A Design Method for Three-Dimensional Twisted Airfoil Sails

Abstract

A three-dimensional twisted airfoil sail design method, which relates to a sail design method. The present invention aims to solve the problem that the existing airfoil sails have poor utilization effect of wind power. The steps of the present invention include Step 1: Two-dimensional airfoil design. According to the existing two-dimensional airfoils, the airfoils are parameterized by the FFD free deformation method; Step 2: Based on the two-dimensional airfoils designed in Step 1, three-dimensional airfoil design is carried out; Step 3: Verify the structural strength of the final airfoil. The present invention belongs to the technical field of sail design.

Description

Technical Field

[0001] The present invention relates to a sail design method, belonging to the technical field of sail design. Background Art

[0002] The existing airfoil sails for ships are mainly fixed straight airfoil sails, without considering that the oncoming flow conditions will change with the height at the same moment on the sea surface. Therefore, the existing airfoil sails have poor wind utilization effect. Summary of the Invention

[0003] In order to solve the problem of poor wind utilization effect of the existing airfoil sails, the present invention further provides a design method for a three-dimensional twisted airfoil sail.

[0004] The technical solution adopted by the present invention to solve the above problems is as follows: The present invention specifically includes:

[0005] Step 1: Two-dimensional airfoil design. According to the existing two-dimensional airfoil, parameterize the airfoil by the FFD free deformation method;

[0006] Step 2: Based on the two-dimensional airfoil designed in Step 1, perform three-dimensional airfoil design;

[0007] Step 3: Verify the structural strength of the final airfoil.

[0008] Further, the FFD free deformation method in Step 1 specifically includes:

[0009] Step 101: Place the two-dimensional airfoil in the control volume;

[0010] Step 102: Establish a mathematical relationship between the control volume vertices and the geometric coordinates of the two-dimensional airfoil through basis functions;

[0011] Step 103: Change the geometric coordinates of the two-dimensional airfoil by adjusting the coordinate changes of the control volume vertices, and finally obtain a new two-dimensional airfoil.

[0012] Further, the three-dimensional design in Step 2 specifically includes:

[0013] Step 201: The uniform undersurface wind speed conforms to the exponential law with height as:

[0014]

[0015] In formula (2), V Z represents the absolute wind speed, V1 represents the absolute wind speed at the reference height, z represents the height, and z1 represents the reference height;

[0016] The atmospheric wind profile on the sea surface satisfies the 1 / 8 exponential law. Taking the wind speed at a height of 15 m as the reference, the wind speeds at different heights on the sea surface are expressed as:

[0017]

[0018] In formula (3), V 15 represents the absolute wind speed at 15 m above the sea surface;

[0019] Step 202: Based on the two-dimensional airfoil design result in Step 1, longitudinally stretch to obtain the original three-dimensional airfoil;

[0020] Step 203: Use formula (3) to set the oncoming flow wind speed condition for CFD simulation calculation, change the oncoming flow attack angle, conduct simulation calculation, and obtain the oncoming flow attack angle α with the maximum lift;

[0021] The calculation formula for the relative wind speed at different heights is:

[0022]

[0023] In formula (4), V e represents the relative wind speed, and V S represents the ship's speed;

[0024] Step 204: Parametrize the original three-dimensional airfoil by the FFD free deformation method;

[0025] Step 205: Use the Latin hypercube method to obtain the three-dimensional airfoil geometry;

[0026] Step 206: Mesh the three-dimensional airfoil, and set the oncoming flow boundary condition by combining formula (4) with the oncoming flow attack angle α, and conduct numerical simulation calculation;

[0027] Step 207: According to the input three-dimensional airfoil geometry and calculation results, construct a Kriging surrogate model with thrust as the target, and use the leave-one-out method to verify the accuracy of the surrogate model;

[0028] Step 208: Take thrust as the target of the genetic algorithm, and optimize to obtain the three-dimensional airfoil with the maximum thrust.

[0029] Furthermore, verifying the structural strength of the final airfoil in Step 3 specifically includes:

[0030] Step 301: Calculate the maximum relative wind speed on the ship through formula (3) and the ship's speed, and combine the maximum relative wind speed with the geometric shape of the sail to calculate the thrust and torque, providing a basis for structural strength checking;

[0031] Step 302: Combine the geometric shape of the sail to calculate the allowable stress at the corresponding position, and compare with the result of numerical calculation to verify the structural strength.

[0032] The beneficial effects of the present invention are:

[0033] The present invention constructs an aerodynamic reduced-order model, which can process a large amount of airfoil geometric coordinate data in a short time, and uses a genetic algorithm to quickly obtain the optimal airfoil results for various shapes of sails;

[0034] The present invention takes thrust as the optimization goal, and finally obtains a sail with the maximum thrust. Loading it on a bulk carrier can provide a large amount of thrust for the ship, reduce the fuel consumption during the ship's navigation, and have significant economic benefits;

[0035] According to the two-dimensional airfoil optimization results, the present invention longitudinally stretches the two-dimensional optimized airfoil to obtain an original three-dimensional airfoil, and conducts numerical simulation calculations on the original three-dimensional airfoil under the inflow conditions shown in Table 1 (arranging three sails on the ship model). Each sail can provide an average thrust of 80,000 N. Calculated based on the performance parameters of a 210,000-ton bulk carrier, each sail can save an average of 1.89 tons of fuel. Calculated at a fuel price of 5,000 yuan / ton, 9,450 yuan can be saved every day. If a twisted airfoil sail after three-dimensional optimization design is adopted, the obtained thrust will be greater than that of the original three-dimensional airfoil, and the fuel consumption can be further reduced. Description of the Drawings

[0036] Figure 1 It is a schematic diagram of the application of the FFD free-form deformation method;

[0037] Figure 2 It is a schematic diagram of the grid division of the two-dimensional computational domain;

[0038] Figure 3 It is a schematic diagram of the optimized airfoil geometry. Detailed Embodiments

[0039] Detailed Embodiment 1: Combined with Figures 1 to 3 This embodiment is described. The design method of a three-dimensional twisted airfoil sail according to this embodiment is characterized in that the specific steps of the design method include:

[0040] Step 1: Two-dimensional airfoil design. According to the existing two-dimensional airfoil, parameterize the airfoil through the FFD free-form deformation method;

[0041] Step 2: Based on the two-dimensional airfoil designed in Step 1, conduct three-dimensional airfoil design;

[0042] Step 3: Verify the structural strength of the final airfoil.

[0043] Detailed Embodiment 2: Combined with Figures 1 to 3 This embodiment is described. The FFD free-form deformation method in Step 1 of the design method of a three-dimensional twisted airfoil sail according to this embodiment specifically includes:

[0044] Step 101: Place the two-dimensional airfoil in the control volume;

[0045] Step 102: Establish a mathematical relationship between the control volume vertices and the geometric coordinates of the two-dimensional airfoil through basis functions;

[0046] Step 103: Change the geometric coordinates of the two-dimensional airfoil by adjusting the coordinate changes of the control volume vertices, and finally obtain a new two-dimensional airfoil.

[0047] The basic formula of the FFD free deformation method is:

[0048]

[0049] In formula (1), X(s, t, u) represents the global coordinates of any geometric point within the control volume, P i,j,k represents the coordinates of the control point vertices, s, t, u represent the local coordinates of the geometric point to be controlled, and R represents the type of basis function.

[0050] Use the Latin hypercube method to sample within the range of ±15% of the X and Y coordinates to obtain 1000 sets of control volume vertex coordinates, that is, 1000 different two-dimensional airfoils; calculate the geometry of the required two-dimensional airfoil through formula (1);

[0051] CFD simulation calculation. Perform fluid domain mesh generation on the above-obtained 1000 sets of two-dimensional airfoils, and use the commercial software Fluent for numerical simulation calculation. The calculation conditions and settings are as follows:

[0052] Table 1 Numerical methods and boundary condition settings

[0053]

[0054] Finally, obtain the lift value of each airfoil.

[0055] Construct a Kriging surrogate model with lift as the objective based on the input airfoil geometric control points and the simulation calculation results.

[0056] Use the leave-one-out method to verify the model accuracy. From the 1000 sample points, select 999 sample points as the training set to construct the Kriging surrogate model. The remaining 1 sample point is used as the test set, substitute it into the surrogate model to obtain the response value, and compare this response value with the true value to verify the accuracy of the surrogate model. Take each of the 1000 samples as the test set one by one, and finally obtain the average error of the surrogate model as 1.29%. After obtaining a surrogate model with reliable accuracy, use the genetic algorithm to obtain the airfoil with the maximum lift.

[0057] Basic principle of genetic algorithm: A number of digital encodings of the problem to be solved are randomly generated to form an initial population. Each individual is given a numerical evaluation through a fitness function, and individuals with low fitness are eliminated while those with high fitness are selected to participate in genetic operations. The set of individuals after genetic operations forms the next generation population, and the next round of evolution is carried out on this population. In the present invention, a number of airfoil control point coordinate sets are randomly generated within a certain range, and the control point coordinates are substituted into the surrogate model to predict their lift. Taking the lift as the objective of the genetic algorithm, airfoil geometries with low lift are eliminated, and airfoil geometries with high lift are selected for genetic operations. Finally, the airfoil with the maximum lift is obtained.

[0058] Specific implementation method three: Combining Figures 1 to 3 To illustrate this implementation method, in step 2 of the three-dimensional twisted airfoil sail design method described in this implementation method, the three-dimensional design specifically includes:

[0059] Step 201, The uniform underlying surface wind speed conforms to the exponential law with height as:

[0060]

[0061] In formula (2), V Z represents the absolute wind speed, V1 represents the absolute wind speed at the reference height, z represents the height, and z1 represents the reference height;

[0062] The atmospheric wind profile on the sea surface satisfies the 1 / 8 exponential law. Taking the wind speed at a height of 15 m as the reference, the wind speeds at different heights on the sea surface are expressed as:

[0063]

[0064] In formula (3), V 15 represents the absolute wind speed at a distance of 15 m from the sea surface;

[0065] Step 202, Based on the two-dimensional airfoil design result in step 1, longitudinally stretch to obtain the original three-dimensional airfoil;

[0066] Step 203, Use formula (3) to set the oncoming flow wind speed condition for CFD simulation calculation, change the oncoming flow attack angle, conduct simulation calculation, and obtain the oncoming flow attack angle α with the maximum lift;

[0067] The calculation formula for the relative wind speed at different heights is:

[0068]

[0069] In formula (4), V e represents the relative wind speed, and V S represents the ship's sailing speed;

[0070] Step 204: Parameterize the original three-dimensional airfoil through the FFD free-form deformation method;

[0071] Step 205: Use the Latin hypercube method to obtain the three-dimensional airfoil geometry;

[0072] Step 206: Mesh the three-dimensional airfoil, and set the oncoming flow boundary conditions by combining with the oncoming flow angle of attack α using formula (4), and perform numerical simulation calculations;

[0073] Step 207: Construct a Kriging surrogate model with thrust as the objective based on the input three-dimensional airfoil geometry and calculation results, and use the leave-one-out method to verify the accuracy of the surrogate model;

[0074] Step 208: Take thrust as the objective of the genetic algorithm and optimize to obtain the three-dimensional airfoil with the maximum thrust.

[0075] When the ship sails at a certain speed, the relative wind speed and relative wind direction at different heights are different, and their velocity triangles are also different. Under ideal conditions, the cross-sectional airfoil shape of the optimized three-dimensional airfoil at different heights will change with the velocity triangle. Therefore, the optimized airfoil is a twisted airfoil.

[0076] Use the same oncoming flow conditions as in the above numerical simulation calculation process to verify the thrust performance of the original three-dimensional airfoil and compare it with the twisted airfoil. The result should be that the thrust of the twisted three-dimensional airfoil is greater.

[0077] Specific Embodiment 4: Combine Figures 1 to 3 To illustrate this embodiment, in step 3 of the method for designing a three-dimensional twisted airfoil sail described in this embodiment, verifying the structural strength of the final airfoil specifically includes:

[0078] Step 301: Calculate the maximum relative wind speed on the ship through formula (3) and the ship speed, and combine the maximum relative wind speed with the geometric shape of the sail to calculate the thrust and torque, providing a basis for structural strength checking;

[0079] Step 302: Combine the geometric shape of the sail to calculate the allowable stress at the corresponding position, and compare it with the result of numerical calculation to verify the structural strength.

[0080] The above are only the preferred embodiments of the present invention, and do not impose any form of limitation on the present invention. Although the present invention has been disclosed above with the preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to the above-disclosed technical content to obtain equivalent embodiments with equivalent changes within the scope of the technical solution of the present invention. However, as long as it does not depart from the content of the technical solution of the present invention and is based on the technical essence of the present invention, any simple modifications, equivalent replacements, and improvements made to the above embodiments still fall within the protection scope of the technical solution of the present invention.

Claims

1. A three-dimensional twisted airfoil sail design method, characterized in that, The specific steps of the design method are as follows: Step 1: Two-dimensional airfoil design. Parametrize the airfoil using the FFD free deformation method based on the existing two-dimensional airfoil. Step 2: Based on the two-dimensional airfoil designed in Step 1, conduct three-dimensional airfoil design. Specifically, it includes: Step 201: The uniform wind speed of the underlying surface with height conforms to the exponential rate as follows: （2）， In formula (2) represents the absolute wind speed represents the absolute wind speed at the reference height represents the height represents the reference height The atmospheric wind profile over the sea surface satisfies the 1 / 8 exponential rate. Taking the wind speed at a height of 15 m as the reference, the wind speeds at different heights over the sea surface are expressed as: （3）， In formula (3), represents the absolute wind speed at 15 m above the sea surface; Step 202: Based on the design result of the two-dimensional airfoil in Step 1, longitudinally stretch to obtain the original three-dimensional airfoil. Step 203: Set the oncoming flow velocity condition for the CFD simulation using formula (3), change the oncoming flow angle of attack, conduct the simulation calculation, and obtain the oncoming flow angle of attack with the maximum lift ; The calculation formula for the relative wind speed at different heights is: （4）， In formula (4), represents the relative wind speed, represents the ship's speed; Step 204: Parametrize the original three-dimensional airfoil using the FFD free deformation method. Step 205: Use the Latin hypercube method to obtain the three-dimensional airfoil geometry. Step 206: Mesh the three-dimensional airfoil and set the incoming flow boundary conditions using Equation (4) in combination with the incoming flow angle of attack, and perform numerical simulation calculations; ​ Step 207: Based on the input three-dimensional airfoil geometry and calculation results, construct a Kriging surrogate model with thrust as the objective, and use the leave-one-out method to verify the accuracy of the surrogate model. Step 208: Take thrust as the objective of the genetic algorithm and optimize to obtain the three-dimensional airfoil with the maximum thrust. Step 3: Verify the structural strength of the final airfoil.

2. The three-dimensional twisted airfoil sail design method according to claim 1, wherein, The specific steps of the FFD free deformation method in Step 1 are as follows: Step 101: Place the two-dimensional airfoil in the control volume. Step 102: Establish a mathematical relationship between the control volume vertices and the geometric coordinates of the two-dimensional airfoil through basis functions. Step 103: Change the geometric coordinates of the two-dimensional airfoil by adjusting the coordinate changes of the control volume vertices, and finally obtain a new two-dimensional airfoil.

3. A three-dimensional twisted airfoil sail design method according to claim 1 or 2, characterized in that, The specific steps of verifying the structural strength of the final airfoil in Step 3 are as follows: Step 301: Calculate the maximum relative wind speed on the ship through formula (3) and the ship speed. Combine the maximum relative wind speed and the geometric shape of the sail to calculate the thrust and torque, providing a basis for structural strength checking. Step 302: Combine the geometric shape of the sail to calculate the allowable stress at the corresponding position, and compare it with the result of numerical calculation to verify the structural strength.

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