Nonlinear Dynamics Analysis For Mechanism Of Slender Wing Rock And Study Of Numerical Simulation Method

Wing rock is atypical phenomenon of lateral—directional instability, which is a complex roll—yaw—vertical oscillation dominated by limit cycle roll motion whose amplitude is more large than that of yaw or vertical directions. It may cause serious maneuvering and tracking problems for fighters. It may also degrade weapon aiming accuracy and cause safety problems during a take off or landing approach. These problems can greatly restrict the flight envelopes of fighters. In order to reduce drag and increase the maximum attainable speed especially in transonic and supersonic regions, modern fighters are often designed as the configuration consisting of thin, low aspect ratio, highly swept-back delta wing and a long slender fuselage, which increase the probability of wing rock (especially for the design of finless aircraft). Thus, wing rock has become a common fault for modern fighters. In the published papers, the research of wing rock is mainly concentrated on experimental methods. There are few papers of applying the method of combining theoretic analysis with numerical simulation to study and predict wing rock in academe. This thesis aiming at slender wing rock studies the qualitative analysis theory and numerical simulation methods for delta-wing in single-DOF (degree of freedom) rolling motion.In the aspect of theoretic analysis: ①With wide investigation and understanding the published papers about wing rock problems in experiment and calculation, this thesis applying the theory of nonlinear dynamics studies the qualitative analysis theory of freedom rolling motion of delta wing in single-DOF. Through the analysis of the depended parameters of solving dynamically rolling moment by unsteady Navier-Stokes equations, a nonlinear autonomy dynamic system governing the single—DOF freedom rolling motion has been formed. With the theory, some conclusions can be drawn: At certain freedom Mach number, the bifurcate parameter μ(α) satisfying μ(α) = 0 is the critical condition for Hopf bifurcation of wing motion. When μ(α) changes from negative (through zero) to positive with the increase of angle of attack, the disturbed wing will arise dynamically bifurcate phenomenon from the motion of steady point attractor and become wing rock motion of periodic attractor. The angle of attack α_cr corresponding to μ(α_cr) = 0 is the critical angleof attack for occurring Hopf bifurcation of wing. ②Based on the Etkin's supposition, this thesis develops the mathematic modeling between dynamically rolling moment and state parameters. The thesis also develops the method of Forced-Harmonic Analysis that is a numerical method of solving some rolling stability parameters including damping-in-roll derivatives. This method is validated by experimental data. Then, the rolling stability parameters of slender delta wing are solved by the method.In the aspect of research in numerical methods: ①According to Liu's weighted idea: thisthesis firstly present the idea of constructing space third-order tlux- or conservational variable- WNND (Weighted-NND) schemes based on the stencils of space second-order flux split- or upwind- NND (Non-oscillatory, containing No free parameters, and Dissipative) schemes. With the same interpolated points in space (five points), WNND scheme obtains one order more than NND scheme. And according to different characteristics of physical problems, different explicit or implicit time discrete schemes are constructed. Some numerical tests, including the linear-wave equation, ID Euler equations and 3D Navier-Stokes equations, are presented to demonstrate the remarkable capability of the WNND scheme. ?In this thesis, the space third-order WNND scheme is applied to simulate the hypersonic flow around lift-body by solving Navier-Stokes equations. The topological structures including surface flow and cross flow with the increasing of angle of attack from 0° to 50° are investigated. The numerical results show: if there is local separation area on the symmetry meridian line of body, the two singular points on symmetry meridian line of body are different with the change of angle of attack, and the topological structures of hypersonic flow field based on the sectional flow patterns perpendicular to the body axis in local separation area have different types. All these results agree well with the theoretic analysis conclusions. At the same time, these results also provide new numerical validation examples for theoretic analysis.In the aspect of the qualitative analysis of wing rolling motion: ?Appling the qualitative analysis theory , the characteristics of freedom rolling motion of disturbed 80° sweep delta wing in single-DOF at M = 0.35 are analyzed and predicted. The results show: when a <22°, the bifurcation parameter //( 22°. the bifurcation parameter //(or) > 0 and A <0. That means the freedom rolling motion of disturbed delta wing willdiverge, and then become into motion of periodic attractor, which is a limit cycle wing rock motion. (2)To validate the conclusions of ?, the wing rock problem of same delta wing is firstly investigated in China by numerically coupling solving 3D unsteady Navier-Stokes equations and Euler rigid body kinematic equation. The grid is O-H type and the freedom flow conditions are M=0.35, a=10°> 20°, 22*\ 25°, 30°, Re=2.5*106. The numerical calculation results show: When a < 22°, the freedom rolling motion of disturbed delta wing is dynamic stability; When a ? 22°, the rolling damping approximates to zero. The freedom rolling motion of disturbed delta wing falls into the state of neutrally dynamic stability. Thus, around the angle of attack 22° is the critical angle of attack at which the Hopf bifurcation occurs; When a > 22° , the freedom rolling motion of disturbed delta wing diverges, and then fallsinto the self-induced wing rock motion. All these results validate the theoretic prediction ofIn the aspect of research on physical characteristics of wing rock: some conclusions can be drawn from the wing rock phenomenon by numerically simulating a 80° sweep delta wing. ?When wing rock occurs, it is clear that the angular acceleration and roll angle are exactly 180° out of phase, while the angular velocity is nearly 90° out of phase. ?When wing rock occurs, the trace of delta wing motion in phase plane is a stable limit cycle. ?When wing rock occurs, the range of instantaneous angle of attack is much less than that of instantaneous angle of yaw and instantaneous angle of attack is less than initial angle of attack. ?When wing rock occurs, all longitudinal/ lateral aerodynamic forces/moments oscillate in stable periodicity. But the curves of longitudinal aerodynamic forces/moments oscillate at twice the frequency of the wing motion, while lateral aerodynamic forces/moments oscillate at the same frequency. The curves of longitudinal aerodynamic forces/moments with roll angle are symmetry, while lateral aerodynamic forces/moments are anti-symmetry. ?Wing Rock motion belongs to one of self-induced oscillation whose amplitude and frequency are constants. If frictional damping is equal to zero, the hysteresis loops of rolling moment coefficient become "8" or double "8" style in C, 0 plane. These lobes represent the energyshift from the wing to the fluid in the outer two lobes (which is counter-clockwise) and from the fluid to the wing in the middle lobe (which is clockwise). The area of the clockwise lobe and counter-clockwise lobes must be equal in a period of wing rock. It means that the total energy that aerodynamic moment acts on the wing is equal to zero in a period. ?The physical mechanism of maintaining the wing rock for the 80° sweep delta wing is the alternate liftoff and reattachment of the leading edge vortices. For the 80° sweep delta wing, there is no evident vortex breakdown phenomenon at 25° and 30° angle of attack.