On the parameter B = Re/KC = D²/vT

The article of record as published may be located at http://dx.doi.org/10.1016/j.jfluidstructs.2005.08.007This brief communication is a summary of the facts regarding the universalization in 1976 of a parameter b to fully nonlinear unsteady separated flows about bluff bodies nearly 125 years after its first appearance in a linearized analysis of unseparated viscous flow with very slow oscillations about a cylindrical rod and sphere by Sir George Gabriel Stokes [1851. On the effect of the internal friction of fluids on the motion of pendulums. Transactions of the Cambridge Philosophical Society 9(II), 8–106]. The primary purpose of Stokes was to show that ‘‘the index of friction’’ (the kinematic viscosity), in the equations of motion may be deduced from experiments for the vindication of the heuristic reasoning that went into the derivation by Navier [1827. Me´moire sur les lois du movement des fluides. Me´moires de l’Acade´mie de Sciences 6, 389–416.], Poisson [1831. Nouvelle the´orie de l’action capillaire Bachelier, Paris.], de Saint- Venant [1843. Note a´ joindre un memoire sur la dynamique des fluides. Comptes Rendus 17, 1240–1244.] and Stokes [1845. On the theories of internal friction of fluids in motion. Transactins of the Cambridge Philosophical Society 8, 287–305.] of what are now called the Navier–Stokes equations

Hydrodynamic Forces From Combined Wave and Current Flow on Smooth and Rough Circular Cylinders at High Reynolds Numbers

16th Annual Offshore Technology Conference (OTC) in Houston, Texas, May 7-9, 1984Experiments were conducted with two smooth and two sand-roughened cylinders in a harmonically oscillating flow with current to determine the drag and inertia coefficients and to examine the effect of current-induced wake biasing on the modified Morison equation. The various flow parameters such as the relative current velocity, Reynolds number, and the Keulegan-Carpenter number were varied systematically and the in-line force measured simultaneously. The principal results, equally valid for smooth and rough cylinders, are as follows: the drag coefficient decreases with increasing relative current for a given Reynolds number and Keulegan-Carpenter number; the effect of wake biasing on the drag and inertia coefficients is most pronounced in the drag/inertia dominated regime; and the two-term Morison equation with force coefficients obtained under no-current conditions is not applicable to the prediction of wave and : current induced loads on circular cylinders.National Science FoundationNational Science Foundatio

A Critical Review of the Transport and Decay of Wake Vortices in Ground Effect

This slide presentation reviews the transport and decay of wake vortices in ground effect and cites a need for a physics-based parametric model. The encounter of a vortex with a solid body is always a complex event involving turbulence enhancement, unsteadiness, and very large gradients of velocity and pressure. Wake counter in ground effect is the most dangerous of them all. The interaction of diverging, area-varying, and decaying aircraft wake vortices with the ground is very complex because both the vortices and the flow field generated by them are altered to accommodate the presence of the ground (where there is very little room to maneuver) and the background turbulent flow. Previous research regarding vortex models, wake vortex decay mechanisms, time evolution within in ground effect of a wake vortex pair, laminar flow in ground effect, and the interaction of the existing boundary layer with a convected vortex are reviewed. Additionally, numerical simulations, 3-dimensional large-eddy simulations, a probabilistic 2-phase wake vortex decay and transport model and a vortex element method are discussed. The devising of physics-based, parametric models for the prediction of (operational) real-time response, mindful of the highly three-dimensional and unsteady structure of vortices, boundary layers, atmospheric thermodynamics, and weather convective phenomena is required. In creating a model, LES and field data will be the most powerful tools

Experimental investigation of the vortical activity in the close wake of a simplified military transport aircraft

This paper focuses on the experimental characterization of the vortex structures that develop in the aft fuselage region and in the wake of a simplified geometry of a military transport aircraft. It comes within the framework of the military applications of airflow influence on airdrop operations. This work relies on particle image velocimetry measurements combined with a vortex-tracking approach. Complex vortex dynamics is revealed, in terms of vortex positions, intensities, sizes, shapes and fluctuation levels, for both closed and opened cargo-door and ramp airdrop configurations

Hysteresis and precession of a swirling jet normal to a wall

Interaction of a swirling jet with a no-slip surface has striking features of fundamental and practical interest. Different flow states and transitions among them occur at the same conditions in combustors, vortex tubes, and tornadoes. The jet axis can undergo precession and bending in combustors; this precession enhances large-scale mixing and reduces emissions of NOx. To explore the mechanisms of these phenomena, we address conically similar swirling jets normal to a wall. In addition to the Serrin model of tornadolike flows, a new model is developed where the flow is singularity free on the axis. New analytical and numerical solutions of the Navier-Stokes equations explain occurrence of multiple states and show that hysteresis is a common feature of wall-normal vortices or swirling jets no matter where sources of motion are located. Then we study the jet stability with the aid of a new approach accounting for deceleration and nonparallelism of the base flow. An appropriate transformation of variables reduces the stability problem for this strongly nonparallel flow to a set of ordinary differential equations. A particular flow whose stability is studied in detail is a half-line vortex normal to a rigid plane-a model of a tornado and of a swirling jet issuing from a nozzle in in a combustor. Helical counter-rotating disturbances appear to be first growing as Reynolds number increases. Disturbance frequency changes its sign along the neutral curve while the wave number remains positive. Short disturbance waves propagate downstream and long waves propagate upstream. This helical instability causes bending of the vortex axis and its precession-the effects observed in technological flows and in tornadoes.V. Shtern, J. M

Hysteresis and precession of a swirling jet normal to a wall

Interaction of a swirling jet with a no-slip surface has striking features of fundamental and practical interest. Different flow states and transitions among them occur at the same conditions in combustors, vortex tubes, and tornadoes. The jet axis can undergo precession and bending in combustors; this precession enhances large-scale mixing and reduces emissions of NOx. To explore the mechanisms of these phenomena, we address conically similar swirling jets normal to a wall. In addition to the Serrin model of tornadolike flows, a new model is developed where the flow is singularity free on the axis. New analytical and numerical solutions of the Navier-Stokes equations explain occurrence of multiple states and show that hysteresis is a common feature of wall-normal vortices or swirling jets no matter where sources of motion are located. Then we study the jet stability with the aid of a new approach accounting for deceleration and nonparallelism of the base flow. An appropriate transformation of variables reduces the stability problem for this strongly nonparallel flow to a set of ordinary differential equations. A particular flow whose stability is studied in detail is a half-line vortex normal to a rigid plane-a model of a tornado and of a swirling jet issuing from a nozzle in in a combustor. Helical counter-rotating disturbances appear to be first growing as Reynolds number increases. Disturbance frequency changes its sign along the neutral curve while the wave number remains positive. Short disturbance waves propagate downstream and long waves propagate upstream. This helical instability causes bending of the vortex axis and its precession-the effects observed in technological flows and in tornadoes.V. Shtern, J. M

The effects of spring stiffness on vortex-induced vibration for energy generation

Vortex-induced vibration (VIV) is the turbulent motion induced on bluff body that generates alternating lift forces and results in irregular movement of the body. VIV-powered system seems a good idea in greening the energy sector and most importantly is its ability to take advantages of low current speed of water to generate electricity. This paper aims to investigate the effects of spring stiffness on the characteristic of VIV. The study is important in order to maximize these potentially destructive vibrations into a valuable resource of energy. Five cylinders with the range of 0.25 to 2.00 inch diameter are tested to study the behavior of VIV. Results from this experiment indicates that, the 2.0 inch cylinder gave the lowest error in frequency ratio which is 1.1% and have a high potential of lock-in condition to occur. In term of maximum amplitude, this cylinder gave the highest amplitude of oscillation motion that is equal to 0.0065 m

Turbulence and aeration in hydraulic jumps: free-surface fluctuation and integral turbulent scale measurements

In an open channel, a change from a supercritical to subcritical flow is a strong dissipative process called a hydraulic jump. Herein some new measurements of free-surface fluctuations of the impingement perimeter and integral turbulent time and length scales in the roller are presented with a focus on turbulence in hydraulic jumps with a marked roller. The observations highlighted the fluctuating nature of the impingement perimeter in terms of both longitudinal and transverse locations. The results showed further the close link between the production and detachment of large eddies in jump shear layer, and the longitudinal fluctuations of the jump toe. They highlighted the importance of the impingement perimeter as the origin of the developing shear layer and a source of vorticity. The air–water flow measurements emphasised the intense flow aeration. The turbulent velocity distributions presented a shape similar to a wall jet solution with a marked shear layer downstream of the impingement point. The integral turbulent length scale distributions exhibited a monotonic increase with increasing vertical elevation within 0.2 < Lz/d1 < 0.8 in the shear layer, where Lz is the integral turbulent length scale and d1 the inflow depth, while the integral turbulent time scales were about two orders of magnitude smaller than the period of impingement position longitudinal oscillations

Instabilities in the wake of an inclined prolate spheroid

We investigate the instabilities, bifurcations and transition in the wake behind a 45-degree inclined 6:1 prolate spheroid, through a series of direct numerical simulations (DNS) over a wide range of Reynolds numbers (Re) from 10 to 3000. We provide a detailed picture of how the originally symmetric and steady laminar wake at low Re gradually looses its symmetry and turns unsteady as Re is gradually increased. Several fascinating flow features have first been revealed and subsequently analysed, e.g. an asymmetric time-averaged flow field, a surprisingly strong side force etc. As the wake partially becomes turbulent, we investigate a dominating coherent wake structure, namely a helical vortex tube, inside of which a helical symmetry alteration scenario was recovered in the intermediate wake, together with self-similarity in the far wake.Comment: Book chapter in "Computational Modeling of Bifurcations and Instabilities in Fluid Dynamics (A. Gelfgat ed.)", Springe