Method for designing drag reduction of non-uniform porous medium slip surface varying with spatial position

Abstract

The present application relates to a kind of non-uniform porous medium slip surface drag reduction design method varying with spatial position, comprising the following steps: S1, determine working condition, select control equation and boundary condition;S2, the navigation body is zoned, constructs linear equation;S3, calculate the resistance data when not spraying, analyze flow field;S4, give the porous medium parameters corresponding to each part;S5, calculate the resistance data under the parameter, analyze flow field;S6, compare the resistance data under the parameter and when not spraying, S7, when not getting maximum drag reduction rate, repeat steps S4-S6, until maximum drag reduction rate is obtained.The present application can provide the optimal parameters corresponding to porous medium according to position change, fully consider actual situation, realize maximum drag reduction rate.

Description

Technical Field

[0001] This invention relates to the field of ship drag reduction, and more specifically, to a drag reduction design method for a non-uniform porous medium sliding surface that varies with spatial position. Background Technology

[0002] Frictional resistance is a major component of a ship's total resistance, accounting for at least 60% and sometimes as much as 80%. Therefore, reducing a ship's total resistance hinges on reducing its frictional resistance. Porous media with slip surfaces achieve drag reduction by altering the slip length. Porous media materials transform the solid-liquid boundary into a liquid-liquid boundary, resulting in a significant apparent slip phenomenon. The slip length and drag reduction efficiency are related to parameters such as permeability, thickness, and viscous drag coefficient. The key to drag reduction lies in ensuring the surface of the vessel has a certain slip length. Existing research has demonstrated that, under laboratory conditions or direct numerical simulations, spraying porous media onto a flat plate surface can effectively reduce drag. However, in practical applications, the drag reduction rate has not reached experimental results, and in some cases, drag has even increased. This is because most researchers only study the flow field changes of flat plates, neglecting the flow field changes of actual vessels. Vessels possess rich three-dimensional curved surfaces, resulting in highly complex flow fields; conclusions drawn from studies on flat plates may not be applicable to actual vessels. Furthermore, most studies only involve uniformly spraying porous media onto flat plates, without considering non-uniform spraying onto aircraft bodies with three-dimensional curved surfaces. Figure 1 This is a schematic diagram of the flow field of a certain aircraft. Unlike the flow field of a flat plate, complex vortices and flow separation phenomena will occur around the aircraft. Figure 1 Region A represents flow separation, point C is the flow separation point, and region B represents eddies. Existing research shows that porous media significantly affect laminar flow stability and the natural transition position, and the transition delay effect becomes more pronounced with increasing slip length. For example, after spraying porous media into region A, the flow separation point shifts backward. The total drag in this region is opposite to the tangential force F, which is beneficial for drag reduction. However, spraying porous media reduces F, which is detrimental to drag reduction. Therefore, it is not necessary to spray porous media or the same type of porous media at every location on the surface of a vehicle. Considering the different optimal slip lengths for drag reduction on the surface of a vehicle, and taking into account parameters such as the thickness, viscous drag coefficient, and permeability of the porous media, it is essential to study drag reduction methods for non-uniform porous media slip surfaces that vary with spatial position.

[0003] Meng et al. proposed a method to improve the endurance of autonomous underwater vehicles (AUVs) by spraying a porous medium onto the surface of the vehicle, which reduces drag during navigation. The study noted that at a speed of 1.54 m / s, the viscous drag coefficient of the porous medium was 830 kg / m. 3 s, the resistance with and without porous material is equivalent; the viscous resistance coefficient of the porous material is less than 830 kg / m3 When the viscosity coefficient is s, the attachment of porous media can reduce the resistance, and the resistance decreases as the viscosity coefficient of the porous media decreases. When the viscosity coefficient of the porous media is the same, calculations are performed with porous media thicknesses of 35mm, 40mm, 45mm, and 50mm, for example, with a viscosity coefficient of 830kg / m³. 3 The resistance is approximately 3N for a thickness of 35mm and approximately 3.5N for a thickness of 50mm. Calculations show that the drag of the vehicle is also related to the thickness of the porous medium, and that the drag increases with increasing thickness when the viscous drag coefficient is the same. This method only considers uniformly sprayed porous media and does not study the drag reduction under non-uniform spraying. (Lingshuai Meng, Lin Yang, Tsung-Chow Su, Haitao Gu. A Study on the influence of porous material on underwater vehicle's hydrodynamic characteristics[J]. Ocean Engineering. 2019.) Some scholars have studied the influence of permeability on drag and surface friction drag coefficient by simulating the flow of fluid in a channel of uniformly sprayed porous media. The permeability values ​​are 2, 5, 10, and 50. When the channel height ratio is 1 and the Reynolds number is 20, the drag reduction rate is approximately 60% when the permeability is 2, and approximately 5% when the permeability is 50. The results indicate that, at the same Reynolds number, the surface friction coefficient increases with increasing permeability, while the drag reduction rate decreases with increasing permeability. This study only focused on the drag reduction effect within a rectangular pipe uniformly coated with porous media and cannot provide a reference for drag reduction in vehicles with complex three-dimensional curved surfaces that are non-uniformly coated with porous media. (Parisa Mirbod, Zhenxing Wu & Goodarz Ahmadi. Laminar flow drag reduction on softporous media[J].Nature.2017)

[0004] Theoretically, it has been proven that a uniform porous medium slip surface can reduce drag; however, in practical applications, some cases of increased drag have occurred. This is because uniformly sprayed porous media alters the flow field near the vehicle, changing its velocity and pressure distributions, which is not always conducive to drag reduction. For example... Figure 1In region A, the tangential force F is opposite to the drag direction. Therefore, increasing F can effectively reduce drag. However, after spraying porous media, the velocity gradient near the wall decreases. According to Newton's law of internal friction, F will decrease accordingly. Therefore, the application of porous media in this location actually increases drag. For region B, the total drag is in the same direction as the tangential force F'. F' increases drag. After spraying porous media, the vortex size decreases, and F' decreases, which is beneficial for drag reduction. Therefore, for a vehicle, not all parts need to be sprayed with porous media or the same type of porous media. The specific spraying method needs to be analyzed in conjunction with changes in the flow field. Currently, most experimental or direct numerical simulation studies focus on flat plates, while ship hulls and underwater vehicles have complex three-dimensional curved surfaces, and the flow field around them is very different from that of flat plates. Moreover, most existing studies focus on the case of uniformly sprayed porous media, without considering the influence of non-uniform spraying (i.e., applying different porous media materials at different locations on the vehicle). The presence of curved surfaces easily causes boundary layer separation and generates vortices. Therefore, simply considering uniformly spraying porous media on flat plates to achieve drag reduction is insufficient. When water flows over the surface of a ship's hull or an underwater vehicle with a three-dimensional surface, the flow field distribution and vortex characteristics vary from place to place, and the optimal parameters of the porous medium surface required also vary. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a drag reduction design method for a non-uniform porous medium sliding surface that varies with spatial position. This method not only helps to maintain the cleanliness of the surface and reduce the attachment of marine organisms, but also reduces maintenance requirements and improves the long-term performance and reliability of surface drag reduction.

[0006] The technical solution adopted by this invention to solve its technical problem is: to construct a drag reduction design method for a non-uniform porous medium sliding surface that varies with spatial position, comprising the following steps:

[0007] S1. Select the route of the vehicle, analyze the route, and classify it according to the water conditions of the navigation area. Different water areas correspond to different working conditions.

[0008] S2. Divide the vehicle into sections and construct linear equations;

[0009] S3. Establish a physical model of the object to be studied, determine the spatial influence area of ​​the object to be analyzed, and divide the outer surface of the vehicle and the entire calculation area into spatial grids.

[0010] S4. Determine the initial conditions, governing equations, and boundary conditions required for the solution based on the actual flow field conditions;

[0011] S5. Calculate the pressure drag, viscous drag, and friction drag at each location when the vehicle body is not coated with porous media material. Based on the simulation experiment drag calculation results and the drag coefficient calculation formula, determine the dimensionless drag coefficient corresponding to different locations, find the location where flow separation occurs, analyze the flow field at each location, and predict the porous media parameters corresponding to different locations.

[0012] S6. Based on the data obtained in step S5 and the characteristics of the corresponding porous medium, the parameters of the initial coating thickness and porosity of each part are given. Based on the parameters of the initial coating thickness and porosity, the porous medium material with the corresponding conditions is coated on each part of the vehicle body.

[0013] S7. Under the conditions of step S6, calculate the navigation of the vehicle under the corresponding working conditions, calculate the pressure drag, viscous drag, and friction drag corresponding to each position, and determine the dimensionless drag coefficient corresponding to different positions based on the simulation experiment drag calculation results and the drag coefficient calculation formula, so as to evaluate the drag reduction efficiency under the condition, observe the flow field change after spraying the porous medium, compare it with the flow field before spraying, and adjust the porous medium parameters according to the specific situation.

[0014] S8. Compare the differential pressure resistance, viscous resistance, frictional resistance, and dimensionless resistance coefficient obtained at each location under the conditions of step S7 with the data obtained when the porous medium was not sprayed, observe the drag reduction effect, and optimize the parameters of porous medium thickness and porosity to obtain the maximum drag reduction rate.

[0015] According to the above scheme, in step S1, the navigation body is divided into passenger ships, cargo ships, special purpose ships and underwater navigation bodies.

[0016] According to the above scheme, in step S2, the vehicle body is divided into four regions using the following method: the X-axis is along the length of the vehicle body, the Y-axis is along the width of the vehicle body, and the Z-axis is perpendicular to the XY plane, representing the height of the vehicle body. The vehicle body is divided into four regions: the bow, the parallel midbody, the tail, and the tail cover. Linear equations are constructed for the bow, the parallel midbody, the tail, and the tail cover. The linear equation for the bow is:

[0017] R = R max (ax(0.3x-1) 4 +bx 2 (0.3x-1) 3 +1-(0.3x-4) 4 (1.2x+1)) 1 / 2.1 (1)

[0018] In equation (1), R represents the radial length, x represents the axial length of the vehicle, and R max This represents the radius of the aircraft, where a and b are fixed coefficients.

[0019] The linear equation of the parallel body is:

[0020] R = R max (2)

[0021] In equation (2), R represents the radial length, R max Indicates the radius of the aircraft;

[0022] The linear equation for the tail is:

[0023]

[0024] In equation (3), R represents the radial length, x represents the axial length of the vehicle, and R max The radius of the aircraft is represented by r. h k1 and k2 are fixed coefficients, and ε is the coefficient value related to the coefficient.

[0025] The linear equation for the tail cover is:

[0026] R = dR max (1-(3.2x-44.73) 2 ) 1 / 2 (4)

[0027] In equation (4), R represents the radial length, x represents the axial length of the vehicle, and R max This represents the radius of the aircraft, where d is a fixed coefficient;

[0028] The formula for the dimensionless parameter is:

[0029]

[0030] In equation (5), L represents the length of the aircraft, x L Represents the coordinates of the measurement point in the x-direction, y-direction... L Indicates the measurement point is at y Coordinates of direction;

[0031] The hull is divided into the bow, the midship section, and the stern.

[0032] According to the above scheme, in step S4, CFD calculation software is used. When the porous medium is not sprayed, the surface of the vehicle is set as a non-slip surface boundary condition. After spraying, it is set as a porous transition boundary condition. The inlet of the calculation domain is set as a velocity inlet, and the outlet of the calculation domain is set as a pressure outlet. The cylindrical surface is set as a symmetrical boundary. The distance from the inlet to the head of the vehicle is L, the outer diameter of the cylinder is 10D, where D is the diameter of the vehicle, and the distance from the outlet to the tail cover end face of the vehicle is 2L. The pressure condition is set according to the depth of the vehicle.

[0033] According to the above scheme, in step S5, the drag reduction rate is calculated using the following method:

[0034] Friction resistance formula:

[0035]

[0036] In equation (6), C f Let ΔC be the coefficient of friction resistance of a smooth flat plate. f Here, ρ represents the roughness compensation coefficient, ν represents the fluid density in the navigation area, and ν represents the speed. S Indicates the wetted surface area;

[0037] Viscous drag is caused by the viscosity of the fluid and the longitudinal pressure gradient at the rear of the object. The approximate formula for the viscous drag coefficient is:

[0038]

[0039] In equation (7), R pv ρ represents viscous pressure drag, ρ represents the fluid density in the navigation area, and ν represents the speed. S Indicates the wetted surface area;

[0040] The dimensionless drag coefficient is:

[0041]

[0042] In equation (8), F represents the total resistance. ρ The fluid density in the navigation area is represented by ν, and the speed of the ship is represented by ν. S Indicates the wetted surface area;

[0043] The drag reduction rate is:

[0044]

[0045] In equation (9), F represents the total resistance and F' represents the total resistance after drag reduction.

[0046] According to the above scheme, in step S8, an optimization method based on homotopy algorithm is used, which includes the following steps:

[0047] S801. First, a 3D model of the vehicle is created, then the initial conditions are calculated, followed by backpropagation, and finally, the conditions for stopping the calculation are set. The convex optimization model is shown below:

[0048]

[0049] In equation (10), β is the measurement vector, α is the unknown vector, B is the known matrix, and τ is the regularization parameter selected by the user. The homotopy algorithm reduces the value of τ by tracing the path and stops the calculation only when τ converges to the required threshold, thus obtaining the optimal solution to the problem.

[0050] S802, Assume α ～ The solution to equation (10) is the homotopy algorithm, which begins with α. ～ =0, and through a series of calculations, gradually reduced to a threshold, α ～ Follow a piecewise linear path:

[0051]

[0052] In equation (11), β is the measurement vector, α is the unknown vector, and B is the known matrix;

[0053] S803, α ～ The update is performed based on the step size and update direction, and all parameters are determined by α. ～ The smaller critical value of the critical value τ is determined by the support and symbol sequence, given the objective function f(α), by the following formula:

[0054]

[0055] S804, Implementing α ～ A necessary condition for the optimal solution is:

[0056]

[0057] S805, Let Ω = {i|α} i ～ ≠0} represents positive support; given any value of τ, z = sgn(α) ～ Ω This causes a slight decrease in δ, and the new solution will be generated according to the following formula:

[0058]

[0059] S806, Calculate the minimum step size δ min Then, make τ = τ - δ min Similarly, make A new α can be obtained ～ Estimate the value. Repeat steps S802-S805 above to reduce τ to the desired threshold;

[0060] S807. Use the optimized parameters for a new round of calculations to obtain the pressure resistance, viscous resistance, frictional resistance and dimensionless resistance coefficients at each location, and observe the drag reduction effect.

[0061] S808. After obtaining the optimal parameters of the porous medium at different locations, the calculation is performed again to obtain the pressure resistance, viscous resistance, frictional resistance and dimensionless resistance coefficient at each location. The results are compared with those before coating to obtain the drag reduction rate.

[0062] The drag reduction design method for non-uniform porous media sliding surfaces that varies with spatial position according to the present invention has the following advantages:

[0063] 1. This invention fully considers the complex three-dimensional curved surface of the vehicle and the unique properties of the flow field in each part. Taking into account phenomena such as eddies and flow separation, it analyzes the specific flow field through calculation, adjusts the parameters of the porous medium for different situations, and proposes a drag reduction method for non-uniform porous medium sliding surfaces that varies with spatial position.

[0064] 2. The porous medium sliding surface of the present invention also has functions such as self-cleaning, anti-fogging, anti-fogging, and anti-icing. It can remove stains such as microorganisms, bacteria, and microparticles by rolling droplets on the surface. This property not only helps to maintain the cleanliness of the surface and reduce the attachment of marine organisms, but also reduces maintenance requirements and improves the long-term performance and reliability of surface drag reduction.

[0065] 3. The drag reduction design method for non-uniform porous media sliding surfaces that varies with spatial position provided by the present invention can provide the optimal parameters corresponding to the porous media according to the position change, fully taking into account the actual situation and achieving the maximum drag reduction rate. Attached Figure Description

[0066] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings:

[0067] Figure 1 This is a schematic diagram of the flow field of a certain type of aircraft according to the present invention;

[0068] Figure 2 This is a simplified flowchart of the drag reduction design method for non-uniform porous media sliding surfaces that varies with spatial position according to the present invention;

[0069] Figure 3 This is a schematic diagram of the navigation body partitions of the present invention;

[0070] Figure 4 This is a schematic diagram of the calculation domain of the navigation body according to the present invention;

[0071] Figure 5 This is a schematic diagram illustrating the effect of the permeability and thickness of a certain porous medium on the drag reduction rate according to the present invention.

[0072] Figure 6 This is a schematic diagram of the velocity change after the porous medium of the present invention is sprayed;

[0073] Figure 7 This is a schematic diagram of a certain spraying scheme of the present invention;

[0074] Figure 8 These are schematic diagrams illustrating different drag reduction schemes of the present invention;

[0075] In the figure: 1. Head, 2. Parallel body, 3. Tail, 4. Tail cover, 5. Surface of the vehicle, 6. Velocity inlet, 7. Pressure outlet, 8. Symmetrical boundary, 9. Porous medium a, 10. Porous medium b, 11. Porous medium c, 12. Porous medium d. Detailed Implementation

[0076] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0077] like Figure 1-8 As shown, the drag reduction design method for non-uniform porous media sliding surfaces that varies with spatial position according to the present invention includes the following steps:

[0078] S1. Select the route of the vessel, analyze the route, and classify it according to the water conditions of the navigation area, with different waters corresponding to different operating conditions. Vessels are divided into passenger ships, cargo ships, special purpose ships, and underwater vessels, etc. After comprehensive consideration, determine the main influencing factors that need to be considered during the calculation, and select an appropriate calculation formula.

[0079] S2. Divide the navigation body into sections. For example... Figure 3 As shown, taking an underwater vehicle as an example, this is a schematic diagram of the vehicle's partitioning. The X-axis is along the length of the vehicle, the Y-axis is along the width of the vehicle, and the Z-axis is perpendicular to the XY plane, representing the height of the vehicle. The vehicle is divided into four regions: bow 1, parallel midbody 2, tail 3, and tail cover 4. Linear equations are constructed for bow 1, parallel midbody 2, tail 3, and tail cover 4, and the coordinates of each point on the vehicle can be represented by the corresponding linear equations. The purpose of partitioning is to better describe the changes in the flow field on the surface of the vehicle. Due to the complex three-dimensional curved surface of the vehicle, pressure-boosting and pressure-reducing zones are formed when fluid flows through it. In the pressure-boosting zone, fluid backflow may occur, causing the boundary layer to shift outward and forming boundary layer separation, which may increase viscous pressure drag. Porous media can change the slip length, and the transition delay effect becomes more significant with the increase of slip length. Spraying porous media materials may change the range of influence of backflow on the surface of the vehicle. It is necessary to analyze the specific flow field state, observe the influence of backflow on drag, and continuously adjust the slip length. Taking a certain underwater vehicle as an example: dividing the vehicle into sections, the linear equation of the bow is:

[0080] R = R max (ax(0.3x-1) 4 +bx 2 (0.3x-1) 3 +1-(0.3x-4) 4 (1.2x+1)) 1 / 2.1 (1)

[0081] In equation (1), R represents the radial length, x represents the axial length of the vehicle, and R max This represents the radius of the aircraft, where a and b are fixed coefficients.

[0082] The linear equation of the parallel body is:

[0083] R = R max (2)

[0084] In equation (2), R represents the radial length, R max Indicates the radius of the aircraft;

[0085] The linear equation for the tail is:

[0086]

[0087] In equation (3), R represents the radial length, x represents the axial length of the vehicle, and R max The radius of the aircraft is represented by r. h k1 and k2 are fixed coefficients, and ε is the coefficient value related to the coefficient.

[0088] The linear equation for the tail cover is:

[0089] R = dR max (1-(3.2x-44.73) 2 ) 1 / 2 (4)

[0090] In equation (4), R represents the radial length, x represents the axial length of the vehicle, and R max This represents the radius of the aircraft, where d is a fixed coefficient;

[0091] The formula for the dimensionless parameter is:

[0092]

[0093] In equation (5), L represents the length of the aircraft, x L Represents the coordinates of the measurement point in the x-direction, y-direction... L This indicates the coordinates of the measurement point in the y-direction;

[0094] If the object of study is a ship, it is recommended to refer to ship hull lines diagrams, hull value tables, and other relevant materials for hull data. The hull is generally divided into the bow, midships, and stern.

[0095] S3. Establish a physical model of the object under study, determine the spatial influence area of ​​the object to be analyzed, and divide the outer surface of the vehicle and the entire computational domain into spatial meshes. The established physical model should fully consider the actual situation, abstract from the actual working conditions, and be as close to the actual working conditions as possible to ensure the authenticity and reliability of the results. Taking an underwater vehicle as an example, in order to better capture the changes in the flow field and obtain more accurate calculation results, the mesh near the surface of the vehicle was refined, and more precise refinement was carried out in areas with large curvature changes. A denser mesh area was set in the tail where vortices may be generated.

[0096] S4. Determine the initial conditions, governing equations, and boundary conditions required for the solution based on the actual flow field. Select an appropriate algorithm and set specific conditions for controlling the solution process and accuracy. Taking an underwater vehicle as an example, the calculation uses existing CFD software, such as Fluent, employing a k-ε turbulence numerical model. The computational domain is cylindrical. When the porous medium is not sprayed, the unsprayed surface 5 of the vehicle is set as a no-slip surface; after spraying, it is set as a porous transition boundary condition. The computational domain inlet is set as a velocity inlet 6, and the computational domain outlet is set as a pressure outlet 7. The cylindrical surface is set as a symmetric boundary 8. The distance from the inlet to the head of the vehicle is L, the outer diameter of the cylinder is 10D (D is the diameter of the vehicle), and the distance from the outlet to the tail cover end face of the vehicle is 2L. Pressure conditions are set according to the depth of the vehicle. Figure 4 The diagram shows a schematic of the computational domain for a flight vehicle.

[0097] S5. Calculate the differential pressure drag, viscous drag, and frictional drag at various locations when the vehicle body is not coated with porous media material. Based on the simulation experiment drag calculation results and the drag coefficient calculation formula, determine the dimensionless drag coefficient corresponding to different locations, find the locations where flow separation occurs, analyze the flow field at each location, and predict the porous media parameters corresponding to different locations. For example... Figure 1 As shown, in region A, the tangential force F is opposite to the total resistance. Spraying a porous medium will actually decrease F, thus increasing the resistance. Therefore, it is not necessary to spray a porous medium in region A. For Figure 1 In region B, the tangential force F' is in the same direction as the total drag. Reducing F' is beneficial for drag reduction. Therefore, a porous medium needs to be sprayed at this location, and the optimal parameters should be found to minimize F'. Figure 5 The figure shows the effect of a certain permeability and thickness on the drag reduction rate. α is the permeability, and δ is the thickness.

[0098] Friction resistance formula:

[0099]

[0100] In equation (6), C f Let ΔC be the coefficient of frictional resistance of a smooth flat plate. fρ represents the roughness compensation coefficient, ν represents the fluid density in the navigation area, ν represents the speed, and S represents the wetted surface area.

[0101] Viscous drag is caused by the viscosity of the fluid and the longitudinal pressure gradient at the rear of the object. The approximate formula for the viscous drag coefficient is:

[0102]

[0103] In equation (7), R pv ρ represents viscous pressure resistance, ν represents the fluid density in the navigation area, S represents the speed, and S represents the wetted surface area.

[0104] The dimensionless drag coefficient is:

[0105]

[0106] In equation (8), F represents total resistance, ρ represents fluid density in the navigation area, ν represents speed, and S represents wetted surface area.

[0107] The drag reduction rate is:

[0108]

[0109] In equation (9), F represents the total resistance and F' represents the total resistance after drag reduction.

[0110] S6. Based on the data obtained in step S5 and the characteristics of the corresponding porous medium, specify the initial coating thickness, porosity, and other parameters for each part. Then, based on these initial parameters, coat each part of the vehicle with the corresponding porous medium material, such as... Figure 6 As shown, the flow velocity after spraying the porous medium is Us, where Us represents the slip velocity.

[0111] S7. Under the conditions of step S6, calculate the navigation of the vehicle under the corresponding operating conditions, calculating the pressure drag, viscous drag, and friction drag at each position. Based on the simulation experiment drag calculation results and the drag coefficient calculation formula, determine the dimensionless drag coefficient corresponding to different positions to evaluate the drag reduction efficiency under this condition. Observe the flow field changes after spraying the porous medium and compare it with the flow field before spraying. Adjust the porous medium parameters according to the specific situation. Figure 1 In region A, the tangential force F needs to be as large as possible, so there is no need to spray porous media in region A; in region B, the tangential force F' needs to be as small as possible, so porous media with corresponding parameters need to be sprayed.

[0112] S8. Compare the differential pressure resistance, viscous resistance, frictional resistance, and dimensionless resistance coefficient obtained under the conditions of step S6 with the data obtained when the porous medium was not sprayed, observe the drag reduction effect, and optimize the parameters such as the thickness and porosity of the porous medium.

[0113] Optimization methods are generally divided into forward optimization and backward optimization. Forward optimization may get stuck in local optima and fail to obtain the global optimum; backward optimization, on the other hand, involves calculating the required unknown physical quantities from other known parameters and physical quantities, and then inversely calculating certain structural features. Backward optimization is recommended. This embodiment uses a backward optimization method based on the homotopy algorithm.

[0114] S801. Perform 3D modeling of the vehicle, calculate the initial conditions, then perform backpropagation, and finally set the conditions for stopping the calculation. The convex optimization model is shown below:

[0115]

[0116] Where β is the measurement vector, α is the unknown vector, B is the known matrix, and τ is the regularization parameter selected by the user. The homotopy algorithm can reduce the value of τ by tracing the path, and stops calculating only when τ converges to the required threshold, thus obtaining the optimal solution to the problem.

[0117] S802, Assume α ～ The solution to equation (10) is the homotopy algorithm, which begins with α. ～ =0, and through a series of calculations, gradually reduced to a threshold, α ～ Follow a piecewise linear path:

[0118]

[0119] In equation (11), β is the measurement vector, α is the unknown vector, and B is the known matrix;

[0120] S803, α ～ The update is performed based on the step size and update direction, and all parameters are determined by α. ～ The smaller critical value of the critical value τ, determined by the support and symbol sequence, can be obtained from the following formula, given the objective function f(α):

[0121]

[0122] S804, Implementing α ～ A necessary condition for the optimal solution is:

[0123]

[0124] S805, Let Ω = {i|α} i ～ ≠0} represents positive support; given any value of τ, z = sgn(α) ～ Ω This causes a slight decrease in δ, and the new solution will be generated according to the following formula:

[0125]

[0126] S806, Calculate the minimum step size δ min Then, make τ = τ - δ min Similarly, make A new α can be obtained ～ Estimate the value. Repeat steps S802-S805 to reduce τ to the desired threshold;

[0127] S807. Use the optimized parameters for a new round of calculations to obtain the differential pressure resistance, viscous resistance, frictional resistance, and dimensionless resistance coefficient at each location, and observe the drag reduction effect. For example... Figure 7 The diagram shown is a schematic of a spraying method. Porous media a9, b10, c11, and d12 represent four types of porous media.

[0128] S808. After obtaining the optimal parameters of the porous medium at different locations, recalculation is performed to obtain the pressure resistance, viscous resistance, frictional resistance, and dimensionless resistance coefficient at each location. These parameters are then compared with those before coating to determine the drag reduction rate. For example... Figure 8 As shown, the drag reduction rates of different schemes are presented.

[0129] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A drag reduction design method for a non-uniform porous medium sliding surface that varies with spatial position, characterized in that, Includes the following steps: S1. Select the route of the vehicle, analyze the route, and classify it according to the water conditions of the navigation area. Different water areas correspond to different working conditions. S2. Divide the vehicle into sections and construct linear equations; The aircraft is divided into four regions using the following method: the X-axis is along the length of the aircraft, the Y-axis is along the width of the aircraft, and the Z-axis is perpendicular to the XY plane, representing the height of the aircraft. These regions are the bow, the midsection, the stern, and the stern cover. Linear equations are then constructed for the bow, midsection, stern, and stern cover. The linear equation for the bow is as follows: R=R max (ax(0.3x-1) 4 +bx 2 (0.3x-1) 3 +1-(0.3x-4) 4 (1.2x+1)) 1 / 2.1 (1) In equation (1), R represents the radial length, x represents the axial length of the vehicle, and R max This represents the radius of the aircraft, where a and b are fixed coefficients. The linear equation of the parallel body is: R=R max (2) The linear equation for the tail is: In equation (3), r h k1 and k2 are fixed coefficients, and ε is the coefficient value related to the coefficient. The linear equation for the tail cover is: R=dR max (1-(3.2x-44.73)2)1 / 2 (4) In equation (4), d is a fixed coefficient; The formula for the dimensionless parameter is: In equation (5), L represents the length of the aircraft, x L Represents the coordinates of the measurement point in the x-direction, y-direction... L This indicates the coordinates of the measurement point in the y-direction; The hull is divided into the bow, the midship section, and the stern. S3. Establish a physical model of the object to be studied, determine the spatial influence area of ​​the object to be analyzed, and divide the outer surface of the vehicle and the entire calculation area into spatial grids. S4. Determine the initial conditions, governing equations, and boundary conditions required for the solution based on the actual flow field conditions; S5. Calculate the pressure drag, viscous drag, and friction drag at each location when the vehicle body is not coated with porous media material. Based on the simulation experiment drag calculation results and the drag coefficient calculation formula, determine the dimensionless drag coefficient corresponding to different locations, find the location where flow separation occurs, analyze the flow field at each location, and predict the porous media parameters corresponding to different locations. S6. Based on the data obtained in step S5 and the characteristics of the corresponding porous medium, the parameters of the initial coating thickness and porosity of each part are given. Based on the parameters of the initial coating thickness and porosity, the porous medium material with the corresponding conditions is coated on each part of the vehicle body. S7. Under the conditions of step S6, calculate the navigation of the vehicle under the corresponding working conditions, calculate the pressure drag, viscous drag, and friction drag corresponding to each position, and determine the dimensionless drag coefficient corresponding to different positions based on the simulation experiment drag calculation results and the drag coefficient calculation formula, so as to evaluate the drag reduction efficiency under the condition, observe the flow field change after spraying the porous medium, compare it with the flow field before spraying, and adjust the porous medium parameters according to the specific situation. S8. Compare the differential pressure resistance, viscous resistance, frictional resistance, and dimensionless resistance coefficient obtained at each location under the conditions of step S7 with the data obtained when the porous medium was not sprayed, observe the drag reduction effect, and optimize the parameters of porous medium thickness and porosity to obtain the maximum drag reduction rate.

2. The drag reduction design method for non-uniform porous media sliding surfaces that vary with spatial position according to claim 1, characterized in that, In step S1, the vehicle includes passenger ships, cargo ships, special purpose ships, and underwater vehicles.

3. The drag reduction design method for non-uniform porous media sliding surfaces that vary with spatial position according to claim 1, characterized in that, In step S4, CFD calculation software is used. When the porous medium is not sprayed, the surface of the vehicle is set as a non-slip surface boundary condition. After spraying, it is set as a porous transition boundary condition. The calculation domain inlet is set as a velocity inlet, the calculation domain outlet is set as a pressure outlet, and the cylindrical surface is set as a symmetrical boundary.

4. The drag reduction design method for non-uniform porous media sliding surfaces that vary with spatial position according to claim 1, characterized in that, In step S5, the drag reduction rate is calculated using the following method: Friction resistance formula: In equation (6), C f Let ΔC be the coefficient of frictional resistance of a smooth flat plate. f The roughness compensation coefficient is ρ, where ρ represents the fluid density in the navigation area, ν represents the speed, and S represents the wetted surface area. The approximate formula for the viscous pressure resistance coefficient is: In equation (7), R pv Indicates viscous pressure resistance; The dimensionless drag coefficient is: In equation (8), F represents the total resistance; The drag reduction rate is: In equation (9), F' represents the total resistance after drag reduction.

5. The drag reduction design method for non-uniform porous media sliding surfaces that vary with spatial position according to claim 1, characterized in that, In step S8, an optimization method based on homotopy algorithm is used for optimization, including the following steps: S801. First, a 3D model of the vehicle is created, then the initial conditions are calculated, followed by backpropagation, and finally, the conditions for stopping the calculation are set. The convex optimization model is shown below: In equation (10), β is the measurement vector, α is the unknown vector, B is the known matrix, and τ is the regularization parameter selected by the user. The homotopy algorithm reduces the value of τ by tracing the path and stops the calculation only when τ converges to the required threshold, thus obtaining the optimal solution to the problem. S802, Assume α ～ It is a solution to equation (10), and the homotopy algorithm starts at α. ～ =0, and through a series of calculations, gradually reduced to a threshold, α ～ Follow a piecewise linear path: S803, α ～ The update is performed based on the step size and update direction, and all parameters are determined by α. ～ The smaller critical value of the critical value τ is determined by the support and symbol sequence, given the objective function f(α), by the following formula: S804, Implementing α ～ A necessary condition for the optimal solution is: S805, Let Ω = {i|α} i ～ ≠0} represents positive support; given any value of τ, z = sgn(α) ～ Ω This causes a slight decrease in δ, and the new solution will be generated according to the following formula: S806, Calculate the minimum step size δ min Then, make τ = τ - δ min Similarly, make A new α can be obtained ～ Estimate the value; repeat steps S802-S805 above to reduce τ to the desired threshold; S807. Use the optimized parameters for a new round of calculations to obtain the pressure resistance, viscous resistance, frictional resistance and dimensionless resistance coefficients at each location, and observe the drag reduction effect. S808. After obtaining the optimal parameters of the porous medium at different locations, the calculation is performed again to obtain the pressure resistance, viscous resistance, frictional resistance and dimensionless resistance coefficient at each location. The results are compared with those before coating to obtain the drag reduction rate.

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