Based on the Ricatti technique, the methodology for preventing the limit cycle accomplished by adding a control function to the original equation of wing rock motion is presented in this paper. To analyze the state va...Based on the Ricatti technique, the methodology for preventing the limit cycle accomplished by adding a control function to the original equation of wing rock motion is presented in this paper. To analyze the state variables of the system, the complete set of nonlinear equations of motion including an effective linear control function was solved for A-4D and Mig-21 Aircraft. The roll angle responding to the linear control function for both models was estimated when the systems were tested under different damping ratios. The numerical results show that a linear control function including both the roll attitude and the roll rate is sufficient to suppress the wing rock motion with an acceptable error in desired time. A good agreement between the numerical results and the published work is obtained for the limit cycle oscillation existence at different damping ratios.展开更多
Previous studies have shown that asymmetric vortex wakes over slender bodies exhibit a multi-vortex structure with an alternate arrangement along a body axis at high angle of attack. In this investigation, the effects...Previous studies have shown that asymmetric vortex wakes over slender bodies exhibit a multi-vortex structure with an alternate arrangement along a body axis at high angle of attack. In this investigation, the effects of wing locations along a body axis on wing rock induced by forebody vortices was studied experimentally at a subcritical Reynolds number based on a body diameter. An artificial perturbation was added onto the nose tip to fix the orientations of forebody vortices. Particle image velocimetry was used to identify flow patterns of forebody vortices in static situations,and time histories of wing rock were obtained using a free-to-roll rig. The results show that the wing locations can affect significantly the motion patterns of wing rock owing to the variation of multivortex patterns of forebody vortices. As the wing locations make the forebody vortices a two-vortex pattern, the wing body exhibits regularly divergence and fixed-point motion with azimuthal variations of the tip perturbation. If a three-vortex pattern exists over the wing, however, the wing-rock patterns depend on the impact of the highest vortex and newborn vortex. As the three vortices together influence the wing flow, wing-rock patterns exhibit regularly fixed-points and limitcycled oscillations. With the wing moving backwards, the newborn vortex becomes stronger, and wing-rock patterns become fixed-points, chaotic oscillations, and limit-cycled oscillations. With further backward movement of wings, the vortices are far away from the upper surface of wings, and the motions exhibit divergence, limit-cycled oscillations and fixed-points. For the rearmost location of the wing, the wing body exhibits stochastic oscillations and fixed-points.展开更多
The wing rock motion is frequently suffered by a wing-body configuration with low swept wing at high angle of attack.It is found from our experimental study that the tip perturbation and wing longitudinal locations af...The wing rock motion is frequently suffered by a wing-body configuration with low swept wing at high angle of attack.It is found from our experimental study that the tip perturbation and wing longitudinal locations affect significantly the wing rock motion of a wing-body.The natural tip perturbation would make the wing rock motion of a nondeterministic nature and an artificial mini-tip perturbation would make the wing rock motion deterministic.The artificial tip perturbation would,as its circumferential location is varied,generate three different types of motion patterns:(1) limit cycle oscillation,(2) irregular oscillation,(3) equilibrium state with tiny oscillation.The amplitude of rolling oscillation corresponding to the limit cycle oscillatory motion pattern is decreased with the wing location shifting downstream along the body axis.展开更多
By considering the effect of hydraulic pressure filled in wing crack and the connected part of main crack on the stress intensity factor at wing crack tip, a new wing crack model exerted by hydraulic pressure and far ...By considering the effect of hydraulic pressure filled in wing crack and the connected part of main crack on the stress intensity factor at wing crack tip, a new wing crack model exerted by hydraulic pressure and far field stresses was proposed. By introducing the equivalent crack length leq of wing crack, two terms make up the stress intensity factor KI at wing crack tip: one is the component for a single isolated straight wing crack of length 2l subjected to hydraulic pressure in wing crack and far field stresses, and the other is the component due to the effective shear stress induced by the presence of the equivalent main crack. The FEM model of wing crack propagation subjected to hydraulic pressure and far field stresses was also established according to different side pressure coefficients and hydraulic pressures in crack. The result shows that a good agreement is found between theoretical model of wing crack proposed and finite element method (FEM). In theory, an unstable crack propagation is shown if there is high hydraulic pressure and lateral tension. The wing crack model proposed can provide references for studying on hydraulic fracturing in rock masses.展开更多
文摘Based on the Ricatti technique, the methodology for preventing the limit cycle accomplished by adding a control function to the original equation of wing rock motion is presented in this paper. To analyze the state variables of the system, the complete set of nonlinear equations of motion including an effective linear control function was solved for A-4D and Mig-21 Aircraft. The roll angle responding to the linear control function for both models was estimated when the systems were tested under different damping ratios. The numerical results show that a linear control function including both the roll attitude and the roll rate is sufficient to suppress the wing rock motion with an acceptable error in desired time. A good agreement between the numerical results and the published work is obtained for the limit cycle oscillation existence at different damping ratios.
基金supported by the National Natural Science Foundation of China (No.11272033)
文摘Previous studies have shown that asymmetric vortex wakes over slender bodies exhibit a multi-vortex structure with an alternate arrangement along a body axis at high angle of attack. In this investigation, the effects of wing locations along a body axis on wing rock induced by forebody vortices was studied experimentally at a subcritical Reynolds number based on a body diameter. An artificial perturbation was added onto the nose tip to fix the orientations of forebody vortices. Particle image velocimetry was used to identify flow patterns of forebody vortices in static situations,and time histories of wing rock were obtained using a free-to-roll rig. The results show that the wing locations can affect significantly the motion patterns of wing rock owing to the variation of multivortex patterns of forebody vortices. As the wing locations make the forebody vortices a two-vortex pattern, the wing body exhibits regularly divergence and fixed-point motion with azimuthal variations of the tip perturbation. If a three-vortex pattern exists over the wing, however, the wing-rock patterns depend on the impact of the highest vortex and newborn vortex. As the three vortices together influence the wing flow, wing-rock patterns exhibit regularly fixed-points and limitcycled oscillations. With the wing moving backwards, the newborn vortex becomes stronger, and wing-rock patterns become fixed-points, chaotic oscillations, and limit-cycled oscillations. With further backward movement of wings, the vortices are far away from the upper surface of wings, and the motions exhibit divergence, limit-cycled oscillations and fixed-points. For the rearmost location of the wing, the wing body exhibits stochastic oscillations and fixed-points.
基金supported by the National Natural Science Foundation of China (10432020, 10872019 and 10702004)
文摘The wing rock motion is frequently suffered by a wing-body configuration with low swept wing at high angle of attack.It is found from our experimental study that the tip perturbation and wing longitudinal locations affect significantly the wing rock motion of a wing-body.The natural tip perturbation would make the wing rock motion of a nondeterministic nature and an artificial mini-tip perturbation would make the wing rock motion deterministic.The artificial tip perturbation would,as its circumferential location is varied,generate three different types of motion patterns:(1) limit cycle oscillation,(2) irregular oscillation,(3) equilibrium state with tiny oscillation.The amplitude of rolling oscillation corresponding to the limit cycle oscillatory motion pattern is decreased with the wing location shifting downstream along the body axis.
基金Projects(10972238,51074071,50974059)supported by the National Natural Science Foundation of ChinaProject(10JJ3007)supported by the Natural Science Foundation of Hunan Province,China+1 种基金Project(11C0539)supported by Scientific Research Fund of Hunan Provincial Education Department,ChinaProject(200905)supported by Open Research Fund of Hunan Provincial Key of Safe Mining Techniques of Coal Mines,China
文摘By considering the effect of hydraulic pressure filled in wing crack and the connected part of main crack on the stress intensity factor at wing crack tip, a new wing crack model exerted by hydraulic pressure and far field stresses was proposed. By introducing the equivalent crack length leq of wing crack, two terms make up the stress intensity factor KI at wing crack tip: one is the component for a single isolated straight wing crack of length 2l subjected to hydraulic pressure in wing crack and far field stresses, and the other is the component due to the effective shear stress induced by the presence of the equivalent main crack. The FEM model of wing crack propagation subjected to hydraulic pressure and far field stresses was also established according to different side pressure coefficients and hydraulic pressures in crack. The result shows that a good agreement is found between theoretical model of wing crack proposed and finite element method (FEM). In theory, an unstable crack propagation is shown if there is high hydraulic pressure and lateral tension. The wing crack model proposed can provide references for studying on hydraulic fracturing in rock masses.
