Starting vortex

About: Starting vortex is a research topic. Over the lifetime, 4785 publications have been published within this topic receiving 100419 citations.

On vortex shedding from an airfoil in low-Reynolds-number flows

Abstract: Development of coherent structures in the separated shear layer and wake of an airfoil in low-Reynolds-number flows was studied experimentally for a range of airfoil chord Reynolds numbers, 55 × 10 3 ≤ Re c ≤ 210 × 10 3 , and three angles of attack, α = 0°, 5° and 10°. To illustrate the effect of separated shear layer development on the characteristics of coherent structures, experiments were conducted for two flow regimes common to airfoil operation at low Reynolds numbers: (i) boundary layer separation without reattachment and (ii) separation bubble formation. The results demonstrate that roll-up vortices form in the separated shear layer due to the amplification of natural disturbances, and these structures play a key role in flow transition to turbulence. The final stage of transition in the separated shear layer, associated with the growth of a sub-harmonic component of fundamental disturbances, is linked to the merging of the roll-up vortices. Turbulent wake vortex shedding is shown to occur for both flow regimes investigated. Each of the two flow regimes produces distinctly different characteristics of the roll-up and wake vortices. The study focuses on frequency scaling of the investigated coherent structures and the effect of flow regime on the frequency scaling. Analysis of the results and available data from previous experiments shows that the fundamental frequency of the shear layer vortices exhibits a power law dependency on the Reynolds number for both flow regimes. In contrast, the wake vortex shedding frequency is shown to vary linearly with the Reynolds number. An alternative frequency scaling is proposed, which results in a good collapse of experimental data across the investigated range of Reynolds numbers.

The instability of a straight vortex filament in a strain field

Abstract: A straight infinite vortex of finite cross section is deformed by the action of weak irrotational plane strain. The deformed vortex is shown, in the absence of axial flow, to be unstable to disturbances whose axial wavelengths lie in a narrow band, whose width is proportional to the imposed strain. The band is centred on the wavelength of the helical wave which does not propagate on the unstrained circular vortex. Thus support is given to the instability mechanism proposed recently by Widnall, Bliss & Tsai (1974). The argument depends, however, on the mirror image of the helical wave also being a possible non-propagating disturbance on the unstrained vortex.

The significance of vortex ring formation to the impulse and thrust of a starting jet

Abstract: The recent work of Gharib, Rambod, and Shariff [J. Fluid Mech. 360, 121 (1998)] studied vortex rings formed by starting jets generated using a piston-cylinder mechanism. Their results showed that vortex rings generated from starting jets stop forming and pinch off from the generating jet for sufficiently large values of the piston stroke to diameter ratio (L/D), suggesting a maximization principle may exist for propulsion utilizing starting jets. The importance of vortex ring formation and pinch off to propulsion, however, rests on the relative contribution of the leading vortex ring and the trailing jet (which appears after pinch off) to the impulse supplied to the flow. To resolve the relative importance of the vortex ring and trailing jet for propulsion, a piston-cylinder mechanism attached to a force balance is used to investigate the impulse and thrust generated by starting jets for L/D ratios in the range 2–8. Two different velocity programs are used, providing two different L/D values beyond which pinch off is observed, in order to determine the effect of vortex ring pinch off. Measurements of the impulse associated with vortex ring formation show it to be much larger than that expected from the jet velocity alone and proportionally larger than that associated with a trailing jet for L/D large enough to observe pinch off. The latter result leads to a local maximum in the average thrust during a pulse near L/D values associated with vortex rings whose circulation has been maximized. These results are shown to be related to the nozzle exit over-pressure generated during vortex ring formation. The over-pressure is in turn shown to be associated with the acceleration of ambient fluid by vortex ring formation in the form of added and entrained mass.

The motion of a vortex filament with axial flow

Abstract: Infinitesimal waves on a uniform vortex with axial flow are studied The equation for the frequency of helical waves is obtained, and solved for the case of long waves which leave the internal structure almost unaltered A method is developed to obtain results for vortices of non-uniform structure and for displacements which are not necessarily small compared with the core radius The approach consists of balancing the Kutta—Joukowski lift force, the momentum flux due to the axial motion, and the ‘tension’ of the vortex lines A general equation for the motion of a vortex filament is obtained, valid for arbitrary shape and internal structure, and in the presence of an external irrotational velocity field When the axial flow vanishes, the method is equivalent to using the Biot—Savart law for the self-induced velocity, with a suitable cutoff The impulse of a vortex filament is discussed and its rate of change is given