Vortex-motion

When a liquid drains through a hole in a container, a vortex may form between the surface and the drainage hole. An interesting phenomenon occurs in the presence of two drainage holes. Only one vortex forms, while the other hole will mostly drain as sink flow. In addition, the vortex can switch between one hole and the other with regular periodicity. The primary goal of this study is to measure this periodicity under varying conditions (height of water in the container, diameter of the drainage holes, and distance between drainage holes). Additionally, a study concerning the volume flow rates of vortical vs. sink flow out of the drainage holes was conducted. In the case of two drainage holes, when the height of the water was decreased in the container, the diameter of drainage holes decreased, or the distance between drainage holes was increased, the switching period was shown to decrease.

The interaction of rotor turbulence with the stator is currently believed to be the predominant mechanism of noise radiation from turbofans in aircraft engines. This thesis presents a general method to compute unsteady 2-D potential flows past a cascade of airfoils. The procedure uses source and vortex distributions on the surface of the airfoils, creation of wakes downstream of the airfoils and non-linear convection of the perturbed flow. These features are designed to satisfy a condition of no-flow through the surface of the airfoils and the Kutta condition at the trailing edge of each of these airfoils. The investigation proves the importance of applying the Kutta condition. It was also shown that an infinite cascade is well approximated by a small number of airfoils and that the non-linear rather than linear convection of vorticity has a large effect on the spectrum of the unsteady lift of an airfoil.

The rollup of a vortex sheet of elliptic span loading in the presence of a vortex of finite core size is studied in the Trefftz plane. The vorticity in the finite vortex is taken to be uniform and sign opposite to that of the sheet and the flow is assumed to be inviscid and incompressible. A numerical scheme is developed to determine the evolution of (a) the finite vortex using the Contour Dynamics technique, (b) the vortex sheet using an algorithm developed by Krasny. The interaction is shown to substantially affect the development of the vortex sheet rollup. The vortex sheet undergoes significant deformation at the rolling up tip region due to its devouring the vortex patch as well as due to the formation of secondary rollup features on the sheet. These features are believed to be important in inhibiting rollup considerably. The interaction is quantified by using a criterion developed to measure the extent of the tip vortex rollup and its characteristics are studied for a range of flow parameters. The strength of the rolling up tip region of the vortex sheet is found to be highly dependent on the location and the vorticity in the finite vortex.

The drag reduction by vortex fusion was investigated. A comparison of flow over a bundle of cylinders in uniform and in disturbed currents was performed in a water channel. The model was subjected to cross flow. A thin cylindrical wire located nearby upstream and leveled at half the height of the test model was used as a source of disturbance. A hydrogen bubble technique was utilized to observe the flow pattern. The accumulation of vortices at stagnating regions in front of a bundle of cylinders transformed into a counter-rotated curl at leading edges of each leading cylinder in the bundle. Measurements were carried out by a computerized data acquisition system. Drag coefficient measurements, digital spectral and fourier analyses were also performed. Results have shown that a drag reduction can be obtained by introducing a thin cylindrical wire in front of the stagnation.

The effect of applied periodic straining field on the behavior of coherent vortical structures in the turbulent boundary layer is studied. In particular, the coherent vortical longitudinal structures in the turbulent boundary layer in the form of isolated vortices or in the form of pairs of counter-rotating vortices is considered. The effect on the pressure fluctuations on the wall due to the applied periodic strain is studied. A numerical method using Contour Dynamics technique and incompressible, inviscid equations of motion is developed to determine the evolution of these structures in time. The pressure fluctuations on the wall are calculated making use of the unsteady Bernoulli's equation. The various parameters associated with the coherent structures in the turbulent boundary layer such as the strength of the vortices, their distance from the wall, separation distance between counter-rotating vortices, the frequency of the applied straining field, the magnitude of the straining field and the stretching rate are varied to study the resultant pressure fluctuations. It is observed that at low applied frequencies, there are high modulations in the surface pressure fluctuations, and at higher applied frequencies of straining field there is reduction in surface pressure fluctuations in the boundary layer.

A numerical model for the simulation of three-dimensional normal blade-vortex interaction has been developed to study the bending and variation of core radius of the vortex due to the influence of the blade and the subsequent unsteady force on the blade. For thin blades, a procedure to enable instantaneous cutting of the vortex has been employed to study the vortex response to cutting. The vortex is represented by a filament model which includes axial flow within the core and non-uniform core area. The vortex is convected with self-induced velocities given by the Biot-Savart line integral, and the effect of the cylinder is obtained using a vortex sheet panel method. The governing equations for the vortex axial velocity have a form similar to that of the one-dimensional gas dynamics equations and admit "shock-like" discontinuities. The results indicate that the amount of vortex bending due to interaction with the blade is primarily dependent on the ratio of blade thickness T to ambient vortex core radius sigma o, although for a given amount of bending of the vortex axis, increase in cylinder forward speed results in a decrease in vortex core radius. For blades with T/sigma o < 0(1), very little bending is observed for attack angles under the stall limit. In the case of vortex cutting by a blade, vortex shocks and expansion waves are observed to propagate on the vortex axis away from the blade.

An experimental study of the vortex response to interaction with and cutting by a thin flat
plate or circular cylinders of various diameters has been performed. The direction of
motion of the flat plate (or circular cylinder) is normal to the vortex axis in the experiments.
The vortex is generated by withdraw of fluid at an orifice at the bottom of an "inner
cylinder" immersed in a rectangular tank, and the flow field is visualized with both water
soluble and immiscible dyes. In the experiments with circular cylinders, the bending of
the vortex is compared to computational predictions from [15], and the mechanism of
subsequent breakup of the vortex as it gets closer to the cylinder is studied. The vortex is
observed to bend farther without breakup for larger forward speeds of the circular cylinder.
Very little bending is observed when the vortex interacts with the flat plate, except for
angles of attack exceeding the stall limit Following cutting of the vortex by the flat plate or
circular cylinder, a vortex shock is observed to form and propagate up the vortex axis. No
vortex shock is observed on the opposite side of the blade. The various forms of these
vortex shocks have been photographed, and they appear very similar to travelling vortex
breakdowns. The propagation speed of the shocks is compared to an analytical solution for
instantaneous vortex cutting by a flat plate of zero thickness.

A study of two-layer quasi-geostrophic vortex flow is performed to determine the effect of a current difference between the layers on a vortex initially extending through both the layers. In particular, the conditions under which the current difference can 'tear' the vortex are examined. In the first set of flows studied, the current difference is generated by a (stronger) third vortex in the upper layer located at a large distance from the (weaker) vortex under study. A set of flows are also considered in which an ambient geostrophic current difference is produced by a non-uniform background potential vorticity field. The results of the study will be useful in determining the conditions under which large geophysical vortex structures, such as cyclones and ocean rings, can extend to large depths even though the mean currents in the ambient flow change significantly along the vortex length.

An experimental study has been conducted to examine the flow field about and the wake behind truncated cylindrical obstacles of varying height, which are towed through a fluid with a free surface in a rotating system. The results show the development of a vortex street-type wake downstream of the obstacle for retrograde (westward) flows, even for very small ratios of obstacle height to water layer depth. For short obstacles, a pronounced backward flowing jet is observed, which impinges on the Taylor column from downstream. Prograde (eastward) flows are found to have a meandering wake that extends farther than eight obstacle diameters downstream and do not exhibit backjetting or vortex street formation. Upwelling is believed to occur within the side boundary layers of the Taylor column, which could play a significant role in deep water production in the ocean.

The sound field associated with the motion of 2-dimensional finite core vortex past a forward facing step is obtained. A numerical scheme using Contour Dynamics technique and incompressible, inviscid equations of motion is developed to determine the evolution of the structure of the vortex, its path over the step and the radiated sound. An appropriate low-frequency Green's function is derived and the expression for the far field acoustic pressure as formulated by Mohring is used. The vortex structure evolves in the non-uniform flow in the vicinity of the step and under certain conditions is found to undergo significant deformation of its core structure. The far field acoustic pressure is found to be a strong function of vortex motion in the vicinity of the step. Results for the vortex trajectory and the associated acoustic pressure are presented for a variety of flow parameters.