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The effects of stroke deviation of a flapping model insect wing on its aerodynamic force production are studied by solving the Navier–Stokes equations. Stroke deviation of a flapping wing often tak...

D RAGONFLIES are accomplished fliers. Scientists have always been fascinated by theirflight. Experimental and computational studies on a single airfoil in dragonfly hovering mode were conducted by Freymuth [1] and Wang [2], respectively. They showed that large vertical force was produced during each downstroke. In each downstroke, a vortex pair was created; the large vertical force was explained by the downward two-dimensional jet induced by the vortex pair [2]. Recently, due to the advances in computational and experimental techniques and facilities, researchers are beginning to study dragonfly aerodynamics and forewing–hindwing interactions using three-dimensional model wings [3–5]. Sun and Lan [3] studied the aerodynamics and the forewing–hindwing interaction of a dragonfly in hover flight, using the method of computational fluid dynamics (CFD). Maybury and Lehmann [4] and Yamamoto and Isogai [5] conducted experimental studies on the forewing–hindwing interaction at hovering conditions. Wang and Sun [6] extended the computational study of Sun and Lan [3] to the case of forward flight. Inmost of these studies, only hovering flight was considered. Only Wang and Sun [6] investigated the effects of forward flight speed, but the investigation was limited to a few phase differences ( d 0, 60, 90, and 180 deg; d denotes the difference in phase angle between the forewing and the hindwing stroke cycles, positive when the hindwing leads the forewing and negative when the forewing leads the hindwing). Because the distance of a wing from the wake of another wing depends on the flight speed and the relative motion of the foreand hindwings, it is expected that the forewing–hindwing interaction is strongly influenced by the flight speed and the relative phase difference. Therefore, it is desirable to study the forewing–hindwing interaction by systematically varying the flight speed and the phase angle. Moreover, in the above studies [3–6], attention was mainly paid on whether or not the aerodynamic forces were changed by the forewing–hindwing interaction, while how the interaction occurred was not well understood. It is of interest tomake further investigation on the flow field of the wing wake to reveal how the forewing– hindwing interaction occurs. In the present study, we address the above questions by numerical simulation of the flows of model dragonfly wings. The phasing and the flight speed are systematically varied. Advance ratio (the nondimensional flight speed) ranges form 0 to 0.6. At each advance ratio, eight phase differences, 180, 135, 90, 45, 0, 45, 90, and 135 deg, are considered.

A method of separation-control using alternating tangential blowing/suction at small speeds on multiple slots was proposed and the properties of this method were studied by applying it to the flow-control of a thick airfoil. The method of numerically solving the Reynolds averaged Navier-Stokes equations was employed for the study. Using alternating tangential blowing/suction with small speeds, in the blowing phase, the boundary layer velocity profiles downstream of the slot are made fuller and more separation resistant and in the suction phase, the boundary-layer velocity profiles both up and downstream of the slot are made fuller and more separation resistant. For the airfoil considered in the paper (which is of 40 percent thickness and has ten slots), with a peak velocity of about 1.5 ∞

IN this paper, a zonal vortex method and its application to simulating the impulsively started flow of a circular cylinder are presented. This method treats the attached viscous flow region and the separated flow region separately. The attached flow region is computed through solving boundarylayer equations by the finite-difference method. Only the separated flow is computed through solving Navier-Stokes equations by the vortex method. Since the separated flow region has a length scale of 0(1), in the vortex method used for this region, the number of new vortices introduced at the surface of the body per time step is relatively insensitive to the Reynolds number of the flow. For simulation of highReynolds-number flows with massive separation, the total number of vortices in the flowfield, hence the computer storage and computer time, is greatly reduced. Contents The impulsively started flow around a circular cylinder is complex and all of the phenomena of fluid mechanics are presented. Because of its fundamental importance, this flow has become a typical problem in the study of separated flows. Bouard and Coutanceau1 have done careful experimental studies on this problem and provided valuable data for comparison with numerical solutions. Smith and Stansby2 have recently calculated this flow using a vortex method. In this method, the vorticity equation is solved using random walk for diffusion and the vortex-in-cell method for convection in a time-stepping procedure. Vortices are introduced at the surface at each time step to satisfy the no-slip condition. Their calculations revealed detailed flow features of the wake and were in good agreement with experimental observations in Ref. 1. Their numerical experiment showed that accurate simulation requires the introduction of a sufficiently large number of vortices at the surface per time step. This number increases as the Reynolds number increases. Therefore, for simulation of a high-Reynolds-number flow by the vortex method, the total number of vortices in the flow may become very large as time increases, requiring large computer storage and computer time. In this paper, the vortex method is improved by a zonal approach. For a high-Reynolds- number flow with massive separation, the vorticity in the upstream of the separation point is confined in a layer near the surface of the body. The length scale of the thickness of this layer is 0(Re~l/2). The length scale of the separated flow region is 0(1). It is difficult to accommodate these two scales when solving the NavierStokes equations in the whole flow region. The approach of