Investigation of Chaotic Flutter Induced by Shock-Boundary-Layer Interactions

Schemmel A., Palakurthy S., Zope A., Collins E., Bhushan S.

Recent trends in aeroelastic analysis have shown a great interest in understanding the role of shock boundary layer interaction in predicting the dynamic instability of aircraft structural components at supersonic and hypersonic flows. The analysis of such complex dynamics requires a time-accurate fluid-structure interaction solver. This study focuses on the development of such a solver by coupling a finite-volume Navier-Stokes solver for fluid flow with a finite-element solver for structural dynamics. The coupled solver is then verified for the prediction of several panel instability cases in 2D and 3D uniform flows and in the presence of an impinging shock for a range of subsonic and supersonic Mach numbers, dynamic pressures, and shock strengths. The panel deflections and limit cycle oscillation amplitudes, frequencies, and bifurcation point predictions were compared within 10% of the benchmark results; thus, the solver was deemed verified. Future studies will focus on extending the solver to 3D turbulent flows and applying the solver to study the effect of turbulent load fluctuations and shock boundary layer interactions on the fluid-structure coupling and structural dynamics of 2D panels.

Dowell E.H.

Antimirova E., Jung J., Zhang Z., Machuca A., Gu G.

Abstract Aeroelastic flutter is a dynamically complex phenomenon that has adverse and unstable effects on elastic structures. It is crucial to better predict the phenomenon of flutter within the scope of aircraft structures to improve upon the design of their wings. This review aims to establish fundamental guidelines for flutter analysis across subsonic, transonic, supersonic, and hypersonic flow regimes providing a thorough overview of established analytic, numerical, and reduced-order models as applicable to each flow regime. The review will shed light on the limitations and missing components within the previous literature on these flow regimes by highlighting the challenges involved in simulating flutter. Additionally, popular methods that employ the aforementioned analyses for optimizing wing structures under the effects of flutter, a subject currently garnering significant research attention, are also discussed. Our discussion offers new perspectives that encourages collaborative effort in the area of computational methods for flutter prediction and optimization.

Palakurthy S., Zope A., Yan Y., Collins E., Bhushan S.

The loading generated by shock wave boundary layer interaction (SBLI) plays a crucial role in the structural design of a high-speed vehicle. They can cause flow separation near the shock impingement, resulting in the onset of chaotic, self-sustained flutter leading to structural failure. This work investigates how a micro-ramp installed upstream of a flexible panel affects its flutter behavior. For this purpose, two-way coupled laminar fluid–structure interaction simulations are performed for two different oblique shock strengths impinging over a flexible panel. A comprehensive study with a micro-ramp, as high as half the boundary layer thickness, is conducted for a wide range of non-dimensional dynamic pressures expected for a supersonic flight. The study provides analysis methodology to characterize the nature of panel oscillations, and the influence of micro-ramp on fluid and structural unsteadiness is evaluated. The results indicate that the chaotic flutter is initiated because of the non-linear interaction between the high-frequency fluid and low-frequency structural unsteadiness. Micro vortices delay the onset of the chaotic flutter by lowering the fluid frequency, thereby synchronizing fluid and structure unsteadiness. The micro vortices also decreased flutter frequency for lower shock strength; however, MVG was somewhat ineffective for some higher shock strength. For the latter taller micro-ramps that can introduce stronger, low-frequency vortices are recommended.

Panchal J., Benaroya H.

In the last few decades, there has been an increasing interest in the field of nonlinear aeroelasticity. With substantial improvements in computing capabilities, the control surface freeplay problem is now being reinvestigated by many researchers with the goal of developing more advanced and accurate analytical models. Modern theoretical and experimental analyses of freeplay are opening many new avenues of studies within aeroelasticity. While the fundamental problem is believed to be understood and numerous modeling approaches exist, freeplay research continues to yield different numerical predictions of the aeroelastic dynamical behavior and its associated properties. This paper reviews the recent literature on this topic, showing many variabilities in the parameters that define freeplay and its aeroelastic response, with the majority of the existing models being developed deterministically. The research is categorized into the major subtopics that define the freeplay problem, observing that the phenomena has characteristics of nonlinear dynamics.

Chai Y., Gao W., Ankay B., Li F., Zhang C.

Flutter is a self-excited vibration under the interaction of the inertial force, aerodynamic force, and elastic force of the structure. After the flutter occurs, the aircraft structures will exhibit limit cycle oscillation, which will cause catastrophic accidents or fatigue damage to the structures. Therefore, it is of great theoretical and practical significance to study the aeroelastic characteristics and flutter control for improving the aeroelastic stability of aircraft structures. This paper reviews the recent advances in aeroelastic analysis and flutter control of wings and panel structures. The mechanism of aeroelastic flutter of wings and panels is presented. The research methods of aeroelastic flutter for different structures developed in recent years are briefly summarized. Various control strategies including the linear and nonlinear control algorithms as well as the active flutter control results of wings and panels are presented. Finally, the paper ends with conclusions, which highlight challenges of the development in aeroelastic analysis and flutter control, and provide a brief outlook on the future investigations. This study aims to present a comprehensive understanding of aeroelastic analysis and flutter control. It can also provide guidance on the design of new wings and panel structures for improving their aeroelastic stability.

Boyer N.R., McNamara J.J., Gaitonde D.V., Barnes C.J., Visbal M.R.

The compounding effects of panel flutter and oblique shock impingement are of great concern to the development of light-weight, high-speed vehicles. Shock-induced panel flutter response is investigated at M = 2 and R e = 120 , 000 using the Navier–Stokes equations closely coupled to the von-Kármán equations. A naturally occurring laminar inflow boundary layer and incident oblique shockwave are specified through the boundary conditions. The shockwave impinges at the midpoint of a flexible panel. Several incident shock strengths and non-dimensional dynamic pressures are examined. The resulting fluid–structure interaction is significant and is described in detail. In general, the incident shockwaves lead to higher frequency, higher mode flutter when compared to the configuration without an impinging shockwave or with an impinging shockwave in inviscid flow . Additionally, the presence of a compliant surface is shown to promote turbulent transition downstream of the shock boundary layer interaction.

Zope A., Horner C., Collins E.M., Bhushan S., Bhatia M.

Mascolo I.

Dynamic instability in the mechanics of elastic structures is a fascinating topic, with many issues still unsettled. Accordingly, there is a wealth of literature examining the problems from different perspectives (analytical, numerical, experimental etc.), and coverings a wide variety of topics (bifurcations, chaos, strange attractors, imperfection sensitivity, tailor-ability, parametric resonance, conservative or non-conservative systems, linear or nonlinear systems, fluid-solid interaction, follower forces etc.). This paper provides a survey of selected topics of current research interest. It aims to collate the key recent developments and international trends, as well as describe any possible future challenges. A paradigmatic example of Ziegler's paradox on the destabilizing effect of small damping is also included.

Li Y., Luo H., Chen X., Xu J.

Panel flutter in the presence of oblique shock waves and the associated shock wave/boundary-layer interaction have been identified as one of typical phenomena in the design and optimization of air-breathing, high-speed flight vehicles. The current study investigates this phenomenon using a previously considered two-dimensional model where an elastic panel with both ends pinned is impinged at the mid-point by an oblique shock wave with specified strength. An in-house code was used to solve the Euler or the full viscous compressible Navier–Stokes equation and nonlinear structural dynamics of the panel, where the conventional serial staggered algorithm was adopted for the fluid–structure interaction. As compared with previous studies of this topic, we focus on the effect of surface velocity feedback (i.e., using boundary blowing and suction for flow control), as well as the effect of the upstream boundary layer thickness, on the panel’s dynamic behavior, surface pressure distribution , and boundary-layer separation. The results show that for inviscid flow , boundary control with feedback gain above one can suppress the panel vibration; however, this effect is not clear for viscous flow , where feedback gain below one has some effect on attenuation of vibration. Further study shows that the panel velocity based control introduces a phase shift for the pressure in the inviscid flow as a damping effect , but the effect is not as strong in the viscous flow. Finally, the boundary layer thickness has a non-monotonic effect on the panel flutter and flow separation. At intermediate thicknesses considered here, the panel flutter is reduced and separation becomes less oscillatory. • Shock-induced vibration of a panel is studied in both inviscid and viscous flows. • A simple flow control strategy based on the surface velocity feedback is studied. • The feedback control can suppress the panel flutter for inviscid flow. • The feedback control has limited attenuation in the presence of boundary layer. • Intermediate boundary layer thickness also reduces panel flutter.

Brouwer K.R., McNamara J.J.

This study assesses the robustness and efficiency of the enriched piston theory approach for modeling aeroelastic loads in the presence of impinging shocks. Both stationary and oscillating shock im...

Boyer N.R., McNamara J.J., Gaitonde D.V., Barnes C.J., Visbal M.R.

Oblique shockwaves may impinge on supersonic vehicles internally in an engine or externally on the outer mold line. They create a severe loading environment and may induce dynamic instabilities such as panel flutter. This study computationally explores the effect of shock-induced panel flutter response in 3D, inviscid, Mach 2 flow. Flutter behavior of a square panel is compared across several incident shock angles and inflow dynamic pressures. The presence of an impinging shockwave is found to produce panel flutter that is characteristically different than the shock-free condition. The response contains significantly larger local pressure gradients, larger spanwise variations, and higher-order modal activity in the panel. Results are also compared to two-dimensional inviscid flow over an infinite-span panel. The 3D centerline is found to compare closely with 2D simulations. However, away from the centerline, 3D effects have a significant influence on the solution. In general, stronger oblique shockwaves raise flutter amplitude and frequency, while weaker shockwaves stabilize the panel response. These latter findings indicate important considerations for both structural lifing and flow control applications.

Bhatia M., Beran P.

A methodology is presented for prediction of dynamic instabilities arising from fluid–structure coupling. The inviscid compressible Euler equations are linearized about a steady-state solution and ...

Ganji H.F., Dowell E.H.

Piston theory may be used in the high Mach number supersonic flow region and/or in very high frequency subsonic or supersonic flow. In this flow model, the pressure at a point on the fluid-solid interface only depends on the downwash at the same point. However the classical piston theory may not be sufficient for some phenomena in aeroelasticity and aeroacoustics (far field prediction). Dowell and Bliss have created an extension of piston theory that allows for higher order effects that take into account the effect the distribution of downwash on pressure at any point. For simple harmonic motion, expansions in reduced frequency, inverse reduced frequency and/or inverse (square of) Mach number have all been created; The effects of higher order terms in these several expansion in creating an enhanced piston theory was illustrated for plunge and pitch motion of an airfoil (discrete system) by Ganji and Dowell. In the present paper, flutter prediction for a flexible panel in two –dimensional flow is investigated using enhanced piston theory. The goal of the present paper is to demonstrate that an enhance version of piston theory can analyze single degree of freedom flutter of a panel as compared to the classical piston theory and quasi-steady aerodynamic models which can only treat coupled mode flutter.

Ma R., Chang X., Zhang L., He X., Li M.

When using the dynamic mesh method to deal with moving boundary problems, the Geometric Conservation Law (GCL) must be considered carefully. This paper reviews the study on GCL problem of dynamic grid in finite volume framework based on Arbitrary Lagrangian-Eulerian (ALE) methods. Several common approaches to satisfy discretized geometric conservation law (DGCL) are studied and simplified to a uniform form. The uniform flow and the isentropic vortex are tested to validate the geometric conservation property and the temporal-accuracy. Numerical results illustrate that although the violating of GCL does not pollute the original time-accuracy of numerical schemes for the governing equations, it may introduce extra artificial errors. When the “Adding Source Term” methods are adopted, the temporal accuracy order of face velocity scheme must match the temporal accuracy order of numerical schemes for the governing equations, otherwise it will pollute the original temporal accuracy.