Transonic Buffet Research Articles

A Comparison of Different Approaches for Predicting Transonic Buffet Onset on Infinite Swept Wings

A comparative study is performed on three different approaches for prediction of transonic buffet onset on infinite swept wings. All three approaches are based on the unsteady Reynolds-averaged Navier–Stokes (URANS) equations, and include: quasi-3D and fully-3D global stability analysis of the corresponding steady 2.5D RANS solutions and direct numerical solution of the 3D URANS equations. The results are presented for an infinite swept wing based on the ONERA OAT15A airfoil section. The quasi-3D stability analysis is shown to be accurate and most efficient and, thus, is best suited for this spanwise-uniform flow. The fully-3D stability analysis ensures the same accuracy, provided that the grid-step in the spanwise direction is sufficiently small. It is much more demanding in terms of computer memory but can be extended to more-general wing configurations. Good agreement is observed between the three approaches in terms of critical conditions for buffet onset and the instability growth characteristics, providing a cross-validation of the methods and an assessment of their computational demands.

Experimental Characterization of Upper Trailing Edge Flaps for Transonic Buffet Control

This experimental study investigates the possibility of controlling transonic buffet by means of a trailing edge flap with an upward deflection (referred to as “upper trailing edge flap”, or: UTEF). Different geometries (straight and serrated) and dimensions of UTEFs (with heights ranging between 1 and 2% of the chord) have been studied with respect to their impact on the buffet behavior. The effectiveness of the UTEFs has been investigated with schlieren and particle image velocimetry (PIV) in the transonic-supersonic wind tunnel of TU Delft at Ma = 0.70, α = 3.5°. The schlieren results demonstrated the efficacy of the use of UTEFs for reducing the range of the buffet oscillations when the height of the UTEF was equal to at least 1.5%c. This result was corroborated by a flow characterization with PIV data and which highlighted that, in presence of a control system, not only the shock oscillation range is reduced but also the intensity of the separated area pulsation. The use of serrated UTEFs, despite having an effect on the local flow field, was found to be ineffective in alleviating buffet oscillations. The adoption of the best behaving UTEF configuration (straight 2%c UTEF) proved to only slightly alter the circulation value compared to the clean configuration, while it also proved to be effective in an off-buffet condition (Ma = 0.74 and α = 2.5°).

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.

Finite-Wing and Sweep Effects on Transonic Buffet Behavior

This study experimentally investigates the effects of the sweep angle and finite wing on transonic buffet, studying two-dimensional (2-D) and three-dimensional wing configurations. Background-oriented schlieren and stereographic particle image velocimetry (PIV) have been used as measurement techniques, performing experiments on an OAT15A airfoil (clamped to both the side windows of the wind tunnel), an unswept wing, and two swept wings with sweep angles of 15 and 30 deg, respectively. The three wings are also based on the OAT15A airfoil and are clamped at the wind tunnel only at their root (free wingtip). All wings have been tested at a constant normal Mach number () with respect to the leading edge. The results show that the buffet oscillations are much stronger for the airfoil than for the three finite-span wings. A large difference in the buffet behavior can be noticed between the airfoil and the unswept wing, as is also seen in oil flow visualizations. This difference is particularly evident in correspondence of the more outboard spanwise locations, suggesting that for the unswept wing, an important role could be played by finite-wing effects: notably, the tip vortex. A spectral analysis has shown that for the swept wings, the classical 2-D buffet peak (occurring at for the present conditions) is substantially attenuated, whereas additional contributions in the range of 450–850 Hz appear. The PIV results showed, for the 30 deg sweep angle wing, a periodical occurrence of a secondary supersonic area downstream of the main shock wave structure, which is absent for the other wing models. The stereographic PIV configuration allowed the reconstruction of the spanwise-oriented velocity component, obtaining, in proximity of the trailing-edge, values of the spanwise velocity component () which are in agreement with the spanwise convection of buffet cells observed in the literature in this region.

Investigating the flow field dynamics of transonic shock buffet using particle image velocimetry

An experimental investigation was performed in order to better understand the transonic shock buffet phenomenon and determine the dominant flow interactions at specific flow conditions. A rigid wing in the shape of an OAT15A airfoil was placed in the Trisonic Wind Tunnel Munich, where both the Mach number and the angle of attack were varied between 0.65<M∞<0.77\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0.65< M_\\infty < 0.77$$\\end{document} and 3.8<α<6.3∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$3.8< \\alpha < 6.3^\\circ$$\\end{document} respectively. With the use of high-speed imaging, high-quality optics and state-of-the-art laser equipment, highly resolved velocity field measurements were obtained via particle image velocimetry, where the streamwise and vertical velocity components were computed over the suction side of the wing center plane. It was shown that sustained buffet first occurs at M∞≥0.74\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_\\infty \\ge 0.74$$\\end{document} when maintaining the angle of attack constant at α=5.8∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha =5.8^\\circ$$\\end{document}. Similarly, an increase in α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document} for a fixed M∞=0.74\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_\\infty =0.74$$\\end{document} also led to the development of shock buffet. Instantaneous snapshots confirmed the presence of a recirculation region downstream of the moving shock, where an increase in the wake size was confirmed when the shock was located most upstream. Streamwise correlations were also computed near the airfoil’s upper surface in order to extract the characteristic convective velocity of flow structures. The convective velocity appeared to increase with streamwise distance, ranging on average between 50 and 150 m/s. Overall, these time-resolved velocity field measurements allow for the investigation of the flow dynamics during shock buffet and highlight the independent effect of Mach number and angle of attack on this complex phenomenon.

Large-eddy simulations and modal reconstruction of laminar transonic buffet

Transonic buffet refers to the self-sustained periodic motion of shock waves observed in transonic flows over wings and can limit the flight envelope of aircraft. Based on the boundary layer characteristics at the shock foot, buffet has been classified as laminar or turbulent and the mechanisms underlying the two have been proposed to be different (Dandois et al., J. Fluid Mech., vol. 18, 2018, pp. 156–178). The effect of various flow parameters (freestream Mach and Reynolds numbers and sweep and incidence angles) on laminar transonic buffet on an infinite wing (Dassault Aviation's supercritical V2C aerofoil) is reported here by performing large-eddy simulations (LES) for a wide range of parameters. A spectral proper orthogonal decomposition identified the presence of a low-frequency mode associated with buffet and high-frequency wake modes related to vortex shedding. A flow reconstruction based only on the former shows periodic boundary-layer separation and reattachment accompanying shock wave motion. A modal reconstruction based only on the wake mode suggests that the separation bubble breathing phenomenon reported by Dandois et al. is due to this mode. Together, these results indicate that the physical mechanisms governing laminar and turbulent buffet are the same. Buffet was also simulated at zero incidence. Shock waves appear on both aerofoil surfaces and oscillate out of phase with each other indicating the occurrence of a Type I buffet (Giannelis et al., Aerosp. Sci. Technol., vol. 18, 2018, pp. 89–101) on a supercritical aerofoil. These results suggest that the mechanisms underlying different buffet types are the same.

Transonic Buffet Active Control with Local Smart Skin

Transonic flight has high economic benefits, but the appearance of transonic buffet limits the flight envelope. The shock control bump currently used for transonic buffet suppression tends to degrade the aerodynamic performance of the non-buffeting state. In this study, a smart skin system is used to eliminate the fluctuating load of transonic buffet by measuring the airfoil lift coefficient as the feedback signal and adjusting the local skin height using data-driven, model-free adaptive control. Since the actuator height is dynamically adjusted only after the occurrence of transonic buffet, the smart skin can completely suppress the fluctuating load and does not affect the aerodynamic performance in the non-buffeting state. The suppression effect of the proposed smart skin on transonic buffet is verified by numerical simulation of the flow. The simulation results show that due to the introduction of closed-loop control, the fluctuating load of transonic buffet can be effectively suppressed for different positions and maximum heights of the actuator. Even when the flow state changes, the robust smart skin system can also achieve the control goal. Therefore, smart skins combining flexible materials and control technologies have the potential to effectively improve the aerodynamic performance of aircraft.

Adjoint-based unsteady shape optimization to suppress transonic buffet

The traditional aerodynamic shape optimization mainly aims at the enhancement of lift-drag ratio in the steady state. In this study, the onset of transonic buffet is improved by the unsteady aerodynamic shape optimization. To achieve this goal, the variance of lift coefficient in a period is adopted as the optimization objective. In addition, the gradients of the objective function with respect to shape parameters are efficiently calculated by the unsteady discrete adjoint method. The proposed method is verified by two optimization examples of NACA0012 and OAT15A. Not only the onsets of transonic buffet are increased by 0.9∘ and 1.7∘ respectively, but also the aerodynamic performance is improved. According to the shape change of optimization examples, we summarize three airfoil geometric characteristics: the position of maximum thickness of the upper airfoil, the thickness near the leading edge, and the thickness near the trailing edge. The influence of the geometric characteristics on the flow stability has been studied.

Buffet boundary prediction using RANS-based criteria and adjoint methods

In this work a procedure is proposed for a fast estimate of the transonic buffet boundary on aerofoils and wings. This algorithm aims to be an alternative to unsteady computational fluid dynamics simulations that are prohibitively expensive for complex flow cases. The algorithm combines steady Reynolds-averaged Navier-Stokes simulations with an adjoint method. Reynolds-averaged Navier-Stokes simulations were used to determine the buffet onset by means of suitable criteria, while the adjoint method was used to compute the sensitivities of the buffet parameters to the flight conditions, and draw the buffet boundary. The procedure was tested for two-dimensional configurations with available experimental data and for two different criteria. Particular attention was paid to the efficiency of the method and its ability to reduce computational cost with respect to purely RANS criteria for buffet boundary estimation. Possible variations to the procedure were also discussed in the results section together with the effect of some key parameters of the proposed algorithm.

An enhanced hybrid deep neural network reduced-order model for transonic buffet flow prediction

In the transonic flight environment, transonic buffet has significant influence on the aerodynamic characteristics of aircraft. In the face of the strong nonlinear characteristics of transonic buffet, the reduced-order model (ROM) technology based on deep learning (DL) is introduced to study the flow field. In this article, an enhanced hybrid deep neural network (eHDNN) consisting of Convolutional Neural Network (CNN) and Convolutional Long Short-Term Memory (ConvLSTM) neural network is constructed as the ROM of unsteady transonic buffet flow field. By mining the spatial-temporal characteristic of buffet flow directly from large-scale flow field data, the eHDNN can predict complex flow characteristics such as shock wave motion in the unsteady buffet flow. Structural similarity information and nonlinear improvement strategies are introduced to improve the nonlinear expression ability of eHDNN. The predicted result is consistent with the numerical simulation and has high degree of prediction accuracy. In addition, the eHDNN has good generalization ability, which can predict the spatial-temporal evolution of buffet flow field at unknown angles of attack. The prediction method has good application prospect of the transonic buffet flow control and prediction, which also provides experience for DL modeling in other complex and strongly nonlinear flows.

Physics-Based Data-Driven Buffet-Onset Constraint for Aerodynamic Shape Optimization

Transonic buffet is undesirable because it causes vibration, and constraining buffet is crucial in transonic wing design. However, there is still a lack of accurate and efficient buffet formulation to impose the constraint. This work proposes a physics-based data-driven buffet analysis model generalizable for airfoil and wing shapes. The model is trained with data obtained from two-dimensional airfoils in a physics-based manner to extend it to buffet analyses of three-dimensional wings. Specifically, the model takes the pressure and friction distributions as inputs to discover the key physics (shock waves and flow separation) of transonic buffeting, rather than using shape and flow parameters as the input. High-quality sample airfoils are used and a mixture model of convolutional neural networks is proposed to improve accuracy. The model exhibits a mean absolute error of 0.05 deg in buffet factor prediction of 14,886 unseen testing data. Buffet boundary predictions using the model compare well with the reference results (a lift-curve break method) for various airfoils and wings. Wing shape optimization using the model appropriately considers buffet constraints, leading to an optimized wing with lower drag (by 1.7 counts) than that obtained by the state-of-the-art method. These results demonstrate the effectiveness of the proposed physics-based data-driven buffet analysis approach. The proposed method is a promising alternative to address other complex off-design constraints in aircraft design.

Two-Dimensional Investigation of the Fundamentals of OGV Buffeting

The increased demands of compact modern aero engine architectures have highlighted the problem of outlet guide vane (OGV) buffeting in off-design conditions. This structural response to aerodynamic excitations is characterised by increased vibration, risking structural fatigue. Investigations focused on understanding, mitigation and avoidance are therefore of high priority. OGV buffet is a type of transonic buffet caused by unsteady shock movement, but the exact parameters driving it are not fully understood. To try and understand them, this paper examines the buffet of a quasi-2D OGV geometry. Parametric studies of the incidence angle and inlet Mach number were performed. Forcing frequencies for both studies were found to be close to the experimentally detected frequency of vibration in the first bow mode, which demonstrates that buffet is driven by quasi-2D flow features. Increasing the inlet Mach number increased the dominant forcing frequency, whereas increasing the incidence yielded little change. Profiles of unsteady pressure amplitudes were shown to smoothly increase in magnitude with an increasing incidence and inlet Mach number.

Large-Eddy Simulation of Transonic Buffet Using Matrix-Free Discontinuous Galerkin Method

We present an implicit large-eddy simulation of transonic buffet over the OAT15A supercritical airfoil at Mach number 0.73, angle of attack 3.5 deg, and Reynolds number . The simulation is performed using a matrix-free discontinuous Galerkin (DG) method and a diagonally implicit Runge–Kutta scheme on graphics processor units. We propose a Jacobian-free Newton–Krylov method to solve nonlinear systems arising from the discretization of the Navier–Stokes equations. The method successfully predicts the buffet onset, the buffet frequency, and turbulence statistics owing to the high-order DG discretization and an efficient mesh refinement for the laminar and turbulent boundary layers. A number of physical phenomena present in the experiment are captured in our simulation, including periodical low-frequency oscillations of shock wave in the streamwise direction, strong shear layer detached from the shock wave due to shock-wave/boundary-layer interaction and small-scale structures broken down by the shear-layer instability in the transition region, and shock-induced flow separation. The pressure coefficient, the root mean square of the fluctuating pressure, and the streamwise range of the shock wave oscillation agree well with the experimental data. The results suggest that the proposed method can accurately predict the onset of turbulence and buffet phenomena at high Reynolds numbers without a subgrid scale model or a wall model.

Numerical investigation of transonic buffet on a prescribed-pitching OAT15A airfoil

The transonic buffet over a prescribed-pitching OAT15A airfoil was numerically investigated using a well-validated delayed detached eddy simulation approach. The present approach successfully reproduced self-sustained shock wave oscillations. The computational results show that the amplitude of the lift fluctuations in the pitching case is approximately six times that of the fixed case. Compared to the fixed case, the presence of a larger shock motion region, two shock wave interactions, and severe boundary separation give rise to higher pressure and velocity fluctuation levels on the whole upper surface in the pitching case. In particular, the highly disordered flow replaces the periodic vortex shedding in the wake, resulting in the disappearance of the secondary fluctuation in unsteady lift coefficients, which is observed at 2274 Hz in the fixed case. A proper orthogonal decomposition analysis shows that the buffet flow in the fixed case exhibits the feature of regular motion, which is closely related to the coherent flow structure of shock oscillations and Karman vortices. Strong interactions between the Karman vortex structure and the shock oscillations are also observed. Compared to those in the fixed case, the fluctuation amplitudes of the coefficients of the first mode pair and the second to fourth mode pairs in the pitching case are 2.5 times and 5 times larger, respectively, and the energy ratio of the nonlinear component in the total mode energy is significantly increased. Furthermore, the main frequencies of modes 1–10 in the pitching case are all located at the shock buffet frequency or its higher-order harmonics.

Stability analysis for laminar separation flutter of an airfoil in the transitional flow regime

Laminar separation flutter (LSF) is a type of aeroelastic instability phenomenon characterized by small-amplitude low-frequency pitching oscillations of the airfoil. The present study aims to gain insight into the intrinsic dynamics of LSF via data-driven stability analysis. The proposed data-driven approach relies on the autoregressive with exogenous input (ARX) technique to design reduced-order models (ROMs) of unsteady aerodynamics in a state-space format. First, high-fidelity full-order numerical simulations of the LSF phenomenon are performed using the incompressible Unsteady Reynolds-Averaged Navier–Stokes equations and the Shear-Stress Transport k−ω turbulence model with Low-Reynolds-number correction. The calculated LSF responses show good agreement with previous experimental data in the literature. Then, linear stability analysis (LSA) of the aeroelastic system is carried out to reveal the underlying fluid-structure interaction mechanism. The LSA model is developed by coupling the ROM with the structure motion equation. LSA results indicate that the LSF phenomenon is primarily caused by the instability of the structure mode (SM), which is induced by the mutual repulsion effect between one static fluid mode (FM) and the SM. The presence of laminar separation near the trailing-edge of the airfoil can significantly reduce the stability of the static FM, which ultimately strengthens the fluid-structure coupling effect and leads to LSF. We would like to emphasize that LSF is essentially different from other flow-induced vibration phenomena, such as transonic buffeting of an airfoil and vortex-induced vibration of bluff bodies, for which the instabilities are triggered by the coupling between one dynamic FM and the SM. Finally, the effects of the mass ratio, structural damping ratio, and freestream turbulence intensity on the aeroelastic system are also investigated.

Bayesian calibration for large‐scale fluid structure interaction problems under embedded/immersed boundary framework

AbstractBayesian calibration is widely used for inverse analysis and uncertainty analysis for complex systems in the presence of both computer models and observation data. In the present work, we focus on large‐scale fluid‐structure interaction systems characterized by large structural deformations. Numerical methods to solve these problems, including embedded/immersed boundary methods, are typically not differentiable and lack smoothness. We propose a framework that is built on unscented Kalman filter/inversion to efficiently calibrate and provide uncertainty estimations of such complicated models with noisy observation data. The approach is derivative‐free and non‐intrusive, and is of particular value for the forward model that is computationally expensive and provided as a black box which is impractical to differentiate. The framework is demonstrated and validated by successfully calibrating the model parameters of a piston problem and identifying the damage field of an aircraft wing under transonic buffeting.

System Identification of Two-Dimensional Transonic Buffet

When modeled within the unsteady Reynolds-averaged Navier–Stokes framework, the shock wave dynamics on a two-dimensional airfoil at transonic buffet conditions is characterized by time-periodic oscillations. Given the time series of the lift coefficient at different angles of attack for the OAT15A supercritical profile, the Sparse Identification of Nonlinear Dynamics (SINDy) technique is used to extract a parameterized, interpretable, and minimal-order description of this dynamics. For all the operating conditions considered, SINDy infers that the dynamics in the lift-coefficient time series can be modeled by a simple parameterized Stuart–Landau oscillator, reducing the computation time from hundreds of core hours to seconds. The identified models are then supplemented with equally parameterized low-dimensional dynamic mode decomposition based state observers enabling real-time estimation of the whole flowfield from the predicted lift. The value of this simple model is in the possibility of enriching sparse data sets in the buffet regime for new geometries. Only a few unsteady simulations need to be performed to adjust the coefficients of the identified model and then supplement the data set with new cases. Simplicity, accuracy, and interpretability make the identified model an attractive tool toward the construction of real-time systems to be used during the design, certification, and operational phases of the aircraft life cycle.

Advanced multi-input system identification for next generation aircraft loads monitoring using linear regression, neural networks and deep learning

Over the past decade, the ideologies surrounding Structural Health Monitoring (SHM) have shifted drastically within the aerospace engineering disciplines, predominantly onus to rapid advancements in machine intelligence. While traditional SHM practices are based on scheduled and pre-emptive maintenance, the NextGen SHM system, known commonly as Prognostics and Health Management (PHM), has a focus on pro-active condition-based maintenance, forecasting and prognostics — a milestone on the trajectory towards Digital Twin technology. In aircraft, particularly defense fighter air platforms, fatigue-critical high-amplitude cyclic behavior is unavoidable, where rapid fatigue life consumption due to an airframe buffet is one of the most problematic phenomena that engineers have encountered throughout the 4th and 5th generation fighter programs. This paper serves as a point-of-reference consolidating a range of machine learning models, under a single benchmark aircraft Multi-Input Single-Output (MISO) loads monitoring problem. Linear regression models, traditional (shallow) artificial neural networks, and deep learning strategies are all explored, where strain sensors are used as inputs to predict representative bending and torsional dynamic (buffet) and quasi-static (maneuver) load spectra on an aircraft wing during transonic buffeting maneuvers. For the benchmark system considered herein, the MISO coherence ranges from high to very weak depending on the load case, hereby providing a unique opportunity to rigorously explore the time-series modeling requirements and make valuable recommendations across a wide range of data-qualities that are likely to be encountered in traditional or modern aircraft data-acquisition systems or, for that matter, in any mechanical systems plagued by fatigue.

IDDES method based on differential Reynolds-stress model and its application in bluff body turbulent flows

A general construction approach for a class of detached-eddy simulation (DES) methods with the turbulent length-scale equation is presented in this study. It supports the rationality of the construction and provides a theoretical estimation of the model coefficients in DES simulation. By using the construction approach, a differential Reynolds-stress model (RSM), referred to as Speziale-Sarkar-Gatski (SSG)/Launder–Reece–Rodi (LRR)-ω RSM, is built into the improved delayed DES (IDDES) method. After calibration of the model parameters in the IDDES method and basic validation for decaying isotropic turbulence, the RSM-based IDDES approach is then applied to simulate the massively separated flows around the tandem cylinders and the transonic buffet flow over a hammerhead launch vehicle. The simulations are validated by the available experimental data, and the performance is evaluated by means of instantaneous, statistical, spectral analysis of the numerical data. It is found that the RSM-based IDDES method shows better performance comparing with the k-ω shear-stress transport (SST)-based IDDES method, especially for predicting the development of massively separated flows behind the bluff body.

Airfoil buffet aerodynamics at plunge and pitch excitation based on long short-term memory neural network prediction

In the present study, a nonlinear system identification approach based on a long short-term memory (LSTM) neural network is applied for the prediction of transonic buffet aerodynamics. The identification approach is applied as a reduced-order modeling (ROM) technique for an efficient computation of time-varying integral quantities such as aerodynamic force and moment coefficients. Therefore, the nonlinear identification procedure as well as the generalization of the ROM are presented. The training data set for the LSTM–ROM is provided by performing forced-motion unsteady Reynolds-averaged Navier–Stokes simulations. Subsequent to the training process, the ROM is applied for the computation of the aerodynamic integral quantities associated with transonic buffet. The performance of the trained ROM is demonstrated by computing the aerodynamic loads of the NACA0012 airfoil investigated at transonic freestream conditions. In contrast to previous studies considering only a pitching excitation, both the pitch and plunge degrees of freedom of the airfoil are individually and simultaneously excited by means of an user-defined training signal. Therefore, strong nonlinear effects are considered for the training of the ROM. By comparing the results with a full-order computational fluid dynamics solution, a good prediction capability of the presented ROM method is indicated. However, compared to the results of previous studies including only the airfoil pitching excitation, a slightly reduced prediction performance is shown.