Simulation and Analysis of Aerodynamic Characteristics during Parafoil Canopy Curving Process and Application by LBM

Abstract

A parafoil is a crucial aerodynamic deceleration device used in the field of airdrop. The overall objective of this paper is to study the aerodynamic characteristics of the curving process of the canopy using the lattice Boltzmann method, to verify it with the experimental results, and to analyze the stalling phenomenon using the finite volume method(FVM). Simulations were conducted to analyze the aerodynamic curves of four−stage models of canopies, examining the flow field characteristics. Additionally, the influence of air chamber structures is also analyzed. The reasons for differences in the aerodynamic characteristics are discussed based on the results obtained. The reliability of utilizing the lattice Boltzmann method for aerodynamic simulations is demonstrated. Overall, the lift coefficient of models II/III/IV was increased by 30.97% compared with model I, which proved the effectiveness of the air chamber structure and curving process. Notably, different curved canopies showed significantly improved lift and drag aerodynamic characteristics to varying extents, highlighting their robustness. Also, it was observed that air chamber partitions exerted a greater influence compared to perforation. Through validation and analysis, it was determined the accuracy of the LBM improved up to 10.9% with respect to the FVM. These findings provide a valuable reference for parafoil experiments and simulation research.

1. Introduction

Parafoils are widely utilized in precision airdrops due to their exceptional aerodynamic performance. This paper discusses the steady-state aerodynamic characteristics of parafoils during gliding, which serves as a crucial process for the overall design. The lift and drag coefficients are the primary parameters affecting the glide ratio. Three-dimensional numerical simulation is widely used to analyze the aerodynamic characteristics of different types of parafoil canopies.

The Lattice Boltzmann Method (LBM) is a computational fluid dynamics method based on the mesoscopic simulation scale [1]. In general, it has been recognized as an effective means to describe low-velocity and incompressible flows for complex geometric borders, while alternative methods including the large eddy method and its wall model do not possess these advantages [2,3,4]. While the Boltzmann equation can combine microscopic particle dynamics with macroscopic fluid law, which has high solving precision, it requires significant memory usage and is not efficient for static fluid calculation; thus, it is unsuitable for strong compressibility.

Research on LBM has been emerging since the 2000s. At the beginning, research on the application of LBM in fluid dynamics was divided into theoretical modification and simulation validation, in which the main objects of simulation validation were multiphase flow and porous media. Mei et al. [5] investigated the computational efficiency and reliability of lattice Boltzmann equations for fluid dynamics applications using LBM simulation, and compared the computational accuracy, efficiency and robustness of the three kinds of non-thermal 3D models: Q15D3, Q19D3 and Q27D3. The treatment of the solid bending boundary conditions and its 3D implementation are discussed. Michihisa et al. [6] used LBM for the numerical simulation of a two-dimensional, incompressible, stratified, mixed-phase flow to forecast the phenomena of obstruction; the results confirmed that the total density change obtained was not large compared with the classical FVM. Nobuyuki et al. [7] used LBM to simulate a nonideal gas multiphase flow. In the simulation, the dot matrix model of the lattice in the standard model was modified, and the motion of a spherical droplet under gravity was studied. The results demonstrated the usability of LBM. In addition, the parallelization of the method was carried out using domain decomposition, which was found to be even faster than that of an equivalent fluidic single phase evaluated in a simulation.

Around 2010, more researchers continued to perform theoretical modifications, and the applications required for a proportion of fluid mechanics problems with porous media were evaluated further. Pan et al. [8] continued to evaluate the usability of LBM for the flow in porous media based on the work of their predecessors. The simulation results of the Poiseuille flow between flat plates and simple cubic sphere arrays that were obtained using two models formed by BGK-LBE and MRT-LBE equations were analyzed. The results proved the advantage of the RT-LBE model in porous media in terms of its numerical accuracy compared with the BGK model. Belov et al. [9] conducted a simulation study on the porosity problem of a fabric model on the surface of a parachute, improved the integrated composite processing step, and further carried out a simulation based on LBM to analyze the complexity of the flow in the fabrics. Jiang et al. [10] used the BGK unpressurized LBM to carry out a simulation study on the cylinder winding flow to analyze the phenomenon of vortex-invigorated vibrations (VIVs). The results of the periodic and non-periodic vibrations of the longitudinal and transverse forces acting on the square cross-section are discussed in detail and compared with the finite volume method to verify the validity of LBM.

Since the 2010s to the present, theoretical modifications to the LBM have continued, while the application areas of LBM have been further expanded. For theoretical modifications, An et al. [11] improved the standard LBM, proposed a new simplified multigrid method to speed up the simulation convergence, and verified the effectiveness of the algorithms by classical roof-driven cavity simulation. Bukreev et al. [12] derived a new format for lattice Boltzmann equations by introducing a pressure correction term. The consistency of the improvement using the standard method for velocity and pressure convergence before second-order accuracy was verified by steady-state and unsteady-state examples. Strzelczykd et al. [13] investigated the theoretical decoupling of the LBM method. A meshless lattice Boltzmann method (MLBM) was used to free the standard LBM from the regular lattice while decoupling the spatial and velocity discretization. The application areas of the LBM were greatly expanded. Alamian et al. [14] used LBM to simulate the surface chemical reactions and to study the heat transfer between gas and solids in porous media. Yan et al. [15] used LBM to simulate the melting of phase-change materials. Gümüssu et al. [16] used LBM to study the radiative heat transfer in participating media.

From the review above, it can be found that the previous LBM research has mainly focused on theoretical modifications. In terms of application area expansion, the research has mainly focused on simple flow, multiphase flow, porous media, heat transfer and other problems. In particular, the research on LBM’s application has mostly involved parametric correction and verification. As there are few studies on the application of LBM to the quasi-static computational fluid dynamic simulation of parafoil, this paper will provide important and new references for engineering and design applications regarding parafoil’s aerodynamic characteristics, compared to former studies. The great significance of LBM used in the paper also lies in its simplicity, adaptability to complex geometries and its high parallelization computing efficiency based on the solution ideas of LBM.

Since the 2010s, the simulation of the aerodynamic characteristics of the parafoil by the fluid-structure interaction method (FSI) has gradually been a research hotspot. With the great improvement of computing resource, this method could easily take into account the multiphysics quasi-static variation analysis of fluids and solids. At present, the research of this method has great contribution and value to the design of flexible canopy during the airdrop process. The research has shifted from the traditional combination of experimental and theory to the numerical simulation method of computational fluid dynamics and computational structural mechanics methods. Tang et al. [17] studied the structural deformation behavior and aerodynamic characteristics of the parafoil trailing edge deflection process, and simulated them based on the ICFD fluid and structure solver in LS−DYNA. Tezduyar et al. [18] studied the experiment validation of the parafoil system and the porosity model of the canopy fabric, and the steady-state aerodynamic shape based on LS-DYNA was also studied. Fogrell et al. [19] investigated the deformation of the parafoil structure and the surrounding flow field characteristics, and carried out simulation studies based on the loose coupling method of fluid-structure interaction. Altmann [20] used the simplified finite element method and potential flow theory to study and extend the fluid-structure interaction method of the parafoil.

However, no studies have carried out the whole process multi-coupling field analysis or discussed the rigidity equivalence of the aerodynamic shape of the parafoil flexible canopy during the filling process. In addition, since aerodynamic analysis mainly investigated the changes in the fluid field of the flow, the single-physics simulation method could decouple the problem and reduce the computational resource occupation and other research costs. Therefore, the final simulation scheme in this paper did not adopt the fluid-structure interaction method.

At the same time, as the exploration of three-dimensional modeling with higher precision, curved parafoil canopies will also play an important guiding role for the aerodynamic design of parafoils based on the aerodynamic design verification by traditional finite volume method. The study of 3D modeling and aerodynamic problems has the following significance in parafoil design:

(1)

Accurate theory and modeling: The surface profile, sweep angle, span characteristics and other parameters of the 3D model are not available in the 2D model. In the flow phenomenon, effects such as wingtip vortices are generated, and the result is closer to the actual flight conditions.

(2)

Better optimization of the aerodynamic performance: By optimizing the aerodynamic shape under the 3D model of the parafoil, the aerodynamic efficiency and stability can be improved, and the test cost can be reduced.

(3)

Display & Rendering: Provide designers, engineers, customers and decision-makers with a visual display that provides a clearer understanding of the design intent and performance, facilitating communication and decision-making.

Due to the difference of the action area of providing aerodynamic force with other parachutes, the aerodynamic characteristics of the parafoil is the main factor and important parameter of the flighting. The study of the steady-state aerodynamic characteristics of the parafoil plays a crucial role for the aerodynamic shape design and optimization, also it could provide reference for airdrop mission and demand. In terms of above, related studies applying traditional finite volume method have been conducted. Zhang et al. [21] and Bergoron et al. [19] respectively conducted fluid-structure coupling aerodynamic simulation studies on the inflation process and glide process of the parafoil, respectively, based on loose coupling. Lingard et al. [22] firstly conducted a moderate theoretical and simulation study on aerodynamic calculation of gliding process. Nie et al. [23], Bergeron et al. [24] studied the influence of leading-edge chamber opening on aerodynamic performance from different parameters. Cao et al. [25] and Tao et al. [26] studied the influence of the lower trailing-edge on the pressure distribution and aerodynamic performance. Gavrilovski et al. [27] conducted experiments to study the influence of the spoiler on the lateral and longitudinal control performance of the parafoil. Bergeron et al. [28] then carried out an experiment on the spoiler using three independent control motors on the 9.29 m2 parachute airdrop system. Ke et al. [29] also conducted the analysis of different status of the parafoil under the control of different working stages through aerodynamic and dynamic simulation. However, some of the above did not fully discuss the steady-state aerodynamic characteristics of the canopy with entire canopy curving process detailly, while paying more attention to the dynamic characteristics of canopy inflation.

2. Method

2.1. Research Object

The 2D and 3D modeling which referred to engineering canopy are carried out by using CATIA. Firstly, a set of phased modeling is established for the curved process of parafoils. Figure 1 shows the four stages of curving modeling for the canopies, including 6 types overall.

Model I(a) shows the original NACA parafoil canopy. Model I(b) has a spanwise curving. Model I(c) makes a leading-edge opened, and the entire interior chamber became one large chamber; Model II divides the parafoil air chamber into separated small chambers. In the model III, walls of the air chambers are perforated. Model IV has the highest extent of surface curving. It curves the upper canopy of each chamber individually.

In summary, the process is divided into four main key stages, and the aerodynamic properties of each stage determine the variation of the aerodynamic characteristics of the whole process. At the same time it will clearly reflect the flow situation under different degrees of curving.

The three views are shown in Figure 2.

2.2. Research Method

Two numerical simulation methods are used to study the aerodynamic characteristics of curved parafoil canopy. They are lattice Boltzmann method (LBM) and traditional finite volume method respectively. LBM is used as the main method to conduct simulation to study aerodynamic characteristics, and finite volume method is mainly used as verification.

2.2.1. Lattice Boltzmann Method

Compared with the traditional finite volume method, the LBM simulation rule is changed to the particle evolution, including the two processes, which are movement and collision [30]. The evolution equation is as follows:

$$\begin{array}{l}{f}_a(x+c{e}_a{\delta }_t,t+\delta t)=f_a(x,t)\\ {\tilde{f}}_a(x,t)=f_a(x,t)+A_{aj}[f_j(x,t)-f_j^{eq}(x,t)]\end{array}$$

(1)

where $a$ is the number of particle motion direction, $a=0,1,\dots ,b-1$. ($b$ is the total amount of motion direction), $j$ is each velocity component in a given lattice. $f_a$ is the distribution function of the direction before collision. ${\tilde{f}}_a$ is the distribution function of the direction after collision. $x$ is the spatial position vector. $t$ is the time. $A_{aj}$ is the collision matrix. $c$ is the particle motion velocity. $f^{eq}$ is the equilibrium distribution function. $e_a$ is the unit vector. ${\delta }_t$ is the time step. The simulation scheme is implemented using Xflow. The Model’s geometric conditions of the simulation are shown in

Table 1. Model’s geometric conditions of the simulation.

Parameters	Value
Polygon count	10,468
Point count	5623
Reference area(m2)	137.087
Reference volume(m3)	31.2083
Length of chord(m)	4.84486
Length of span(m)	9.78134
Height of arch	2.84421
Center of aerodynamic	Center of mass

.

The simulated environment is shown in

Table 2. Simulation environment.

Parameters			Value
Simulation Engine		Field types of analysis	External field
		Flow pattern	Single phase
		Turbulence model	Auto
		Thermal model	Isotherm
Simulation Environment	Global Feature	Scope type	Virtual wind tunnel
		Extermal velocity field	X:0 Y:0 Z:9.8 m·s−2
		Initial velocity field	X:15 m/s Y:0 Z:0
		Initial pressure field(Pa)	101,325
		Reference area	Front
		Reference velocity	Local
	Wind Tunnel characteristics	Location	(0,0,0)
		Dimensionality	(80,80,40)
		Boundary layer model	Periodic
		Boundary conditions	X:15 m/s Y:0 Z:0
		Angle-of-attack(°)	0, ±5, ±10, ±15, ±20, ±25, ±30

.

The physical properties of medium materials are shown in

Table 3. Physical properties of medium materials.

Parameters	Value
Molecular weight(u)	28.996
Temperature(K)	288.15
Dynamic viscosity(Pa·s)	0.001
Specific heat(J·(kg·K)−1)	1006.43
Reference density(kg·m3)	1.225
Viscosity model	Newtonian fluid
Thermal conductivity(W·(m·K)−1)	0.0243

.

The setting of simulation conditions is shown in

Table 4. Simulation conditions.

Parameters	Value
Time frame(s)	10
Resolution	0.04 (Flow field), 0.02 (Boundary)
Wall boundary condition	No-slip
Time step	Fixed automatically
Thinning algorithm	Near static walls

.

2.2.2. Finite Volume Method

As verification and comparison of LBM, the finite volume method is used to calculate the flow characteristics of the field around the parafoil canopy. According to the low speed and low altitude flight conditions, the parameters were chosen and shown in

Table 5. Aerodynamic simulation parameters of finite volume method.

Parameters	Value
Number of blocks(million)	≈0.54
Type of grid	Structured grid for partition interconnection
Boundary conditions	Velocity inlet, pressure outlet
Flow speed(m/s)	15
Angle-of-attack(°)	0°, 10°, 20°, 30°, 45°, 60° 3°, 6°, 9°, 12°, 15° and 18°
Relaxation factor λ	0
Wall boundary condition	No-slip
Turbulence model	$k-\epsilon$ [32]
Solver format	Implicit format for separating models [33]
Viscous term discrete	Central difference format
Convective term discrete	Second-order upwind format

. Multiple calculated angles-of-attack were added to the simulation based on Burke ‘s research [31].

2.2.3. External Flow Field and Parameters

In the simulation analysis, it is necessary to select the appropriate definition of external flow field and related geometric parameters. The overall principle is that the flow field measurement is more than 10 times the size of the parafoil canopy. The external flow field size chosen in the paper is shown in Figure 3, which meets the calculation requirements.

3. Results and Analysis

3.1. Aerodynamic and Flow Characteristics by LBM for Curving Stages and Air Chamber Structure

Firstly, the lift & drag characteristics are verified using experiment data. Lift coefficient CL and drag coefficient CD are classically defined as follows:

$$CL=\frac{F_L}{\frac{1}{2}\rho u^{2}S},CD=\frac{F_D}{\frac{1}{2}\rho u^{2}S}$$

(2)

where, $F_L$ denotes lift force, $F_D$ denotes drag force, and $S$ is the characteristic area of the parafoil.

The difference of lift & drag characteristics of the parafoil with different curved extent was studied. The upcoming flow velocity was 10m/s for simulation, and other conditions remained unchanged. The lift & drag curves of different curving stages in the range of 0°~80° angle-of-attack were obtained from the simulation, as shown in Figure 4.

First, the trend of aerodynamic coefficient curve was analyzed. In terms of lift coefficient, the overall change trend of the result was complicated which increased with the angle-of-attack at first, reaching the maximum value around 30° and 50°, and then it decreased gradually due to stall slowly. For the drag coefficient, it increased monotonically with the angle-of-attack before 80° and decreased rapidly after 60°. For the four different models of parafoil canopies. As for model I(c) (no chamber with leading-edge opened), II (air chamber with no perforation), III (air chamber with perforation) and IV (upper canopy curved), the coefficients had the same trend with the angle-of-attack. In small range of angle-of-attack (<10°), the drag forces of the model II and III were small, and the aerodynamic performance was great; While the angle-of-attack continued to increase, the growth rate of the drag coefficient was greater than that of model I and less than that of model IV. In addition, the coefficients of model II parafoil canopy with no perforation and model III with perforation basically coincided. From the perspective of quantitative analysis, the lift coefficient of model II/III/IV was increased by 30.97% compared with model I which proved the effectiveness of the air chamber structure and curving process.

Then, from the perspective of flow distribution and characteristics, the aerodynamic characteristics reflected in the above aerodynamic curves for different models in curving process. Also, the differences between two kinds of air chamber structure would be analyzed and discussed. The pressure nephograms of the internal air chamber partition wall of model II and III are shown in Figure 5. The flow field distribution of the parafoil profiles of model I and model III are obtained respectively as in Figure 6.

It could be seen from the figures that the pressure on the wall and the velocity field inside the canopy with perforation between the air chambers are more evenly distributed than those without perforation. Additionally, the flow field distribution trend of these models was overall consistent. In model I there was no air chamber inside the canopy, the air flow inside had a reflux, especially along both sides of the wingspan. Moreover, the internal air flow velocity was significantly higher than that of the parafoils with separated air chambers inside. When there were separated air chambers inside the parafoil canopy, the internal flow field was more evenly distributed and tended to be into a stagnant state.

The steady-state aerodynamic characteristics of different curved parafoil canopies and the characteristic differences caused by different aerodynamic structures are to be analyzed by aerodynamic curves and flow field distribution. First, the reasons for the difference in aerodynamic coefficients of the different curving extent was studied. When the model I with no air chamber was compared with model II and III, the flow layer of its internal flow field was not in a completely stagnant state or an approximate stagnant state at the cut of leading edge, but it still presented a gradient distribution, resulting in a decrease in the flow stability of the entire air chamber. Therefore, it had a great influence on the lift & drag coefficients. The pressure streamlines also showed that the relative pressure in the low-pressure area of the upper surface of model III was lower, which was reflected in the aerodynamic characteristics that the lift coefficient was larger. In addition, model IV, III and II could maintain a relatively stable lift-drag ratio, which also proved the robustness of the aerodynamic characteristics of the parafoil.

Then, the analysis has focused on the aerodynamic characteristics of the perforation structure on the air chamber connections. From the flow mechanism, it could be seen that when the air chambers were separated inside the parafoil, whether there existed perforation will affect the communication of air flow along the wingspan. Based on the flow distribution, it could be concluded that the pressure gradient distribution of model II and model III in the air chambers were basically the same, which also explained that the perforation structure had no great influence on the lift & drag characteristics of the air flow.

Model IV represented the highest curved extent during the curving process. It was essential to studied the flow characteristics further. Figure 7 shows the velocity nephogram of the canopy surface obtained by LBM simulation. The time steps of the numerical solutions are 1 s, 3 s, 8 s, 12 s, 16 s, 20 s, respectively. From the overhead perspective of the upper surface that during the initial convergence period of the simulation, the low-pressure area at the leading edge slowly formed and began to generate the wingtip vortex at the trailing edge. After 12s, the convergence was basically completed, and the air flow pattern was obviously symmetrical along the wingspan. However, the high-pressure area formed in the canopy caving-in part at each connection of air chambers was concentrated at the highest position along the wingspan, and the pressure decreased gradually as the distribution spread outwards along the wingspan. On the contrary, the low-pressure area at the trailing edge was more dispersed at the highest position along the wingspan, and the area gradually expanded when it was distributed outwards.

The pressure nephogram of the canopy and the X = −2, Y = 0 pressure streamline are shown in Figure 8. The transition between the flow streamline and the nephogram at the connections of the air chambers caused by the caving-in part of the canopy in the final aerodynamic shape model of the curved parafoil was more complicated, showing signs of stagnation in the flow pattern at the caving-in connections, which was quite different from the model I.

As shown in Figure 9, with the increase of the angle-of-attack, the low-pressure area in the troposphere of the upper canopy expanded, and the range of the wake area is longitudinally elongated, leading to an increasement in the lift of the parafoil which is manifested as the upward variation of the lift coefficient.

Examining the fluid state of the four models, the difference of aerodynamic shape made the troposphere of the upper surface more complicated, resulting in the contours (velocity and pressure) of the flow layer more approximate to roughness and opposite to the streamlined parafoil canopy, thus increasing the drag coefficients. Similarly, the air chamber partition of model II, III and IV resulted in lower relative pressure in the low−pressure area of the upper flow layer and higher lift coefficients than model I. The analysis above could also help explain the differences of aerodynamic characteristics between the models.

3.2. Stalling Phenomena Analysis and Validation by Finite Volume Method for Model IV

There were plenty of researches on the aerodynamic characteristics of parafoils using the finite volume method, so it was used to conduct the comparison and verification simulation. Also, the stalling phenomena analysis of model IV was based on its computational results.

As shown in Figure 10, the lift & drag coefficients CL_LBM and CD_LBM were obtained by LBM simulation. CL_EX and CD_EX were obtained by the wind tunnel experiment results of the same proportion. CL_FVM and CD_FVM were obtained by FVM through ANSYS Fluent.

To evaluate the differences in results obtained by each method or experiment, two aspects of results and analysis could be highlighted through the comparison of curves. The calculated lift and drag coefficients by LBM were overall in good agreement with those of the experiment. However, there existed errors in most range of $\alpha$. The reason was the disturbance of air flow caused by the flexible canopy due to the parafoil fabrication media, which was slightly different from the rigid hypothesis of canopy used in the LBM simulation. Besides, the curves obtained by LBM and FVM were more consistent with each other. Detailly, the errors became larger as the angle-of-attack increased to the range of 15°~30°. Due to the difference in methodology and modeling, a more theoretical analysis was needed to explain the variance of two simulation methods. Also, in this range the curve obtained by LBM was closer to which obtained by the experiment compared with FVM especially in large angles-of-attack. This has proven the better adaptation of the LBM relative to the FVM to complex boundary conditions such as upper parafoil curves for conditions where vortices under large angle-of-attack developed to be more significant. The adaptability of LBM improved up to 10.9% with respect to FVM, as shown in the figure.

Furthermore, it is essential to carry out the flow field analysis to explain the model IV aerodynamic coefficient results obtained from the FVM simulation. Figure 11 showed the distribution of parafoil flow field at different angles-of-attack. By analyzing the diagram, it could be found that with the increase of the angle-of-attack, the flow was obviously separated on the upper surface of the parafoil canopy, and a large detached vortex appeared above it. The size and position of the detached vortex are also different with the variation of the angle-of-attack. With the increase of the angle-of-attack, the stagnation point gradually moves back, and the pressure difference between the upper and lower canopy was larger, so the lift force became larger. As the angle-of-attack continued to increase, the boundary layer in the rear area of the upper surface is partially separated due to the gradually increasing inverse pressure gradient, and the trailing edge separation area expanded forward. When the angle-of-attack increased to a certain critical value, the attachment flow of the upper canopy was completely destroyed, resulting in the decreasing of the lift force and a great increase in the drag force. At this point, the air flow became unstable and the stalling phenomenon occurred.

The internal pressure of the parafoil’s profile was basically equal to that of the stagnation point. The pressure inside the air chamber was high and the flow velocity was low. The stable aerodynamic shape could be maintained and the flow characteristics of the model IV canopy could also supplement the explanation for the results of the aerodynamic characteristics.

4. Conclusions

In this study, the Lattice Boltzmann method(LBM) was used to investigate the aerodynamic characteristics of three-dimensional parafoils. The aerodynamic curve and flow field distribution under different curving extent of the parafoils were obtained, with the experiment results used to verify the simulation data. The finite volume method was used to analyze the stalling phenomenon. The reliability of applying the LBM and model to low pressure airdrop was proved by the verification, which provided a new method for the aerodynamic simulation of parafoils.

In addition, the internal flow field could significantly change the aerodynamic coefficients after the curving operation and the flow obstruction structure such as the air chambers and perforation are added. Overall, the lift coefficient of model II/III/IV was in-creased by 30.97% compared with model I which proved the effectiveness of the air chamber structure and curving process. According to the curving extent of different parafoil aerodynamic shapes, the velocity and pressure nephogram of its cross-section profile could reflect that the higher the curving extent is, the greater the influence on air flow at each air chamber. Moreover, the differences of aerodynamic coefficients between various aerodynamic shapes with distinct curving extent can be effectively explained and analyzed through the examining of the flow field characteristics and distribution. The addition of the air chamber has a great influence on the aerodynamic performance, while the addition of the perforation structure has little effect. The accuracy of LBM improved up to 10.9% with respect to FVM through validation and analysis. The findings of the paper will have important reference and significant guiding effect for the experiment validation and design of curved parafoil’s low-altitude and low-velocity airdrop. However, the current results mainly address the longitudinal aerodynamic stability of the parafoil canopy. The influence on the lateral aerodynamic stability has not been thoroughly investigated and may require additional study.