Unsteady Aerodynamic Calculations Research Articles

Wing Kinematics and Unsteady Aerodynamics of a Hummingbird Pure Yawing Maneuver.

As one of few animals with the capability to execute agile yawing maneuvers, it is quite desirable to take inspiration from hummingbird flight aerodynamics. To understand the wing and body kinematics and associated aerodynamics of a hummingbird performing a free yawing maneuver, a crucial step in mimicking the biological motion in robotic systems, we paired accurate digital reconstruction techniques with high-fidelity computational fluid dynamics (CFD) simulations. Results of the body and wing kinematics reveal that to achieve the pure yaw maneuver, the hummingbird utilizes very little body pitching, rolling, vertical, or horizontal motion. Wing angle of incidence, stroke, and twist angles are found to be higher for the inner wing (IW) than the outer wing (OW). Unsteady aerodynamic calculations reveal that drag-based asymmetric force generation during the downstroke (DS) and upstroke (US) serves to control the speed of the turn, a characteristic that allows for great maneuvering precision. A dual-loop vortex formation during each half-stroke is found to contribute to asymmetric drag production. Wake analysis revealed that asymmetric wing kinematics led to leading-edge vortex strength differences of around 59% between the IW and OW. Finally, analysis of the role of wing flexibility revealed that flexibility is essential for generating the large torque necessary for completing the turn as well as producing sufficient lift for weight support.

Parametric reduced-order modeling of unsteady aerodynamics for hypersonic vehicles

A novel parametric reduced-order model (ROM) is proposed for efficiently predicting hypersonic unsteady aerodynamic responses under different flight conditions. The construction of the ROM is realized by computational fluid dynamics (CFD) simulations under the prescribed motion of the structure, while the results are processed via the proper orthogonal decomposition (POD) to obtain the predominant flow modes. Subsequently, to obtain the ROM valid for varying flight conditions, the method of interpolation in a tangent space to a Grassmann manifold is used to generate a new POD modal matrix for the arbitrary operating point in the considered parameter space. Finally, the least squares support vector machine (LS-SVM) is carried out to obtain the nonlinear relations between the applied excitations and the resulting POD coefficients. Once the parametric ROM is constructed, it can behave as a substitution of the full-order CFD flow solver in the considered parameter space. For demonstration purposes, the parametric ROM is used to predict hypersonic unsteady aerodynamic loads, flutter boundaries and limit-cycle oscillations of a double wedge airfoil over a wide range of the flight conditions, respectively. Numerical investigations show a good agreement between the results obtained by the ROM methodology in comparison to the full-order CFD solution over a wide range of the parameters. In addition, the ROM approach yields a significant speedup regarding unsteady aerodynamic calculations, which is beneficial for aeroelastic analysis, control and optimization applications.

Efficient unsteady aerodynamic loads prediction based on nonlinear system identification and proper orthogonal decomposition

In the present work, an efficient surrogate-based framework is developed for the prediction of motion-induced surface pressure fluctuations and integral force and moment coefficients. The model construction is realized by performing forced-motion computational fluid dynamics (CFD) simulations, while the result is processed via the proper orthogonal decomposition (POD) to obtain the predominant flow modes. Subsequently, a nonlinear system identification is carried out with respect to the applied excitation and the resulting POD coefficients. For the input/output model identification task, a recurrent local linear neuro-fuzzy approach is employed in order to capture the linear and nonlinear characteristics of the dynamic system. Once the reduced-order model (ROM) is trained, it can substitute the flow solver within unsteady aerodynamic or aeroelastic simulation frameworks for a given configuration at fixed freestream conditions. For demonstration purposes, the ROM approach is applied to the LANN wing in high subsonic and transonic flow. Due to the characteristic lambda-shock system, the unsteady aerodynamic surface pressure distribution is dominated by nonlinear effects. Numerical investigations show a good correlation between the results obtained by the ROM methodology in comparison to the full-order CFD solution. In addition, the surrogate approach yields a significant speed-up regarding unsteady aerodynamic calculations, which is beneficial for multidisciplinary computations.

Reduced-Order Modeling of Unsteady Aerodynamics Across Multiple Mach Regimes

A reduced-order model for unsteady aerodynamic calculations across a range of Mach regimes based on linear convolution and a nonlinear correction factor is developed. Separate investigations are conducted for the sub-, trans-, and supersonic Mach regimes, and overall good results are seen when reduced-order model results are compared with full-order computational-fluid-dynamics solutions, though the reduced-order model errors tend to decrease as the Mach number increases. To assist reduced-order model construction, the method-of-segments simplified model has been created and tested throughout these same Mach regimes. Finally, a practical example of the reduced-order model’s applicability is presented by following a single test case from subsonic up through supersonic flight.

Correction of aerodynamic influence matrices for transonic flow

The authors present a novel correction approach for the doublet-lattice method in this paper. The doublet-lattice method is a standard tool for calculating unsteady aerodynamic loads in aeroelasticity. It solves the linear potential equations and is thus valid only at subsonic flow conditions. Hence, corrections have to be applied for transonic flow. The proposed correction method, CREAM (CorREction of Aerodynamic Matrices), uses surface pressure distributions obtained using computational fluid dynamics (CFD) simulations for the correction. It is based on a Taylor expansion of the aerodynamic influence coefficient matrix, where the Taylor coefficients are corrected successively. The approach can be applied to quasi-steady as well as to unsteady aerodynamic calculations. The method is demonstrated on the AGARD LANN wing at transonic attached flow conditions and compared to linearized unsteady CFD computations. Two different correction orders are examined: a “zeroth order correction” with a quasi-steady CFD sample as correction input and a “first order correction” with an additional unsteady CFD sample. It is shown that CREAM gives improved results for small reduced frequencies, where the first-order correction is always superior to the zeroth order correction.

Flutter Analysis of Wing, Booster Fin and Vertical Tail

Aerospace vehicles are subjected to various types of severe environmental loads. The basic design criterion includes the minimum weight configuration that results in very flexible structures, which leads to various types of structural interaction problems like flutter, divergence etc. Hence every aerospace vehicle should be analysed for its aeroelastic instabilities. In the present work the flutter analysis of a typical space vehicle was carried out in substructure level with the interface fixed condition. The doublet lattice, zona51 and piston theories are used in the unsteady aerodynamic calculations for the subsonic, supersonic and hypersonic speed regimes. As there is no theoretical procedure for transonic speeds, doublet lattice method has been used in the present analysis. Frequency and damping versus velocity are presented to identify the flutter velocities and the flutter behavior.

Aerodynamic Loads on Airfoil with Trailing-Edge Flap Pitching with Different Frequencies

Unsteady aerodynamic loads on NACA 0012 airfoil with a trailing-edge flap were measured in wind tunnel and calculated from a simple theoretical model. The airfoil model of 0.18 m chord length used in wind-tunnel test was oscillating in pitch about an axis located at 35% chord length from the airfoil leading edge. The length of trailingedge flap was 22.6% of airfoil chord. The flap was also deflecting harmonically, but with frequency different from airfoil pitching motion. The influence of phase delay between airfoil angle of incidence and flap deflection at the beginning of the motion was considered. The theoretical method used for calculation of unsteady airfoil loads is based on two-dimensional, inviscid, incompressible flow model at subsonic Mach numbers. The expressions for unsteady aerodynamic loads calculations on the airfoil and on the flap were obtained in a closed form using distribution of flow velocity potential along the airfoil chord and along the flap length. Lift and aerodynamic moment measured in the wind tunnel were compared with results of calculations. The correlation between experimental and theoretical results is adequate.

Chebyshev Polynomials for Unsteady Aerodynamic Calculations in Aeroservoelasticity

The aerodynamic forces in the reduced frequency domain have to be approximated in the Laplace domain, in order to study the effects of the control laws on the flexible aircraft structure. This type of approximation of unsteady generalized aerodynamic forces from the frequency domain into the Laplace domain, acting on a Fly-By-Wire aircraft, presents an important challenge in the aeroservoelasticity area. In this paper we present a new method for approximation of the generalized aerodynamic forces, using Chebyshev polynomials and their orthogonality properties. A comparison of results expressed in terms of flutter speeds and frequencies obtained

Unsteady aerodynamic calculations using three-dimensional Euler equations on unstructured dynamic grids

AbstractThis paper presents an algorithm to solve the three-dimensional unsteady Euler equations on unstructured tetrahedral meshes using a dynamic mesh algorithm. The driving algorithm is an upwind biased implicit second order accurate cell-centered finite volume scheme. The spatial discretisation technique involves a naturally dissipative flux-split approach that accounts for the local wave propagation characteristics of the flow and captures shock waves sharply. A continuously differentiable flux limiter has been employed to eliminate the spurious oscillations near shock waves, generally arising in calculations involving upwind biased schemes. The temporal discretisation is also second order accurate and uses a Newton linearisation for unsteady calculations. To calculate time dependent flows a dynamic mesh algorithm has been implemented in which the mesh is moved to conform to the instantaneous position of the body by modelling each edge of each cell by a spring. The paper presents a description of the solver and the grid movement algorithm along with results and comparison that assess their capabilities.

Computational Fluid Dynamics and Doublet-Lattice Calculation of Unsteady Control Surface Aerodynamics

Accurate prediction of control surface aerodynamics has been a challenge since the dawn of aviation. Whereas this has been an important problem for many years, recent increases in the use of control surfaces for active control (load alleviation and e utter suppression ) have increased the importance of accurate steady and unsteady control surface aerodynamics. Because of the strong ine uence of viscosity on the pressures on a trailing-edge control surface, the aerodynamic theories based on the linear potential equation have had only marginal success in predicting control surface aerodynamics, and in practice, large corrections (based on wind-tunnel data ) are often required for acceptable accuracy. Recent advances in computing technology and unsteady aerodynamic codes based on the Navier ‐Stokes equation areallowing moreaccurate analysesto be performed. Unsteady aerodynamic calculations due to control surface oscillations are made using a linear potential code (N5K) and a Navier‐Stokes code (CFL3D.AE-BA version 4.1 ). The Navier‐Stokes calculations are performed in the time domain using an exponential pulse technique and are transformed to the frequency domain using Fourier transform. For low reduced-frequency cases, theNavier ‐Stokes calculations arecompared to the doublet-lattice method and to experiment, and the advantages of the nonlinear analysis are clearly demonstrated. Correlation between Navier ‐Stokes and doublet-lattice results is then studied for higher reduced frequencies.

MULTIDISCIPLINARY OPTIMIZATION OF COMPOSITE WINGS USING REFINED STRUCTURAL AND AEROELASTIC ANALYSIS METHODOLOGIES

An integrated multidisciplinary procedure has been developed for structural and aeroelastic optimization of composite wings based on refined analysis techniques. A refined higher-order theory is used to analyze a composite box beam, which represents the load carrying member of the wing. Unsteady aerodynamic computations are performed using a panel code based on the constant-pressure lifting surface method. Flutter/ divergence dynamic pressure is obtained by the Laplace domain method through rational function approximation of unsteady aerodynamic loads. The objective of the optimization procedure is to minimize wing structural weight with constraints on flutter/ divergence speed and stresses at the root due to the static load. Composite ply orientations and laminate thicknesses are used as design variables. The Kreisselmeier-Stcinhauscr function approach is used to efficiently integrate the objective function and constraints into a single envelope function. The resulting unconstrained optimization problem is solved using the Davidon-Fletcher-Powell algorithm. Numerical results are presented showing significant improvements, after optimization, compared to a reference design.

Current status of computational methods for transonic unsteady aerodynamics and aeroelastic applications

The current status of computational methods for unsteady aerodynamics and aeroelasticity is reviewed. The key features of challenging aeroelastic applications are discussed in terms of the flowfield state—low-angle high speed flows and high-angle vortex-dominated flows. The critical role played by viscous effects in determining aeroelastic stability for conditions of incipient flow separation is stressed. The need for a variety of flow modeling tools, from linear formulations to implementations of the Navier-Stokes equations, is emphasized. Estimates of computer run-times for flutter calculations using several computational methods are given. Applications of these methods for unsteady aerodynamic and transonic flutter calculations for airfoils, wings and configurations are summarized. Finally, recommendations are made concerning future research directions.

Semianalytical technique for sensitivity analysis of unsteady aerodynamic computations

A semianalytical approach is developed for the sensitivity analysis of linear unsteady aerodynamic loads. The semianalytical approach is easier to implement than the analytical approach. It is also computationally less expensive than the finite difference approach when used with panel methods, which require a large number of panels. The semianalytical approach is applied to an isolated airfoil in a 2-D flow and rotating propfan blades in 3-D flow. Sensitivity coefficients with respect to non-shape-dependent variables are shown for some cases. It is expected that the semianalytical approach will be useful in aeroelastic design procedures particularly when mistuning is present, and that it is potentially useful for shape sensitivity analysis of linear unsteady aerodynamics.

Unsteady aerodynamic and aeroelastic calculations for wings using Euler equations

A procedure to solve simultaneously the Euler flow equations and modal structural equations of motion is presented for computing aeroelastic responses of wings. The Euler flow equations are solved by a finite-difference scheme with dynamic grids. The coupled aeroelastic equations of motion are solved using the linear-acceleration method. The aeroelastic configuration adaptive dynamic grids are time-accurately generated using the aeroelastically deformed shape of the wing. The unsteady flow calculations are validated with the experiment, both for a semi-infinite wing and a wall-mounted cantilever rectangular wing. Aeroelastic responses are computed for a rectangular wing using the modal data generated by the finite-element method. The robustness of the present approach in computing unsteady flows and aeroelastic responses that are beyond the capability of earlier approaches using potential equations are demonstrated.

Transonic unsteady aerodynamic and aeroelastic calculations about airfoils and wings

Some of the research in the area of computational unsteady transonic flow about airfoils and wings, including aeroelastic effects, is surveyed. Results are presented for the unsteady, transonic, small-disturbance potential equation. Several calculations are shown of unsteady transonic flow over airfoils and wings, including cases that employ viscous modeling and cases that compare with experimental data. First an early result of transonic flow with moving shock waves over an airfoil is described. Next a calculation is compared with an experiment of flow over an NACA 0012 airfoil, for which there is a large shock movement. For flow over wings, first calculations are shown of flow over a transport wing, including comparisons with experiment of aeroelastic results. Next calculations of flow over a low aspect ratio wing are compared with experimental results. Finally, aerodynamic calculations of flow over a variable-sweep wing are compared with experiment, and the effect of varying the sweep on the aeroelastic damping is studied.

Effects of viscosity on transonic-aerodynamic and aeroelastic characteristics of oscillating airfoils

Studies were made to investigate the effects of viscosity on aerodynamic and aeroelastic characteristics of oscillating airfoils. The computer code LTRAN2 (viscous), which is based on a small disturbance aerodynamic theory, was used to make aerodynamic computations. Two viscous models, the viscous-ramp model and the lag-entrainment model were considered. The unsteady viscous effects were obtained by use of the quasi-steady assumptions. Two cases, a conventional airfoil, NACA 64A010, and a supercritical airfoil, MBB-A3, were studied at Mach numbers 0.796 and 0.7557, respectively. For both the airfoils, steady and unsteady aerodynamic computations were made by using inviscid and viscous theories. The steady and the unsteady results for the NACA 64A010 airfoil and the steady results for the MBB-A3 airfoil were compared with the available wind-tunnel results. Flutter speeds were computed for both airfoils by using the U-g method and the effects of viscosity on the airfoils were studied. Results from the viscous methods show improvements over the inviscid method.

New Frequency Parameter for Unsteady Aerodynamics

A new frequency parameter that minimizes the number of points required to represent unsteady aerodynamics has been developed. The parameter expands the low range of the reduced frequencies where the aerodynamics vary rapidly and compresses the moderate to high frequency range into a finite domain. Four examples showing the general applicability of the parameter are presented. I. Background and Basis Aeroelastic analyses require unsteady aerodynamic coefficients at a large number of reduced frequency values (k). For transports the range of reduced frequency that must be accurately defined is from k=O to about k=1.0 (where k = and b is the reference semichord, u is circular frequency and V is freestream velocity). Because the computation of these unsteady coefficients is expensive, many aeroelastic programs rely on precomputed tables which are interpolated to determine the unsteady aerodynamics. An accurate representation of the aerodynamics requires a large number of entries in the table, particularly in the low k area, where the aerodynamics vary most rapidly. The cost of the computation and the need for accuracy, therefore, motivate the search for a parameter that would transform the reduced frequency scale in such a way as to minimize the number of unsteady aerodynamic calculations while retaining the required accuracy. The requirements on such a parameter may be sum