Efficient coupling numerical calculation method for flexible parafoil

Abstract

The invention provides an efficient coupling numerical calculation method for a flexible parafoil in order to improve the fluid-solid coupling calculation precision and efficiency of the flexible parafoil. According to the method, a parafoil canopy is taken as a calculation boundary according to the distribution characteristics of pressure inside and outside a parafoil air chamber, fluid inside the canopy is solved by adopting an ideal gas state equation, fluid outside the canopy is solved by adopting a Navier-Stokes equation, the problem of inaccurate aerodynamic configuration calculation caused by calculation errors of pressure difference inside and outside a wingtip is avoided, and the accuracy of aerodynamic configuration calculation is improved. And more importantly, the calculation amount is reduced, and the calculation efficiency is improved. According to the method, a new analysis means is provided for parafoil working performance research, and a new thought is provided for numerical simulation of a similar flexible flight structure.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of aerodynamic deceleration and air-drop equipment, and particularly relates to a high-efficiency coupling numerical calculation method of a flexible wing parachute. BACKGROUND

[0002] The wing parachute has the characteristics of strong maneuverability and high glide ratio, and has been widely used in aerospace, air-drop and other fields.

[0003] The working process of the wing parachute is a process of intense coupling between the flexible canopy structure and the external flow field. In order to understand the fluid-structure coupling mechanism and obtain various information of the flow field and the structure, most scholars use the fluid-structure coupling method for numerical simulation. However, the fluid-structure coupling calculation of the wing parachute is very difficult, mainly because: first, the wing parachute is a typical flexible fabric, and its fluid-structure coupling calculation has the characteristics of large deformation and large displacement, which is prone to problems such as grid distortion and negative volume, and the calculation is difficult to converge. Secondly, the wing parachute is a complex structure of double-curved surface and multi-chamber, and the chamber is a long and narrow cavity with flow fields inside and outside. The accurate calculation of the thin wing surface of the canopy, especially the wing tip, is particularly difficult, and more fine grids are generally needed to achieve ideal calculation accuracy. However, the fluid-structure coupling calculation consumes a lot of resources, and the increase in the number of grids often means further increase in the required calculation resources.

[0004] Therefore, fluid-structure interaction studies of parachutes often require simplification, primarily focusing on rigid / semi-rigid parachutes (see Nie Shuai, Cao Yihua, Wu Zhenlong. Numerical Simulation of Parafoil Inflation via a Robin-neumann Transmission-based Approach. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2018, 232(4): 797–810.) or steady-state calculations based on loose coupling methods (see N. Fogell, SJ Sherwin, CJ Cotter, et al. Fluid-Structure Interaction Simulation of the Inflated Shape of Ram-Air Parachutes. 22nd AIAA Aerodynamic Decelerator Systems Technology Conference, 2013.). Since the parachute canopy is a highly flexible fabric, the fabric structure undergoes intense coupling with the external flow field during operation, and the above simplifications cannot accurately describe the interaction between the flow field and the flexible canopy.

[0005] With the development of computer technology, and considering the good application capabilities of the Arbitrary Lagrange-Eulerian method (ALE method) in handling large displacement and large deformation problems, some scholars have gradually extended the ALE method from conventional circular umbrellas to the fluid-structure interaction calculation of wing umbrellas (see Zhang SiYu, Yu Li, Wu ZhuoHeng, et al. Numerical investigation of ram-air parachutes inflation with fluid-structure interaction method in wind environments. Aerospace Science and Technology, 109 (2021) 106400.). This is currently a relatively effective tightly coupled method, but it still has certain limitations: due to the limitation of the number of meshes on the thin airfoil of the canopy, especially at the wingtip, it is difficult to obtain the fine flow field distribution in the above-mentioned parts, which leads to inaccurate calculation of the wing umbrella canopy structure and causes certain calculation errors. At the same time, the calculation is extremely expensive and the computational resources are very high.

[0006] In summary, fluid-structure interaction (FSI) calculations for parachutes are very challenging, and existing methods struggle to efficiently and accurately describe the flow fields inside and outside the parachute canopy, as well as the aerodynamic shape of the parachute. Therefore, improving the accuracy and efficiency of FSI calculations for parachutes remains a research challenge that urgently needs to be addressed. Summary of the Invention

[0007] To address the aforementioned shortcomings, this invention proposes an efficient numerical calculation method for flexible paraglider coupling, which can improve the efficiency and accuracy of paraglider fluid-structure interaction calculations.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] A highly efficient coupled numerical calculation method for flexible paragliders includes the following steps:

[0010] Step 1: Establish the initial finite element model of the parachute structure;

[0011] Step 2: Determine the internal gas volume V based on the current shape of the canopy structure. Using the canopy structure as the calculation boundary, and considering the near-stagnant and uniformly pressured gas distribution within the canopy's air chambers, solve the internal fluid flow equation using the ideal gas law to obtain the internal gas pressure. ;

[0012] Step 3: The external gas pressure is obtained by solving the Navier-Stokes equations for the fluid outside the canopy. ;

[0013] Step 4: Calculate the internal gas pressure of the umbrella structure. external gas pressure The deformation caused by the pressure difference is solved by solving the structural dynamics equations to update the nodal coordinates and shape of the umbrella structure, and thus update the internal gas volume V used for internal fluid calculation in the next iteration;

[0014] Step 5: Repeat steps 2-4 until the change in parachute aerodynamic force is less than the preset value, and the solution is complete.

[0015] Furthermore, in step 2, the solution for the fluid inside the canopy is based on the ideal gas law:

[0016] ,

[0017] In the formula, Internal energy of the internal fluid; For the internal gas volume, The normal vector of the surface element; This refers to the internal gas pressure. denoted as the adiabatic coefficient of the internal gas.

[0018] Furthermore, in step 3, the solution for the fluid outside the canopy is based on the Navier-Stokes equations:

[0019] ,

[0020] In the formula, For external fluid density, For time, Using Euler coordinates, For convection velocity and That is, material velocity With grid speed difference; Let be the stress tensor of the external flow field, and , External gas pressure, For the Kronecker function, External fluid dynamic viscosity; For volume forces, Let i be the internal energy of the external fluid, where the subscripts i and j are tensor indices.

[0021] Furthermore, in step 4, the internal and external pressure difference of the umbrella canopy structure is calculated as follows:

[0022] ,

[0023] In the formula, , These represent the pressure exerted by the internal and external fluids on the umbrella canopy structure. , These represent the fluid pressures inside and outside the umbrella canopy, respectively. , This represents the area and normal vector of the i-th surface element in the structure.

[0024] Furthermore, in step 4, the calculated... As the main load term, it is incorporated into the structural volume forces through finite element discretization calculation as equivalent nodal forces. In the middle, and substituting it into the dynamic equation of the parachute structure: In the formula, For the structural density of the umbrella canopy and parachute lines, For structural node displacements, The stress tensor of the structure; based on the structural nodal displacements of the previous time step, the new nodal coordinates of the umbrella structure can be calculated. , Update internal gas volume The internal gas volume V is obtained by integrating the spatial region bounded by the coordinates of the umbrella structure nodes, along with the computational grid of the external fluid.

[0025] Furthermore, the internal gas volume is calculated as follows: , The coordinates of the umbrella canopy structure nodes are: This is the normal vector of the surface element.

[0026] Beneficial Effects: To improve the accuracy and efficiency of fluid-structure interaction (FSI) calculations for flexible ramjet parachutes, this invention proposes a highly efficient FSI numerical calculation method for flexible parachutes, addressing the characteristics of large pressure distribution variations on the upper and lower wing surfaces and relatively uniform pressure inside the air chambers. This method uses the parachute canopy as the computational boundary. The fluid inside the canopy is solved using the ideal gas law, while the fluid outside the canopy is calculated using the Navier-Stokes equations. The aerodynamic shape of the parachute gradually forms under the influence of the pressure difference between the internal and external fluids. This method not only avoids the problem of inaccurate aerodynamic shape calculations caused by errors in calculating the pressure difference at the wingtip, but more importantly, it reduces the computational load and improves computational efficiency. This invention provides a new analytical tool for studying the performance of flexible parachutes and also offers new ideas for the numerical simulation of similar flexible flight structures. Attached Figure Description

[0027] Figure 1 This is a flowchart illustrating the method coupling in an embodiment of the present invention;

[0028] Figure 2 This is the finite element model of the folding wing umbrella structure in the embodiment of the present invention;

[0029] Figure 3 This is a schematic diagram of the flow field inside / outside the umbrella canopy in an embodiment of the present invention;

[0030] Figure 4 The parasol in this embodiment of the invention is full of shape contrast;

[0031] Figure 5 The speed change during the parachute inflation process in this embodiment of the invention.

[0032] In the diagram, 1 represents the fluid inside the canopy, 2 represents the fluid outside the canopy, and 3 represents the wing canopy. Detailed Implementation

[0033] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0034] This invention discloses an efficient coupled numerical calculation method for flexible parachutes. Based on the pressure distribution characteristics inside and outside the parachute chamber, the method uses the parachute canopy as the calculation boundary, employs the ideal gas law to calculate the fluid inside the canopy, and uses the Navier-Stokes equations to solve for the fluid outside the canopy. This simplifies the calculation of the pressure difference between the inside and outside of the canopy and improves its calculation accuracy. Therefore, this new method can improve the accuracy and efficiency of calculating the structural shape and the spatiotemporal distribution of the flow field.

[0035] To better describe the technical gains of the efficient coupling numerical calculation method for a flexible parachute proposed in this invention, considering that the parachute inflation process is the stage with the most intense coupling between the surrounding flow field and the structure and the most complex coupling mechanism in the entire working process, the requirements for the fluid-structure interaction method are extremely high. Therefore, in this embodiment, the efficient coupling numerical calculation method for a flexible parachute proposed in this invention and the ALE method are used to simulate the inflation and deployment process of a certain parachute, and the results are compared and analyzed with the parachute tower test.

[0036] This embodiment uses a parachute as an example, with a parachute area of ​​30m². 2 The aspect ratio is 2.5. The opening conditions in this embodiment are: opening height 80m, opening speed 12.3m / s, opening trajectory angle 90°, and load weight 40kg.

[0037] Combination Figures 1 to 4 As shown, this embodiment of the invention provides an efficient coupled numerical calculation method for flexible paragliders. The research approach is as follows: Figure 1 As shown, the specific steps include:

[0038] Step 1, establish the initial finite element model of the parachute structure, such as... Figure 2 As shown in Figure 3, the internal and external flow fields with the parachute canopy as the structural boundary are schematically defined. The fluid 1 inside the canopy is simplified to a uniform pressure field controlled by the ideal gas law. The fluid 2 outside the canopy needs to be solved accurately using the Navier-Stokes equations. The parachute canopy 3 is the key coupling boundary that separates the internal and external flow fields and transmits the pressure difference.Figure 3 The left-hand stereoscopic view shows the overall three-dimensional shape, while the right-hand magnified view reveals the details of the umbrella canopy as a thin-walled computational boundary.

[0039] Step 2: Solve for the internal fluid of the canopy using the ideal gas law. The gas flow velocity inside the canopy's chambers is very slow, almost stagnant, and the pressure is uniformly distributed. Therefore, this embodiment does not use the computationally intensive Navier-Stokes equation, but instead uses the simplified differential form of the ideal gas law. The internal fluid energy inside the multiple chambers of the canopy's internal fluid 1 is accurately and efficiently calculated using the ideal gas law. and gas pressure .

[0040] The ideal gas law is as follows:

[0041] ,

[0042] In the formula, Internal energy of the internal fluid; For the internal gas volume, , The coordinates of the umbrella canopy structure nodes are: This is the normal vector of the surface element. When the canopy deforms, causing a change in volume V, it does work and alters the internal energy of the internal fluid. The internal gas pressure provides the internal driving force for structural deformation. Let be the adiabatic coefficient of the internal gas, and , For isobaric molar heat capacity, This represents the molar heat capacity at constant volume.

[0043] Furthermore, the change in gas mass of the fluid inside the canopy is as follows: In the formula, The velocity of the parachute structure. , Let be the coordinates of the i-th umbrella canopy structural node in space. for time; Let be the normal vector of the air inlet unit at the leading edge of the canopy. This refers to the area of ​​the air intake unit. According to... It can further solve for the fluid density inside the parachute canopy. Let be the gas density. Initial conditions are: The subscript 0 represents the initial time.

[0044] Step 3: Due to the complexity of the external flow field, this embodiment uses the complete Navier-Stokes equations to solve for the external fluid of the umbrella canopy to ensure accuracy.

[0045] Specifically, the external fluid 2 of the umbrella canopy is calculated using the following formula:

[0046]

[0047] In the formula, For external fluid density, For time, Using Euler coordinates, ( () represents the convection velocity, i.e., the material velocity. With grid speed difference; Let be the stress tensor of the external flow field. , The external gas pressure provides external aerodynamic force for structural deformation. For the Kronecker function, External fluid dynamic viscosity; For volume forces, Let i be the internal energy of the external fluid; in the formula, the subscripts i and j are tensor indices. According to the convention, i and j are individual free indices, representing the component in a certain direction; ij represents the element in the i-th row and j-th column of the second-order tensor; i,j and j,i are spatial direction indices.

[0048] The initial conditions of the fluid outside the parachute are: , The subscript 0 represents the initial time.

[0049] The external fluid boundary conditions of the umbrella canopy are as follows: at the free boundary: , At the wall boundary: .

[0050] Step 4: The umbrella structure deforms under the pressure difference between the inside and outside, and the new structural shape is obtained through structural dynamics calculation.

[0051] Specifically, the pressure difference between the internal and external fluids at the boundary 3 of the umbrella structure. Represented as:

[0052] ,

[0053] In the formula, , These represent the pressure exerted by the internal and external fluids on the umbrella canopy structure. , These are the pressures inside and outside the canopy, respectively. , This represents the geometric properties of the umbrella structure, indicating the area and normal vector of the i-th surface element on the structure (calculated using the coordinates of each element node). This formula connects the fluid domain and the structural domain, combining the calculation results of the two fluid formulas obtained in steps 2 and 3. , This is converted into the load that drives the deformation of the umbrella canopy structure. The calculated... As the main load term, it is incorporated into the structural volume forces through finite element discretization calculation as equivalent nodal forces. Furthermore, the equations are substituted into the dynamic equations of the parachute structure to solve for the deformation and motion of the structure.

[0054] The dynamic equations of the parachute structure are:

[0055] ,

[0056] In the formula, For the structural density of the umbrella canopy and parachute lines, For structural node displacements, The stress tensor of the structure; the new nodal coordinates of the umbrella structure can be calculated based on the nodal displacements of the structure in the previous time step. ( (where the subscript t represents time t, and i represents the i-th unit), based on the formula The new structural shape obtained by solving (i.e., the new coordinates of the nodes) Update the computational grid for the internal fluid volume V and the external fluid.

[0057] Step 5: Repeat steps 2-4 until the aerodynamic change of the parachute is less than 10%, and the solution is complete.

[0058] Figure 4 This figure shows a comparison of the fully inflated shape of the parachute in this embodiment of the invention. As can be seen from the figure, compared with the experimental situation, the ALE method results in poor inflation of each air chamber, especially the leading edge air inlet, the two wingtip air chambers, and the trailing edge air chamber, with some wrinkles. After being fully inflated, the span and dihedral angle are smaller, which is significantly different from the actual situation. In contrast, the efficient coupled numerical calculation method of the flexible parachute of this invention improves many wrinkle problems, resulting in a fuller shape and a parachute structure shape that is closer to the actual situation.

[0059] Table 1 shows a comparison of the full-shape results (the shape data in the parachute tower test was obtained through geometric mapping):

[0060] Table 1

[0061]

[0062] Compared with the ALE method, the new method of this invention reduces the calculation errors of projected span, dihedral angle, and projected area from 21.7%, 16.4%, and 41.3% to 2.8%, 9.3%, and 2.5%, respectively. It can be seen that the inflatable shape accuracy of the efficient coupled numerical calculation method for flexible paraglider proposed in this invention is greatly improved, and the structural calculation accuracy is significantly enhanced, which is beneficial to the accurate evaluation of the aerodynamic and gliding flight performance of the paraglider.

[0063] Since the canopy structure and the surrounding flow field interact during the operation of the parachute, the improvement of the structural calculation accuracy also means that the new method of this invention can improve the calculation accuracy of the flow field inside and outside the parachute canopy.

[0064] Figure 5 By analyzing the velocity changes during the parachute inflation process, it can be observed that after time T, the new method of this invention more closely approximates the experimental results. This demonstrates that the calculation results of the flow field distribution and aerodynamic characteristics around the parachute canopy obtained by this invention are more accurate.

[0065] Based on the comparative analysis of the accuracy of structure and motion speed in the above embodiments, the efficient coupling numerical calculation method of flexible paraglider of the present invention can significantly improve the accuracy of fluid-structure interaction calculation of flexible paraglider.

[0066] The efficient coupled numerical calculation method for flexible paragliders of this invention and the ALE method were used to perform parallel computation on the same fluid-structure interaction numerical model on the same workstation (Intel processor, 3.50GHz) with 60 cores. The efficiency was compared, and the results are shown in Table 2.

[0067] Table 2

[0068]

[0069] The results show that the novel method of this invention can improve computational efficiency by 21.9% while reducing memory usage by 22.8%. This is because the ALE method calculates the pressure difference inside and outside the parachute canopy using the Eugen equation, which has a large error and requires a huge amount of computation. In contrast, the novel method of this invention, based on the uniform pressure distribution within the canopy's air chambers, uses the ideal gas equation to calculate the internal flow field pressure and the Navier-Stokes equation to calculate the external flow field pressure. This allows for a faster and more accurate determination of the internal and external pressure difference and the aerodynamic shape of the parachute, reducing iterative computation and significantly improving computational efficiency while reducing memory usage. The results demonstrate that the method of this invention is indeed a highly efficient fluid-structure interaction calculation method.

[0070] In summary, the efficient coupling numerical calculation method for flexible parachutes proposed in this invention significantly improves the accuracy and efficiency of fluid-structure interaction calculations for parachutes, provides new ideas for improving parachute theory, offers new analytical methods for studying parachute performance, and provides a certain reference for fluid-structure interaction calculations of complex flexible structures.

[0071] The specific embodiments described above are further explanations of the purpose, technical solution, and beneficial effects of this invention, and should not be construed as limiting the invention. Any modifications, improvements, or equivalent substitutions made within the spirit and principles of this invention should fall within the protection scope of this invention.

[0072] The embodiments described above are merely illustrative of the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solutions based on the technical concept proposed in this invention shall fall within the scope of protection of this invention.

Claims

1. A highly efficient coupled numerical calculation method for flexible paragliders, characterized in that, Includes the following steps: Step 1: Establish the initial finite element model of the parachute structure; Step 2: Determine the internal gas volume V based on the current shape of the canopy structure. Using the canopy structure as the calculation boundary, and considering the near-stagnant and uniformly pressured gas distribution within the canopy's air chambers, solve the internal fluid flow equation using the ideal gas law to obtain the internal gas pressure. ; Step 3: The external gas pressure is obtained by solving the Navier-Stokes equations for the fluid outside the canopy. ; Step 4: Calculate the internal gas pressure of the umbrella structure. external gas pressure The deformation caused by the pressure difference is solved by solving the structural dynamics equations to update the nodal coordinates and shape of the umbrella structure, and thus update the internal gas volume V used for internal fluid calculation in the next iteration; Step 5: Repeat steps 2-4 until the change in parachute aerodynamic force is less than the preset value, and the solution is complete.

2. The calculation method according to claim 1, characterized in that, In step 2, the solution for the fluid inside the canopy is based on the ideal gas law: ， In the formula, It is the internal energy of the internal fluid; For the internal gas volume, The normal vector of the surface element; This refers to the internal gas pressure. denoted as the adiabatic coefficient of the internal gas.

3. The calculation method according to claim 1, characterized in that, In step 3, the solution for the fluid outside the canopy is based on the Navier-Stokes equations: , In the formula, For external fluid density, For time, Using Euler coordinates, For convection velocity and That is, material velocity With grid speed difference; Let be the stress tensor of the external flow field, and , External gas pressure, For the Kronecker function, External fluid dynamic viscosity; For volume forces, Let i be the internal energy of the external fluid, where the subscripts i and j are tensor indices.

4. The calculation method according to any one of claims 1-3, characterized in that, In step 4, the pressure difference between the inside and outside of the umbrella structure is calculated as follows: ， In the formula, , These represent the pressure exerted by the internal and external fluids on the umbrella canopy structure. , These represent the fluid pressures inside and outside the umbrella canopy, respectively. , This represents the area and normal vector of the i-th surface element in the structure.

5. The calculation method according to claim 4, characterized in that, In step 4, the calculated As the main load term, it is incorporated into the structural volume forces through finite element discretization calculation as equivalent nodal forces. In the middle, and substituting it into the wing-parachute structure dynamics equation: ， In the formula, For the structural density of the umbrella canopy and parachute lines, For structural node displacements, The stress tensor of the structure; Based on the structural node displacements from the previous time step, the new umbrella-shaped structural node coordinates can be calculated. Update the internal gas volume The internal gas volume V is obtained by integrating the spatial region bounded by the coordinates of the umbrella structure nodes, along with the computational grid of the external fluid.

6. The calculation method according to claim 5, characterized in that, The internal gas volume is calculated as follows: , The coordinates of the umbrella canopy structure nodes are: This is the normal vector of the surface element.

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