Transonic Dip Research Articles

Numerical investigation on transonic flutter characteristics of an airfoil with split drag rudder

In this paper, a series of flutter simulations are carried out to investigate the effects of split drag rudder (SDR) on the transonic flutter characteristic of rigid NACA 64A010. A structural dynamic model addressing two-degree-of-freedom pitch-plunge aeroelastic oscillations was coupled with the unsteady Reynolds-averaged Navier-Stokes equations to perform flutter simulation. Meanwhile, the influence mechanism of SDR on flutter boundary is explained through aerodynamic work and the correlated shock wave location. The results show that the SDR delays the shock wave shifting downstream, and the Mach number corresponding to reaching freeze region increases as the split angle increases. Therefore, the peak value of aerodynamic moment coefficient amplitude and the sharp ascent process of phase occurs at higher Mach number, which leads to the delay in the occurrence of the transonic dip. Besides, before the transonic dip of airfoil without SDR occurs, the aerodynamic moment phase of airfoil with the SDR decreases slowly due to the decrease in the speed of shock wave moving downstream. This results in an increased flutter speed when employing the SDR before the transonic dip of airfoil without SDR occurs. Meanwhile, the effects of asymmetric split angles on the transonic flutter characteristics are also investigated. Before the transonic dip of airfoil without SDR occurs, the flutter characteristic is dominated by the smaller split angle.

Active control of transonic airfoil flutter using synthetic jets through deep reinforcement learning

This paper presents a novel framework for the active control of transonic airfoil flutter using synthetic jets through deep reinforcement learning (DRL). The research, conducted in a wide range of Mach numbers and flutter velocities, involves an elastically mounted airfoil with two degrees of freedom of pitching and plunging oscillations, subjected to transonic flow conditions at varying Mach numbers. Synthetic jets with zero-mass flux are strategically placed on the airfoil's upper and lower surfaces. This fluid–structure interaction (FSI) problem is treated as the learning environment and is addressed by using the arbitrary Lagrangian–Eulerian lattice Boltzmann flux solver (ALE-LBFS) coupled with a structural solver on dynamic meshes. DRL strategies with proximal policy optimization agents are introduced and trained, based on the velocities probed around the airfoil and the dynamic responses of the structure. The results demonstrate that the pitching and plunging motions of the airfoil in the limited cycle oscillation (LCO) can be effectively alleviated across an extended range of Mach numbers and critical flutter velocities beyond the initial training conditions for control onset. Furthermore, the aerodynamic performance of the airfoil is also enhanced, with an increase in lift coefficient and a reduction in drag coefficient. Even in previously unseen environments with higher flutter velocities, the present strategy is achievable satisfactory control results, including an extended flutter boundary and a reduction in the transonic dip phenomenon. This work underscores the potential of DRL in addressing complex flow control challenges and highlights its potential to expedite the application of DRL in transonic flutter control for aeronautical applications.

Machine learning of unsteady transonic aerodynamics of a pitching truss-braced wing section

A detailed analysis of transonic aerodynamics of a pitching conceptual Boeing Truss-Braced Wing (TBW) section has been carried out at various Mach numbers at a typical reduced frequency, k = 0.15. A new important flow feature of hysteresis loop cross-over has been discovered through the analysis of the cl hysteresis loops. Transonic dip has been located at M = 0.87, where the mean cl attains a minimum value. Hysteresis loop cross-over and transonic dip are important in the transonic flutter analysis of these wing sections. High fidelity database for the TBW section corresponding to different M in the range [0.7 - 0.9] has been generated by numerically solving the Navier-Stokes equations on a supercomputer at the NASA Advanced Supercomputing Division. A regularization-based machine learning (ML) methodology has been developed to predict the transonic aerodynamics of the pitching TBW section, using the training data as a subset of this high fidelity database. The ML model was then tested on test data as a subset of this database exclusive of the training data. Each ML model prediction is achieved well within a minute of computing time, as opposed to tens of hours of super-computing time required for each high fidelity CFD solution, thus making it a feasible tool for the design of a TBW, with the wing flutter in perspective. The TBW section flow was simulated corresponding to an altitude of 44,000 ft.

An Effective Arbitrary Lagrangian-Eulerian-Lattice Boltzmann Flux Solver Integrated with the Mode Superposition Method for Flutter Prediction

An Effective Arbitrary Lagrangian-Eulerian-Lattice Boltzmann Flux Solver Integrated with the Mode Superposition Method for Flutter Prediction

Sinusoidally Pitching Foils in Transonic Flow: Insights into Flutter from Time Accurate Simulations

The impact of shock formation and vortex dynamics on airfoil flutter in the transonic regime is investigated through a series of two-dimensional time-accurate simulations of a sinusoidally pitching airfoil at a Reynolds number of 10,000. To gain insight into transonic flutter in the fully nonlinear regime, an energy-based approach that employs prescribed kinematics is utilized. Flutter stability boundaries are identified as a function of the Mach number and the reduced velocity, the latter of which is a surrogate for structural stiffness or flight speed. The results show a subcritical instability near Mach numbers of M∞=0.7 for a range of oscillation frequencies. Additionally, three shock-induced mechanisms are identified that influence the transfer of energy from the flow to the airfoil. The primary mechanism is flow separation triggered by the generation of a lambda shock. The influence of the lambda-shock dynamics on airfoil flow separation is determined for different Mach numbers, providing insight into the well-known “transonic dip” observed in flutter boundaries.

Study of Effect of Aerodynamic Interference on Transonic Flutter Characteristics of Airfoil

Aerodynamic interference occurs when biplane wings are placed close to each other. Investigating aerodynamic interference on the transonic flutter characteristics of these wings is an important issue. A numerical model is configured with the rigid airfoil positioned above the elastic airfoil at different positions to simulate various levels of aerodynamic interference. The flutter characteristics of the elastic airfoil are analyzed using an efficient aeroelastic analysis method based on the reduced order model. The results suggest that when the rigid airfoil is positioned directly above the elastic airfoil the aerodynamic interference accelerates the airflow on the upper surface of the elastic airfoil. This leads to a subsonic dip phenomenon, and the instability mode after the subsonic dip gradually transitions from first order to second order. Furthermore, aerodynamic interference leads to an earlier occurrence of a shock wave on the upper surface of the elastic airfoil, which causes earlier appearances of transonic dip and S-shape flutter boundary. Moreover, the S-shape flutter boundary is widened as a consequence of the interference. Remarkably, the part of the S-shape flutter boundary is solely induced by the first-order mode instability, which is different from the typical alternating instability of the first-order and second-order modes together. When the rigid airfoil is positioned diagonally above the elastic airfoil, aerodynamic interference causes a later occurrence of a shock wave on the upper surface of the elastic airfoil, which leads to later appearances of the transonic dip and S-shape flutter boundary. Additionally, the S-shape flutter boundary is widened.

Numerical Investigation of Double Transonic Dip Behaviors in Supercritical Airfoil Flutter

This numerical study examines the behavior of the double transonic dip with a supercritical airfoil. A two-dimensional model of a wing section with two degrees of freedom was used for the investigation. The flowfield was modeled by solving the unsteady Reynolds-averaged compressible Navier–Stokes equations using the Spalart–Allmaras turbulence model, and the equations of motion were solved to determine the structural dynamics. The present model successfully captured the behavior of the double transonic dip on the flutter boundary of the supercritical airfoil, which contrasts with the well-known behavior of the single transonic dip exhibited by conventional symmetric airfoils. Although the mechanism of the first dip at a lower Mach number corresponded to that of the well-known conventional transonic dip, the second dip at a higher Mach number was uniquely observed for the supercritical airfoil. The analysis established that, for the supercritical airfoil, the motion of the shock wave over the upper surface was significantly affected by the behavior of the boundary layer around the highly cambered aft region of the lower surface during flutter. The behavior of the boundary layer involving the separation and reattachment over the lower surface caused the unusual shock wave motion over the upper surface under the Mach number condition at the bottom of the second dip. This motion exerted negative damping forces on the motion of the airfoil, thereby becoming the primary contributor to generating the second dip experienced by the supercritical airfoil.

Structural and aeroelastic characteristics of wing model for transonic flutter wind tunnel test fabricated by additive manufacturing with AlSi10Mg alloys

In this paper, the potentials of wing models fabricated by metal additive manufacturing for transonic flutter wind tunnel testing are investigated. The additive manufacturing technique would be a tool for the fast production of wind tunnel models at low cost and enable multiple experiments with various wing designs while precisely realizing designed geometries and structural properties for aeroelastic evaluations. The novelties in this paper are: 1) a concept of the transonic flutter wing model, which can be used to investigate phenomena involving transonic aeroelastic instabilities in transonic flutter wind tunnel testing, fabricated with the AM technique for cost-effective manufacturing and extension of design freedom, and 2) its design and manufacturing methodology combining the AM technique and post machining treatments. As a proof-of-concept study, this paper mainly investigates the feasibility of a transonic flutter wing model fabricated by the proposed methodology based on the AM technique and post-processing, which realizes not only aerodynamic shapes but also designed elastic and modal characteristics, to evaluate typical transonic aeroelastic responses such as the LCO and the transonic dip. The geometrical accuracy of additively manufactured wing models is firstly accessed. Structural/aeroelastic characteristics of an additively manufactured wing model for wind tunnel testing are then evaluated numerically and experimentally. Finally, the aeroelastic characteristics of the fabricated flutter wing model are also investigated by performing a transonic flutter wind tunnel experiment. Through a series of evaluations, the feasibility and capability of such AM-based transonic flutter wing models for transonic wind tunnel testing are demonstrated.

Integrated flutter test of a horizontal-tail model in the large-scale continuous transonic wind tunnel

Wind tunnel test is a critical way to investigate flutter characteristics of aircraft, particularly in identifying the transonic dip phenomenon in the aeroelastic design. The continuous wind tunnel has advantages over the blow-down wind tunnel in long running time, wide bandwidth of dynamic pressure, and stable flow field. Thus, the continuous wind tunnel is more suitable for transonic flutter tests. Flutter test techniques are studied for FL-62 wind tunnel, the first large-scale continuous transonic wind tunnel in China. A protection system and a real-time signal processing are developed to ensure the safety and efficiency. Flutter boundaries of a horizontal-tail model are investigated in FL-62 wind tunnel in the Mach number regime between 0.65 and 0.98. In the test, structural vibrations are measured via strain gauges, deformations and pressure distributions are measured via non-contact optical techniques, and flutter boundaries are predicted via a modal identification method.

Three dimensional aeroelastic analyses considering free-play nonlinearity using computational fluid dynamics/computational structural dynamics coupling

Most of the previous studies on free-play aeroelasticity were based on the linear aerodynamic theory, which cannot consider the aerodynamic nonlinear effects. This paper proposes a framework of computational fluid dynamics/computational structural dynamics (CFD/CSD) coupling approach that can deal with the three dimensional aeroelastic problems with both the free-play nonlinearity and the aerodynamic nonlinearity. The fictitious mass method is used to construct the reduced structural equations of motion and the switching point is detected using the bisection method. The adaptive time step obtained by the bisection method is returned to the CFD solver so that both the structural and the fluid equations are integrated using the same time step. An all-movable wing with free-play at the root is considered for numerical studies. Results demonstrate the CFD/CSD coupling method can predict the stable limit cycle oscillation (LCO) effectively. The initial condition study shows that the LCO behavior is subcritical and the hysteresis response can be predicted in time domain effectively by the presented method. The viscous effect is shown to increase the LCO boundary and shift the LCO amplitude to a larger velocity in transonic regime. The LCO boundary is determined from subsonic to transonic Mach numbers. The transonic dip in LCO boundary is found by the CFD/CSD coupling method, but the equivalent linearization with doublet lattice method fails to predict this phenomenon. From the results of this study, the LCO boundary is shown to be 43.5% below the flutter boundary at most.

Transonic flutter characteristics of an airfoil with morphing devices

An investigation into transonic flutter characteristic of an airfoil conceived with the morphing leading and trailing edges has been carried out. Computational fluid dynamics (CFD) is used to calculate the unsteady aerodynamic force in transonic flow. An aerodynamic reduced order model (ROM) based on autoregressive model with exogenous input (ARX) is used in the numerical simulation. The flutter solution is determined by eigenvalue analysis at specific Mach number. The approach is validated by comparing the transonic flutter characteristics of the Isogai wing with relevant literatures before applied to a morphing airfoil. The study reveals that by employing the morphing trailing edge, the shock wave forms and shifts to the trailing edge at a lower Mach number, and aerodynamic force stabilization happens earlier. Meanwhile, the minimum flutter speed increases and transonic dip occurs at a lower Mach number. It is also noted that leading edge morphing has negligible effect on the appearance of the shock wave and transonic flutter. The mechanism of improving the transonic flutter characteristics by morphing technology is discussed by correlating shock wave location on airfoil surface, unsteady aerodynamics with flutter solution.

Study of Fast Prediction Method for Transonic Flutter Boundary Using Radial Basis Function

A spectral volume method for hybrid unstructured mesh developed earlier is built in an aeroelastic code to determine transonic flutter boundary of AGARD 445.6 wing. It is shown that the computed transonic dip of flutter boundary reasonably agrees with the experimental data. In the present study, we focus on to develop a fast numerical method for evaluating the bottom of transonic dip. In order to reduce the number of computational cases to determine the flutter boundary, an interpolation method using the radial basis function is examined. The initial sampling points are sparsely distributed over the entire parameter plane to roughly determine the flutter boundary by interpolating damping ratio of wing oscillation. Then, based on the consideration of load distribution over the wing, some additional sampling points are introduced in the region where the transonic dip likely appears. It is demonstrated that the present approach allows us to evaluate the bottom of transonic dip with less computational efforts for the present problem. Discussions are included to examine the possible efforts of the arrangement of initial sampling points and interpolation method on the shape of flutter boundary near the dip.

Flutter Boundary Prediction of a Two Dimensional Airfoil in Transonic Flight Regime with the Preset Angles of Attack

Angle of attack has impact on transonic flow filed and aerodynamic force, but most of current researches on flutter use zero angle hypothesis, which has no consideration about angle of attack. Therefore, we use unsteady Reynold Averaged Navier-Stokes (RANS) equation and structural dynamic equation to establish the time domain aeroelastic analysis method. The solution in time domain is the fourth-order implicit Adams linear multi-step method which is based on prediction-correction method. The numerical simulations were used to analyze the transonic flutter boundary of Isogai Case A Model which was based on zero angle condition and nonzero angle respectively. The simulation results show that the reduced flutter speed decreases as the preset angle of attack decreases between 0.73 and 0.76, which shows a 12.5% decrease of the flutter speed at the farthest. Nonzero angle makes the transonic dip weaker and wider than fully turbulent flow. Changing in angle of attack of 6°, the flutter speed in the deepest position of transonic dip has increased by 124% compared to the flutter speed of 0°. Therefore, when flutter characters of airfoil is analyzed, the effects of the initial angle of attack must be taken into account in order to analyze flutter boundary correctly. In other words, increasing the angle of attack offers a way to control the system in terms of delaying flutter.

Rapid Transonic Flutter Analysis for Aircraft Conceptual Design Applications

This study presents a new approach for the rapid transonic flutter analysis of large-aspect-ratio wings via a combination of time-linearized two-dimensional unsteady indicial functions and a database of steady two-dimensional Reynolds-averaged Navier–Stokes simulations. The approach is limited to large-aspect-ratio wings that can be discretized into multiple, streamwise, independent strips; and the well-documented “strip theory” with sweep corrections is applicable. This formulation allows the extension of Leishman’s indicial functions (“Validation of Approximate Indicial Aerodynamic Functions for Two-Dimensional Subsonic Flow,” Journal of Aircraft, Vol. 25, No. 10, 1988, pp. 914–922) to three-dimensional wings but also restricts the present method to attached flows. However, when supported with two-dimensional steady Reynolds-averaged Navier–Stokes simulations, the present method predicts flutter speeds that are within 10% of that predicted by two-dimensional time-accurate Reynolds-averaged Navier–Stokes simulations. Application of the proposed method for a large-aspect-ratio wing is validated by comparing the predicted flutter boundary against wind-tunnel experiments. More importantly, the current method predicts the transonic dip phenomena observed in the experiments but not predicted by NASTRAN analysis. This is achieved at several orders-of-magnitude lower computation time than high-fidelity time-accurate computational fluid dynamics simulations. The level of accuracy obtained at such an extremely low computation time makes the present approach very suitable for applications in conceptual design studies of large-aspect-ratio transonic vehicles.

Delayed detached Eddy simulation of wing flutter boundary using high order schemes

This paper conducts Delayed Detached Eddy Simulation (DDES) of a 3D transonic wing flutter using a fully coupled fluid/structure interaction (FSI) with high order shock capturing schemes. Unsteady 3D compressible Navier–Stokes equations are solved with a system of 5 decoupled structure modal equations in a fully coupled manner. The low diffusion E-CUSP scheme with a 5th order WENO reconstruction for the inviscid flux and a set of 2nd order central differencing for the viscous terms are used to accurately capture the shock wave/turbulent boundary layer interaction of the vibrating wing. The predicted flutter boundary at different free stream Mach numbers achieves very good agreement with experiment, including the supersonic flutter boundary point, which is often substantially over-predicted by most of the other simulations based on RANS models. Some new observations and explanation are given for the sonic dip mechanism. The transonic dip phenomenon is related to the anticlimax contribution of the second mode, which is caused by the complicated shock oscillation that decreases the wing pitching moment sharply. At the flutter boundary including the sonic dip, no flow separation due to shock/boundary layer interaction is observed.

Assessment and development of a ROM for linearized aeroelastic analyses of aerospace vehicles

In the present work, a reduced order model (ROM) for aeroelastic analysis linearized around non-linear steady solutions has been assessed and implemented to perform high-fidelity predictions, in particular for transonic flow. The ROM has been specifically adopted for identifying the unsteady aerodynamics by means of a modal-based approach. This goal has been achieved by performing a series of prescribed modal-transient boundary conditions on a Euler-based computational fluid-dynamics code and then post-processing the input/output data in the frequency domain. A fast and efficient morphing code based on the use of radial basis functions has been introduced at this phase of the procedure to reach a wide range of applicability for significant cases with complex geometries as in the case of aeronautical and space vehicles. Flutter boundaries have been investigated by capturing the so-called transonic dip phenomenon, mainly due to compressibility and evidenced in the literature also by wind tunnel tests. Comparisons of the present results with linear lower fidelity approaches, based on potential flows, have demonstrated the capabilities of the proposed ROM. Finally, in order to show the general-purpose applicability of the proposed approach, the method has been applied to the aeroelastic analysis of a launch vehicle. For this application no commercial codes for linear aeroelastic analysis are available for comparisons.

Coupled fluid structure analysis for wing 445.6 flutter using a fast dynamic mesh technology

ABSTRACTThe flow around wing 445.6 was modelled using Navier–Stokes equations and S-A model. The wing vibration and flow mesh deformation were computed using a fast dynamic mesh technology proposed by our own group. Wing 445.6 flutter was analysed through a strong coupling between the wing vibration and flow. The reduced flutter velocity was predicted and results are in good agreement with the experimental data. It is found that the subsonic flutter is mainly induced by the flow separation and the transonic and supersonic flutter are mainly caused by the oscillating shock wave and its induced flow separation. The positive aerodynamic work increases due to the oscillating shock wave when the subsonic flow becomes transonic reducing the flutter velocity. While the positive aerodynamic work induced by the oscillating shock wave decreases when the transonic flow becomes supersonic increasing the flutter velocity. That is why the transonic dip exists.

Influence of boundary layer transition on the flutter behavior of a supercritical airfoil

This paper presents a flutter analysis for the supercritical CAST 10-2 airfoil in a flow with free boundary layer transition based on CFD computations with the \(\gamma \)-\(\hbox {Re}_{\theta }\) transition model. The results are compared to fully turbulent results obtained with the SST \(k\)-\(\omega \) turbulence model. Unsteady RANS computations at \(\hbox {Re}_{\rm{c}} = 2 \times 10^{6}\) are used to determine the aerodynamic derivatives. These derivatives are required to identify the flutter boundary for a 2 degree-of-freedom model by a k method. The transonic flutter boundary decreases for a flow with free boundary layer transition compared to a fully turbulent flow in the vicinity of the transonic dip. However, the flutter boundary at subsonic Mach numbers is raised for a transitional flow. In addition, the transitional frequency response is discussed: an aerodynamic resonance in connection with an instability of the transition region is observed and the possibility of a 1 degree-of-freedom flutter for transitional flows is shown.

The transonic dip in aeroelastic divergence speed—An explicit formula

Using continuum models we develop a closed form analytical formula for the divergence speed as a function of the Mach number and in particular its dependence on wing camber. There is a transonic dip even when the angle of attack is zero and it depends on the wing thickness ratio. For nonzero camber the angle of attack in fact plays a lesser role. The main analytical tool is the Possio integral equation which is shown to have an explicit solution. Neither CFD nor FEM is employed.

小型超音速実験機全機フラッタ模型風洞試験について

Three wind tunnel tests for flutter have been conducted under the development of the National Experimental Airplane for Supersonic Transport (NEXST-1) of JAXA launched in 2005. Three kinds of flutter were investigated by using three different wind tunnel models at that time. Discussion of this paper is mostly on the one for a main wing model. The planform of the NEXST-1 wing is a cranked arrow having warp in the out of plane direction. For flutter, the model showed the so called transonic dip of which bottom speed was at Mach 1.02. It was also subjected to limit cycle oscillation (LCO) in the transonic regime. The flutter was dominantly the bending of the out board wing. In the design stage of the NEXST-1, a 20% reduction was anticipated for the transonic regime by the flutter analysis with the linear aerodynamic theory. The wind tunnel experiment resulted in 21% lower in the flutter speed that was slightly higher than the assumption. The NEXST-1 aircraft was launched in the piggy back style by the solid rocket booster. Therefore, the flutter was also investigated for this launching configuration. The flutter speed reduction in this case was 27%, which was larger than that for a sole airframe. As a consequence, the design methodology for transonic flutter is thought to be confirmed for supersonic flight vehicles.