Finite difference methods for the solution of unsteady potential flows

Various problems which are confronted in the development of an unsteady finite difference potential code are reviewed mainly in the context of what is done for a typical small disturbance and full potential method. The issues discussed include choice of equations, linearization and conservation, differencing schemes, and algorithm development. A number of applications, including unsteady three dimensional rotor calculations, are demonstrated

Experimental and analytical studies of a model helicopter rotor in hover

A benchmark test to aid the development of various rotor performance codes was conducted. Simultaneous blade pressure measurements and tip vortex surveys were made for a wide range of tip Mach numbers including the transonic flow regime. The measured tip vortex strength and geometry permit effective blade loading predictions when used as input to a prescribed wake lifting surface code. It is also shown that with proper inflow and boundary layer modeling, the supercritical flow regime can be accurately predicted

Full-potential modeling of blade-vortex interactions

A comparison is made of four different models for predicting the unsteady loading induced by a vortex passing close to an airfoil. (1) The first model approximates the vortex effect as a change in the airfoil angle of attack. (2) The second model is related to the first but, instead of imposing only a constant velocity on the airfoil, the distributed effect of the vortex is computed and used. This is analogous to a lifting surface method. (3) The third model is to specify a branch cut discontinuity in the potential field. The vortex is modeled as a jump in potential across the branch cut, the edge of which represents the center of the vortex. (4) The fourth method models the vortex expressing the potential as the sum of a known potential due to the vortex and an unknown perturbation due to the airfoil. The purpose of the current study is to investigate the four vortex models described above and to determine their relative merits and suitability for use in large three-dimensional codes

The development of CFD methods for rotor applications

The optimum design of the advancing helicopter rotor for high-speed forward flight always involves a tradeoff between transonic and stall limitations. However, the preoccupation of the rotor industry was primarily concerned with stall until well into the 1970s. This emphasis on stall resulted from the prevalent use of low-solidity rotors with rather outdated airfoil sections. The use of cambered airfoil sections and higher-solidity rotors substantially reduced stall and revealed the advancing transonic flow to be a more persistent limitation to high-speed rotor performance. Work in this area was spurred not only by operational necessity but also by the development of a tool for the prediction of these flows (the method of computational fluid dynamics). The development of computational fluid dynamics for these rotor problems was a major Army and NASA achievement. This work is now being extended to other rotor flow problems. The developments are outlined

A conservative implicit finite difference algorithm for the unsteady transonic full potential equation

An implicit finite difference procedure is developed to solve the unsteady full potential equation in conservation law form. Computational efficiency is maintained by use of approximate factorization techniques. The numerical algorithm is first order in time and second order in space. A circulation model and difference equations are developed for lifting airfoils in unsteady flow; however, thin airfoil body boundary conditions have been used with stretching functions to simplify the development of the numerical algorithm

Finite difference modeling of rotor flows including wake effects

Rotary wing finite difference methods are investigated. The main concern is the specification of boundary conditions to properly account for the effect of the wake on the blade. Examples are given of an approach where wake effects are introduced by specifying an equivalent angle of attack. An alternate approach is also given where discrete vortices are introduced into the finite difference grid. The resulting computations of hovering and high advance ratio cases compare well with experiment. Some consideration is also given to the modeling of low to moderate advance ratio flows

An experimental investigation of the parallel blade-vortex interaction

A scheme for investigating the parallel blade vortex interaction (BVI) has been designed and tested. The scheme involves setting a vortex generator upstream of a nonlifting rotor so that the vortex interacts with the blade at the forward azimuth. The method has revealed two propagation mechanisms: a type C shock propagation from the leading edge induced by the vortex at high tip speeds, and a rapid but continuous pressure pulse associated with the proximity of the vortex to the leading edge. The latter is thought to be the more important source. The effects of Mach number and vortex proximity are discussed

The structure of trailing vortices generated by model rotor blades

Hot-wire anemometry to analyze the structure and geometry of rotary wing trailing vortices is studied. Tests cover a range of aspect ratios and blade twist. For all configurations, measured vortex strength correlates well with maximum blade-bound circulation. Measurements of wake geometry are in agreement with classical data for high-aspect ratios. The detailed vortex structure is similar to that found for fixed wings and consists of four well defined regions--a viscous core, a turbulent mixing region, a merging region, and an inviscid outer region. A single set of empirical formulas for the entire set of test data is described

Analysis of model rotor blade pressures during parallel interaction with twin vortices

This paper presents and provides analysis of unsteady surface pressures measured on a model rotor blade as the blade experienced near parallel blade vortex interaction with a twin vortex system. To provide a basis for analysis, the vortex system was characterized by hot-wire measurements made in the interaction plane but in the absence of the rotor. The unsteady pressure response resulting from a single vortex interaction is then presented to provide a frame of reference for the twin vortex results. A series of twin vortex interaction cases are then presented and analyzed. It is shown that the unsteady blade pressures and forces are very sensitive to the inclination angle and separation distance of the vortex pair. When the vortex cores lie almost parallel to the blade chord, the interaction is characterized by a two-stage response associated with the sequential passage of the two cores. Conversely, when the cores lie on a plane that is almost perpendicular to the blade chord, the response is similar to that of a single vortex interaction. In all cases, the normal force response is consistent with the distribution of vertical velocity in the flow field of the vortex system. The pitching moment response, on the other hand, depends on the localized suction associated with the vortex cores as they traverse the blade chord