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Velocity components and radial pressure distributions in vortex contained in short cylindrical chamber
Profiles of velocity components and radial pressure distributions in vortex contained in short cylinder with plane end walls
Tangential velocity effects on spinning transverse combustion instability
Stationary, two-dimensional solutions of Euler equation which contain closed regions of constant vorticity
Vortex lift calculation for sharp-edge delta wings based on leading edge suction analogy
Liquid rotation and vortexing during draining
Negative critical Taylor number for stability of swirling fluid with variable density in circular magnetic field
End-wall pressure distributions in confined vortex
Rotational velocity and ion density profiles of plasma vortices by measuring radial electric field
The role of vortices in producing intense localized hea ting to the leeward regions of a variety of configurations is shown and discussed. From experimental results, flow-field models are proposed which account for the interaction of the vortex and the upper surface boundary layer; correlation of the heating is then possible for planar delta wings. Guidelines derived from these studies are offered which reduce the vortex-induced heating by appropriate shaping of configurations such as the space shuttle. Reynolds number is shown to exert a large influence on the magnitude and location of the induced heating.
Implicit finite-difference procedures for the primitive form of the incompressible Navier-Stokes and the compressible Euler equations are used to compute vortex wake flows. The partial differential equations in strong conservation-law form are transformed to cluster grid points in regions with large changes in vorticity. In addition to clustering, fourth-order accurate, spatial difference operators are used to help resolve the flow-field gradients. The use of implicit time-differencing permits large time steps to be taken since temporal variations are typically small. Computational efficiency is achieved by approximate factorization. Both two-dimensional and preliminary three-dimensional calculations are described and qualitatively compared with existing experimental data.
The advanced propeller developed for high Mach number cruise incorporates swept blades to reduce compressibility losses. In order to evaluate the induced flow-field vortex lattice methods are applied to a swept propeller blade. The blade is modeled by a radial distribution of helical horseshoe vortices with a single swept bound vortex at the quarter chord and the control point at the three-quarter chord of each radial section. The results of numerical calculations show that the power coefficient decreases as the blade is swept and the power loading distribution shifts inboard.
A computational study has been conducted to gain a better understanding of the role of turbulence in the merger of corotating vortices and in the decay of a single vortex. The flow field is simulated by using an inviscid flow model and zero-, one-, and two-equation turbulent-flow models. An implicit finite-difference procedure is employed to integrate the unsteady, two-dimensional, incompressible flow equations in a cross-plane. In the zero- and one-equation models, a spatially varying mixing-length model that simulates the streamline curvature effect is used to define an eddy viscosity. The computational merging distance criterion is in good agreement with the experimental one. In the case of the two-equation model, the turbulent kinetic energy and a modified rate of dissipation equation incorporating a curvature correction term are solved. A comparative study of the computational results corresponding to the various flow models and the available experimental data is presented.
Laser velocimeter measurements were made during the study of a two-dimensional NACA 0012 airfoil undergoing conditions of dynamic stall. The measurements, which were obtained in the Ames 2 foot wind tunnel at reduced frequencies of 0.12 and 1.2, show significant flow field hysteresis around the static stall angle. Comparisons were also made with dual-plate interferograms and good agreement was found for the attached flow cases. For separated flow, characteristic vortex shedding caused poor agreement and significantly increased the measured Reynolds shear stresses.
Recent advances in CFD are surveyed, with a focus on the applicability of codes based on the Navier-Stokes (NS) equations to helicopter aerodynamics. The developmental history of two- and three-dimensional NS codes is recalled; the formulations employed by codes of increasing complexity are outlined; and previous reviews are noted. Particular attention is given to Reynolds-averaged NS methods and their use in analyzing subsonic, transonic, and vortex-dominated flows. Typical numerical results are compared with experimental data in diagrams and graphs, and a number of outstanding problems are considered.
Three-dimensional steady and unsteady vortex-dominated flows around sharp-edged delta wings are considered in this paper. The problem is formulated by using the unsteady conservative Euler equations for the flow relative motion with respect to a moving frame of reference. An implicit approximately-factored finite volume scheme is used to solve the resulting equations on a three-dimensional computational grid which is generated by using a modified Joukowski transformation in cross-flow planes at the grid chord stations. The scheme is applied to a delta wing undergoing pitching oscillation around a large angle of attack. The initial conditions correspond to a steady flow around a delta wing of aspect ratio of one, freestream Mach number of 0.3 and mean angle of attack of 20.5. The steady flow results are compared with those of an explicit computational scheme and the experimental data, and they are in good agreement.
A conical Euler code was developed to study unsteady vortex-dominated flows about rolling highly-swept delta wings, undergoing either forced or free-to-roll motions including active roll suppression. The flow solver of the code involves a multistage Runge-Kutta time-stepping scheme which uses a finite volume spatial discretization of the Euler equations on an unstructured grid of triangles. The code allows for the additional analysis of the free-to-roll case, by including the rigid-body equation of motion for its simultaneous time integration with the governing flow equations. Results are presented for a 75 deg swept sharp leading edge delta wing at a freestream Mach number of 1.2 and at alpha equal to 10 and 30 deg angle of attack. A forced harmonic analysis indicates that the rolling moment coefficient provides: (1) a positive damping at the lower angle of attack equal to 10 deg, which is verified in a free-to-roll calculation; (2) a negative damping at the higher angle of attack equal to 30 deg at the small roll amplitudes. A free-to-roll calculation for the latter case produces an initially divergent response, but as the amplitude of motion grows with time, the response transitions to a wing-rock type of limit cycle oscillation. The wing rocking motion may be actively suppressed, however, through the use of a rate-feedback control law and antisymmetrically deflected leading edge flaps. The descriptions of the conical Euler flow solver and the free-to-roll analysis are presented. Results are also presented which give insight into the flow physics associated with unsteady vortical flows about forced and free-to-roll delta wings, including the active roll suppression of this wing-rock phenomenon.