A method for calculating aerodynamic characteristics of an inflatable return capsule based on Fluent-UDF

Abstract

The application discloses a kind of based on Fluent-UDF's inflatable return capsule aerodynamic characteristic calculation method, comprising: solving each group component density in specified temperature and pressure range, each group component density in specified temperature range and pressure range is brought into air property calculation formula to obtain the viscosity coefficient and thermal conductivity of air in specified temperature range and pressure range;According to the viscosity coefficient and thermal conductivity of air in specified temperature range and pressure range, UDF code is prepared, the UDF code is with temperature and pressure as variable, the viscosity coefficient and thermal conductivity of air in this specified temperature range and pressure range are two-dimensional interpolation, obtain the viscosity coefficient and thermal conductivity of air at specific temperature and pressure;UDF code is loaded into Fluent software, and the calculation grid of inflatable return capsule flow field calculation domain is imported, the boundary condition of calculation grid is set, and the aerodynamic characteristic of inflatable return capsule is obtained.The application greatly reduces the amount of calculation.

Description

Technical Field

[0001] This invention belongs to the field of aerodynamic deceleration design technology for spacecraft entry, and particularly relates to a method for calculating the aerodynamic characteristics of an inflatable return capsule based on Fluent-UDF. Background Technology

[0002] With the continuous development of the space industry, spacecraft missions are becoming increasingly numerous, leading to higher demands for mission cost control. To meet future low-cost requirements, inflatable reentry capsules made of flexible materials are attracting growing attention. Their working principle involves folding flexible fabric around the payload bay. Before atmospheric entry, the heat shield inflates to form a cone shape, protecting the payload and providing aerodynamic deceleration. Finally, the flexible material itself provides a landing cushioning effect. Inflatable reentry capsules made of flexible materials are lightweight and have a high payload-to-weight ratio, significantly reducing launch costs and showing broad application prospects in future space missions.

[0003] The study of aerodynamic characteristics is a crucial prerequisite for the design of inflatable reentry capsules, and numerical simulation is an important means of conducting aerodynamic characteristic research. Commercial software such as Fluent, CFD++, and Fastran are frequently used in engineering research for numerical modeling. During reentry, inflatable reentry capsules traverse hypersonic, supersonic, and subsonic flow regions, where the surrounding gas flow characteristics change drastically. Traditional rigid reentry vehicles such as recoverable satellites and manned spacecraft often rely on parachutes for deceleration in the subsonic range, and the drag characteristics of the reentry vehicle itself in the subsonic range have little impact on the overall deceleration effect. However, inflatable reentry capsules rely on their own aerodynamic shape for deceleration throughout the entire speed range; therefore, obtaining the aerodynamic characteristic parameters of inflatable reentry capsules across the entire speed range is particularly important.

[0004] Currently, chemical nonequilibrium models are commonly used for hypersonic flows, while ideal gas models are often employed for supersonic and subsonic flows. Chemical nonequilibrium models, in particular, require the addition of component equations, resulting in extremely high computational costs, which increase significantly with the number of components considered. Although commercial software has optimized the algorithms, the computational burden remains enormous due to the unchanged fundamental properties of chemical nonequilibrium models, especially in 3D flow field simulations, where large supercomputing platforms are often necessary to obtain results quickly. Furthermore, using different computational methods for different flow domains increases modeling time and may lead to inconsistent theoretical references for design. Summary of the Invention

[0005] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a method for calculating the aerodynamic characteristics of an inflatable reentry capsule based on Fluent-UDF. For hypersonic flow, the method considers the drastic changes in the physical properties of air caused by chemical reactions, but does not solve the air composition equations. Moreover, the calculation workload does not increase with the increase in the number of air components considered. The method always maintains the same number of equations for calculation as for supersonic and subsonic flow, which greatly reduces the amount of calculation.

[0006] The objective of this invention is achieved through the following technical solution: a method for calculating the aerodynamic characteristics of an inflatable reentry capsule based on Fluent-UDF, comprising: solving for fractional densities within a specified temperature and pressure range; substituting the fractional densities within the specified temperature and pressure range into air property calculation formulas to obtain the viscosity coefficient and thermal conductivity of air within the specified temperature and pressure range; compiling UDF code based on the viscosity coefficient and thermal conductivity of air within the specified temperature and pressure range, wherein the UDF code uses temperature and pressure as variables to perform two-dimensional interpolation on the viscosity coefficient and thermal conductivity of air within the specified temperature and pressure range to obtain the viscosity coefficient and thermal conductivity of air at a specific temperature and pressure; loading the UDF code into Fluent software and importing the computational grid of the inflatable reentry capsule flow field calculation domain, setting the boundary conditions of the computational grid, and obtaining the aerodynamic characteristics of the inflatable reentry capsule.

[0007] In the above-mentioned method for calculating the aerodynamic characteristics of an inflatable reentry capsule based on Fluent-UDF, the fractional densities of each group within a specified temperature and pressure range are obtained by solving the Saha equation.

[0008] In the above-mentioned calculation method for the aerodynamic characteristics of the inflatable reentry capsule based on Fluent-UDF, the components include O2, O2 + O2 - O - O + O ++ O +++ N2, N2 + N + N ++ N +++ NO, NO + 、O、N、e.

[0009] In the above calculation method for the aerodynamic characteristics of the inflatable reentry capsule based on Fluent-UDF, the viscosity coefficient of air is obtained by the following formula:

[0010]

[0011] Where μ is the viscosity coefficient of air, μ i n is the viscosity coefficient of a single component.i Let n be the number density of component i. j Let x be the number density of component j, i represent the i-th component, j represent the j-th component, n is the total number of components, and x is the number density of component j. ij This is an intermediate quantity.

[0012] In the above calculation method for the aerodynamic characteristics of the inflatable reentry capsule based on Fluent-UDF, x ij The expression is as follows:

[0013]

[0014] Where, m ij To calculate the mass, m i Ω represents the mass of the element in component i. ii Let Ω be the collision integral between components i and i. ij Let be the collision integral between components i and j.

[0015] In the above method for calculating the aerodynamic characteristics of the inflatable reentry capsule based on Fluent-UDF, the viscosity coefficient of a single component is obtained using the following formula:

[0016]

[0017] Where, μ i The viscosity coefficient of a single component is given by Ω, where m is the relative atomic mass of each element in the component, T is the temperature, and Ω is the viscosity coefficient of the component. ii Let i be the collision integral between components i and i.

[0018] In the above calculation method for the aerodynamic characteristics of the inflatable reentry capsule based on Fluent-UDF, the thermal conductivity of air is obtained by the following formula:

[0019]

[0020] Where k is the thermal conductivity of air, k i Let n be the thermal conductivity of a single component. i Let n be the number density of component i. j Let x be the number density of component j, i represent the i-th component, j represent the j-th component, n is the total number of components, and x is the number density of component j. ij The expression is as shown above.

[0021] In the above calculation method for the aerodynamic characteristics of the inflatable reentry capsule based on Fluent-UDF, when a single component is a pure monatomic gas, the thermal conductivity of the single component is:

[0022]

[0023] Where, k i Where R is the thermal conductivity of a single component, and μ is the gas constant.i denoted as the viscosity coefficient of a single component, M as the relative atomic mass, and the subscript i indicates the i-th component.

[0024] In the above calculation method for the aerodynamic characteristics of the inflatable reentry capsule based on Fluent-UDF, when a single component is a diatomic gas, the thermal conductivity of the single component is:

[0025]

[0026] Where, k i Where R is the thermal conductivity of a single component, and μ is the gas constant. i denoted as the viscosity coefficient of a single component, M as the relative atomic mass, and the subscript i indicates the i-th component.

[0027] In the above calculation method for the aerodynamic characteristics of the inflatable return capsule based on Fluent-UDF, the specified pressure range is 0.1 Pa to 500,000 Pa; and the specified temperature range is 200 K to 45,000 K.

[0028] Compared with the prior art, the present invention has the following advantages:

[0029] (1) This invention obtains air property parameters with a large range of parameters by solving, which can cover the temperature and pressure range of subsonic, supersonic and hypersonic flow fields during the reentry of the inflatable return capsule, and meet the requirements of its full velocity domain calculation.

[0030] (2) In solving the hypersonic flow field, the present invention does not require the addition of component equations, which can greatly reduce the amount of calculation compared with the commonly used chemical nonequilibrium method.

[0031] (3) The present invention adopts a unified calculation method in the subsonic, supersonic and hypersonic speeds, i.e. the entire speed range, which can reduce modeling time and also help avoid theoretical reference discrepancies caused by using different models in different speed ranges. Attached Figure Description

[0032] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings:

[0033] Figure 1 This is a schematic diagram of the external structure of the inflatable return capsule provided in an embodiment of the present invention;

[0034] Figure 2 This is an illustration of two-dimensional linear interpolation provided in an embodiment of the present invention;

[0035] Figure 3This is an explanatory diagram illustrating the calculation settings for air thermal conductivity and viscosity coefficient provided in an embodiment of the present invention;

[0036] Figure 4(a) is an illustration of the subsonic boundary condition setting provided in an embodiment of the present invention;

[0037] Figure 4(b) is an illustration of the setting of supersonic and hypersonic boundary conditions provided in the embodiment of the present invention. Detailed Implementation

[0038] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the disclosure to those skilled in the art. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0039] This embodiment provides a method for calculating the aerodynamic characteristics of an inflatable reentry capsule based on Fluent-UDF, including the following steps:

[0040] Step 1: Solve the Saha equation to obtain the fractional density of each group within the specified temperature and pressure range, and substitute each fractional density into the air property calculation formula to obtain the viscosity and thermal conductivity of air.

[0041] Step 2: Based on the air viscosity and thermal conductivity within the specified temperature and pressure range in Step 1, compile UDF code. The main function of this code is to perform two-dimensional interpolation of air viscosity and thermal conductivity within this range using temperature and pressure as variables, to obtain air viscosity and thermal conductivity at a specific temperature and pressure.

[0042] Step 3: Load the UDF code from Step 2 into Fluent software, import the computational mesh, set the boundary conditions, and then you can perform the calculation.

[0043] In this embodiment, the differences in gas flow characteristics across different velocity ranges are essentially due to variations in air properties caused by temperature and pressure. Under hypersonic conditions, the gas undergoes chemical reactions such as dissociation and ionization due to high temperatures, while these chemical reactions are weaker in the supersonic and subsonic velocity ranges. Therefore, by calculating the air's physical properties over a wide range and then coupling these properties into the flow field calculation, it can be used for flow field calculations across the entire velocity range of an inflatable reentry capsule. Based on this approach and still adhering to the ideal gas assumption, the air's physical properties are first calculated within the temperature range of 200-45000K and pressure range of 0.1pa-500000pa. Then, UDF code is compiled, and the air's physical properties are coupled into the flow field calculation through two-dimensional interpolation using pressure and temperature as variables. Finally, the geometric model is imported into Fluent software, the UDF code is loaded and compiled, boundary conditions are set, and the calculation is performed.

[0044] The specific implementation steps of this embodiment are as follows:

[0045] (1) The Saha equation was used to calculate the changes in the fractional density of each air component with temperature and pressure. The air components considered in this method include O2 and O2. + O2 - O - O + O ++ O +++ N2, N2 + N + N ++ N +++ NO, NO + O, N, e, the fractional density of each of the above groups is represented by n1, n2, ... n 17 The table below lists the chemical reactions under consideration and their corresponding Saha equations.

[0046] Table 1 Chemical Reactions and Corresponding Saha Equations

[0047]

[0048] The table above lists 14 chemical reactions, corresponding to 14 Saha equations, where kp i Let n be the equilibrium constant for the corresponding reaction, and let n be a function of temperature. The Saha equation above contains 17 unknowns (n1, n2, ... nn). 17 However, there are only 14 equations. Three more equations need to be added: the equation of state, the equation of electrical neutrality, and the equation of molar ratio, as shown below:

[0049] p = (n1 + n2 + ... + nn) 17 )k b T

[0050] n17 = n2-n3-n4+n5+2n6+3n7+n9+n 10 +2n 11 +3n 12 +n 14

[0051] (2n8+2n9+n 10 +n 11 +n 12 +n 13 +n 14 +n 16 ) / (2n1+2n2+2n3+n4+n5+n6+n7+n 15 )=x mole In the above formula, P represents pressure, and K represents... b Here, x is the Boltzmann constant, T is the temperature, and x is the value of x. mole The molar ratio is 3.74 for air. By solving the above equations simultaneously, the number density of each component at a specified temperature and pressure can be obtained.

[0052] (2) Solve for the viscosity and thermal conductivity of air.

[0053] The viscosity coefficients of individual components are shown below:

[0054]

[0055] In the above formula, m is the relative atomic mass of each component element, T is the temperature, and Ω is the relative atomic mass. ii Let be the collision integral for each component. After obtaining the viscosity coefficient of each individual component, the viscosity coefficient of air can be obtained by fitting the following formula:

[0056]

[0057] in m ij To calculate the mass, m i Let be the mass of the element in component i.

[0058] The thermal conductivity of a single component can be obtained from the following expressions.

[0059] Formula for calculating the thermal conductivity of a pure monatomic gas:

[0060] Formula for calculating the thermal conductivity of diatomic gases:

[0061] Where R is the gas constant. The fitting method for thermal conductivity is the same as that for viscosity, as shown below:

[0062]

[0063] The viscosity coefficient and thermal conductivity of air within a specific pressure and temperature range can be obtained using the above formula.

[0064] (3) Based on the formulas in steps (1) and (2), a cycle with temperature and pressure as variables is compiled to obtain the air viscosity coefficient and thermal conductivity within the specified pressure and temperature range. This invention requires the compilation of a two-dimensional numerical table with pressure and temperature as variables. Combined with the reentry environmental conditions of the inflatable reentry capsule, the pressure range is 0.1 Pa to 500,000 Pa (0.1 Pa to 1 Pa with intervals of 0.1 Pa, 1 Pa to 10 Pa with intervals of 1 Pa, 10 Pa to 100 Pa with intervals of 10 Pa, 100 Pa to 1000 Pa with intervals of 100 Pa, 1000 Pa to 10000 Pa with intervals of 100 Pa, 10000 Pa to 100000 Pa with intervals of 1000 Pa, 100000 Pa to 500000 Pa with intervals of 100000 Pa), and the temperature range is 200 K to 45000 K (with intervals of 100 K). By creating a cycle for the parameters within the above pressure and temperature range, a two-dimensional table of air viscosity coefficient and thermal conductivity with temperature and pressure as variables can be calculated.

[0065] (4) Compile Fluent-UDF code, using the temperature and pressure of a grid node in the flow field as input variables, and obtain the viscosity coefficient and thermal conductivity of that grid node through two-dimensional linear interpolation. Taking the thermal conductivity obtained by interpolation as an example, the specific method of two-dimensional linear interpolation is explained. First, locate the specific temperature and pressure range of the node in the table, find the upper and lower boundaries of the pressure, temperature, and thermal conductivity within this range, and use T as the upper and lower boundaries of the temperature. u and T d The upper and lower boundaries of the pressure are represented by P. u and P d The thermal conductivity at the upper temperature and upper pressure boundaries is expressed in k. uu The thermal conductivity at the upper temperature boundary and the lower pressure boundary is represented by k. du The thermal conductivity at the temperature boundary and the pressure boundary is represented by k. ud The thermal conductivity at the lower boundary under temperature and pressure is expressed by k. dd Let the temperature and pressure at this node be represented by T and P, respectively. Then, the thermal conductivity of this node can be obtained by interpolation using the following formula.

[0066]

[0067]

[0068]

[0069] (5) Open Fluent software, import the computational grid of the flow field computational domain of the inflatable return capsule, load Fluent-UDF code, and select user-defined for viscosity coefficient and thermal conductivity when selecting air properties.

[0070] (6) Set the boundary conditions of the computational domain. It should be noted that for subsonic flow, the pressure far field should be selected for all four boundary conditions. For supersonic and hypersonic flow, the pressure far field should be selected for the inlet, and the pressure outlet should be selected for the other boundary conditions.

[0071] (7) Set the calculation parameters, including the solution method, calculation accuracy, calculation residual and number of calculation steps, and then start the calculation.

[0072] The schematic diagram of the external structure of the inflatable return capsule involved in this invention is shown below. Figure 1 As shown in the figure. The two-dimensional linear interpolation in this invention is illustrated in the diagram below. Figure 2 As shown, linear interpolation is first performed with temperature as the independent variable, then interpolation is performed with pressure as the independent variable, and vice versa. The diagram illustrating the selection of calculation methods for air thermal conductivity and viscosity coefficient in this invention is shown below. Figure 3 As shown, both are selected as user-defined in the calculation.

[0073] The boundary conditions for the computational domain in this invention are illustrated in Figures 4(a) and 4(b). For subsonic flows, all four sides are set as pressure far-field boundaries; for supersonic and hypersonic flows, pressure far-field boundaries are set at the inlet; and the remaining boundaries are set as pressure outlet boundaries. Furthermore, the computational domain for subsonic flows should be wider around the perimeter, with a recommended distance of 15-20 times the equivalent length of the object being computed. For supersonic and hypersonic flows, the boundary width should be designed to encompass the shock wave boundary.

[0074] This invention takes into account the drastic changes in the physical properties of air caused by chemical reactions for hypersonic flow, but does not solve the air composition equations. Moreover, the computational workload does not increase with the increase in the number of air components considered. The number of equations for calculation is always the same as that for supersonic and subsonic flow, which greatly reduces the computational workload.

[0075] This invention employs a unified calculation method across different watersheds, saving modeling time and helping to avoid theoretical reference discrepancies arising from different models.

[0076] The method used in this invention is not only applicable to the study of reentry flow field characteristics of inflatable return capsules, but also applicable to flow field calculations for any medium using air. Since it takes into account the physical properties of air over a large range of parameters, and this range of parameters can be expanded, its applicability is very wide.

[0077] The method used in this invention can be extended to the calculation of Martian atmospheric reentry flow field, or to the calculation of flow field using other gases as media, such as nitrogen dioxide, argon, and nitrogen. It is only necessary to calculate the physical property parameters of different gases and load them into Fluent.

[0078] This invention is based on computational research using the commercial software Fluent, which not only greatly improves computational efficiency but also lowers the basic knowledge barrier for researchers with different technical backgrounds, making it easier to promote in engineering applications.

[0079] This invention obtains air physical properties over a wide range (200K~45000K, 0.1pa~500000pa) by solving for these parameters, covering the temperature and pressure ranges of subsonic, supersonic, and hypersonic flow fields during the reentry of an inflatable reentry capsule, thus meeting the requirements for full-velocity domain calculations. In solving the hypersonic flow field, this invention eliminates the need for component equations, significantly reducing computational load compared to commonly used non-equilibrium chemical methods. Furthermore, this invention employs a unified calculation method across the subsonic, supersonic, and hypersonic domains—the entire velocity domain—reducing modeling time and helping to avoid theoretical reference discrepancies caused by using different models for different velocity domains.

[0080] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

Claims

1. A method for calculating the aerodynamic characteristics of an inflatable reentry capsule based on Fluent-UDF, characterized in that... include: The fractional densities of each group within the specified temperature and pressure range are obtained by solving the problem. The fractional densities of each group within the specified temperature and pressure range are then substituted into the air property calculation formula to obtain the viscosity coefficient and thermal conductivity of air within the specified temperature and pressure range. Based on the viscosity and thermal conductivity of air within a specified temperature and pressure range, a UDF (User-Defined Function) code is created. This UDF code uses temperature and pressure as variables to perform two-dimensional interpolation on the viscosity and thermal conductivity of air within the specified temperature and pressure range, obtaining the viscosity and thermal conductivity of air at a specific temperature and pressure. First, the specific temperature and pressure range of the node is located in the numerical table. The upper and lower boundaries of the pressure, temperature, and thermal conductivity within this range are then found. The upper and lower boundaries of the temperature are represented by... T u and T d The upper and lower boundaries of the pressure are indicated by... P u and P d The thermal conductivity at the upper temperature and upper pressure boundaries is expressed as... k uu Thermal conductivity at the upper temperature boundary and the lower pressure boundary is used k du Thermal conductivity at the temperature boundary and pressure boundary is used k ud Thermal conductivity at the lower boundary under temperature and pressure is used k dd The temperature and pressure at this node are respectively represented by... T and P If this is the case, then the thermal conductivity of the node can be obtained by interpolation using the following formula: ； ； ； Load the UDF code into Fluent software and import the computational grid of the inflatable reentry capsule flow field computational domain. Set the boundary conditions of the computational grid to obtain the aerodynamic characteristics of the inflatable reentry capsule. The fractional densities of each group within a specified temperature and pressure range are obtained by solving the Saha equation. The components include O₂, O₂ + , O₂ - , O - , O + , O ++ , O +++ , N₂, N₂ + , N + , N ++ , N +++ , NO, NO + , O, N, e; Table 1 below lists the chemical reactions under consideration and the corresponding Saha equations; Table 1 Chemical reactions and corresponding Saha equations The table above lists 14 chemical reactions, which correspond to 14 Saha equations. k p i Let n be the equilibrium constant for the corresponding reaction, and let n be a function of temperature; the Saha equation above has a total of 17 unknowns (n1, n2, ... nn). 17 However, there are only 14 equations. Three more equations need to be added: the equation of state, the equation of electrical neutrality, and the equation of molar ratio, as shown below: ； ； ； In the above formula P For pressure, K b Boltzmann's constant, T For temperature, x mole The molar ratio is given; by solving the above equations simultaneously, the number density of each component at a specified temperature and pressure can be obtained. The viscosity coefficient of air is obtained by the following formula: ； in, The viscosity coefficient of air. The viscosity coefficient of a single component. Components i number density, Components j number density, Indicates the first i Each component Indicates the first j Each component The total number of components. This is an intermediate quantity; The expression is as follows: ； in, To calculate the mass, Components i The mass of the elements, Components i and i The collision integral, Components i and j The collision integral; The viscosity coefficient of a single component is obtained by the following formula: ； in, The viscosity coefficient of a single component. m Here are the relative atomic masses of the elements in each component. T For temperature, Components i and i The collision integral; The thermal conductivity of air is obtained by the following formula: ； in, The thermal conductivity of air, The thermal conductivity of a single component is , Components i number density, Components j number density, Indicates the first i Each component Indicates the first j Each component The total number of components. The expression is as shown above; When a single component is a pure monatomic gas, the thermal conductivity of that single component is: ； in, Where R is the thermal conductivity of a single component, and R is the gas constant. The viscosity coefficient of a single component. The subscript represents the relative atomic mass. Indicates the first i One component; When a single component is a diatomic gas, the thermal conductivity of that single component is: ； in, Where R is the thermal conductivity of a single component, and R is the gas constant. The viscosity coefficient of a single component. The subscript represents the relative atomic mass. Indicates the first i One component; The specified pressure range is 0.1 Pa to 500,000 Pa; the specified temperature range is 200 K to 45,000 K.

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