Transonic Limit Cycle Oscillations Research Articles

Investigation of Shock Motion in Transonic Flow Using an Oscillating, Straked, Delta Wing

A computational analysis was performed on a straked, delta wing undergoing pitch motion in order to investigate the influence of shock-induced, trailing-edge separation (SITES) on simulated limit-cycle oscillations (LCO). The research presented herein describes an aeroelastic analysis of a wing oscillating in pitch using Euler-based aerodynamics with boundary-layer coupling (BLC). Results indicate that oscillatory shock movement occurs in response to the pitching motion of the wing, both with and without BLC. However, the BLC solution predicted more significant shock movement, and the inviscid solution predicted more aggressive shocks located further aft on the wing. Increasing the amplitude of the pitch oscillations resulted in a greater range of shock motion than lower amplitude cases, but variation of oscillation frequencies tested did not show any noteworthy differences. These findings support the theory that oscillatory shock movement associated with SITES can occur during certain cases of transonic LCO. In addition, based on the results from pure pitch motion of the wing and on the flow solver used, shock motion can occur without a boundary-layer model, although the modeling of viscous effects does affect the range of shock motion.

Nonlinear Reduced-Order Models for Transonic Aeroelastic and Aeroservoelastic Problems

Nonlinear reduced-order modeling approaches have been a promising tool for predicting the transonic aerodynamic and aeroelastic behaviors of aircraft structures. However, the accuracy of the approaches in predicting the transonic limit-cycle oscillations and aeroservoelastic behaviors needs to be further improved. For example, because of the complexity induced by the coupling among deflection of control surfaces, oscillating shock waves, structural vibration, and aerodynamic viscosity, it is difficult to adjust the system order and number of neurons of the Wiener-based reduced-order model. Moreover, the increasing of the system order may lead to overfitting. This paper presents a novel reduced-order aerodynamic modeling methodology based on the theory of nonlinear state-space identification. The accuracy of the method is demonstrated for predicting aerodynamic loads, limit-cycle oscillations, and frequency responses of aeroservoelastic systems at transonic flow conditions. Results are compared with full-order simulations solving the Reynolds-averaged Navier-Stokes equations.

Improved One-Shot Approach for Modeling Viscous Transonic Limit Cycle Oscillations

In this paper, the harmonic-balance-based One-shot method is presented for modeling limit cycle oscillations (LCO) of two-degree-of-freedom (2-DOF) pitch/plunge airfoils in viscous, transonic flow regimes. It is shown that using the original version of the One-shot approach for which the reduced velocity is prescribed as an input, only the stable LCO branch can be captured. A modification to the technique is proposed to extend its capability to capture the unstable LCO branch below the linear flutter point. In this new approach, the amplitude of pitching is prescribed instead of the reduced velocity. This necessitates simultaneously updating the reduced frequency and the reduced velocity at each aeroelastic iteration. The update procedure is based on optimization of a simple figure-of-merit. The original and improved versions of the One-shot approach are implemented in a single solver with minor modifications to attain maximum flexibility in determining LCO conditions. Numerical results demonstrate a good agreement with those reported in the literature as well as those obtained using the HB/LCO method and a traditional time-accurate approach. Finally, the computational efficiency of the One-shot method is discussed.

A harmonic balance method for nonlinear fluid structure interaction problems

Over the past decade the Harmonic-Balance technique has been established as a viable alternative to direct time integration methods to predict periodic aeroelastic instabilities. This article reports the progress made in using a frequency updating procedure, based on a coupled fluid-structural solver using the Harmonic-Balance formulation. In particular, this paper presents an efficient implicit time-integrator that accelerates the convergence of the structural equations of motion to the final solution. To demonstrate the proposed approached, the paper includes a detailed investigation of the impact of input parameters and exercises the method for two types of fluid-structural nonlinear instabilities: transonic limit-cycle oscillations and vortex-induced vibrations.

Transonic limit cycle oscillation behavior of an aeroelastic airfoil with free-play

The limit cycle oscillation (LCO) behaviors of an aeroelastic airfoil with free-play for different Mach numbers are studied. Euler equations are adopted to obtain the unsteady aerodynamic forces. Aerodynamic and structural describing functions are employed to deal with aerodynamic and structural nonlinearities, respectively. Then the flutter speed and flutter frequency are obtained by V-g method. The LCO solutions for the aeroelastic airfoil obtained by using dynamically linear aerodynamics agree well with those obtained directly by using nonlinear aerodynamics. Subsequently, the dynamically linear aerodynamics is assumed, and results show that the LCOs behave variously in different Mach number ranges. A subcritical bifurcation, consisting of both stable and unstable branches, is firstly observed in subsonic and high subsonic regime. Then in a narrow Mach number range, the unstable LCOs with small amplitudes turn to be stable ones dominated by the single degree of freedom flutter. Meanwhile, these LCOs can persist down to very low flutter speeds. When the Mach number is increased further, the stable branch turns back to be unstable. To address the reason of the stability variation for different Mach numbers at small amplitude LCOs, we find that the Mach number freeze phenomenon provides a physics-based explanation and the phase reversal of the aerodynamic forces will trigger the single degree of freedom flutter in the narrow Mach number range between the low and high Mach numbers of the chimney region. The high Mach number can be predicted by the freeze Mach number, and the low one can be estimated by the Mach number at which the aerodynamic center of the airfoil lies near its elastic axis. Influence of angle of attack and viscous effects on the LCO behavior is also discussed.

Prediction of Transonic Limit-Cycle Oscillations Using an Aeroelastic Harmonic Balance Method

This work proposes a novel approach to compute transonic limit-cycle oscillations using high-fidelity analysis. Computational-Fluid-Dynamics based harmonic balance methods have proven to be efficient tools to predict periodic phenomena. This paper’s contribution is to present a new methodology to determine the unknown frequency of oscillations, enabling harmonic balance methods to accurately capture limit-cycle oscillations; this is achieved by defining a frequency-updating procedure based on a coupled computational-fluid-dynamics/computational-structural-dynamics harmonic balance formulation to find the limit-cycle oscillation condition. A pitch/plunge airfoil and delta wing aerodynamic and respective linear structural models are used to validate the new method against conventional time-domain simulations. Results show consistent agreement between the proposed and time-marching methods for both limit-cycle oscillation amplitude and frequency while producing at least a one-order-of-magnitude reduction in computational time.

Transonic Limit Cycle Oscillation Analysis Using Aerodynamic Describing Functions and Superposition Principle

Limit cycle oscillation for an airfoil in transonic air flow considering aerodynamic nonlinearity is studied. Transonic nonlinear aerodynamic forces are calculated by solving Euler equations or Navier–Stokes equations with respect to harmonic airfoil plunging/pitching motion, and then the aerodynamic describing functions and the superposition principle are used to build an equivalent linearized aerodynamic model in the frequency domain; hence, the transonic limit cycle oscillation solutions can be obtained by the frequency domain flutter analysis method. The procedures for building the aerodynamic describing function and obtaining the limit cycle oscillation solution are described in detail. Four examples are adopted to verify the accuracy of the present method. The Isogai wing model with NACA 64A010 airfoil is used as the first example to verify the accuracy of the transonic linear flutter solution of the present method. Another NACA 64A010 airfoil model with different structural parameters is then adopted to study its transonic limit cycle oscillation characteristics considering only aerodynamic nonlinearity, and the NACA 0012 airfoil model with both aerodynamic and structural nonlinearities is investigated for its transonic limit cycle oscillation properties. The NLR 7301 airfoil is studied for its limit cycle oscillation characteristics in inviscid and viscous transonic flows, respectively. The results obtained by the present method are in good agreement with those obtained by the existing research with the harmonic balance method and time-marching method. The limitations of the present method are also discussed.

Nonlinear Aerodynamic Effects on Transonic Flap Buzz, Tail Flutter and Limit-Cycle Oscillations of Two-Dimensional Wing-Flap-Tail Configurations

ABSTRACTThe transonic tail flutter and flap buzz under the wing-flap-tail configurations are analyzed utilizing a dynamic grid capability of unstructured Euler solver coupled with an appropriate aeroelastic solver. From the results, the presence of a forewing, either stationary or oscillating, has significant effect on the tail flutter characteristics. In particular, the tail motion may be in resonance with the oscillating wing before the onset of flutter, which is dangerous to the tail structure because of the large amplitude oscillations. Besides, a complicated aerodynamic and aeroelastic interference of the tail have been found due to the unsteady disturbance which is a strong variability of flow structure induced by the buzz of the flap. In the high transonic flow regime, the flap buzz with limit-cycle oscillations does occur, and the influence induced by the tail is not important. The increasing restoring force at the pivot where the flap joints with the wing will reduce the flap oscillations that improves the effect of the flap buzz.

Transport Wing Flutter Model Transonic Limit Cycle Oscillation Test

The model for aeroelastic validation research involving computation semispan wind-tunnel model, a transport wing-fuselage flutter model, was tested in NASA Langley's Transonic Dynamics Tunnel with the goal of obtaining experimental limit cycle oscillation behavior data at transonic separation onset conditions. This research model is notable for its inexpensive construction and instrumentation installation procedures. Unsteady pressures and wing responses were obtained for three wing-tip configurations: clean, tip store, and winglet. Traditional flutter boundaries were measured over the range of M = 0.6-0.9, and maps of limit cycle oscillation behavior were made in the range of M = 0.85-0.95. The effects of dynamic pressure and angle of attack were measured. Testing in both R134a heavy gas and air provided unique data on the Reynolds number, transition effects, and the effect of speed of sound on limit cycle oscillation behavior. This report gives an overview of the test results, including experimental flutter boundaries, and the conditions involving shock-induced transonic flow separation onset at low wing angles, including maps of limit cycle oscillation behavior.

Aeroelastic system identification using transonic CFD data for a wing/store configuration

This paper is part of a study investigating the prediction of the aeroelastic behaviour of aircraft subjected to non-linear aerodynamic forces. The main objective of the work is the characterization of the dynamic response of aeroelastic models resulting from coupled Computational Fluid Dynamic and Finite Element calculations. Of interest here is the identification of the flight condition at which the response bifurcates to limited or divergent amplitude self-sustained oscillations without carrying out a comprehensive set of full, computationally expensive, time-marching calculations. The model treated in this work is a three-dimensional wing in a transonic flowfield. Short datasets of pre-bifurcation behaviour are analysed to determine the system's stability and degree of non-linearity. It is found that the calculated responses on the run-up to a transonic Limit Cycle Oscillation show little or no evidence of non-linearity. The non-linearity appears abruptly at the bifurcation flight condition. The variation of the local Mach number over the wing's surface in the steady-state case is used to demonstrate that the non-linearity is due to a shock wave that can move along the surface. At Mach numbers where this is not possible the system behaves in a linear manner and its stability can be analysed using linear methods.

Transonic limit cycle oscillation analysis using reduced order aerodynamic models

Limit cycle oscillations have been observed in flight operations of modern aircraft, wind tunnel experiments and mathematical models. Both fluid and structural nonlinearities are thought to contribute to these phenomena. With recent advances in reduced order aerodynamic modeling, it is now feasible to analyze limit cycle oscillations that may occur in transonic flow including the effects of structural and fluid nonlinearities. In this paper an airfoil with control surface freeplay (a common structural nonlinearity) is used to investigate transonic flutter and limit cycle oscillations. The reduced order aerodynamic model used in this paper assumes the shock motion is small and in proportion to the structural motions.

Reduced-Order Modeling of an Elastic Panel in Transonic Flow

Reduced-order modeling is applied to a transonic aeroelastic panel that experiences oscillatory motions of a normal shock. Two-dimensional, transonic inviscid flow over an elastic panel produces transonic limit-cycle oscillations over a range of panel parameters. Proper orthogonal decomposition, in concert with domain decomposition, is shown to produce an accurate reduced-order model for the coupled aeroelastic system. Panel flutter in the transonic regime results in a large streamwise movement of a transonic normal shock across the panel surface. The accuracy and order reduction of the reduced-order model is quantified. In addition, the computational savings for this implementation is documented, and the robustness of the reduced-order model to changes in a panel parameter is explored.

Numerical investigation of transonic limit cycle oscillations of a two-dimensional supercritical wing

CFD-based aeroelastic computations are performed to investigate the effect of nonlinear aerodynamics on transonic limit cycle oscillation (LCO) characteristics of the NLR7301 airfoil section. It is found that the LCO solutions from Navier–Stokes computations deviate less from the experiment than an Euler solution but strongly depend on the employed turbulence model. The Degani–Schiff modification to the Baldwin–Lomax turbulence model provokes spurious vorticity spots causing multiple shocks which might be unphysical, while the Spalart–Allmaras turbulence model yields physically reasonable unsteady shocks. In the cases examined, smaller initial perturbations lead to larger LCO amplitudes and vice versa, in contradiction to what one might expect. The amplitude of the initial perturbation is also found to have an impact on the mean position of LCO. Also addressed in the paper are aspects of multiblock message passing interface (MPI) parallel computation techniques as related to the present problem.

Nonlinear inviscid aerodynamic effects on transonic divergence, flutter, and limit-cycle oscillations

Nonlinear inviscid aerodynamic effects on transonic divergence, flutter, and limit-cycle oscillations

Experimental and analytical investigation of transonic limit-cycle oscillations of a flaperon

Forced oscillation testing of a control surface on a rigid model is conducted in a transonic tunnel to identify the possibility of limit-cycle oscillations (LCO) induced by aerodynamic sources. Identification is possible through an energy concept by observing the direction of hysteresis loop in the test data. Two flow devices have also been tested and their effectiveness in eliminating the LCQ examined. In addition, test data of hinge moment response in forced oscillation at various frequencies are analyzed through Fourier functional analysis to result in a generalized forcing function in an indicial form. The latter is used in the structural equation of motion for the control surface deflection angle. The resulting nonlinear equation is integrated by Hamming's predictor-corrector method to investigate the effect of structural freeplay. It is demonstrated that if the curves of hinge moment response vs deflection angle in dynamic testing exhibit triple hysteresis, LCO is possible. However, whether the latter actually occurs depends on the initial excitation. Structural freeplay is shown to induce LCO at M = 0.97 for the model tested.