Dynamic Response of an Aircraft to Atmospheric Turbulence Cissy Thomas Civil Engineering Dept, M.G university

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1 Dynamic Response of an Aircraft to Atmospheric Turbulence Cissy Thomas Civil Engineering Dept, M.G university Jancy Rose K Scientist/Engineer,VSSC, Thiruvananthapuram, India R Neetha Division Head, VSSC, Thiruvananthapuram, India Abstract The response of an aircraft in flight to atmospheric gusts is one of the dynamic response problems, which controls the wing design and dimensioning of large aircraft. In the present work, dynamic analysis of an aircraft subjected to a one-dimensional random gust is carried out. Power spectral density (PSD) of gust is represented by both von Karman and Dryden mathematical gust model. Finite element model (FEM) of a typical aircraft is generated using Finite Element software. Aero dynamic modelling is also carried out. The Doublet-Lattice method (DLM) is used for interfering lifting surfaces in subsonic flow. The analysis was performed using the advanced FEM software. Natural frequencies are computed and mode shapes are identified. Continuous gust is applied on the aircraft and the dynamic acceleration and bending moments are computed at critical locations. This work provides dynamic loads due to gust using von Karman and Dryden models. Keywords Gust, Power spectral density (PSD), Aeroelasticity, Aerodynamics, Spline. I. INTRODUCTION Gusts are the predominant excitation source that induces aircraft modal vibration. Gusts are considered to be random in nature and play a major role in the design of various aspects of aircraft operation. The calculation of gust load on an airplane is a two-fold problem involving consideration of both the character of the gust and the response of the airplane. When a gust acting upon an aircraft is continuous, it is defined as turbulence. The local velocity fluctuations sensed by an airplane flying through atmospheric turbulence constitute a random process. Gust is the most important dynamic problem; the gust condition is usually controlling strength condition in large aircraft. Consequently the responses of the airplane, whether they are in motions (linear or angular displacements, velocities or accelerations),forces ( lift, pitching moment, bending moment and so on), stresses, or any other phenomena is determined by the turbulence. Aircraft design requires the evaluation of dynamic loads in response to continuous and random gust excitations. Gust response affects many aspects of aircraft characteristics, including stability and control, dynamic structural loads flight safety. The primary purpose of this work was the computation of dynamic (Design) loads on an aircraft structure due to continuous gust. In the past, the gust response of these aircraft has been mainly investigated using the Pratt-Walker formula, the Pratt-Walker formula does not capture the effects of structural flexibility and the span-wise variation of gust velocity. The atmosphere gust is mathematically described by the PSD function and transforms the problem from the time to a frequency domain. The structure is modelled as a symmetric model; symmetric geometrical, aerodynamic and inertial properties are given by applying symmetric boundary conditions. Aeroelasticity is defined as a science which studies the mutual interaction between aerodynamic forces and elastic forces and the influence of the interaction on airplane design. Aeroelastic problem could not exist if airplane structures are perfectly rigid, flexibility is fundamentally responsible for the various types of aero elastic phenomena. Aeroelastic phenomena arise when structural deformations induce additional aerodynamic forces. This class of aeroelastic problem has its primary effect on structural design in the prediction of design loads on airplane structure in an accelerated condition. External loads that are rapidly applied not only cause translation and rotation of the airplane as a whole, but tend to excite vibrations of the structure. The additional inertia forces associated with these vibrations produce the dynamic overstress. Dynamic stresses induced in the form of bending and torsional stresses in the wing and fuselage beams. The design of these beams must take into account of dynamic stresses by increasing the normal and shear carrying areas. Two important dynamic response problems are the gust and landing problems. Aeroelastic effects may have an important influence on gust design conditions. Scope of this work is to deliver optimized products to specific areas of aeronautical use Objectives To estimate the aeroelastic response of an aircraft under gust loads, thereby compute the dynamic (Design) loads on aircraft using von Karman and Dryden Model respectively. To calculates the probability parameters of the response quantities Gust Gust is a sudden, brief increase in speed of the wind and the duration of a gust is usually less than 20 seconds. Gusts are the predominant excitation source that induces aircraft modal vibration. An understanding of gust response plays a vital role in the design of aircraft surfaces, and the evaluation of this phenomenon is a considerable random dynamic problem. 2014, IJIRAE- All Rights Reserved Page -246

2 II. GUST RESPONSE OF A TYPICAL AIRCRAFT 2.1. General For the purpose of gust analysis a typical aircraft is used, analysis performed using advanced FEM software. The parts of the aircraft to be modelled are right wing, central body or boom, vertical tail and horizontal tail. The structure is modelled as a symmetric model, symmetric geometrical, aerodynamic and inertial properties are given by applying symmetric boundary conditions. The high aspect ratio wing is modelled with inboard and outboard panel. Aerodynamic modelling is carried out and flat plate lifting surfaces. Finite element model is coupled with aerodynamic model using surface splining technique. The modal displacements of aerodynamic boxes are related to displacements of the structural grids by this technique.in the phase of the gust response evaluation, the continuous turbulence approach was selected. The atmosphere is described by the power spectral density function and transforms the problem from the time to a frequency domain. The power spectral density (PSD) of the gust load is represented by the von Karman and Dryden model for the gust analysis. Excitation frequency up to 50 Hertz and forward velocity of vehicle is 30 m/s was considered in the analysis. The flight condition at a Mach number 0.1 considered. The PSD of response quantities such as moments and dynamic accelerations at critical locations of the structure were generated and plotted versus a range of frequencies covering the elastic mode of vibration Finite Element Modelling Finite element model (FEM) of a typical aircraft is generated. The boom, wing and tails are generated. The inertia and stiffness properties along the elastic axis are provided for a typical aircraft under consideration. In FEM model, grids along the central body and elastic axis of wing are connected by the CBEAM elements, which defines a beam element and chord-wise grids on the lifting surfaces were joined to the elastic axis grids by rigid (RBE2) elements by replacing very stiff beam element, thereby the number of degrees of freedom was substantially reduced. The entire model mass is contained in the concentrated masses which are offset from the grids that lie along the elastic axes. Rigid body elements connect the grid points at the leading and trailing edges of the wing, and leading edges of the tails. The purpose of the grids connected to the main structure by the rigid body elements is to provide mode shape displacements so that motion can be splined onto the aerodynamic surfaces. Fig: 2.1 shows FEM model of aircraft with wing,boom, and horizontal and vertical tail. Symmetric modal frequencies were produced by applying symmetric boundary conditions Normal Modes Analysis To perform real eigenvalue analysis select a frequency band up to 50 Hertz were included in the analysis. Lanczos method is used for extraction of eigenvalues. Natural frequencies and the corresponding bending modes are computed using normal modes solution. A frequency response analysis is an integral part of random response analysis and transient analysis. Fig. 2.1 FEM model of aircraft with wing,boom, and horizontal and vertical tail Inference Normal modes analysis was done to determine the natural frequencies and mode shapes of the structure. Table: 2.1 and Table: 2.2 show the natural frequencies and corresponding mode shapes of aircraft for a symmetric condition. Table: 2.1 Natural frequencies of aircraft Mode Mode Frequency, Frequency, Hz No No Hz , IJIRAE- All Rights Reserved Page -247

3 Table: 2.2 Natural frequencies and Mode shapes of aircraft BENDING MODE MODE SHAPE 1 st Bending mode of wing at Hz 2 nd Bending mode of wing at 1.33 Hz 1 st bending mode of central body at2.260 Hz 3rd Bending mode of wing at 4.132Hz 1 st Bending mode of vertical tail at Hz Fig. 2.2 Aerodynamic panel with wing, horizontal and vertical tail 2 nd Bending of vertical tail at Hz Bending of central body and 4 th mode of wing at Hz 5 th Bending mode of wing and 2 nd mode of central body at 16.73Hz 2.4 Aerodynamic Panelling Flat plate Lifting surfaces are used for Aerodynamic modelling. In aerodynamic model, the main wing was divided into inboard and outboard panels, with the break occurring at a span station of 5.68 m. Fig: 2.2 shows aerodynamic panel with wing, horizontal and vertical tail. The modal displacements of aerodynamic boxes are related to displacements of the structural grids by a surface splining technique. 2014, IJIRAE- All Rights Reserved Page -248

4 2.5 Aerodynamics Unsteady aerodynamic forces and gust loads are applied using Bulk data cards. Reference chord length is 1.5m. and Table: 2.3 tabulated the flight conditions for analysis. Input data are generated based on Ref.7 and Ref.8. Table: 2.3 Flight conditions and properties of Gust Mach no (m) 0.1 Dampi 1 % Excitation Frequency (ω) 0-50 Hz Dynamic pressure 500 N/m 2 True Air speed (V) 30 m/s Scale of turbulence (L) 300 m 2.6 Continuous Turbulence Atmospheric turbulence is in fact a continuous phenomenon. In the phase of the gust response evaluation, the continuous turbulence approach was selected. The power spectral density (PSD) of the gust was represented by Equation (1). Table: 2.4 gives the parameters. S a (ω) ={ } (1) Where, S a (ω) w g ω L V = PSD in units of 1/Hz = Root mean square of gust velocity = Circular frequency = Scale of turbulance = Airplane speed Table: 2.4 von Karman and Dry den parameters Parameters von Karman Dryden k p 1/3 ½ M hh, B hh, K hh = Modal mass damping and stiffness matrix k = Reduced frequency Q hh = Aerodynamic force matrix ω = Circular frequency g = Artificial structural damping = Density V = Velocity = Modal amplitude vector u h 2.7 Aeroelastic Response Analysis Aeroelastic responses like bending moments and accelerations at critical locations of aircraft are computed. The resulting aeroelastic modal equations of motion can be written in the form: Where, (2) III. RESULTS AND DISCUSSIONS The Fig: 3.1 shows the comparison of PSD moments between von Karman and Dryden PSD model at wing root. In PSD analysis using, Dryden gust model, the peak response of PSD bending moment is 430 (N-m) 2 /Hz occurs at 1.3 Hz,which is the frequency of second bending mode of wing. In the case of von Karman model largest response is 1018 (N-m) 2 /Hz at the same frequency. Similarly at wing tip Fig: 3.2 using Dryden gust model, the peak response for bending moment is 12 (N-m) 2 /Hz occurs at a frequency of 2.25 Hz, which is the frequency of first bending mode of central body. In the case of von Karman model largest response is 36 (N-m) 2 /Hz occurs at the same frequency. PSD of the acceleration in vertical direction using von Karman model is compared the same with the Dryden PSD model at wing root is shown in Figure: 3.3 Using Dryden model peak responses 513 (mm/s 2 ) 2 /Hz occurs at the frequency of 0.15 Hz, which is the frequency of first bending mode of wing. In the case of von Karman model maximum PSD acceleration in vertical direction 876 (mm/s 2 ) 2 /Hz occurs at the frequency of 1.8 Hz, that is at second bending mode of wing. 2014, IJIRAE- All Rights Reserved Page -249

5 Fig. 3.2 Comparison of horizontal moments using von Karman and Dryden PSD model at wing tip Fig. 3.3 Comparison between vertical acceleration using von Karman and Dryden PSD model at Wing root Maximum responses (Bending moments and acceleration) are occurs in the wing root compared to the others. The peaks of the different design loads for each of girds vary depending on the location and type of response. von Karman PSD model gives a high response of 1018(N-m) 2 /Hz compared. The root mean square value ( ) of the responses and the expected rate of zero crossings with positive slope (N 0 ) are tabulated in Table: 3.1. Table: 3.1 Probability parameters at critical location Location Response N 0 (Hz) Wing root Moment Wing tip Moment Fig.3.1 Comparison of horizontal moments using von Karman and Dryden PSD model at wing root IV. CONCLUSIONS The dynamic (Design) loads on an aircraft structure due to continuous gust are computed with the aid of PSD models.gust responses are predominently in the second bending mode of wing. von Karman PSD function gives a higher response. For continuous turbulence, the analysis returns the values of root mean square value ( ) of the responses and the expected rate of zero crossings with positive slope (N 0 ). These statistical quantities are important for failure and fatigue analyses. REFERENCES [1] S. A. Fazelzadeh. and H. Sadat-Hoseini., Nonlinear Flight Dynamics Of Flexible Aircraft Subjected To Aeroelastic And Gust Loads, Journal Of Aerospace Engineering January 2012.Vol.25, page [2] A. V. Balakrishnan., Modeling Response Of Flexible High-Aspect-Ratio Wings To Wind Turbulence, Journal Of Aerospace Engineering, Vol.19.April [3] James P. Krieger. and Miroslav. Krstic.,Extremum Seeking Based On Atmospheric Turbulence For Aircraft Endurance, Journal Of Guidance, Control, And Dynamics, Vol. 34, No. 6, November December [4] David Lundstrom and Petterkrus, Testing Of Atmospheric Turbulence Effects on the Performance of Micro Air Vehicles 2012, International Journal Of Micro Air Vehicles, Vol [5] Elisa Capello, Giorgio Guglieri, and Fulvia Quagliotti, A Comprehensive Robust Adaptive Controller for Gust Load Alleviation, The Scientific World Journal,Volume 2014, Article ID [6] Jia Xu and Ilan Kroo, Aircraft Design With Maneuver And Gust Load Alleviation,The American Institute Of Aeronautics And Astronautics. Inc 29th AIAA Applied Aerodynamics Conference June [7] P. Chudy, Response of a Light Aircraft Under Gust Loads, Acta Polytechnica Vol. 44 No. 2/2004. [8] A. S. Naser, A. S. Pototzky, and C. V. Spain, Response of the Alliance 1 Proof of Concept Airplane Under Gust Loads, NASA/CR [9] Federal Aviation Regulations,Part 25:Appendix G., Airworthiness standards: Transport category airplanes. [10] Bisplinghoff. R..L., and Ashley Halfman. (1955) Aeroelasticity Addison-Wesley Publication Company Inc. [11] Bisplinghoff R. L., and Ashley Halfman. (1962). Principles of Aeroelasticity, Wiley, New York. 2014, IJIRAE- All Rights Reserved Page -250