Search NASA⌕ Search

SEARCH · Search NASA

Results for “VORTEX SHEETS - WINGS”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

A panel method study of vortex sheets with special emphasis on sheets of axisymmetric geometry

The self induced evolution of a vortex sheet was simulated by modeling the sheet using an integration of discrete elements of vorticity. Replacing small sections of a vortex sheet by flat panels of constant vorticity is found to reproduce more accurately the initial conditions for the Lagrangian simulation technique than replacement by point vortices. The flat panel method for the vortex sheet was then extended to model axisymmetric vortex sheets. The local and far field velocities induced by the axisymmetric panels were obtained using matched asymptotic analysis, and some of the uncertainties involved in other models of the axisymmetric vortex sheet have been eliminated. One important result of this analysis is the determination of the proper choice of core size for a circular vortex filament which may replace a section of an axisymmetric vortex sheet. Roll-up of both two dimensional and axisymmetric vortex sheets was computed using the panel methods developed in the report.

Sugioka, I.↗
NASA NTRS1984

Resonance in flows with vortex sheets and edges

It is shown that the vortex sheet in a slot between two semi-infinite plates does not admit incompressible resonant perturbations. The semi-infinite vortex sheet entering a duct does admit incompressible resonance. These results indicate that the vortex-sheet approximation is less useful for impinging shear flows than for non-impinging flows. They also suggest an important role of downstream vortical disturbances in resonant flows. The general solution for perturbations to flow with a vortex sheet and edges is written in terms of a Cauchy integral. Requirements on the behavior of this solution at edges and at downstream infinity fix the criteria for resonance.

Durbin, P. A.↗
NASA NTRS1986

Calculations of axisymmetric vortex sheet roll-up using a panel and a filament model

A method for calculating the self-induced motion of a vortex sheet using discrete vortex elements is presented. Vortex panels and vortex filaments are used to simulate two-dimensional and axisymmetric vortex sheet roll-up. A straight forward application using vortex elements to simulate the motion of a disk of vorticity with an elliptic circulation distribution yields unsatisfactroy results where the vortex elements move in a chaotic manner. The difficulty is assumed to be due to the inability of a finite number of discrete vortex elements to model the singularity at the sheet edge and due to large velocity calculation errors which result from uneven sheet stretching. A model of the inner portion of the spiral is introduced to eliminate the difficulty with the sheet edge singularity. The model replaces the outermost portion of the sheet with a single vortex of equivalent circulation and a number of higher order terms which account for the asymmetry of the spiral. The resulting discrete vortex model is applied to both two-dimensional and axisymmetric sheets. The two-dimensional roll-up is compared to the solution for a semi-infinite sheet with good results.

Kantelis, J. P.↗
NASA NTRS1977

Passage of a weak vortex sheet through an oblique shock

The two-dimensional problem of the passage of a free vortex sheet of weak strength through an oblique shock wave of finite strength is investigated. Conditions are established which define the changes of the strength and shape of the vortex sheet after its passage through the shock wave in terms of the shock strength and the angle between the shock wave and the vortex sheet.

Ting, L.↗
NASA NTRS1993

On the 'delta-equations' for vortex sheet evolution

We use a set of equations, sometimes referred to as the 'delta-equations', to approximate the two-dimensional inviscid motion of an initially circular vortex sheet released from rest in a cross-flow. We present numerical solutions of these equations for the case with delta-square = 0 (for which the equations are exact) and for delta-square greater than 0. For small values of the smoothing parameter delta, a spectral filter must be used to eliminate spurious instabilities due to round-off error. Two singularities appear simultaneously in the vortex sheet when delta-square = 0 at a critical time t(c). After t(c), the solutions do not converge as the computational mesh is refined. With delta-square greater than 0, converged solutions were found for all values of delta-square when t is less than t(c), and for all but the two smallest values of delta-square used when t is greater than t(c). Our results show that, when delta-square is greater than 0, the vortex sheet deforms into two doubly branched spirals some time after t(c). The limiting solution as delta approaching 0 clearly exists and equals the delta = 0 solution when t is less than t(c).

Rottman, James W.↗
NASA NTRS1986

A numerical method for vortex sheet roll-up

The problem of computing vortex sheet roll-up from periodic analytic initial data is studied. Previous theoretical and numerical work is reviewed. Computational difficulties arising from ill posedness and singularity formation are discussed. A desingularization method is proposed to diminish these difficulties. Computations indicate that this approach converges past the time at which previous numerical investigations have failed to converge.

Krasny, R.↗
NASA NTRS1980

Transmitted sound field due to an impulsive line acoustic source bounded by a plate followed by a vortex sheet

The propagation of sound due to a line acoustic source in the moving stream across a semiinfinite vortex sheet which trails from a rigid plate is examined in a linear theory for the subsonic case. A solution for the transmitted sound field is obtained with the aid of multiple integral transforms and the Wiener-Hopf technique for both the steady state (time harmonic) and initial value (impulsive source) situations. The contour of inverse transform and hence the decomposition of the functions are determined through causality and radiation conditions. The solution obtained satisfies causality and the full Kutta conditions. The transmitted sound field is composed of two waves in both the stady state and initial value problems. One is the wave scattered from the edge of the plate which is associated with the bow wave and the instability wave. These waves exist in the downstream sectors. The other is the wave transmitted through the vortex sheet which is also associated with the instability wave. Regional divisions of the transmitted sound field are identified.

Miura, T.↗
NASA NTRS1987

Computation of vortex sheet roll-up in the Trefftz plane

Two vortex-sheet evolution problems arising in aerodynamics are studied numerically. The approach is based on desingularizing the Cauchy principal value integral which defines the sheet's velocity. Numerical evidence is presented which indicates that the approach converges with respect to refinement in the mesh-size and the smoothing parameter. For elliptic loading, the computed roll-up is in good agreement with Kaden's asymptoic spiral at early times. Some aspects of the solution's instability to short-wavelength perturbations, for a small value of the smoothing parameter, are inferred by comparing calculations performed with different levels of computer round-off error. The tip vortices' deformation, due to their mutual interaction, is shown in a long-time calculation. Computations for a simulated fuselage-flap configuration show a complicated process of roll-up, deformation and interaction involving the tip vortex and the inboard neighboring vortices.

Krasny, Robert↗
NASA NTRS1986

Recent extensions to the free-vortex-sheet theory for expanded convergence capability

A new version of the free vortex sheet formulation is presented which has greatly improved convergence characteristics for a broad range of geometries. The enhanced convergence properties were achieved largely with extended modeling capabilities of the leading edge vortex and the near field trailing wake. Results from the new code, designated FVS-1, are presented for a variety of configurations and flow conditions with emphasis on vortex flap applications.

Luckring, J. M.↗
NASA NTRS1975

A subvortex technique for the close approach to a discretized vortex sheet

The close-approach problem associated with flow calculation methods based on vortex-lattice theory was examined numerically using two-dimensional discretized vortex sheets. The analysis first yields a near-field radius of approximately the distance apart of the vortices in the lattice; only within this distance from the sheet are the errors arising from the discretization significant. Various modifications to the discrete vortices are then considered with the objective of reducing the errors. This leads to a near-field model in which a vortex splits into an increasing number of subvortices as it is approached. The subvortices, whose strengths vary linearly from the vortex position, are evenly distributed along an interpolated curve passing through the basic vortices. This subvortex technique can be extended to the three-dimensional case and is efficient because the number of vortices is effectively increased, but only where and when needed.

Maskew, B.↗
NASA NTRS1987

Analysis of induced velocities in the wake of a hovering helicopter rotor

A simple analytical method has been developed to predict the induced velocities at the tip vortex in the wake of a hovering helicopter rotor. The wake model in the analysis includes the blade bound vortex as well as a tip vortex and vortex sheet trailed from each blade. Standard, prescribed wake models were used to describe the geometry of the tip vortex and the vortex sheet. Curved vortex elements were used to model the tip vortices and the vortex sheets. The analysis was used to study the contribution from each wake component to the axial-induced velocity of the tip vortex. Results show a highly variable induced velocity at the tip vortex both before and after the first blade passage. However, the prescribed tip vortex models require a constant axial velocity of the tip vortex. This inconsistency between the prescribed axial velocity of the tip vortex and the velocity that the wake geometry induces on the tip vortex points to a limitation of the current prescribed tip vortex geometry models.

Light, Jeffrey S.↗
NASA NTRS1980

Acoustic resonances and sound scattering by a shear layer

The reflection and transmission characteristics of plane waves scattered by a finite-thickness shear layer having a linear velocity profile and bounded by two otherwise uniform parallel flows is examined using the pressure perturbation equation solutions in the shear layer shown previously to be in terms of Whittaker M functions. In addition to the angle of plane wave incidence and the relative Mach number of the flows bounding the shear layer, it is found that the scattering properties of the shear layer depend crucially upon a parameter tau in such a manner that the case tau approaching zero characterizes the long wavelength properties of the layer and the case tau approaching infinity characterizes the short wavelength properties of the layer. In contrast to the region of ordinary reflection in the cases where the corresponding vortex sheet does not have a Brewster angle, the values of the reflection coefficient up to tau of 2 follow those of the vortex sheet; for the case for which the corresponding vortex sheet has a Brewster angle, the magnitude of the reflection coefficient may be sensitive to even small changes in tau in certain cases.

Koutsoyannis, S. P.↗
NASA NTRS1989

A linear shock cell model for jets of arbitrary exit geometry

The shock cell structures of single supersonic non-ideally expanded jets with arbitrary exit geometry are studied. Both vortex sheets and realistic mean profiles are considered for the jet shear layer. The boundary element method is used to predict the shock spacing and screech tones in a vortex sheet model of a single jet. This formulation enables the calculations to be performed only on the vortex sheet. This permits the efficient and convenient study of complicated jet geometries. Results are given for circular, elliptic and rectangular jets and the results are compared with analysis and experiment. The agreement between the predictions and measurements is very good but depends on the assumptions made to predict the geometry of the fully expanded jet. A finite diffference technique is used to examine the effect of finite mixing layer thickness for a single jet. The finite thickness of the mixing layer is found to decrease the shock spacing by approximately 20 percent over the length of the jet potential core.

Morris, P. J.↗
NASA NTRS1987

Shock structure in jets of arbitrary exit geometry

The shock structure and hydrodynamic stability of single and twin jets with arbitrary exit geometry are studied. Both vortex sheets and realistic mean profiles are considered for the jet shear layer. The boundary element method is used to predict the shock spacing and screech tones in a vortex sheet model of a single jet. Results are given for circular, elliptic and rectangular jets and the results compared with analysis and experiment. A finite difference technique is used to examine the effect of finite mixing layer thickness for a single jet. The hydrodynamic stability of twin circular jets is also considered. The variation of the stability characteristics are presented for the vortex sheet case for several separation distances. The formulation of the problem to account for finite thickness effects is also given.

Morris, P. J.↗