Control of flight forces and moments by flapping wings of model bumblebee

The control of flight forces and moments by flapping wings of a model bumblebee is studied using the method of computational fluid dynamics. Hovering flight is taken as the reference flight： Wing kinematic parameters are varied with respect to their values at hovering flight. Moments about （and forces along） x, y, z axes that pass the center of mass are computed. Changing stroke amplitude （or wingbeat frequency） mainly produces a vertical force. Changing mean stroke angle mainly produces a pitch moment. Changing wing angle of attack, when down- and upstrokes have equal change, mainly produces a vertical force, while when down- and upstrokes have opposite changes, mainly produces a horizontal force and a pitch moment. Changing wing rotation timing, when dorsal and ventral rotations have the same timing, mainly produces a vertical force, while when dorsal and ventral rotations have opposite timings, mainly produces a pitch moment and a horizontal force. Changing rotation duration has very small effect on forces and moments. Anti-symmetrically changing stroke amplitude （or wingbeat frequency） of the contralateral wings mainly produces a roll moment. Anti-symmetrically changing angles of attack of the contralateral wings, when down- and upstrokes have equal change, mainly produces a roll moment, while when down- and upstrokes have opposite changes, mainly produces a yaw moment. Anti-symmetrically changing wing rotation timing of the contralateral wings, when dorsal and ventral rotations have the same timing, mainly produces a roll moment and a side force, while when dorsal and ventral rotations have opposite timings, mainly produces a yaw moment. Vertical force and moments about the three axes can be separately controlled by separate kinematic variables. A very fast rotation can be achieved with moderate changes in wing kinematics.

SECOND-ORDER DRIFT FORCES AND MOMENTS BETWEEN TWO SUBMERGED BODIES IN WAVES ON 3D METHOD

Two near field methods, namely the integral method and differential method, were presented for giving second order mean drift forces and moments between two fixed submerged bodies in regular waves. For the integral method, with a series of mathematical manipulations, second order drift forces and moments could be easily expressed by distributed sources which could be calculated by source distribution techniques with the assumption that the amplitude of ship motions are small on the basis of the linear 3D frequency theory. For the differential method, drift forces and moments could be expressed by the derivative of velocity potential with respect to space coordinate. Because two bodies would behave as a single body while the clearance is very large, the numerical results of one sphere in such case were given and compared with analytical results of a single sphere which does not involve the effect of free surface. When submerged depth becomes enough large, a good agreement can be reached. Then the integral method was used to predict the second order drift forces and moments of two submerged spheres and spheroids with a small lateral separation distance in waves compared with the numerical results obtained by the differential method and they agree well. By comparison, it indicates the interaction effects between two submerged bodies have a profound influence on the drift forces and moments. In this paper, the forward speed effect on submerged spheres was also considered.

Wave Forces and Moments on a Gravity Pier Foundation

In order to understand the wave forces and moments on a gravity pier foundation which consists of an upper column and a bottom gravity base,a model experiment with a scale of 1:60 has been conducted in a laboratory flume.A corresponding numerical calculation by using the boundary element method has been carried out to provide a comparative analysis.It is shown by the comparisons that the numerical wave forces and moments agree well with the experimental results.It is proved that the wave forces and moments acting on the foundation are completely in their inertia dominative areas for wave loads.With the diffraction effects considered into the inertia item,appropriate inertia coefficients are assessed by the experimental results for the inertia item of the Morison equation.The formula of the inertia item can be used to estimate wave forces and moments on such gravity foundations.