Aerodynamic Derivatives Research Articles

Establishment and verification of longitudinal aerodynamic model of tandem wing aircraft

This paper clarified the contribution of front wing and rear wing to the longitudinal aerodynamic derivative by analyzing the characteristics of tandem wing aircraft. By combining the structure and aerodynamic simulation data of the aircraft, the aerodynamic derivative can be directly solved through simplification of force without introducing the tail capacity Vh, and the longitudinal short-period (control) transfer function of the tandem wing aircraft can be obtained by substituting the aerodynamic model which is composed by aerodynamic derivative into the short period motion equation. This transfer function can be used to build the control system in Simulink. When the input signal is the same, the short-period response of the system has high goodness of fit with the value measured in flight test. Therefore, the longitudinal aerodynamic model of the aircraft is well verified, and it can be used for the design of the aircraft controller and its aerodynamic shape. The modeling method and the verification method are applicable to fixed-wing aircraft including tandem wing aircraft.

Identification of In-Flight Wingtip Folding Effects on the Roll Characteristics of a Flexible Aircraft

Wingtip folding is a means by which an aircraft’s wingspan can be extended, allowing designers to take advantage of the associated reduction in induced drag. This type of device can provide other benefits if used in flight, such as flight control and load alleviation. In this paper, the authors present a method to develop reduced order flight dynamic models for in-flight wingtip folding, which are suitable for implementation in real-time pilot-in-the-loop simulations. Aspects such as the impact of wingtip size and folding angle on aircraft roll dynamics are investigated along with failure scenarios using a time domain aeroservoelastic framework and an established system identification method. The process discussed in this paper helps remove the need for direct connection of complex physics based models to engineering flight simulators and the need for tedious programming of large look-up-tables in simulators. Instead, it has been shown that a generic polynomial model for roll aeroderivatives can be used in small roll perturbation conditions to simulate the roll characteristics of an aerodynamic derivative based large transport aircraft equipped with varying fold hinge lines and tip deflections. Moreover, the effects of wing flexibility are also considered.

Kalman-filter based online system identification of fixed-wing aircraft in upset condition

Online system identification became an integral part of the design process for aerodynamic parameter estimation with the technological progress. This paper presents two Kalman-filter based online system identification (SID) techniques for estimating aerodynamic parameters of fixed-wing aircraft in upset condition like stall. Unlike existing SID ones, the proposed methods first include aerodynamic characteristics directly in the aircraft dynamics, i.e. variation of aerodynamic derivatives or flow separation point, associated with the upset condition. Then, the conventional or unscented Kalman filter is applied in real time to obtain optimal estimates of the aerodynamic parameters under consideration. The proposed methods are tested with real flight data sets of several aircraft to demonstrate their effectiveness and superiority to a recently proposed method.

A point vortex model for aerodynamic derivatives for tandem multi-deck structures

The problem of aerodynamic flutter has received much attention and continues to be important for slender structures, such as long-span suspension bridges. The wind flow across the structure can approximately be described as a two-dimensional flow across a moving flat plate, and the bridge motion can be expanded in heave and pitch motions, leading to the traditional aerodynamic derivatives description.In this paper, the classical Theodorsen model [NACA report no. 496, 1934] is revisited, and an extended method is proposed, allowing computation of the aerodynamic derivatives for more complex planar geometries, such as tandem configuration multi-deck bridges. In keeping with the Theodorsen model, the vorticity in the wake is modelled as a vortex sheet advected passively with the free-stream velocity.The bridge deck influence on the wind flow is described by a number of point vortices, and the aerodynamic forces and moments on the bridge are obtained as the rate-of-change of their aerodynamic impulse and angular impulse.Twin-deck bridges are considered for a number of inter-deck spacings. A set of critical reduced wind speeds, depending on the spacing between decks, are identified. Preliminary wind tunnel test results are reported and shown to correspond well to the point vortex model predictions.

Energy budget analysis and engineering modeling of post-flutter limit cycle oscillation of a bridge deck

The post-flutter limit cycle oscillation (LCO) of a two-degree-of-freedom bridge deck involving aerodynamic nonlinearities is studied using computational fluid dynamics (CFD) simulations. To investigate the aerodynamic mechanism for the post-flutter LCO, a comprehensive energy budget analysis is conducted based on the simulated responses, in which the energy input properties of the 1st-order and higher-order force components are considered separately. Results show that only the 1st-order force components contribute significantly in the energy input, while the contributions of the higher-order force components are insignificant. The sensitivities of aerodynamic derivatives to vibration amplitudes and phase difference between vibration modes are investigated using forced vibration CFD simulations. For the concerned bridge deck, some aerodynamic derivatives are highly sensitive to vibration amplitude, while the influences of modal coupling effects are insignificant. A simplified multi-input multi-output nonlinear self-excited force model with amplitude-dependent aerodynamic derivatives is developed according to the sensitivity analysis. An example of bridge post-flutter LCO with two degrees of freedom is utilized to demonstrate the accuracy of the amplitude-dependent aerodynamic derivative-based model. The model also applies to single-degree-of-freedom LCOs, e.g., galloping and vortex-induced vibration, and hence it may serve as a unified analysis framework for nonlinear bridge aeroelasticity.

Isogeometric Modeling and Experimental Investigation of Moving-Domain Bridge Aerodynamics

Computational fluid dynamics (CFD) and fluid–structure interaction (FSI) are growing disciplines in the aeroelastic analysis and design of long-span bridges, which, with their bluff body characteristics, offer major challenges to efficient simulation. In this paper, we employ isogeometric analysis (IGA) based on nonuniform rational B-splines (NURBS) to numerically simulate turbulent flows over moving bridge sections in three dimensions (3D). Stationary and dynamic analyses of two bridge sections, an idealized rectangular shape with aspect ratio 1∶10 and a 1∶50-scale model of the Hardanger bridge, were performed. Wind tunnel experiments and comparative finite-element (FE) analyses of the same sections were also conducted. Studies on the convergence, static dependencies on the angle of attack, and self-excited forces in terms of the aerodynamic derivatives show that IGA successfully captures the bluff-body flow characteristics and exhibits superior per-degree-of-freedom accuracy compared to the more traditional lower-order FE discretizations.

Influences of airfoil profile on lateral-directional stability of aircraft with flying wing layout

PurposeThe purpose of this study is to analyze influence of airfoil profile on lateral-directional flying quality of flying wing aircraft. The lateral-directional stability is always insufficient for aircraft with the layout due to the absence of vertical stabilizer. A flying wing aircraft with double-swept wing is used as research object in the paper.Design/methodology/approachThe 3D model is established for the aircraft with flying wing layout, and parametric modeling is carried out for airfoil mean camber line of the aircraft to analyze lateral-directional stability of the aircraft with different camber line parameters. To increase computational efficiency, vortex lattice method is adopted to calculate aerodynamic coefficients and aerodynamic derivatives of the aircraft.FindingsIt is found from the research results that roll mode and spiral mode have a little effect on lateral-directional stability of the aircraft but Dutch roll mode is the critical factor affecting flying quality level of such aircraft. Even though changes of airfoil mean line parameters can greatly change assessment parameters of aircraft lateral-directional flying quality, that is kind of change cannot have a fundamental impact on level of flying quality of the aircraft. In case flat shape parameters are determined, the airfoil profile has a limited impact on Dutch roll mode.Originality/valueInfluences of airfoil profile on lateral-directional flying quality of aircraft with double-swept flying wing layout are revealed in the thesis and some important rules and characteristics are also summarized to lay a theoretical basis for design of airfoil and flight control system of aircraft with the layout.

Computational Simulation of Flight Behavior of Flying Wing UAV

Abstract — The aim of this work is to model and simulate a Flying Wing Aircraft and compare acquired flight data from two different simulations. The framework proposed constitutes of the development of a graphical model as well as the use of a mathematical model of the aircraft. In order to implement the Software-in-the-Loop (SIL), we used a commercial flight simulation environment, X-plane 10, which simulates the dynamics of the aircraft through the Blade Element Theory, and the software MATLAB/Simulink, which simulates and implement the control laws. We collected the flight data from the simulator, as well as the responses of the mathematical model based on equations of motion and the aerodynamic derivatives, which were computed via the Digital DATCOM software. Both analytical simulation and the SIL simulation were performed with the same flight conditions, validating the longitudinal dynamic of the computational model and allowing further studies of this type of aircraft in future projects.

Dynamic flight stability of hovering mosquitoes

The flight of mosquitoes is unusual compared with many other insects, such as fruit-flies and honey bees: mosquitoes fly with their legs spread; they also have rather short stroke amplitude, hence use different aerodynamic mechanisms to produce lift. Could their flight-stability properties be different from those of other insects? Here, we first measured wing kinematics and morphological parameters of two hovering mosquitoes, and then use the method of computational fluid dynamics to compute the aerodynamic derivatives and the techniques of eigenvalue and eigenvector analysis to study their stability properties. We found that their natural-mode structure is the same as that of many other insects: for the longitudinal motion, one unstable oscillatory mode, one stable fast subsidence mode and one stable slow subsidence mode; for the lateral motion: an unstable divergence mode, a stable oscillatory mode and a stable subsidence mode. The different aerodynamic mechanisms of mosquitoes do not change the major aerodynamic derivatives. The spread legs of mosquitoes have great effect on the moments of inertia and make the eigenvalue of the stable lateral mode much smaller. However, the leg-spreading has only a small quantitative effect on the unstable eigenvalues: the magnitudes of the eigenvalues in the two unstable modes, or the growth rate of the disturbances, are reduced by approximately 11%, compared to those calculated without considering the spread legs.

Yaw-control efficiency analysis for a diamond wing configuration with outboard split flaps

The yaw-control device of a low-aspect ratio flying wing with diamond-shaped wing planform is investigated. Extensive low-speed wind tunnel experiments have been carried out to obtain surface pressure data and the aerodynamic forces and moments of the configuration for six different flap deflection angles at varying angles of attack and sideslip. Complementary unsteady Reynolds-averaged Navier–Stokes simulations are performed for selected configurations. The experimental data is used to examine the validity of the numerical results. The analysis is focused on the aerodynamic coefficients and derivatives. Yaw-control effectiveness, yaw-control efficiency, crosswind landing capabilities and coupling effects are discussed. The results show sufficient yaw-control effectiveness and efficiency for a wide range of considered freestream conditions. The outboard flap exhibits a non-linear characteristic with respect to the flap deflection angle and freestream conditions. The efficiency is considerably reduced at high angles of attack due to large-scale flow separation in the wing outboard section. Non-linear coupling effects with the rolling moment become obvious for moderate to large flap deflections over the whole angle of attack polar. The numerical results show good agreement with the experimental data in the surface pressure distributions and longitudinal aerodynamic coefficients. The yawing moment is overpredicted by numerical simulations for large flap deflection angles.

Superposition principle in bridge aerodynamics: Modelling of self-excited forces for bridge decks in random vibrations

The modeling of self-excited forces in modern bridge aerodynamics traditionally involves the assumption of superposition. The use of a linear load model allows to perform sophisticated buffeting analyses, where the response consists of multiple frequency components, even though the aerodynamic derivatives have been determined by single harmonic forced vibration test. The principle of superposition is also of crucial importance when assessing the critical flutter velocity, since the flutter motion is dissimilar to the motion considered in the standard wind tunnel tests. In this study, a recently-developed forced vibration setup that can force arbitrary motions is used to examine the linearity of the load model for self-excited forces considering several frequency components. The section model is first forced into bi-harmonic motions to be able to determine the aerodynamic derivatives for two different reduced velocities at the time. The results correspond in an excellent manner to aerodynamic derivatives from standard forced vibration tests. Further, the aeroelastic forces are measured during broad-banded motions and compared in time and frequency domains with self-excited forces predicted using rational functions. The experimental results confirm that the principle of superposition is valid for lift and pitch for the wedged-shape box cross-section considered. Significant nonlinearities are, however, observed for the self-excited drag, which implies that the principle of superposition does not apply.

Identification of aerodynamic derivatives of bridge decks at high testing wind speed

An identification of eight aerodynamic derivatives based on dual-mode and single-mode extraction of system is presented to improve the applicability and accuracy of identification at high testing wind speed. The participation rate to measure the contribution of modes on free-vibration responses is defined and the single-mode extraction is presented to extract the modal parameters of the system at high wind speed. To verify the reliability and applicability of the presented method, the aerodynamic derivatives of a dummy section with known self-excited forces are identified. It is noted that there is a very good agreement between the identified results and the target ones in the range of the low and high wind speeds and the presented method works well after the critical state of flutter. The sectional wind tunnel test of the Tanggu-haihe bridge is performed to identify the aerodynamic derivatives of the deck at the attack angles of −3°, 0°, and 3°.

Modeling of self-excited forces during multimode flutter: an experimental study

The prediction of multimode flutter relies, to a larger extent than bimodal flutter, on accurate modeling of the self-excited forces since it is challenging to perform experimental validation by using aeroelastic tests for a multimode case. This paper sheds some light on the accuracy of predicted self-excited forces by comparing numerical predictions of self-excited forces with measured forces from wind tunnel tests considering the flutter vibration mode. The critical velocity and the corresponding flutter vibration mode of the Hardanger Bridge are first determined using the classical multimode approach. Then, a section model of the bridge is forced to undergo a motion corresponding to the flutter vibration mode at selected points along the bridge, during which the forces that act upon it are measured. The measured self-excited forces are compared with numerical predictions to assess the uncertainty involved in the modeling. The self-excited lift and pitching moment are captured in an excellent manner by the aerodynamic derivatives. The self-excited drag force is, on the other hand, not well represented since second-order effects dominate. However, the self-excited drag force is very small for the cross-section considered, making its influence on the critical velocity marginal. The self-excited drag force can, however, be of higher importance for other cross-sections.

Aircraft neural modeling and parameter estimation using neural partial differentiation

PurposeThe purpose of this paper is to build a neural model of an aircraft from flight data and online estimation of the aerodynamic derivatives from established neural model.Design/methodology/approachA neural model capable of predicting generalized force and moment coefficients of an aircraft using measured motion and control variable is used to extract aerodynamic derivatives. The use of neural partial differentiation (NPD) method to the multi-input-multi-output (MIMO) aircraft system for the online estimation of aerodynamic parameters from flight data is extended.FindingsThe estimation of aerodynamic derivatives of rigid and flexible aircrafts is treated separately. In the case of rigid aircraft, longitudinal and lateral-directional derivatives are estimated from flight data. Whereas simulated data are used for a flexible aircraft in the absence of its flight data. The unknown frequencies of structural modes of flexible aircraft are also identified as part of estimation problem in addition to the stability and control derivatives. The estimated results are compared with the parameter estimates obtained from output error method. The validity of estimates has been checked by the model validation method, wherein the estimated model response is matched with the flight data that are not used for estimating the derivatives.Research limitations/implicationsCompared to the Delta and Zero methods of neural networks for parameter estimation, the NPD method has an additional advantage of providing the direct theoretical insight into the statistical information (standard deviation and relative standard deviation) of estimates from noisy data. The NPD method does not require the initial value of estimates, but it requires a priori information about the model structure of aircraft dynamics to extract the flight stability and control parameters. In the case of aircraft with a high degree of flexibility, aircraft dynamics may contain many parameters that are required to be estimated. Thus, NPD seems to be a more appropriate method for the flexible aircraft parameter estimation, as it has potential to estimate most of the parameters without having the issue of convergence.Originality/valueThis paper highlights the application of NPD for MIMO aircraft system; previously it was used only for multi-input and single-output system for extraction of parameters. The neural modeling and application of NPD approach to the MIMO aircraft system facilitate to the design of neural network-based adaptive flight control system. Some interesting results of parameter estimation of flexible aircraft are also presented from established neural model using simulated data as a novelty. This gives more value addition to analyzing the flight data of flexible aircraft as it is a challenging problem in parameter estimation of flexible aircraft.

Heavy rain effects on aircraft lateral/directional stability and control determined from numerical simulation data

In this paper, effects of heavy rain on the lateral/directional stability and control performance of a DHC-6 Twin Otter aircraft are determined based on from the numerical simulation data. A two-way momentum coupled Eulerian–Lagrangian approach developed for two-phase flow simulation is adopted to obtain the fundamental aerodynamic coefficients in the rain condition. Then the lateral/directional aerodynamic derivatives of the aircraft in rain are evaluated based on the linear fitting processing and the strip theory. Finally, the lateral/directional stability of the aircraft in rain is obtained and the controllability is analyzed by simulation of the responses to unit step changes in the control surface deflections. The present results indicate that heavy rain can cause penalties in both the aerodynamic and flight mechanical performance of aircraft.

Using ALE-VMS to compute aerodynamic derivatives of bridge sections

Aeroelastic analysis is a major task in the design of long-span bridges, and recent developments in computer power and technology have made Computational Fluid Dynamics (CFD) an important supplement to wind tunnel experiments. In this paper, we employ the Finite Element Method (FEM) with an effective mesh-moving algorithm to simulate the forced-vibration experiments of bridge sectional models. We have augmented the formulation with weakly-enforced essential boundary conditions, and a numerical example illustrates how weak enforcement of the no-slip boundary condition gives a very accurate representation of the aeroelastic forces in the case of relatively coarse boundary layer mesh resolution. To demonstrate the accuracy of the method for industrial applications, the complete aerodynamic derivatives for lateral, vertical and pitching degrees-of-freedom are computed for two bridge deck sectional models and compared with experimental wind-tunnel results. Although some discrepancies are seen in the high range of reduced velocities, the proposed numerical framework generally reproduces the experiments with good accuracy and proves to be a beneficial tool in simulation of bluff body aerodynamics for bridge design.

An enhanced identification procedure to determine the rational functions and aerodynamic derivatives of bridge decks

Development of time-efficient and reliable methods for estimating the aeroelastic properties of bridge decks is of major importance for bridge engineers to make wind tunnel testing more productive and less expensive. This paper presents an enhanced and more efficient procedure to identify rational functions and aerodynamic derivatives from wind tunnel tests of section models. The accuracy of the proposed method was investigated for a wedged shaped box section, a rectangular section with B/D 1:10 aspect ratio and a twin deck section. In comparison with the data from standard forced vibration tests, the proposed procedure obtained nearly identical results for the eight most influential aerodynamic derivatives. In the case of the twin deck section, the experimental results show that the aerodynamic derivatives are very sensitive to the motion applied and that a linear model therefore cannot uniquely define the self-excited forces for the particular twin deck section tested. The identified results were used to predict the self-excited forces induced under various motion and wind conditions to verify the accuracy of the identified models. Some comments are also given regarding the observed nonlinear effects in the recorded self-excited forces.

Roll performance assessment of a light aircraft: Flight simulations and flight tests

A methodology is presented for the roll performance assessment of a light aircraft. The study is based both on flight simulations and flight tests, focusing on the accurate determination of the lateral control power. The chosen test airplane was a Tecnam P92, a two-seat ultralight aircraft which was specifically equipped with a lightweight and accurate instrumentation for the planned set of flight data measurements. A matrix of flight experiments for the test campaign was established with the support of 6-degree-of-freedom simulations, implementing a carefully constructed baseline dynamic model of the aircraft. The article discusses first the general problem of a reliable evaluation of aircraft roll performance indicators, i.e. the estimation of the aerodynamic derivatives that mainly influence the airplane ability to roll. Next, the results of extensive flight test activities are presented. The analysis of several roll maneuvers performed at different flight speeds and with different aileron maximum deflections showed interesting rolling characteristics for this non-aerobatic aircraft. One notable finding was a clear nonlinear dependency of the aileron efficiency index on aileron deflection amplitude. A control power derivative extracted from flight data in the form of lookup table was used to correct the baseline flight dynamics model. Flight simulations outputs based on the updated model showed a satisfactory agreement with experimental time histories. According to this, the present effort proposes a new method to estimate the aileron control derivative in whole the flight envelope for light aircraft.

Calculation and Identification of the Aerodynamic Parameters for Small-Scaled Fixed-Wing UAVs.

The establishment of the Aircraft Dynamic Model (ADM) constitutes the prerequisite for the design of the navigation and control system, but the aerodynamic parameters in the model could not be readily obtained especially for small-scaled fixed-wing UAVs. In this paper, the procedure of computing the aerodynamic parameters is developed. All the longitudinal and lateral aerodynamic derivatives are firstly calculated through semi-empirical method based on the aerodynamics, rather than the wind tunnel tests or fluid dynamics software analysis. Secondly, the residuals of each derivative are proposed to be identified or estimated further via Extended Kalman Filter (EKF), with the observations of the attitude and velocity from the airborne integrated navigation system. Meanwhile, the observability of the targeted parameters is analyzed and strengthened through multiple maneuvers. Based on a small-scaled fixed-wing aircraft driven by propeller, the airborne sensors are chosen and the model of the actuators are constructed. Then, real flight tests are implemented to verify the calculation and identification process. Test results tell the rationality of the semi-empirical method and show the improvement of accuracy of ADM after the compensation of the parameters.

Aerodynamic Admittance Function using Impulse Response Function Approach

An explanation described here is how the aerodynamic admittance function(AAF) is to derive by means of impulse response function(IMF) which is modified for two peaks (movement-induced and Karman Vortex-induced) intending to be able to deal with the response condition under higher reduced wind speed. By using the analogy of the Sears function and the flutter derivatives, the relationship between the aerodynamic derivatives(AD) and aerodynamic admittance function is clarified. The equivalent Sears function(ESF) is obtained through Fourier transform of IMF incorporate with some shape parameters. After AD has been approximated, the corresponding AAF, which is the square value of ESF, is achieved. This paper includes the verification that the AAF of thin airfoil estimated applying the formulation is found to agree well with thin airfoil Sears function proposed by Holmes and Liepmann.