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This final report describes research work on vortex flows done during a four-year period beginning in March 1984 and funded by NASA Grant NCC2-294 from the Fluid Dynamics Research Branch of NASA Ames Research Center. After a brief introduction of the main topics addressed by the completed research, the accomplishments are summarized in chronological order.
The Tayler instability (TI) is a kink-type flow instability which occurs when the electrical current through a conducting fluid exceeds a certain critical value. Originally studied in the astrophysical context, the instability was recently discussed as a possible limiting factor for the upward scalability of liquid metal batteries. In this paper, we continue our efforts to simulate this instability for liquid metals within the framework of an integro-differential equation approach. The original solver is enhanced by multi-domain support with Dirichlet-Neumann partitioning for the static boundaries. Particular focus is laid on the detailed influence of the axial electrical boundary conditions on the characteristic features of the Tayler instability and, second, on the occurrence of electro-vortex flows and their relevance for liquid metal batteries. Electro-vortex flows might pose a larger risk to the integrity of the battery than the TI.
An experimental investigation of tip vortex flow from a NACA0012 airfoil, pitched periodically at various frequencies, is conducted in a low-speed wind tunnel. Initially, data for stationary airfoil held fixed at various angles-of-attack are gathered. Flow visualization pictures as well as detailed cross-sectional properties areobtained at various streamwise locations using hot-wire anemometry. Data include mean velocity, streamwise vorticity as well as various turbulent stresses. Preliminary data are also acquired for periodically pitched airfoil. These results are briefly presented in this extended abstract.
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.
Effects of fluid mass flow rate and exit orifice diameter on radial static pressure distribution in compressible vortex flow field
Measurements of the unsteady vortex flow over a wing-body at high angles of attack were carried out on a generic test model of a pointed body of revolution with double-delta wings. Vortex patterns and trajectories were quantified from digitized laser sheet video images. The velocity-field measurements showed the jetlike flow in the unburst vortex, unsteady secondary structures below the primary core, and then the reversed flow in the burst vortex. Results of hot-film anemometry revealed the presence of peak frequencies in the velocity spectra over the wing and near the trailing edge, which varied linearly with freestream speed and increased as the measurement point moved upstream. Good Strouhal correlation was found with previous results obtained for a smaller generic wing-body model.
Recent progress in a research program directed toward an improved vortex flow technology base was reviewed. Analysis methods for conical flow and analysis and design methods for nonconical flows are presented. Applications are made for a variety of planar, nonplanar, and interferring lifting surfaces. Several methods are shown to provide reasonable estimates of over-all forces and moments for simple wing planforms with the suction analogy method currently offering the most versatility for arbitrary configuration applications. For the prediction of surface loadings the free vortex sheet method being developed by Boeing is shown to have considerable promise and further development of this type of method is encouraged. A data base for ogee strake-wing configurations is summarized with an emphasis on the requirements for maximizing the interference lift. A strake planform design procedure is discussed and a first solution (gothic in planview) is integrated with a wing body. The data show the strake to exhibit expected stable vortex characteristics. It was found that, apart from increasing sweep, conically cambered delta wings developed drag levels approaching that of attached flow with increasing either the lift or the wing camber height, lastly, an approximate vortex flow design method, based on the suction analogy, is outlined and an example is given.
An experiment on a 45-degree swept wing was conducted to study three-dimensional boundary-layer characteristics using surface-mounted, micro-thin, multi-element hot-film sensors. Cross-flow vortex structure and boundary-layer transition were measured from the simultaneously acquired signals of the hot films. Spanwise variation of the root-mean-square (RMS) hot-film signal show a local minima and maxima. The distance between two minima corresponds to the stationary cross-flow vortex wavelength and agrees with naphthalene flow-visualization results. The chordwise and spanwise variation of amplified traveling (nonstationary) cross-flow disturbance characteristics were measured as Reynolds number was varied. The frequency of the most amplified cross-flow disturbances agrees with linear stability theory.
A relatively simple but accurate potential flow model was developed for studying the symmetric vortex flow on cones. The model is a modified version of the model first developed by Bryson, in which discrete vortices and straight-line feeding sheets were used to represent the flow field. It differs, however, in the zero-force condition used to position the vortices and determine their circulation strengths. The Bryson model imposed the condition that the net force on the feeding sheets and discrete vortices must be zero. The proposed model satisfies this zero-force condition by having the vortices move as free vortices, at a velocity equal to at the local crossflow velocity at their centers. When the free-vortex assumption is made, a solution is obtained in the form of two nonlinear algebraic equations that relate the vortex center coordinates and vortex strengths to the cone angle and angle of attack. The vortex center locations calculated using the model are in good agreement with experimental values. The cone normal forces as well as center locations are in good agreement with the vortex cloud method of calculating symmetric flow fields.
A wind tunnel experiment was conducted in the NASA Langley Research Center (LaRC) Unitary Plan Wind Tunnel (UPWT) to determine the effects of passive surface porosity and vertical tail placement on vortex flow development and interactions about a general research fighter configuration at supersonic speeds. Optical flow measurement and flow visualization techniques were used that featured pressure sensitive paint (PSP), laser vapor screen (LVS), and schlieren, These techniques were combined with conventional electronically-scanned pressure (ESP) and six-component force and moment measurements to quantify and to visualize the effects of flow-through porosity applied to a wing leading edge extension (LEX) and the placement of centerline and twin vertical tails on the vortex-dominated flow field of a 65 cropped delta wing model. Test results were obtained at free-stream Mach numbers of 1.6, 1.8, and 2.1 and a Reynolds number per foot of 2.0 million. LEX porosity promoted a wing vortex-dominated flow field as a result of a diffusion and weakening of the LEX vortex. The redistribution of the vortex-induced suction pressures contributed to large nose-down pitching moment increments but did not significantly affect the vortex-induced lift. The trends associated with LEX porosity were unaffected by vertical tail placement. The centerline tail configuration generally provided more stable rolling moments and yawing moments compared to the twin wing-mounted vertical tails. The strength of a complex system of shock waves between the twin tails was reduced by LEX porosity.
A technique for noise calculation on the basis of vortex flow models is described. The 'reflection principle' is first extended to the whole class of potential flows which may be solved by the method of images. This allows the sound radiation to be computed solely through a volume integral over both the exterior and interior of any surfaces which may be present. The source distribution is then rewritten in terms of the vorticity within the flow which yields a highly computationally efficient formulation of the aeroacoustic theory. Several examples of such noise calculations are included.
A group-velocity criterion for vortex breakdown implied by wave trapping theory is applied to vortex flows in a slightly divergent duct that exhibits breakdown. The group velocities for both symmetric (n = 0) and nonsymmetric (n = plus or - 1) modes of wave propagation are calculated for the experimental data. It is found that the flow ahead of the breakdown region is always supercritical and stable to these modes of disturbances. However, the flow field behind the breakdown region may be either supercritical or subcritical to the modes n = 0 and n = 1, and always supercritical to mode n = -1. The flow field behind this breakdown region is unstable to the asymmetric mode disturbance (n = 1) for a finite range of wavenumbers. The calculated frequencies of the unstable disturbances are in good agreement with the frequencies obtained from the experimental measurements.
Vortex flows caused by a swept wing are described in some detail. The thin-shear-layer Navier-Stokes equations with an algebraic eddy-viscosity turbulence model are solved. An implicit, factored numerical scheme is used. On the upper surface of the wing, flow is primarily along the free-stream and spanwise direction, respectively, at small and large angles of attack.
A review of research conducted at the National Aeronautics and Space Administration (NASA) Langley Research Center (LaRC) into high-speed vortex flows during the 1970s, 1980s, and 1990s is presented. The data are for flat plates, cavities, bodies, missiles, wings, and aircraft with Mach numbers of 1.5 to 4.6. Data are presented to show the types of vortex structures that occur at supersonic speeds and the impact of these flow structures on vehicle performance and control. The data show the presence of both small- and large-scale vortex structures for a variety of vehicles, from missiles to transports. For cavities, the data show very complex multiple vortex structures exist at all combinations of cavity depth to length ratios and Mach number. The data for missiles show the existence of very strong interference effects between body and/or fin vortices. Data are shown that highlight the effect of leading-edge sweep, leading-edge bluntness, wing thickness, location of maximum thickness, and camber on the aerodynamics of and flow over delta wings. Finally, a discussion of a design approach for wings that use vortex flows for improved aerodynamic performance at supersonic speeds is presented.
An annular-mode gliding arc discharge powered by a 50 Hz alternating current (ac) supply was studied in a vortex flow of dry and humid air. Its temporal evolution characteristics were investigated by electrical measurement, temporally resolved imaging, and temporally resolved optical emission spectroscopic measurements. Three discharge stages of arc-ignition, arc-gliding, and arc-extinction were clearly observed in each half-cycle of the discharge. During the arc-gliding stage, the intensity of light emission from the arc root at the cathode was remarkably higher than that at other areas. The spectral intensity of N{sub 2}(C{sup 3}Π{sub u}−B{sup 3}Π{sub g}) during the arc-ignition stage was much higher than that during the arc-gliding stage, which was contrary to the temporal evolutions of spectral intensities for N{sub 2}{sup +}(B{sup 2}Σ{sub u}{sup +}−X{sup 2}Σ{sub g}{sup +}) and OH(A{sup 2}Σ{sup +}−X{sup 2}Π{sub i}). Temporally resolved vibrational and rotational temperatures of N{sub 2} were also presented and decreased with increasing the water vapor content.
Slender wings leading edge vortex flow effect on roll damping at subsonic speeds
The phenomenon of vortex breakdown is believed to be associated with a finite amplitude wave that has become trapped at the critical or breakdown location. The conditions at which the propagating waves become trapped at a certain axial location were examined by use of a group-velocity criterion implied by Landahl's general theory of wave trapping. An ideal vortex having constant vorticity and uniform axial velocity at the inlet of a slowly diverging duct was studied. The linear wave propagation analysis is applied to the base flow at several axial stations for several values of the ratio of swirl velocity to axial velocity at the inlet of the divergent duct, assuming a locally parallel flow. The dipsersion relations and hence the group velocities of both the symmetric (n = 0) and asymmetric modes (n = + or - 1) were investigated. The existence of a critical state in the flow (at which the group velocity vanishes), and its relationship to the stagnation point on the axis of the duct and to the occurrence of an irregular singularity in the equations governing wave propagation in the flow field are discussed.
A visual and quantitative study of the vortex flow field over a 70-deg delta wing with an external jet blowing parallel to and at the leading edge was conducted. In the experiment, the vortex core was visually marked with TiCl4, and LDA was used to measure the velocity parallel and normal to the wing surface. It is found that jet blowing moved vortex breakdown farther downstream from its natural position and influenced the breakdown characteristics.