Near surface turbulence and its relationship to air-water gas transfer rates S. Banerjee 1 D. Turney 2 1 Department of Chemical Engineering, City College of the City University of New York, 140 th St at Convent Ave, New York, NY10031, USA, 2 Energy Science & Technology Department, Brookhaven National Laboratory, 32 Lewis Rd, Building 130,Upton, NY 11973, USA, Kyoto, Japan, May 17-21, 2010 The 6th International Symposium on Gas Transfer at Water Surfaces

Main Topics 1. Near interface turbulence structure 2. Gas Transfer Models 3. Comparisons of Models to Empirical Data 4. Tests of the main Surface Divergence models 5. Mixture of Surface Renewal and Surface Divergence concepts

Interphase Mass and Energy Exchange H20H20 C20C20

Concentration profiles & mass transfer coeff. For sparingly soluble gas, resistance to absorption is on liquid side k = N/(Cint –Cbulk) k-mass transfer coeff (m/s) N-mass flux (kg/m2s) C- concentration (kg/m3 )

Comparison of RELAP5 predicted values for the interfacial heat transfer coefficient in subcooled boiling vs. McMasters University data Scalar transfer: sheared interfaces MacIntyre et al. 1995

Global oceanic CO2 uptake estimates (Donelan and Wanninkhof 2002)

Near Surface Motions Mix Gas into the Bulk After LIF results of Herlina & Jirka 2004 Saturated water in the near the surface is stretched and mixed into the bulk. Upwelling water presses against the interface and becomes saturated by diffusion.

Near-Interface Turbulence Intensities (DeAngelis et al 1997, DeAngelis 1998, DeAngelis et al 2000) GasLiquid Only Fluctuations relative to the wave velocity are considered

Early Models for Interphase Transport Lewis and Whitman’s (1924) film theory Higbie’s (1935) penetration theory Danckwerts (1951) assumed random distribution of surface ages for renewed elements (surface renewal),

The Large Eddy and Small Eddy Model Mass transfer coefficient – surface renewal model Fortescue and Pearson (1967) – large eddy model Banerjee et al. (1968)- small eddy model Gas Liquid

Surface Divergence Models Origins in Chan & Scriven (1970) solution to advection-diffusion eqn. Further analysis by McCready, Hanratty and coworkers (1970s and 1980s) For high frequency surface For low frequency surface divergence divergence sinusoidal oscillations sinusoidal oscillations

Blocking Theory Applied to the Surface Divergence Model (Banerjee 1990)

Interfacial Motion

Interfacial heat transfer Interfacial shear HTC (flat & wavy interface); Pr=1 Interfacial Scalar Exchange

Liquid Side Mass Flux vs. Shear Stress (DeAngelis et al 1997, DeAngelis 1998, DeAngelis et al 2000) Mass Flux Shear Stress

Local Scalar Flux and Surface Divergence (Kasagi Group) Quick response to surface divergence even at high Sc: R cv ~ 0.6

Liquid side mass transfer mechanisim sweeps renew interfacial fluid: high surface divergence events Unsteady diff. In stagnant media: K = sqrt (D/T) If sweeps are the renewing events T+ = time between sweeps ~ Expression for K+ from surface renewal theory

Surface Renewal Prediction (Banerjee 1990, DeAngelis et al 1997, DeAngelis 1998, DeAngelis et al 2000) Experiment (Rashidi and Banerjee Phys. Fluids A (1990)) + DNS (Lombardi, De Angelis and Banerjee Phys. Of Fluids (1996)) suggest: Time between burst Lines between ejections and sweeps: From surface renewal theory: Liquid side: mobile boundary D ~ molecular diffusivity; ~ time between renewals. Liquid side: Gas side:

Prediction versus experiment (DeAngelis et al 1997, DeAngelis 1998, DeAngelis et al 2000) Comparison with the data by Wanninkhof and Bliven (1994). The outlying points are large amplitude waves that were breaking. Comparison of Eq. 1 with wind-wave tank gas transfer data from (Ocampo-Torres et al.) Assuming Sc =660. Comparison of Eq. 2 for moisture flux coefficient with data from Ocampo-Torres et al. (1994)

Bubble column mass transfer (Cockx et al 1995)

3D-IPIV 3-Dimensional Interfacial Particle Image Velocimetry Turney DE, Anderer A, Banerjee S Measurement Science & Technology, 20 (4) 2009 New Velocimetry Technique for Flow within 1mm of Interface

Turney DE, Anderer A, Banerjee S Measurement Science & Technology, 20 (4) D-IPIV

3D-IPIV Raw Images for Open Channel Flow, Reynolds Number 30,000

Zoom-In of Calculations for Channel Flow (Turney 2009)

Test of McCready et al. Surface Divergence Prediction for Open Channel Flows (Turney 2009)

Test of Banerjee Blocking Theory Surface Divergence Prediction for Open Channel Flows (Turney 2009) Raw calculation, no corrections, using turbulence measurements from bulk flow one L underneath interface. Turbulence intensity is calculated using surface 3D-PIV results instead of bulk PIV results.

3D-IPIV Raw Images with Wind Shear U10 ~ 6m/s

3D-IPIV Velocity Measurements with Wind Shear, U10 ~ 6m/s,

3D-IPIV Processed Images for Wind Shear U10 ~ 6m/s, Surface Divergence Calculated From Velocity Measurements

Test of McCready et al. Surface Divergence Prediction for Wind Sheared Flows (Turney 2009) Microscale Breaking Waves are Present

A physical explanation: Return Flows (Turney 2009) Capillary waves appear in association with microscale breaking waves. Capillary waves have large divergence / convergence motions but their lifetime is so short that surface water does not mix with bulk water. Therefore, a robust equation for predicting k must include 1) a parameter accounting for the strength of upwelling / downwelling motions 2) a parameter accounting for the lifetime of the upwelling / downwelling motions Mixing the surface renewal concepts with surface divergence concepts gives a new solution to the advection diffusion equation (next slide). (Turney 2009) c)

The New Model Matches Experimental Data (Turney 2009) Mixture of Surface Divergence and Surface Renewal Models (Turney 2009) Open Channel Flow Wind Sheared Flow

Conclusions Early surface renewal models predict correct liquid-side scalar exchange dependence on diffusivities Renewal rates cannot easily be measured directly Large uncertainties exist in current estimates of liquid- side controlled scalar exchange Surface divergence can be measured directly and hydrodynamic theory can be tested Current surface divergence theories work well when capillary waves are absent. Mixture of surface divergence theory and surface renewal theory allows more robust parameterization.