New Phenomena in Vortex-Induced Vibrations

Transcription

1 New Phenomena in Vortex-Induced Vibrations C.H.K. Williamson Fluid Dynamics Research Laboratories Cornell University Supported by the Office of Naval Research

2 Motivation Large vibrations of: Riser tubes bringing oil from the seabed Bridges and chimney stacks Heat exchangers Overhead power cables Many other applications Tacoma Narrows Bridge Hoover Diana Project Exxon-Mobil

3 Generic -Universal Nature of Diverse VIV Systems Paradigm for more complex systems U U y x GENERIC PHENOMENA Carry across to: Y-CYLINDER XY-CYLINDER High Re All VIV Systems PIVOTED ROD FLEXIBLE CYLINDER MIT, Norway, Exxon U or STRUMMING CABLE TETHERED SPHERE

4 Does Resonance Look Anything Like This? f N f V U f V f N

5 Parameters in the problem Flow speed U Expect resonant oscillation f f V N U = U f D N U = U f D N = U f D V = 1 S ~ 5 NORMALIZED VELOCITY Oscillating mass m m = m displaced fluid mass Air m is large ~ O(100) Water m is small ~ 1-10 MASS RATIO Structural damping c ζ = c critical damping mζ = mass-damping parameter VERY LOW VALUES HERE! DAMPING RATIO

6 Typical VIV System Equation of Motion: m y + cy + ky = F fluid Cylinder displacement: Fluid force: y( t) = A sin ωt F( t) = F sin t 0 ( ω + φ ) φ IS VERY IMPORTANT! Amplitude response A = A D = (m 1 + C A CY sin φ U 3 ) ζ 4π f 2 f MASS-DAMPING PARAMETER Frequency response f = f f N = (m +1) (m + C EA ) C EA = 1 2π A U f 2 C 3 Y cos φ DEPENDS ON m

7 1 VIV Response Modes

8 What is known about the wake vortex dynamics for a transversely oscillating cylinder Williamson & Roshko (1988) Example vortex wake modes 2S MODE 2 single vortices / cycle 2P MODE 2 pairs of vortices / cycle 2P Ongoren & Rockwell (1988) for in-line oscillations

9 Map of Wake Modes Williamson & Roshko (1988)

10 High Mass-Damping 2 Modes 1 Discontinuity 2S Mode 2P Mode Experiments in AIR m ~ Feng (1968) Brika & Laneville (1993)

11 Low Mass-Damping Experiments in WATER m ~ 5 Khalak & Williamson (1996, 1999) 3 Modes 2 Discontinuities Large A Wide regime of resonance f > 1.0!! Depart from classical resonance

12 Very Low m Very Wide Regime! 5 Collapses beautifully with: U f S = f f vo Suggests W-R Map: Initial 2S Upper 2P Lower 2P Ratio of the 2 most basic frequencies Now see VORTEX MODES!

13 Vortex Modes Initial Branch 2S Lower Branch 2P Seen effects: mζ, m See extreme later

14 2 Numerical Simulations & Laminar VIV

15 Compilation of Low-Re Results Consistent with A peak < 0.6 Hysteresis Anagnostopolous & Bearman (1992) Anagnostopolous (1994) Newman & Karniadakis (1997) Shiels, Leonard, & Roshko (2001) Wilden & Graham (2000) Vortex mode changes to P+S A > 0.6 Experiment P+S mode must not be able to impart positive energy transfer i.e. C y sin φ < 0 Numerical simulation Ponta and Aref (2003) Meneghini & Bearman (1995)

16 VIV Simulations Govardhan & Williamson (2000) Blackburn et. al. (2001) Lucor & Karniadakis (2005) Experiment 3D DNS Challenges for CFD: Must use 3D simulations to produce: 2P mode A > 0.6 Pushing up Re: 1995 Re max ~ 200 (Newman & Karniadakis) 1999 Re max ~ 2000 (Evangelinos & Karniadakis) 2005 Re max ~ ,000? (Lucor & Karniadakis ) LES: Not yet good agreement with experiments or between LES studies.

17 Flexible Pivoted 3 XY Motion & Complex Flows Tapered Tethered

18 X-Y Motion m < 6 Jauvtis & Williamson JFM (2004) A = 1.5! Much bigger than Y-only Slight streamwise motion has dramatic effect! NOTE: Forced motion of Jeon & Gharib (2004) Small change in φ due to vortex dynamics Big change in A

19 Spanwise Variation of A Techet, Hover, & Triantafyllou (1998) Williamson-Roshko Map: Suggests you can get 2S along part of span, 2P along other part of span 2S-2P Hybrid Mode Relevant to Cable Dynamics Gumby

20 U Pivoted Cylinder Simplest case of spanwise amplitude variation relevant to cable dynamics Flemming & Williamson (2004) Cross over of branches Need 3D W-R Map 2S-2P Hybrid Biggest amplitude mode 2C 2C Mode

21 Sphere VIV Govardhan & Williamson (2005) Streamwise vorticity Analogy to airplane trailing vortices Sphere wake Aircraft trailing vortex wake Lift force Lift force

22 4 Griffin Plot Perhaps the most basic question! What is A peak

23 Classical Griffin Plot log-log First extensive compilations of many studies Griffin, et. al. (1975) Skop-Griffin parameter (mζ S 2 )

24 linear-log Big Scatter! All Cases: Y cylinders Pivoted bodies Flexible Cantilever + others

25 Slightly Better Collapse Cylinder y-motion only A PEAK NOT SATURATED! After 30 Years The Griffin Plot is not yet fully defined! Even for the paradigm case!

26 Controlled Damping Damping Control Works!

27 Effect of Re Note: curves look similar for each Re

28 Effect of Re ALSO: A α = 0 Good collapse of data: = log 10 [0.41 Re 0.36 ] Klamo, Leonard, & Roshko (2005) Independently find trend of amplitude increase with Re (controlled damping)

29 The Modified Griffin Plot A A α = 0 We define: A MODIFIED = A A α = 0 Collapses our data well!

30 Can we now collapse the large scatter in the classical Griffin plot A MODIFIED = A A α = 0? Take into account Re!

31 Griffin Plot Modified Griffin Plot Data collapses onto a single curve!

32 5 Critical Mass

33 Equation for Oscillation Frequency Govardhan & Williamson (2000) Khalak & Williamson (1999) Hover, Techet & Triantafyllou (1998) Anand (1985) f LOWER = f f N = ( m + 1) ( m + C ) EA Best fit : C EA =

34 f LOWER = f f N = ( m + 1) ( m 0.54) CRITICAL MASS RATIO m CRIT = 0.54 If m 0.54, If m < m CRIT, f Lower branch does not exist Get stuck on upper branch

35 m = 0.52 What if m below critical? Radically different from classical resonance Consider : U = 100 f osc ~ 17 f N U = 500 f osc ~ 87 f N Why not?

36 You are here Get bigger / faster water channel Reach much higher U Will not prove anything! GO RIGHT TO INFINITY!

37 Infinite U U = U D 0 f N 0 U f D N NO! NO! YES! f N ~ k / m... make k = 0 REMOVE SPRINGS!

38 Remove springs!!! m = 1.7 Easily move with a feather Strong vortices Expect large vibrations.now what happens???

39 m = 1.7 k = 0, NO SPRINGS

40 m = 0.6 k = 0, NO SPRINGS Now: Remove mass gradually

41 m = 0.53 k = 0, NO SPRINGS

42 Experiments for INFINITE U

43 Rising Cylinder Trajectories m = 0.78 m = 0.45

44 m = 0.08 Vortex Dynamics Behind a Rising Sphere

45 m = 0.08 Vortex Dynamics Behind a Rising Sphere