Robust design of natural laminar flow supercritical airfoil by multi-objective evolution method

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.

Low-Speed Aerodynamic Characteristics of Supercritical Airfoil with Small High-Lift Devices from Flow Pattern Measurements

In this paper, the lift coefficients of SC-0414 airfoil are estimated by applying modified Yamana’s method to the flow visualization results, which are obtained by utilizing the smoke tunnel. The application of the modified Yamana’s method is evaluated with two calculation methods. Additionally, the lift estimation, wake measurements, and numerical simulations are performed to clarify the low-speed aerodynamic characteristics of the SC airfoil with flaps. The angle of attack was varied from −5° to 8°. The flow velocity was 12 m/s and the Reynolds number was 1.6 × 105. As a result, the estimated lift coefficients show a good agreement with the results from reference data and numerical simulations. In clean condition, the lift coefficients calculated from the two methods show quantitative agreement, and no significant difference could be confirmed. However, the slope of the lifts calculated from ys is higher and closer to the reference data than those obtained from sc, where ys denotes the height where the distance from the streamline to the reference line is the largest, and sc denotes the displacement of the center of pressure from the origin of the coordinate, respectively. In the case of flaps, the GFs have an observable effect on the aerodynamic performance of the SC-0414 airfoil. When the height of the flap was increased, the lift and drag coefficients increased. The installation of a GF with a height equal to 1% of the chord length of the airfoil significantly improved the low-speed aerodynamic performance of SC airfoils.

Transfer learning from two-dimensional supercritical airfoils to three-dimensional transonic swept wings

Machine learning has been widely utilized in flow field modeling and aerodynamic optimization.However,most applications are limited to two-dimensional problems.The dimensionality and the cost per simulation of three-dimensional problems are so high that it is often too expensive to prepare sufficient samples.Therefore,transfer learning has become a promising approach to reuse well-trained two-dimensional models and greatly reduce the need for samples for threedimensional problems.This paper proposes to reuse the baseline models trained on supercritical airfoils to predict finite-span swept supercritical wings,where the simple swept theory is embedded to improve the prediction accuracy.Two baseline models are investigated:one is commonly referred to as the forward problem of predicting the pressure coefficient distribution based on the geometry,and the other is the inverse problem that predicts the geometry based on the pressure coefficient distribution.Two transfer learning strategies are compared for both baseline models.The transferred models are then tested on complete wings.The results show that transfer learning requires only approximately 500 wing samples to achieve good prediction accuracy on different wing planforms and different free stream conditions.Compared to the two baseline models,the transferred models reduce the prediction error by 60%and 80%,respectively.

Simulation of shock wave buffet and its suppression on an OAT15A supercritical airfoil by IDDES

In the present paper,extremely unsteady shock wave buffet induced by strong shock wave/boundary-layer interactions (SWBLI) on the upper surface of an OAT15A supercritical airfoil at Mach number of 0.73 and angle of attack of 3.5 degrees is first numerically simulated by IDDES,one of the most advanced RANS/LES hybrid methods.The results imply that conventional URANS methods are unable to effectively predict the buffet phenomenon on the wing surface;IDDES,which involves more flow physics,predicted buffet phenomenon.Some complex flow phenomena are predicted and demonstrated,such as periodical oscillations of shock wave in the streamwise direction,strong shear layer detached from the shock wave due to SWBLI and plenty of small scale structures broken down by the shear layer instability and in the wake.The root mean square (RMS) of fluctuating pressure coefficients and streamwise range of shock wave oscillation reasonably agree with experimental data.Then,two vortex generators (VG) both with an inclination angle of 30 degrees to the main flow directions are mounted in front of the shock wave region on the upper surface to suppress shock wave buffet.The results show that shock wave buffet can be significantly suppressed by VGs,the RMS level of pressure in the buffet region is effectively reduced,and averaged shock wave position is obviously pushed downstream,resulting in increased total lift.

An inverse design method for supercritical airfoil based on conditional generative models

Inverse design has long been an efficient and powerful design tool in the aircraft industry.In this paper,a novel inverse design method for supercritical airfoils is proposed based on generative models in deep learning.A Conditional Variational Auto Encoder(CVAE)and an integrated generative network CVAE-GAN that combines the CVAE with the Wasserstein Generative Adversarial Networks(WGAN),are conducted as generative models.They are used to generate target wall Mach distributions for the inverse design that matches specified features,such as locations of suction peak,shock and aft loading.Qualitative and quantitative results show that both adopted generative models can generate diverse and realistic wall Mach number distributions satisfying the given features.The CVAE-GAN model outperforms the CVAE model and achieves better reconstruction accuracies for all the samples in the dataset.Furthermore,a deep neural network for nonlinear mapping is adopted to obtain the airfoil shape corresponding to the target wall Mach number distribution.The performances of the designed deep neural network are fully demonstrated and a smoothness measurement is proposed to quantify small oscillations in the airfoil surface,proving the authenticity and accuracy of the generated airfoil shapes.

Numerical study of a supercritical airfoil/wing with variable-camber technology

Variable-camber technology is considered an effective way to adaptively improve the aerodynamic performance of aircraft under various flight conditions.This paper studies the aerodynamic characteristics of the trailing-edge variable-camber technology by means of Computational Fluid Dynamics(CFD)and a drag decomposition method.Trailing-edge variable-camber technology can be simply realized by the continuous deflection of the flaps and ailerons of a wing.A supercritical airfoil is used to study the two-dimensional effect of variable-camber technology,and a wide-body airplane model is used to validate the three-dimensional improvement in the wing’s airfoil made by variable-camber technology.An optimization strategy for airfoil that incorporates variable-camber technology is proposed.The optimization results demonstrate that the proposed method can obtain better results than the traditional segregated shape optimization.

Shock control bump parametric research on supercritical airfoil

High precision of CFD code was used to study supercritical Airfoil RAE2822 superimposed with different shock control bumps under the transonic conditions.A successful improvement was made to current widely used Hicks-Henne functions which describe shock control bumps.Based on improving the airfoil's lift-drag ratio,the study shows that,(1) the best bump crest position is at the position close to 50% of bump chord,which is almost independent of free stream or pre-shock Mach numbers,but the bump height is highly coupled with the crest position,which means that the higher the bump is,the more obviously the crest position affects the airfoil lift-drag ratio,and it becomes more evident with the increase of free stream or pre-shock Mach numbers;(2) in case that the lift-drag ratio of airfoil with bump is higher than basic airfoil,almost all the optimum distances between bump crest and shock wave are close to 30% of bump chord;(3) almost all the lift-drag ratios of airfoil with bump increase as bump chord length increases,of which this trend becomes more evident as bump height increases;(4) with the increase of the bump height,almost all the lift-drag ratios of airfoil with bump decrease at low free stream or pre-shock Mach numbers.When the Mach numbers are higher,the lift-drag ratio of airfoil increases as the increase of the bump height,and particularly,the trend tends to be visible when the Mach numbers are at a high level.

Pressure distribution feature-oriented sampling for statistical analysis of supercritical airfoil aerodynamics

In the field of supercritical wing design, various principles and rules have been summarized through theoretical and experimental analyses. Compared with black-box relationships between geometry parameters and performances, quantitative physical laws about pressure distributions and performances are clearer and more beneficial to designers. With the advancement of computational fluid dynamics and computational intelligence, discovering new rules through statistical analysis on computers has become increasingly attractive and affordable. This paper proposes a novel sampling method for the statistical study on pressure distribution features and performances, so that new physical laws can be revealed. It utilizes an adaptive sampling algorithm, of which the criteria are developed based on Kullback–Leibler divergence and Euclidean distance.In this paper, the proposed method is employed to generate airfoil samples to study the relationships between the supercritical pressure distribution features and the drag divergence Mach number as well as the drag creep characteristic. Compared with conventional sampling methods, the proposed method can efficiently distribute samples in the pressure distribution feature space rather than directly sampling airfoil geometry parameters. The corresponding geometry parameters are searched and found under constraints, so that supercritical airfoil samples that are well distributed in the pressure distribution space are obtained. These samples allow statistical studies to obtain more reliable and universal aerodynamic rules that can be applied to supercritical airfoil designs.

Oscillation quenching and physical explanation on freeplay-based aeroelastic airfoil in transonic viscous flow

Limit Cycle Oscillation(LCO)quenching of a supercritical airfoil(NLR 7301)considering freeplay is investigated in transonic viscous flow.Computational Fluid Dynamics(CFD)based on Navier-Stokes equations is implemented to calculate transonic aerodynamic forces.A loosely coupled scheme with steady CFD and an efficient graphic method are developed to obtain the aerodynamic preload.LCO quenching phenomenon is observed from the nonlinear dynamic aeroelastic response obtained by using time marching approach.As the airspeed increases,LCO appears then quenches,forming the first LCO branch.Following the quenching region,LCO occurs again and sustains until the divergence of the response,forming the second LCO branch.The quenching of LCOs was addressed physically based on the aerodynamic preload and the linear flutter characteristic.An“island”of stable region is observed in the flutter boundary,i.e.the flutter speed versus the mean Angle of Attack(AoA).The LCO quenches when the aerodynamic preload crosses this stable region with the increasing of airspeed.The LCO quenching of this model in transonic flow is essentially induced by destabilizing effect from aerodynamic preload,since the flutter speed is sensitive to AoA due to aerodynamic nonlinearity.

A generative deep learning framework for airfoil flow field prediction with sparse data

Deep learning has been probed for the airfoil performance prediction in recent years.Compared with the expensive CFD simulations and wind tunnel experiments,deep learning models can be leveraged to somewhat mitigate such expenses with proper means.Nevertheless,effective training of the data-driven models in deep learning severely hinges on the data in diversity and quantity.In this paper,we present a novel data augmented Generative Adversarial Network(GAN),daGAN,for rapid and accurate flow filed prediction,allowing the adaption to the task with sparse data.The presented approach consists of two modules,pre-training module and fine-tuning module.The pre-training module utilizes a conditional GAN(cGAN)to preliminarily estimate the distribution of the training data.In the fine-tuning module,we propose a novel adversarial architecture with two generators one of which fulfils a promising data augmentation operation,so that the complement data is adequately incorporated to boost the generalization of the model.We use numerical simulation data to verify the generalization of daGAN on airfoils and flow conditions with sparse training data.The results show that daGAN is a promising tool for rapid and accurate evaluation of detailed flow field without the requirement for big training data.