Multi-vector propeller thrust modeling method for high-altitude aerostat

Abstract

The invention discloses a multi-vector propeller thrust modeling method for a high-altitude aerostat. The method comprises the following steps: respectively establishing external flow field grid models of a single propeller body, an airship body and an on-ship vector propeller body; embedding the vector propeller body external flow field grid model on the airship into the airship body external flow field grid model by adopting an overlapping grid technology; solving a steady-state solution of the propeller thrust by adopting an MRF multi-reference system method, and obtaining a transient solution of the propeller thrust by combining an SM slip grid technology; a user-defined module is adopted to automatically set different vector rotation angle states of the vector propeller; repeating the steps to obtain a thrust transient solution of the single propeller and the multi-vector propeller on the boat; based on a thrust transient solution of a single propeller and a thrust transient solution of a vector propeller on the ship, vector rotation angle, incoming flow speed and rotation speed data are used as variables, and a multi-vector propeller thrust model is constructed by adopting a multi-stage fitting strategy.

Description

Technical Field

[0001] This invention belongs to the field of computational fluid dynamics, specifically relating to a multi-vector propeller thrust modeling method for high-altitude airships. Background Technology

[0002] High-altitude airships, also known as near-space aerostats, typically operate in the stratosphere at an altitude of 20 km. At low speeds and high altitudes, the control surfaces of airships suffer from a significant decrease in propulsion efficiency. Therefore, a solution was developed to replace the control surfaces with multiple vectoring propellers.

[0003] Currently, there is limited research on the aerodynamic performance of vector propellers both domestically and internationally. Most studies focus on the performance analysis and design of high-altitude propellers. For example, the paper "Numerical Analysis of Aerodynamic Performance of Stratospheric Airships with Propellers" uses Fluent's MRF technology to numerically simulate the impact of the tail propeller on the aerodynamic performance of the airship, but does not perform mathematical modeling of propeller thrust. Papers such as "Analysis and Verification of Propeller Similarity Criteria for Stratospheric Airships" design propeller similarity theories and predict the thrust of a single high-altitude propeller through low-altitude wind tunnel tests, but do not consider the coupling effect of multiple propellers on the airship, nor... Thrust modeling was performed; "Numerical Simulation and Wind Tunnel Test of Aerodynamic Characteristics of a Propeller of an Electric Aircraft" conducted numerical simulation of a single propeller at low altitude using the MRF method based on the RANS equations and SST turbulence model, but did not perform aerodynamic analysis of multiple propeller combinations; "Study on Aerodynamic Characteristics of Stratospheric Aircraft and Propellers" adopted the CFD method and applied Fluent's MRF technology to study the aerodynamic performance of propellers under different incoming flow angles of attack, considering the influence of the hull on the propeller aerodynamics, but the steady-state solution of the MRF cannot reflect the nonlinear aerodynamic characteristics of the propeller. Summary of the Invention

[0004] This invention provides a multi-vector propeller thrust modeling method for high-altitude airships, aiming to solve the technical problems in the prior art, such as the lack of thrust modeling for vector propellers that can simulate actual working conditions and the inability of using only MRF steady-state solutions to reflect the nonlinear aerodynamic characteristics of propellers. It can establish an accurate multi-vector propeller thrust model, laying the foundation for the control of the airship's vector propulsion system.

[0005] This invention can be achieved through the following technical solutions:

[0006] A method for modeling multi-vector propeller thrust for high-altitude aerostats includes the following steps:

[0007] Step 1: Establish external flow field mesh models for the single propeller body, the airship body, and the onboard vector propeller body, respectively;

[0008] Step 2: Using overlapping mesh technology, embed the external flow field mesh model of the vector propeller body on the airship into the external flow field mesh model of the airship body;

[0009] Step 3: Solve the steady-state solution of propeller thrust using the MRF multiple reference frame method, and then combine it with the SM slip mesh technique to obtain the transient solution of propeller thrust;

[0010] Step 4: Use the custom settings module to automatically set different vector rotation angle states for the vector propeller;

[0011] Step 5: Repeat step 3 to obtain the transient thrust solutions of multiple single propellers under different incoming flow velocities and rotational speeds; repeat steps 3 and 4 to obtain the transient thrust solutions of the onboard vector propeller under different vector angles, incoming flow velocities, and rotational speeds.

[0012] Step 6: Based on the transient thrust solution of a single propeller, the transient thrust solution of the onboard vector propeller, vector angle, incoming flow velocity, and rotational speed data, construct a multi-vector propeller thrust model using data fitting methods and a multi-level fitting strategy.

[0013] Furthermore, in step six, a single thrust model of the single propeller varying with the incoming flow velocity and rotational speed is obtained using a polynomial fitting method.

[0014] Based on the single thrust model, a multinomial fitting method is used to obtain a mathematical model of the thrust of the front vector propeller as a function of the incoming flow velocity and rotational speed at a certain vector angle. By analogy, multiple mathematical models of the front thrust are obtained for different vector angles. Based on these mathematical models of the front thrust, a set of front fitting parameters corresponding to different vector angles is constructed. Then, based on the set of front fitting parameters, a mathematical model of the front fitting parameters as a function of the vector angle is obtained using a multinomial fitting method, thus completing the construction of the thrust model of the front vector propeller.

[0015] Then, based on the aforementioned front thrust mathematical model, a polynomial fitting method is used to obtain a rear thrust mathematical model in which the thrust of the rear vector propeller varies with the incoming flow velocity and rotational speed at a certain vector angle. By analogy, multiple rear thrust mathematical models corresponding to different vector angles are obtained. Based on these rear thrust mathematical models, a set of rear fitting parameters corresponding to different vector angles is constructed. Then, based on the set of rear fitting parameters, a polynomial fitting method is used to obtain a rear fitting parameter mathematical model in which the fitting parameters vary with the vector angle, thus completing the construction of the rear vector propeller thrust model.

[0016] Finally, a multi-vector propeller thrust model is constructed based on a single thrust model, a front-end fitting parameter mathematical model, a front-end thrust mathematical model, a back-end fitting parameter mathematical model, and a back-end thrust mathematical model.

[0017] Furthermore, the calculation formula for the multi-vector propeller thrust model is as follows:

[0018]

[0019] The values ​​of parameters k′4 to k′8 for the front-end mathematical model under different vector rotation angles μ are as follows:

[0020]

[0021] The parameters k′4~k′8 correspond to the parameter a in the front-end parameter mathematical model. i ~e i The possible values ​​are as follows:

[0022] <![CDATA[a i ]]> <![CDATA[b i ]]> <![CDATA[c i ]]> <![CDATA[d i ]]> <![CDATA[e i ]]> i＝4 <![CDATA[-4.8×10 -9 ]]> <![CDATA[7.335×10 -7 ]]> <![CDATA[-3.619×10 -5 ]]> <![CDATA[5.506×10 -4 ]]> <![CDATA[3.174×10 -3 ]]> i＝5 <![CDATA[3.966×10 -7 ]]> <![CDATA[-6.034×10 -5 ]]> <![CDATA[3.065×10 -3 ]]> <![CDATA[-6.135×10 -2 ]]> -0.747 i＝6 <![CDATA[1.29×10 -8 ]]> <![CDATA[2.207×10 -6 ]]> <![CDATA[9.876×10 -5 ]]> <![CDATA[-4.804×10 -4 ]]> <![CDATA[5.798×10 -3 ]]> i＝7 0 <![CDATA[2.4×10 -9 ]]> <![CDATA[1.318×10 -7 ]]> <![CDATA[2.282×10 -6 ]]> <![CDATA[4.499×10 -7 ]]> i＝8 <![CDATA[-1×10 -9 ]]> <![CDATA[1.695×10 -7 ]]> <![CDATA[-8.865×10 -6 ]]> <![CDATA[1.3×10 -4 ]]> <![CDATA[5.62×10 -4 ]]>

[0023] The values ​​of parameters k″4 to k″8 for the back-end mathematical model under different vector rotation angles μ are as follows:

[0024]

[0025]

[0026] The parameters k″4~k″8 correspond to the parameter a′ in the backend parameter mathematical model. i ~c′ i The possible values ​​are as follows:

[0027] <![CDATA[a′ i ]]> <![CDATA[b′ i ]]> <![CDATA[c′ i ]]> i＝4 0.00053543 -0.00591136 0.00125902 i＝5 -0.04675083 0.58569892 -1.17024304 i＝6 0.00129301 -0.00529682 -0.07550377 i＝7 0.00000021 -0.00000513 0.00003326 i＝8 0.00002072 -0.00069340 0.00497292

[0028] T Fit The thrust of a single propeller is represented by U, the velocity of the incoming flow is U, and the rotational speed of the propeller is n. This indicates the thrust of the vectoring propeller at the bow of the submarine. This indicates the thrust of the vectoring propeller at the rear of the submarine. This indicates the thrust difference between the front and rear vector propellers. This indicates the thrust difference generated by the coupling effect between the propeller and the airship body.

[0029] Furthermore, in step one, a geometric model of the external flow field computational domain of a single propeller body is established using SpaceClaim software. Then, the geometric model of the external flow field computational domain of a single propeller body is imported into Fluent software, and the FluentMeshing module is used to perform mesh generation to complete the construction of the external flow field mesh model of a single propeller body.

[0030] The geometric model of the external flow field computational domain of the airship body was established using SpaceClaim software. Then, the geometric model of the external flow field computational domain of the airship body was imported into Fluent software. The Fluent Meshing module was used to perform mesh generation, and the construction of the external flow field mesh model of the airship body was completed.

[0031] The geometric model of the external flow field of the onboard vector propeller was established using SpaceClaim software. Then, the geometric model of the external flow field of the onboard vector propeller was imported into Fluent software, and the Fluent Meshing module was used to perform mesh generation, thus completing the construction of the external flow field mesh model of the onboard vector propeller.

[0032] Furthermore, in step two, the overlapping mesh technique in Fluent software is used to nest the external flow field mesh model of the vector propeller body on the airship into the external flow field mesh model of the airship body.

[0033] Next, in the Domain menu bar of Fluent software, click on the Additional Case File in the Additional Options within the Region module, and import the pre-divided vector propeller external flow field mesh model. After importing, select Steady-State Simulation, open the motion mesh reference frame for the four vector propeller rotation regions, and enter `mesh / modify / mrf-to-sliding-mesh` in the TUI command window of Fluent software, followed by the corresponding ID number of the vector propeller rotation region, to separate the rotation and revolution regions into sliding meshes. In the boundary condition wall, select the outer surfaces of the four revolution regions, change their type to overlap, and then select the vector propeller external flow field mesh in the background mesh region and the vector propeller revolution fluid region in the component region of the overlap mesh interface. Enter the name of the overlap mesh interface to complete the overlap mesh settings, and click Initialize. The nesting of the overlap mesh is now complete.

[0034] The beneficial technical effects of this invention are as follows:

[0035] 1) This invention uses overlapping mesh technology to complete the coupled modeling of the vector propeller on the airship and the airship body, realizes the data transmission of the propeller revolution region and the external flow field of the airship body, and can include the propeller rotation region, realize the collaborative simulation of multiple flow field domains such as the propeller rotation domain, revolution domain, and fixed external flow field domain of the airship.

[0036] 2) By employing the Multiple Reference Frame (MRF) method and the Sliding Mesh (SM) technique, the rotation of the propeller within the revolution region was realized, and transient solution simulation results were obtained. This ensures the continuity and stability of data transfer between the rotating and stationary regions, which helps improve the convergence of the overall simulation. Compared with the MRF method alone, it improves the computational accuracy and avoids the problem of easy divergence in direct transient solutions.

[0037] 3) A custom module was used to realize the coordinated motion of the vector propeller's rotation and revolution. This means that when simulating different vector rotation angles, there is no need to repeatedly generate new external flow field meshes. Only the spatial attitude of the nested meshes needs to be adjusted to complete the multi-angle simulation settings, which greatly improves the computational efficiency.

[0038] 4) Based on the thrust simulation data, the effects of single propeller thrust on incoming flow velocity U and propeller speed n were first considered. Then, the effects of hull coupling, propeller wake effect, and the influence of vector angle μ on vector propeller thrust were considered. Finally, a polynomial fitting method combined with a hierarchical fitting strategy was used to achieve thrust modeling for multi-vector propellers, meeting the implementation requirements of engineering control and demonstrating strong practicality.

[0039] Furthermore, the modeling method of this invention is not limited to airships, but can be extended to various fields where vector propellers are used. Attached Figure Description

[0040] Figure 1 This is the overall logic block diagram of the present invention;

[0041] Figure 2 The diagram shows the S1223 airfoil structure of the present invention and the three-bladed propeller thereof, wherein (a)-(d) represent the structural diagram, front view, side view and top view, respectively.

[0042] Figure 3 This is a schematic diagram of the computational domain and mesh model of the external flow field of a single propeller according to the present invention;

[0043] Figure 4 The three-view diagram of the airship equipped with four vector propellers according to the present invention is shown, wherein (a)-(c) represent the top view, front view and side view, respectively;

[0044] Figure 5 This is a schematic diagram of the whole-vessel simulation domain setup of the present invention;

[0045] Figure 6 This is a schematic diagram of the external flow field mesh model of the airship body of the present invention;

[0046] Figure 7 This is a schematic diagram of the external flow field mesh model of the onboard vector propeller body of the present invention;

[0047] Figure 8 This is a schematic diagram of the overall mesh assembly of the airship body and the onboard vector propeller of the present invention.

[0048] Figure 9 This is a schematic diagram of the flow field trajectory results of the present invention;

[0049] Figure 10This is a schematic diagram of the external flow field velocity distribution under different vector rotation angles of the present invention, where (a)-(f) represent vector rotation angles of 0 degrees, 5 degrees, 10 degrees, 30 degrees, 60 degrees and 90 degrees, respectively;

[0050] Figure 11 This is a schematic diagram of the verification results of the propeller thrust model of the present invention, wherein (a) and (b) represent the thrust of the front vector propeller and the thrust of the rear vector propeller, respectively. Detailed Implementation

[0051] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings and preferred embodiments.

[0052] This invention provides a method for multi-vector propeller thrust modeling for high-altitude aerostats. First, a computational domain model of the geometric external flow field of a single propeller is established using the three-dimensional geometric modeling software SpaceClaim, such as... Figure 3 As shown in (a); then, a refined geometric external flow field computational domain model is established, including the airship's main structure and its assembled multiple vector propeller components, as shown in (a). Figure 5 As shown, the model was imported into the Fluent software's Fluent meshing module for finite element mesh generation. The mesh generation result is as follows. Figure 3 (b) Figure 6 and Figure 7 As shown, a sliding mesh (SM) technique is used within the rotating region of the vector propeller to construct the flow field boundary conditions under a dynamic rotating reference frame, enabling high-precision simulation of the propeller's continuous rotational motion in a fixed coordinate system. Furthermore, combining the multiple reference frame (MRF) method, the propeller's rotating region is set as the rotating reference frame in steady-state simulations, while the sliding mesh is used in transient simulations to simulate the real rotational effects over time, thus achieving efficient solution of propeller thrust under both static and dynamic operating conditions. In a custom module, an overset mesh technique is introduced, defining the local motion region of the propeller's vector motion components as an independent overset mesh domain, and adjusting its spatial attitude relative to the fixed hull background mesh, thereby enabling rapid modeling of the propeller under different vector rotation angles. Finally, using the vector rotation angle μ, the incoming flow velocity U, and the propeller speed n as fitting variables, a data fitting method is employed to perform step-by-step fitting of the vector propeller thrust. Considering the influence of hull coupling and propeller wake effects, a unified onboard multi-vector propeller thrust model is established.

[0053] Specifically as follows:

[0054] Step 1: Establish the external flow field mesh model of the single-vector propeller body, the airship body, and the onboard vector propeller body.

[0055] This invention employs a three-bladed propeller with a high lift-to-drag ratio S1223 airfoil, a design previously developed. This vector propeller exhibits excellent aerodynamic efficiency in high-altitude, low-density environments. The selected vector propeller diameter D... P It is 3.3m, and the hub diameter is d. P The diameter is 315mm, the hub length is 708mm, the thrust generated by the blades acts at the aerodynamic center of the propeller, the distance from the aerodynamic center to the tail of the hub is 480mm, and the maximum blade width is b. max It is 121mm. The S1223 airfoil and three-bladed propeller geometry are as follows: Figure 2 As shown.

[0056] The designed airship has a length of L, a maximum diameter of D, a surface area of ​​S, and a volume of V. Its geometric plan view and vector propeller layout are as follows: Figure 4 As shown. The tail fin adopts the naca0010 airfoil, distributed in a cross shape. The longitudinal distance from the leading edge of the tail fin to the skin contact point to the bow is L1, the tail fin sweep angle is 40°, the wingtip length is 3.9m, and the distance between the two wingtips is D1. Figure 4 As shown in (a), the airship is equipped with four vectoring propellers, symmetrically distributed on both sides of the hull. Each side has two vectoring propellers, distributed forward and backward. The forward and backward vectoring propellers on both sides have the same aerodynamic performance. Propellers P1 and P2 are defined as the forward vectoring propeller P... f Propellers P3 and P4 are rear-end vectoring propellers. r The overall parameters of the multi-vector propeller airship are shown in Table 1.

[0057] Table 1 Overall Parameters of the Multi-Vector Propeller Airship

[0058]

[0059]

[0060] Establish the geometric coordinate system of the submarine hull as o b x b y b z b Its coordinate origin o b Located at the center of the airship, such as Figure 4 As shown in (b), establish the planar coordinate system o of the vector propeller. p x p z p Its coordinate origin o p The aerodynamic centers of the four vector propellers coincide with the center of the vector rotation axis. The coordinates of these centers in the hull's geometric coordinate system are shown in Table 2.

[0061] Table 2 shows the aerodynamic center of the vector propeller on board the vessel at o. b xb y b z b Coordinates in coordinate system

[0062] serial number Aerodynamic center coordinates Propeller 1 (7.575,10,0) Propeller 2 (7.575,-10,0) Propeller 3 (-7.425,10,0) Propeller 4 (-7.425,-10,0)

[0063] I. Finite element modeling of the external flow field of a single propeller:

[0064] The geometry of a vector propeller is as follows: Figure 2 As shown, a computational domain geometric model of a single vector propeller is established in SpaceClaim software, such as... Figure 3 As shown in (a), the computational domain for the external flow field of a single propeller is divided into three parts: a fixed domain, a rotating domain, and a refinement zone. The rotating domain realizes the rotation of the propeller, and the refinement zone captures the development of the propeller wake. The distance between the propeller and the upstream and circumferential velocity inlets is 10D. P The distance from the downstream pressure outlet is 20D. P The diameter of the propeller's rotational domain is 1.5D. P The width is 0.6D. P .

[0065] Import the established single propeller computational domain geometric model into Fluent software, and perform mesh generation using the Fluent Meshing module. The specific mesh generation steps and parameter settings are as follows:

[0066] 1. Add local dimensions; set the propeller hub surface grid size to 0.1m and the growth rate to 1.2.

[0067] 2. Configure the global face mesh: Set the maximum global face mesh size to 3m, the minimum global face mesh size to 0.0012m, the face mesh growth rate to 1.18, and the size function to Curvature and Proximity. Ignore proximity between objects by selecting Yes, set the curvature normal angle (degrees) to 6, set the number of gap filling cell layers to 4, apply proximity detection by selecting edges, and keep other settings at their default values.

[0068] 3. Describe the computational domain: The computational domain can be divided into a solid domain, a fluid domain, and a dead zone. Select "Geometric structure consists only of fluid regions without voids" as the computational domain type. Change the type of all fluid-fluid interface from "Wall" to "Interior" and select "Yes". Select "Yes" for "Apply shared topology". Update the boundary settings: set the propeller structure surface as a wall, and the surrounding walls as the velocity inlet and pressure outlet. Set the interior of the propeller structure as a dead zone, and the entire outer region of the propeller as a fluid domain.

[0069] 4. Add boundary layer: For the velocity gradient change of the external flow field near the propeller blades, select last-ratio as the boundary layer offset method type, set the number of layers to 20, the transition ratio to 0.272, the height of the first layer to 0.0006m, add the boundary layer in the fluid region, and select three blade regions as the boundary layer growth region.

[0070] 5. Generate Volume Mesh: Select Hexcore for the volume mesh fill method, set the buffer layer to 2, the stripping layer to 1, the minimum volume mesh size to 0.0006m, and keep the maximum volume mesh size at its default value. The minimum orthogonal mass for generating the external flow field is 0.21, and the average orthogonal mass is 0.75. The meshed external flow field of a single propeller under the hull is shown below. Figure 3 As shown in label (b).

[0071] II. Finite element modeling of the external flow field mesh of the airship body:

[0072] In SpaceClaim software, a geometric model of the external flow field computational domain of the airship body is established. The external flow field computational domain of the airship body is as follows: Figure 5 As shown. To ensure that the boundary conditions do not affect the flow field around the airship, the external flow field space of the hull must be large enough. The distance from the hull to the front and circumferential velocity inlets is set to 20L, and the distance from the rear pressure outlet is set to 40L. To prevent the mesh from being too large and affecting the convergence of the propeller thrust calculation, and considering that too many meshes would waste computational resources, local densification regions are divided in the external flow field around the airship hull and the propeller installation area.

[0073] Import the established geometric model of the external flow field computational domain of the airship body into Fluent software, and use the FluentMeshing module to perform mesh generation. The specific mesh generation steps and parameter settings are as follows:

[0074] 1. Add local dimensions: Add local mesh dimensions that need attention, such as the mesh of the main airbag surface and the surrounding encrypted area. The mesh size of the main airbag skin is set to 0.5m, and the growth rate is set to 1.2. Add local encrypted areas; set the mesh size of the encrypted area around the airbag body to 1m, and the mesh size of the propeller encrypted area to 0.15m.

[0075] 2. Set the global surface mesh: Set the surface dimensions for other parts, with lower priority than local size settings. Set the global maximum size to 80m, the global minimum size to 0.006m, the growth rate to 1.2, the size function to Curvature and Proximity, the curvature normal angle to 9°, and the number of gap filling element layers to 2.

[0076] 3. Describe the computational domain: In the software, the computational domain type is set to consist solely of fluid regions without voids. All fluid-fluid region interface types are changed from wall to interior (select "No"). Shared topology is selected "No". Boundary settings are updated: the outer surface of the airship is set as a wall, and the corresponding walls are set as velocity inlet and pressure outlet. The interior of the hull is set as a dead zone, and the entire exterior of the hull is a fluid domain.

[0077] 4. Add a boundary layer: To capture the velocity gradient of the flow field on the outer surface of the airship, the smooth-transition boundary layer migration method is used. The transition ratio is set to 0.272, the growth rate is set to 1.2, and the boundary layer growth region is selected as the airship wall.

[0078] 5. Generating the volume mesh: The volume mesh fill method is selected as Hexcore, the peel layer is set to 1, the minimum volume mesh size is set to 0.006m, and the maximum mesh size is set to 50m. The final generated minimum orthogonal mesh quality is 0.25, and the average mesh quality is 0.88. The generated finite element mesh of the airship's external flow field is as follows: Figure 6 As shown

[0079] III. Finite Element Modeling of External Flow Field Mesh for the Vector Propeller on the Submarine

[0080] The layout of the four vector propellers on the boat is as follows Figure 4 As shown, in the same coordinate system as the computational domain of the airship's external flow field, four corresponding vector propeller external flow fields are established in SpaceClaim according to the propeller layout. The vector propellers consider both the propeller's vector rotation (propeller revolution) and the propeller's blade rotation (propeller spin). A cylindrical external flow field is used for the propeller spin region, with the cylinder's axis as the propeller's spin axis. Boolean operations are applied to the propeller structure to remove the internal propeller structural parts. A cylindrical external flow field is also used for the propeller revolution region, with the cylinder's axis as the propeller's revolution axis. Boolean operations are applied to the cylindrical external flow field in the spin region to remove the internal spin region. The propeller external flow field computational domains are established in SpaceClaim according to the different propeller rotation regions. The distribution of the four vector propeller computational domain models on the airship is shown below. Figure 5 As shown, the propeller's revolution region realizes the propeller's vector rotation, and the propeller's rotation region realizes the propeller's own rotation.

[0081] The geometric model of the external flow field computational domain of the vector propeller on the submarine was imported into Fluent software, and the FluentMeshing module was used for mesh generation. The specific mesh generation process is as follows:

[0082] 1. Add local dimensions; set the grid size of the outer surface of the revolution region to 0.25m and the growth rate to 1.2; set the grid size of the intersecting surfaces of the propeller revolution region and the rotation region to 0.1m and the growth rate to 1.15; set the grid size of the propeller hub surface to 0.1m and the growth rate to 1.2.

[0083] 2. Configure the global face mesh: Set the maximum global face mesh size to 1m, the minimum global face mesh size to 0.0012m, the face mesh growth rate to 1.18, and the size function to Curvature and Proximity. Ignore proximity between objects by selecting Yes, set the curvature normal angle (degrees) to 6, set the number of gap filling cell layers to 4, apply proximity detection by selecting edges, and keep other settings at their default values.

[0084] 3. Describe the computational domain: Select "Geometrically composed only of fluid regions without voids" as the computational domain type. Change the type of all fluid-fluid interface from "Wall" to "Interior" and select "Yes". Select "Yes" for "Whether to apply shared topology". Since the external flow field mesh of the vector propeller on the airship needs to be nested within the external flow field mesh of the airship body, the boundary condition type in the updated boundary does not need to set velocity inlet and pressure outlet. Set the walls around the external flow field as interior, and set the propeller structure surface as a wall. Set the interior of the propeller structure as a dead zone, and the entire external region of the propeller is a fluid domain.

[0085] 4. Add boundary layer: For the velocity gradient change of the external flow field near the propeller blades, select last-ratio as the boundary layer offset method type, set the number of layers to 20, the transition ratio to 0.272, the height of the first layer to 0.0006m, add the boundary layer in the fluid region, and select three blade regions as the boundary layer growth region.

[0086] 5. Generating the volume mesh: The volume mesh fill method is selected as hexcore, the buffer layer is set to 2, the stripping layer is set to 1, the minimum volume mesh size is set to 0.0006m, and the maximum volume mesh size remains at the default. The generated volume mesh for the rotation region has a minimum orthogonal mass of 0.16 and an average orthogonal mass of 0.71; the volume mesh for the revolution region has a minimum mass of 0.2 and an average orthogonal mass of 0.73. The mesh quality meets the requirements. The generated finite element mesh of the external flow field of the vector propeller is as follows: Figure 7 As shown

[0087] Step 2: Using overlapping mesh technology, embed the external flow field mesh model of the vector propeller body of the airship into the external flow field mesh model of the airship body.

[0088] Import the pre-divided airship body external flow field mesh model into Fluent software, check the mesh size and unit settings, and then in Fluent software, click Attach Case File in the Region-Attachment option in the Domain menu bar to import the pre-divided airship vector propeller body external flow field mesh model in sequence.

[0089] After importing, in Fluent software, select steady state for time in Settings - General. In Settings - Element Region Conditions - Fluid, open the motion mesh reference frame for the four vector propeller rotation regions. In the TUI command window of Fluent software, enter `mesh / modify / mrf-to-sliding-mesh`, and then enter the corresponding ID number of the vector propeller rotation region to separate the rotation and revolution regions into sliding meshes. In Settings - Boundary Conditions - Walls, select the outer surfaces of the four revolution regions and change their type to overlap. Then, in the overlap mesh interface, select the propeller external flow field mesh for the background mesh region and the propeller revolution fluid region for the component region. Enter the overlap mesh interface name to complete the overlap mesh settings. Finally, click Initialize to complete the nesting of the overlap meshes. The nested airship assembly layout is as follows. Figure 8 As shown

[0090] Step 3: Solve for the steady-state and transient solutions of the vector propeller thrust.

[0091] First, a steady-state MRF simulation of the vector propeller was performed. In Fluent software, under Settings-General, the solver was selected as pressure-based, the time was set to steady-state, and the turbulence model was selected as the k-omega SST model, with the model parameters kept at their default values. Based on the atmospheric environment at an altitude of 20 km, the working conditions in the physical model menu were set to 5474.9 Pa, and the reference pressure location was set to a position far from the hull. The fluid was selected as air, the density was set to ideal-gas, and the viscosity was set to 1.4261 × 10⁻⁵. In Settings-Boundary Conditions-Inlet and Outlet, the temperatures at the velocity inlet and pressure outlet were set to 216.7 K. For single propeller simulation, the vector rotation angle was not considered, and the incoming flow velocity was set to 5 m / s, 10 m / s, 15 m / s, 20 m / s, and 25 m / s. When simulating the vector propeller on the submarine, the relationship between thrust and vector rotation angle needs to be considered. Meanwhile, the incoming flow velocity needs to be set according to different vector angle ranges. When the vector angle is 0, 5, or 10 degrees, the airship's drag is relatively small, and the incoming flow velocity is set to 5 m / s, 10 m / s, 15 m / s, 20 m / s, and 25 m / s, respectively. When the vector angle is 30°, considering the increased drag when the airship flies at an angle, the incoming flow velocity is set to 4 m / s, 8 m / s, 12 m / s, 16 m / s, and 20 m / s. When the vector angle is 60°, the incoming flow velocity is set to 3 m / s, 6 m / s, 9 m / s, 12 m / s, and 15 m / s. When the vector angle is 90°, the incoming flow velocity is set to 1 m / s, 3 m / s, 5 m / s, 7 m / s, and 9 m / s. In the Settings - Element Region Conditions - Fluid section, set the origin, direction, and rotation speed of the propeller's self-rotating fluid region accordingly. Set the propeller rotation speed *n* to 400 rpm, 600 rpm, 800 rpm, 1000 rpm, and 1200 rpm. In the Solution - Method section, set the pressure-velocity coupling scheme to Coupled, select LeastSquaresCell Based for the gradient option in Spatial Discretization, and select Second Order Upwind for all other discretization methods. To balance stability and convergence speed, set the momentum relaxation factor in Solution - Control to 0.3. In Solution - Report Definition, set the corresponding output reports for propeller thrust and torque. In Results - Graphics - Contour Plot, create the required contour plot. In Solution - Initialization, select Standard Initialization, choose Inlet for the calculation reference location, set the temperature to 216.7 K, and click Initialize to provide an initial solution for the flow field. In the Solver - Calculation Settings - Run Calculation section, set the number of iteration steps to 200 and click Start Calculation. Based on the calculated residual convergence curve and the propeller output parameters, determine the convergence of the simulation. After iterative calculation, the simulation convergence is good, and a stable steady-state solution is obtained.

[0092] After completing the steady-state solution using MRF, the steady-state solution data of the external flow field has been interpolated into the mesh. Based on this, open Settings > General > Time > Transient Solution, and change the discretization format of the time term in Solution > Method to FirstOrder Implicit. Open the settings for the propeller rotation region in the fluid, open Mesh Motion in Settings, and copy the rotation-related settings from the motion reference frame to Mesh Motion. Open the Run Calculation settings, set the time step to 0.002s, and the number of time steps to 100 steps to complete the transient simulation solution settings.

[0093] Step 4: Automatically set different vector rotation angles for the vector propeller. In the custom module, the origin and direction of the rotation axis of the vector propeller's rotation region are related to the vector rotation angle μ. The settings are shown in Table 3.

[0094] Table 3 Vector Propeller Rotation Zone Settings

[0095] Rotation area Origin of rotation axis Rotation axis direction Propeller 1 (6.325+1.25*cosμ,10,1.25*sinμ) (-cosμ,0,sinμ) Propeller 2 (6.325+1.25*cosμ,-10,1.25*sinμ) (cosμ,0,-sinμ) Propeller 3 (-8.675+1.25*cosμ,10,1.25*sinμ) (-cosμ,0,sinμ) Propeller 4 (-8.675+1.25*cosμ,-10,1.25*sinμ) (cosμ,0,-sinμ)

[0096] In Fluent software, in Settings - General Module, select Transient as the solver type. In Settings - Element Region Conditions - Fluid, set the propeller revolution region and propeller rotation region. Turn on Mesh Motion and set the corresponding propeller revolution axis origin and rotation axis direction. See Table 4 for specific parameters. Set the rotation speed to 1° / s.

[0097] Table 4. Propeller Revolution Area Settings

[0098] Public revolution area Origin of rotation axis Rotation axis direction Propeller 1 (6.325，7.5，0) (0，1，0) Propeller 2 (6.325，-7.5，0) (0，1，0) Propeller 3 (-8.675，7.5，0) (0，1，0) Propeller 4 (-8.675，7.5，0) (0，1，0)

[0099] In Settings - Dynamic Mesh, click Preview Mesh Motion, set the appropriate time step and number of time steps, and click Preview. The external flow field mesh of the vector propeller will begin to rotate. After the mesh motion is complete, the corresponding vector rotation angle μ is obtained. The formula for calculating the vector rotation angle μ is as follows:

[0100] μ = Rotation speed × Time step × Time steps

[0101] By setting different time steps, the required vector rotation angle can be obtained. Through model updates, the working conditions under different vector rotation angles can be set.

[0102] Step 5: For the single propeller external flow field model, repeat step 3 to obtain multiple thrust transient solutions for the single propeller. For the onboard vector propeller external flow field model, repeat steps 3 and 4 to obtain transient solutions corresponding to different vector rotation angles. The thrust transient solutions for the single propeller are shown in Table 5, and the thrust transient solutions for the onboard vector propeller are shown in Tables 6 and 7.

[0103] Table 5 Thrust of a single propeller

[0104]

[0105]

[0106] Table 6. Thrust of the front-end vector propeller at different vector rotation angles.

[0107]

[0108] Table 7. Thrust of the rear-end vector propeller at different vector rotation angles.

[0109]

[0110]

[0111] Step 6: Using data fitting methods, complete the thrust modeling of the vector propeller on the submarine.

[0112] Considering that the thrust of a vector propeller is affected by multiple variables such as incoming flow velocity, rotational speed, and vector angle, a polynomial fitting method can be used to obtain the thrust model of the vector propeller. However, simulation data and measured results show that the thrust data of a single propeller and the thrust data of the vector propeller on the submarine are not consistent. To improve the accuracy of polynomial fitting while reducing the fitting difficulty, this invention adopts a hierarchical fitting strategy to achieve thrust modeling of the vector propeller. That is, using the polynomial fitting method, a single thrust model of the single propeller varies with incoming flow velocity and rotational speed.

[0113] Based on a single thrust model, a multinomial fitting method is used to obtain a mathematical model of the thrust of the front vector propeller as a function of the incoming flow velocity and rotational speed at a certain vector angle. By analogy, multiple mathematical models of the front thrust are obtained for different vector angles. Based on these mathematical models of the front thrust, a set of front fitting parameters corresponding to different vector angles is constructed. Then, based on the set of front fitting parameters, a mathematical model of the front fitting parameters as a function of the vector angle is obtained using a multinomial fitting method, thus completing the construction of the thrust model of the front vector propeller.

[0114] Then, based on the front thrust mathematical model, a polynomial fitting method is used to obtain the back thrust mathematical model of the rear vector propeller under a certain vector angle, which shows the change of thrust with the incoming flow velocity and rotation speed. By analogy, multiple back thrust mathematical models are obtained for different vector angles. Based on these back thrust mathematical models, a set of back fitting parameters corresponding to different vector angles is constructed. Then, based on the set of back fitting parameters, a polynomial fitting method is used to obtain the back fitting parameter mathematical model of the fitting parameters changing with the vector angle, thus completing the construction of the thrust model of the rear vector propeller.

[0115] Finally, a multi-vector propeller thrust model is constructed based on a single thrust model, a front-end fitting parameter mathematical model, a front-end thrust mathematical model, a back-end fitting parameter mathematical model, and a back-end thrust mathematical model.

[0116] Specifically as follows:

[0117] i. Thrust modeling of a single propeller

[0118] For a single propeller, considering only the effects of the incoming flow velocity U and the rotational speed n, thrust fitting can be performed on the data of a single propeller under different operating conditions. The fitting coefficients of the thrust model of the single propeller are: k′1=0.00025307, k′2=0.00281335 and k′3=-0.14623238. The corresponding fitting formula, i.e., the single thrust model, is shown in Equation 1, where T Fit The thrust of a single propeller;

[0119] T Fit =k′1n 2 +k′2nU+k′3U 2 (1)

[0120] ii. Based on the thrust model of a single propeller, perform thrust modeling for the forward vector propeller on the submarine.

[0121] For a given vector angle, first perform polynomial fitting on the thrust data (i.e., transient solutions) of the front-end vector propeller under different operating conditions, such as different incoming flow velocities U and different rotational speeds n, to obtain the fitting coefficients k′ of the mathematical model of the front-end thrust at that vector angle. i For i = 4, 5, 6, 7, 8, the corresponding fitting formula is shown in Equation 2, where, To obtain the thrust of the forward vector propeller on the submarine, the above steps are repeated to obtain the fitting coefficient k′ of the mathematical model of the forward thrust at different vector rotation angles of 0°, 5°, 10°, 30°, 60° and 90°. i See Table 8 for details.

[0122]

[0123] Therefore, the thrust of the vector propeller at the front of the boat can be increased. With single propeller thrust T Fit The difference between them is defined as the sum of the thrust differences caused by the coupling effect between the vector propeller and the hull.

[0124] Then, according to Table 8, for the same fitting parameter k′ i Corresponding to different vector rotation angles, they collectively constitute the front-end fitting parameter set. Based on this front-end fitting parameter set, for any fitting parameter k′ iBy performing polynomial fitting on the corresponding different vector rotation angles, the fitting parameters k′ can be obtained. i The fitting relationship between the vector rotation angle μ and the corresponding fitting parameter a i b i c i d i e i See Table 9 for details, where the fitting relationship is shown in Formula 3.

[0125] k′ i =a i μ 4 +b i μ 3 +c i μ 2 +d i μ+e i (3)

[0126] This shows that the thrust of the vector propeller at the front of the computing boat... At the same time, the thrust difference generated by the coupling effect of the hull needs to be considered. The thrust difference caused by the coupling effect of the hull It is a function of vector rotation angle μ, incoming flow velocity U, and rotation number n.

[0127] iii. Based on the thrust model of the front-end vector propeller, construct the thrust model of the rear-end vector propeller.

[0128] When constructing the thrust model of the rear-end vector propeller, based on the front-end thrust mathematical model, for a certain vector angle, polynomial fitting is first performed on the thrust data (i.e., transient solutions) of the rear-end vector propeller under different operating conditions, such as different incoming flow velocities U and different rotational speeds n, to obtain the fitting parameters k″ of the rear-end thrust mathematical model under that vector angle. i For i = 4, 5, 6, 7, 8, the corresponding fitting formula is shown in Equation 4, where, To obtain the thrust of the vector propeller at the rear end of the submarine, the above steps are repeated to obtain the fitting parameters k″ of the mathematical model of the rear thrust at different vector angles of 0°, 5°, 10°, 30°, 60° and 90°. i i = 4, 5, 6, 7, 8, see Table 10 for details.

[0129]

[0130] Therefore, the difference in thrust between the front and rear vectoring propellers on the submarine can be defined as the thrust difference between the front and rear propellers.

[0131] Then, according to Table 8, the same fitting parameter k″ iCorresponding to different vector rotation angles, they collectively constitute the back-end fitting parameter set. Based on this back-end fitting parameter set, for any fitting parameter k″ i The fitting parameters k″ are obtained by polynomial fitting of the corresponding different vector rotation angles. i The fitting relationship between the vector rotation angle μ and the corresponding fitting parameter a′ i b′ i c′ i See Table 11 for details, and the fitting relationship is shown in Formula 5.

[0132] k″ i =a′ i μ 2 +b′ i μ+c′ i (5)

[0133] This shows that the thrust of the vector propeller at the rear of the computing boat... At this time, it is necessary to consider the possibility that the difference in thrust between the front and rear propellers may be caused by the wake. Similarly, it is a function of the vector rotation angle μ, the incoming flow velocity U, and the number of revolutions n.

[0134] Verification has shown that the wake of the front-end vector propeller at small vector angles will have a certain impact on the thrust of the rear-end vector propeller. Numerical simulation shows that the influence range of the vector angle is 0°-10°. Within this vector angle range, the calculated thrust of the rear-end vector propeller is... The difference in thrust between the front and rear propellers due to the wake needs to be considered. When the vectoring angle exceeds 10°, the thrust of the rear vectoring propeller is basically the same as that of the front vectoring propeller, and the same thrust model can be used.

[0135] In summary, based on the transient solutions of the single propeller and the onboard vector propeller obtained in steps three and four above, polynomial fitting was performed on the numerical simulation results of the single propeller under different incoming flow velocities U and different revolutions n, and the onboard vector propeller under different vector angles μ, to obtain the thrust models of the single propeller and the front and rear vector propellers of the boat as follows:

[0136]

[0137] Table 8. Coefficients of the front-end vector propeller thrust model under different vector rotation angles.

[0138]

[0139]

[0140] Table 9 Fitting coefficients of the front-end vector propeller thrust model and vector rotation angle

[0141] <![CDATA[a i ]]> <![CDATA[b i ]]> <![CDATA[c i ]]> <![CDATA[d i ]]> <![CDATA[e i <!-- 14 -->]]> i＝4 <![CDATA[-4.8×10 -9 ]]> <![CDATA[7.335×10 -7 ]]> <![CDATA[-3.619×10 -5 ]]> <![CDATA[5.506×10 -4 ]]> <![CDATA[3.174×10 -3 ]]> i＝5 <![CDATA[3.966×10 -7 ]]> <![CDATA[-6.034×10 -5 ]]> <![CDATA[3.065×10 -3 ]]> <![CDATA[-6.135×10 -2 ]]> -0.747 i＝6 <![CDATA[1.29×10 -8 ]]> <![CDATA[2.207×10 -6 ]]> <![CDATA[9.876×10 -5 ]]> <![CDATA[-4.804×10 -4 ]]> <![CDATA[5.798×10 -3 ]]> i＝7 0 <![CDATA[2.4×10 -9 ]]> <![CDATA[1.318×10 -7 ]]> <![CDATA[2.282×10 -6 ]]> <![CDATA[4.499×10 -7 ]]> i＝8 <![CDATA[-1×10 -9 ]]> <![CDATA[1.695×10 -7 ]]> <![CDATA[-8.865×10 -6 ]]> <![CDATA[1.3×10 -4 ]]> <![CDATA[5.62×10 -4 ]]>

[0142] Table 10 shows the fitting results of the relationship between the thrust model coefficients of the rear-end vector propeller and different vector angles.

[0143]

[0144] Table 11 Fitting coefficients of the rear-end vector propeller thrust model coefficients and vector rotation angle

[0145] <![CDATA[a′ i ]]> <![CDATA[b′ i ]]> <![CDATA[c′ i ]]> i＝4 0.00053543 -0.00591136 0.00125902 i＝5 -0.04675083 0.58569892 -1.17024304 i＝6 0.00129301 -0.00529682 -0.07550377 i＝7 0.00000021 -0.00000513 0.00003326 i＝8 0.00002072 -0.00069340 0.00497292

[0146] To verify the feasibility of this invention, the following experiments were conducted:

[0147] When the vector rotation angle is 3°, the thrust model established in this invention is used to predict the thrust of the forward and aft vector propellers on the submarine. The prediction results are compared with the CFD numerical simulation results. Figure 11 As shown, and using single-valued errors ERROR, RMSE, and R... 2 To evaluate the accuracy of the thrust fitting, consider the individual error ERROR, root mean square error RMSE, and goodness of fit R. 2 The formula is as follows:

[0148]

[0149] Table 12 Thrust Fit Verification of Front-End and Rear-End Vector Propellers at a 3° Vector Rotation Angle

[0150]

[0151] When the vector rotation angle is 3°, the thrust model established in this paper is used to predict the thrust of the forward and rear-end vector propellers. The RMSE of the predicted thrust of the forward vector propeller is 0.4647, and the R² is 0.9985. The RMSE of the predicted thrust of the rear-end vector propeller is 8.8929, and the R² is 0.9925. Overall, the fitting error is small, and the model has high reliability. The fitted data is visualized, and the prediction results are compared with the CFD numerical simulation results. Figure 11 As shown.

[0152] Depend on Figure 11As can be seen, the fitted surface represents the prediction result of the thrust model under a 3° vector rotation angle. The red dots in the figure represent the CFD numerical simulation results. Under a 3° vector rotation angle, the maximum single-value error (ERROR) for the thrust prediction of the front vector propeller is 49.3% under the condition of an incoming flow velocity of 25 m / s and a propeller speed of 600 rpm. Due to the relatively low speed, the CFD numerical simulation value under this condition is 19.59 N, while the fitted thrust value is 29.25 N. The actual error is not significant. Similarly, the maximum error for the rear vector propeller is 23.44% under the condition of an incoming flow velocity of 25 m / s and a propeller speed of 600 rpm. The single-value error ERROR under other conditions is generally below 10%, and the local errors are not significant. Overall, this indicates that the propeller thrust model has good prediction performance and verifies the accuracy of the onboard vector propeller thrust model. This model can accurately predict the thrust changes of the front and rear propellers on the airship under different operating conditions, providing theoretical support and new ideas for thrust modeling and flight control strategy design of high-altitude airship multi-vector propeller systems.

[0153] Figure 9 This demonstrates that using overlapping grid technology to realize the propeller vector rotation motion on the boat, and using MRF and SM technology to realize the propeller's rotation motion, can yield a stable external flow field trace map of the entire boat, indicating that the method of the present invention has strong convergence. Figure 10 The velocity contour maps of the front and rear propellers under different vector angles show that the propeller wakes are evenly distributed and the range of influence of the wakes varies under different vector angles, demonstrating the impact of the wake of the front vector propeller on the rear vector propeller.

[0154] In summary, the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for modeling the thrust of a multi-vector propeller for high-altitude aerostats, characterized in that... Includes the following steps: Step 1: Establish external flow field mesh models for the single propeller body, the airship body, and the onboard vector propeller body, respectively; Step 2: Using overlapping mesh technology, embed the external flow field mesh model of the vector propeller body on the airship into the external flow field mesh model of the airship body; Step 3: Solve the steady-state solution of propeller thrust using the MRF multiple reference frame method, and then combine it with the SM slip mesh technique to obtain the transient solution of propeller thrust; Step 4: Use the custom settings module to automatically set different vector rotation angle states for the vector propeller; Step 5: Repeat step 3 to obtain the transient thrust solutions of multiple single propellers under different incoming flow velocities and rotational speeds; repeat steps 3 and 4 to obtain the transient thrust solutions of the onboard vector propeller under different vector angles, incoming flow velocities, and rotational speeds. Step 6: Based on the transient thrust solution of a single propeller, the transient thrust solution of the onboard vector propeller, vector angle, incoming flow velocity, and rotational speed data, construct a multi-vector propeller thrust model using data fitting methods and a multi-level fitting strategy.

2. The multi-vector propeller thrust modeling method for high-altitude aerostats according to claim 1, characterized in that: In step six, a single thrust model of a single propeller varying with the incoming flow velocity and rotational speed is obtained using a polynomial fitting method. Based on the single thrust model, a multinomial fitting method is used to obtain a mathematical model of the thrust of the front vector propeller as a function of the incoming flow velocity and rotational speed at a certain vector angle. By analogy, multiple mathematical models of the front thrust are obtained for different vector angles. Based on these mathematical models of the front thrust, a set of front fitting parameters corresponding to different vector angles is constructed. Then, based on the set of front fitting parameters, a mathematical model of the front fitting parameters as a function of the vector angle is obtained using a multinomial fitting method, thus completing the construction of the thrust model of the front vector propeller. Then, based on the aforementioned front thrust mathematical model, a polynomial fitting method is used to obtain a rear thrust mathematical model in which the thrust of the rear vector propeller varies with the incoming flow velocity and rotational speed at a certain vector angle. By analogy, multiple rear thrust mathematical models corresponding to different vector angles are obtained. Based on these rear thrust mathematical models, a set of rear fitting parameters corresponding to different vector angles is constructed. Then, based on the set of rear fitting parameters, a polynomial fitting method is used to obtain a rear fitting parameter mathematical model in which the fitting parameters vary with the vector angle, thus completing the construction of the rear vector propeller thrust model. Finally, a multi-vector propeller thrust model is constructed based on a single thrust model, a front-end fitting parameter mathematical model, a front-end thrust mathematical model, a back-end fitting parameter mathematical model, and a back-end thrust mathematical model.

3. The multi-vector propeller thrust modeling method for high-altitude aerostats according to claim 2, characterized in that: The calculation formula for the multi-vector propeller thrust model is as follows: The values ​​of parameters k4′~k8′ for the front-end mathematical model under different vector rotation angles μ are as follows: The parameters k4′~k8′ correspond to the parameter a in the front-end parameter mathematical model. i ~e i The possible values ​​are as follows: The values ​​of parameters k4″~k8″ for the back-end mathematical model under different vector rotation angles μ are as follows: The parameters k4″~k8″ correspond to the parameter a′ in the backend parameter mathematical model. i ~c′ i The possible values ​​are as follows: T Fit The thrust of a single propeller is represented by U, the velocity of the incoming flow is U, and the rotational speed of the propeller is n. This represents the thrust of the vectoring propeller at the bow of the submarine. This indicates the thrust of the vectoring propeller at the rear of the submarine. This indicates the thrust difference between the front and rear vector propellers. This indicates the thrust difference generated by the coupling effect between the propeller and the airship body.

4. The multi-vector propeller thrust modeling method for high-altitude aerostats according to claim 1, characterized in that: In step one, the geometric model of the external flow field of a single propeller body is established using SpaceClaim software. Then, the geometric model of the external flow field of a single propeller body is imported into Fluent software, and the Fluent Meshing module is used to perform mesh generation to complete the construction of the external flow field mesh model of a single propeller body. The geometric model of the external flow field computational domain of the airship body was established using SpaceClaim software. Then, the geometric model of the external flow field computational domain of the airship body was imported into Fluent software. The Fluent Meshing module was used to perform mesh generation, and the construction of the external flow field mesh model of the airship body was completed. The geometric model of the external flow field of the onboard vector propeller was established using SpaceClaim software. Then, the geometric model of the external flow field of the onboard vector propeller was imported into Fluent software, and the Fluent Meshing module was used to perform mesh generation, thus completing the construction of the external flow field mesh model of the onboard vector propeller.

5. The multi-vector propeller thrust modeling method for high-altitude aerostats according to claim 4, characterized in that: In step two, the overlapping mesh technique in Fluent software is used to nest the external flow field mesh model of the vector propeller body on the airship into the external flow field mesh model of the airship body.

6. The multi-vector propeller thrust modeling method for high-altitude aerostats according to claim 5, characterized in that: In Fluent software, in the Domain menu bar, under the Region module, click the Additional Options and then Additional Case Files to import the pre-defined vector propeller external flow field mesh model. After importing, select Steady-State Simulation, open the motion mesh reference frame for the four vector propeller rotation regions, and in the TUI command window of Fluent software, enter `mesh / modify / mrf-to-sliding-mesh`, followed by the corresponding ID number of the vector propeller rotation region, to separate the rotation and revolution regions into sliding meshes. In the boundary condition wall, select the outer surfaces of the four revolution regions, change their type to Overlap, and then in the Overlap Mesh Interface, select the vector propeller external flow field mesh in the background mesh region and the vector propeller revolution fluid region in the component region. Enter the name of the Overlap Mesh Interface to complete the Overlap Mesh settings, and click Initialize. The nesting of the Overlap Mesh is now complete.

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