Supercritical Airfoil Research Articles

Investigation of Three-Dimensional Shock Control Bumps for Transonic Buffet Alleviation

This experimental study investigates the use of shock control bumps (SCBs) for controlling transonic buffet. Three-dimensional SCBs have been applied on the suction side of an OAT15A supercritical airfoil with the experiments conducted in the transonic–supersonic wind tunnel of Delft University of Technology at fully developed buffet conditions (, and ). The effectiveness of the SCBs for different spanwise array spacings (ranging from 20 to ) was verified using two optical techniques: schlieren visualization and particle image velocimetry. Both techniques confirmed the potential of controlling buffet using such devices, resulting in a reduction of the flow unsteadiness in terms of both shock oscillation and pulsation of the separated area. A dedicated particle image velocimetry investigation in a spanwise–chordwise measurement plane was conducted in order to characterize the effect of the spatial distribution of the bumps, focusing on the interaction of the shock-wave structures along the span. The configuration with a spacing of was demonstrated to be the most efficient in reducing the transonic buffet oscillations and was able to reduce the reverse flow region size as compared to the clean configuration.

Multifidelity Prediction Framework with Convolutional Neural Networks Using High-Dimensional Data

This paper proposes two novel multifidelity neural network architectures developed for high-dimensional inputs such as computational flowfields. We employed a two-dimensional flow-varying transonic supercritical airfoil problem while exploring and comparing our methods with the former “multifidelity deep neural networks” from the literature. We call these novel methods “modified multifidelity deep neural networks” and “multifidelity convolutional neural networks.” The main objective of this study is to establish an advanced multifidelity prediction framework that can be applied to any computational data; however, here, we applied our methods to the prediction of aerodynamic coefficients using pressure coefficient fields around the airfoil. To generate the dataset, first, a coarse grid is employed using the SU2 Euler solver for low-fidelity data; then, a relatively finer grid is used to obtain the viscous solutions by using the Spalart–Allmaras turbulence model for the high-fidelity data. The performance metrics to compare the methods are determined as the test accuracy, the physical training time, and the size of the high-fidelity samples. The results demonstrate that the proposed multifidelity neural network architectures outperform the multifidelity deep neural networks in predictive modeling using high-dimensional inputs by improving the multifidelity prediction accuracy significantly.

Characterization of transonic shock oscillations over the span of an OAT15A profile

The flow over a wing model with aspect ratio 2 and based on the supercritical airfoil (OAT15A) was experimentally investigated for a fixed Reynolds number (Re_textrm{c}) of 3times 10^{6} and numerous aerodynamic conditions. The angle of attack (AOA) and the Mach number (M_mathrm {infty }) were varied between 5^{circ } and 6.5^{circ }, and between 0.72 and 0.75, respectively. Here we focused on the dynamics of the shock front at incipient and developed buffet conditions, by employing background-oriented schlieren measurements on the wing’s upper surface. The spanwise variations of the shock front statistics and its frequency content were examined. The shock oscillations appeared to be the superposition of multiple fluid modes, of which the most dominant was the classic 2-D buffet, which induced uniform chordwise oscillations of the shock front. The hypothesis was formulated that the remaining modes are linked to physical phenomena reported in the literature, namely the side-wall boundary layer and the vortices detected in the mid-span separated flow.

The effects of geometry parameters on the aerodynamic performance of CFJ airfoil used by a STOL transport

With the purpose of investigating the effects of geometry parameters of CFJ (Coflow jet) device on the aerodynamic characteristics of the supercritical bacj airfoil used by a STOL transport, we have carried out a computational analysis of CFJ airfoil with different values of injection slot size and location under the low-speed condition. The results show that the lift coefficient decreases gradually with decreasing stall angle, when the injection slot size is increased. When α=8°, with increasing injection slot size, the velocity of blowing jet decreases with decreasing power consumption and increasing aerodynamic effectiveness. Further, with the injection slot shifted towards the downstream direction, the α value corresponding to the maximum effective lift-drag-ratio increases with increasing maximum lift coefficient.

Aerodynamic Load Reduction on a Supercritical Airfoil Using Tilted Microjets

Microjets arranged on the wing surfaces of civil transport aircraft have been shown to have great potential in suppressing high-frequency gust loads. This paper presents a study of aerodynamic load reduction on a supercritical airfoil using tilted microjets by solving the Reynolds-averaged Navier-Stokes (RANS) equations. The numerical method was first validated against the experimental and previous numerical data. Afterward, the subsonic and transonic flowfields around the supercritical airfoil were simulated with various angled microjets. The results show that both the lift reduction and the power efficiencies significantly increase as the blowing direction shifts downstream to upstream. The movement and weakening of the shock due to the jet are observed at α > 2 ∘ in transonic flow, resulting in a drag reduction compared to the baseline airfoil. However, the transient subsonic results revealed that the upstream jet induces a strong vortex shedding, which is suppressed in transonic flows. During jet deployment, there are three distinct phases: time lag, vortex rolling-up, and rebalancing, in that order. Once it reaches the trailing edge in subsonic flows, the starting vortex rapidly modifies the load and induced a strong roll-up vortex from the pressure surface. Nevertheless, in transonic flow, the rebalancing stage contributes to a greater reduction in lift due to the additional shock movement and weakening effect.

Influence of geometric parameters of leading edge horn-ice on stall characteristics of airfoil

The irregular characteristics and geometric randomness of horn-type ice are significant while the behaviors of separation are complex. The mechanism and factor leading to the essential change of stall performance are still not clear. According to actual requirements of airworthiness certification of a large passenger aircraft, a family of horn-type ice shapes with different parameters are constructed based on typical supercritical airfoil and icing environment. By combining with wind tunnel test and numerical simulation methods, the parameter sensitivity of airfoil stall characteristics to the change of ice height and angle is systematically analyzed and the essential influence mechanism of the ice shape parameters leading to the change of separation bubble development under stall process is summarized, which provides a theoretical basis for ice airworthiness certification of large passenger aircraft.

Lift Airfoils Close to the Airfoils in a Flow with the Maximum “Critical” Mach Numbers

The lift airfoils close to the airfoils optimal with respect to the critical Mach numbers М* of two-dimensional bodies optimal with respect to М* are constructed using the direct method. Their almost zero wave drag coefficients сх remain the same not only at the free-stream Mach numbers М0 which are lower than М* but also at М0 perceptibly higher than М*. These new lift airfoils differ from the supercritical lift airfoils whose сх grow extremely rapidly when М0 becomes higher than the designed values. At identical thicknesses and М0 = М* the supercritical lift airfoils implement the greater lift coefficients су. However, due to the difference in the behavior of сх at М0 which are higher than the designed ones, the lift-drag ratio of the supercritical airfoils can become lower for the ratio of су not to сх, but even to the coefficient of total drag.

Knowledge discovery with computational fluid dynamics: Supercritical airfoil database and drag divergence prediction

Aerodynamic rules and knowledge are often obtained through theoretical research and experiments, which have contributed greatly to aircraft design. For example, Korn's equation predicts the airfoil drag divergence Mach number using the airfoil maximum thickness and the lift coefficient. It is very helpful in the aircraft initial design. However, it neither reveals the key factors of fluid features on the drag divergence nor contributes to the detailed design. This paper designs a supercritical airfoil database that covers the typical free stream Mach number, angle of attack, lift coefficient, and geometry of modern transonic commercial aircraft. Correlation screening and multivariate regression are carried out to discover knowledge about the airfoil drag divergence Mach number and pressure distribution features. A new linear correlation is discovered and validated by existed airfoil databases. Compared with Korn's equation, the discovered correlation reduces the maximum prediction error by approximately 40%. It indicates that the drag divergence Mach number can be increased by obtaining a shock wave that is further upstream in the detailed design. Furthermore, it enables the cruise performance and drag divergence Mach number to be predicted with only one simulation of the cruise point, which will greatly save the computational cost of optimizations.

Temporal predictions of periodic flows using a mesh transformation and deep learning-based strategy

This paper focuses on the temporal prediction of unsteady flow based on a combination of mesh transformation and deep learning technology. To this end, a body-fitted mesh interpolation was first implemented to extract the flow information in the region of interest and maintain the detailed flow information in the boundary layer. Subsequently, a mesh transformation technique was applied to map the physical coordinates into the curvilinear coordinates to obtain a structural uniform mesh, which is facilitated for the implementation the structural neural networks. Ultimately, two advanced neural networks, i.e., Unet and Fourier Neural Operator (FNO), were used for establishing the relationship between flow at previous time steps and that at future time steps. Two flow configurations numerically simulated—i.e., a laminar flow around a cylinder at Re=200 and a transonic buffet of a supercritical airfoil at Ma=0.73—were selected as the benchmarks to demonstrate the effectiveness and robustness of the proposed strategy. The results indicated that the flow at future time steps can be accurately obtained using that at the previous time steps via both neural networks, even in a complicated flow scenario. The velocity and pressure of the periodic flow can be faithfully predicted with a remarkable accuracy. Additionally, the derived flow physical quantities were comprehensively compared, which demonstrated that better performance can be achieved using FNO with a lower relative loss and a shorter training time-consuming.

Unsteady Flow Transition Effects on a Pitching Transonic Laminar Airfoil

This paper presents a computational study of unsteady transonic effects on a pitching supercritical laminar airfoil using high-order implicit large-eddy simulation. A CAST10-2 airfoil operating at a chord-based Reynolds number of , a transonic freestream Mach number of , and a small nominal angle of attack of deg was subjected to forced pitching oscillations about the quarter-chord with a small amplitude of deg and reduced frequencies of , 0.23, and 0.285. Complex interactions between flow separation, the motion of multiple shocks, and excursions of transitional flow were elucidated and compared against inviscid simulations. The boundary layer was found to be highly sensitive to pitch frequency, due in large part to the effects of frequency on shock motion. was found to be indirectly affected by the impact of shock motion on the boundary-layer state. Aerodynamic damping diminished with increasing oscillation frequency until becoming negative at , indicating potential for aeroelastic instability.

The Bump Suppression Strategy for the Transonic Buffet of the Supercritical Airfoil

Transonic buffet brings challenges to civil aircraft design, including but not limited to the structural fatigue and the handling quality degradation. Therefore, it is necessary to analyze the transonic buffet of the supercritical airfoil and propose the buffet suppression strategy. This paper first employs the delayed detached-eddy simulation method to simulate the unsteady buffet process of the OAT15A supercritical airfoil. Then, the temporal–spatial characteristics of the flowfield and the separation region dynamics are analyzed based on the time-domain analysis method and the dynamic mode decomposition method. After that, different two-dimensional bumps are arranged in the shock motion region to suppress the shock oscillation, and the suppression mechanism and suppression strategy are studied. The results show that the process of the developed transonic buffet is significantly influenced by the merging of the front and the rear separation regions. In case the bump obstructs this confluence phenomenon, the developed transonic buffet can be suppressed. Furthermore, it is also found that a two-dimensional bump with superior buffet performance should have the following features: The bump should be placed after the shock-induced boundary-layer separation point to make the shock-induced boundary-layer separation bubble generate on the bump ramp. Also, the height of the bump should be carefully designed to prevent the front and rear separation regions from merging and to make the front separation region disappear quickly. Finally, this strategy is successfully applied to another supercritical airfoil to confirm the universality of the controlling strategy proposed.

Contribution of lift-to-drag ratio on power coefficient of HAWT blade for different cross-sections

Abstract The aim of this study is to integrate the best lift-to-drag ratio zone to chief the highest power coefficient for horizontal axis wind turbine (HAWT) blade. Different cross-section, symmetrical, unsymmetrical, and supercritical airfoils (NACA 0012, NACA 4412, and Eppler 417) are used. FORTRAN code (f.90) was built to calculate aerodynamic data and the power coefficient based on Blade Element Momentum theory. This article deals selection of the most effective zone from the lift-to-drag ratio versus blade radius curve that gives the best incidence angle distribution. The results show a good performance that leads to approximated equal lift-to-drag distribution along the blade radius that indicates the highest power coefficient of at least 15% increases. The highest values of the power coefficient of NACA 0012, NACA 4412, and Eppler 417 were 0.476, 0.4966, and 0.482, respectively. The lift-to-drag ratio distribution zones were the most specific method of generating the maximum power coefficient for the HAWT blade. Important results and conclusion were found for further blade design.

A general deep transfer learning framework for predicting the flow field of airfoils with small data

The flow field under different flow conditions contains abundant structure information and is of great significance for aerodynamic analysis and aircraft design. Deep learning (DL) techniques have received great interest for flow field prediction due to their high capability of capturing structure characteristics in recent years. However, successful training of DL models usually requires a large amount of data, whose acquisition is prohibitively expensive and learning from insufficient flow field data still remains underexplored for DL models. This paper proposes a general deep transfer learning framework to predict the flow field of airfoils with insufficient data by transferring knowledge learned from other conditions with a large amount of data. A novel and robust flow field prediction model based on the idea of generative adversarial networks, BiFlowAN, is first proposed to precisely predict the flow field over an airfoil under a condition with sufficient data. Transfer learning technique is then introduced to transfer the learned knowledge of BiFlowAN to a new model, BiFlowAN-TL, for improving the generalization of the model under another condition with a small-scale dataset. Compared with other alternatives, the flow field predictions of supercritical airfoils show that BiFlowAN achieves higher accuracy and generalization in predicting the flow fields with sufficient data and BiFlowAN-TL significantly improves the prediction accuracy than BiFlowAN on the small-scale dataset, exhibiting the potential applicability of the proposed methods to solve the problem of rapidly and accurately evaluating aerodynamic performance with insufficient data.

Effect of Mach Number and Pitching Eigenfrequency on Transonic Buffet Onset

The transonic flow around an elastically suspended supercritical airfoil was experimentally investigated in order to enhance knowledge of buffet boundary dependencies and the corresponding self-excited fluid–structure interaction (buffeting). For that purpose, an experimental setup was designed, manufactured, and integrated in the Trisonic Wind Tunnel Munich. The design consisted of a rigid, two-dimensional, supercritical airfoil (OAT15A) with optional pitching degree of freedom and variable torsional spring stiffness. High-speed background-oriented schlieren measurements were used to observe the shock with its dynamics, while a high-speed stereo camera setup for correlation-based deformation measurements was implemented to track the dynamics of the structural motion. Pre-buffet and buffet flows were analyzed by a continuous increase of the angle of attack. The detailed observation of the shock position with increasing angle of attack exhibited a clear effect of Mach number and pitch eigenfrequency on the buffet phenomenon. The corresponding onset boundary clearly shifted into the “pre-buffet” regime given specific structural settings. Furthermore, the resulting fluid–structure interaction of shock and coupled pitch–heave motion showed characteristics of structural frequency lock-in for the pitch-to-buffet frequency ratios of 1.2 and the mode veering region for ratios of 1 and 0.9, indicating the transition region from fluid mode flutter to structural mode flutter.

Cooperation of Trailing-Edge Flap and Shock Control Bump for Robust Buffet Control and Drag Reduction

At transonic flight conditions, the buffet caused by the interaction between the shock waves and the boundary layers can degrade an aircraft’s aerodynamic performance and even threaten its safety. In this paper, the shock control bumps, originally designed to reduce the wave drag at cruise speeds, are applied to enhance the robustness of the closed-loop buffet control system using the trailing-edge flap. For the OAT15A supercritical airfoil, a closed-loop buffet control system is first designed with a feedback signal of lift coefficient. Then, the shock control bumps designed for drag reduction are integrated into the active buffet control system. The results show that the closed-loop flap control can be greatly enhanced by coupling with the shock control bumps. At the steady state under control, the shock control bumps can slightly increase the airfoil lift–drag ratio. More importantly, the ranges of control parameters that can effectively suppress the buffet are significantly enlarged with the help of the bumps; thus, the robustness of the control system is greatly enhanced.

Two-equation turbulent viscosity model for simulation of transitional flows: An efficient artificial neural network strategy

Laminar-to-turbulent transition phenomena are ubiquitous in natural and industrial flows. As to the Reynolds-averaged Navier–Stokes (RANS) simulation method, the workhorse for accurate prediction of such flow regime boils down to the consideration of the transition effect in turbulence modeling. In this paper, an industrial–practical transition–turbulence model with excellent accuracy, robustness, and efficiency is established by the fully connected artificial neural network (ANN), which maps the relation between the RANS mean flow variables and an intermittency factor. A one-equation local correlation-based transition model coupled with Menter's shear stress transport (SST) model is taken as the benchmark. The present two-way coupling ANN model is trained with two National Advisory Committee for Aeronautics (NACA) airfoils, that is, NACA0012 and NACA2418, at various angles of attack and Mach numbers, while tested with the A-airfoil, NACA0015, and RAE 2822 supercritical airfoils in different flow states. The a posteriori test results manifest that the mean pressure coefficient, skin friction coefficient, size of laminar separation bubble, mean streamwise velocity, Reynolds shear stress, and lift/drag/moment coefficient predicted by the ANN model are all in good agreement with those given by the benchmark transition-based SST model. Furthermore, the ANN model exhibits higher calculation efficiency and convergence speed than the traditional transition-predictive SST model. The present work may pave a new way for machine learning methods to be used in integrated transition–turbulence modeling toward industrial applications.

Uncertainty optimization design of airfoil based on adaptive point adding strategy

A new and effective uncertainty optimization design framework based on adaptive point adding strategy is proposed to design and optimize the supercritical airfoil which is sensitive to Mach number variation. The new framework combines non-intrusive polynomial chaos (NIPC) method, Kriging model, lower confidence bounding (LCB) infill criterion, and global GlobalSearch algorithm. NIPC method is used to quantify the uncertainty of Mach number. A new class/shape function transformation method is used to parameterize the airfoil shapes and Kriging model is selected to establish the surrogate model of the aerodynamic optimization design. The LCB infill criterion is proposed to update the initial surrogate model by adding the optimal design point. The global GlobalSearch algorithm is used to optimize the surrogate model. The uncertainty optimization results are compared with the deterministic optimization results. It is shown that the proposed uncertainty optimization design based on adaptive point adding strategy has higher robustness under condition of Mach number variation, the optimization expense can be reduced to 20.76%, and the efficiency of optimization design is improved.

Physically Interpretable Feature Learning of Supercritical Airfoils Based on Variational Autoencoders

Machine-learning models have demonstrated a great ability to learn complex patterns and make predictions. In high-dimensional nonlinear problems of fluid dynamics, data representation often greatly affects the performance and interpretability of machine learning algorithms. With the increasing application of machine learning in fluid dynamics studies, the need for physically explainable models continues to grow. This paper proposes a feature learning algorithm based on variational autoencoders, which can assign physical features to some latent variables of the variational autoencoder. It is theoretically proved that the remaining latent variables are independent of the physical features. The proposed algorithm is trained to include shock wave features in its latent variables for the reconstruction of supercritical wall Mach number distributions. The reconstruction accuracy and disentanglement are compared with those of other variational autoencoders. Then, the proposed algorithm is used for the inverse design of supercritical airfoils. The proposed algorithm demonstrates the ability to manipulate certain physical features of an airfoil without changing the others, as well as the ability to generate different airfoils with the same physical features by sampling the disentangled latent variables.

Characterization Of Shock Buffet On A Supercritical 2D Airfoil In Transonic Flow

The transonic flow over the supercritical OAT15A airfoil is investigated experimentally. Using time-resolved focusing schlieren sequences, we extracted the temporal evolution of the chordwise shock location for a wide range of combinations of Mach number and angle of attack. Based on this data, we identified the conditions of pre-buffet, buffet onset, fully-established buffet, and buffet-offset behavior. Key parameters characterizing most pronounced buffet behavior are presented and quantified in terms of the shock amplitude, its variation over multiple buffet cycles, and the associated frequency of the periodic shock oscillation. Fully-established buffet is identified at a Mach number of 0.72 and angle of attack of 5 deg. It is demonstrated that these operating conditions are characterized by a quasi-sinusoidal shock oscillation at a distinct frequency of 113 Hz, in good agreement with previous studies. This analysis reveals that the harmonic shock oscillation spanning a range of about 16.5% of the airfoil chord is accompanied by a coupled large-scale variation of the global flow topology. Both instantaneous and mean velocity components in the chordwise and vertical directions are discussed for representative phases of the buffet cycle. Instantaneous vector fields of both components provide insight into the flow organization throughout the buffet cycle and allow to identify the streamwise distance traveled by the shock wave within a full cycle. We can thus precisely capture the state of the shock wave and quantify the evolution of the shock-induced separation and the size of the turbulent wake. Severe variations of the flow topology are induced by the large-scale upstream and downstream shock displacement. The results show that incidents of massive flow separation are observed for shock positions being close to the upstream limit, and more general, that the wake influence is more pronounced when induced by an upstream traveling shock wave. Phase-averaged velocity profiles at significant locations along the airfoil suction side complement this analysis. Characteristic sets of velocity profiles are discussed in detail that allow to uniquely describe the development of the flow in each phase of the buffet cycle. Detailed contours and profiles of both velocity and Reynolds shear stress contributions across the wake region highlight the strong downstream influence the shock-induced turbulent wake. Phases of severe flow separation result in reverse flow persisting until the trailing edge which further substantiates the induced momentum deficit.

PIV investigations of shock-buffet dynamics on a supercritical airfoil with a pitching degree of freedom

The interaction between the transonic flow around a spring mounted OAT15A airfoil model and the resulting pitching motion of the model was investigated with the goal of understanding the dynamics of the occurring phenomena. The experiments were performed at free-stream Mach numbers from 0.70 to 0.77 and at a Reynolds number of Rec ≈ 3 × 10^6. The dominant structural frequency of the airfoil’s pitch motion was adjusted to be in the range of the natural buffet frequency of the flow with inhibited pitching motion of the model. The variation of the Mach number allowed for an investigation in the pre-buffet, buffet and post-buffet regime. A periodic pitch motion with an amplitude of the angle of attack of up to ±1.17° was observed for buffeting flow conditions while it was significantly less in pre-buffet and post-buffet conditions. Velocity field measurements by means of high repetition rate particle image velocimetry (PIV) were used to capture the motion of the shock and to determine the state of the boundary layer flow for the different phases of the model motion. For the Mach number range Ma = 0.72 − 0.75 the change of the angle of attack and the shock position correlate strongly with each other. From the measurements, the delay of both quantities during the coupled motion could be determined.