In this study, the wing design problem for different planforms for supersonic transport (SST) under supersonic and transonic cruise conditions is discussed to obtain knowledge of the supersonic air-foil from the viewp...In this study, the wing design problem for different planforms for supersonic transport (SST) under supersonic and transonic cruise conditions is discussed to obtain knowledge of the supersonic air-foil from the viewpoint of wing planform dependency. Two types of planforms were considered—a cranked arrow wing with a high sweep-back angle and a tapered wing with a low sweep- back angle. The optimum airfoils of these planforms were designed by efficient global optimization, which combined the evolutionary algorithm with the Kriging surrogate model. To acquire design knowledge, the functional analysis of variance was applied to the solution space and the design space. The design results show that the optimum airfoil and the contribution ratios of design variables for the airfoils of the two planform are different.展开更多
Recent advances in contrastive language-image pretraining(CLIP)models and generative AI have demonstrated significant capabilities in cross-modal understanding and content generation.Based on these developments,this s...Recent advances in contrastive language-image pretraining(CLIP)models and generative AI have demonstrated significant capabilities in cross-modal understanding and content generation.Based on these developments,this study introduces a novel framework for airfoil design via natural language interfaces.To the authors’knowledge,this study establishes the first end-to-end,bidirectional mapping between textual descriptions(e.g.,“low-drag supercritical wing for transonic conditions”)and parametric airfoil geometries represented by class-shape transformation parameters.The proposed approach integrates a CLIP-inspired architecture that aligns text embeddings with airfoil parameter spaces through contrastive learning,along with a semantically conditioned decoder that produces physically plausible airfoil geometries from latent representations.The experimental results validate the framework’s ability to generate aerodynamically plausible airfoils from natural language specifications and to classify airfoils accurately based on given textual labels.This research reduces the expertise threshold for preliminary airfoil design and highlights the potential for human-AI collaboration in aerospace engineering.展开更多
Under complex flight conditions,such as obstacle avoidance and extreme sea state,wing-in-ground(WIG)effect aircraft need to ascend to higher altitudes,resulting in the disappearance of the ground effect.A design of hi...Under complex flight conditions,such as obstacle avoidance and extreme sea state,wing-in-ground(WIG)effect aircraft need to ascend to higher altitudes,resulting in the disappearance of the ground effect.A design of high-speed WIG airfoil considering non-ground effect is carried out by a novel two-step inverse airfoil design method that combines conditional generative adversarial network(CGAN)and artificial neural network(ANN).The CGAN model is employed to generate a variety of airfoil designs that satisfy the desired lift-drag ratios in both ground effect and non-ground effect conditions.Subsequently,the ANN model is utilized to forecast aerodynamic parameters of the generated airfoils.The results indicate that the CGAN model contributes to a high accuracy rate for airfoil design and enables the creation of novel airfoil designs.Furthermore,it demonstrates high accuracy in predicting aerodynamic parameters of these airfoils due to the ANN model.This method eliminates the necessity for numerical simulations and experimental testing through the design procedure,showcasing notable efficiency.The analysis of airfoils generated by the CGAN model shows that airfoils exhibiting high lift-drag ratios under both flight conditions typically have cambers of among[0.08c,0.105c],with the positions of maximum camber occurring among[0.35c,0.5c]of the chord length,and the leading-edge radiuses of these airfoils primarily cluster among[0.008c,0.025c]展开更多
Well-designed airfoil is very important for high-performance rotor.This paper developed an efficient multi-objective and multi-constraint optimization design system for rotor airfoils based on RANS analysis,and verifi...Well-designed airfoil is very important for high-performance rotor.This paper developed an efficient multi-objective and multi-constraint optimization design system for rotor airfoils based on RANS analysis,and verified the performance of the optimized airfoil.Using CRA09-A as the baseline rotor airfoil,the CRA09-B optimized rotor airfoil was designed successfully.Combined with the foundation of high-precision rotor airfoil stationary test technology,the CRA09-B and CRA09-A rotor airfoils were tested in the S3 MA high-speed wind tunnel of ONERA.In order to correct the aerodynamic data,a single parameter linear wall pressure method is used to consider the tunnel effects.The results indicate that multi-objective and multi-constraint optimization design method developed in this study is reliable,and that CRA09-B optimized airfoil provides better stationary performance than CRA09-A airfoil in terms of maximum lift coefficient and lift-to-drag ratio.展开更多
This study proposes a process to obtain an optimal helicopter rotor blade shape for aerodynamic performance in hover flight. A new geometry representation algorithm which uses the class function/shape function transfo...This study proposes a process to obtain an optimal helicopter rotor blade shape for aerodynamic performance in hover flight. A new geometry representation algorithm which uses the class function/shape function transformation （CST） is employed to generate airfoil coordinates. With this approach, airfoil shape is considered in terms of design variables. The optimization process is constructed by integrating several programs developed by author. The design variables include twist, taper ratio, point of taper initiation, blade root chord, and coefficients of the airfoil distribution function. Aerodynamic constraints consist of limits on power available in hover and forward flight. The trim condition must be attainable. This paper considers rotor blade configuration for the hover flight condition only, so that the required power in hover is chosen as the objective function of the optimization problem. Sensitivity analysis of each design variable shows that airfoil shape has an important role in rotor performance. The optimum rotor blade reduces the required hover power by 7.4% and increases the figure of merit by 6.5%, which is a good improvement for rotor blade design.展开更多
A robust optimization design approach of natural laminar airfoils is developed in this paper. First, the non-uniform rational B-splines （NURBS） free form deformation method based on NURBS basis function is introduce...A robust optimization design approach of natural laminar airfoils is developed in this paper. First, the non-uniform rational B-splines （NURBS） free form deformation method based on NURBS basis function is introduced to the airfoil parameterization. Second, aerodynamic characteristics are evaluated by solving Navier-Stokes equations, and theγ-Reθt transition model coupling with shear-stress transport （SST） turbulent model is introduced to simulate boundary layer transition. A numerical simulation of transition flow around NLF0416 airfoil is conducted to test the code. The comparison between numerical simulation results and wind tunnel test data approves the validity and applicability of the present transition model. Third, the optimization system is set up, which uses the separated particle swarm optimization （SPSO） as search algorithm and combines the Kriging models as surrogate model during optimization. The system is applied to carry out robust design about the uncertainty of lift coefficient and Mach number for NASA NLF-0115 airfoil. The data of optimized airfoil aerodynamic characteristics indicates that the optimized airfoil can maintain laminar flow stably in an uncertain range and has a wider range of low drag.展开更多
Abstract A transonic, high Reynolds number natural laminar flow airfoil is designed and studied. The γ-θ transition model is combined with the shear stress transport （SST） k-w turbulence model to predict the trans...Abstract A transonic, high Reynolds number natural laminar flow airfoil is designed and studied. The γ-θ transition model is combined with the shear stress transport （SST） k-w turbulence model to predict the transition region for a laminar-turbulent boundary layer. The non-uniform free-form deformation （NFFD） method based on the non-uniform rational B-spline （NURBS） basis function is introduced to the airfoil parameterization. The non-dominated sorting genetic algorithm-II （NSGA-II） is used as the search algo- rithm, and the surrogate model based on the Kriging models is introduced to improve the efficiency of the optimization system. The optimization system is set up based on the above technologies, and the robust design about the uncertainty of the Mach number is carried out for NASA0412 airfoil. The optimized airfoil is analyzed and compared with the original airfoil. The results show that natural laminar flow can be achieved on a supercritical airfoil to improve the aerodynamic characteristic of airfoils.展开更多
A transonic airfoil designed by means of classical point-optimization may result in its dramatically inferior performance under off-design conditions. To overcome this shortcoming, robust design is proposed to find ou...A transonic airfoil designed by means of classical point-optimization may result in its dramatically inferior performance under off-design conditions. To overcome this shortcoming, robust design is proposed to find out the optimal profile of an airfoil to maintain its performance in an uncertain environment. The robust airfoil optimization is aimed to minimize mean values and variances of drag coefficients while satisfying the lift and thickness constraints over a range of Mach numbers. A multi-objective estimation of distribution algorithm is applied to the robust airfoil optimization on the base of the RAE2822 benchmark airfoil. The shape of the airfoil is obtained through superposing ten Hick-Henne shape functions upon the benchmark airfoil. A set of design points is selected according to a uniform design table for aerodynamic evaluation. A Kriging model of drag coefficient is constructed with those points to reduce computing costs. Over the Mach range from 0.7 to 0.8, the airfoil generated by the robust optimization has a configuration characterized by supercritical airfoil with low drag coefficients. The small fluctuation in its drag coefficients means that the performance of the robust airfoil is insensitive to variation of Mach number.展开更多
Trailing-edge flap is traditionally used to improve the takeoff and landing aerodynamic performance of aircraft.In order to improve flight efficiency during takeoff,cruise and landing states,the flexible variable camb...Trailing-edge flap is traditionally used to improve the takeoff and landing aerodynamic performance of aircraft.In order to improve flight efficiency during takeoff,cruise and landing states,the flexible variable camber trailing-edge flap is introduced,capable of changing its shape smoothly from 50% flap chord to the rear of the flap.Using a numerical simulation method for the case of the GA（W）-2 airfoil,the multi-objective optimization of the overlap,gap,deflection angle,and bending angle of the flap under takeoff and landing configurations is studied.The optimization results show that under takeoff configuration,the variable camber trailing-edge flap can increase lift coefficient by about 8% and lift-to-drag ratio by about 7% compared with the traditional flap at a takeoff angle of 8°.Under landing configuration,the flap can improve the lift coefficient at a stall angle of attack about 1.3%.Under cruise state,the flap helps to improve the lift-todrag ratio over a wide range of lift coefficients,and the maximum increment is about 30%.Finally,a corrugated structure–eccentric beam combination bending mechanism is introduced in this paper to bend the flap by rotating the eccentric beam.展开更多
Advanced engineering systems, like aircraft, are defined by tens or even hundreds of design variables. Building an accurate surrogate model for use in such high-dimensional optimization problems is a difficult task ow...Advanced engineering systems, like aircraft, are defined by tens or even hundreds of design variables. Building an accurate surrogate model for use in such high-dimensional optimization problems is a difficult task owing to the curse of dimensionality. This paper presents a new algorithm to reduce the size of a design space to a smaller region of interest allowing a more accurate surrogate model to be generated. The framework requires a set of models of different physical or numerical fidelities. The low-fidelity （LF） model provides physics-based approximation of the high-fidelity （HF） model at a fraction of the computational cost. It is also instrumental in identifying the small region of interest in the design space that encloses the high-fidelity optimum. A surrogate model is then constructed to match the low-fidelity model to the high-fidelity model in the identified region of interest. The optimization process is managed by an update strategy to prevent convergence to false optima. The algorithm is applied on mathematical problems and a two-dimen-sional aerodynamic shape optimization problem in a variable-fidelity context. Results obtained are in excellent agreement with high-fidelity results, even with lower-fidelity flow solvers, while showing up to 39% time savings.展开更多
Simulations have been done to assess the lift, thrust and propulsive efficiency of different types of non-symmetrical airfoils under different flapping configurations. The variables involved are reduced frequency, Str...Simulations have been done to assess the lift, thrust and propulsive efficiency of different types of non-symmetrical airfoils under different flapping configurations. The variables involved are reduced frequency, Strouhal number, pitch amplitude and phase angle. In order to analyze the variables more efficiently, the design of experiments using the response surface methodology is applied. Results show that both the variables and shape of the airfoil have a profound effect on the lift, thrust, and efficiency. By using non- symmetrical airfoils, average lift coefficient as high as 2.23 can be obtained. The average thrust coefficient and efficiency also reach high values of 2.53 and 0.61, respectively. The lift production is highly dependent on the airfoil＇s shape while thrust production is influenced more heavily by the variables. Efficiency falls somewhere in between. Two-factor interac- tions are found to exist among the variables. This shows that it is not sufficient to analyze each variable individually. Vorticity diagrams are analyzed to explain the results obtained. Overall, the S1020 airfoil is able to provide relatively good efficiency and at the same time generate high thrust and lift force. These results aid in the design of a better ornithopter＇s wing.展开更多
Aerodynamic noise is the main problem restricting its development nowadays in green energy,ocean engineering and aerospace engineering.In order to limit the aerodynamic noise of an airfoil structure,a method is propos...Aerodynamic noise is the main problem restricting its development nowadays in green energy,ocean engineering and aerospace engineering.In order to limit the aerodynamic noise of an airfoil structure,a method is proposed in this paper by designing low noise airfoils.This method optimized the aerodynamic noise of two-dimensional airfoil,and considered the aerodynamic performance of the airfoil at the same time.Based on Joukowski conformal transformation,airfoil geometry is parameterized firstly.Then,the optimization model taking the lift-to-drag ratio and airfoil self-noise as the design objective,is established to modify the airfoil by active set algorithm until the airfoil can satisfy the design condition.Finally,the noise of the optimized airfoil is verified according to the prediction theory of airfoil noise.Moreover,the relationship between airfoil geometry and noise is analyzed.The results show that the lift-to-drag ratio of the optimized airfoil increased,and the noise also decreased.Thus,the optimization method can be used to address special design of low-noise airfoil.Besides,the optimization method in this paper can provide reference for improving lift-to-drag ratio and reducing noise of the airfoil in aircraft and submarine rudder system.展开更多
文摘In this study, the wing design problem for different planforms for supersonic transport (SST) under supersonic and transonic cruise conditions is discussed to obtain knowledge of the supersonic air-foil from the viewpoint of wing planform dependency. Two types of planforms were considered—a cranked arrow wing with a high sweep-back angle and a tapered wing with a low sweep- back angle. The optimum airfoils of these planforms were designed by efficient global optimization, which combined the evolutionary algorithm with the Kriging surrogate model. To acquire design knowledge, the functional analysis of variance was applied to the solution space and the design space. The design results show that the optimum airfoil and the contribution ratios of design variables for the airfoils of the two planform are different.
基金supported by the National Natural Science Foundation of China(Grant Nos.U23A2069,12372288,12388101,and 92152301)Jilin Province Science and Technology Development Program,China(Grant No.20220301013GX)Aeronautical Science Foundation of China(Grant No.2020Z006058002)。
文摘Recent advances in contrastive language-image pretraining(CLIP)models and generative AI have demonstrated significant capabilities in cross-modal understanding and content generation.Based on these developments,this study introduces a novel framework for airfoil design via natural language interfaces.To the authors’knowledge,this study establishes the first end-to-end,bidirectional mapping between textual descriptions(e.g.,“low-drag supercritical wing for transonic conditions”)and parametric airfoil geometries represented by class-shape transformation parameters.The proposed approach integrates a CLIP-inspired architecture that aligns text embeddings with airfoil parameter spaces through contrastive learning,along with a semantically conditioned decoder that produces physically plausible airfoil geometries from latent representations.The experimental results validate the framework’s ability to generate aerodynamically plausible airfoils from natural language specifications and to classify airfoils accurately based on given textual labels.This research reduces the expertise threshold for preliminary airfoil design and highlights the potential for human-AI collaboration in aerospace engineering.
基金supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions,the Fundamental Research Funds for the Central Universities(No.ILA220101A23)CARDC Fundamental and Frontier Technology Research Fund(No.PJD20200210)the Aeronautical Science Foundation of China(No.20200023052002).
文摘Under complex flight conditions,such as obstacle avoidance and extreme sea state,wing-in-ground(WIG)effect aircraft need to ascend to higher altitudes,resulting in the disappearance of the ground effect.A design of high-speed WIG airfoil considering non-ground effect is carried out by a novel two-step inverse airfoil design method that combines conditional generative adversarial network(CGAN)and artificial neural network(ANN).The CGAN model is employed to generate a variety of airfoil designs that satisfy the desired lift-drag ratios in both ground effect and non-ground effect conditions.Subsequently,the ANN model is utilized to forecast aerodynamic parameters of the generated airfoils.The results indicate that the CGAN model contributes to a high accuracy rate for airfoil design and enables the creation of novel airfoil designs.Furthermore,it demonstrates high accuracy in predicting aerodynamic parameters of these airfoils due to the ANN model.This method eliminates the necessity for numerical simulations and experimental testing through the design procedure,showcasing notable efficiency.The analysis of airfoils generated by the CGAN model shows that airfoils exhibiting high lift-drag ratios under both flight conditions typically have cambers of among[0.08c,0.105c],with the positions of maximum camber occurring among[0.35c,0.5c]of the chord length,and the leading-edge radiuses of these airfoils primarily cluster among[0.008c,0.025c]
基金supported by the National Natural Science Foundation of China(No.11902335)。
文摘Well-designed airfoil is very important for high-performance rotor.This paper developed an efficient multi-objective and multi-constraint optimization design system for rotor airfoils based on RANS analysis,and verified the performance of the optimized airfoil.Using CRA09-A as the baseline rotor airfoil,the CRA09-B optimized rotor airfoil was designed successfully.Combined with the foundation of high-precision rotor airfoil stationary test technology,the CRA09-B and CRA09-A rotor airfoils were tested in the S3 MA high-speed wind tunnel of ONERA.In order to correct the aerodynamic data,a single parameter linear wall pressure method is used to consider the tunnel effects.The results indicate that multi-objective and multi-constraint optimization design method developed in this study is reliable,and that CRA09-B optimized airfoil provides better stationary performance than CRA09-A airfoil in terms of maximum lift coefficient and lift-to-drag ratio.
基金co-supported by National Foundation for Science and Technology Development(NAFOSTED) of Vietnam (Project No. 107.04-2012.25)the Agency for Defense Development in the Republic of Korea under contract UD100048JDthe project KARI-University Partnership Program 2009-09-2
文摘This study proposes a process to obtain an optimal helicopter rotor blade shape for aerodynamic performance in hover flight. A new geometry representation algorithm which uses the class function/shape function transformation （CST） is employed to generate airfoil coordinates. With this approach, airfoil shape is considered in terms of design variables. The optimization process is constructed by integrating several programs developed by author. The design variables include twist, taper ratio, point of taper initiation, blade root chord, and coefficients of the airfoil distribution function. Aerodynamic constraints consist of limits on power available in hover and forward flight. The trim condition must be attainable. This paper considers rotor blade configuration for the hover flight condition only, so that the required power in hover is chosen as the objective function of the optimization problem. Sensitivity analysis of each design variable shows that airfoil shape has an important role in rotor performance. The optimum rotor blade reduces the required hover power by 7.4% and increases the figure of merit by 6.5%, which is a good improvement for rotor blade design.
文摘A robust optimization design approach of natural laminar airfoils is developed in this paper. First, the non-uniform rational B-splines （NURBS） free form deformation method based on NURBS basis function is introduced to the airfoil parameterization. Second, aerodynamic characteristics are evaluated by solving Navier-Stokes equations, and theγ-Reθt transition model coupling with shear-stress transport （SST） turbulent model is introduced to simulate boundary layer transition. A numerical simulation of transition flow around NLF0416 airfoil is conducted to test the code. The comparison between numerical simulation results and wind tunnel test data approves the validity and applicability of the present transition model. Third, the optimization system is set up, which uses the separated particle swarm optimization （SPSO） as search algorithm and combines the Kriging models as surrogate model during optimization. The system is applied to carry out robust design about the uncertainty of lift coefficient and Mach number for NASA NLF-0115 airfoil. The data of optimized airfoil aerodynamic characteristics indicates that the optimized airfoil can maintain laminar flow stably in an uncertain range and has a wider range of low drag.
文摘Abstract A transonic, high Reynolds number natural laminar flow airfoil is designed and studied. The γ-θ transition model is combined with the shear stress transport （SST） k-w turbulence model to predict the transition region for a laminar-turbulent boundary layer. The non-uniform free-form deformation （NFFD） method based on the non-uniform rational B-spline （NURBS） basis function is introduced to the airfoil parameterization. The non-dominated sorting genetic algorithm-II （NSGA-II） is used as the search algo- rithm, and the surrogate model based on the Kriging models is introduced to improve the efficiency of the optimization system. The optimization system is set up based on the above technologies, and the robust design about the uncertainty of the Mach number is carried out for NASA0412 airfoil. The optimized airfoil is analyzed and compared with the original airfoil. The results show that natural laminar flow can be achieved on a supercritical airfoil to improve the aerodynamic characteristic of airfoils.
基金National Natural Science Foundation of China (10377015)
文摘A transonic airfoil designed by means of classical point-optimization may result in its dramatically inferior performance under off-design conditions. To overcome this shortcoming, robust design is proposed to find out the optimal profile of an airfoil to maintain its performance in an uncertain environment. The robust airfoil optimization is aimed to minimize mean values and variances of drag coefficients while satisfying the lift and thickness constraints over a range of Mach numbers. A multi-objective estimation of distribution algorithm is applied to the robust airfoil optimization on the base of the RAE2822 benchmark airfoil. The shape of the airfoil is obtained through superposing ten Hick-Henne shape functions upon the benchmark airfoil. A set of design points is selected according to a uniform design table for aerodynamic evaluation. A Kriging model of drag coefficient is constructed with those points to reduce computing costs. Over the Mach range from 0.7 to 0.8, the airfoil generated by the robust optimization has a configuration characterized by supercritical airfoil with low drag coefficients. The small fluctuation in its drag coefficients means that the performance of the robust airfoil is insensitive to variation of Mach number.
文摘Trailing-edge flap is traditionally used to improve the takeoff and landing aerodynamic performance of aircraft.In order to improve flight efficiency during takeoff,cruise and landing states,the flexible variable camber trailing-edge flap is introduced,capable of changing its shape smoothly from 50% flap chord to the rear of the flap.Using a numerical simulation method for the case of the GA（W）-2 airfoil,the multi-objective optimization of the overlap,gap,deflection angle,and bending angle of the flap under takeoff and landing configurations is studied.The optimization results show that under takeoff configuration,the variable camber trailing-edge flap can increase lift coefficient by about 8% and lift-to-drag ratio by about 7% compared with the traditional flap at a takeoff angle of 8°.Under landing configuration,the flap can improve the lift coefficient at a stall angle of attack about 1.3%.Under cruise state,the flap helps to improve the lift-todrag ratio over a wide range of lift coefficients,and the maximum increment is about 30%.Finally,a corrugated structure–eccentric beam combination bending mechanism is introduced in this paper to bend the flap by rotating the eccentric beam.
文摘Advanced engineering systems, like aircraft, are defined by tens or even hundreds of design variables. Building an accurate surrogate model for use in such high-dimensional optimization problems is a difficult task owing to the curse of dimensionality. This paper presents a new algorithm to reduce the size of a design space to a smaller region of interest allowing a more accurate surrogate model to be generated. The framework requires a set of models of different physical or numerical fidelities. The low-fidelity （LF） model provides physics-based approximation of the high-fidelity （HF） model at a fraction of the computational cost. It is also instrumental in identifying the small region of interest in the design space that encloses the high-fidelity optimum. A surrogate model is then constructed to match the low-fidelity model to the high-fidelity model in the identified region of interest. The optimization process is managed by an update strategy to prevent convergence to false optima. The algorithm is applied on mathematical problems and a two-dimen-sional aerodynamic shape optimization problem in a variable-fidelity context. Results obtained are in excellent agreement with high-fidelity results, even with lower-fidelity flow solvers, while showing up to 39% time savings.
文摘Simulations have been done to assess the lift, thrust and propulsive efficiency of different types of non-symmetrical airfoils under different flapping configurations. The variables involved are reduced frequency, Strouhal number, pitch amplitude and phase angle. In order to analyze the variables more efficiently, the design of experiments using the response surface methodology is applied. Results show that both the variables and shape of the airfoil have a profound effect on the lift, thrust, and efficiency. By using non- symmetrical airfoils, average lift coefficient as high as 2.23 can be obtained. The average thrust coefficient and efficiency also reach high values of 2.53 and 0.61, respectively. The lift production is highly dependent on the airfoil＇s shape while thrust production is influenced more heavily by the variables. Efficiency falls somewhere in between. Two-factor interac- tions are found to exist among the variables. This shows that it is not sufficient to analyze each variable individually. Vorticity diagrams are analyzed to explain the results obtained. Overall, the S1020 airfoil is able to provide relatively good efficiency and at the same time generate high thrust and lift force. These results aid in the design of a better ornithopter＇s wing.
基金Supported by the Natural Science Foundation of Jiangsu Province(BK20190871)the National Natural Science Foundation of China(11672261)。
文摘Aerodynamic noise is the main problem restricting its development nowadays in green energy,ocean engineering and aerospace engineering.In order to limit the aerodynamic noise of an airfoil structure,a method is proposed in this paper by designing low noise airfoils.This method optimized the aerodynamic noise of two-dimensional airfoil,and considered the aerodynamic performance of the airfoil at the same time.Based on Joukowski conformal transformation,airfoil geometry is parameterized firstly.Then,the optimization model taking the lift-to-drag ratio and airfoil self-noise as the design objective,is established to modify the airfoil by active set algorithm until the airfoil can satisfy the design condition.Finally,the noise of the optimized airfoil is verified according to the prediction theory of airfoil noise.Moreover,the relationship between airfoil geometry and noise is analyzed.The results show that the lift-to-drag ratio of the optimized airfoil increased,and the noise also decreased.Thus,the optimization method can be used to address special design of low-noise airfoil.Besides,the optimization method in this paper can provide reference for improving lift-to-drag ratio and reducing noise of the airfoil in aircraft and submarine rudder system.
