E.H. Dowell

Duke University | DU · Department of Mechanical Engineering and Materials Science (MEMS)

A nonlinear aeroelastic model for a flexible panel is expanded to consider the effect of the viscous boundary layer using a RANS solver. This study presents the use of a Reduced Order Model (ROM) to compute the generalized aerodynamic force from a CFD simulation and compares the results obtained using the same approach with an inviscid solver and t...

Fluid–structure interaction of an elastic plate with piezoelectric elements, turbulent freestream flow at Mach 2.5, and a pressurized cavity is investigated computationally and correlated with a recent experiment. The pressure field on the plate is measured using pressure-sensitive paint, and the structural response is observed using the measured v...

The asymmetric instability in two streamwise orthogonal planes for three-dimensional flow-induced vibration (FIV) of an elastically mounted cube at a moderate Reynolds number of 300 is numerically investigated in this paper. The full-order computational fluid dynamics method, data-driven stability analysis via the eigensystem realization algorithm...

A nonlinear aeroelastic model for a flexible panel is extended to consider the Euler equation as the aerodynamic model. A highly efficient method is presented to compute the generalized aerodynamic forces from a CFD simulation, and the results are compared to those results previously obtained using full potential flow aerodynamics and the linear pi...

The concept of local shock strength and a quantitative measure index str of local shock strength are proposed, derived from the oblique shock relation and the monotonic relationship between total pressure loss ratio and normal Mach number. Utilizing the high density gradient characteristic of shock waves and the oblique shock relation, a post-proce...

The flow dynamics and aeroacoustics propagation for flow-induced vibration system consisting of three-dimensional flow past an elastically-mounted square cylinder are investigated using the Ffowcs Williams-Hawkings (FW-H) method and detached eddy simulation (DES) model for the first time. Previous experimental and numerical data are compared with t...

The aeroelastic responses and nonlinear behaviors of a two-dimensional panel impinged by an oscillating Mach stem shock are investigated through theoretical analysis. Through the nonlinear descriptors, such as Poincaré maps and Largest Lyapunov exponents, the panel with oscillating shock impingement is found to exhibit multiple responses, including...

In this study, a novel dynamically linearized Euler time-domain approach is used to compute the generalized aerodynamic force from a CFD simulation. The aerodynamic forcing term is implemented in a theoretical/computational nonlinear aeroelastic model to assess the dynamic response of a flexible clamped-clamped panel considering the pressure profil...

In this paper, we present novel identification strategies to develop a unified framework for vortex-induced vibration (VIV) prediction based on the general semi-empirical wake oscillator. Greybox nonlinear system identification method accompanying high-fidelity computational fluid dynamics (CFD) and/or experimental data could be applied for the ide...

The application of a nonlinear aeroelastic model for a flexible panel is expanded to consider the Euler equation as the aerodynamic model. This study presents the method to compute the generalized aerodynamic force from a CFD simulation and compares the results previously obtained using Full Potential Flow Aerodynamics and the Linear Piston Theory....

The unsteady pressure distribution over a NACA 0012 airfoil is measured in a low-speed wind tunnel for a rigid airfoil and control surface configuration. The experimental protocol is to give a step change in the airfoil angle of attack and the control surface deflection angle to capture the time history of the flow given this excitation. The data i...

Wall-modeled large eddy simulation (WMLES) and a theoretical-computational aeroelastic solver are used to predict the motion of a thin flexible panel under an impinging shock wave. Panel displacements imposed by the resulting shock-wave/boundary-layer interactions are compared to measured displacements from an experiment at matching conditions. The...

The potential aerodynamic theory is implemented to model the flow over a flexible panel. The present study compares the more complete unsteady version of the potential flow theory with its simplification known as the linear piston theory for different Mach numbers and the two- and three-dimensional aerodynamic models. The piston theory is “local” i...

Supersonic wind tunnel test data is compared with a nonlinear aeroelastic computational model, considering a freestream flow with Mach nearly 2, coupled cavity, and no-shock impingement. The measurements include Limit Cycle Oscillations (LCO) for the given set of flow and structural parameters. The effect of a static pressure differential, temperat...

The critical effect of the windward interior angles of elastically mounted trapezoidal bodies on a galloping instability is numerically investigated in this paper using two methodologies of high-fidelity computational fluid dynamics simulations and data-driven stability analysis using the eigensystem realization algorithm. A micro exploration of th...

The difference between solarelastic interaction and aeroelastic interaction is illustrated from the perspective of external forces. Membrane solarelastic responses of the solar cell and solar sail are studied through a wave model and a corpuscular model of light, respectively, where the light intensity and phase are considered in the wave model to...

This work deals with the fundamentally similar dynamic behavior of two apparently different aircraft systems, namely, landing gears and all-movable control surfaces. Both systems typically contain stiffness and damping nonlinearities, leading to shimmy/flutter limit cycle oscillations (LCOs). In a series of earlier papers the authors have developed...

Control surfaces nonlinearities can lead to limit cycle oscillations (LCO). Several methods have been proposed to predict LCO, such as Harmonic Balance-based methods (HB). Describing function (DF) is the HB with a single harmonic motion assumed, and the approach can be combined with a classic eigenvalue stability analysis via the Equivalent Lineari...

The fundamental mechanisms that are important for the triggering of galloping in a flow-induced vibration (FIV) system consisting of the flow past an elastically-mounted body (D-section, isosceles-triangular, rectangular) is investigated in this paper using three key-enabling methodologies: namely, high-fidelity full-order model/computational fluid...

This study applies computational fluid dynamics (CFD) to transonic buffet, a flow field instability characterized by an oscillating shock on the upper surface of an airfoil in transonic flow. Despite years of research in this area, understanding of the underlying physical mechanisms driving buffet remains incomplete. This study expands on prior com...

The Potential Aerodynamic Theory is implemented to model the flow over a flexible panel. The present study compares the more complete unsteady version of the potential flow theory with its simplification known as the Linear Piston Theory for different Mach numbers and the two- and three-dimensional aerodynamic models. Piston Theory is "local" in sp...

The main objective of the present study is to identify the best structural model for both aeroelastic and structural analysis of unswept rectangular wings with aspect ratios between 2 to 5. The paper presents a detailed study of the similarities and differences between the classical beam and plate theories, which provides new insight into this clas...

In this paper, we present a novel data-driven theory for the stability analysis of a flow-induced vibration (FIV) system consisting of an elastically mounted circular cylinder submerged in three-dimensional (3D) spanwise shear inflow at a subcritical Reynolds number. The presented data-driven theory separates the cylinder into several elements alon...

The aeroelastic response of a plate with supersonic freestream flow on one side and a shallow cavity on the other to turbulent pressure fluctuations is investigated computationally and experimentally. An empirical model is developed for the pressure fluctuations in a turbulent boundary layer that accounts for spatial and spectral variations in the...

A methodology for leveraging a combination of linear (through convolution integrals) and nonlinear (through Volterra series) reduced-order modeling (ROM) development was demonstrated on both a two- and three-degree-of-freedom (2-DOF and 3-DOF, respectively) aeroelastic system. The linear/nonlinear ROM approach was demonstrated against previous work...

Recent efforts have shown machine learning to be useful for the prediction of nonlinear fluid dynamics. Predictive accuracy is often a central motivation for employing neural networks, but the pattern recognition central to the network function is equally valuable for purposes of enhancing our dynamical insight into confounding dynamics. In this pa...

View Video Presentation: https://doi.org/10.2514/6.2022-3869.vid Presented is a point collocation non-intrusive polynomial chaos approach for nonlinear aeroelastic uncertainty quantification analysis. A unique aspect of our approach is that we are using a nonlinear frequency-domain harmonic balance aeroelastic solution methodology, which allows us...

This paper presents a review and assessment of more than six decades of research in aeroelastic stability, including control-surface nonlinearities. The work covers free play, friction, cubic stiffness, and an actuator in a failure mode. The basic modeling of each nonlinearity is introduced to provide insights for those new in this field. A detaile...

View Video Presentation: https://doi.org/10.2514/6.2022-0991.vid A methodology for leveraging a combination of linear (through convolution integrals) and nonlinear (through Volterra series) reduced-order modeling (ROM) development was demonstrated on both a 2 and 3 degree of freedom (DOF) aeroelastic system. The linear/non-linear ROM approach was d...

Several examples of experimental model designs, wind tunnel tests and correlation with new theory are presented in this chapter. The goal is not only to evaluate a new theory, new computational method or new aeroelastic phonomenon, but also to provide new insights into nonlinear aeroelastic phenomena, flutter, limit cycle oscillation (LCO), gust re...

The basics of static aeroelasticty, in contrast to dynamic aeroelasticity, are reviewed and some classic subjects such as divergence and control surface reversal are treated. The discussion starts with simple mathematical and physical models and progresses to more complex models and solution methods. Most of these models and methods prove to be use...

Modeling of aerodynamic forces has now moved beyond the classical potential flow theory at least in the research community and to some degree in engineering practice. These more sophisticated fluid models are based upon the Euler or Navier- Stokes equations and require substantial computer resources. This has led to the search for reduced order mod...

This is a brief account of the basic elements underlying experiments in Aeroelasticity.

Hypersonic flight is a major technical challenge and substantial efforts are currently underway to provide the understanding and technology required to design and operate effectively and safely a hypersonic aircraft for commercial or military purposes. Leyva [1] has recently described the essence of this challenge. The present chapter provides a su...

The classical theory for unsteady potential flow models in the supersonic, Subsonic and transonic mach number ranges is presented including representative computational methods and results. The discussion with the simplest case of super- sonic flow in two dimensions and then proceeds to consider the generalization to three dimensional flow, then su...

Dynamic aeroelasticty is considered and the dynamic stability (Flutter) of linear aeroelastic systems is considered as well as the response to external disturbances including atmospheric turbulence (Gusts). The discussion proceeds from simpler physical models and mathematical methods to more complex ones. An introduction to the modeling of aerodyna...

This is an introduction and overview of the work that has been done in nonlinear aeroelasticity prior to the last decade. Many of the issues discussed here are still under active investigation. Of particular interest are the limit cycle oscillations that may occur once the dynamic stability (flutter) boundary has been exceeded.

This brings the discussion of nonlinear aeroelasticity up to date. See the earlier discussion in Chap. 11. Much of the recent advances are based on new understanding of such subjects as limit cycle oscillations due to structural non-linearities, including freeplay, and fluid nonlinearities associated with unsteady separated flow including self exci...

A combined approach of linear convolution and higher-order Volterra series (VS) to reduced-order modeling of unsteady transonic aerodynamic loads is presented. Our framework offers a simple method to determine the memory depth of the system, clearly separates the linear and the nonlinear (NL) contributions, and significantly reduces the effort requ...

View Video Presentation: https://doi.org/10.2514/6.2021-3048.vid We have recently developed an automatic differentiation based nonlinear reduced-order modeling technique. The method is based on a Taylor series expansion of a nonlinear frequency- domain harmonic balance based computational fluid dynamic solver residual. In this work, we expand the m...

The large deflections of cantilevered beams and plates are modeled and discussed. Traditional non-linear elastic models (e.g., that of von Karman) employ elastic restoring forces based on the effect of stretching on bending, and these are less applicable to cantilevers. Recent experimental work indicates that elastic cantilevers are subject to nonl...

A recent structural model of a plate is extended to include a nonuniform temperature differential that varies in time using a modal expansion. The nonlinear structural plate model with first-order piston theory aerodynamics and cavity dynamics is coupled with the heat equation to form a single system of dynamical equations for the fluid-structural-...

It is well known that the nonlinear response of a beam or plate is sensitive to the assumptions made about the in-plane boundary constraints. This is true for any static or dynamic loading, and especially for aerodynamic loads that may lead to a dynamic instability and limit cycle oscillations. In the present paper, a mathematical and computational...

Presented is an automatic differentiation based nonlinear reduced-order modeling technique which includes geometric variation computation capability. The method is based on a Taylor series expansion of a nonlinear frequency-domain harmonic balance based computational fluid dynamic solver residual. In our original development of the methodology, the...

Experiments were conducted to study the fluid-thermal-structural interactions of a compliant panel exposed to ramp-induced shock-wave/boundary-layer interactions (SWBLIs) at Mach 6 for laminar and transitional incoming boundary-layers. For some cases, boundary-layer trips were introduced to generate a turbulent boundary layer over half of the inter...

A fundamental limitation of fluid flow reduced-order models (ROMs) which utilize the proper orthogonal decomposition is that there is little capability to determine one’s confidence in the fidelity of the ROM a priori. One reason why fluid ROMs are plagued by this issue is that nonlinear fluid flows are fundamentally multi-scale, often chaotic dyna...

Computational cost and model accuracy are central concerns when modeling nonlinear fluid flows. A conventional method of formulating a Galerkin fluid flow reduced-order model (ROM) is to decompose the velocity field into a mean component and a fluctuating component. When an empirical modal basis construction method like the proper orthogonal decomp...

An analytical and computational investigation of the effect of control surface freeplay on aeroelastic behavior, including random gust response and limit cycle oscillations (LCO), is presented. An efficient method to compute the total gust+LCO response is developed using random input describing functions (RIDF), in a manner analogous to harmonic in...

Modern computational fluid dynamic simulations of flows about naval vessels produce an enormous amount of flow-field data. The computations are performed in order to model details of the erratic unsteady flows that can occur about naval superstructures. The flow-field data can then be used in flight simulators for naval pilot training purposes. Oft...

This paper presents a study of the shock buffet phenomenon on the RA16SC1 supercritical airfoil using the proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) modal approaches. The computational fluid dynamics simulation is validated, and the full buffet envelope of the RA16SC1 airfoil is mapped. POD and DMD techniques are the...

Presented is a discrete adjoint approach for computing nonlinear unsteady aeroelastic geometric design sensitivities, which can subsequently be used for nonlinear unsteady aeroelastic geometric design optimization. The methodology is applicable to compressible Reynolds-averaged Navier–Stokes computational-fluid-dynamics solvers and is based on a ha...

Linear and nonlinear aeroelastic analyses and results for a cantilevered beam subjected to an unsteady subsonic airflow are presented as a model of a high aspect ratio wing. A third-order nonlinear beam model is used as the structural model. This model includes nonlinear inertial and damping terms as well as nonlinear stiffness terms. To model aero...

The presence of a static preload can significantly alter the limit cycle oscillation response of nonlinear aeroelastic systems. This paper reports a numerical study of two distinct types of preload, mechanical (i.e., independent of flow velocity) and aerodynamic (i.e., dependent on flow velocity), and their effects on limit cycle behavior. Simulati...

Freeplay is a significant source of nonlinearity in aeroelastic systems and is strictly regulated by airworthiness authorities. It splits the phase plane of such systems into three piecewise linear subdomains. Depending on the location of the freeplay, limit cycle oscillations can result that span either two or three of these subdomains. The purpos...

A nonlinear elastic plate in a supersonic unsteady flow forced by a dynamic excitation and a biaxial compressive load is studied. The physical behavior of the plate is modelized by the Von Kármán equations and the aerodynamic loads are modeled by using the piston theory including nonlinearities up to the third order. The space-continuum model is sp...

We give a survey of recent results on flow-structure interactions modeled by a modified wave equation coupled at an interface with equations of nonlinear elasticity. Both subsonic and supersonic flow velocities are considered. The focus of the discussion here is on the interesting mathematical aspects of physical phenomena occurring in aeroelastici...

Several examples of experimental model designs, wind tunnel tests and correlation with new theory are presented in this paper. The goal is not only to evaluate a new theory, new computational method or new aeroelastic phonomenon, but also to provide new insights into nonlinear aeroelastic phenomena, flutter, limit cycle oscillation (LCO) and gust r...

This study considers the bifurcation evolutions for a combining spiral gear transmission through parameter domain structure analysis. The system nonlinear vibration equations are created with piecewise backlash and general errors. Gill’s numerical integration algorithm is implemented in calculating the vibration equation sets. Based on cell-mapping...

A variety of models describing the interaction between flows and oscillating structures are discussed. The main aim is to analyze conditions under which structural instability (flutter) induced by a fluid flow can be suppressed or eliminated. The analysis provided focuses on effects brought about by: (i) different plate and fluid boundary condition...

We give a survey of recent results on flow-structure interactions modeled by a modified wave equation coupled at an interface with equations of nonlinear elasticity. Both subsonic and supersonic flow velocities are considered. The focus of the discussion here is on the interesting mathematical aspects of physical phenomena occurring in aeroelastici...

A concise harmonic-balance-(HB) based method is demonstrated that yields the limit-cycle oscillation (LCO) response as a function of forward speed for models of any order. The linear shimmy boundary of the system is generated as a function of stiffness in the degree of freedom (DOF) containing the freeplay. Harmonic motion is assumed; and the first...

A computational aeroelastic model is presented for a cantilevered plate rotated from a position with the clamped edge normal to the flow (0 deg) to where the clamped edge is aligned with the flow (90 deg) using a new inextensible plate theory. A large-amplitude limit-cycle oscillation has been observed beyond the linear flutter speed in both the co...

For a projection-based reduced order model (ROM) to be stable and accurate, the dynamics of the truncated subspace must be taken into account. This paper proposes an approach for stabilizing and enhancing projection-based fluid ROMs in which truncated modes are accounted for a priori via a minimal rotation of the projection subspace. Attention is f...

Results from recent NASA sponsored research on the structural dynamics, stability, and control characteristics of heliogyro solar sails are summarized. Specific areas under investigation include coupled nonlinear finite element analysis of heliogyro membrane blade with solar radiation pressure effects, system identification of spinning membrane str...

A theoretical aeroelastic stability analysis has been performed on the flexible thermal protection system for an inflatable aerodynamic decelerator. Structural models consist of one or more truncated conical shells of the Donnell type, which may be elastically supported along the middle surface. The aerodynamic model is first-order piston theory. T...

This paper explores the use of the proper orthogonal decomposition (POD) method for supersonic nonlinear flutter of a cantilever plate or wing. The aeroelastic equations are constructed using von Karman plate theory and first-order piston theory. The two-dimensional POD modes (POMs) in xy plane are determined from the chaotic results given by the t...

The proper orthogonal decomposition (POD) method for analysis of nonlinear panel flutter subjected to supersonic flow is presented. Optimal POD modes are extracted from a chaotic Galerkin mode responses. The aeroelastic equations of motion are constructed using von Karman plate theory, first-order piston theory and quasi-steady thermal stress theor...

For a wing-like plate in supersonic flow cantilevered at its root, chaotic motions are studied in this paper. Prior literature has mainly focused on a simply supported plate or the limit cycle oscillations (LCOs) of a cantilever plate. The governing equations are constructed using von Karman plate theory and first-order piston theory. The Rayleigh–...

A single, simply supported plate resting on a unidirectional elastic foundation was studied for nonlinear oscillation. Linear quasi-steady supersonic theory (piston theory) is used for the aerodynamic pressure. The aeroelastic equations of motion are derived using a hybrid Rayleigh-Ritz-Galerkin method, and a vectorized numerical scheme is develope...

Aircraft wings carrying stores are susceptible to nonlinear aeroelastic limit-cycle oscillations, which can lead to reduced flight and mission performance. Limit-cycle-oscillation dynamics and control simulation studies, although of great importance, are often based on simplified typical-section airfoil models. In this work, the more accurate beam-...

The aeroelastic stability of cantilevered plates with their clamped edge oriented both parallel and normal to subsonic flow is a classical fluid–structure interaction problem. When the clamped edge is parallel to the flow the system loses stability in a coupled bending and torsion motion known as wing flutter. When the clamped edge is normal to the...

The flapping flag is a canonical fluid–structure interaction problem that describes a cantilever plate with flow along its elastic axis. When the flapping flag loses stability it enters a large amplitude Limit Cycle Oscillation (LCO). While theoretical models can accurately predict the flutter velocity and frequency, there are still discrepancies b...

Nonlinear damping suspension is a promising method to be used in a rotor-bearing system for vibration isolation between the bearing and environment. However, the nonlinearity of the suspension may influence the stability of the rotor-bearing system. In this paper, the motions of a flexible rotor in short journal bearings with nonlinear damping susp...

A study was conducted to investigate membrane paradox for solar sails. The study particularly provided a framework for analyzing the stability of a restrained solar sail membrane where the aspect ratio was large or the ratio of the tension on the bending stiffness was large. The results of these investigations were applied to explore the stability...

In prior work, several authors including the present ones have noted the analogy between the fluid oscillations induced by a bluff body in cross flow (e.g., the classic von Karman vortex street behind a cylinder) and the flow oscillations often called buffet that occur for flow around wings and airfoils in transonic flow at sufficiently large angle...

The aeroelastic stability of rectangular plates in subsonic flow is well documented in literature. For example, the stability of a cantilever plate with a clamped edge parallel to the flow is well understood due to the similarity of this system to an aircraft wing. However, an ongoing push for lighter aerospace structures and novel designs requires...

Navier-Stokes simulations are performed to determine the responses of a single-degree-of-freedom pitch airfoil system, as well as those of a two-degree-of-freedom pitch-and-heave system, in buffeting flows. The buffeting flow exhibits shock-wave oscillations of a unique frequency that occurs for some combinations of mean flow angle of attack and tr...

The aim of this paper is to determine by a singular perturbation approach the dynamic response of a harmonically forced system experiencing a pitchfork bifurcation. The model of an extensible beam forced by a harmonic excitation and subject to an axial static buckling is space-discretized by a Galerkin approach and studied by the Normal Form Method...

A pinned–pinned beam with one end fixed and the other end free to slide horizontally is studied. Dry friction damping is modeled at the support boundaries of the beam. In order to analyze the variation of the equivalent viscous damping caused by the presliding friction, the LuGre friction model is employed. The relationship between the equivalent v...