烟圈

Mount Etna

Extract from the Gallery of Fluid Motion, Physics of Fluids A, Vol Extract from the Gallery of Fluid Motion, Physics of Fluids A, Vol. 5, September 1993. Contribution by Hiroshi Higuchi (Syracuse University).

This picture was taken for the Cessna Company by Mr. Paul Bowen This picture was taken for the Cessna Company by Mr. Paul Bowen. As the trailing vortices descended over the fog layer due to the downwash, the flow field in the wake was made visible by the distortion of the fog layer. For details on the flight, see Cessna.

Picture courtesy of DANTEC Measurement Technology.

James E. Hobbs, from Lockheed Aircraft service Co James E. Hobbs, from Lockheed Aircraft service Co., Ontario, California

Hurricane Laura Sept 30 2008

vortex

北半球 大型自由涡

Chapter 14 flow with moderate Re

Flow around a cylinder

Integral analysis, mass conservation

Integral analysis, momentum

Reynolds Number Dependency Transition to turbulence 300 < Rd < 3*105 3*105 < Rd < 3.5*106 3.5*106 < Rd

Classic VIV Catastrophe If ignored, these vibrations can prove catastrophic to structures, as they did in the case of the Tacoma Narrows Bridge in 1940.

Shear layer instability causes vortex roll-up Flow speed outside wake is much higher than inside Vorticity gathers at downcrossing points in upper layer Vorticity gathers at upcrossings in lower layer Induced velocities (due to vortices) causes this perturbation to amplify

Wake Instability

Classical Vortex Shedding Von Karman Vortex Street Alternately shed opposite signed vortices

Additional VIV Parameters Reynolds Number subcritical (Re<105) (laminar boundary) Reduced Velocity Vortex Shedding Frequency S0.2 for subcritical flow

Strouhal Number vs. Reynolds Number

Vortex Shedding Generates forces on Cylinder Uo Both Lift and Drag forces persist on a cylinder in cross flow. Lift is perpendicular to the inflow velocity and drag is parallel. FL(t) FD(t) Due to the alternating vortex wake (“Karman street”) the oscillations in lift force occur at the vortex shedding frequency and oscillations in drag force occur at twice the vortex shedding frequency.

Vortex Induced Forces Due to unsteady flow, forces, X(t) and Y(t), vary with time. Force coefficients: D(t) 1/2 r U2 d L(t) 1/2 r U2 d Cx = Cy =

VIV in the Ocean Non-uniform currents effect the spanwise vortex shedding on a cable or riser. The frequency of shedding can be different along length. This leads to “cells” of vortex shedding with some length, lc.

VIV Suppression Helical strake Shroud Axial slats Streamlined fairing Splitter plate Ribboned cable Pivoted guiding vane Spoiler plates

VIV Suppression by Helical Strakes Helical strakes are a common VIV suppresion device.