Low Reynolds number aerodynamic configuration optimization method for 4D printed propeller

Abstract

The invention provides a low Reynolds number aerodynamic configuration optimization method for a 4D printing propeller, and relates to the technical field of 4D printing and aircraft propeller aerodynamic design, and the method comprises the steps: determining a working Reynolds number and a target thrust according to a miniature unmanned plane design index; selecting an adaptive low-Reynolds-number high-lift reference airfoil profile; generating a three-dimensional propeller model meeting thrust based on the airfoil, and unfolding the three-dimensional propeller model into a two-dimensional planar precursor; the surface area of the precursor blade is planned as a radial printing path, and the internal deformation area is planned as a mixed angle printing path; the precursor is manufactured by adopting a PLA / PETG multi-material 4D printing process; thermal stimulation is applied to the component, and the component is triggered to be automatically deformed from two dimensions and locked into a three-dimensional propeller. Accurate programming and integrated manufacturing of the aerodynamic configuration of the propeller under the low Reynolds number are achieved, and the aerodynamic efficiency, the surface quality and the design reliability are effectively improved.

Description

Technical Field

[0001] This invention relates to the fields of 4D printing and aircraft propeller aerodynamic design technology, and in particular to a method for optimizing the aerodynamic shape of 4D printed propellers with low Reynolds number. Background Technology

[0002] With the widespread application of unmanned aerial vehicle (UAV) technology in military reconnaissance, agricultural monitoring, and logistics delivery, especially the increasing demand for portability, rapid deployment, and lightweight micro-UAVs, the design and manufacturing of their core power component—the propeller—faces severe challenges. Micro-UAVs typically operate in low-altitude, low-speed environments. Their propellers have small characteristic dimensions and relatively low rotational speeds, resulting in operating Reynolds numbers often in the low Reynolds number range, typically on the order of 10^4. Under these flow conditions, air viscosity is significantly enhanced, and flow separation is easily achieved. Traditional propeller airfoils designed based on high Reynolds numbers exhibit problems such as a sharp decrease in lift coefficient, premature stall, and a drastic reduction in efficiency, severely restricting the endurance, payload, and flight stability of micro-UAVs.

[0003] Traditional propeller manufacturing relies primarily on mold forming or CNC machining, which is not only costly and time-consuming but also struggles to achieve complex three-dimensional surfaces optimized for low Reynolds number flow fields, especially for blades with continuous spatial twist distributions. In recent years, additive manufacturing (3D printing) technology has enabled the rapid prototyping of complex structures and has been used to directly manufacture drone propellers. However, when manufacturing propellers with large twist angles and thin walls using traditional fused deposition modeling (FDM) processes, the inherent layer-by-layer deposition method creates significant step effects and interlayer textures on the blade surface. This surface roughness disrupts the already sensitive boundary layer flow at low Reynolds numbers, inducing additional turbulence and flow separation, leading to significant aerodynamic performance degradation and severe thrust loss. Furthermore, 3D printing produces static, rigid structures that cannot be post-manufacturing shaped to compensate for design errors or adapt to different flight conditions.

[0004] Emerging 4D printing technology endows structures with the ability to undergo controllable deformation in response to external stimuli, offering a new approach to solving the aforementioned problems. However, research on applying 4D printing to high-performance aerodynamic structures (such as propellers) is still in its early stages. The main challenge lies in the lack of a systematic approach that integrates aerodynamic design, deformation programming, performance prediction, and verification. Existing technologies often separate shape-changing functionality from aerodynamic performance optimization: either focusing only on the deformation characteristics of the material while neglecting the aerodynamic efficiency of the final structure, or optimizing only the three-dimensional aerodynamic shape without being able to achieve it through programmable manufacturing. How to specifically select or optimize airfoils for low Reynolds number conditions and accurately "encode" them into a two-dimensional planar precursor, so that the precursor can be locked into a three-dimensional propeller with both excellent aerodynamic shape and high surface quality after controlled deformation, is a key technical problem that has not yet been effectively solved. In addition, the lack of reliable means to predict the aerodynamic performance of the propeller after deformation before manufacturing leads to high design iteration costs and long cycles, making it difficult to achieve performance-driven design and manufacturing integration. Summary of the Invention

[0005] To address the challenges of existing technologies, such as the difficulty of achieving both high aerodynamic efficiency and complex surface forming flexibility for micro propellers at low Reynolds numbers using traditional manufacturing methods, the aerodynamic performance degradation caused by surface defects in direct 3D printing, and the lack of a systematic solution for optimizing aerodynamic shapes at low Reynolds numbers and programmable deformation manufacturing in existing 4D printing technologies, which leads to unpredictable and unguaranteed final performance due to the disconnect between various stages, this invention provides a method for optimizing the aerodynamic shape at low Reynolds numbers for 4D-printed propellers.

[0006] The technical solution provided by this invention is as follows: The present invention provides a method for optimizing the low Reynolds number aerodynamic shape of 4D-printed propellers, comprising: S1: Determine the operating Reynolds number range and target thrust of the propeller based on the design specifications of the micro UAV; S2: Select a preset airfoil with high maximum lift coefficient, delayed stall characteristics and wide lift-to-drag ratio platform from the low Reynolds number airfoil library as the reference airfoil; S3: Based on the cross-sectional data of the reference airfoil, use propeller design software to generate a three-dimensional propeller initial model that meets the target thrust, and obtain its two-dimensional planar precursor unfolding model. S4: Perform region division and printing path planning on the two-dimensional planar precursor model, wherein the blade surface region is planned as the first printing region using a radial printing path, and the internal region used to construct the spatial torsion angle is planned as the second printing region using a mixed angle printing path. S5: Based on the printing path planning, the two-dimensional planar precursor component is manufactured using a 4D printing process containing shape memory polymer materials; S6: Apply an external stimulus to the printed component to trigger its autonomous deformation from a two-dimensional planar precursor and lock it into a three-dimensional propeller structure.

[0007] Furthermore, in step S2, the preset airfoil is the SD7062 airfoil.

[0008] Further, in step S3, the propeller aerodynamics is designed using Passwing software and point cloud data is generated, which is then imported into 3D modeling software for model reconstruction and 2D unfolding.

[0009] Further, in step S4, the region division specifically includes: dividing the upper and lower surfaces of the blade into the first printing region, and printing using a single radial path from the blade hub to the blade tip; dividing the internal region located between the upper and lower surfaces into the second printing region, and printing using a mixed angle path that continuously changes from radial to circumferential, so as to program the gradient-changing material anisotropy, thereby inducing a continuous spatial torsion angle after deformation.

[0010] Furthermore, in step S5, the shape memory polymer material is polylactic acid (PLA); the 4D printing process is multi-material composite printing, which simultaneously prints polyethylene terephthalate copolymer (PETG) in areas where structural constraints are required.

[0011] Furthermore, after step S5 and before step S6, step S5a is also included: performing aerodynamic performance simulation on the initial three-dimensional propeller model using computational fluid dynamics (CFD) methods. The simulation includes establishing a rotating flow field computational domain, dividing the mesh, setting boundary conditions, and solving to obtain thrust, power, and flow field distribution data. If the simulation results do not meet the design requirements, the process returns to step S3 to adjust the model parameters.

[0012] Furthermore, in step S5a, the specific steps of the CFD simulation include: S5a1: Establish a cylindrical computational domain containing a rotating domain. The diameter of the rotating domain is slightly larger than the diameter of the propeller. The overall size of the computational domain satisfies the far-field boundary conditions. S5a2: The computational domain is discretized using an unstructured mesh, and the mesh is refined on the blade surface; S5a3: Set the velocity inlet, pressure outlet, and blade wall boundary conditions, and use the SST k-ω turbulence model; S5a4: The propeller rotation is simulated using the sliding mesh method to calculate the steady-state and transient aerodynamic performance.

[0013] Furthermore, in step S6, the external stimulus is a thermal stimulus, specifically placing the component in a thermal environment of 70-75°C for 3-5 minutes.

[0014] Furthermore, after step S6, step S7 is also included: testing the surface morphology and aerodynamic performance of the deformed three-dimensional propeller structure; wherein, the surface morphology test uses atomic force microscopy (AFM) to quantify the surface roughness, and the aerodynamic performance test uses a tension-speed test platform to measure the thrust output under different voltages.

[0015] Furthermore, in step S7, the performance of the 4D printed propeller is compared with that of a similar propeller printed by conventional fused deposition modeling (FDM) 3D printing. The evaluation indicators include at least surface roughness, maximum lift, and energy efficiency.

[0016] The beneficial effects of the technical solution provided by this invention include at least the following: (1) In this invention, the problem of low aerodynamic efficiency of micro propellers in low Reynolds number flow fields is effectively solved by combining low Reynolds number aerodynamic shape optimization with 4D printing deformation programming depth. First, the Reynolds number range is determined according to the specific working conditions of the micro UAV, and a special airfoil with high lift and delayed stall characteristics within this range is selected as the design benchmark. Then, a three-dimensional model that meets the target thrust is generated using propeller design software, and it is precisely unfolded into a two-dimensional planar precursor. Most importantly, by dividing the precursor into sections and printing a mixed angle path that continuously changes from radial to circumferential in the core internal region that determines the spatial twist angle, the anisotropy of the gradient is programmed inside the material. When subjected to thermal stimulation, this preset material memory drives the two-dimensional plane to autonomously and precisely fold and twist into the expected three-dimensional propeller shape. Its continuous curved surface and precise twist angle distribution are difficult to achieve directly by traditional 3D printing, thereby ensuring that the propeller can still maintain excellent lift generation efficiency and stable working characteristics at low Reynolds numbers.

[0017] (2) In this invention, the problems of high surface roughness in traditional 3D printed propellers and difficulty in deformation control in 4D printing are solved synergistically by heterogeneous material composite printing and refined regional path planning. In manufacturing, PLA is used as the shape memory driving material, and PETG material is composite printed in the areas that need to be constrained. When heated, PETG material mainly softens rather than shrinks in a directional manner, which can effectively constrain the free deformation of PLA and guide the deformation to a preset direction. In terms of path planning, the areas that ultimately constitute the upper and lower aerodynamic surfaces of the blade are planned to be printed using a single radial path, which ensures the smooth continuity of the surface after deformation and minimizes the interference of layer textures on the airflow. The internal deformation area is planned as a special hybrid path. This combination of the "driving-constraint" material system and the "surface-internal" differentiated path design enables the two-dimensional precursor to not only reliably transform into a complex three-dimensional structure after heating, but also the final propeller has a smooth aerodynamic surface close to that of traditional precision machining, which significantly reduces surface friction resistance and flow separation risk and improves overall aerodynamic efficiency.

[0018] (3) In this invention, by embedding computational fluid dynamics simulation into the manufacturing process, a closed loop of "design-simulation-optimization" is constructed, which solves the problems of design relying on experience, performance being difficult to predict, and iteration costs in traditional methods. After generating the initial three-dimensional propeller model based on the optimized airfoil and planning the printing path, it is not directly manufactured, but the model is first simulated in detail using CFD methods. By establishing a flow field model containing the rotation domain, dividing high-precision meshes, setting realistic boundary conditions, and performing numerical solutions, key data such as thrust, power, and flow field distribution of the design scheme can be obtained in advance. If the simulation results do not meet the design requirements, the geometric parameters of the propeller, such as the twist angle distribution and chord length, can be adjusted immediately, and then the simulation is performed again for verification until the performance meets the standards. This process moves the performance verification and optimization to before manufacturing, so that the manufacturing of propellers based on 4D printing is no longer a blind "trial and error", but a performance-driven design based on accurate numerical simulation, which greatly improves the success rate of the first manufacturing and the performance reliability of the final product, and provides an effective tool for the rapid development of high-performance customized propellers. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 A flowchart illustrating the low Reynolds number aerodynamic shape optimization method for 4D printed propellers provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of blade planar precursor region division and printing path planning in the low Reynolds number aerodynamic shape optimization method for 4D printed propellers provided in an embodiment of the present invention. Figure 3 A schematic diagram of the computational fluid dynamics (CFD) simulation setup and convergence process in the low Reynolds number aerodynamic shape optimization method for 4D printed propellers provided in an embodiment of the present invention; Figure 4 A schematic diagram comparing the surface morphology of traditional 3D printed and 4D printed propellers in the low Reynolds number aerodynamic shape optimization method for 4D printed propellers provided in an embodiment of the present invention. Figure 5 This is a schematic diagram showing the aerodynamic performance testing platform and lift comparison results in the low Reynolds number aerodynamic shape optimization method for 4D printed propellers provided in an embodiment of the present invention. Detailed Implementation

[0021] The technical solution of the present invention will now be described with reference to the accompanying drawings.

[0022] In embodiments of the present invention, words such as "exemplarily," "for example," etc., are used to indicate that something is an example, illustration, or description. Any embodiment or design described as "exemplary" in the present invention should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of the word "exemplary" is intended to present the concept in a concrete manner. Furthermore, in embodiments of the present invention, the meaning expressed by "and / or" can be both, or either one.

[0023] In the embodiments of this invention, the terms "image" and "picture" may sometimes be used interchangeably. It should be noted that, without emphasizing the distinction between them, their intended meanings are consistent. Similarly, the terms "of," "corresponding (relevant)," and "corresponding" may sometimes be used interchangeably. It should be noted that, without emphasizing the distinction between them, their intended meanings are consistent.

[0024] In embodiments of the present invention, sometimes the subscript is as follows: It may be mistakenly written as a non-subscript form such as W1. When the distinction is not emphasized, the meaning they express is the same.

[0025] To make the technical problems, technical solutions and advantages of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings and specific embodiments.

[0026] Reference manual attached Figure 1 The diagram illustrates a flowchart of a low Reynolds number aerodynamic shape optimization method for 4D printed propellers provided in an embodiment of the present invention.

[0027] This invention provides a method for optimizing the aerodynamic shape of 4D-printed propellers with low Reynolds number, and the process may include the following steps: S1: Determine the operating Reynolds number range and target thrust of the propeller based on the design specifications of the micro UAV.

[0028] In the initial stages of micro-UAV design, it is crucial to define its core performance indicators, which directly determine the propeller design inputs. Specifically, based on the UAV's expected takeoff weight, target hovering time, and the performance parameters of the selected micromotor, the total thrust required to overcome gravity and maintain stable flight must be calculated. Furthermore, by combining the propeller's expected operating speed and characteristic chord length with the Reynolds number calculation formula, the range of low Reynolds number flow fields in which the propeller actually operates can be determined. This Reynolds number range is the fundamental basis for subsequent selection of suitable airfoils, and its typical value is usually on the order of 10^4.

[0029] S2: Select a preset airfoil with a high maximum lift coefficient, delayed stall characteristics and a wide lift-to-drag ratio platform from the low Reynolds number airfoil library as the reference airfoil.

[0030] After determining the operating Reynolds number range, a selection process needs to be conducted from a database of low Reynolds number airfoils that have been validated through wind tunnel testing. The core selection criterion is to find airfoils with excellent aerodynamic performance within this Reynolds number range. Key performance parameters to focus on include a high maximum lift coefficient, good delayed stall characteristics, and a wide lift-to-drag ratio plateau. These characteristics ensure that the propeller can still generate sufficient lift under low speed and small size conditions, while maintaining good efficiency and operational stability. The selected airfoil will serve as the benchmark for generating the radial cross-sectional shapes of the propeller.

[0031] S3: Based on the cross-sectional data of the reference airfoil, use propeller design software to generate a three-dimensional propeller initial model that meets the target thrust, and obtain its two-dimensional planar precursor unfolding model.

[0032] The selected reference airfoil section data is imported into specialized propeller aerodynamic design software. Within this software, based on the target thrust requirements determined in step S1, key geometric parameters such as the propeller diameter and pitch distribution are set. The software performs iterative calculations based on aerodynamic models such as blade element momentum theory to generate a three-dimensional theoretical propeller model that meets the thrust requirements. This model is typically presented as a point cloud or curve network. Subsequently, this three-dimensional model is imported into three-dimensional computer-aided design software for geometric reconstruction and smoothing, resulting in a three-dimensional solid model suitable for manufacturing. Finally, through a computational unfolding algorithm, the three-dimensional propeller model is precisely unfolded into a continuous two-dimensional planar graphic, which is the planar precursor model required for subsequent printing.

[0033] S4: Perform region division and printing path planning on the two-dimensional planar precursor model, wherein the blade surface region is planned as the first printing region using a radial printing path, and the internal region used to construct the spatial torsion angle is planned as the second printing region using a mixed angle printing path.

[0034] On the obtained two-dimensional planar precursor model, the printing areas need to be divided according to the structural and functional requirements of the final three-dimensional propeller. The main principle of the division is to distinguish the regions that play different roles in deformation. Among them, the region that ultimately constitutes the upper and lower surfaces of the propeller is planned as the first printing area. In order to obtain a smooth aerodynamic surface after deformation, the printing path of this area is set as a straight line from the center of the hub radially to the blade tip. The region located inside the blade, which is responsible for generating the spatial torsion angle during deformation, is planned as the second printing area. The printing path of this area needs to be specially designed to achieve a gradient change in material anisotropy.

[0035] S5: Based on the printing path planning, the two-dimensional planar precursor component is manufactured using a 4D printing process containing shape memory polymer materials.

[0036] Based on the path planning completed in step S4, manufacturing is performed using a fused deposition modeling (FDM) system with multi-material printing capabilities. The core material for printing is a thermotropic shape memory polymer, which can recover its shape according to the preset molecular chain orientation when heated. The printing process strictly follows the layered slicing file, with the nozzle depositing specific materials in specific areas according to code instructions, stacking them layer by layer to ultimately create a completely flat two-dimensional component. The component has already been incubated with the "seeds" of deformation through differentiated paths.

[0037] S6: Apply an external stimulus to the printed component to trigger its autonomous deformation from a two-dimensional planar precursor and lock it into a three-dimensional propeller structure.

[0038] The manufactured two-dimensional planar precursor component is static and flat. A pre-defined external environmental stimulus needs to be applied to trigger deformation. This stimulus requires the component's temperature to reach the trigger transition range of the shape memory polymer. Under this stimulus, the molecular chain segments within the material gain mobility, driving the material to contract or expand along the programmed direction of the printing path. Due to different path designs in different regions, this deformation macroscopically manifests as non-uniform, pre-defined bending and torsional movements, thereby causing the entire two-dimensional planar structure to autonomously and progressively fold and lock into a target propeller structure with a complex three-dimensional curved surface morphology.

[0039] In one possible implementation, in step S2, the preset airfoil is the SD7062 airfoil.

[0040] The selected preset airfoil is the SD7062 airfoil. This airfoil is one of the classic airfoils that has been verified through extensive low Reynolds number wind tunnel tests. It exhibits significant technical advantages within the target Reynolds number range: a high maximum lift coefficient, providing greater lift potential for the micro propeller; good delayed stall characteristics, making the propeller more stable under complex flight conditions; and a wide lift-to-drag ratio plateau range, which helps maintain high aerodynamic efficiency within a certain range of flight state variations. These characteristics make it particularly suitable for the low-speed, low-chord-length working environment of the micro UAVs targeted by this method.

[0041] In one possible implementation, in step S3, the propeller aerodynamics is designed using Passwing software and point cloud data is generated, which is then imported into 3D modeling software for model reconstruction and 2D unfolding.

[0042] The generation of the initial 3D propeller model relies on the collaborative work of specialized aerodynamic design software and 3D modeling software. In practice, Passwing software is used for the initial aerodynamic design of the propeller. After inputting parameters such as the baseline airfoil data, target thrust, and diameter, the software calculates based on aerodynamic theory and generates point cloud data representing the 3D shape of the propeller. Subsequently, the point cloud data is imported into 3D modeling software such as Rhino 7. In the modeling software, a smooth blade surface is reconstructed based on the point cloud, and further converted into a solid model, while simultaneously completing the detailed design of connecting structures such as the propeller hub. Finally, using the functions or auxiliary scripts of the modeling software, the 3D solid model is unfolded into a printable 2D planar precursor model.

[0043] In one possible implementation, step S4 specifically includes: dividing the upper and lower surfaces of the blade into the first printing area, and printing using a single radial path from the blade hub to the blade tip; dividing the inner area between the upper and lower surfaces into the second printing area, and printing using a mixed angle path that continuously changes from radial to circumferentially to program gradient-changing material anisotropy, thereby inducing a continuous spatial torsion angle after deformation.

[0044] Region division and path planning require refined design for the flat precursor model of the propeller. Specifically, the two large areas that will ultimately form the pressure and suction surfaces of the blade are marked as the first printing areas on the 2D model, namely surfaces a and d. These two areas are forced to be printed using a single radial straight path radiating from the center of the hub to the tip of the blade. The purpose is to ensure a smooth and continuous blade surface after deformation, avoiding surface textures caused by path changes, thereby optimizing aerodynamic performance. The internal support and deformation driving layer area located between the upper and lower surfaces is marked as the second printing area on the 2D model, namely surfaces b and c. Surface b mainly functions to construct the blade twist angle, and its printing path angle gradually transitions from the radial direction at the root to the circumferential direction at the tip, forming a continuously changing gradient. Surface c, as the transition layer between surfaces a, d, and b, is designed as a hybrid of the aforementioned two paths to form a natural curved surface transition and the required slight taper angle after deformation. Figure 2 As shown in the figure, the design scheme of dividing the propeller precursor into four regions, a, b, c, and d, and carrying out differentiated path planning is clearly illustrated.

[0045] In one possible implementation, in step S5, the shape memory polymer material is polylactic acid (PLA); the 4D printing process is multi-material composite printing, which simultaneously prints polyethylene terephthalate copolymer (PETG) in areas where structural constraints are required.

[0046] The specific materials used in the printing process are polylactic acid (PLA), a thermotropic shape memory polymer, and polyethylene terephthalate (PETG) copolymer, which serves as a constraint material. PLA materials, such as PolyMax™ PLA, are selected due to their significant thermotropic shape memory effect. PETG materials are from commercial brands compatible with the 3D printer, such as those provided by Shenzhen Tuozhu Technology Co., Ltd. In multi-material composite printing, PLA material is deposited primarily or entirely in the pre-defined deformation areas requiring bending or torsion. In areas requiring shape stability or rigid support, such as near the propeller hub or specific reinforcing ribs, PETG material is deposited simultaneously. The two materials are integrated into a single printing operation using the printer's multi-nozzle system.

[0047] The fundamental reason for choosing to combine PLA and PETG lies in their contrasting thermomechanical properties. PLA, as a semi-crystalline polymer, readily aligns its molecular chains along the printing path during melt deposition, and subsequently exhibits significant, directional shape recovery based on this "memory" upon heating, thus making it a deformation-driven material. Conversely, PETG has lower crystallinity and weaker molecular chain orientation capabilities, exhibiting primarily overall softening rather than directional deformation under the same thermal stimulus. Therefore, deploying PETG in areas requiring geometric stability effectively constrains the free contraction or expansion of adjacent PLA regions, thereby guiding and limiting the deformation potential of PLA to a predetermined bending or torsion. This "drive-constraint" synergistic design based on the intrinsic properties of the materials is the physical basis for achieving precise programming of complex three-dimensional aerodynamic surfaces.

[0048] In one possible implementation, after step S5 and before step S6, step S5a is also included: performing aerodynamic performance simulation on the initial three-dimensional propeller model using computational fluid dynamics (CFD) methods. The simulation includes establishing a rotating flow field computational domain, dividing the grid, setting boundary conditions, and solving to obtain thrust, power, and flow field distribution data. If the simulation results do not meet the design requirements, the process returns to step S3 to adjust the model parameters.

[0049] After completing the 3D model design and printing path planning, a computational fluid dynamics (CFD) simulation verification step is added. This step aims to predict and evaluate the propeller's aerodynamic performance in a virtual environment, thereby identifying potential defects and optimizing the model during the design phase. The specific process is as follows: First, the initial 3D propeller model obtained in step S3 is imported into the CFD preprocessing software. Then, a physical calculation model containing a rotating flow field is established, and corresponding boundary conditions and material properties are set. By numerically solving the Navier-Stokes equations, key data such as the propeller's thrust, torque, power efficiency, and the pressure and velocity distribution of the surrounding flow field under operating conditions are obtained. If the simulation results show that the thrust does not meet the target or the efficiency is too low, it is necessary to return to the 3D modeling step to adjust parameters such as the blade twist angle distribution, chord length distribution, or local airfoil modification, and then perform the simulation again until the design specifications are met.

[0050] In one possible implementation, step S5a includes the following specific steps of the CFD simulation: S5a1: Establish a cylindrical computational domain containing a rotating domain. The diameter of the rotating domain is slightly larger than the diameter of the propeller. The overall size of the computational domain satisfies the far-field boundary conditions. S5a2: The computational domain is discretized using an unstructured mesh, and the mesh is refined on the blade surface; S5a3: Set the velocity inlet, pressure outlet, and blade wall boundary conditions, and use the SST k-ω turbulence model; S5a4: The propeller rotation is simulated using the sliding mesh method to calculate the steady-state and transient aerodynamic performance.

[0051] CFD simulations require a detailed and effective setup procedure to ensure the reliability of the results. First, a cylindrical computational domain is established, nested within which a subdomain rotates coaxially and synchronously with the propeller. The diameter of the rotating domain is set to 105% of the propeller diameter. The inlet of the computational domain is 3 times the diameter of the rotating domain, and the outlet is 9 times the diameter, with a diameter at least 2.5 times that of the rotating domain. Second, an unstructured tetrahedral mesh is used to divide the computational domain, and a boundary layer mesh is generated on the blade surface. The thickness of the first layer mesh is checked using the Y+ value, and local refinement is applied to the blade surface to ensure the capture of geometric details and flow gradients. Figure 3 a and Figure 3 Figure b shows the detailed mesh generation of the blade surface and the schematic diagram of the overall flow field computational domain, respectively. Boundary conditions were set as follows: the far-field boundary of the computational domain was either the pressure far-field or the velocity inlet, the outlet was the pressure outlet, and the blade surface was a no-slip adiabatic wall. The SST k-ω model was chosen as the turbulence model to better handle near-wall and separated flows. Finally, the solver employed a pressure-based coupled algorithm and activated the slip mesh model to simulate the actual rotational motion of the propeller. Steady-state initialization and transient calculations were performed, and the convergence of key parameters such as thrust and torque was monitored. Figure 3c. Figure 3 d and Figure 3 As shown in Figure e, it illustrates the convergence process of the residual with the number of iterations, the convergence process of the lift coefficient with the number of iterations, and the periodic change of the lift coefficient with time after reaching steady state during the CFD simulation. These are the key criteria for judging whether the simulation is reliable and whether the results are stable.

[0052] In one possible implementation, in step S6, the external stimulus is a thermal stimulus, specifically placing the component in a thermal environment of 70-75°C for 3-5 minutes.

[0053] The external stimulus triggering the deformation is specifically a controllable input of thermal energy. During implementation, a hot air gun or a constant-temperature oven is used as the heat source. The printed two-dimensional planar precursor component is placed horizontally or suspended in a thermal environment. The heat source temperature is adjusted to stabilize the air temperature around the component within the range of 70°C to 75°C. This temperature condition is maintained for 3 to 5 minutes to ensure uniform heat transfer to the interior of the component, allowing the PLA material to reach above its glass transition temperature. During this process, the component can be observed to gradually undergo predetermined bending and torsional movements from a planar state, ultimately transforming completely into a three-dimensional propeller shape, which is then locked in after cooling.

[0054] In one possible implementation, after step S6, step S7 is further included: performing surface morphology and aerodynamic performance tests on the deformed three-dimensional propeller structure; wherein, the surface morphology test uses atomic force microscopy (AFM) to quantify surface roughness, and the aerodynamic performance test uses a tension-speed test platform to measure thrust output under different voltages.

[0055] The deformed propellers undergo rigorous performance testing to verify their manufacturing quality and aerodynamic performance. Surface morphology testing is performed using atomic force microscopy in tapping mode. A 2μm × 2μm scanning area is selected on a typical location on the propeller surface, and high-resolution scanning is performed using a silicon probe with a tip radius of less than 10 nm to obtain a three-dimensional surface morphology image and roughness parameters. This is used to quantitatively evaluate the effect of 4D printing on eliminating delamination and smoothing the surface. Figure 4 The image shows a comparison of the surface morphology of a 4D-printed propeller (right column) prepared by the method of this invention (left column) using traditional 3D printing. Figure 4 a and Figure 4 b are macroscopic surface morphology photos of the two, showing that the surface of the 4D printed blade is smoother and flatter; Figure 4 c and Figure 4 d represents the nanoscale morphology images of both objects obtained using atomic force microscopy. Figure 4 e and Figure 4f represents the corresponding micron-scale 3D surface morphology reconstruction images. The comparison results show that the surface undulation amplitude of the 4D-printed blade is significantly reduced, and the layered structure is effectively eliminated. Aerodynamic performance testing was conducted on a dedicated tension-speed testing platform. Figure 5 As shown in Figure a, the test platform consists of a high-precision electronic scale, a motor, and a regulated power supply. The propeller is mounted on a matching micro-motor, which is powered by a programmable power supply. By gradually increasing the voltage and simultaneously recording the thrust value measured by the high-precision electronic scale and the rotational speed value measured by the optical tachometer, the propeller's thrust-speed characteristic curve is plotted to evaluate its actual lift generation capability and efficiency.

[0056] In one possible implementation, in step S7, the performance of the 4D printed propeller is compared with that of a similar propeller printed by conventional fused deposition modeling (FDM) 3D printing, and the evaluation indicators include at least surface roughness, maximum lift, and energy efficiency.

[0057] To highlight the advantages of the method of this invention, comparative testing is necessary. A three-dimensional model with the same diameter, pitch, and airfoil as the optimized 4D-printed propeller was selected and directly printed into a rigid propeller using a traditional fused deposition modeling process as a control sample. The same AFM surface morphology test and tension-speed test were performed on both samples. The main comparative indicators include: the arithmetic mean deviation and maximum height difference of surface roughness to demonstrate the effect of 4D printing in improving surface finish; the maximum static thrust at rated voltage to demonstrate the advantages of the aerodynamic shape after deformation optimization; and the input electrical power at the same thrust output to calculate and compare energy efficiency. Figure 5 As shown in Figure b, the thrust-speed comparison curve clearly demonstrates that, under the same voltage, the 4D-printed propeller prepared by the method of this invention generates significantly higher lift than that of a traditional 3D-printed propeller. Through systematic comparative data, the effectiveness of this optimization method in improving the overall performance of micro propellers is quantitatively proven.

[0058] The beneficial effects of the technical solutions provided in the embodiments of the present invention include at least the following: (1) In this invention, the problem of low aerodynamic efficiency of micro propellers in low Reynolds number flow fields is effectively solved by combining low Reynolds number aerodynamic shape optimization with 4D printing deformation programming depth. First, the Reynolds number range is determined according to the specific working conditions of the micro UAV, and a special airfoil with high lift and delayed stall characteristics within this range is selected as the design benchmark. Then, a three-dimensional model that meets the target thrust is generated using propeller design software, and it is precisely unfolded into a two-dimensional planar precursor. Most importantly, by dividing the precursor into sections and printing a mixed angle path that continuously changes from radial to circumferential in the core internal region that determines the spatial twist angle, the anisotropy of the gradient is programmed inside the material. When subjected to thermal stimulation, this preset material memory drives the two-dimensional plane to autonomously and precisely fold and twist into the expected three-dimensional propeller shape. Its continuous curved surface and precise twist angle distribution are difficult to achieve directly by traditional 3D printing, thereby ensuring that the propeller can still maintain excellent lift generation efficiency and stable working characteristics at low Reynolds numbers.

[0059] (2) In this invention, the problems of high surface roughness in traditional 3D printed propellers and difficulty in deformation control in 4D printing are solved synergistically by heterogeneous material composite printing and refined regional path planning. In manufacturing, PLA is used as the shape memory driving material, and PETG material is composite printed in the areas that need to be constrained. When heated, PETG material mainly softens rather than shrinks in a directional manner, which can effectively constrain the free deformation of PLA and guide the deformation to a preset direction. In terms of path planning, the areas that ultimately constitute the upper and lower aerodynamic surfaces of the blade are planned to be printed using a single radial path, which ensures the smooth continuity of the surface after deformation and minimizes the interference of layer textures on the airflow. The internal deformation area is planned as a special hybrid path. This combination of the "driving-constraint" material system and the "surface-internal" differentiated path design enables the two-dimensional precursor to not only reliably transform into a complex three-dimensional structure after heating, but also the final propeller has a smooth aerodynamic surface close to that of traditional precision machining, which significantly reduces surface friction resistance and flow separation risk and improves overall aerodynamic efficiency.

[0060] (3) In this invention, by embedding computational fluid dynamics simulation into the manufacturing process, a closed loop of "design-simulation-optimization" is constructed, which solves the problems of design relying on experience, performance being difficult to predict, and iteration costs in traditional methods. After generating the initial three-dimensional propeller model based on the optimized airfoil and planning the printing path, it is not directly manufactured, but the model is first simulated in detail using CFD methods. By establishing a flow field model containing the rotation domain, dividing high-precision meshes, setting realistic boundary conditions, and performing numerical solutions, key data such as thrust, power, and flow field distribution of the design scheme can be obtained in advance. If the simulation results do not meet the design requirements, the geometric parameters of the propeller, such as the twist angle distribution and chord length, can be adjusted immediately, and then the simulation is performed again for verification until the performance meets the standards. This process moves the performance verification and optimization to before manufacturing, so that the manufacturing of propellers based on 4D printing is no longer a blind "trial and error", but a performance-driven design based on accurate numerical simulation, which greatly improves the success rate of the first manufacturing and the performance reliability of the final product, and provides an effective tool for the rapid development of high-performance customized propellers.

[0061] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

[0062] The following points need to be explained: (1) The accompanying drawings of the embodiments of the present invention only involve the structures involved in the embodiments of the present invention. Other structures can refer to the general design.

[0063] (2) For clarity, the thickness of layers or regions is enlarged or reduced in the drawings used to describe embodiments of the invention, i.e., these drawings are not drawn to scale. It is understood that when an element such as a layer, film, region or substrate is referred to as being “above” or “below” another element, the element may be “directly” located “above” or “below” the other element or there may be intermediate elements.

[0064] (3) Where there is no conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other to obtain new embodiments.

[0065] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. The scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for optimizing the aerodynamic shape of a 4D-printed propeller at a low Reynolds number, characterized in that, include: S1: Determine the operating Reynolds number range and target thrust of the propeller based on the design specifications of the micro UAV; S2: Select a preset airfoil with high maximum lift coefficient, delayed stall characteristics and wide lift-to-drag ratio platform from the low Reynolds number airfoil library as the reference airfoil; S3: Based on the cross-sectional data of the reference airfoil, use propeller design software to generate a three-dimensional propeller initial model that meets the target thrust, and obtain its two-dimensional planar precursor unfolding model. S4: Perform region division and printing path planning on the two-dimensional planar precursor model, wherein the blade surface region is planned as the first printing region using a radial printing path, and the internal region used to construct the spatial torsion angle is planned as the second printing region using a mixed angle printing path. S5: Based on the printing path planning, the two-dimensional planar precursor component is manufactured using a 4D printing process containing shape memory polymer materials; S6: Apply an external stimulus to the printed component to trigger its autonomous deformation from a two-dimensional planar precursor and lock it into a three-dimensional propeller structure.

2. The method for optimizing the low Reynolds number aerodynamic shape of a 4D-printed propeller according to claim 1, characterized in that, In step S2, the preset airfoil is the SD7062 airfoil.

3. The method for optimizing the low Reynolds number aerodynamic shape of a 4D-printed propeller according to claim 1, characterized in that, In step S3, the propeller aerodynamic design is performed using Passwing software to generate point cloud data, which is then imported into 3D modeling software for model reconstruction and 2D unfolding.

4. The method for optimizing the low Reynolds number aerodynamic shape of a 4D-printed propeller according to claim 1, characterized in that, In step S4, the region division specifically includes: dividing the upper and lower surfaces of the blade into the first printing region, and printing using a single radial path from the blade hub to the blade tip; dividing the internal region located between the upper and lower surfaces into the second printing region, and printing using a mixed angle path that continuously changes from radial to circumferential, so as to program the gradient-changing material anisotropy, thereby inducing a continuous spatial torsion angle after deformation.

5. The method for optimizing the low Reynolds number aerodynamic shape of a 4D-printed propeller according to claim 1, characterized in that, In step S5, the shape memory polymer material is polylactic acid (PLA); the 4D printing process is multi-material composite printing, which simultaneously prints polyethylene terephthalate copolymer (PETG) in areas where structural constraints are required.

6. The method for optimizing the low Reynolds number aerodynamic shape of a 4D-printed propeller according to claim 1, characterized in that, After step S5 and before step S6, step S5a is also included: performing aerodynamic performance simulation on the initial three-dimensional propeller model using computational fluid dynamics (CFD) method. The simulation includes establishing a rotating flow field computational domain, dividing the mesh, setting boundary conditions, and solving to obtain thrust, power, and flow field distribution data. If the simulation results do not meet the design requirements, the process returns to step S3 to adjust the model parameters.

7. The method for optimizing the low Reynolds number aerodynamic shape of a 4D-printed propeller according to claim 6, characterized in that, In step S5a, the specific steps of the CFD simulation include: S5a1: Establish a cylindrical computational domain containing a rotating domain. The diameter of the rotating domain is slightly larger than the diameter of the propeller. The overall size of the computational domain satisfies the far-field boundary conditions. S5a2: The computational domain is discretized using an unstructured mesh, and the mesh is refined on the blade surface; S5a3: Set the velocity inlet, pressure outlet, and blade wall boundary conditions, and use the SST k-ω turbulence model; S5a4: The propeller rotation is simulated using the sliding mesh method to calculate the steady-state and transient aerodynamic performance.

8. The method for optimizing the low Reynolds number aerodynamic shape of a 4D-printed propeller according to claim 1, characterized in that, In step S6, the external stimulus is a thermal stimulus, specifically placing the component in a thermal environment of 70-75°C for 3-5 minutes.

9. The method for optimizing the low Reynolds number aerodynamic shape of a 4D-printed propeller according to claim 1, characterized in that, After step S6, step S7 is also included: the surface morphology and aerodynamic performance of the deformed three-dimensional propeller structure are tested; wherein, the surface morphology test uses atomic force microscopy (AFM) to quantify the surface roughness, and the aerodynamic performance test uses a tension-speed test platform to measure the thrust output under different voltages.

10. The method for optimizing the low Reynolds number aerodynamic shape of a 4D-printed propeller according to claim 9, characterized in that, In step S7, the performance of the 4D printed propeller is compared with that of a similar propeller printed by traditional fused deposition modeling (FDM) 3D printing. The evaluation indicators include at least surface roughness, maximum lift, and energy efficiency.

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