Numerical Simulation of wind load on Inflated Membrane Structure

The fluid-structure interaction (FSI) program were used to simulate the condition that inflated membrane structure transport process in incoming flow. A comparison between the results from numerical simulation and from the ground simulation test was used to validate the computational method. Due to the analysis of flow field and membrane structure’s deformation, the law of force variation of inflated membrane structure during FSI was discussed, and the causes of deformation instability in FSI problems were preliminary discussed. Possible ways to reduce the sensitivity of envelope deformation caused by constraint position were explored, and the effect of this improved method on the surface stress of the envelope was investigated.


Introduction
The adjacent space usually refers to the atmospheric space in the altitude range of 20~120km, which includes the stratosphere, the mesosphere, and the lower thermosphere.The atmospheric density in this area is small, and is affected by the lower boundary troposphere, the upper boundary thermosphere, and external energy inputs such as ground radiation, solar radiation, and solar wind.As the altitude increases, atmospheric pressure gradually decreases, and the atmospheric pressure near a height of 20km above the ground is usually about 5.4% of the ground level.Statistical data shows that the annual average wind speed is the smallest in the altitude range of 20 kilometers to 22 kilometers, making it easy for aerostat to stay for long periods of time.Nearby space aerostat provide net lift by floating gas inside their bodies, and stay in place for a long time.In order to ensure that the aerostat has sufficient buoyancy to stay in nearby space, it is usually required that the aerostat has a sufficient volume, and its length is generally over 200m.At the same time, the weight of aerostat should not be too large.Generally, lighter soft materials are used, and their overall stiffness is small, similar to an elastic thin film structure.The interaction between the nonlinear large deformation of the capsule body and the surrounding flow field is a complex fluid structure coupling problem [1][2][3].
In response to the complex fluid structure coupling problem encountered by aerostat in close space, this article uses a membrane structure model to simulate the aerostat's bladder structure, uses a finite volume method based on unstructured grids to calculate the flow field structure, and then uses the alternating coupling calculation method of fluid and solid structures to obtain information such as the structure of the outer flow field, aerodynamic characteristics, aerostat shape, and capsule tensile stress distribution of the aerostat under wind load, Understand the characteristics and laws of fluid solid coupling, and seek effective control methods and approaches [4][5][6].

Ground simulation experiment
Experiments were conducted using fiber woven materials with obvious anisotropic characteristics.When making an inflatable beam, the elongation direction of the inflatable beam is set at a 45°angle to the fiber direction of the material, and the modulus selected for calculation is also measured by maintaining a 45°inclination angle with the fiber direction.Preliminary experiments were conducted using the experimental setup shown in Figure 1.

Numerical calculation
Using finite element analysis, calculate the variation of the specified point disturbance of the inflatable beam with the change of load after inflation, and ensure that the loading and inspection disturbance are consistent with the experimental results.In the calculation, the pressure is first filled in multiple steps, and the load is added after reaching the specified pressure.The addition of the load is also carried out in steps.The calculation accuracy is selected as 0.00001, and the pressurization is completed through 10 steps, with each step increasing the load by 0.441N, which is consistent with the experiment [7].

Comparison of experimental and numerical simulation results
Figures 2, 3, and 4 provide a comparison of experimental and calculated results under different inflation pressures.It can be found that the calculated results and experiments are in good agreement at 4000Pa and 5000Pa.Although there is a certain difference at 6000Pa, it is still acceptable.This may be due to the fact that when the inflation pressure is high, the deformation of the membrane may not only be elastic deformation, but the calculation can only simulate elastic deformation.Therefore, there is a certain error in the experimental results and calculations under higher pressure and load.Another possible reason is that there is an unavoidable bias in using isotropic models to numerically simulate anisotropic materials, which is more pronounced under larger strains [8].

Research Model
The capsule model used in the calculation is a rotating body with a length of 152 meters and a maximum waist diameter of 48.7 meters, as shown in Figure 5.The x direction represents the flow direction, the z direction represents the direction of gravity, and the y direction represents the spanwise (or lateral) direction.The coordinates are all in meters [9].
The numerical calculation parameters are: incoming wind speed of 10m/s, incoming flow density of 1.225kg/m3, pressure difference between inside and outside the capsule of 200Pa, and incoming flow viscosity coefficient of 1.7894×10 -5 Pa•s, the Young's modulus E of the capsule material is 1.3×10 8 Pa, Poisson's ratio 0.3, thickness 0.0003m.

Setting of constraints and experimental parameters
Based on the flight situation of real capsule carrying loads, we investigate an asymmetric bottom constraint.Asymmetric constraints are used to control the displacement in all directions, i.e. fixed, and a total of five relatively close constraint positions are set.These constraint positions are consistent in the z-direction, i.e. "z<-22", but have slight deviations in the x-direction, in order to reveal the sensitivity of the constraint positions on the deformation of the capsule, i.e. "x>58", "x>59", "x>60", "x>61", and "x>62".The specific positions of "x>60, z<-22" are shown in Figure 6.As shown in Figure 7, with the development of the fluid solid coupling step, the five curves gradually divide into two branches.One of them is composed of three curves: "x>58", "x>59", and "x>60", while the other is composed of two curves: "x>61" and "x>62".We can also see that the windward resistance curve of "x>60" is relatively close to that of "x>61" and "x>62" in the first three steps, and in the later flow coupling steps, its curve is relatively close to that of "x>58" and "x>59".Therefore, it can be seen that the constraint position of "x>60" is indeed a critical point.In addition, it can also be seen that all the curves in the first three coupling steps have gone down but immediately turned up, and after the third step, the five curves are divided into two branches with significantly different slopes, reflecting the turning point of the capsule in the third coupling step, resulting in completely different deformation characteristics of the capsule.This will be further discussed in the flow field structure.We can see from the two curve clusters with completely different slopes after the third coupling step in the figure that the constraint positions of "x>58", "x>59", and "x>60" will eventually make the capsule approach stability, while the constraint positions of "x>61" and "x>62" may continue to increase in deformation after 10 steps of coupling, and even ultimately lead to the instability of the capsule.During the first fluid calculation, the flow field structures of the two constraint methods were basically the same, with a vortex that was basically symmetric about the x-axis at the tail of the capsule, thus maintaining consistent pressure on its upper and lower surfaces and basically zero pitch torque.But by the second fluid calculation, it can be seen that the flow field structure of both has undergone significant changes.For the constraint case of "x>58", although the vortex structure at the tail is no longer symmetrical, resulting in the generation of pitch torque, there is still a clear vortex structure, and its asymmetry is still within a certain range.However, for the constraint case of "x>62", during the second fluid calculation, the asymmetry of the vortex ring was already very severe, and the vortex ring in the lower half had weakened to a level that was difficult to identify.It can be seen that the pressure imbalance on the upper and lower surfaces was already obvious, resulting in significant deformation of the capsule due to the large pitch moment, which further led to the asymmetry of the external flow field, as a result, the shape of the capsule undergoes significant changes at each coupling step, and even ultimately becomes unstable.From the 10th coupling step, it can be seen that there is always a vortex structure at the tail of the capsule at the constraint position of "x>58", and the symmetry of this vortex structure is gradually being repaired; But for the constraint position of "x>62", the vortex structure at the tail of the capsule is already relatively vague.Based on this, it is predicted that after 10 coupling steps, the constraint of "x>58" will gradually make the capsule of the capsule approach stability, while the constraint of "x>62" will ultimately lead to the instability of the capsule.It can be seen that the maximum principal stress occurs on both sides of the front end of the abdominal restraint, and the range of high stress zones generated by the constraint position of "x>58" is larger than that of "x>62", but the extreme value of the first principal stress is smaller: the maximum stress value of the constraint position of "x>58" is 2.59 × The maximum stress value at the constraint position of "x>62" at 107Pa is 3.30 × 107Pa。 It can be seen that the constraint position of "x>62" has a greater risk of rupture compared to the constraint position of "x>58".

Improvement of wind load on capsule structure
Considering the significant difference in pitch deformation caused by different constraint positions and the fact that the maximum principal stress occurs at the bottom when the capsule undergoes wind load deformation, two reinforcement positions were selected to improve the capsule structure of the capsule: one is to reinforce the capsule by surrounding it in the y-direction along the centerline (Figure 12), and the other is to reinforce it at the bottom of the capsule (Figure 13).Select two reinforcement methods simultaneously: increasing the thickness of the capsule material and increasing the modulus of the capsule material, that is, increasing the thickness of the membrane to twice the original value at the reinforcement point or increasing the modulus of the membrane to twice the original value at the reinforcement point during calculation.
After reinforcement, the wind load deformation of the capsule at the three constraint positions of "x>58", "x>60", and "x>62" after 10 fluid structure coupling steps is shown in the following figure.The dashed lines represent the shape of "x>62", and the other two almost overlapping contours are formed by the constraint methods of "x>58" and "x>60".From the above figures, it can be seen that the midline reinforcement has not achieved any significant effect on suppressing the deformation of the capsule.However, the bottom reinforcement, whether it is thickness reinforcement or modulus reinforcement, effectively suppresses the deformation of the capsule and reduces its sensitivity to the constraint position.
After the above reinforcement, the stress distribution changes on the surface of the capsule are shown in Figures 18-21.
The stress distribution map obtained by using the centerline reinforcement method shows little difference at the bottom of the capsule, except for some slight changes in the centerline section; The bottom reinforcement affects the distribution of stress to varying degrees.In the bottom reinforcement, doubling the thickness leads to a significant increase in the area of the high stress zone, and stress is more concentrated around the reinforcement area; However, the doubling of modulus only results in an increase in the area of the high stress zone within a certain range, and the stress distribution remains generally consistent with that without reinforcement.

Conclusion
The correctness of the numerical calculation method was verified by comparing it with experimental results.On this basis, the development law of capsule shape under the alternating influence of fluid calculation and solid calculation of capsule membrane structure was explored, demonstrating the mutual influence and constraint between fluid and solid calculation.The main conclusions are as follows: 1) The first few coupling steps play a decisive role in the entire fluid structure coupling process.
2) The improved method of bottom reinforcement can not only suppress the deformation of the capsule, but also effectively reduce the maximum principal stress.

Figure 1 .
Figure 1.Schematic diagram of experimental equipment

Figure 2 .
Figure 2. Deflection comparison of experiment and computation at inflation pressure 4000Pa

Figure 3 .
Figure 3. Deflection comparison of experiment and computation at inflation pressure 5000Pa

Figure 4 .
Figure 4. Deflection comparison of experiment and computation at inflation pressure 6000Pa

Figure 6 .
Figure 6.Constraint position diagram of x>60 and z<-22 3.3.The force and external flow field results of capsule The variation law of the windward resistance of the capsule with the development of the coupling step under different capsule constraints.As shown in Figure7, with the development of the fluid solid coupling step, the five curves gradually divide into two branches.One of them is composed of three curves: "x>58", "x>59", and "x>60", while the other is composed of two curves: "x>61" and "x>62".We can also see that the windward resistance curve of "x>60" is relatively close to that of "x>61" and "x>62" in the first three steps, and in the later flow coupling steps, its curve is relatively close to that of "x>58" and "x>59".Therefore, it can be seen that the constraint position of "x>60" is indeed a critical point.In addition, it can also be seen that all the curves in the first three coupling steps have gone down but immediately turned up, and after the third step, the five curves are divided into two branches with significantly different slopes, reflecting the turning point of the capsule in the third coupling step, resulting in completely different deformation characteristics of the capsule.This will be further discussed in the flow field structure.We can see from the two curve clusters with completely different slopes after the third coupling step in the figure that the constraint positions of "x>58", "x>59", and "x>60" will eventually make the capsule approach stability, while the constraint positions of "x>61" and "x>62" may continue to increase in deformation after 10 steps of coupling, and even ultimately lead to the instability of the capsule.

Figure 7 .
Figure 7. Drag coefficient curves in different constraint position We will compare the flow field structures of the two constraint positions "x>58" and "x>62" with the results of coupling step development, as shown in Figures 8 to 10, mainly examining the pressure distribution and streamline of the flow field.During the first fluid calculation, the flow field structures of the two constraint methods were basically the same, with a vortex that was basically symmetric about

Figure 11 .
Figure 11.First main stress comparison of capsule surface in different constraint position