Floating air ball ice load induced structural deformation and pneumatic grid real-time updating method

Abstract

The invention relates to a real-time updating method for structural deformation caused by an ice load and a pneumatic grid in a floating air ball icing process, and belongs to the field of floating air ball icing simulation and structural dynamics. The method comprises the following three core steps: firstly, mapping the ice mass increment of a surface grid unit into an equivalent node load through a finite element shape function; modeling the floating air ball skin into a pretension film, and solving a displacement field by adopting a co-rotation format finite element method; and finally, based on the displacement field, adopting a hybrid dynamic grid strategy to update a pneumatic calculation grid, and respectively adopting a spring approximation method, an elastomer method or local regeneration according to the deformation rate. According to the method, the structural response of the flexible skin is considered in floating air ball icing simulation for the first time, bidirectional coupling of icing, structural deformation and pneumatic analysis is achieved, the prediction precision is remarkably improved, meanwhile, the calculation efficiency is greatly improved on the premise that the grid quality is guaranteed through an intelligent grid updating strategy, and the method is suitable for large-scale popularization and application. And a reliable technical means is provided for ice-resistant design and safety evaluation of the floating air ball.

Description

Technical Field

[0001] This invention belongs to the field of air balloon icing simulation and structural dynamics, and specifically relates to a method for considering the deformation of flexible skin caused by ice load and realizing real-time updating of aerodynamic mesh in icing simulation. Background Technology

[0002] Stratospheric balloons (typically flying at altitudes of 18-30 km) need to traverse cloud layers with temperatures below 0°C (such as cirrus and altocumulus) when performing long-endurance missions like scientific observation and atmospheric sounding. These clouds contain supercooled liquid water (SLW), and when the surface temperature of the balloon's skin falls below freezing, ice buildup occurs. Ice buildup also occurs on the flexible wings of high-altitude unmanned aerial vehicles (UAVs) traversing clouds and fog, and on large wind turbine blades in cold, damp environments.

[0003] To assess the impact of such dynamic loads on structural safety, aerodynamic performance, and operational reliability, high-fidelity fluid-structure interaction (FSI) numerical simulation has become an indispensable technical means. However, this type of simulation faces a long-standing common technical challenge: how to efficiently and accurately handle large deformations of flexible structures caused by dynamically distributed surface loads (such as ice growth) while simultaneously achieving real-time updates of high-quality fluid computational meshes. This challenge is a crucial bridge connecting solid mechanical response and fluid dynamics analysis, and its solution directly determines the accuracy, stability, and computational efficiency of the coupled simulation.

[0004] Existing simulation technologies generally employ simplified engineering methods, which have the following fundamental drawbacks, particularly prominent in simulations involving flexible bodies and large deformations:

[0005] 1. Structural Rigidity Assumption: Traditional methods treat balloon skins as rigid bodies, assuming their geometry remains unchanged during icing. However, the skins of inflatable balloons are typically made of flexible thin-film materials such as polyethylene (approximately 20-50 μm thick), and the added mass of local ice layers can reach several kg / m³. 2 This can cause significant non-uniform deformation, which alters local curvature and affects the characteristics of water droplet impact and ice growth patterns.

[0006] 2. Unidirectional Coupling Process: Existing icing simulations employ a sequential calculation process, namely, calculating the flow field under a fixed geometry → calculating water droplet impact and icing based on the fixed flow field → adding ice as a static mass increment to the dynamic model → updating the flight state. This process completely ignores the real-time feedback of ice-induced deformation on the flow field, the impact of shape changes on aerodynamic drag, and the local stress concentration caused by deformation.

[0007] 3. Shortcomings of mesh updates: Existing mesh update methods mainly include static meshing, global regeneration, and simple interpolation. Among them, static meshing uses the same set of meshes throughout the simulation process, which cannot adapt to changes in shape; global regeneration regenerates the entire computational domain mesh at each time step, resulting in extremely high computational costs; and simple interpolation uses linear or radial basis function interpolation, which cannot guarantee the quality of the boundary layer mesh.

[0008] Due to the aforementioned technical limitations, existing methods exhibit significant biases when predicting flexible structures such as balloons under severe icing conditions. They cannot accurately assess the reduction in structural safety margin caused by ice loads, the impact of deformation on flow field separation and drag, or the icing-intensifying effect caused by local indentations. Therefore, there is an urgent need for a method that can accurately simulate structural deformation caused by ice loads and achieve high-quality real-time mesh updates.

[0009] In summary, this invention proposes an innovative solution to this unique and widespread technical problem. The core value of this method lies in its versatility and portability: it is not only specifically designed to address the needs of simulating icing on aerosol balloons, but its technical principles and implementation framework are also applicable to the fluid-structure interaction numerical analysis of other lightweight flexible aircraft and large membrane structures under various dynamic loads such as deposition and icing, providing common key technical support for high-fidelity simulation in related fields. Summary of the Invention

[0010] The purpose of this invention is to provide a method that can accurately simulate the deformation of the flexible skin of a floating balloon caused by ice load, realize the real-time updating of high-quality aerodynamic mesh under deformation conditions, achieve bidirectional coupling of structural response and aerodynamic analysis in icing simulation, and improve computational efficiency while ensuring computational accuracy, so as to overcome the shortcomings of the existing simulation methods proposed in the background art.

[0011] To achieve the above objectives, the technical solution adopted by the present invention includes the following steps performed sequentially:

[0012] Step S1: Precise mapping of ice load to structural nodes. The growth of ice on the skin surface is non-uniform, and traditional methods that simply distribute ice mass to the nearest node lead to load distortion. This invention converts the continuously distributed ice mass increment output by the icing module onto the skin surface into concentrated force loads acting on the nodes of the structural finite element model in a conserved manner. Further, the specific implementation steps are as follows:

[0013] Step S1.1: Calculation of unit ice mass distribution. For each surface triangular unit e (area A) e Ice mass increment Provided by the icing module. Assuming the ice is uniformly distributed within the cell, the ice mass density is:

[0014]

[0015] Step S1.2: Shape function interpolation mapping. For each node i, collect the set Ω(i) of all cells containing that node. The equivalent ice mass of node i is:

[0016]

[0017] in Let i be the shape function of node i on element e.

[0018] Step S1.3: Convert the equivalent ice mass into nodal load force vectors. Convert the nodal equivalent ice mass into gravity loads:

[0019]

[0020] Using Gaussian integrals for surface integral calculations, for linear triangular elements, the above integral can be simplified to:

[0021]

[0022] Step S2: Efficient solution for the deformation of the pre-tensioned membrane structure. Solve the deformation displacement field of the flexible skin under the combined action of the pre-tension formed by the initial internal pressure and the ice load obtained in step S1. The air-bomb skin is in a pre-tensioned state under the initial internal pressure. This invention models it as a pre-tensioned membrane, neglecting bending stiffness but considering geometric nonlinear effects.

[0023] Step S2.1: Establish a mechanical model of the pre-tensioned membrane of the air-bearing balloon skin. Consider the equilibrium conditions of the membrane element, under the conditions of pre-tension T and ice load f. ice Under the following conditions:

[0024]

[0025] in, For the pretension tensor, w = [w x ,w y ,w z ] T f is the displacement vector. ice =[f x ,f y ,f z ] T Let be the ice load intensity. For the spherical approximation, the equation can be simplified to:

[0026]

[0027] Where R is the radius of the balloon, and θ and φ are spherical coordinate angles.

[0028] Step S2.2: The skin structure is discretized using triangular membrane elements in a co-rotational formulation. A local coordinate system is defined for each element, tracking the element's rotation; the linear stiffness matrix K is calculated in the local coordinate system. L And by rotating the local stiffness matrix K, the local stiffness matrix K is... L Transform to global coordinate system (K) G =R T K L R); Assemble the stiffness matrices of all elements to obtain the overall stiffness matrix K and the nodal force vector F.

[0029] Step S2.3: Solve the linear system Kw=F to obtain the displacement vector w of all nodes on the skin surface. The preprocessed conjugate gradient method (PCG) is used for the solution, and the preprocessing matrix is ​​decomposed using incomplete Cholesky decomposition.

[0030] Step S3: Real-time dynamic mesh update based on hybrid strategy. The aerodynamic computational domain mesh is updated based on the skin displacement field calculated in Step S2, ensuring that the updated mesh quality meets computational fluid dynamics requirements.

[0031] Step S3.1: Identify deformable regions. Calculate the deformation rate for each node:

[0032]

[0033] Where L char The characteristic length is the average size of the unit cell.

[0034] Step S3.2: According to η i Divide the region into regions of varying sizes and assign update strategies. If η i If η < 0.05, the spring approximation method is used in the corresponding region; if 0.05 ≤ η i If η < 0.20, the corresponding region uses the elastomer method; if η i For values ​​≥0.20, the corresponding region uses the local mesh regeneration method.

[0035] Step S3.3: Perform grid update according to the strategy.

[0036] Spring approximation method: Treat the mesh edges as springs, where the spring stiffness is inversely proportional to the edge length.

[0037]

[0038] Solve the equilibrium equations of the spring network to update the internal node positions:

[0039]

[0040] Where N(i) is the set of neighboring nodes of node i.

[0041] Elastic body method: Treat the mesh as a linear elastic body and solve the equilibrium equations:

[0042]

[0043] The boundary condition is u = w on Γ surface This updates the internal grid nodes.

[0044] Local mesh regeneration method: Extract the boundary of the large deformation region, regenerate mesh points within it based on the Delaunay criterion and perform triangulation, then reconstruct the boundary layer mesh, and finally stitch it with the mesh of the surrounding undeformed region.

[0045] Step S3.4: Perform a quality check on the updated mesh to ensure that its orthogonality, aspect ratio, and volume change rate meet the preset thresholds. If not, start the mesh optimization program until the standards are met. Generally, orthogonality θ is required. min >20°, aspect ratio AR max <50. Volume change:

[0046] The innovative point of this invention is:

[0047] 1. For the first time, flexible structure response was introduced into the simulation of air balloon icing, breaking through the limitations of the traditional rigid assumption.

[0048] 2. A conservation mapping method based on finite element shape functions is proposed, which solves the problem of accurate transfer of ice load from continuous distribution to discrete nodes.

[0049] 3. A co-rotational pre-tensioned thin film solver was developed, which significantly improved computational efficiency while ensuring accuracy.

[0050] 4. A hybrid dynamic mesh update strategy was designed, realizing an intelligent update mechanism of "smooth deformation + local reconstruction".

[0051] 5. A complete quality monitoring system was established to ensure that the mesh quality meets the requirements of CFD calculation throughout the simulation process.

[0052] Compared with the prior art, the present invention has the following significant advantages:

[0053] 1. More accurate physical modeling. By introducing a pre-tensioned membrane model and accurate ice load mapping, the structural response of flexible skin is fully considered for the first time in the simulation of icing of air balloons, breaking through the limitations of the traditional rigid body assumption.

[0054] 2. The coupling mechanism is more complete. It realizes two-way real-time coupling of icing, structural deformation and aerodynamic analysis, and can capture the key physical feedback mechanism that "deformation affects the flow field, and the flow field affects subsequent icing".

[0055] 3. Higher computational efficiency. The proposed hybrid dynamic mesh update strategy employs optimized update methods for regions with different degrees of deformation, reducing computation time by 60%-80% compared to the global regeneration method while maintaining mesh quality. Attached Figure Description

[0056] Figure 1 The overall implementation process of the method for real-time updating of aerodynamic mesh induced by ice load on a floating balloon as described in this invention includes three core steps: accurate mapping of ice load to structural nodes (S1), efficient solution of pre-tensioned membrane structure deformation (S2), and real-time updating of dynamic mesh based on hybrid strategy (S3), as well as the data flow and coupling relationship between each step. Detailed Implementation

[0057] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0058] Please see Figure 1 This invention provides a simulation method for the icing process of an air balloon flying in supercooled clouds, specifically including the following steps:

[0059] 1. Initial Condition Setting

[0060] The airborne balloon's skin is made of polyethylene film, 30 μm thick, with an initial internal pressure of 150 Pa. The computational domain uses a structured mesh, with the balloon surface consisting of a triangular mesh. The initial flight altitude is 20 km, and the ambient temperature is -50 °C.

[0061] 2. Precise mapping of ice load to structural nodes (corresponding to step S1 in claim 1)

[0062] The icing module outputs the ice mass increment for each surface triangular unit at each time step. The element ice mass is converted into nodal loads through shape function interpolation mapping. The calculation is performed using Gaussian integrals, and the specific formula is as follows:

[0063]

[0064] in For shape functions,

[0065] 3. Efficient solution for the deformation of pre-tensioned membrane structures. (Corresponding to step S2 in claim 2)

[0066] The skin is modeled as a pre-tensioned membrane, with the pre-tension tensor being... Finite element discretization was performed using triangular membrane elements in a conrotational scheme. The global stiffness matrix K and nodal force vectors F were assembled, and the displacement field w was solved using the preprocessed conjugate gradient method, satisfying the following equation:

[0067] Kw = F

[0068] 4. Real-time dynamic mesh update based on a hybrid strategy (corresponding to step S3 in claim 3)

[0069] Calculate the deformation rate η of each node. i =||w i || / L char According to η i Value partitioning: If η i If η < 0.05, the spring approximation method is used to update the mesh; if 0.05 ≤ η i If η < 0.20, update the mesh using the elastic body method; if η < 0.20, update the mesh using the elastic body method. i For values ​​≥0.20, the local mesh regeneration method is used.

[0070] 5. Perform a quality check on the updated mesh.

[0071] After updating, check the mesh orthogonality θ min >20°, aspect ratio AR max <50. Volume change rate | (V new -V old ) / V old |<0.1. If this condition is not met, the mesh optimization program will be started until the condition is met.

[0072] 6. Coupling Iteration and Result Output

[0073] The updated mesh is fed back to the flow field solver for icing calculations in the next time step, achieving two-way coupling. The simulation output includes the deformed balloon shape, ice layer distribution, local stress, and aerodynamic drag changes.

[0074] This embodiment demonstrates that the method can effectively simulate the deformation of flexible skin caused by ice load and achieve high-quality mesh updates. Compared with the traditional rigid assumption method, the prediction accuracy is improved by about 35% and the computation time is reduced by about 70%.

[0075] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for real-time updating of structural deformation and aerodynamic mesh caused by ice load during the icing process of a floating airball, characterized in that, Includes the following steps: Step S1: Precise mapping of ice load to structural nodes, converting the ice mass increment output by the icing module, which is continuously distributed on the skin surface, into concentrated force loads acting on the nodes of the structural finite element model in a conserved manner. Step S2: Efficiently solve the deformation of the pre-tensioned membrane structure, and solve the deformation displacement field of the flexible skin under the combined action of the pre-tension formed by the initial internal pressure and the ice load obtained in step S1. Step S3: Real-time dynamic mesh update based on hybrid strategy. The aerodynamic computational domain mesh is updated according to the skin displacement field calculated in step S2, and the updated mesh quality is ensured to meet the computational fluid dynamics requirements.

2. The method according to claim 1, characterized in that, Step S1 specifically includes: Step S1.1: For each surface triangular unit e, according to the ice mass increment provided by the icing module... Calculate the ice mass density of the unit Step S1.2: For each node i, collect the set Ω(i) of all elements containing that node, and calculate the equivalent ice mass of the node using shape function interpolation: in Let i be the shape function of node i on element e; Step S1.3: Convert the equivalent ice mass of the node into a gravity load vector:

3. The method according to claim 1, characterized in that, Step S2 specifically includes: Step S2.1: Establish the mechanical model of the pre-tensioned membrane of the floating balloon skin, and its governing equations are: Where T is the pretension tensor, w is the displacement vector, and f ice Ice load intensity; Step S2.2: The skin structure is discretized using triangular membrane elements in a co-rotational scheme, and the overall stiffness matrix K and nodal force vector F are assembled. Step S2.3: Solve the linear system Kw=F to obtain the displacement vector w of all nodes on the skin surface.

4. The method according to claim 1, characterized in that, Step S3 specifically includes: Step S3.1: Calculate the deformation rate η of each node. i =||w i || / L char L char The characteristic length; Step S3.2: Based on the deformation rate η i Divide the region by size and assign an update strategy: if η i If η < 0.05, the spring approximation method is used; if 0.05 ≤ η i If η < 0.20, the elastomer method is used; if η i For values ​​≥0.20, the local mesh regeneration method is used; Step S3.3: Perform grid updates according to the specific strategy; Step S3.4: Perform quality checks and optimizations on the updated mesh to ensure that orthogonality, aspect ratio, and volume change rate meet preset thresholds. If not, start the mesh optimization program until the standards are met.

5. The method according to claim 4, characterized in that, The spring approximation method treats the mesh edges as springs, with the spring stiffness inversely proportional to the edge length. The positions of the internal nodes are updated by solving the equilibrium equations of the spring network.

6. The method according to claim 4, characterized in that, The elastic body method treats the mesh as a linear elastic body and solves the equilibrium equations. And apply displacement boundary conditions to update the internal mesh nodes.

7. The method according to claim 4, characterized in that, The local mesh regeneration method includes extracting the boundary of the large deformation region, regenerating the mesh based on the Delaunay criterion, reconstructing the boundary layer mesh, and stitching it with the surrounding mesh.

Images