Penetration of a blade into a vortex core: vorticity response and unsteady blade forces

Abstract

Numerical calculations are performed for the problem of penetration into a vortex core of a blade travelling normal to the vortex axis, where the plane formed by the blade span and the direction of blade motion coincides with the normal plane of the vortex axis at the point of penetration. The calculations are based on a computational method, applicable for unsteady three-dimensional flow past immersed bodies, in which a collocation solution of the vorticity transport equation is obtained on a set of Lagrangian control points. Differences between this method and other Lagrangian vorticity-based methods in the literature are discussed. Lagrangian methods of this type are particularly attractive for problems of unsteady vortex-body interaction, since control points need only be placed on the surface of the body and in regions of the flow with non-negligible vorticity magnitude. The computations for normal blade-vortex interaction (BVI) are performed for an inviscid fluid and focus on the relationship between the vortex core deformation due to penetration of the blade into the vortex ambient position and the resulting unsteady pressure field and unsteady force acting on the blade. Computations for cases with different vortex circulations are performed, and the accuracy of an approximate formulation using rapid distortion theory is assessed by comparison with the full computational results for unsteady blade force. The force generated from blade penetration into the vortex ambient position is found to be of a comparable magnitude to various other types of unsteady BVI forces, such as that due to cutting of the vortex axial flow.

Helicopter tail rotor orthogonal blade vortex interaction

“…The inviscid force in the direction of blade motion U was examined in a series of computations by Marshall and Grant [77] using an inviscid vortex method to study impact of a vortex ring on a blade with different impact parameter values. The inviscid force, which acts to pull the blade toward the vortex, is due to the decrease in pressure near the blade leading edge as the blade penetrates into the vortex core, as shown in Fig.…”

Gridless Compressible Flow: A White Paper

“…This becomes quite inaccurate, however, when obtaining the Laplacian. Marshall and Grant [37] point out that the MLS method also yields much better results than a centered dif-δ c…”

Vorticity Transport on a Lagrangian Tetrahedral Mesh

“…In this subsection, we report on a series of test computations for Hill's spherical vortex [2] that examine the speed-up and total error produced by the indirect velocity calculation method with different box error settings. Results for tetrahedral elements are also compared to results obtained using a vortex blob method [25].…”

“…Other methods, such as that of Shankar and van Dommelen [37], maintain good accuracy on irregular points, but require a great deal of computation time (on the same order as the velocity calculation). Approximation of the velocity derivative in the vortex stretching term is usually performed either analytically (by differentiating the velocity induced by each vorticity element and then summing over the elements) or by a finite difference approximation of the velocity derivative in the direction of vorticity [25]. The latter procedure requires two velocity calculations for each computational point (approximately doubling the computational time for large N ) and the former procedure is even less efficient.…”