A high-temperature non-equilibrium flow simulation missing component floating processing method
By floating the selection of default components and performing gas density harmonization correction in high-temperature nonequilibrium flow simulation, the numerical error caused by changes in gas component content at high temperatures is solved, thus improving the accuracy and stability of the calculation.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CALCULATION AERODYNAMICS INST CHINA AERODYNAMICS RES & DEV CENT
- Filing Date
- 2026-05-20
- Publication Date
- 2026-07-21
AI Technical Summary
In high-temperature nonequilibrium flow simulations, the method of always selecting the gas component with the highest content in the high-speed incoming flow as the default component may lead to a decrease in its content at high temperatures, introducing a large numerical error and reducing the accuracy of the calculation.
A floating selection method for default components is adopted. On each grid micro-element, the component with the largest content or the largest iterative change is selected as the default component based on the characteristics of the gas components. By matching and harmonizing the gas density, the total density is ensured to be equal to the sum of the densities of each component, thereby reducing the error.
It improves the accuracy and stability of calculations, reduces relative errors on mesh micro-elements, is applicable to various mesh types and flow control equations, and enhances the accuracy of numerical simulations.
Smart Images
Figure CN122242383B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the fields of aerodynamics and computational fluid dynamics, and in particular to a method for handling the floating of missing components in high-temperature nonequilibrium flow simulation. Background Technology
[0002] As aircraft speed increases, intense aerodynamic heating occurs in the high-speed flow field. When the flow field temperature reaches above 2500K, oxygen in the air begins to dissociate significantly, and when the temperature reaches above 4000K, nitrogen dissociates. Because these chemical reactions occur in high-speed flow, there is a non-equilibrium phenomenon of "incomplete" or "inadequate" reactions, known as the high-temperature non-equilibrium effect. The high-temperature non-equilibrium effect alters the properties of the gas mixture, thus severely impacting the aerodynamic characteristics, aerothermal characteristics, electromagnetic transmission characteristics, and target radiation characteristics of the aircraft, and has always been a crucial aspect of high-speed aircraft design and evaluation.
[0003] Due to limitations in experimental conditions and costs, numerical simulation is often used to study the high-temperature nonequilibrium effects of aircraft. Numerical solution of the high-temperature nonequilibrium flow control equations is one of the most important steps. By iteratively solving the high-temperature nonequilibrium flow control equations, which include component equations, the distribution of parameters such as flow field pressure, temperature, density, velocity, and composition can be obtained, thereby yielding the aircraft's flight performance parameters.
[0004] The governing equations for high-temperature nonequilibrium flow contain two types of mass conservation equations: one is the overall mass conservation equation, and the other is the mass conservation equation for each gas component. Since the total density of the gas is equal to the sum of the densities of each gas component, one of the mass conservation equations must be omitted during iterative solution to avoid overdetermining the equation set.
[0005] A common approach is to omit the mass conservation equation for a certain gas component (hereinafter referred to as "default component"). The advantage of this approach is that the overall mass conservation equation remains unchanged, and it can better inherit and be compatible with a complete gas system. However, since the density of the default component is obtained by subtracting the sum of the densities of other gas components from the total density, the numerical error of the default component density is equivalent to the cumulative error between the total density and the densities of other gas components (hereinafter referred to as "cumulative error"). When the default component is a trace component in the flow field, the error of the default gas component is relatively large, which affects the accuracy of the calculation.
[0006] To address this issue, engineering practice typically selects the component with the highest content in the high-speed incoming stream as a fixed default component. This means that the mass conservation equation for this gas component is consistently omitted during numerical iteration. When the cumulative error is constant, the relative error of the default component is relatively small due to its large absolute quantity, thus having a relatively minor impact on the iterative calculation.
[0007] However, for high-temperature non-equilibrium flow, in certain regions of the flow field, the most abundant gaseous component in the high-speed incoming flow may undergo extensive dissociation, ionization, and other chemical reactions at high temperatures, leading to a decrease in its content or even its reduction to trace components. In this case, if the solution to the mass conservation equation for this component is still omitted, it may introduce a large numerical error, thereby reducing the accuracy of the calculation.
[0008] To address this issue, it remains necessary to develop a more reasonable default gas density handling method. Summary of the Invention
[0009] The purpose of this invention is to provide a method for handling the floating of missing components in high-temperature non-equilibrium flow simulation, which addresses the above-mentioned shortcomings. This method solves the problem that in the prior art, the most abundant gaseous component in a high-speed incoming flow may undergo a large number of dissociations, ionizations and other chemical reactions at high temperatures, leading to a decrease in its content or even a reduction to a trace component. This eliminates the need to solve the mass conservation equation for that component, which may introduce large numerical errors and reduce the accuracy of the calculation.
[0010] This invention is achieved through the following scheme: A method for handling missing component floating in high-temperature nonequilibrium flow simulation includes the following steps: Step 1: Establish a complete discrete framework for numerical simulation of high-temperature nonequilibrium flow; Step 2: Select the default component using a floating selection; Step 3, gas density matching; Step 4, gas density adjustment and correction; Step 5: Complete the numerical iteration of the flow equations and provide simulation results according to the requirements of numerical simulation.
[0011] Step 1 includes the following steps: Import the numerical computation grid, and discretize the complete set of high-temperature nonequilibrium flow control equations using spatial and temporal schemes to construct the basic framework for numerical iterative solution.
[0012] Step 2 includes the following steps: In the nth iteration of the numerical simulation, the gas component with the largest content or the largest change in iteration is selected as the default component of each grid element; n=1,2,3,……,Nmax; Nmax is the maximum number of iteration steps, which is set according to the simulation requirements.
[0013] Step 3 includes the following steps: By combining the default components, the gas density on each grid element is adjusted so that it satisfies the physical constraint that "the total density of the gas is equal to the sum of the densities of each gas component" after the nth iteration.
[0014] Step 4 includes the following steps: For each grid element, the gas component density is harmonized and corrected based on the default component characteristics of its neighboring grid elements to reduce the impact of differences in solving the mass conservation equation among the grid elements.
[0015] Step 3 specifically includes the following steps: Step 3.1, estimation:
[0016] Step 3.2, Calibration:
[0017] here and These are the densities obtained from the nth iteration of the gas total density mass conservation equation and the s-th gas component density mass conservation equation, respectively. Estimate the density of the s-th gas component; and The total density and the corrected density of the s-th gas component are obtained in the nth iteration calculation; This summation is performed over all non-default components; N is the number of gaseous components. and These are the density obtained from the nth iteration of the density-mass conservation equation for the i-th gas component and the estimated density of the i-th gas component, respectively. To sum over all components, This is a function that takes a larger value.
[0018] Step 4 specifically includes the following steps: Step 4.1, determine the edge mesh element and record its edge information: For each mesh element, if the default component on its adjacent mesh elements is inconsistent with its default component, then the mesh element is an edge mesh element. Record the inconsistent default component information in array a[j], j=1,2,3,……,m; m is the total number of adjacent mesh elements with inconsistent default components, and a[j] is the default component number of the j-th mesh element; Step 4.2: For the edge mesh element, based on the default component information recorded in a[j], calculate the harmonic density of each gas component according to Step 3. ; Step 4.3: Correct the calculation of the density of each gas component on each grid element.
[0019] In step 4.3, the revised calculation formula is as follows:
[0020] here is the harmonic coefficient, with a value range of [0.5, 1].
[0021] In step 1, the computational grid includes a high-speed flow simulation grid consisting of a structured grid, an unstructured grid, or a structured-unstructured hybrid grid. The flow field of the aircraft is divided into thousands of grid micro-elements by the grid, and the flow control equations are discretized on the grid micro-elements.
[0022] The flow control equations in step 1 include chemical nonequilibrium flow control equations and thermochemical nonequilibrium flow control equations; Spatial formats include windward or centrally discrete formats; Time formats include explicit or implicit discrete time formats.
[0023] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: 1. This method can effectively take into account the differences in gas composition in different regions of the flow field, reduce the relative error on each grid element, and achieve high accuracy and good stability in numerical simulation.
[0024] 2. The overall mass conservation equation remains unchanged in this method, which can better inherit and be compatible with complete gas systems; 3. This method avoids the large numerical errors that may be introduced by the traditional fixed default component method by "floating selection of default components".
[0025] 4. This method improves numerical stability by reducing the impact of differences in the mass conservation equations solved by different grid elements through gas density harmonization correction.
[0026] 5. This method has a wide range of applications. The computational grids include, but are not limited to, common high-speed flow simulation grids such as structured grids, unstructured grids, or structured-unstructured hybrid grids. The flow control equations involved include, but are not limited to, chemical nonequilibrium flow control equations and thermochemical nonequilibrium flow control equations. The spatial formats involved include, but are not limited to, various upwind or center-discretion formats. The temporal formats involved include, but are not limited to, various explicit or implicit time-discretion formats. Attached Figure Description
[0027] Figure 1 This is a schematic diagram of the flowchart of the present invention; Figure 2 The nitrogen mass fraction distribution in the flow field at the nose of an aircraft is shown in the traditional coupled simulation method. Figure 3 This is a nitrogen mass fraction distribution diagram of the flow field at the nose of an aircraft, which is the result of the coupled simulation method of this invention. Detailed Implementation
[0028] All features disclosed in this specification, or all steps in all disclosed methods or processes, may be combined in any way, except for mutually exclusive features and / or steps.
[0029] Any feature disclosed in this specification (including any appended claims and abstract) may be replaced by other equivalent or similar features, unless specifically stated otherwise. That is, unless specifically stated otherwise, each feature is merely one example of a series of equivalent or similar features.
[0030] Example 1 like Figure 1 As shown, the present invention provides a technical solution: A method for handling default components in high-temperature non-equilibrium flow simulation: This method first meshes the flow field of the aircraft to construct a complete discrete framework for high-temperature non-equilibrium flow numerical simulation, including but not limited to the numerical discretization of the total mass conservation equation and the mass conservation equations of each gas component; then, during the numerical iteration process, based on the gas component characteristics on each grid micro-element, a default component is selected by floating to complete the gas density matching on each grid micro-element; finally, gas density harmonization is performed to complete the numerical simulation.
[0031] Specifically, it includes the following steps: Step 1: Establish a complete discretization framework for high-temperature nonequilibrium flow numerical simulation: Import the numerical computation grid, discretize the complete set of high-temperature nonequilibrium flow control equations (including but not limited to the total density mass conservation equation and the density mass conservation equations of each gas component) using spatial and temporal schemes, and construct the basic framework for numerical iterative solution.
[0032] Step-by-step instructions: Numerical iterative solution of the control equations for high-temperature nonequilibrium flow is one of the most commonly used methods for numerical simulation of high-speed "real gas" flow fields in aircraft. Its basic principles and iterative solution framework are described in detail in many published documents, so they will not be repeated here.
[0033] The computational grids involved in this invention include, but are not limited to, common high-speed flow simulation grids such as structured grids, unstructured grids, or structured-unstructured hybrid grids. The flow field of an aircraft is divided into tens of thousands of micro-elements, and the flow control equations are discretized on these micro-elements. The flow control equations involved include, but are not limited to, chemical nonequilibrium flow control equations and thermochemical nonequilibrium flow control equations. The spatial formats involved include, but are not limited to, various upwind or center-discretion formats. The temporal formats involved include, but are not limited to, various explicit or implicit time-discretion formats. The above-mentioned grids, equations, and formats are described in detail in many published documents and will not be elaborated upon here.
[0034] It is worth noting that this invention requires a "complete" set of governing equations for high-temperature non-equilibrium flow. Here, "complete" specifically means that the set of equations must include, but is not limited to, the "conservation equation for the total mass and the mass conservation equation for each gas component." Since the total density of the gas is equal to the sum of the densities of each gas component, this form of equation set is mathematically overdetermined and cannot be solved numerically directly; it must be processed.
[0035] Step 2, Selecting the default component: During the nth iteration of the numerical simulation, select the gas component with the largest content or the largest change in iteration on each grid element as the default component of that grid element; n=1,2,3,……,Nmax; Nmax is the maximum number of iterations, which can be set according to the needs of the simulation project.
[0036] This step is explained as follows: When the cumulative error is constant, the larger the absolute amount of the default gas component, the smaller its relative error, i.e., the higher the relative accuracy. Therefore, to improve calculation accuracy, the component with the highest content should be selected as the default component whenever possible.
[0037] Furthermore, since the "cumulative error" is generated in each iteration, and the total density of the gas must equal the sum of the densities of each gas component before and after each iteration, this "cumulative error" is also another form of absolute error in the iteration change. When the absolute error of the iteration change is constant, the larger the iteration change of the default gas component, the smaller its relative error, the smaller the disturbance to the iteration value, and the more stable the iteration calculation. Therefore, to improve computational stability, the gas component with the largest iteration change can also be selected as the default component.
[0038] In high-temperature non-equilibrium flow, the content of each gas component will change significantly due to strong chemical reactions. The gas component with the largest content or the largest iterative change is uncertain. Therefore, this invention uses a floating selection method.
[0039] Step 3, Gas density matching: Combined with the default components, the gas density on each grid element is adjusted so that it satisfies the physical constraint that "the total density of the gas is equal to the sum of the densities of each gas component" after the nth iteration.
[0040] The specific method is as follows: Step 3.1, estimation:
[0041] Step 3.2, Calibration:
[0042] here and These are the densities obtained from the nth iteration of the gas total density mass conservation equation and the s-th gas component density mass conservation equation, respectively. Estimate the density of the s-th gas component; and The total density and the corrected density of the s-th gas component are obtained in the nth iteration calculation; and These are the density obtained from the nth iteration of the density-mass conservation equation for the i-th gas component and the estimated density of the i-th gas component, respectively. This summation is performed over all non-default components; N is the number of gaseous components. To sum over all components, This is a function that takes a larger value.
[0043] This step is explained as follows: Forecast: On each grid element, the density of the default component is not calculated from the density-mass conservation equation for that component, in order to avoid overdetermined problems in the equation system.
[0044] To satisfy the physical constraint that "the total density of a gas is equal to the sum of the densities of its components", the estimated density of the default component is obtained by subtracting the sum of the densities of the other components from the total density. To avoid numerical divergence caused by negative densities, the default component density is made non-negative (when the estimated density of the default component is negative, it is set to 0.0).
[0045] Correction: The total gas density is obtained by solving the total density mass conservation equation to ensure inheritance and compatibility with the processing methods of the complete gas model. Since the estimated densities of the default components are non-negatively processed, it is possible that "the total gas density is not equal to the sum of the densities of each gas component," thus requiring further correction. Using the correction method of this invention, the deviation caused by the non-negative processing can be proportionally distributed to each gas component, thereby avoiding large deviations in a single component.
[0046] Step 4, Gas density harmonization correction: For each grid element, the gas component density is harmonized and corrected based on the default component characteristics of its neighboring grid elements to reduce the impact of differences in solving the mass conservation equation among grid elements.
[0047] The specific method is as follows: Step 4.1: Determine the edge mesh element and record its edge information: For each mesh element, if the default component on its adjacent mesh elements is inconsistent with its default component, then the mesh element is an edge mesh element. Record the inconsistent default component information in array a[j], j=1,2,3,……,m; m is the total number of adjacent mesh elements with inconsistent default components, and a[j] is the default component number of the j-th mesh element.
[0048] Step 4.2: For the edge mesh element, based on the default component information recorded in a[j], calculate the harmonic density of each gas component according to Step 3. ; Step 4.3, correct the calculation of the density of each gas component on each grid element:
[0049] here is the harmonic coefficient, with a value range of [0.5, 1].
[0050] This step is explained as follows: By employing a default component floating approach, the flow control equations solved on each grid element are actually different, which affects the solution stability to some extent. For adjacent grid elements with inconsistent default components, a harmonic correction is performed to reduce the impact of differences in the solution equations.
[0051] Step 5. Complete the numerical iteration of the flow equations and provide simulation results according to the requirements of numerical simulation.
[0052] Step-by-step instructions: The numerical simulation is complete when the numerical iteration of the flow control equations reaches the maximum number of iterations or meets the pre-set convergence condition of the iteration residuals, and the calculation results can be output according to the simulation requirements. The specific methods for completing the numerical iteration of the flow control equations and processing the numerical simulation results are discussed or introduced in detail in many published documents or materials, and will not be repeated here. This invention can well apply these general methods.
[0053] The numerical simulation results provided by this invention, including but not limited to the temporal or spatial distribution of high-speed flow parameters, the influence of flow phenomena, the aerodynamic characteristics of aircraft, the aerothermal environment, flight trajectory, control strategies, and system design schemes, can provide key technical support for the design and evaluation of high-speed aircraft.
[0054] Application effect example: High-speed aircraft typically employ a spherical design for their nose area. The higher the aircraft's speed and the larger its size, the more pronounced the gas effects, such as high-temperature chemical reactions and thermodynamic excitation, become. Therefore, this simulation is conducted under the following conditions: a flight altitude of 50 km, a Mach number of 26, and a nose size of 1 m (a typical high-temperature non-equilibrium flow condition). A 5-component air Park chemical reaction model is used. Since nitrogen accounts for 78% of the air, it is used as the default component in traditional methods. To assess the computational error caused by an inappropriate default component, the numerical simulation is assumed to be performed in a pure oxygen environment, where the error from an inappropriate default component is more readily apparent.
[0055] Numerical simulations show that the maximum N2 mass fraction calculated by the traditional method is 0.005 (see...). Figure 2 Since the simulation is of a pure oxygen environment, nitrogen should not be present. Therefore, the traditional method of fixing nitrogen as the default component introduces a numerical error of 0.5%. However, the method of this invention (see...) Figure 3 The N2 mass fraction is close to zero (10-40), and the numerical error is close to zero in the machine. The above analysis shows that the method of the present invention has smaller numerical errors and higher accuracy.
[0056] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for handling missing component floating in high-temperature non-equilibrium flow simulation, characterized in that: Includes the following steps: Step 1: Establish a complete discrete framework for numerical simulation of high-temperature nonequilibrium flow; Step 2: Select the default component using a floating selection; Step 3, gas density matching; Step 3 includes the following steps: By combining the default components, the gas density on each grid element is adjusted so that it satisfies the physical constraint that "the total gas density is equal to the sum of the densities of each gas component" after the nth iteration. Step 4, gas density adjustment and correction; Step 4 specifically includes the following steps: Step 4.1, determine the edge mesh element and record its edge information: For each mesh element, if the default component on its adjacent mesh elements is inconsistent with its default component, then the mesh element is an edge mesh element. Record the inconsistent default component information in array a[j], j=1,2,3,……,m; m is the total number of adjacent mesh elements with inconsistent default components, and a[j] is the default component number of the j-th mesh element; Step 4.2: For the edge mesh element, based on the default component information recorded in a[j], calculate the harmonic density of each gas component according to Step 3. ; Step 4.3: Correct the calculation of the density of each gas component on each grid element; Step 5: Complete the numerical iteration of the flow equations and provide simulation results according to the requirements of numerical simulation.
2. The method for handling missing component floating in high-temperature non-equilibrium flow simulation as described in claim 1, characterized in that: Step 1 includes the following steps: Import the numerical computation grid, and discretize the complete set of high-temperature nonequilibrium flow control equations using spatial and temporal schemes to construct the basic framework for numerical iterative solution.
3. The method for handling missing component floating in high-temperature non-equilibrium flow simulation as described in claim 1, characterized in that: Step 2 includes the following steps: In the nth iteration of the numerical simulation, the gas component with the largest content or the largest change in iteration is selected as the default component of each grid element; n=1,2,3,……,Nmax; Nmax is the maximum number of iteration steps, which is set according to the simulation requirements.
4. The method for handling missing component floating in high-temperature non-equilibrium flow simulation as described in claim 1, characterized in that: Step 4 includes the following steps: For each grid element, the gas component density is harmonized and corrected based on the default component characteristics of its neighboring grid elements to reduce the impact of differences in solving the mass conservation equation among the grid elements.
5. The method for handling missing component floating in high-temperature non-equilibrium flow simulation as described in claim 1, characterized in that: Step 3 specifically includes the following steps: Step 3.1, estimation: Step 3.2, Calibration: here and These are the densities obtained from the nth iteration of the gas total density mass conservation equation and the s-th gas component density mass conservation equation, respectively. Estimate the density of the s-th gas component; and The total density and the corrected density of the s-th gas component are obtained in the nth iteration calculation; and These are the density obtained from the nth iteration of the density-mass conservation equation for the i-th gas component and the estimated density of the i-th gas component, respectively. This summation is performed over all non-default components; N is the number of gaseous components. To sum over all components, This is a function that takes a larger value.
6. The method for handling missing component floating in high-temperature non-equilibrium flow simulation as described in claim 1, characterized in that: In step 4.3, the revised calculation formula is as follows: here is the harmonic coefficient, with a value range of [0.5, 1].
7. The method for handling missing component floating in high-temperature non-equilibrium flow simulation as described in claim 2, characterized in that: In step 1, the computational grid includes a high-speed flow simulation grid consisting of a structured grid, an unstructured grid, or a structured-unstructured hybrid grid. The flow field of the aircraft is divided into thousands of grid micro-elements by the grid, and the flow control equations are discretized on the grid micro-elements.
8. A method for handling missing component floating in high-temperature non-equilibrium flow simulation as described in claim 2 or 7, characterized in that: The flow control equations in step 1 include chemical nonequilibrium flow control equations and thermochemical nonequilibrium flow control equations. Spatial formats include windward or centrally discrete formats; Time formats include explicit or implicit discrete time formats.