Professor Conlisk has also worked in the area of helicopter aerodynamics since 1989, with funding from the Army Research Office and the Geogia Tech Rotorcraft Center of Excellence.
Modern aerodynamic phenomena are extremely complex and thus pose significant problems for the computation of the flow fields of interest. The ability to model such flows is crucial to the efficient and accurate design of aerodynamic surfaces. Indeed, the ability to generate dynamic load data may be significant in extending the life of a given surface.
We are involved in several different aspects of these flows including the resolution of large-amplitude, high-frequency suction peaks on surfaces caused by vortex collisions and the prediction of the characteristics of tip-vortices shed from fixed and rotary wings. The author is an expert in developing computational schemes associated with the motion of three-dimensional vortices.
Much of the computational work is performed at the Ohio Supercomputer Center and the data reduction is performed at the Computational and Visual Fluid Dynamics Laboratory in the Department of Mechanical Engineering at Ohio State University. Visualization capabilities include on-line and interactive animation of both two and three-dimensional flow phenomena. In what follows several different projects presently ongoing at the Ohio State University are summarized. Most of the work on helicopter flows is done jointly with Professor Narayanan Komerath and at the Rotorcraft Center of Excellence at Georgia Tech.
The flow field generated by a helicopter in flight is extremely complex and it has been recognized that interactions between different components can significantly affect helicopter performance. Recent experimental results indicate that significant impulsive loads may be exerted on a helicopter airframe due to the influence of the tip-vortex and a simplified model for this interaction has been developed. The numerical calculations for the vortex position and the pressure indicate that a large adverse pressure gradient develops under the vortex on the fuselage causing a rapid drop in the pressure there; this large suction peak is removed within milliseconds as the vortex core flow is essentially destroyed. On the left figure is a sketch of a single bladed rotor showing how the tip-vortex will impinge on the airframe. On the right is a sketch of the local behavior as the vortex collides with the airframe. Present work suggests that the process is essentially inviscid.
We use the term ``collision'' to describe the physical process in which the core structure of the vortex defined as a specified region of large vorticity surrounded by irrotational fluid is substantially and permanently altered; most often the core is locally destroyed. This is illustrated on the right figure just above. Characteristic of collisions is that the dominant flow features occur on local length and time scales different from those before the collision. There are various types of collisions and these are discussed is an AIAA paper 98-2858 ``A Theory of Vortex-Surface Collisions'', presented at the 2nd Theoretical Fluid Mechanics Meeting in Albuquerque in June 1998. Helicopter aerodynamics problems always involve three-dimensional collisions and the axial flow in the core of the vortex is a critical feature and generally the primary cause of the collision. Experiments suggest that a strong suction peak persists on the side of the airframe where the axial flow in the vortex is directed away from the surface and is removed where the axial flow in the vortex is directed toward the surface. We are presently working on the full 3D collision, but these basic experimental results may be explained by the solution of a much simpler problem.
The 90o Collision
Lee et al. (1998) (see the reference below) has solved the axisymmetric and incompressible Euler equations for the case where a vortex is split instantaneously at a right angle by a thin flat plate. The figures below show the swirl velocity and the axial vorticity on the wall as a function of radius for a number of times. We start with a Lamb vortex and watch as the swirl velocity in the core of the vortex gets progressively weaker. At the same time, the axial vorticity gets progressively weaker in the core of the vortex as well. This is shown in the figures below which are sketches of the swirl velocity, the axial vorticity and the pressure. These figures are for an axial velocity in the vortex of the same order of magnitude as the swirl and directed toward the surface. Note that there is no collision unless the axial velocity in the vortex is non-zero.
Locally Steady Rotor Wakes and Interactions Between Tip-Vortices
The regions over which steady and unsteady rotor wake patterns exist have been examined numerically for one and two-bladed rotors. A lifting-line theory is used to model each rotor blade and a time-stepping vortex method is used to calculate the tip-vortex motion. The velocities within the first few turns of the wake have been obtained and the results indicate a periodic nature of the wake in both time and space. Temporal aperiodicity is observed beyond the first few turns of the tip-vortex for hovering rotors, while for rotors in sufficient climb, the entire wake is steady relative to the blades and both spatially and temporally periodic. The numerical results are shown to be independent of both time step and spatial grid below clearly defined values.
The velocity field within thewake of a two-bladed rotor is shown in the plot (far right). Note that the velocity pattern in the x, y and z directions is periodic with a time period corresponding to 180o rotation of the blades. The steady, periodic nature of the wake is best illustrated in the figure (right) which shows the wake structure at increasing wake ages from 180o to 720o. Note that the geometry at wake ages of 180o and 540o are identical and so are those at 360o and 720o, displaying total spatial and temporal periodicity.
Experiments (Caradonna et al. 1997), hereafter referred to as CK, have shown that deep in the wake of a 2-bladed rotor in near-hover states, the tip vortices roll around each other, pair and eventually merge as seen in figure (far left). Similar rollup phenomena has been observed in the computed results. The situation is shown in the figure (left). The merging of the tip-vortices appears to be the process by which transition to the far wake occurs. This process is deterministic and periodic, and appears to be intrinsic to rotor wakes. It is easy to show that this vortex-vortex interaction in the wake of a rotor is to be expected based on classical vortex dynamics and that the interaction is most intense in hover and in descent.
The velocity field around and across the tip-vortex of a single rigid blade was computed and compared with experiments conducted by McAlister. Velocities induced by the entire field were computed at vertical cuts through the tip-vortex at wake ages of 30o, 60o and 100o. The figure(far right) shows the vertical velocity induced across the tip-vortex at a wake age of 60o and the figure (right) shows the horizontal velocity induced across thetip-vortex at a wake age of 60o. It should be noted that all parameters used in the computations, such as circulationand core radius, were obtained directly from experiments. The computations involve no adjustable constants.
The Formation of Rotor Tip-Vortices
The major objective of this current work is to apply classical inviscid lifting line and lifting surface theories locally near the rotor tip and describe the origin of the tip-vortex.
The x-y section view of the roll-up process for the rotor after 800 iterations at which convergency has been achieved upto 30.0 chord-lengths distance downstream from the leading edge of the blade is shown in figure (far right). The vortex lines emanating from each panel is shown. Note that the trailing vortices near the tip region roll over to form a strong tip-vortex. However, ina region away from the tip, the trailing vortices do not roll-up in distances of the order shown in the figure. They collectively form the weak inboard sheet which is shown to move inboard. The 3-D view of the roll-up process is also shown in the figure (right).
The growth of the circulation of the tip-vortex as a function of 'x' is shown in figure (far left). The circulation of the tip-vortex is obtained by summing the circulations of each individual filaments. Note that the tip-vortex circulation is approaching an asymptotically constant value far downstream of the blade. The variation of the trailing circulation - which is nothing but the derivative of the bound circulation - with spanwise distance along the blade, is shown in the figure (left). This figure is useful in noting the relative strengths of the strong tip-vortex made up of the rolled-up trailing vortices and the weak inboard vortex sheet made up ofthe non-rolled-up trailing vortices. It is found that the strength of the inboard sheet is approximately 5 percent as that of the strength of the tip-vortex and hence its role can be neglected while computing the tip-vortex circulation.
It is observed that the strength of the tip-vortex grows asymptotically to a certain value. This value is always smaller than the corresponding maximum bound circulation value as shown in the figure on the left. The reason behind this is that not all the trailing vortices emanating from the blade tip upto the spanwise location where the maximum bound circulation occurs roll up to form the tip-vortex. The ratio of the maximum tip-vortex strength to the maximum bound vortexstrength is found to lie between 0.73-0.93.