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  • הצגה קצרה של עצמי

Presentation Kenes Presentation Kenes Presentation Transcript

  • Investigation of capillary waves on the surface of Taylor bubble propagating in vertical tubes By Dan Liberzon Under the supervision of: Prof. Dvora Barnea & Prof. Lev Shemer Department of Fluid Mechanics and Heat Transfer, Tel Aviv University
  • Scope of the presentation
    • Taylor bubbles
    • Wind/Wave, Wave/Current interaction
    • Theoretical model
    • Experimental research
    • Future plans
  • Sir Geoffrey Ingram Taylor 1886-1975 Taylor bubbles
    • Oil / Gas industry:
    • Flow rates, monitoring equipment, pumps health/efficiency.
    • Chemical industry:
    • Design / Exploitation of heaters, boilers, etc.
    • Power plants
    • Boiling processes, heaters / coolants transport.
    View slide
  • Understanding Taylor bubbles
    • Generation / Creation
    • Flow parameters
    • Propagation
    • Breaking
    • Coalescence
    • Theoretical models
    • Numerical models
    • Experimental research
    View slide
  • Experimental facilities
    • Nd: YAG laser producing short, sec pulse
    • Ability to capture relatively fast motion
    • Sharp air-water interface
  • Short bubble in 44mm diameter pipe Rising in stagnant water
  • Waves characteristics
    • Waves on a vertical water surface
    • Capillary waves, few millimetres in length
    • Absent on longer bubbles and at higher water Re numbers
    • Wave length decreases on longer bubbles and at higher water Re numbers
    • Shorter at the rear part, longer near the nose
  • Previous Studies
    • Nigmatulin and Bonetto (1997): study observing the nature of capillary waves on standing short Taylor bubbles. Suggested the presence of standing capillary waves on the bubble interface. The waves amplitude seemed to increase on shorter waves .
    • Kockx et al . (2005): experiments conducted on elongated air Taylor bubble standing inside a relatively wide pipe against opposite flowing water. Suggested the presence of downward traveling capillary waves of equal length.
    Waves on the Taylor bubble interface
  • Taylor bubble Translational velocity Liquid holdup in the film Drift velocity Momentum equation on the liquid film, B.C. Cross-sectional average velocity in the liquid film Barnea (1990)
  • Bottom oscillations as wave maker Polonsky (1998)
  • Pure capillary waves Dispersion relation of capillary waves traveling on water. λ – Wave length T – Water-air surface tension f – Wave frequency Wave – current interaction should be taken in to consideration Waves are traveling on vertical surface:
  • Doppler shift
    • X : frame of reference moving with the bubble
    • X ’ : frame of reference moving with liquid film
    Wave traveling in frame of reference X : The same wave traveling in frame of reference X ’ :
  • Dispersion relation
    • In X’ coordinate system:
    , Barnea (1990) Results in calculation of : For pure capillary wave on current in water
  • Frequency sensitivity
  • Experiments
    • Large (140~200) series of bubbles
    • Image processing to detect wave lengths
    • Ensemble average
  • Image processing
    • Enhancement
    • Edge detection
    • Wave lengths and position detection
  • Error Factors
    • Unequal illumination (pipe diameter, distance from the laser)
    • Optical distortions
    • Image resolution
    • Algorithm accuracy
    Ø 44 mm Ø 26 mm
  • Ensemble average Averaging bin
  • Ensemble average
    • Random phase causes spectra widening
  • The results, stagnant water
  • Results for non-zero Reynolds numbers
  • Waves Dissipation The group velocity C relates the spatial and the temporal wave amplitude decay rate. Amplitude variation of the pure-capillary wave subjected to the viscous dissipation
  • Waves Dissipation No waves shorter than 0.5 mm were present, causing the shift in the average values The ensemble is the bubbles rising in 26 mm diameter pipe inside stagnant water . The red curve is the Gaussian distribution with mean at 0.9 mm .
  • Waves Propagation
  • Conclusions
    • Pure capillary waves
    • Development of a theoretical computational model and comparison with experimental results
    • Effect of wave-current interaction
    • Determination of wave inception condition
  • New facilities 5 m
  • Acknowledgments
    • My supervisors:
    • Prof. Lev Shemer & Prof. Dvora Barnea
    Faculty technical and administrative stuff
  • Waves Breaking Capillary wave steepness In our case the steepness did not exceed S =0.5 The critical steepness for capillary waves on clean water is S =0.730 , Crapper (1957)
  • Short bubble in 26mm diameter pipe rising in stagnant water
  • Liquid film velocity D.E. B.C. Cross-sectional average velocity in the liquid film
  • Points for discussion
    • Critical Re number and/or bubble length sustaining presence of pure-capillary waves
    • To develop more accurate approach to account for film velocity profile and interface shape
    • Exact calculations and/or measurements of bottom oscillation frequency
  • Numerical Calculations
    • The method: Fluent software CFD model:
    • Axisymmetric at average
    • Taylor bubble profile calculated by Barnea (1990) model
    • Stationary bubble and moving walls of the pipe
    • Separate model for each hydrodynamic conditions
    The goal: Exact liquid film velocity distribution
  • Transition criterion, Wallis (1969) : Ø 44 mm, stagnant water Ø 14 mm, stagnant water
  • CFD Results Comparison Stagnant water
  • Laser
  • Predicted waves lengths on bubbles rising in stagnant water
  • Kelvin-Helmholtz instability Convection of the wave in the x direction
  • Previous Researches Wave-current / Wave-wind interaction
    • Peregrine (1976): Theoretical basis
    • Plate and Trawle (1970) and Long and Huang (1976): experiments of wind generated large scale waves in presence of water currents, no quantitative kinematic results .
    • Thomas (1981): numerical and experimental studies of wave-current interaction, depth averaged mean current velocity used as interacting velocity.
    • Lai et al. (1989): experimental work of wave-current interaction on large scale waves.
    • Y ao and Wu (2004): experiments on large scale wave-group dynamics and breakings on following and opposite currents.
  • Goals
    • Waves generation mechanism
    • Hydrodynamic conditions allowing waves existence
    • Calculation model predicting waves characteristics
  • Bottom oscillations Open sheet circular basin: Potential: -- Sloshing oscillations frequency -- Rotating frequency Sir Horace Lamb, 1879
  • Rotating bottom oscillations
  • Kelvin-Helmholtz instability KH instability range upper bound K=2.13 [rad/m], λ=2.95 [m] F(k) Long waves mode K=0, λ  ∞ Most unstable mode No KH instability KH instability range
  • Sloshing frequency calculations From the disperse relation: B.C. :