilibrium zone, freezing zone, and non-equilibrium zone are obtained as shown in equation (14); the two criteria of 2500 and 0.1 make the fluid in the chemical equilibrium zone move at u s The time required for the flow rate to flow through the characteristic length L is at least 10 times the time required for the local components to reach chemical equilibrium under isochoric and adiabatic conditions; in the chemically frozen zone, the latter is at least 10 times the former.

[0058]

[0059] S6. According to Da L A unified dimensionless governing equation system incorporating chemical nonequilibrium was obtained and used for numerical simulation. Examples include equations (15)-(19); equation (20) provides the specific dimensionless method, where the superscript "^" represents a dimensionless physical quantity and the subscript ∞ represents the incoming flow physical quantity. In numerical calculations, if based on Da... L If the corresponding grid belongs to the chemical equilibrium region or the freezing region, then the grid containing Da is omitted. L The implicit advancement scheme omits the source term Jacobian matrix and its determinant calculations required to solve the rigid problem of multi-scale nonlinear systems, which significantly improves the solution efficiency.

[0060]

[0061]

[0062] In the above formula, ρ is the local thermodynamic physical quantity density of the flow field, u is the velocity vector, and Y is the velocity vector. i Y represents the mass fraction of component i. i,eq To balance the mass fraction of the components, D i Let y be the diffusion coefficient of component i, D be the mass-average diffusion coefficient of the component, and y be the diffusion coefficient of component i. s Da represents the local velocity along the streamline direction in the flow field. L,i Let m be the local Darmck-Köhler number of component i, m be the constant defining the equilibrium condition, L be the characteristic length, P be the pressure, τ be the Stokes viscous stress tensor, and H be the local Darmck-Köhler number of component i. sen h i These are the sensible enthalpy density and the static enthalpy of component i, respectively, k. tr k v T represents the thermal conductivity at translational, rotational, and vibrational temperatures, respectively. tr The rotational temperature, i.e., the ambient temperature, is T. v e represents the vibrational temperature under the Park two-temperature model; both are dimensionless and similar in their approach. 0,i Let E be the zero-point energy of component i. v and e v,i These are the total vibrational energy density and the vibrational energy density corresponding to component i, respectively. v,i Let Re be the characteristic time of energy transfer between the translational-rotational and vibrational energy levels as determined by the Landau-Teller model. Re, Sc, and Pr are the Reynolds number, Schmidt number, and Prandtl number, respectively, as detailed in Equation (20).

[0063] Specifically, blunt-nosed flat plates are a typical shape in hypersonic vehicles, commonly found in configurations such as the leading edge of a waverider and the wing of a space shuttle. The following, with reference to the accompanying drawings, uses this model flow as an example to further explain in detail the specific process of partitioning the flow field into chemically non-equilibrium states using local Damköhler numbers and performing numerical calculations. It should be understood that the specific embodiments described herein are only for explaining the invention and are not intended to limit the invention.

[0064] Figure 2 A schematic diagram of a flow around a blunt plate is given, with a head radius of 0.1m, a blunt plate length of 1m, an incoming flow angle of attack of 0 degrees, an incoming flow of Mach number 15, and an upper-level airflow 30km above the ground. It is assumed that the proportions of oxygen and nitrogen in the flow are 23% and 77%, respectively. Figure 3A schematic diagram of the mesh used in the numerical calculations is provided. For ease of illustration, the flow-direction and normal meshes were thinned by a factor of 5 and 3, respectively, resulting in a total mesh size of 601*151. Symmetrical boundary conditions were applied to the head symmetry plane, inflow boundary conditions were applied to the upper boundary, the lower wall was a non-catalytic, no-slip isothermal wall with a fixed wall temperature of 350 K, and the outlet boundary was subjected to second-order extrapolation conditions. In the numerical calculations, the convection term was obtained using the AUSMPW+ flux splitting scheme, the interfacial flux was obtained by third-order MUSCL interpolation, and the viscosity term was discretized using a fourth-order central scheme. When considering chemical nonequilibrium effects, the time propagation was performed using the LUSGS scheme; otherwise, when not considering chemical nonequilibrium effects, the time propagation was performed using a third-order Runge-Kutta explicit scheme.

[0065] Figure 4 The graph shows the distribution of the local Damcole number in the flow field, calculated according to the definition of the local Damcole number (10). The black solid line marks the location of the bow-shaped shock wave generated by the hypersonic inflow. After the shock wave, the kinetic energy of the following gas is converted into internal energy, causing an increase in ambient temperature and resulting in corresponding chemical reactions and non-equilibrium phenomena. In the graph, the black area represents the chemical equilibrium region, the dark gray area represents the chemical non-equilibrium region, and the remaining areas represent the chemical freezing region. Complex calculation steps, including chemical reaction rate calculations, only need to be considered within the dark gray area.

[0066] Here, in the numerical solution of the Navier-Stokes equations considering thermochemical nonequilibrium effects, an iterative approach with unsteady time-step progression is adopted, alternating between the calculation process of chemical partitioning and the time-step progression process. For example, every 100 time steps, the flow field is partitioned into chemical nonequilibrium regions based on the results of the current time step. Thus, in the subsequent 100 calculation steps, chemical reactions are only calculated as finite-rate processes within the chemical nonequilibrium regions, while equilibrium or freezing models, which have lower computational complexity and higher efficiency, are used for calculations in the equilibrium and freezing regions.

[0067] Figure 5a and Figure 5b A comparison diagram is presented, showing the flow field calculated using the partitioned calculation results and the original, unpartitioned results considering the chemical nonequilibrium effects throughout the entire flow field. Figure 5a This is a comparison chart along the normal direction of the calculated ambient temperature along the partitioned and unpartitioned axes at the calculation domain exit location (x = 1m). Figure 5b This is a comparison chart of the mass fractions of oxygen and nitrogen atoms at the same location, combined with... Figure 4 The partitioning results, by omitting the treatment of chemical non-equilibrium effects over large areas of the equilibrium and frozen regions, effectively improve the efficiency of numerical simulation.

[0068] Figure 6The calculation models used in the chemical equilibrium, frozen, and non-equilibrium regions are shown. The black part represents the calculation model used in the chemical frozen region. The calculation content in the chemical equilibrium region is the same as that in the frozen region, except that the equilibrium components need to be considered when calculating thermodynamic parameters and viscosity coefficients. These are obtained by iterative calculation formulas (3)-(7) under isothermal and isochoric reaction conditions. Unlike the previous adiabatic conditions, which required additional consideration of the total enthalpy conservation condition, the convergence iteration step only requires about 5 steps, and the additional calculation amount is negligible. The remaining red part represents the multi-component chemical reaction rate term and multi-component diffusion term, which need to be considered in the chemical non-equilibrium region. The blue part represents the special implicit propagation treatment used to solve the rigid problem formed by the coupling of chemical and flow problems. Taking the Gupta5 component reaction model as an example, within a grid point, the calculation time of the black, red, and blue parts accounts for about 12.1%, 46.4%, and 41.5%, respectively. In this example, the balanced region and the frozen region account for approximately 35%, so overall, the computation time after adopting the partitioning algorithm is approximately 69.2% of the original.

[0069] Preferably, embodiments of this application also provide a specific implementation of an electronic device capable of implementing all steps in the chemical non-equilibrium partitioning method based on local Damköhler numbers in the above embodiments. The electronic device specifically includes the following:

[0070] Processor, memory, communications interface, and bus;

[0071] The processor, memory, and communication interface communicate with each other via a bus; the communication interface is used to realize information transmission between server-side devices, metering devices, and user-side devices.

[0072] The processor is used to call a computer program in memory, and when the processor executes the computer program, it implements all the steps in the chemical non-equilibrium partitioning method based on the local Darmquerel number in the above embodiments.

[0073] Embodiments of this application also provide a computer-readable storage medium capable of implementing all steps of the chemical non-equilibrium partitioning method based on local Damcole numbers in the above embodiments. The computer-readable storage medium stores a computer program that, when executed by a processor, implements all steps of the chemical non-equilibrium partitioning method based on local Damcole numbers in the above embodiments.

[0074] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on its differences from other embodiments. In particular, hardware + program embodiments are relatively simple in description because they are fundamentally similar to method embodiments; relevant parts can be referred to the descriptions in the method embodiments.

[0075] The foregoing has described specific embodiments of this specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired result. In some embodiments, multitasking and parallel processing are possible or may be advantageous.

[0076] While this application provides method operation steps as shown in the embodiments or flowcharts, more or fewer operation steps may be included based on conventional or non-inventive labor. The order of steps listed in the embodiments is merely one possible execution order among many and does not represent the only execution order. In actual device or client product execution, the method can be executed sequentially as shown in the embodiments or drawings, or in parallel (e.g., in a parallel processor or multi-threaded processing environment).

[0077] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0078] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0079] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0080] This invention is not limited to the embodiments described above. The above description of specific embodiments is intended to illustrate and explain the technical solutions of this invention. The specific embodiments described above are merely illustrative and not restrictive. Without departing from the spirit and scope of the claims, those skilled in the art can make many specific modifications based on the teachings of this invention, and these modifications all fall within the scope of protection of this invention.

Claims

1. A chemical nonequilibrium partitioning method based on local Damköhler numbers, characterized in that, include: S1. Select the characteristic length L based on the flow field characteristics. The characteristic length L reflects the dimensions of the aircraft's shape, including the cylinder radius in a cylindrical shape and the plate length in a blunt plate shape. S2. Calculating chemical reaction rates Given by the Arrhenius formula, as in equations (1)-(2), where M i C is the molar mass of component i. i The concentration is expressed as a molar mass concentration. Other quantities of the reaction are given by Gupta's experimental data, including the stoichiometric coefficient v and the forward and reverse reaction coefficients k. f and k b The superscript · represents the generation rate per unit time, the subscripts i and j represent the component and reaction code, and ns is the total number of components involved in the chemical reaction. S3. Calculate the equilibrium composition Y of each component under isochoric and adiabatic reaction conditions using the local thermodynamic density ρ and static enthalpy h of the flow field. i,eq ; S4. Establish the local Darmque number Da, which relates the relative magnitude of quantitative chemical reactions and flow scales. L Give the local Darmck-Köhler number Da for component i. L,i The expression, as shown in equation (3), Da L,i Preserving information about the flow characteristics over time t f With the characteristic time t of chemical reaction c The original definition of t c,i The characteristic time of the chemical reaction of component i; Decomposing component i yields equations (4)-(5); where u s Let be the local velocity along the streamline direction of the analyzed flow field; in a rectangular coordinate system, u and v are the velocities in the x and y directions, respectively; m is a constant defining the equilibrium condition, when the mass fraction of the component Y... i With equilibrium component mass fraction Y i,eq When the difference is less than 5%, the reaction is considered to have reached equilibrium. i <Y i,eq When m = 0.95; when Y i >Y i,eq When m = 1.05; ε is a small constant introduced to avoid singularity, and is fixed at 1e-11; S5. According to Da L,i The degree of chemical nonequilibrium at different locations in the flow field is quantified, and a zoning discrimination criterion is established to divide the flow field into equilibrium, freezing, and nonequilibrium regions. When defining the discrimination criterion, the oxygen atomic composition is taken as the standard, as shown in equation (6). Da L =Da L,O (6) According to Da L The partitioning criteria for the chemical equilibrium zone, freezing zone, and non-equilibrium zone are obtained as shown in equation (7); the two criteria of 2500 and 0.1 make the fluid in the chemical equilibrium zone move at u s The time required for the flow rate to flow through the characteristic length L is at least 10 times the time required for the local components to reach chemical equilibrium under isochoric and adiabatic conditions; in the chemically frozen zone, the latter is at least 10 times the former. S6. According to Da L A unified system of dimensionless governing equations, encompassing the degree of chemical nonequilibrium, was obtained and used for numerical simulations.

2. The chemical nonequilibrium partitioning method based on local Darmquerel numbers according to claim 1, characterized in that, In step S1, when defining the chemical equilibrium state, the smaller L is, the shorter the distance required for the local components of the chemical equilibrium state to achieve reaction equilibrium; when defining the frozen state, the larger L is, the longer the distance required for the local components of the chemically frozen state to be affected by the chemical reaction without significant changes.

3. The chemical nonequilibrium partitioning method based on local Darmquerel numbers according to claim 1, characterized in that, In step S3, equilibrium component Y i,eq The system of algebraic equations is obtained by iteratively solving the system of equations, where i is the component symbol; the iterative equations are shown in equations (8)-(14), where K eq,j The chemical equilibrium constant represents the reaction; j is the symbol for the reaction equation, given by Gupta's experimental data; r is the mass ratio of oxygen to nitrogen, which for Earth's atmosphere is approximately 0.23 / 0.77 = 0.2987. Equation (14) gives the specific expression for the equivalent isobaric specific heat of component i, where These represent the translational energy, rotational energy, vibrational energy, electronic energy, and zero-point energy density corresponding to component i, respectively. i Let be the molar mass of component i; given by statistical thermodynamics, where T is the local ambient temperature of the flow field; the equilibrium composition under isochoric and adiabatic reaction conditions is obtained upon convergence. Y i,eq h is the local static enthalpy of the flow field; R0 is the gas constant, taken as 8.314 J / (mol·K); 4. The chemical nonequilibrium partitioning method based on local Darmquerel numbers according to claim 1, characterized in that, In step S6, as shown in equations (15)-(19); equation (20) gives the specific dimensionless method, where the superscript "^" represents a dimensionless physical quantity and the subscript ∞ represents the incoming flow physical quantity; in numerical calculation, if according to Da L If the corresponding grid belongs to the chemical equilibrium region or the freezing region, then the grid containing Da is omitted. L Items; In the above formula, ρ is the local thermodynamic physical quantity density of the flow field, u is the velocity vector, and Y is the velocity vector. i Y represents the mass fraction of component i. i,eq To balance the mass fraction of the components, D i Let u be the diffusion coefficient of component i, D be the mass-average diffusion coefficient of the component, and u be the diffusion coefficient of component i. s Da represents the local velocity along the streamline direction in the flow field. L,i Let m be the local Darmck-Köhler number of component i, m be the constant defining the equilibrium condition, L be the characteristic length, P be the pressure, τ be the Stokes viscous stress tensor, and H be the local Darmck-Köhler number of component i. sen h i These are the sensible enthalpy density and the static enthalpy of component i, respectively, k. tr k v T represents the thermal conductivity at translational, rotational, and vibrational temperatures, respectively. tr The rotational temperature, i.e., the ambient temperature, is T. v This refers to the vibration temperature corresponding to the Park two-temperature model; both are dimensionless and similar. 0,i Let E be the zero-point energy of component i. v and e v,i These are the total vibrational energy density and the vibrational energy density corresponding to component i, respectively. v,i The characteristic time of energy transfer between the translational-rotational-vibrational energy levels is determined according to the Landau-Teller model; Re, Sc, and Pr are the Reynolds number, Schmidt number, and Prandtl number, respectively, as shown in Equation (20).

5. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the chemical nonequilibrium partitioning method based on local Darmcole numbers as described in any one of claims 1 to 4.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the steps of the chemical nonequilibrium partitioning method based on local Darmcole numbers as described in any one of claims 1 to 4.

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