Richard D. Snyder

Numerical Analysis of Store-Induced Limit-Cycle Oscillation

Store-induced limit-cycle oscillation of a rectangular wing with tip store in transonic flow is simulated using a variety of mathematical models for the flowfield: transonic small-disturbance theory (with and without inclusion of store aerodynamics) and transonic small-disturbance theory with interactive boundary layer (without inclusion of store aerodynamics). For the conditions investigated, assuming inviscid flow, limit-cycle oscillations are observed to occur as a result of a weakly subcritical Hopf bifurcation and are obtained at speeds lower than those predicted 1) nonlinearly for clean-wing flutter and 2) linearly for wing/store flutter. The ability of transonic small-disturbance theory to predict the occurrence and strength of this type of limit-cycle oscillation is compared for the different models. Differences in unmatched and matched aeroelastic analysis are described. Solutions computed for the clean rectangular wing are compared to those computed with the Euler equations for a case of static aeroelastic behavior and for a case of forced, rigid-wing oscillation at Mach 0.92.

Predictions of Store-Induced Limit-Cylce Oscillations Using Euler and Navier-Stokes Fluid Dynamics

Store-induced limit cycle oscillation of a rectangular wing with a tip store in transonic flow is simulated. Stability boundaries for this wing are computed for both clean and tip store configurations and behavior beyond the critical freestream velocity is examined at a Mach number of 0.92. The Euler equations are used to model the fluid dynamics and a modal approach is used to model the structural response. Solutions obtained with the Euler equations are compared with results obtained using linear and transonic small disturbance theories. All methods are shown to give similar predictions of the stability boundary in the lower transonic regime but differences develop as the Mach number approaches unity. The linear method fails to capture the rise in flutter speed beyond the flutter dip and is, of course, unable to capture limit cycle behavior. The Euler and transonic small disturbance theories show reasonable qualitative agreement in predicting both unbounded and bounded behavior across a wide range of Mach numbers. There are, however, notable quantitative differences between the Euler and transonic small disturbance theories in the limit cycle onset velocities and response amplitudes and frequencies. The results suggest that the transonic small disturbance theory is a practical alternative to the Euler and Navier-Stokes theories for predicting store-induced limit cycle behavior so long as the small disturbance assumption is valid.

Aeroelastic Shape Optimization of a Flapping Wing

This paper presents the theory and results for the shape and structural optimization of a platelike flapping wing. The aeroelastic system is analyzed by coupling an unsteady vortex lattice aerodynamics model with a plate finite element model. The assumptions in the aerodynamic model allow the system of equations to be calculated with the inversion of a single matrix, greatly reducing the computational cost. The design variables are the shape parameters from the modified Zimmerman method and the polynomial coefficients that describe the wing thickness. The wing shape and structure are optimized using two multiobjective optimization formulations. The first optimization minimizes the input power while maximizing the cycle-averaged thrust. The input power is the secondary objective function and is treated as a nonlinear constraint, whereas the cycle-averaged thrust is the primary objective function. A second multiobjective formulation that treats wing mass as the secondary objective function is also performed...

Deterministic Global Optimization of Flapping Wing Motion for Micro Air Vehicles

The kinematics of a ∞apping plate are optimized by combining the unsteady vortex lattice method with a deterministic global optimization algorithm. A constraint to keep the lift from taking large negative values at anytime is also imposed by following a penalty function approach. The design parameters are the amplitudes, mean values, frequencies, and phase angles of the ∞apping motion. The results suggest that imposing a delay between the difierent oscillatory motions and controlling the way through which the wing rotates at the end of each half stroke would enhance the lift generation. The use of a general unsteady numerical aerodynamic model and the implementation of a deterministic global optimization algorithm provide guidance and a baseline for future efiorts to identify optimal stroke trajectories for micro air vehicles with higher fldelity models.

Static Nonlinear Aeroelastic Analysis of a Blended Wing Body

*† ‡ § ** †† A high -fidelity computational process is applied to assess the contributions of aerodynamic nonlin earities to the airloads sustained by a blended -wing configuration with different static aeroelastic deflections . The effects of nonlinearities are inferred through comparison of the computational results with those predicted by a widely accepted linear aeroelastic procedure. Structural deflections prescribed in the nonlinear analysis are those obtained from the linear methodology, a step taken in prelude to developing a production quality, high -fidelity aeroelastic methodology that has the added benefit of ensuring the consistency of the geometrical changes. Of specific interest is the ability of the current process to re -generate rapidly grids for aerodynamic analysis in response to structural deflections.

A Design Optimization Strategy for Micro Air Vehicles

This paper presents progress on the development of a computational framework for synthesizing and optimizing the design of micro air vehicles with flapping wings. It is anticipated that aeroelastic tailoring can be used to improve the performance of mechanical flapping-wing micro air vehicles relative to designs with rigid structure. Due to the physics associated with micro air vehicles, the design framework must be able to capture nonlinear physical behavior with high fidelity, while at the same time maintaining the computational efficiency required for effective design space exploration. In the present paper, the authors present three newly developed components of the framework: a spectral element method for computing the system dynamics, an adjoint method for calculating sensitivities of the system with respect to changing structural design variables and an optimization component built upon existing gradient-based methods. These new components are integrated with existing components and the entire framework is used to compute flapping cycles for both rigid and flexible micro air vehicle models and to demonstrate consistency between the direct and adjoint forms for sensitivity computation.

Parametric Mesh Deformation and Sensitivity Analysis for Design of a Joined-Wing Aircraft

*† ‡ # + § New processes that enable a state-of-the-art MDO framework for future air vehicles were explored in this paper. First, a unified technique for defining a high-quality geometry and associated Computational Fluid Dynamics (CFD) mesh for a candidate configuration was developed. This method was designed to augment an existing framework-oriented tool for high-fidelity analysis of air vehicle configurations developed at the Air Force Research Laboratory that accounts for system nonlinearities and vehicle flexibility. Second, the mesh generation technique was generalized to account for geometries that deform under the influence of either static or dynamic airloads. Fidelity of the deformation was found to be high, and found to be sufficient for CFD computations. Third, the concept of parametric shape functions was proposed to represent characteristic structural deformations in a fashion consistent with the geometry/mesh definition. As demonstrated with example problems, these functions analytically related the primary structural variables (defined in a generalized manner) to the aerodynamic mesh. The relation produced the grid sensitivity expression resulting from fluid/structure coupling. The significance of this quantity for enforcing conservation of energy during an aeroelastic interaction was discussed.

Aeroelastic Optimization of a Two-Dimensional Flapping Mechanism

A two-dimensional aeroelastic simulation capability is developed for the study of flapping flight. The impact of flexibility on performance of flapping wing micro air vehicles in low- speed forward flight is studied. Flapping motion in pitching and translation is imparted on a two-dimensional rigid plate via elastic supports. The body and wake are modeled using discrete vortices and the structure by a multi-degree-of-freedom spring-mass-damper system. A parametric study and optimization are performed to obtain the maximum propulsive efficiency for the system. Maximum aerodynamic force generation is found to occur near resonance in pitch and plunge where flapping amplitudes are largest and beneficial pitch-plunge phasing is achieved. Response phasing is particularly important in production of thrust versus drag. Comparison of results including and neglecting aeroelastic coupling show that aeroelastic effects must be considered to accurately model the system response.

A Computational Design Framework for Flapping Micro Air Vehicles

The authors have embarked on the development of a Computational Design Framework as the means to synthesize and optimize highly integrated Micro Air Vehicle designs with flapping wings. This paper describes both the computational physics and the framework requirements that contribute to the overall design. Computational physics address inherently non-linear flapping aerodynamics and non-linear structures. Mathematical models of symbiotic non-linear behavior will feed design optimization in ways that bring out new and beneficial aeroelastic interactions. A preliminary design was initiated with simplified physics in order to begin design connectivity within the design framework. The framework builds on earlier reported developments with software classes (objects) that facilitate coordinated graphical animation using either a single or multiple windows.

Study of Deflected Wake Phenomena by 2D Unsteady Vortex Lattice

Point vortex calculations are compared to experimental results for a 2D pitching and plunging airfoil. The point vortex method is then used to simulate a flat plate in high frequency pitch, plunge, and combined motions. Low frequency motion causes the wake to convect away from the trailing edge parallel to the freestream. Above a certain threshold, high frequency motion causes the wake to deflect relative to the freestream. Combined pitch plunge motion results in deflected wakes for parameter values greater than a certain range for pitch amplitude, plunge amplitude, frequency, and relative phase between pitch and plunge.