Family of similarity flows with vortex sheets
Prandtl two dimensional time dependent similarity flows with vortex sheets
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Prandtl two dimensional time dependent similarity flows with vortex sheets
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.
Stability of plane vortex sheet between gases exchanging heat by radiation applied to gas core in coaxial jet nuclear rocket
A method is presented for predicting the geometry of a vortex sheet trailing a lift generating wing in its vicinity. It differs from others in that it uses a continuous vorticity distribution rather than discrete vortex filaments. It was found that the results were in good agreement with available experimental data, after the initial cycle of what was to be a relaxation scheme, so that iterations for this end were unnecessary. While the technique is computing intensive, it becomes attractive when used in conjunction with panel methods applications for complete aircraft configurations. The panel method solution needs to be found only once for each streamwise station downstream of the wing. Corrections applied are geometric in nature and are independent of other computational aspects.
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.
The aerodynamic characteristics of highly sweptback wings with separations induced vortex flows have been numerically investigated using the free vortex sheet method, developed by Boeing Company, under a contract with NASA/Langley Research Center. The models studied included delta and straked wings, and wings with leading edge extensions. Also, PAN-AIR code has been used to design a fixed leading edge extension into a thick delta wing. The theoretical results predicted have been compared with the experimental data wherever available, and the code capabilities and limitations explored. New fuselage effects also have been considered in some cases.
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.
The close-approach problem associated with vortex-lattice methods was examined numerically with the objective of calculating velocities at arbitrary points, not just at midpoints, between the vortices. The objective was achieved using a subvortex technique in which a vortex splits into an increasing number of subvortices as it is approached. The technique, incorporated in a two-dimensional potential flow method using "submerged" vortices and sources, was evaluated for a cambered Joukowski airfoil. The method could be extended to three dimensions, and should improve non-linear methods, which calculate interference effects between multiple wings and vortex wakes, and which include procedures for force-free wakes.
The random motions of the vortex elements behind a wing that sheds a disturbed, translating array of vortices are analyzed. The analysis indicates that the wake would diffuse and decay rapidly when viscosity is present and would produce small rolling moments on encountering aircraft. It was found that comparable results could also be achieved with an array consisting of vortices that are equal in magnitude but which alternate in sign. This observation indicates that random motion can probably be achieved with a variety of stepped loadings.
A configuration concept for developing vortex lift, which replaces the physical wing strake with a jet sheet generated fluid strake, was investigated on a general research fighter model. The vertical and horizontal location of the jet sheet with respect to the wing leading edge was studied over a momentum coefficient range from 0 to 0.24 in the Langley 7- by 10-foot high speed tunnel over a Mach number range from 0.3 to 0.8. The angle of attack range studied was from -2 to 30 deg at sideslip angles of 0, -5, and 5 deg. Test data are presented without analysis.
A configuration concept for augmenting the lift capability of low aspect ratio, thin wings, typically used on fighter aircraft was investigated. The fluid strake concept uses a jet sheet formed by blowing from a series of small orifices located in the side of the fuselage ahead of the wing to generate a stable vortex flow over the wing at high angle of attack. The effect of the location of the fluid strake relative to the wing was investigated for three different designs of the in-line orifices using a half-span model tested in a 7 by 10 foot low speed tunnel. Based on the results of the low speed test, a jet sheet producing module was incorporated into a NASA general research fighter model and tested in the Langley 7 by 10 foot high speed tunnel to determine the effectiveness of the fluid strake as a lift-enhancement device in the high-speed maneuver regime. Tests were conducted over a Mach number range from 0.3 to 0.8, with a jet momentum coefficient range from 0 to 0.24. Significant lift increments resulted at the higher angles of attack and drag polars were improved.
The induced drag polar is developed for wt-ngs capable of attaining extremely high loadings while possessing an elliptical distribution of circulation. This development is accomplished through a theoretical investigation of the vortex-wake deformation process and the deduction of the airfoil forces from the impulse and kinetic energy contents of the ultimate wake form. The investigation shows that the induced velocities of the wake limit the maximum lift coefficient to a value of 1.94 times the wing aspect ratio, for aspect ratios equal to or less than 6.5, and that the section properties of the airfoil limit the lift coefficient to 12.6 for aspect ratios greater than 6.5. Relations are developed for the rate of deformation of the vortex wake. It is also shown that linear wing theory is app1icable up to lift coefficients equal to 1.1 times the aspect ratio.
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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.
The aerodynamic characteristics of slender wings having separation induced vortex flows are investigated by employing three different computer codes--free vortex sheet, quasi vortex lattice, and suction analogy methods. Their capabilities and limitations are examined, and modifications are discussed. Flat wings of different configurations: arrow, delta, and diamond shapes, as well as cambered delta wings, are studied. The effect of notch ratio on the load distributions and the longitudinal characteristics of a family of arrow and diamond wings is explored. The sectional lift coefficients and the accumulated span loadings are determined for an arrow wing and are seen to be unusual in comparison with the attached flow results. The theoretically predicted results are compared with the existing experimental values.
The wake shape under symmetrical flight conditions and its effects on aerodynamic characteristics are examined. In addition, the effect of wake shape in sideslip and discrete vortices such as strake or forebody vortex on lateral characteristics is presented. The present numerical method for airplane configurations, which is based on discretization of the vortex sheet into vortex segments, verified the symmetrical and asymmetrical roll-up process of the trailing vortices. Also, the effect of wing wake on tail planes is calculated. It is concluded that at high lift the assumption of flat wake for longitudinal and lateral-directional characteristics should be reexamined.