Showing papers by "Earl H. Dowell published in 2000"

Proper Orthogonal Decomposition Technique for Transonic Unsteady Aerodynamic Flows

Abstract: A new method for constructing reduced-order models (ROM) of unsteady small-disturbance e ows is presented. The reduced-order models are constructed using basis vectors determined from the proper orthogonal decomposition (POD) of an ensemble of small-disturbance frequency-domain solutions. Each of the individual frequencydomain solutions is computed using an efe cient time-linearized e ow solver. We show that reduced-order models can be constructed using just a handful of POD basis vectors, producing low-order but highly accurate models of the unsteady e ow over a wide range of frequencies. We apply the POD/ROM technique to compute the unsteady aerodynamic and aeroelastic behavior of an isolated transonic airfoil and to a two-dimensional cascade of airfoils.

Nonlinear Response of Airfoil Section with Control Surface Freeplay to Gust Loads

Abstract: A nonlinear response analysis of a typical airfoil section with control surface freeplay excited by periodic gust loads in low subsonic flow is presented along with a companion wind-tunnel test program. The analytical model uses Peters's finite state model for the two-dimensional aerodynamic flow over the airfoil (Peters, D. A., Finite-State Airloads for Deformable Airfoils on Fixed and Rotating Wings, Symposium on Aeroelasticity and Fluid/Structure Interaction, American Society of Mechanical Engineers, Winter Annual Meeting, Nov. 1994, rev. 3, May 1996). Results for a single harmonic gust and a continuous frequency sweep gust have been computed and measured for flow velocities below the flutter speed. A theoretical and experimental chaotic response phenomenon for the nonlinear structural model was observed. These results further confirm some conclusions about limit cycle oscillations and complement our earlier theoretical and experimental studies of self-excited oscillations. The experimental investigation has been carried out in the Duke University wind tunnel using a rotating slotted cylinder gust generator. The fair to good quantitative agreement between theory and experiment verifies that the present analytical approach has reasonable accuracy and good computational efficiency for nonlinear gust response analysis in the time domain.

Nonlinear Aeroelastic Response of Delta Wing to Periodic Gust

Abstract: A nonlinear response analysis of a simple delta wing excited by periodic gust loads in low subsonic flow is presented along with a companion wind-tunnel test program. The analytical model uses a three-dimensional time-domain vortex lattice aerodynamic method and a reduced order aerodynamic technique. Results for a single harmonic gust and a continuous frequency sweep gust have been computed and measured for both flow velocities below and above the flutter speed. A theoretical jump response phenomenon for the nonlinear structural model was observed both for the single harmonic and the continuous frequency sweep gust excitation. Those results further confirm some conclusions about limit cycle oscillations above the flutter speed and complement our earlier theoretical and experimental studies. Also an experimental investigation has been carried out in the Duke wind tunnel using a rotating slotted cylinder gust generator and an Ometron VPI 4000 scanning laser vibrometer measurement system. The fair to good quantitative agreement between theory and experiment verifies that the present analytical approach has reasonable accuracy and good computational efficiency for nonlinear gust response analysis in the time domain. Without the use of reduced order models, calculations of the gust response for the nonlinear model treated here would be impractical.

Eigenmode Analysis and Reduced-Order Modeling of Unsteady Transonic Potential Flow Around Airfoils

Abstract: An eigenmode analysis and reduced-order models of the unsteady transonic aerodynamic e ow around isolated airfoilsarepresented.Theunsteadye owismodeledusingthetime-linearizedfrequency-domainunsteadytransonic full potential equation. The full potential was discretized in space using a e nite element method. The resulting equations are linear in the unknown velocity potential and quadratic in the reduced frequency of excitation. The dominant eigenfrequencies and corresponding mode shapes of the discretized potential model are computed, and theeffect ofdifferent parametersthat determinethesteady and unsteady e owe eld (e.g.,thefar-e eld Mach number, theangleofattack,and theairfoilshape )areinvestigated.Anormalmodeanalysisanda staticcorrectiontechnique are then used to construct a low degree-of-freedom, reduced-order model of the unsteady e owe eld. Depending on the range of frequencies of interest, a relatively small number of eigenmodes are required. An alternative reducedorder modeling technique based on Arnoldi ‐Ritz vectors is also presented. For the case where the structural excitations are known a priori, the latter method is more efe cient. Using the aerodynamic reduced-order models, we construct aeroelastic reduced-order models and compute e utter boundaries for different airfoils at several different Mach numbers.

The Influence of a Nonzero Angle of Attack and Gust Loads on the Nonlinear Response of a Typical Airfoil Section with a Control Surface Freeplay

Abstract: The influence of a \"frozen\" harmonic gust excitation on an aeroelastic nonlinear system with a control surface freeplay at nonzero angles of attack is examined in the context of a three-degree-of-freedom airfoil. The formulation of the numerical model is based on Theodorsen's aerodynamics and is extended to account for nonlinear arbitrary motion and gust loads. By time marching of the governing equations, the system response is determined and the complex nonlinear behavior is observed. Results indicate that there is no suppressing effect due to a nonzero mean angle of attack for such a system under gust loads. A companion experimental test program in a wind tunnel with a gust generator is used to validate the numerical results. The good agreement between theory and experiment demonstrates the efficiency and accuracy of the computational method.

Nonlinear dynamics of aeroelastic systems

Abstract: Aeroelastic systems are those that involve the coupled interaction between a convecting fluid and a flexible elastic structure. The nonlinear dynamical response of such systems is known to encounter limit cycle oscillations (LCO) in certain flight regimes and relatively simple experimental wind tunnel models have been designed to exhibit LCO as well. In the present paper, the results of these wind tunnel experiments are discussed and compared to comparable results from mathematical models. The physical models include (1) an airfoil and a control surface attached with an elastic spring including free‐play, and (2) a delta wing with elastic geometrical nonlinearities due to bending and torsional deformations. Both self‐excited oscillations such as flutter and LCO, as well as forced oscillations due to an aerodynamic gust, are discussed. The advantages of representing the unsteady aerodynamic flow field in terms of global modes for such studies are emphasized and illustrated.

Nonlinear Reduced Order Modeling of Limit Cycle Oscillations of Aircraft Wings

Abstract: : This report documents the result of an STTR Phase I on the investigation in the use of a frequency-domain proper orthogonal decomposition (POD) / Reduced Order Modeling (ROM) procedure in conjunction with a harmonic balance nonlinear scheme for the prediction and analysis of limit cycle oscillations (LCO) of aircraft wings/airfoils in transonic flow regimes. A significant milestone has been reached in the phase I work. With four related cases studied in LCO and flutter, the result is that our frequency-domain method producing highly accurate solutions over a wide ranges of frequencies is potentially two orders of magnitude faster than conventional time-marching methods for determining LCO and flutter. Further, the nonlinear solutions of LCO using harmonic balance scheme in frequency domain could lead to a much better understanding of LCO physics. Its adopted Eigen-mode solution methodology on the other hand should render it readily acceptable by the industry practice. Finally, STTR Phase II plan is presented in detail. Commercialization strategy of the would-be production-ready software is also discussed.