Rotary-wing Aeroelasticity Research Articles

Application of Time-Variant Systems Theory to the Unsteady Aerodynamics of Rotary Wings

This work employs the principles of time-variant systems theory to investigate the unsteady aerodynamics of rotary-wing configurations under periodic equilibrium conditions. Their application enables an extension of the pulse technique for system identification, as well as the adaptation of the linear-frequency-domain formulation commonly utilized in fixed-wing to rotary-wing scenarios. These methodologies effectively incorporate the aerodynamic nonlinearities associated with the equilibrium state into an efficient time-variant linearized representation of the unsteady aerodynamics. To promote its application in the context of rotary-wing aeroelasticity, a state-space realization based on a periodic autoregressive model with exogenous input is subsequently employed. Upon transformation from discrete to continuous time, the resulting aerodynamic model adopts a linear continuous-time periodic state-space formulation, offering compatibility for its coupling with a wide range of structural models. The proposed aerodynamic framework tailored to rotary-wing aeroelasticity holds applicability across a spectrum of aerodynamic models of arbitrary complexity, spanning from incompressible potential flow approximations to potentially more sophisticated methods. Showcasing the potential of this framework, the widely studied lossy Mathieu equation and the aerodynamic response to a flap perturbation about the periodic equilibrium condition of a prototypical rotor blade section, incorporating nonlinearities through an analytical dynamic stall model, are considered.

Reduced-Order Dynamic Stall Modeling with Swept Flow Effects Using a Surrogate-Based Recurrence Framework

The extension of the surrogate-based recurrence framework approach to account for time-varying swept flow effects under dynamic stall conditions is described. Using full-order solutions generated by the OVERFLOW computational fluid dynamics code, the surrogate-based recurrence framework reduced-order modeling approach is shown to effectively mimic full-order solutions of unsteady lift, moment, and drag under dynamic stall conditions while maintaining the computational efficiency associated with semiempirical dynamic stall models. This level of functionality represents a new capability for rotary-wing aeroelasticity applications. Furthermore, a generalized kriging formulation based on nonstationary Gaussian process modeling is implemented in a tractable manner by locally optimizing the high-dimensional likelihood function in the vicinity of the stationary solution. The resulting nonstationary covariance structures are shown to significantly improve the accuracy of the surrogate-based recurrence framework predicted moment stall characteristics compared to a stationary model. It is shown that the nonstationary surrogate-based recurrence framework approach is better able to adapt to abrupt changes in airload behavior caused by the underlying dynamic stall vortex dynamics. The results indicate that the surrogate-based recurrence framework approach based on nonstationary Gaussian process models is a promising alternative to widely used semiempirical rotorcraft dynamic stall models that cannot account for the effects of time-varying velocity components associated with forward flight.

A Surrogate-Based Approach to Reduced-Order Dynamic Stall Modeling

The surrogate-based recurrence framework (SBRF) approach to reduced-order dynamic stall modeling associated with pitching/plunging airfoils subject to fixed or time-varying freestream Mach numbers is described. The SBRF is shown to effectively mimic full-order two-dimensional computational fluid dynamics solutions for unsteady lift, moment, and drag, but at a fraction of the computational cost. In addition to accounting for realistic helicopter rotor blade dynamics, it is shown that the SBRF can model advancing rotor shock induced separation as well as retreating blade stall associated with excessive angles of attack. Therefore, the SBRF is ideally suited for a variety of rotary-wing aeroelasticity and active/passive design optimization studies that require high-fidelity aerodynamic response solutions with minimal computational expense.

Influence of Blade Geometric Parameters on Aeroelastic Response of a Helicopter Rotor System

Rotary wing aeroelasticity is a highly complex phenomenon involving coupling between flexible blade dynamics and unsteady aerodynamics including stall and unsteady wake effects. In this paper, a low-cost computational aeroelastic model including the structural coupling from geometric parameters and nonlinearities associated with structural modeling and dynamic stall, applicable to steady, level forward flight, has been developed. The differential equations of motion are solved in time domain in a sequential manner to obtain the response of all the blades in the rotor system, the dynamic inflow variables, and the sectional loads at every time step. A fourth-order Runge-Kutta integration scheme has been adopted for solving the differential equations. Iterations are carried out until convergence is achieved in blade response and helicopter trim. The effect of blade geometric parameters such as pretwist, hinge offset, and torque offset on aeroelastic response of a helicopter rotor system is investigated numerically. It is shown that the structural coupling from blade geometric parameters significantly influences the rotor blade response and loads.

Rotary-Wing Aeroelasticity: Current Status and Future Trends

Concise Perspective and Previous Surveys W HEN reviewing research in rotary-wing aeroelasticity (RWA), it is important to mention a few historical facts. The Wright brothers flew in 1903, and Sikorsky built and started flying the first operational helicopter, the R-4 or (VS-316), in 1942. The R-4 was a three-bladed helicopter with a rotor diameter of 11.6 m and was powered by a 185-hp engine. Thus, there is an initial gap of approximately four decades between fixed-wing and rotary-wing technologies. Therefore, it is not surprising that certain rotary-wing problems, particularly those pertaining to unsteady aerodynamics, are still not well understood. The situation is further compounded by the complexity of the vehicle when compared to fixed-wing aircraft. The field of RWA has been the most active area in aeroelasticity during the last three decades. This vigorous research activity has generated a considerable number of survey papers as well as several books that have been published on this topic. These review papers, when considered in chronological order, provide a historical perspective on this evolving field.1−13 One of the first significant reviews of rotary-wing dynamic and aeroelastic problems was provided by Loewy,11 where a wide range of dynamic problems was reviewed in considerable detail. A more limited survey emphasizing the role of unsteady aerodynamics and vibration problems in forward flight was presented by Dat.2 Two comprehensive reviews of rotary-wing aeroelasticity were presented by Friedmann.3,4 In Ref. 3, a detailed chronological discussion of the flap-lag and coupled flap-lag-torsion problems in hover and forward flight was presented, emphasizing the inherently nonlinear nature of the hingeless-blade aeroelastic stability problem. The nonlinearities considered were geometrical nonlinearities because of moderate blade deflections. In Ref. 4, the role of unsteady aerodynamics, including dynamic stall, was examined, together with the treatment of nonlinear aeroelastic problems in forward flight. Finite element solutions to RWA problems were also considered, together with the treatment of coupled rotor-fuselage problems. Another detailed survey by Ormiston12 discussed the aeroelasticity of hingeless and bearingless rotors, in hover, from an experimental and theoretical point of view.

Past and future progress in fixed and rotary wing aeroelasticity

AbstractProgress in aeroelasticity of fixed and rotary wing aircraft is compared by means of a selective review. Discussion of the role of concurrent engineering leads into modelling and validation, these being dealt with under the headings of aerodynamics, structural and integrated models. Formulation and solution of equations of motion are considered, which relate mainly to rotorcraft, and then aeroelastic performance improvement is covered. This includes optimisation, aeroservoelasticity and passive devices. Basic insight providing models are reviewed and the paper concludes with, further comments on insight, and also future progress in aeroelasticity.

Semianalytical sensitivity of Floquet characteristic exponents with application to rotary-wing aeroelasticity

The stability of a nonlinear dynamic system with periodic coefficients can be evaluated by linearizing the equations of motion of the system about a steady-state equilibrium position and then, using Floquet -Liapunov theory, by calculating the eigenvalues, or characteristi c multipliers, of the transition matrix at the end of one period, and finally by examining the real parts of the characteristic exponents corresponding to the characteristic multipliers. This article describes a methodology to calculate the sensitivity of the characteristic exponents to changes in system parameters, taken as design variables, using semianalytic derivatives rather than finite difference approximations. Linear and nonlinear contributions to such sensitivities are identified and algorithms for the calculation of each contribution are provided. The linear contribution to the sensitivity to each design variable can be calculated at a fraction of the cost of one analysis, with appropriate attention to the details of the computer implementation. The nonlinear contribution requires a fixed overhead cost of as many analyses as the number of variables that define the equilibrium position, regardless of the number of design variables with respect to which the sensitivities are sought. A potential problem in the calculation of finite difference gradients is identified and discussed. The linear portion alone is sufficiently accurate for the helicopter problem of the study.

Modeling of unsteady aerodynamics for rotary-wing aeroelasticity

The modeling of unsteady aerodynamics for rotary-wing applications requires an understanding of the type of aeroelastic phenomena that is of interest. Different regimes require different modeling techniques. This modeling also requires a distinction between the blade-lift model and the induced-flow model. Finally, aerodynamic modeling for aeroelasticity (as contrasted with performance) requires that state variables be defined for the aerodynamic states. If the aerodynamic states are not defined, then conventional Floquet and eigenvalue stability analyses can not be performed.

Arbitrary motion unsteady aerodynamics and its application to rotary-wing aeroelasticity

This paper presents in a unified manner recent research on arbitrary motion unsteady aerodynamics with an emphasis on applications to a number of rotary wing aeroelastic problems. The term arbitrary motion is used to denote growing or decaying oscillations with a certain frequency. The specific topics treated in this paper are: (1) generalization of Greenberg's theory and its application to hingeless rotor aeroelastic stability; (2) description of a new technique for formulating finite state approximations to steady aerodynamic theories, which are suitable for both fixed-wing and rotary-wing applications, and its application to generalize Loewy's theory; (3) comparison of fixed wing and rotary-wing indicial response functions; (4) influence of arbitrary motion aerodynamics, as represented by dynamic inflow on a helicopter in ground resonance. From the discussion of these topics a number of useful conclusions on the fundamental nature of arbitrary motion aerodynamics and its role in rotary-wing aeroelasticity are obtained.

Application of time-domain unsteady aerodynamics to rotary-wing aeroelasticity

Application of time-domain unsteady aerodynamics to rotary-wing aeroelasticity

Recent Developments in Rotary-wing Aeroelasticity

The purpose of this review is to present the research done in rotary-wing aeroelasticity during the past eight years in a unified manner. The following topics are reviewed with considerable detail: (1) recent development in the aeroelastic modeling of the coupled flap-lag-torsional problem in hover (2) effect of unsteady aerodynamics on the coupled flap-lag-torsional aeroelastic problem in hover (3) the coupled flap-lag and the coupled flap-lag-torsional problem in forward flight (4) complete rotor and coupled rotor fuselage aeroelastic problems including both hingeless and teetering rotors.