Reduced Order Aerodynamic Models Research Articles

Reliability and Sensitivity Analysis of Transonic Flutter Using Improved Line Sampling Technique

The improved line sampling (LS) technique, an effective numerical simulation method, is employed to analyze the probabilistic characteristics and reliability sensitivity of flutter with random structural parameter in transonic flow. The improved LS technique is a novel methodology for reliability and sensitivity analysis of high dimensionality and low probability problem with implicit limit state function, and it does not require any approximating surrogate of the implicit limit state equation. The improved LS is used to estimate the flutter reliability and the sensitivity of a two-dimensional wing, in which some structural properties, such as frequency, parameters of gravity center and mass ratio, are considered as random variables. Computational fluid dynamics (CFD) based unsteady aerodynamic reduced order model (ROM) method is used to construct the aerodynamic state equations. Coupling structural state equations with aerodynamic state equations, the safety margin of flutter is founded by using the critical velocity of flutter. The results show that the improved LS technique can effectively decrease the computational cost in the random uncertainty analysis of flutter. The reliability sensitivity, defined by the partial derivative of the failure probability with respect to the distribution parameter of random variable, can help to identify the important parameters and guide the structural optimization design.

Aeroelastic analysis of helicopter rotor blade in hover using an efficient reduced-order aerodynamic model

This paper presents a coupled flap–lag–torsion aeroelastic stability analysis and response of a hingeless helicopter blade in the hovering flight condition. The boundary element method based on the wake eigenvalues is used for the prediction of unsteady airloads of the rotor blade . The aeroelastic equations of motion of the rotor blade are derived by Galerkin's method. To obtain the aeroelastic stability and response, the governing nonlinear equations of motion are linearized about the nonlinear steady equilibrium positions using small perturbation theory . The equilibrium deflections are calculated through the iterative Newton–Raphson method. Numerical results comprising steady equilibrium state deflections, aeroelastic eigenvalues and time history response about these states for a two-bladed rotor are presented, and some of them are compared with those obtained from a two-dimensional quasi-steady strip aerodynamic theory. Also, the effect of the number of aerodynamic eigenmodes is investigated. The results show that the three-dimensional aerodynamic formulation has considerable impact on the determination of both the equilibrium condition and lead-lag instability.

Application of the modified reduced-order aerodynamics modelling approach to aeroelastic analysis

This study presents the application of the Proposed Modified Reduced-Order Aerodynamics Modelling approach for aeroelastic analysis based on the boundary element method (BEM) as a novel approach. The used BEM has the capability to capture the thickness effect and geometric complexity of a general three-dimensional model. In this approach the reduced-order aerodynamic model is defined through the eigenvalue problem of unsteady flow based on the unknown wake singularities. Based on the used aerodynamic model an explicit algebraic form of the aeroelastic equations is derived that reduces computational efforts and complexity. This special feature enables us to determine the aeroelastic instability directly via eigenanalysis of the aeroelastic problem. The eigenanalysis and reduced-order modelling of unsteady flow over a NACA 0012 airfoil are performed as an example and the results are compared with those obtained from conventional reduced-order modelling (CROM) method. The obtained results demonstrate the accuracy and superior efficiency of the present method over the CROM method. The method was then applied to the aeroelastic analyses of a typical section, in order to show the procedure of driving the explicit algebraic form. Furthermore, to illustrate the capability of the method in the handling of the three-dimensional problems, aeroelastic results for a wing are presented and compared with the results of the Theodorsen's aerodynamic theory.

Comparisons of computational fluid dynamics solutions of static and manoeuvring fighter aircraft with flight test data

As the capabilities of computational fluid dynamics (CFD) to model full aircraft configurations improve, and the speeds of massively parallel machines increase, it is expected that CFD simulations will be used more and more to steer or in some cases even replace traditional flight test analyses. The mission of the US Air Force SEEK EAGLE office is to clear any new weapon configurations and loadings for operational use. As more complex weapons are developed and highly asymmetric loadings are requested, the SEEK EAGLE office is tasked with providing operational clearances for literally thousands of different flight configurations. High-fidelity CFD simulations employing the turbulent Navier—Stokes equations are in a prime position to help reduce some of the required wind-tunnel and/or flight test workload. However, these types of CFD simulations are still too time consuming to populate a full stability and control parameter database in a brute-force manner. This article reviews results previously published by the authors, which validate the ability of high-fidelity CFD techniques to compute static force and moment characteristics of aircraft configurations. A methodology to generate efficient but non-linear reduced-order aerodynamic loads models from dynamic CFD solutions, which in-turn may be used to quickly analyse various stability and control characteristics at a particular flight condition, is introduced, and the results based on the US Air Force F-16C fighter aircraft that exemplify the process are discussed.

Simultaneous Excitation of Multiple-Input/Multiple-Output CFD-Based Unsteady Aerodynamic Systems

A significant improvement to the development of computational-fluid-dynamics-based unsteady aerodynamic reduced-order models is presented. The improvement involves the simultaneous excitation of the structural modes of the computational-fluid-dynamics-based unsteady aerodynamic system. This improvement enables the computation of the unsteady aerodynamic state-space model using a single computational fluid dynamics execution, independent of the number of structural modes. Two new types of input functions are presented that can be used for the simultaneous excitation of the unsteady aerodynamic system via the excitation of the structural modes. Results are presented for a semispan configuration using the CFL3Dv6.4 code.

Reduced-Order-Model-Based Flutter Analysis at High Angle of Attack

C ONFIGURATIONS with a highly flexible delta wing are considered for the next generation of unmanned air vehicles (UAV). Delta wing flowfield is dominated by vortical structures at high angle of attack, the most prominent is called leading-edge vortex. Ye and Zhao [1] used a nonlinear lifting line method to compute the aerodynamic loads of the delta wing at high angle of attack. With the development of computer technology, computational fluid dynamics (CFD) technique has been used in the simulation of delta wing-induced vortical flow. The study [2] shows that the Reynolds number affects primary vortex slightly, and so Euler codes can be employed to simulate the vortex and aerodynamic loads; the shortness is that it cannot simulate the secondary vortex caused by the effect of viscosity. The CFD and computational structural dynamics (CSD) direct coupling method has been used in aeroelastic analysis of deltawing.Gordnier et al. [3,4] coupled Euler/ Navier–Stokes codes and nonlinear plant element to study the buffet problem of the flexible delta wing at high angle of attack. The CFD and CSD direct coupling method [5–7] has also been used in the nonlinear flutter simulation of delta wing at small angle of attack (<5 deg). The limitation of the direct aeroelastic simulation method is the high cost of the computational time. To solve the contradiction between computational efficiency and computational quality, many researchers turn to CFD-based unsteady aerodynamic reduced-order modeling (ROM) to improve the aeroelastic computational efficiency in the last decade. Dowell and Hall [8], Lucia et al. [9], and Zhang and Ye [10] present some overviews of ROM and its applications on nonlinear aeroelastic research. There are two kinds of methods for ROMof unsteady aerodynamic loads at the present time. The one is the proper orthogonal decomposition (POD) based reduced-order modeling method, the other is aerodynamic modeling based on structural modes by using identification technology. The second method is used in this work. Zhang [11] compared the efficiency between the ROM-based method and the CFD direct simulation method. Efficiency can be improved by 1 2 orders with accuracy still retained by ROM-based method. Zhang used CFDbased ROM to perform aeroservoelastic analysis [12] and transonic flutter suppression by active control [13].

Reduced Order Aerodynamic Model for Aeroelastic Analysis of Complex Configurations in Incompressible Flow

D ETERMINATION of the aeroelastic behavior of subsonic flying vehicles is of great importance. This is partly due to lighter airframe requirements for most applications. Consequently, aeroelastic analyses are becoming regular routines in airframe design processes. Aeroelastic responses can be predicted using aeroelastic codes based on Euler or Navier–Stokes solvers coupled with structural dynamics solvers. However, the major drawback of the aforementioned technique, even for simple three-dimensional geometries, is the required computational time and memory to run the full aeroelastic simulation. In practice, however, simple and accurate methods are needed to predict aeroelastic responses accurately. The modal analysis technique for structural dynamics analysis is quite routine and widely used for constructing reduced-order models (ROMs). It should be mentioned that this technique was recently applied for unsteady flow analysis, as well. The reduced-order structure andfluidmodels were employed to construct reduced-order aeroelastic models [1–5] that are mostly applicable to simple geometries such as 2-D airfoils and flat wings in the discrete-time domain. The objective of this work is to develop a general reduced-order aeroelastic model for 3-D complex geometries in subsonic incompressible flow regimes in the continuous-time domain. In this regard, a boundary element method (BEM) based fluid eigenanalysis solver [6] is integrated with a finite element method (FEM) based modal technique of structural modeling. II. Structural Modeling

Control law design for transonic aeroservoelasticity

Existing computational transonic aeroservoelastic researches focus on directly coupling the structural dynamic equations, CFD solver and servo system in time domain, study the effect of the given feedback control laws on the responses of the aeroelastic system. These works have not involved the design of the flutter active control law. The non-linearity of transonic flow brings great difficulties to aeroservoelastic analysis and design. Recent research of the unsteady aerodynamic reduced order models (ROM) based on CFD provides a challenging approach for transonic aeroservoelastic analysis and design. Coupling the structural state equations with the aerodynamic state equations of the wing and the control surface based on the ROM, we construct a transonic aeroservoelastic model in state-space. Then the sub-optimal control method based on output feedback is used to design the flutter suppressing law. The study first demonstrates the open loop of the Benchmark Active Controls Technology (BACT) wing. The computational results of the CFD direct simulation method and the ROM analysis method are both agree well with the experimental data. Then both the closed loop time responses and the flutter results by ROM technique are compared with those of numerical aeroservoelastic simulation based on Euler codes to validate the correctness of the design method of the control law and aeroservoelastic analysis method. An increase of up to 20% of the speed index can be achieved by the control law designed by sub-optimal control method for this model.

Aeroelastic Model Reduction for Affordable Computational Fluid Dynamics-Based Flutter Analysis

A new approach is presented to generate computational fluid dynamics (CFD)-based reduced-order aerodynamic and aeroelastic models for rapid flutter analysis at an affordable cost. The technique is based on the single-composite-input/eigensystem realization algorithm (SCI/ERA) that has been newly developed at Boeing. Given a large-scaled, discrete-time CFD model whose moving surface boundary is described by multiple structural mode shapes, the SCI/ERA takes time samples of the unsteady response due to a simultaneous excitation of the inputs and identifies the aerodynamic system in terms of low-order matrices. Because the CFD response is sampled almost exclusively for the single representative input this technique can significantly reduce the model construction time. The reduced-order aerodynamic model is coupled with a discrete-time structural model to generate a reduced-order aeroelastic model. For a demonstration of the method, a representative Boeing wind-tunnel airplane modeled by a finite element method and the CFL3D CFD code is studied. It is shown that for the case of 10 structural modes the proposed scheme can reduce the model construction time by a factor of 4-6, yet its unsteady aerodynamic and flutter results are as accurate as those created by other reduction methods.

A comparison of full non‐linear and reduced order aerodynamic models in control law design using a two‐dimensional aerofoil model

AbstractThe prediction of the flutter boundary of an aircraft is a necessary but time consuming process, particularly as for the most realistic results a time accurate simulation of the interaction between the non‐linear aerodynamic and structural forces is required. Extension of the flight envelope by the design of active control laws to suppress flutter further increases the demands on computational time, to presently unrealistic levels. Use of a reduced order model (ROM) derived from, and in place of, the full non‐linear aerodynamics greatly reduces the time required for calculation of aerodynamic forces. However, this is necessarily accompanied by some loss in accuracy, and hence the method must be verified by comparison with results obtained by the full aerodynamic model before it may be used with confidence.Such a comparison is presented here, using a two‐dimensional aerofoil and control surface combination as a test case. Active control of the deflectable surface is used to attempt to increase the flutter speed across the complete Mach range, feedback control being achieved by gains acting on heave and pitch proportional and differential signals, interpreted as a hinge moment demand. Full non‐linear and reduced order aerodynamic models are then used to obtain optimum control law gain for flutter suppression. The results demonstrate that the ROM accurately predicts the open loop flutter boundary, gives a good approximation to the increase in flutter speed that may be produced by gain optimization, and produces a similar response given the identical gain values in each system for a significantly reduced cost. Copyright © 2005 John Wiley &amp; Sons, Ltd.

Time-Dependent Coefficient Reduced-Order Model for Unsteady Aerodynamics of Proprotors

We present a methodology for the identification of a periodic-coefficient reduced-order model (ROM) for the prediction of perturbation aerodynamic loads on tiltrotor propellers in cruise flight. Although the result is a periodic-coefficient model, the process requires only frequency-domain aerodynamic solutions. Assuming the unperturbed proprotor in axial flow, the matrix that collects the aerodynamic transfer functions between blade perturbative boundary conditions and generalized aerodynamic forces is first derived. Then its rational matrix approximation, followed by combination with the equations describing the wing/pylon/proprotor kinetic coupling, yields the aerodynamic ROM. This ROM is expressed in terms of a set of linear equations that relate the time evolution of the aerodynamic loads acting on the proprotor blades to wing/pylon and deformable-blade degrees of freedom

Transient response study on rolling effectiveness of multiple control surfaces

A study of the effectiveness of trailing- and leading-edge control surfaces has been made for a rolling wing-fuselage model. An experimental model and wind tunnel test are used to assess the theoretical results. The theoretical model includes the inherently nonlinear dry friction damping moment that is present between the spindle support and the experimental aeroelastic wing model. The roll trim equation of motion and the appropriate aeroelastic equations are solved for different combinations of leading- and trailing-edge control surface rotations using a reduced-order aerodynamic model based upon the fluid eigenmodes of three-dimensional vortex lattice aerodynamic theory. The focus is on the transient response of the system. The present paper provides new insights into the transient dynamic behavior and design of an adaptive aeroelastic wing using trailing- and leading-edge control surfaces.

Transonic limit cycle oscillation analysis using reduced order aerodynamic models

Limit cycle oscillations have been observed in flight operations of modern aircraft, wind tunnel experiments and mathematical models. Both fluid and structural nonlinearities are thought to contribute to these phenomena. With recent advances in reduced order aerodynamic modeling, it is now feasible to analyze limit cycle oscillations that may occur in transonic flow including the effects of structural and fluid nonlinearities. In this paper an airfoil with control surface freeplay (a common structural nonlinearity) is used to investigate transonic flutter and limit cycle oscillations. The reduced order aerodynamic model used in this paper assumes the shock motion is small and in proportion to the structural motions.

Analyzing Mistuning of Bladed Disks by Symmetry and Reduced-Order Aerodynamic Modeling

Analyzing Mistuning of Bladed Disks by Symmetry and Reduced-Order Aerodynamic Modeling

Flutter and limit cycle oscillations of two-dimensional panels in three-dimensional axial flow

Experimental flutter and limit cycle oscillations (LCO) of two-dimensional elastic plates in three-dimensional axial flow were observed. The plate is clamped at its leading edge and free at its trailing edge, i.e., it is a “flag” albeit one dominated by its bending stiffness. In the companion theoretical model the structural nonlinearity arises in both the bending stiffness and the mass inertia. Aerodynamic nonlinearities are neglected, however, and linear three-dimensional incompressible vortex lattice aerodynamic theory and a corresponding reduced order aerodynamic model were used to calculate the linear flutter boundary and also the LCO (that occur beyond the linear flutter boundary). The results from the theory and experiment are in good agreement for the onset of flutter, including the critical flow velocity at which the aeroelastic system becomes unstable, as well as the aeroelastic mode of oscillation and frequency. However, there are significant differences between the present theory and experiment for large-amplitude LCO. It is hypothesized that aerodynamic nonlinearities (not modelled in the present theory) are the primary cause of these differences.

Limit cycle oscillations of two-dimensional panels in low subsonic flow

Limit cycle oscillations of a two-dimensional panel in low subsonic flow have been studied theoretically and experimentally. The panel is clamped at its leading edge and free at its trailing edge. A structural non-linearity arises in both the bending stiffness and the mass inertia. Two-dimensional incompressible (linear) vortex lattice aerodynamic theory and a corresponding reduced order aerodynamic model were used to calculate the linear flutter boundary and also the limit cycle oscillations (that occur beyond the linear flutter boundary).

An Arnoldi approach for generation of reduced-order models for turbomachinery

A linear reduced-order aerodynamic model is developed for aeroelastic analysis of turbomachines. The basis vectors are constructed using a block Arnoldi method. Although the model is cast in the time domain in state-space form, the spatial periodicity of the problem is exploited in the frequency domain to obtain these vectors efficiently. The frequency domain proper orthogonal decomposition is identified as a special case of the Arnoldi method. We show an application where the aerodynamic model is coupled with a simple structural model that has two degrees of freedom for each blade. The technique is applicable to viscous and three-dimensional problems as well as multi-stage problems with inlet and exit disturbance flows, although here results are presented for two-dimensional, inviscid flow through a 20-blade single-stage rotor. In this case, the number of states of the model is on the order of 10 per blade passage, making it appropriate for control applications.

Design of an Aeroelastic Delta Wing Model for Active Flutter Control

Ongoing research into the active control of aeroelastic structures has resulted in a new model for the control of delta wing e utter. An analytical and numerical formulation for both the aerodynamic forcing and structural response of the wing was developed. The order of the aerodynamic model was reduced through balanced model reduction, yielding an accurate, low-orderrepresentation of the three-dimensional e owe eld around the delta wing. This fully coupled aero/structural model was used to investigate the optimal placement of piezoelectric sensors and actuators to design an adaptive structure that emphasized control of the e utter mode. Previous work has shown that such control schemes can delay the onset of e utter to increased dynamic pressure. This work extends the practical use of reduced-order aerodynamic modeling to the realm of real-time control system design, while simultaneously applyingrecently developedtechniquesforopen-loop designand selection ofsensorsandactuators. Results indicate that a single sensor/actuator pair can be designed to signie cantly extend the e utter boundary.

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

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.

Reduced Order Aerodynamic Models Based Upon Inflow Eigenmodes

Reduced Order Aerodynamic Models Based Upon Inflow Eigenmodes