Chin-Chou Chu

An experimental investigation of vortex motions near surfaces

Laminar vortex rings approaching a solid planar surface and a free surface have been investigated experimentally over the range of Reynolds numbers based on the circulation, ReΓ, from 900 to 2350. The emphasis is on the process of vortex stretching, induction of boundary layer on the surface, formation of secondary vortices, and rebounding of the primary vortex ring. Detailed measurements were made using laser‐induced photochemical anemometry (LIPA), a nonintrusive visualization technique which enables multipoint simultaneous measurement of the unsteady velocity field. Results show that enstrophy, rather than circulation, clearly signifies three stages of the behavior of the primary vortex ring—free‐traveling stage, vortex stretching stage, and vortex rebounding stage. Although the flow phenomena are very similar when a vortex ring approaches a solid surface or a slightly contaminated free surface, the difference between the induced boundary layers under two surface conditions is obvious in terms of the c...

A vortex ring impinging on a solid plane surface—Vortex structure and surface force

A joint numerical and experimental investigation has been performed to study a vortex ring normally impinging on a solid plane surface. Specific emphasis is placed upon the vortex structure and the associated surface force at Reynolds numbers between 500 and 2000. Along the line of Chang [Proc. R. Soc. London Ser. A 437, 517 (1992)], the force was viewed to be contributed by fluid elements with nonvanishing vorticity in the flow. This viewpoint enables the paper to provide a unique opportunity to shed light on the detailed mechanism which causes a small net surface force during the impingement process. It is found that the small net surface force results from the cancellation of a force pushing on the surface, due to the primary vortex ring, and a suction force, due to the induced boundary layer. Nevertheless, both the pushing and suction forces are much larger than that of the net surface force by several orders of magnitude. This fact provides proper directions for flow manipulation regarding forces exe...

A quantitative study of the flow around an impulsively started circular cylinder

The detailed flow structure behind an impulsively started circular cylinder has been investigated experimentally. The Reynolds number based on the steady state velocity and the diameter of the cylinder was 500 to 3,000. This work is unique in that unsteady spatial velocities were measured simultaneously by a quantitative visualization technique — Laser Induced Photochemical Anemometry (LIPA). The surface vorticity at g/q = π/2 and vorticity distribution behind the cylinder in the Lagrangian coordinates (i.e. coordinates fixed on the cylinder) were calculated from the measured velocities. The surface vorticity shows in the early stage of flow development a close agreement with the previous results obtained by analytical and numerical approaches. The large-field velocity and vorticity information provides an insight into the formation process of the vortices downstream of the cylinder. In addition to the quantitative information, the results of visualized flow pattern obtained by LIPA technique are also presented.

A microfluidic nanoliter mixer with optimized grooved structures driven by capillary pumping

It is known that surface tension-capillary pumping is an effective driving force in a microchannel, however a power-free mixer that uses only surface tension has not yet been achieved. In the present study, a power-free method is explored to perform mixing in a microchannel without any external active mechanisms such as pumps, valves or external energies like electrostatic or magnetic fields. The mixer is cost effective as the channel is designed to have no sidewalls with the liquid being confined to flow between a bottom hydrophilic stripe and a top-covered hydrophobic substrate. It is found from both theoretical analysis and experiments that for a given channel width, the flow rate solely due to capillary pumping can be maximized at an optimal channel height. The flow rate is in the order of nanoliters per second, for example, the flow rate is 0.65 nL s?1 at the optimal channel height 13 ?m, given the channel width 100 ?m. It is most crucial to this power-free mixing device that two liquid species must be well mixed before the liquids are transported to exit to a reservoir. For this purpose, asymmetric staggered grooved cavities are optimally arranged on the bottom substrate of the channel to help mixing two different liquid species. It is shown that maximum mixing occurs when the depth of the grooved structures is about two-thirds of the total channel height.

Unsteady aerodynamics of dragonfly using a simple wing–wing model from the perspective of a force decomposition

Insects perform their multitude of flight skills at frequencies of tens to hundreds of Hertz, and the aerodynamics of these skills are fundamentally unsteady. Intuitively, unsteadiness may come from unsteady wing motion, unsteady surface vorticity or vorticity being shed into the rear and front wakes. In this study, we propose to investigate the aerodynamics of dragonfly using a simplified wing–wing model from the perspective of many-body force decomposition and the associated force elements. Insect flight usually operates at Reynolds numbers of the order of several hundreds, at which the surface vorticity is shown to play a substantial role. There are important cases where the added mass effect is non-negligible. Nevertheless, the major contribution to the forces comes from the vorticity within the flow. This study focused on the effects of mutual interactions due to phase differences between the fore- and hindwings in the translational as well as rotational motions. It is well known that the dynamic stall vortex is an important mechanism for an unsteady wing to gain lift. In analysing the life cycles of lift and thrust elements, we also associate some high lift and thrust with the mechanisms identified as ‘riding on’ lift elements, ‘driven by’ thrust elements and ‘sucked by’ thrust elements, by which a wing makes use of a shed or fused vortex below, in front of, and behind it, respectively. In addition, a shear layer attaching to each wing may also provide significant thrust elements.

A many-body force decomposition with applications to flow about bluff bodies

The study presents a force theory for incompressible flow about several solid bodies, which enables us to examine the force contribution to each body from individual fluid elements. By employing auxiliary potential functions, we decompose hydrodynamic forces in terms of the unsteadiness of the incoming stream, vorticity within the flow, and surface vorticity on the solid bodies. The usefulness of this force decomposition is illustrated by examining separated flow about several circular cylinders. Guidelines were obtained for finding an optimal arrangement to achieve significantly small drag exerted on the cylinders.

Head-on collision of two coaxial vortex rings: experiment and computation

Head-on collision of two coaxial vortex rings has been studied by joint experimental and numerical investigation. The Reynolds number, Re T , based on the initial circulation of the vortex rings, ranged from 400 to 2700. Besides numerical data, the vorticity field was also resolved by a non-intrusive visualization technique, LIPA, which enabled simultaneous measurement of velocities at multiple locations on a plane area. It was found that the enstrophy, rather than circulation, revealed three stages of evolution of the vortex rings prior to their breakdown. These include the free-travelling stage, stage of vortex stretching and the stage of viscous dissipation dominance. The results indicate that it would be incorrect to neglect the viscous effect, in particular, for the latter two stages of flow development. In fact, the rebound behaviour of the vortex rings for lower Re T is essentially a viscous phenomenon and is found to be closely related to the dissipation of enstrophy when the vortex rings are brought to interact actively with each other and is also related to the increase of the vorticity core diameter in the stage of dominance of viscous dissipation.

Revisiting the aerodynamics of hovering flight using simple models

In this study, we revisit two simplified models of hovering motion for fruit fly and dragonfly from the perspective of force decomposition. The unsteady aerodynamics are analysed by examining the lift force and its four constituent components, each of which is directly related to a physical effect. These force components include one from the vorticity within the flow, one from the surface vorticity and two contributions credited to the motion of the insect wing. According to the phase difference in the models, a hovering motion can be classified into one of three types: symmetric, advanced and delayed rotations. The relative importance of the force components under various flow conditions are carefully analysed. It is shown that the symmetric rotation has the maximum vorticity lift (from volume and surface vorticity), but the optimal average lift is attained for an advanced rotation, which, compared to the symmetric rotation, increases the force contribution due to the unsteady surface motion at the expense of sacrificing contribution from the vorticity. By identifying the variations of the vorticity lift with flow characteristics, we may further explore the detailed mechanisms associated with the unsteady aerodynamics at different phases of hovering motion. For the different types of rotation, the insect wing shares the same mechanism of gaining lift when in the phase of driving with a fuller speed but exhibits different mechanisms at turning from one phase of motion to another. Moreover, we also examine the effects of the Reynolds number in an appropriate range and evaluate the performance of different wing profiles from symmetric to largely cambered.

Monte Carlo Simulation of Optical Properties of Phosphor-Screened Ultraviolet Light in a White Light-Emitting Device

In this paper, we study the optical properties of phosphor-screened ultraviolet light emitted by a quantum well through a chamber. The chamber contains randomly distributed red, blue and green phosphors, and is top-covered with a layer of omnidirectional photonic bandgap material. A Monte Carlo ray tracing method is developed to model the absorption, reflection and transmission for the excited radiation of the ultraviolet light as well as the visible light by the individual phosphor particles. The efficiency of emitting white light by synthesizing the visible light through the top substrate is investigated with respect to the weight ratio, the size of phosphor particles, the dimension of the chamber and the reflectivity of the side wall and the bottom substrate.

Initial Motion of a Viscous Vortex Ring

The behaviour of a viscous vortex ring is examined by a matched asymptotic analysis up to three orders. This study aims at investigating how much the location of maximum vorticity deviates from the centroid of the vortex ring, defined by P. G. Saffman (1970). All the results are presented in dimensionless form, as indicated in the following context. Let Γ be the initial circulation of the vortex ring, and R denote the ring radius normalized by its initial radius Ri. For the asymptotic analysis, a small parameter ∊ = ( t/Re)½ is introduced, where t denotes time normalized by R2i/Γ, and Re = Γ/v is the Reynolds number defined with Γ and the kinematic viscosity v. Our analysis shows that the trajectory of maximum vorticity moves with the velocity (normalized by Γ/Ri) Um = – 1/4πR {ln 4R/∊ + Hm} + O(∊ ln ∊), where Hm = Hm(Re, t) depends on the Reynolds number Re and may change slightly with time t for the initial motion. For the centroid of the vortex ring, we obtain the velocity Uc by merely replacing Hm by Hc, which is a constant –0.558 for all values of the Reynolds number. Only in the limit of Re → ∞, the values of Hm and Hc are found to coincide with each other, while the deviation of Hm from the constant Hc is getting significant with decreasing the Reynolds number. Also of interest is that the radial motion is shown to exist for the trajectory of maximum vorticity at finite Reynolds numbers. Furthermore, the present analysis clarifies the earlier discrepancy between Saffman’s result and that obtained by C. Tung and L. Ting (1967).