FLUTTER ANALYSIS OF WING, BOOSTER FIN AND VERTICAL TAIL Dr.S.Nadaraja Pillai**, **Assistant Professor, Dept. of Aerospace Engineering *Student,**Assistant Professor, Dept. of Aerospace Engg. SRM University, Chennai, India. Madras Institute of Technology, Anna University,
[email protected] Chennai, India, E-mail:
[email protected], which are increasing due to aerodynamic energy being Abstract— Aerospace vehicles are subjected to various added to the structure. These vibrations can cause structural types of severe environmental loads. The basic design failure and therefore considering flutter characteristics is an criterion includes the minimum weight configuration that essential part of designing an aircraft and space vehicles. results in very flexible structures, which leads to various This instability [3] is a catastrophic phenomenon that types of structural interaction problems like flutter, must be avoided at all costs, and all flying vehicles must be divergence etc. Hence every aerospace vehicle should be clear from flutter and many other aeroelastic phenomena in analysed for its aeroelastic instabilities. In the present work their flight envelope. Flight and wind tunnel testing are two the flutter analysis of a typical space vehicle was carried ways to analyse the flutter margin or the flutter, but both are out in substructure level with the interface fixed condition. expensive and occur late in the design process. Therefore The doublet lattice, zona51 and piston theories are used in engineers rely on the computational methods to assess the the unsteady aerodynamic calculations for the subsonic, aeroelastic characteristics of flight vehicles. The successes supersonic and hypersonic speed regimes. As there is no of CAE [5] are routed in the aeroelastic characterization theoretical procedure for transonic speeds, doublet lattice process. method has been used in the present analysis. Frequency Here, in this paper an overview of the procedure for and damping versus velocity are presented to identify the flutter analysis of a wing is discussed and the results are flutter velocities and the flutter behavior. shown for the other sub-structure of space vehicle, since the Keywords- Computational Aeroelasticity, Flutter Analysis, procedure is same as the wing for the other structures.
G.Vinayagamurthy*, Dr. K.M.Parammasivam**,
Unsteady Aerodynamics
I.
INTRODUCTION
Today every lifting component of the crew vehicle that flies through the atmosphere undergoes a level of aeroelastic analysis before flight [1,2,3]. After World War I, higher airspeeds and a shift from external wire-braced biplanes to aircraft with cantilevered wings resulted in more wing flutter incidents. Primary surface Flutter began to appear around 1925. Air racers experienced many incidents of flutter from the mid-1920 until the mid-1930 as attempts were made to break speed records. Another form of flutter dealt with in the 1930’s was servo tab flutter. Collar [4] predicted that this type of flutter would be around for many years. This prediction was correct, for between 1947 and 1956, 11 cases of tab flutter incidences were reported for military aircraft alone. In 1944, while flight testing the new P-80 airplane, NACA pilots reported incidents of aileron buzz. From 1947 to 1956, there were 21 incidences of flutter involving transonic control surface buzz. Prototypes of both the F-100 and F-14 fighters had incidences of rudder buzz. Today, the transonic flight regime is still considered the most critical from a flutter standpoint of view. So, it is the most necessary to study the aeroelastic instabilities like flutter, buffeting, divergence etc. before flight. Flutter [3] is a dynamic instability phenomenon which involves interactions among the aerodynamic, elastic and inertial forces of a flight vehicle. It is self induced oscillations occurs in an aircraft during the flight due to the interaction of its structural dynamics and the surrounding aerodynamics. In an aircraft, as the velocity of the space vehicle increases, there may be a point at which the structural damping is insufficient to damp out the motions
II.
METHODOLOGY FOR THE FLUTTER ANALYSIS
In order to carry out the flutter analysis for a integrated part of the space vehicle, the primary step is to ensure that the substructures like wings, fins and vertical tails are free from flutter. So, each part is tested separately for flutter analysis in the substructure before the integration of the space vehicle. Flutter analysis
Finite Element Modeling
Dynamic Characterization Steady Aerodynamic analysis
Mode shapes
Unsteady Aerodynamic analysis
[M] & [K] Matrices
Flutter solution
Fig.1 Schematic view of flutter analysis The methodology followed for Flutter analysis is divided in to four steps. The primary one is the Finite Element Modeling of the space vehicle components, the secondary one is the dynamic characterization of the
structure and the third step is the application of aerodynamic loads using aerodynamic theories and fourth is the flutter solution. The methodology [6] followed for the flutter analysis is explained as fig 1. A. Finite Element Modeling The primary step involves the modeling of the space vehicle. The space vehicle consists of four Booster fins, two wings, and two vertical tails. For the subcomponent level analysis, the finite element model is created and the skeletal structure is made of assemblage of one, two, three-dimensional elements such as bar elements (axial action), beam elements, plate elements and solid elements. The relationship between forces and displacements of each member is represented by the stiffness matrix, which is derived directly through the principle of virtual work and principle of minimum potential energy. Each part is modeled and the finite element mesh was generated. The Finite Element Model of the wing is shown in the fig. 2.
Fig. 2 Finite Element Model of Wing (Elevon attached) B. Dynamic Characterization of the space vehicle components Structural equations [7] of motion for the finite-element model of the wing are of the form,
(t)}+[D] { A (t)}+[K] {A(t)} = 0 [M]{ A
…(1)
Where, [M] is the modal mass matrix, [K] is the modal stiffness matrix; [D] is the damping matrix, {A}= {A1…An}, is called normal or principal coordinates, or the modal amplitudes. Then structural dynamic analysis is carried out to study the behavior of the structure and the first five flexible modes and its frequencies are considered to be the predominant modes. The generalized eigen value equation is represented as Ki= M i where K and M are stiffness and mass matrices of the system.
The results of the dynamic analysis of the wing are shown in the Table (1) Table 1. Dynamic Characterization of the wing Mode 1
Frequency (Hz) 21.29
Behavior of the structure Bending Mode Bending Mode at Leading 2 28.28 edge 3 33.28 Bending Mode at Elevon Similarly the modal frequencies and the mode shapes are obtained for Booster fin and vertical tail. After obtaining the frequency modes the unsteady aerodynamic model was generated for the substructures. C. Unsteady Aerodynamics An aerodynamic model that represents the forces acting on a structure is required for conditions where aeroelastic effects are present (static aeroelastics, flutter, gusts, etc.). The Aerodynamic model of the wing section is shown in fig. 3.
Fig. 3 Aerodynamic model of fin The aerodynamic forces are calculated as modal forces. The modal aerodynamic forces represent the oscillation of the wing in one mode induces forces on itse1f and each of the other modes:
}=0 {F}=[Qr] {A}+[Qi] { A …. (2) The matrices [Qrl and [Qi] are non-diagonal matrices of components of modal aerodynamic forces, respectively in phase and out of phase with the modal deflection. the modal aerodynamic forces depend on the frequency of the oscillation by which they are induced. The modal aerodynamic forces are obtained through a numerical method referred to as the doublet lattice method [8,9] or piston theory [9]. These aerodynamic forces induce additional displacements. Displacements over the surface are transferred to the structure in addition to the displacement caused by the structural dynamic analysis by means of 2Dimensional spline interpolation. Thus finally the aerodynamic forces and the structural dynamics of the structure are coupled to by means of aerodynamic and structural finite elements, leading to the aeroelastic model [8]. The Aeroelastic equation is obtained by combining (1) and (2) gives,
} - [Qi] { A } + ([K] - [Qr]) {A} = {0}…. (4) [M]{ A
D.
Flutter Solution By specifying the flight speed, reduced frequency, number of modes to be extracted we arrived at the flutter solution. The flutter analysis is carried out for all the lifting structures of the space vehicle to ensure the safety of the space vehicle while flying through the atmosphere. The flutter analysis is carried out using the Doublet lattice method for subsonic regime of Mach numbers (0.5-1.2), zona51 for supersonic regime of Mach numbers (1.2-1.9) and piston theory for hypersonic Mach numbers (2.0-8.0). Even though the doublet lattice method does not predict the flutter at transonic regime, still the analysis was carried out. In transonic regime, out of the three types of flutter solutions i.e., p-method, k-method and p-k method, the p-k method was found to be more appropriate for the present analysis. The flutter can be observed from the frequencydamping-velocity plot called as flutter plots or ν-g-ω [7] plot.
III.
RESULTS AND DISCUSSIONS ON FLUTTER RESULTS OF THE SUBCOMPONENT LEVEL ANALYSIS
The figure 4, pictured out the observation of the flutter for a mach number 4.0, similarly the flutter obtained for every Mach numbers ranging from 0.5-8.0 are shown in figures (5,6 and 7) for booster fin, wing and vertical tail. Mach number Vs Flutter velocity of Fin 5000 4500 4000
Flutter Velocity (m/s)
The modal mass matrix [M] and the modal stiffness matrix [K] are diagonal. The external forces are the induced aerodynamic forces, are expressed as modal forces. A deflection in any of the natural mode shapes induces aerodynamic forces. Structural equations and aerodynamic forces taken together yield the modal aeroelastic equation (4),
From the fig. 4, the modes 3 and 5 coalesce in the frequency plot causing a mild flutter, and at the same time damping plot crosses the zero line causing mild flutter instability at a velocity of 1538.4 m/s.
3500
3000 2500
Flutter Velocity
2000 1500 1000 500 0 0
0.5
1
1.5
2
2.5
Transonic dip or Flutter Bucket
3
3.5
4
4.5
5
5.5
6
6.5
Mach No.
Fig. 5 Mach number vs. flutter velocity (Booster fin)
Mach no. Vs F lutter Velocity of Wing
2500
Flutter Velocity (m/s)
(t)}+[D] { A (t)}+[K] {A(t)} = {F(t)… (3) [M]{ A
2000 1500 1000 500
F lutter Velocity
0
Fig. 07 Mach 1 number 2 vs. 3 flutter 4 velocity 5 6(wing) 7
Transonic dip
Mach No.
Fig. 6 Mach number vs. flutter velocity (Wing)
Fig. 7 Mach number vs. flutter velocity (Vertical tail) Figure 4 Sample plot- Frequency and damping versus flight velocity of wing at Mach 4.0
8
The results of the substructure level analysis show that there is flutter in transonic regime. There occurs a dip in the transonic regime, which is called as the transonic dip or flutter bucket. This flutter mode can be taken care by increasing the damping. IV.
[4] A. R. Collar “The Expanding Domain of Aeroelasticity", The Journal of Royal Aeronautical Society, Vol. 50, Aug. 1946, pp. 613-636.
CONCLUSION
The flutter analysis was carried out for various components to ensure the safety of the space vehicle while flying through the atmosphere. The flutter analysis was carried out using the Doublet lattice method for subsonic regime of mach numbers (0.5-1.2), zona51 for supersonic regime of Mach numbers (1.2-1.9) and piston theory for hypersonic mach numbers (2.0-8.0). Further work can be done to find flutter in the transonic regime by developing new aerodynamic theories to predict shock waves in the transonic regime. V.
[3] Raymond L. Bisplinghoff, Holt Ashley and Robert L. Halfman, “Aeroelasticity”, Addison-Wesley Publishing Company INC. Reading, Massachusetts,1978
REFERENCES
[1] Theodore Theodorsen “General Theory of Aerodynamic Instability and the mechanism of Flutter", NACA Report No. 496, 1935 [2] Y.C.Fung, “An Introduction to the Theory of Aeroelasticity” GALCIT Aeronautical Series, May 1955
[5] David M. Schuster, D. D. Liu, Lawrence, J. Huttsell, “Computational Aeroelasticity: Success, Progress, Challenge”, Journal of Aircraft, Vol. 40, No.5, SeptemberOctober 2003, Page no. 843-856 [6] Jan R. Wright Jonathan E. Cooper, Introduction to Aircraft Aeroelasticity and loads, John Wiley & Sons Ltd, 2007 [7] Dewey H. Hodges, G Alvin Pierce, “Introduction to Structural Dynamics and Aeroelasticity”, Cambridge University Press, 2001
[8] Edward Albano and William. P. Rodden “A Doublet-Lattice Method for Calculating Lift Distributions on Oscillating Surfaces in Subsonic Flows”, AIAA Journal, Vol.7, No. 2, Feb.1969, Pp279-285
[9] William P. Rodden, Erwin H. “MSC/NASTRAN- Aeroelastic Analysis”
Johnson,
