Underwater vehicle non-uniform modified resistance reduction surface design method based on transition characteristics, program, equipment and storage medium

Abstract

The invention belongs to the technical field of resistance reduction of underwater vehicles, and particularly relates to an underwater vehicle non-uniform modified resistance reduction surface design method based on transition characteristics, a program, equipment and a storage medium. According to the method, the surface of the underwater vehicle is accurately partitioned through the transition model, and the resistance reduction schemes matched with the laminar flow region, the transition region and the turbulent flow region of the surface of the underwater vehicle are configured respectively, so that the problem of insufficient adaptability of a single resistance reduction scheme in different flow states is avoided. According to the method, transition calculation and structure parameters can be dynamically adjusted according to the appearance curvature and working condition parameters of the vehicle, and the method is adaptive to different types of underwater vehicles. By means of the drag reduction surface design method, the resistance borne by the underwater vehicle is effectively reduced, and the hydrodynamic performance of the underwater vehicle can be effectively improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of underwater vehicle drag reduction, and particularly relates to a design method, program, device and storage medium for a non-uniform modified drag reduction surface of an underwater vehicle based on transition characteristics. BACKGROUND

[0002] Drag is an important factor affecting the rapidity and endurance of an underwater vehicle, and reducing drag can improve the navigation efficiency under limited energy. The frictional drag accounts for as high as 70% of the total drag of an underwater vehicle during navigation; relevant research shows that if the drag of an underwater vehicle is reduced by 10%, the speed and range thereof can be simultaneously increased by about 3.57%, so reducing the surface frictional drag as a general solution has important significance.

[0003] The current mainstream drag reduction technology has obvious limitations: first, the drag reduction structure is not matched and adapted to the flow field characteristics of different regions of the vehicle surface, but a single structure is mostly used to cover the whole region. For example, the super-hydrophobic surface can achieve good drag reduction effect in the laminar boundary layer, but in the turbulent boundary layer, the drag reduction effect gradually decreases with the increase of the Reynolds number. The micro-groove structure can only play a role in reducing drag in the turbulent boundary layer, and even increase the drag in the laminar boundary layer; second, the flow field of the vehicle surface has a transition process from laminar flow to turbulent flow, and the transition position dynamically changes with the navigation speed and shape parameters. The existing design does not achieve zoned drag reduction by accurately calculating the transition position, resulting in low drag reduction efficiency.

[0004] Therefore, there is an urgent need for a method combining the transition characteristics of the flow field and zoned design of the drag reduction structure to solve the problems of poor adaptability and limited drag reduction effect of the existing uniform modification scheme. SUMMARY

[0005] The application aims to provide a design method, program, device and storage medium for a non-uniform modified drag reduction surface of an underwater vehicle based on transition characteristics, accurately calculate the transition position through a transition model, design adaptive drag reduction structures for the laminar flow region, transition region and turbulent flow region respectively, and avoid increasing the drag to maximize the overall drag reduction efficiency.

[0006] A design method for a non-uniform modified drag reduction surface of an underwater vehicle based on transition characteristics: determine an underwater vehicle model in a calculation domain, create a calculation grid and corresponding flow field boundary conditions; use a Transition model embedded in the commercial software to calculate the transition position of the flow field, and divide the calculation domain into a laminar flow region, a transition region and a turbulent flow region according to the transition position; design adaptive drag reduction structures for the laminar flow region, the transition region and the turbulent flow region respectively, and combine the structures to obtain a non-uniform modified drag reduction surface of the underwater vehicle. The CFD solver of the transition turbulent model carries out flow field solving, determines the boundary layer transition position of the underwater vehicle surface based on the flow field solving result, divides the flow field area into laminar flow area, transition area and turbulent flow area, arranges adaptive schemes in each area respectively according to different flow field characteristics of the laminar flow area, the transition area and the turbulent flow area, executes the overall scheme verification of the integrated laminar flow drag reduction, transition drag reduction and turbulent flow drag reduction, and determines the non-uniform surface drag reduction combined scheme adaptive to specific working conditions.

[0007] Further, the Transition The transition turbulent model comprises a turbulent kinetic energy transport equation, a laminar kinetic energy transport equation and a scale determining variable transport equation. The turbulent kinetic energy transport equation is: The laminar kinetic energy transport equation is: The scale determining variable transport equation is: Wherein, is the turbulent kinetic energy, is the laminar kinetic energy, and the scale determining variable is the isotropic dissipation ratio of the turbulent kinetic energy , that is, ; is the kinematic viscosity of the fluid; is the effective diffusion coefficient; and are generation terms of the bypass transition and the natural transition respectively; is a damping function related to the motion wall effect; is a motion damping function; and are generation terms of and : , Wherein, is the turbulent eddy viscosity coefficient related to the generation of the turbulent kinetic energy , is the turbulent eddy viscosity coefficient related to the generation of the laminar kinetic energy , used for describing the influence of vortex motion on momentum transport in turbulent flow; S is the modulus of the average strain rate tensor; and are generation terms of and Anisotropic near-wall dissipation terms: .

[0008] Furthermore, based on the flow field solution results, the boundary layer transition position on the surface of the underwater vehicle is determined, and the flow field region is divided into laminar, transition, and turbulent regions, specifically as follows: The laminar flow region is located in the head area of ​​the underwater vehicle, where the surface friction coefficient is low and fluctuates very little; the boundary layer is a stable laminar flow with laminar kinetic energy. The development of dominant fluid disturbances and turbulent kinetic energy It is nearly zero; the wall shear stress is stable, demonstrating the characteristics of laminar flow with low shear resistance; The transition zone is located at the leading edge of the parallel midbody region of the underwater vehicle, where the surface friction coefficient distribution exhibits localized non-uniform variations. Disturbance energy gradually accumulates within the laminar flow, triggering the transition when the disturbance reaches a critical level. Subsequently, the fluid motion transitions from ordered to disordered, and turbulent kinetic energy... It begins to generate and gradually intensifies, a process accompanied by strong turbulent fluctuations, which leads to a significant increase in wall friction resistance and a spatially non-uniform distribution of the surface friction coefficient. The turbulent region is located in the middle and tail of the parallel midbody region of the underwater vehicle. The surface friction coefficient is stable and the overall distribution is more uniform. At this time, the transition process is completely over, the boundary layer develops into a turbulent boundary layer, the flow is dominated by turbulent kinetic energy, and strong turbulent mixing dominates momentum transport, causing the wall shear stress to remain stable at a high level.

[0009] Furthermore, in response to the different flow field characteristics of the laminar flow region, transition region, and turbulent flow region, a superhydrophobic coating is sprayed on the laminar flow region to reduce drag, a flexible wall is used to reduce drag in the transition region, and a V-groove structure is arranged to reduce drag in the turbulent flow region.

[0010] Furthermore, the superhydrophobic coating comprises a primer and a topcoat. The primer is composed of silicone resin, calcium carbonate, polyamide powder, and butyl acetate, while the topcoat is composed of superhydrophobic nano-silica particles and ethanol. The coating coverage extends from the bow of the underwater vehicle to the transition point, completely covering the laminar flow zone. It is uniformly coated on the predetermined area using an air spraying process and cured at room temperature or under heating conditions to form a robust and durable superhydrophobic surface.

[0011] Furthermore, the flexible wall surface includes an inner stainless steel core and an outer hydrogel; the hydrogel is integrated with the stainless steel core through cross-linking, thereby delaying the boundary layer transition under fluid-structure interaction; the flexible wall surface covers the entire transition zone from the transition start point to the transition end point.

[0012] Furthermore, the height of the V-shaped grooves is equal to the spacing between the grooves, and the arrangement range of the V-shaped grooves extends from the end point of the transition to the end point of the parallel midbody. The tail of the underwater vehicle is not treated.

[0013] A computer device includes a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above-described method for non-uniform modification and drag reduction surface design of underwater vehicles based on transition characteristics.

[0014] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method for non-uniform modification and drag reduction surface design of underwater vehicles based on transition characteristics.

[0015] A computer program product includes computer instructions that, when executed by a processor, implement the steps of the above-described method for designing a non-uniformly modified drag-reducing surface for underwater vehicles based on transition characteristics.

[0016] The beneficial effects of this invention are as follows: This invention precisely partitions the surface of an underwater vehicle using a transition model, configuring appropriate drag reduction schemes for the laminar, transition, and turbulent regions of the surface. This avoids the problem of insufficient adaptability of a single drag reduction scheme under different flow conditions. This invention can dynamically adjust transition calculations and structural parameters based on the vehicle's curvature and operating parameters, adapting to different types of underwater vehicles. Using the drag-reducing surface design method of this invention, the drag experienced by the underwater vehicle is effectively reduced, significantly improving its hydrodynamic performance. Attached Figure Description

[0017] Figure 1 This is a flowchart of the present invention.

[0018] Figure 2 This is a schematic diagram of an underwater vehicle in an embodiment of the present invention.

[0019] Figure 3 This is a schematic diagram of the CFD computation domain setting in an embodiment of the present invention.

[0020] Figure 4 This is a schematic diagram of the CFD computational domain grid in an embodiment of the present invention.

[0021] Figure 5 The underwater vehicle C in this embodiment of the invention f Cloud map.

[0022] Figure 6 This is a schematic diagram of a non-uniform design implementation scheme for an underwater vehicle with a speed of 1.5 m / s, whose surface is partitioned based on flow characteristics and subjected to different drag reduction modifications. Detailed Implementation

[0023] The present invention will now be further described with reference to the accompanying drawings.

[0024] This invention relates to a method for designing a non-uniform modified drag-reducing surface for underwater vehicles based on transition characteristics. The boundary layer characteristics under different flow states vary significantly, and the corresponding drag reduction methods are also different.

[0025] Laminar flow region: The flow field in this region exhibits regular laminar flow, with viscous drag dominating. Common drag reduction methods include spraying superhydrophobic coatings onto the surface. Superhydrophobic coatings trap air through micro- and nano-structures to form an air film, reducing the solid-liquid contact area and lowering the wall velocity gradient, thereby weakening viscous shear forces.

[0026] Transition region: As a dynamic region transitioning from laminar to turbulent flow, the flow field exhibits both laminar order and turbulent disturbance characteristics. The core objective of drag reduction in the transition region is to slow down the transition process and curb the amplification of disturbances. Common drag reduction methods include flexible wall technology and local heating control. Flexible walls can reduce the pressure gradient at the wall through fluid-structure interaction, thus delaying transition. Local heating control reduces the viscosity of the near-wall fluid and alters the velocity profile through non-uniform heating, improving the overall stability of the flow. Simultaneously, it utilizes thermal convection to disrupt vortex merging, thereby increasing the critical Reynolds number for transition.

[0027] Turbulent region: The flow field exhibits irregular pulsations, with turbulent bursts and vortex motion leading to severe energy dissipation. Common drag reduction methods include microgroove structures, drag-reducing polymer additives, and grooved superhydrophobic composite surfaces. Microgroove structures guide near-wall fluid flow along the grooves, limiting lateral motion and suppressing turbulent bursts. Simultaneously, the groove structure generates secondary vortices, weakening the flow-directed vortex intensity and reducing turbulent pulsations. In grooved superhydrophobic composite surfaces, microgrooves suppress turbulent bursts and reduce shear forces, while the superhydrophobic coating reduces solid-liquid contact through an air film. Furthermore, the groove structure enhances air film stability, and the slip effect of the air film, combined with the microgroove structure, achieves efficient drag reduction.

[0028] In existing technologies, both superhydrophobic coatings and grooved superhydrophobic composite structures are effective underwater drag reduction methods, but their drag reduction mechanisms differ: superhydrophobic coatings form an air film at the solid-liquid interface, significantly reducing the liquid-solid contact area and thus lowering surface frictional resistance; flexible walls can reduce the pressure gradient at the wall surface through fluid-structure interaction, delaying transition; and grooved superhydrophobic composite structures utilize micro-grooves to guide the fluid near the wall to generate directional vortex structures, suppressing turbulent bursts and momentum exchange, thus achieving turbulent drag reduction. This invention proposes a zoned arrangement strategy for different flow states on the surface of a vehicle: superhydrophobic coatings are placed in laminar flow regions; flexible walls are arranged in transition regions; and grooved superhydrophobic composite structures are arranged in turbulent flow regions. Through the above-mentioned non-uniform surface modification methods, the boundary layer characteristics under different flow states are synergistically optimized to achieve efficient drag reduction throughout the entire process, thereby improving the overall hydrodynamic performance of the vehicle. The steps are as follows: S1. Establish a three-dimensional computational domain based on the underwater vehicle; A three-dimensional model of the underwater vehicle and the fluid domain was constructed using SOLIDWORKS software. The underwater vehicle is a near-rotating body structure, and the parameter L is defined as the total length of the bare vessel, taken as 1.934 meters, with a diameter of 0.3 meters. To simulate the hydrodynamic performance of the underwater vehicle in the unbounded flow domain, eliminate the influence of the wall on its hydrodynamics, and allow the flow field to develop fully, the origin of the Cartesian coordinate system is located on the centerline of the underwater vehicle's head. The length, width, and height of the computational domain are all based on the total length L of the bare vessel, with the total length set to 7L, and the width and height both set to 3L, to avoid the influence of the computational domain boundary on the numerical calculation results. The underwater vehicle's axis is located on the central axis of the computational domain, with the inlet boundary at a distance of 2L from the head of the rotating body and the outlet boundary at a distance of 4L from the tail of the rotating body.

[0029] S2. Create the computational grid and the corresponding flow field boundary conditions; The above 3D model was imported into ICEM software for structured mesh generation. Specifically, tetrahedral meshes were used for both the fluid domain and the surface of the underwater vehicle. To accurately capture changes in navigation resistance, mesh refinement was applied to the area around and on the surface of the underwater vehicle to ensure accurate simulation of boundary layer flow.

[0030] The boundary conditions are set as follows: the inlet boundary is set as a velocity inlet, the outlet boundary is set as a pressure outlet, the computational domain is set as a symmetry plane to simulate a deep-water environment, and the surface of the underwater vehicle is set as a non-slip wall to ensure that the inflow velocity at the inlet boundary is consistent with the speed of the rotating body.

[0031] S3, Employing embedded Transition A CFD solver for the transition turbulence model is used to perform flow field calculations on the computational model. Transition The transition model introduces laminar flow energy. , and turbulent kinetic energy Co-describes the transition process. Layer kinetic energy. This study captures the disturbance energy in laminar flow, characterizing the development of minute disturbances within the laminar flow during the initial transition phase and the energy accumulation of weak disturbances near the boundary layer walls during the initial boundary layer phase. Once this energy accumulation reaches a certain level, triggering transition, the energy is transferred from turbulent kinetic energy... The generation mechanism gradually becomes dominant, and this dual-turbulent kinetic energy setting enables a more detailed description of the transition process.

[0032] Transition Transitional turbulence models include turbulent kinetic energy transport equations, laminar kinetic energy transport equations, and scale-determined variable transport equations. Turbulent kinetic energy transport equations: Laminar kinetic transport equation: Scale determines the variable transport equation: in, For turbulent kinetic energy, For laminar kinetic energy, scale is a determining variable. isotropic dissipation With turbulent kinetic energy The ratio, i.e. ;use As a scale-determining variable, it can reduce the intermittent effects in the outer region of the turbulent boundary layer, thereby eliminating the wake region in the velocity profile. The kinematic viscosity of the fluid; The effective diffusion coefficient; and These are the generation terms for bypass transition and natural transition, respectively; The damping function is related to the moving wall effect; Let be the motion damping function; and They are respectively and Generated items: , in, It is related to turbulent kinetic energy Generate the relevant turbulent eddy viscosity coefficient. It is related to laminar kinetic energy Generate relevant turbulent eddy viscosity coefficients to describe the effect of vortex motion on momentum transport in turbulent flow; SIt is the modulus of the average strain rate tensor; and They are respectively and Anisotropic near-wall dissipation terms: S4. Based on the flow field solution results in step 3, determine the boundary layer transition position and region division on the surface of the underwater vehicle; This study focuses on underwater vehicles, employing the Transition method at a speed of 1.5 m / s. The flow field was solved. The obtained surface friction coefficient (C) f The spatial distribution of the boundary layer can accurately determine the location and process of boundary layer transition, as detailed below: Laminar flow stage: Within the nose region of the underwater vehicle, the surface friction coefficient contour map shows an almost uniform green color, with values ​​concentrated below 0.003 and exhibiting minimal fluctuations. During this stage, the boundary layer exhibits stable laminar flow: laminar kinetic energy... The development of dominant fluid disturbances and turbulent kinetic energy It is nearly zero; the wall shear stress is stable, exhibiting the typical characteristics of laminar flow with low shear resistance.

[0033] The beginning and development stages of the turning point: At the leading edge of the parallel midbody region of the underwater vehicle, the color of the surface friction coefficient contour map gradually transitions from blue to green and then to yellow, with the value continuously climbing from 0.0005 to around 0.004, and the distribution begins to show localized non-uniform changes. This stage corresponds to the core stage of the transition process: the disturbance energy within the laminar flow gradually accumulates, and when the disturbance grows to a "critical level," the transition begins; subsequently, the fluid motion transitions from ordered to disordered, and turbulent kinetic energy... The formation and gradual enhancement of turbulent pseudo-ordered structures occur during the boundary layer transition. This process involves intense turbulent fluctuations, leading to a significant increase in wall friction drag. The spatially non-uniform distribution of the friction coefficient directly reflects the emergence and development of these turbulent pseudo-ordered structures.

[0034] Turbulent phase: At the leading edge of the parallel midbody region of the underwater vehicle, the surface friction coefficient contour map is predominantly yellow-green, with a stable value of around 0.0035 and a more uniform overall distribution. At this point, the transition process is completely finished, and the boundary layer develops into a turbulent boundary layer. During this stage, the flow is dominated by turbulent kinetic energy, and intense turbulent mixing dominates momentum transport, resulting in stable high levels of wall shear stress.

[0035] S5. Based on the flow field region division in step 4, drag reduction structures are arranged to match the different flow field characteristics of the laminar flow region, transition region and turbulent flow region. Laminar flow region: A superhydrophobic coating is applied to reduce drag. The superhydrophobic coating material consists of a primer and a topcoat. The primer is composed of silicone resin, calcium carbonate, polyamide powder, and butyl acetate. The topcoat is composed of superhydrophobic nano-silica particles and ethanol (the nano-silica particles are prepared using a sol-gel method, and then modified with low-surface-weight materials to obtain the superhydrophobic nano-silica particles). The coating coverage extends from the bow of the underwater vehicle to the transition point, completely covering the laminar flow area. It is uniformly applied to the predetermined area using an air spraying process and cured at room temperature or under heating conditions to form a robust and durable superhydrophobic surface.

[0036] Transition zone: Drag reduction is achieved using a flexible wall. It consists of an inner stainless steel core and an outer hydrogel; the hydrogel is cross-linked and solidified with the stainless steel core, thereby delaying boundary layer transition under fluid-structure interaction. The flexible wall covers the entire transition region from the transition initiation point to the transition end point.

[0037] Turbulent region: A V-groove structure is used to reduce drag. When the groove size... h + When ≤ 25 and s+≤ 30, the arrangement of longitudinal trenches can achieve better drag reduction effect, and when the trench height is... h Spacing between trenches s When the values ​​are equal, optimal drag reduction performance is usually achieved. Referring to empirical formulas for boundary layer flow on flat plates, and taking the flat plate surface as the research object, the dimensions of the trench structure are determined. For the underwater vehicle involved in this embodiment, under the condition of a travel speed of 1.5 m / s, the calculated Reynolds number is approximately 2.9 × 10⁻⁶. 6 Based on this Reynolds number, further calculations yielded the initial design parameters for the surface trench structure of the underwater vehicle: trench height. h Approximately 0.44 mm, groove spacing s It is approximately 0.52 mm.

[0038] To optimize the trench structure and simplify the manufacturing process, this invention uses trench height as the primary parameter for the aforementioned trench parameters. h Spacing between trenches s Equal design schemes (i.e.) h = s Taking into account practical processing feasibility, process simplification requirements, and precision control requirements, the final trench height was determined. h Spacing between trenches sThe value is set to 0.4 mm. The trench structure is not arranged to cover the entire turbulent region, but rather within the area from the transition point to the parallel midbody cutoff. Within this region, the boundary layer has developed into fully stable turbulence. The V-shaped trenches effectively reduce wall friction drag by suppressing turbulent bursts near the wall and reducing momentum exchange. However, at the stern of the underwater vehicle, the flow field becomes extremely complex, accompanied by adverse pressure gradients and flow separation. Under these conditions, the trenches not only lose their turbulence suppression and drag reduction functions but may also exacerbate flow separation, leading to a significant increase in pressure drag and ultimately causing the total drag to increase instead of decrease.

[0039] S6. Conduct overall scheme verification of integrated laminar flow drag reduction, transition drag reduction and turbulent flow drag reduction technologies to determine a non-uniform surface drag reduction combination scheme suitable for specific working conditions; By combining the above schemes, a non-uniform surface drag reduction scheme suitable for underwater vehicles with a target speed of 1.5 m / s can be formed.

[0040] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for designing non-uniformly modified drag-reducing surfaces for underwater vehicles based on transition characteristics, characterized in that: An underwater vehicle model is defined within the computational domain, and a computational mesh and corresponding flow field boundary conditions are created; an embedded transition is employed. The CFD solver of the transition turbulence model is used to solve the flow field. Based on the flow field solution, the boundary layer transition position on the surface of the underwater vehicle is determined, and the flow field region is divided into laminar, transition, and turbulent regions. For the different flow field characteristics of the laminar, transition, and turbulent regions, appropriate schemes are arranged in each region. The overall scheme verification integrating laminar drag reduction, transition drag reduction, and turbulent drag reduction is performed to determine the non-uniform surface drag reduction combination scheme suitable for specific operating conditions.

2. The method for non-uniform modification and drag reduction surface design of underwater vehicles based on transition characteristics according to claim 1, characterized in that: The Transition Transitional turbulence models include turbulent kinetic energy transport equations, laminar kinetic energy transport equations, and scale-determined variable transport equations. Turbulent kinetic energy transport equations: Laminar kinetic transport equation: Scale determines the variable transport equation: in, For turbulent kinetic energy, For laminar kinetic energy, scale is a determining variable. isotropic dissipation With turbulent kinetic energy The ratio, i.e. ; The kinematic viscosity of the fluid; The effective diffusion coefficient; and These are the generation terms for bypass transition and natural transition, respectively; The damping function is related to the moving wall effect; Let be the motion damping function; and They are respectively and Generated items: ， in, It is related to turbulent kinetic energy Generate the relevant turbulent eddy viscosity coefficient. It is related to laminar kinetic energy Generate relevant turbulent eddy viscosity coefficients to describe the effect of vortex motion on momentum transport in turbulent flow; S It is the modulus of the average strain rate tensor; and They are respectively and Anisotropic near-wall dissipation terms: 。 3. The method for non-uniform modification and drag reduction surface design of underwater vehicles based on transition characteristics according to claim 1, characterized in that: Based on the flow field solution results, the boundary layer transition position on the surface of the underwater vehicle is determined, and the flow field region is divided into laminar, transition, and turbulent regions, specifically: The laminar flow region is located in the head area of ​​the underwater vehicle, where the surface friction coefficient is low and fluctuates very little; the boundary layer is a stable laminar flow with laminar kinetic energy. The development of dominant fluid disturbances and turbulent kinetic energy It is nearly zero; the wall shear stress is stable, demonstrating the characteristics of laminar flow with low shear resistance; The transition zone is located at the leading edge of the parallel midbody region of the underwater vehicle, where the surface friction coefficient distribution exhibits localized non-uniform variations. Disturbance energy gradually accumulates within the laminar flow, triggering the transition when the disturbance reaches a critical level. Subsequently, the fluid motion transitions from ordered to disordered, and turbulent kinetic energy... It begins to generate and gradually intensifies, a process accompanied by strong turbulent fluctuations, which leads to a significant increase in wall friction resistance and a spatially non-uniform distribution of the surface friction coefficient. The turbulent region is located in the middle and tail of the parallel midbody region of the underwater vehicle. The surface friction coefficient is stable and the overall distribution is more uniform. At this time, the transition process is completely over, the boundary layer develops into a turbulent boundary layer, the flow is dominated by turbulent kinetic energy, and strong turbulent mixing dominates momentum transport, causing the wall shear stress to remain stable at a high level.

4. The method for designing a non-uniformly modified drag-reducing surface for underwater vehicles based on transition characteristics according to claim 3, characterized in that: The method addresses the different flow field characteristics of the laminar, transition, and turbulent regions by applying a superhydrophobic coating to reduce drag in the laminar region, using a flexible wall to reduce drag in the transition region, and arranging a V-groove structure to reduce drag in the turbulent region.

5. The method for non-uniform modification and drag reduction surface design of underwater vehicles based on transition characteristics according to claim 4, characterized in that: The superhydrophobic coating comprises a primer and a topcoat. The primer is composed of silicone resin, calcium carbonate, polyamide powder, and butyl acetate, while the topcoat is composed of superhydrophobic nano-silica particles and ethanol. The coating covers the entire laminar flow zone from the bow of the underwater vehicle to the transition point. It is uniformly applied to the predetermined area using an air spraying process and cured at room temperature or under heating conditions to form a robust and durable superhydrophobic surface.

6. The method for designing a non-uniformly modified drag-reducing surface for underwater vehicles based on transition characteristics according to claim 4, characterized in that: The flexible wall surface includes an inner stainless steel core and an outer hydrogel. The hydrogel is integrated with the stainless steel core through cross-linking, thereby delaying the boundary layer transition under fluid-structure interaction; the flexible wall covers the entire transition zone from the transition initiation point to the transition end point.

7. The method for designing a non-uniformly modified drag-reducing surface for underwater vehicles based on transition characteristics according to claim 4, characterized in that: The height of the V-shaped grooves is equal to the spacing between the grooves. The arrangement range of the V-shaped grooves extends from the end point of the transition to the end point of the parallel midbody. The tail of the underwater vehicle is not treated.

8. A computer device, comprising a memory, a processor, and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When executed by a processor, the computer program implements the steps of the method according to any one of claims 1 to 7.

10. A computer program product comprising computer instructions, characterized in that: When executed by a processor, the computer instructions implement the steps of the method according to any one of claims 1 to 7.

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