A robust optimization design method for airfoil considering the influence of flexible skin deformation

Abstract

The present invention discloses a robust optimization design method for airfoils that takes into account the influence of flexible skin deformation, which relates to the technical field of aircraft design, and includes completing the following steps through an airfoil multi-level optimization module: Step S1, completing the deterministic optimization design of the airfoil without considering skin deformation through an adaptive proxy model that does not contain random variables, and obtaining a deterministic optimal solution; Step S2, reconstructing the design space with the deterministic optimal solution of the airfoil as the center, and then completing the robust optimization design of the airfoil through an adaptive proxy model that contains random variables, and obtaining a robust optimal solution. The present invention adopts the above-mentioned robust optimization design method for airfoils that takes into account the influence of flexible skin deformation, which can be applied to the robust optimization design of airfoils under the influence of flexible skin in a low Reynolds number range, and the robust optimal airfoil can still maintain relatively good aerodynamic performance when the wing surface is not deformed / deformed, and has good aerodynamic robustness.

Description

Technical Field

[0001] The present invention relates to the technical field of aircraft design, and in particular to an airfoil robustness optimization design method taking into account the influence of flexible skin deformation. Background Art

[0002] Near-space solar-powered drones, levitating aircraft, and other aircraft generally use flexible photovoltaic skin wings to adapt to the wing characteristics of large aspect ratio and low wing loading. The flexible skin will undergo elastic deformation under the action of aerodynamic forces, which will further react on the pressure distribution on the wing surface, bringing uncertainty to the aerodynamic characteristics of the wing. Existing airfoil aerodynamic optimization design methods for such aircraft generally ignore the influence of flexible skin deformation and treat the airfoil as a rigid model. Therefore, the design results obtained are significantly different from the actual cross-sectional airfoil of the wing during flight, and may lead to deterioration of the aircraft's aerodynamic performance. Therefore, in the process of airfoil design for flexible skin wings, the influence of flexible skin deformation on the airfoil profile and aerodynamic characteristics must be fully considered. However, related technologies have not yet been involved in existing research. Summary of the Invention

[0003] The purpose of the present invention is to provide an airfoil robustness optimization design method taking into account the influence of flexible skin deformation, so as to solve the problem that the existing airfoil optimization method based on rigidity assumption has limitations in its application to near-space low-dynamic aircraft.

[0004] To achieve the above objectives, the present invention provides an airfoil robustness optimization design method that considers the influence of flexible skin deformation, comprising the following steps performed through an airfoil multi-level optimization module:

[0005] Step S1: completing the deterministic optimization design of the airfoil without considering skin deformation by using an adaptive proxy model without random variables, and obtaining a deterministic optimal solution;

[0006] Step S2: Reconstruct the design space with the deterministic optimal solution of the airfoil as the center, and then complete the robust optimization design of the airfoil through the adaptive surrogate model containing random variables to obtain the robust optimal solution.

[0007] Preferably, the specific steps of step S1 include:

[0008] Step S11, constructing an initial proxy model: constructing an initial design space, generating initial sample points, and training the proxy model;

[0009] Step S12, deterministic optimization model: selecting a proxy model that meets high prediction accuracy and performing deterministic optimization;

[0010] Step S13, updating the adaptive agent model: constructing a new sampling space centered on the deterministic optimal solution, sampling in the updated subspace and expanding the sample library, thus completing the update of the adaptive agent model without random variables;

[0011] Step S14: Repeat steps S12 and S13 until the convergence condition is met and a deterministic optimal design is obtained.

[0012] Preferably, the specific steps of step S2 include:

[0013] Step S21, constructing an initial surrogate model: constructing an initial design space for robust optimization centered on the deterministic optimal solution, generating initial sample points, adding random variables to the original input parameters, and training an adaptive surrogate model containing random variables;

[0014] Step S22, robustness optimization model: perform robustness optimization, the optimization target is the output response Y The mean and standard deviation ;

[0015] Step S23, updating the adaptive surrogate model: constructing a new sampling subspace with the representative point on the Perato frontier as the center, sampling in the updated sample space and completing the expansion of the sample library, thus completing the update of the adaptive surrogate model containing random variables;

[0016] Step S24: Repeat steps S22 and S23 until the convergence condition is met and the robust optimal design is obtained.

[0017] Preferably, in step S11 and step S21, a fluid mechanics calculation module is used to calculate the aerodynamic characteristics of the primary sample points, and the fluid mechanics calculation module includes the local transition Reynolds number The equation and the intermittent factor equation, reflecting the low Reynolds number The lower layer flow transition, separation and reattachment process.

[0018] Preferably, constructing the initialization design space in step S11 and step S21 and obtaining the airfoil profile using an airfoil parameterization module specifically includes the following steps:

[0019] Step S31: parameterize the reference airfoil using the CST parameterization method, which has the advantage of achieving higher fitting accuracy with fewer parameters.

[0020] Step S32: Based on the regional deformation characteristics of the flexible skin wing in the wind tunnel test, a curve reflecting the local deformation of the wing surface is superimposed using a non-uniform B-spline curve method to obtain an airfoil profile that takes into account the influence of skin deformation.

[0021] Therefore, the present invention adopts the above-mentioned airfoil robustness optimization design method considering the influence of flexible skin deformation, which includes the following beneficial effects:

[0022] (1) In the airfoil parameterization stage, the Bernstein polynomial is first used to control the overall shape of the airfoil. Then, a non-uniform B-spline curve representing the local deformation of the airfoil is superimposed on the CST curve of the original airfoil. This method can fully combine the advantages of the CST method's strong ability to fit the overall shape and the non-uniform B-spline curve method's strong local control ability to achieve high-precision fitting of the airfoil curve of the flexible skin wing section.

[0023] (2) In the fluid mechanics calculation stage, it can independently complete the construction of structured grids, numerical calculations and convergence judgment based on the input initial geometric model, with high optimization efficiency and good accuracy, and no manual intervention is required; The fluid mechanics calculation module of the turbulence model can predict the flow behavior and aerodynamic force at low Reynolds numbers with high precision and good calculation accuracy.

[0024] (3) In the stage of robustness optimization design of airfoil, the advantages of adaptive agent model and genetic algorithm are combined to construct the design space with the deterministic optimal solution of airfoil as the center. Then, the robustness optimization design of airfoil is completed through the adaptive agent model containing random variables. This can decouple the complex optimization process and avoid the problem of increased computational complexity caused by too many dependent variables.

[0025] (4) The airfoil designed using the multi-stage airfoil optimization design method proposed in this invention can maintain excellent aerodynamic performance in both the non-deformed and deformed states. Based on the robust optimization design method, the lift-to-drag ratio of the robust optimal airfoil in the random deformation space is 3.5% higher than that of the deterministic optimal airfoil and 16.8% higher than that of the initial airfoil. In addition, the lift-to-drag ratio of the robust optimal airfoil in the worst deformation state only decreases by 2.7% compared to the non-deformed state, while the lift-to-drag ratio of the deterministic optimal airfoil decreases by 16.7%.

[0026] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 This is a flow chart of an embodiment of an airfoil robustness optimization design method considering the influence of flexible skin deformation according to the present invention;

[0028] Figure 2 It is the main deformation area of the flexible skin under the action of aerodynamic load;

[0029] Figure 3 is the original airfoil represented by the CST curve, where (a) is the component curve diagram and (b) is the composite curve diagram;

[0030] Figure 4 The local deformation of the skin represented by the non-uniform B-spline curve, where (a) is the component curve graph and (b) is the composite curve graph;

[0031] Figure 5 Comparison of the original airfoil profile before and after superimposing the non-uniform B-spline curve;

[0032] Figure 6 Comparison between the calculation results of the fluid mechanics calculation module and the wind tunnel test data, where (a) is Comparison chart, (b) is Comparison chart;

[0033] Figure 7 Comparison of the accuracy of different types of proxy models, where (a) is C D Actual value diagram, (b) is X tr Actual value graph;

[0034] Figure 8 It is the iterative convergence process of the Pareto frontier;

[0035] Figure 9 It is the drag coefficient composition of the three airfoils in the worst deformation state. DETAILED DESCRIPTION

[0036] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0037] Unless otherwise defined, the technical or scientific terms used in the present invention shall have the usual meanings understood by persons of ordinary skill in the field to which the present invention belongs. The words "first", "second" and similar terms used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. Words such as "include" or "comprise" mean that the elements or objects preceding the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. Words such as "connect" or "connected" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the object being described changes, the relative positional relationship may also change accordingly.

[0038] Example

[0039] See also Figure 1-9 The present invention provides an airfoil robustness optimization design method considering the influence of flexible skin deformation, comprising the following steps of performing an airfoil multi-level optimization module:

[0040] Step S1: Complete the deterministic optimization design of the airfoil without considering skin deformation through an adaptive proxy model without random variables to obtain a deterministic optimal solution. The specific steps include:

[0041] Step S11, constructing an initial proxy model: constructing an initial design space, generating initial sample points, and training the proxy model;

[0042] Step S12, deterministic optimization model: selecting a proxy model that meets high prediction accuracy and performing deterministic optimization;

[0043] Step S13, updating the adaptive agent model: constructing a new sampling space centered on the deterministic optimal solution, sampling in the updated subspace and expanding the sample library, thus completing the update of the adaptive agent model without random variables;

[0044] Step S14: Repeat steps S12 and S13 until the convergence condition is met and a deterministic optimal design is obtained.

[0045] Step S2: Reconstruct the design space with the deterministic optimal solution of the airfoil as the center, and then complete the robust optimization design of the airfoil through the adaptive surrogate model containing random variables to obtain the robust optimal solution. The specific steps include:

[0046] Step S21, constructing an initial surrogate model: constructing an initial design space for robust optimization centered on the deterministic optimal solution, generating initial sample points, adding random variables to the original input parameters, and training an adaptive surrogate model containing random variables;

[0047] Step S22, robustness optimization model: perform robustness optimization, the optimization target is the output response Y The mean and standard deviation ;

[0048] Step S23, updating the adaptive surrogate model: constructing a new sampling subspace with the representative point on the Perato frontier as the center, sampling in the updated sample space and completing the expansion of the sample library, thus completing the update of the adaptive surrogate model containing random variables;

[0049] Step S24: Repeat steps S22 and S23 until the convergence condition is met and the robust optimal design is obtained.

[0050] Steps S11 and S21 involve airfoil parameterization when constructing the initial design space. The airfoil profile is obtained using the airfoil parameterization module. Wind tunnel tests show that under a typical skin support structure, there are four main deformation areas of the airfoil in the cruising state, two on each of the upper and lower wing surfaces.

[0051] like Figures 2 to 4 As shown in the figure, the CST (Class Shape Transformation) parameterization method is used to control the overall shape of the airfoil, and the local deformation of the control curve is combined with the non-uniform B-spline curve to represent the local deformation of the skin, thereby obtaining the airfoil profile that takes into account the influence of skin deformation. A reasonable number of control points can be selected based on the requirements for optimization performance and the limitation of computing power. Taking a solar drone airfoil as an example, two 5th-order CST curves are used to parameterize the upper and lower surfaces of the reference airfoil respectively, and the parameter control is expressed as ( A 1, A 2, A 3, A 4, A 5, A 6, A 7, A 8, A 9, A 10 , A 11 , A 12 ),in A 1- A 6 controls the upper wing surface, A 7- A 12 Control the lower wing surface; two third-order non-uniform B-spline curves are used to parameterize the deformation of the upper and lower wing surfaces respectively, and the parameter control is expressed as ( B 1, B 2, B 3, B 4), where B 1 and B 2. Control the deformation of the two deformation areas on the upper wing surface. B 3 and B 4. Control the deformation amount of the two deformation areas of the lower wing surface.

[0052] After constructing the design space and generating sample points in step S11 and step S21, it is necessary to adopt The fluid mechanics calculation module of the turbulence model calculates the aerodynamic characteristics of the sample points. The fluid mechanics calculation module includes the local transition Reynolds number The equation and the intermittent factor The equation for low Reynolds numbers The lower layer flow transition, separation and reattachment process.

[0053] local transition Reynolds number Used to predict the transition starting position, the expression equation is:

[0054] ;

[0055] Where, U j is the local velocity in j The direction component, It is used to force the transport of scalar and The local value of matches the source term, is a constant used to control the diffusion coefficient, is the molecular viscosity, is the eddy viscosity.

[0056] Intermittent Factor The equation used to simulate the flow in the transition region is:

[0057] ;

[0058] Where, and is the transition source term, is the source of destruction, is the relaminarization source term.

[0059] like Figure 6 As shown, The lift coefficient and drag coefficient of the Eppler387 airfoil at low Reynolds numbers were calculated and compared with the wind tunnel test data. The results show that the fluid calculation module in the present invention has a small prediction error for the lift and drag coefficients of the low Reynolds number airfoil, and the results are reliable.

[0060] Build a proxy model based on the sample space data points, Figure 7 The different surrogate models show the drag coefficient C D and transition positions X tr Prediction accuracy. Select a surrogate model that meets high prediction accuracy and perform deterministic optimization. Build a new sampling space centered around the deterministic optimal solution. Sampling within the updated subspace expands the sample library. Repeat this process to update the adaptive surrogate model without random variables until convergence conditions are met, resulting in a deterministic optimal design.

[0061] The deterministic optimization model of the airfoil without considering the influence of skin deformation can be expressed as:

[0062] ;

[0063] Where, represents the airfoil design variables; represents the maximum relative thickness of the airfoil, It represents the maximum relative thickness constraint of the airfoil set to meet the internal loading requirements of the wing and the height requirements of the main beam structure; represents the airfoil lift coefficient, represents the airfoil design lift coefficient; It represents the range of values of the airfoil design variables and can be given according to the size of the deformation range.

[0064] The initial design space for robust optimization is constructed with the deterministic optimal solution as the center. Random variables are added to the original input parameters, and the adaptive agent model containing random variables is trained to perform robust optimization. The optimization goal is to output the response. Y The mean and standard deviation (e.g. the mean and standard deviation of the drag coefficient of the airfoil in the deformed state). There are two optimization objectives, so the optimal solution of this robust optimization problem is the Pareto front solution set, which is represented by a curve on the objective function plane. The points represent the optimal solution set of robustness, respectively. Construct a subspace with the point as the center, and take this The new sampling space can be obtained by taking the union of the subspaces. Sampling in the updated sample space and completing the expansion of the sample library, repeating the steps to complete the update of the adaptive agent model containing random variables until the convergence conditions are met, and the robust optimal design is obtained. Figure 8 As shown, as the number of iterations increases, the optimized Pareto frontier P k Will continue to approach the true Pareto frontier P actual When the convergence condition is met, the optimized Pareto frontier P final will converge to the true Pareto front P actual nearby, so the P final As the final robustness optimization design result.

[0065] The airfoil robustness optimization model considering the influence of skin deformation can be expressed as:

[0066] ;

[0067] Where, represents the airfoil design variables; represents the maximum relative thickness of the airfoil, It represents the maximum relative thickness constraint of the airfoil set to meet the internal loading requirements of the wing and the height requirements of the main beam structure; represents the airfoil lift coefficient, represents the airfoil design lift coefficient; It represents the range of values of the airfoil design variables and can be given according to the size of the deformation range; represents the mean drag coefficient of the airfoil in the deformed state, represents the standard deviation of the drag coefficient of the airfoil in the deformed state, is the deformation control parameter of the airfoil, is a random variable that follows a uniform distribution, and Respectively The upper and lower bounds of .

[0068] like Figure 9 As shown in the figure, in their respective worst-case deformation states, the pressure differential drag coefficient of the deterministic optimal airfoil Dopt is significantly greater than that of the initial airfoil Orig and the robust optimal airfoil Ropt. This directly causes its total drag coefficient to exceed that of the initial and robust optimal airfoils, resulting in a significant reduction in lift-to-drag ratio. Based on the robust optimization design method, the mean lift-to-drag ratio of the robust optimal airfoil in the random deformation space is 3.5% higher than that of the deterministic optimal airfoil and 16.8% higher than that of the initial airfoil. Furthermore, the lift-to-drag ratio of the robust optimal airfoil in the worst-case deformation state only decreases by 2.7% compared to the undeformed state, while that of the deterministic optimal airfoil decreases by 16.7%.

[0069] Therefore, the present invention adopts the above-mentioned airfoil robustness optimization design method considering the influence of flexible skin deformation, which can utilize the advantage of strong local control ability of non-uniform B-spline curves to perform local curve control on the basis of the CST curve of the non-deformed airfoil, so that the parameterized airfoil can reflect the regional deformation characteristics of the flexible skin; it can perform high-precision calculation of the airfoil aerodynamic force under low Reynolds number conditions, and perform high-precision prediction of the laminar separation, transition, and reattachment position unique to low Reynolds number flow; it can realize the airfoil design considering the influence of flexible skin uncertainty through multi-stage optimization, and can be applied to the robustness optimization design of airfoils under the influence of flexible skin in the low Reynolds number range, and the airfoil with the best robustness can still maintain better aerodynamic performance when the airfoil surface is not deformed / deformed, and has good aerodynamic robustness.

[0070] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A robust optimization design method for airfoil considering the influence of flexible skin deformation, characterized in that: The following steps are completed through the airfoil multi-level optimization module: Step S1: completing the deterministic optimization design of the airfoil without considering skin deformation by using an adaptive proxy model without random variables, and obtaining a deterministic optimal solution; Step S2: reconstructing the design space with the deterministic optimal solution of the airfoil as the center, and then completing the robust optimization design of the airfoil through the adaptive surrogate model containing random variables to obtain the robust optimal solution; In both step S1 and step S2, a fluid mechanics calculation module is used to calculate the aerodynamic characteristics of the primary sample points. The fluid mechanics calculation module includes the local transition Reynolds number. The equation and the intermittent factor The equation reflects the transition, separation and reattachment process of laminar flow at low Reynolds numbers; local transition Reynolds number Used to predict the transition starting position, the expression equation is: ； Where, is the local velocity in The direction component, It is used to force the transport of scalar and The local value of matches the source term, is a constant used to control the diffusion coefficient, is the molecular viscosity, is the eddy viscosity; Intermittent Factor The equation used to simulate the flow in the transition region is: ； Where, and is the transition source term, is the source of destruction, is a re-laminarization source term; in both step S1 and step S2, an airfoil parameterization module is used to obtain an airfoil profile, specifically comprising the following steps: Step S31, parameterizing the reference airfoil using the CST parameterization method; Step S32: Based on the regional deformation characteristics of the flexible skin wing in the wind tunnel test, a curve reflecting the local deformation of the wing surface is superimposed using a non-uniform B-spline curve method to obtain an airfoil profile that takes into account the influence of skin deformation.

2. The airfoil robustness optimization design method considering the influence of flexible skin deformation according to claim 1 is characterized in that: The specific steps of step S1 include: Step S11, constructing an initial proxy model: constructing an initial design space, generating initial sample points, and training the proxy model; Step S12, deterministic optimization model: selecting a proxy model that meets high prediction accuracy and performing deterministic optimization; Step S13, updating the adaptive agent model: constructing a new sampling space centered on the deterministic optimal solution, sampling in the updated subspace and expanding the sample library, thus completing the update of the adaptive agent model without random variables; Step S14: Repeat steps S12 and S13 until the convergence condition is met and a deterministic optimal design is obtained.

3. The airfoil robustness optimization design method considering the influence of flexible skin deformation according to claim 2 is characterized in that: The specific steps of step S2 include: Step S21, constructing an initial surrogate model: constructing an initial design space for robust optimization centered on the deterministic optimal solution, generating initial sample points, adding random variables to the original input parameters, and training an adaptive surrogate model containing random variables; Step S22, robustness optimization model: perform robustness optimization, the optimization target is the output response The mean and standard deviation ; Step S23, updating the adaptive surrogate model: constructing a new sampling subspace with the representative point on the Perato frontier as the center, sampling in the updated sample space and completing the expansion of the sample library, thus completing the update of the adaptive surrogate model containing random variables; Step S24: Repeat steps S22 and S23 until the convergence condition is met and the robust optimal design is obtained.

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