Murray Tobak

Asymmetric vortices on a slender body of revolution

The symmetric and asymmetric leeward-side flow fields on an inclined ogive-cylinder have been investigated using a number of experimental techniques. Naturally occurring and perturbed flow fields were studied at a moderate Reynolds number and at many incidence angles. By close examination of the steady side force behavior at different roll orientations of the tip, it has been established that micro-variations in the tip geometry of the model have a large influence on the downstream development of the flow field. Under certain conditions, a bistable flow field was observed.

Experimental study of controlled tip disturbance effect on flow asymmetry

The effect on the asymmetric mean flow observed on pointed bodies of revolution at incidence of changing the size and location of a controlled disturbance as well as changes in angle of attack and flow conditions are evaluated experimentally. Flow visualization and side‐force measurements are carried out for a generic ogive‐cylinder body inclined at high angle of attack in a low‐speed wind tunnel. For all angles of attack tested (30°–60°), minute changes in the size or location of the controlled disturbance result in finite changes in the asymmetric flow field, even to the extent of reversing the sign of the side force or becoming almost symmetric. The process is reversible; returning the wire to an original position likewise restores the corresponding flow field and mean side force. The variation of side force with continuous variation of a perturbation’s size or location remains continuous and single valued, even in the incidence range of 50° to 60°, where ‘‘bistable’’ behavior of the asymmetric flow fi...

Numerical, experimental, and theoretical study of convective instability of flows over pointed bodies at incidence

A study is conducted to investigate whether the behavior of the asymmetric mean flow observed on pointed bodies of revolution at incidence remains consistent with the presence of a convective instability of an original symmetric flow, even in the incidence range where virtually bistable behavior of the asymmetric flow is observed. By means of a retractable wire located near the tip, it is determined experimentally that for all angles of attack tested (30 to 60 degs), changing the size or location of the controlled disturbance results in a finite change in the asymmetric flow field, even to the extent of reversing the sign of the side force or becoming almost symmetric. The process is reversible; returning the wire to an original position likewise restores the corresponding flow field and mean side force. The effect of wire location (roll angle and distance from the tip) as well as angle of attack and flow conditions are evaluated experimentally by means of flow visualization and side-force measurements for a generic ogive-cylinder model in a low-speed wind tunnel. Evaluation of the results in the light of computational observations and theoretical considerations yields an affirmative answer to the question posed.

Experimental study of saddle point of attachment in laminar juncture flow

An experimental study of laminar horseshoe vortex flows upstream of a cylinder/flat plate juncture has been conducted to verify the existence of saddle-point-of-attachment topologies. In the classical depiction of this flowfield, a saddle point of separation exists on the flat plate upstream of the cylinder, and the boundary layer separates from the surface. Recent computations have indicated that the topology may actually involve a saddle point of attachment on the surface and additional singular points in the flow. Laser light sheet flow visualizations have been performed on the symmetry plane and crossflow planes to identify the saddle-point-of-attachment flowfields. The visualizations reveal that saddle-point-of-attachment topologies occur over a range of Reynolds number in both single and multiple vortex regimes. An analysis of the flow topologies is presented that describes the existence and evolution of the singular points in the flowfield.

Effect of upstream disturbance on flow asymmetry

Results are presented of an experimental study aimed at revealing the origin of the asymmetric mean flow that occurs on pointed bodies of revolution at moderate-to-high angles of attack. The placement of a small fixed disturbance (a minute spherical bead) on a very thin wire at various locations in the flow near the tip of the model is shown to provoke the same range of behavior of the asymmetric flow that was produced earlier by use of a controlled retractable wire protuberance, here without touching or altering the tip at all. Results remain consistent with the presence of a convective instability mechanism, and demonstrate the potential for a precise mapping of the bodys receptivity to fixed disturbances in the flowfield.

Surface flow patterns on an ogive-cylinder at incidence

A set of photographs has been obtained which documents the oil-imaged surface flow patterns of an ogive-cylinder at angles-of-attack between 30 and 85 deg, and Reynolds number of 26,000. Attention is given to the possibility that the bistable nature of the flow within the 50-65 deg angle-of-attack range is linked to the coincident appearance of foci in the surface flow patterns, in view of the suggestion that these foci act as the anchor points allowing the forebody vortical structures to roll up and form the forebodys trailing vortex system.

Spectral stability of Taylor’s vortex array

It has been proven that the two‐dimensional Taylor vortex array, which is an exact solution of the Navier–Stokes equation, is absolutely and monotonically stable, in a global sense, with respect to infinitesimal disturbances of all discrete frequencies.

Numerical simulation of upstream disturbance on flows around a slender body

Numerical solutions of the thin-layer approximation of the compressible Navier-Stokes equations have been obtained for flows around an ogive-cylinder body with and without a small fixed disturbance placed upstream of the body tip. Locating the disturbance at positions in the flow field upstream of the tip provokes the same range of behavior of the asymmetric flow that was numerically produced earlier by use of a geometrical disturbance on the body tip. Results remain consistent with the presence of a convective instability mechanism, and demonstrate the potential for a precise mapping of the bodys receptivity to fixed disturbances in the flow field. Numerical solutions were also obtained for the flow-field responses to impulsive upstream disturbances to determine whether there is a growing response to an asymmetric impulsive disturbance that is consistent with presence of a convective instability mechanism. Results for surface pressure are interpreted with the aid of a mathematical model. The model suggests that the observed growth of surface pressure gradient with time and distance along a ray in response to an asymmetnc impulsive disturbance is in accord with the solution of a Ginzberg-Landau equation, with distinguishing features of the solution being consistent with the convective instability mode of behavior.

Nonlinear stability of a flow with bound eddies

Kovasznay [Proc. Cambridge Philos. Soc. 44, 58 (1948)] obtained an exact solution of the Navier–Stokes equations that describes a flow with periodic bound eddies. The stability of this nonparallel flow with respect to three‐dimensional finite amplitude disturbances is analyzed by use of the energy method. A sufficient condition for global stability is obtained. It is shown that the additional nonhomogeneity in shear stress distribution in a nonparallel flow is a destabilizing factor.

Nonlinear stability of Taylor's vortex array

It is proved that the two‐dimensional Taylor vortex array, which is an exact unsteady solution of the Navier–Stokes equation, is globally and asymptotically stable in the mean with respect to three‐dimensional periodic disturbances. A time‐dependent bound on the decay rate of the kinetic energy of disturbances is obtained.