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Investigation of Empennage Buffeting

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Investigation of Empennage Buffeting NASA Contractor Report 179426 Investigation of Empennage Buffeting C. Edward Lan and I. G. Lee Flight Research Laboratory The University of Kansas Center for Research, Inc. Lawrence, Kansas 66045 Appendix by William H. Wentz, Jr. Wichita State University Prepared for Ames Research Center Dryden Flight Research Facility Edwards, California Under Contract NAG2- 371 1987 N/ $A National Aeronautics and Space Administration Ames Research Center Dryden Flight Research Facility Edwards, California 93523- 5000 TABLE OF CONTENTS Page SUMMARY ......................................................... iii LIST OF SYMBOLS .................................................. iv I. INTRODUCTION ................................................. 1 2. THEORETICAL DEVELOPMENT ...................................... 3 2.1 Formulation of Equations ................................ 3 2.2 Existing Theoretical Methods for Buffet Prediction ..... I0 2.3 The Present Proposed Method ............................ 17 3. NUMERICAL RESULTS ........................................... 25 3.1 Results for a 65-degree Delta Wing ..................... 26 3.2 Results for an F-18 Configuration ...................... 27 4. CONCLUSIONS AND RECOMMENDATIONS ............................. 30 5. REFERENCES .................................................. 31 APPENDIX: Water Tunnel Studies of Vortex Flow and Vortex-Fin Interaction on the F/A-18 Aircraft ......... 51 PRECEDING pAGE BLANK NOT FILMED [ii LIST OF SYMBOLS the generalized aerodynamic force matrix Anj - f/ Cpj% bending moment transfer function due to BMgn(i_) externally applied load bending moment transfer function due to BMMn(Ira) structural motion b span b o reference length, e.g. the root semichord C local chord C mean geometric chord C a characteristic length for augmented vortex llft C B dimensionless buffeting coefficient ACpj lifting pressure coefficient at point (x,_ En on the wing caused by the motion of the j normal mode CBB(M, cz) wing root strain signal/q_ CBd RMS values of root bending moment coefficient c S sectional suction coefficient c S = c S c/c sin2_ E 2 non-dimensional aerodynamic excitation parameter F(t) random forcing function F(t) 7 mean square value of F(t) f wing bending frequency, cps gn structural damping coefficient for the n th mode HBM(_) bending moment transfer function iv K aerodynamic damping parameter KB scaling factor k reduced frequency parameter E(Y,t) sectional llft due to external forces M(Y,t) sectional llft due to structural motion imn(Y,i_) sectional llft due to a unit generalized force in the n th mode (n) length of the separated flow at a spanwise station of the wing Mo(t) root bending moment o mean square values of root bending moment Mn = ff*n2 m dx dy the generalized mass m(x,y) mass per unit area n frequency parameter PE pressure loading due to externally applied disturbance PM pressure loading due to structural motion Apj lifting pressure at point _x,y) on the wing caused by motion of the jth normal mode p-z total RMS pressure fluctuation Qn the generalized force QE(t) random excitation force due to externally applied force qn(t) generalized coordinates qn generalized velocity °. qn generalized acceleration q--_2 mean square displacement .-:-2 qn mean square acceleration free stream dynamic pressure q_ = -_1 r I ,r2 (xl,Yl) , (x2,Y 2) Rl2(rl ,r 2,T) space-tlme correlation Rb/s ratio of buffeting vortex strength to steady vortex strength =i___ distance from vortex force centrold to the av S f CsC dy £c leading edge S reference area Sl2(rl,r 2,_) cross power spectral density of pressures at r I and r2 S_e length of the leading edge s(_) power spectral density Sw(_) power spectral density of total displacement Sq (_) power spectral density of buffeting response SBM(_) power spectral density of root bending moment power spectral density of the buffeting excitation VCO free stream velocity V' I =_V® vortex-induced normal velocity V tunnel flow velocity W tunnel width w% e normal velocity at the leading edge Y% dis!ance from apex to centroid of c distribution from inboard to n --s of Cs(max_ , measured along the leading edge and r@_erPed to half span Za(X,y,t) structural displacement _2 z a mean square value of displacement vi Znj the complex impedance of the system Z-I the inverse of Zn_(_) , or the structural transfer function J angle of attack %D a for vortex breakdown at the trailing edge in symmetrical loading A_ = a- aBD _a aerodynamic damping ratio _s structural damping ratio total damping ratio, aerodynamic and structural 0 free stream density angular frequency, 2_f _n natural frequency of the system _n(X,Y) normal mode shapes of the system r sectional curculation r t total buffeting vortex strength F total buffeting vortex strength per unit t length of the leading edge F steady vortex strength per unit length of S the leading edge ANPLG buffeting excitation RMS, rms root mean square vii I. INTRODUCTION Buffeting flow arises when flow separation occurs on an airplane. The resulting flow field is highly turbulent, thus producing fluctuating pressures on lifting surfaces in the detached flow region. Boundary layer separation is perhaps the most common source producing buffet on most conventional configurations. Research in this area has been quite extensive and involved measurements of fluctuating pressures on models together with some theoretical methods to extrapolate these results to full-scale vehicles (see, for example, Refs. I-3). Frequently, these pressure measurements are made on a conventional "rigid" model, instead of an aeroelastic one, because the latter may not be able to withstand high enough dynamic pressures to be realistic. Based on this consideration, several theoretical methods to use these pressure measurements to predict buffet response have been developed. Some of these methods will be reviewed later. Review of some test results can be found in References 4 and 5; and of theoretical methods, in References 6 and 7. Of particular interest in the present investigation is the buffeting caused by leading-edge vortices on slender wings. Test results showed that (1) buffeting was low before vortex breakdown and became severe after that (Refs. 8 and 9); (2) Low-frequency buffeting was more severe (Ref. 8); (3) high-frequency buffeting was caused by boundary layer fluctuation, and leading-edge vortices produced mainly low-frequency fluctuation (Ref. I0); (4) the results were not sensitive to Reynolds numbers (Refs. I0 and II), so that flight and tunnel measurements could be well correlated (Ref. 12); (5) buffeting at vortex breakdown was associated with the wing response at the fundamental mode (Ref. 8). One conclusion from this early-day research on leading-edge vortices was that the buffeting induced by vortex breakdown would mostly be academic because a slender-wlng airplane would normally not operate in the vortex-breakdown region of angles of attack. Investigation on the effect of vortex breakdown on the buffeting of nearby lifting surfaces, such as tails, was scarce. However, it is known that the vortex from the strake (or leadlng-edge extension, LEX) may reduce the buffet intensity on the wing before it bursts (p. 109, Ref. 7). In the present study, the main objective is to predict buffeting on vertical tails Induced by LEX vortex bursting. Fundamental equations for structural response will first be derived. Existing theoretical methods for buffet prediction will be reviewed. The present method and some numerical results will then be presented. In the Appendix, results of water tunnel testing of an F-18 model are described. 2. THEORETICALDEVELOPMENT 2.1 Formulation of Equations Structural Equations of Motion: Let the structural displacement, Za(X, y, t), be expressed in terms of normal mode shapes, _n(X, y). Then N z (x, y, t) = [ qn(t)_n(X, y) (i) a n=l where qn(t) is the so-called generalized coordinate . It can be shown that the structural equations of motion in forced oscillation in generalized coordinates can be written as (Ref. 13, pp. 131-139, or Ref. 14, Chapter i0): Mnq n + M_n n 2 qn = Qn - ff[PE + PM]_n (_' _)d_dB (2) where M n --Sf_n2mdxdy, the generalized mass re(x, y) = mass per unit area _n = frequency of the n th normal mode Qn = the generalized force. The generalized force consists of two terms, one being the externally applied force (i.e., the PE-term) and the other being the force due to structural motion (i.e., the PM-term). The PM-term caa be further decomposed in terms of the generalized coordinates as N PM = aT Apj(x, y; _, M ) qjb (3) j=l o where Apj is the lifting pressure at point (x, y) on the wing caused by the motion of the jth normal modeand bo is the reference length, e.g. the root semichord. It follows that N N QMn= _ qj ff _drl q= Y qj ff ACpj _dq j=I b oS APj _nd = j--I boS _n d W W q,, N (4) = _ Anj qj b°£ "_o j=l where Anj is the generalized aerodynamic force matrix and is defined as Anj = ff ACpj@n d'_d'q ( 5 ) _;=b_ 0 (6) n= In Equation (4), q,, is the dynamic pressure (= pV#/2). Equation (2) can now be written as N "" 2 Mnqn+ M _ qn - £q® _ Anjqj = ff PE(_'_'t)$n(_' q)d_dn n n j=l = QnE(t) (7) In the above derivation, neither structural nor viscous dampings 9 have been included. To include the former, _n- is usually replaced with _n2([ + ign) , where gn is the structural damping coefficient for the n th mode and is usually taken to be 0.03 if not known experimentally. To account for the latter, 2_Mn_nq n- ts added to the equation with _ being tile damping ratio. Equation (7) becomes N Mnq"n + 2_Mnmnqn + M _ 2(i + ign)qn - £qoo _ Anjq j = QnE(t) n n j=l (8) Structural Response to Random Excitation: If the excitation force QnE(t) is random, it may be represented in a Fourier integral (Chapter 14, Ref° 15), QnE(t) = / QnE(i_)ei_tdm (9) where T QnE(t) e-i_tdt (I0) QnE(i_) = T+°°lira_ -ST The displacement qn(t) will also vary randomly, so that a Fourier integral representation is appropriate.
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