Vortex Core and Its Effects on the Stability of Vortex Flow over Slender Conical Bodies

Abstract

A three-dimensional Euler solver is used to study the vortex core over slender conical bodies at high angles of attack and low speeds. A three-dimensional conical overset-grid is established to reduce the computational efforts while accurately resolve the vortex flow. The numerical results on the vortex core are verified by available experimental data and theoretical solutions. The line vortex model used in the theoretical stability analyses made by the present authors for the vortex flow is modified to account for the effects of the vortex cores. The jetlike flow in the vortex core and inflow at its outer edge are modeled based on numerical experiments by the Euler methods on slender conical bodies incorporated with known theoretical and experimental results on vortex cores. Using the Euler solutions as a benchmark, the modified model yields a better predictions in the vortex positions than the original, and a favorable shifts of the transition point of stability in the Sychev similarity parameter.

A combined experimental and analytical investigation of the vortex stability over sharp-edged slender bodies

“…However, the inviscid model used in the present study does not account for this. In earlier studies, 23,24 the analytical results also consistently show a more outboard location of the stationary vortex pair compared to those obtained via Euler computations. The Euler computation, like the experiment, also has a shear region forming the vortex sheet, in which the effects of numerical dissipation and grid resolution play the part rather than physical viscosity, as in the experiment.…”

“…23 In additional, quantitative agreement with the numerical simulation is further improved if semiempirical modifications to the model are made to account for the effects of the vortex core. 24 However, direct experimental verification of the stability analysis method is still incomplete. Previous studies by Cai et al [20][21][22] show qualitative agreement with available experimental data in most of the cases considered.…”

Plasma Flow Control over Slender Delta Wing and Low Dorsal Fin Combination

“…Later, Cai et al improved their stability predictions by considering the effects of vortex core. [2] In the mean time, models of strictly slender and conical flat-plate fins added to a sharp-edged flat-plate delta wing were made, and smoke-laser-sheet visualizations, [3] six-component internal strain-gage-balance measurements [4] and two-dimensional particle image velocimetry (PIV) [5] were performed to verify the theoretical results. [1,2] In recent years, flow control with electromagnetic energy addition has received growing attention because of the advantages of not having mechanical parts while at the same time having broader frequency band-widths.…”

Euler Solutions of Flow Around a Rectangular Wing with Square Tip

“…More than 30 × 30 grid points are used in the cross flow plane to resolve the vortex core, which is equivalent to a grid spacing of 5 × 10 −3 c or smaller. It is noted that to resolve the vortex core about 100 × 100 grid points may be needed in the cross-flow plane as shown by Cai et al 18 The fine grid used in this paper is chosen based on a balance between the grid-independence requirement and the computing resources available to the present authors. The computation grid is designed to study the wing tip vortex only in the near field of the wing.…”

“…the primary vortex and the distributions of the static pressure, the velocity components and the total-pressure loss in the vortex core are reproduced. See, for example, Murman et al, 14 Rizzi, 15 Rizzetta et al, 16 Powell et al 17 and Cai, et al 18 For the case of the rectangular wing, air particles from the lower surface near the square tip follow a trajectory that takes them around two sharp corners before forming a vortex on the upper surface. Between the two sharp corners the boundary layer over the lateral surface of the wing tip may experience separations, but they have likely minor effects on the entire flow around the square tip of the wing.…”