Bubbles in Turbulence Physics of Fluids Group University of Twente. C. Sun, V.N. Prakash, Y. Tagawa, J. Martinez, D. Lohse Physics of Fluids Group, University of Twente Enrico Calzavarini Laboratoire de Mecanique de Lille, University of Lille 1 Federico Toschi Department of Physics, and Department of Mathematics and Computer Science, Eindhoven University of Technology particles in turbulence
Bubbly flow in industries http://www.raviindustries.biz/index.htm
Rising bubbles: bubbly pseudo-turbulence The liquid is quiescent before injecting bubbles Bubble motion causes velocity fluctuations Bubbles are the only source of energy
Bubbly pseudo-turbulence Statistics of bubble velocity Preferential range and orientation for bubble clustering Energy spectrum of the interstitial fluid fluctuations?
Previous studies on bubble velocity Harteveld, TUdelft PhD thesis (2005) Zenit, Koch & Sangani, JFM 429, 307 (2001)
Bubble clustering Zenit, Koch & Sangani, JFM 429, 307 (2001) Images are converted into binary images
3D-PTV PTV code from ETH
3D-PTV: very low concentration Martinez, Chahata, van Gils, Sun & Lohse, J. Fluid Mech. 650, 287 (2010)
Velocity statistics Martinez, Chahata, van Gils, Sun & Lohse, J. Fluid Mech. 650, 287 (2010)
DNS: Front tracking method 16 bubbles Solid symbols represent simulations (a = 5%) Open symbols experiments (a = 0.74%) Roghair, Martinez, van sint Annaland, Kuipers, Sun & Lohse, Int. J. Multiphase Flow 37, 1093 (2011)
Bubbles in fully developed turbulence How size and gravity affect bubble acceleration
Tracer particles in turbulence A. La Porta et al., Nature, 2001 La Porta, Voth, Crawford, Alexander, Bodenschatz, Nature, 409, 1017 (2001)
Finite-size particles in turbulence D D >> 1 Finite-size particles cannot follow small-scale fluctuations, and the local flow around the particle is different
Finite-size particles : Real world examples Cloud formation Iceland Volcanic Eruption (Eyjafjallajökull) 2010 Plankton dynamics Pollutant dispersion
Density ratio Γ = ρ p /ρ f 10 2 Finite-size particles in turbulence 10 4 Heavy 10 2 10 0 Neutrally buoyant 10 0 Light 10 4 10 0 10 1 D/η Size ratio
Finite-size particles in turbulence 10 4 Heavy 10 2 Γ = ρ p /ρ f 10 0 10 0 10 2 Neutrally buoyant Light 10 4 10 0 10 1 D/η Voth et al. 2002 <a 2 > as D/η Voth, La Porta, Crawford, Alexander, Bodenschatz, JFM 469, 121 (2002)
Finite-size particles in turbulence 10 4 Heavy 10 2 Γ = ρ p /ρ f 10 0 10 0 10 2 Neutrally buoyant Light 10 4 10 0 10 1 D/η Voth et al. 2002 Brown et al. 2008 <a 2 > as D/η Brown, Warhaft, & Voth, PRL 103, 194501 (2009)
Finite-size particles in turbulence <a 2 > as D/η PDF: no clear difference compared to tracers Brown, Warhaft, & Voth, PRL 103, 194501 (2009)
Finite-size particles in turbulence 10 4 Heavy 10 2 Γ = ρ p /ρ f 10 0 10 0 10 2 Neutrally buoyant Light 10 4 10 0 10 1 D/η Voth et al. 2002 Brown et al. 2008 Volk et al. 2011 <a 2 > as D/η Volk, Calzavarini, Leveque, Pinton, JFM 668, 223 (2011)
Finite-size particles in turbulence PDF: Finite-size effects are visible F as D/η Volk, Calzavarini, Leveque, Pinton, JFM 668, 223 (2011)
Finite-size particles in turbulence 10 4 Heavy 10 2 Γ = ρ p /ρ f 10 0 10 0 10 2 Neutrally buoyant Light 10 4 10 0 10 1 D/η Voth et al. 2002 Qureshi et al. 2008 Brown et al. 2008 Volk et al. 2011 <a 2 > as D/η Qureshi, Bourgoin, Baudet, Cartellier & Gagne PRL 99, 184502 (2007) Qureshi, Arrieta, Baudet, Cartellier, Gagne & Bourgoin, EPJB 66, 531 (2008)
Finite-size particles in turbulence PDF does not show a clear dependence on D/η from 7 to 25 <a 2 > as D/η Qureshi, Bourgoin, Baudet, Cartellier & Gagne PRL 99, 184502 (2007) Qureshi, Arrieta, Baudet, Cartellier, Gagne & Bourgoin, EPJB 66, 531 (2008)
Finite-size particles in turbulence Γ = ρ p /ρ f 10 4 Heavy 10 2 10 0 Neutrally buoyant 10 0 Light 10 2 10 4 10 0 10 1 D/η PDF 10 0 10 1 10 2 10 3 10 4 10 5 Re λ = 140 Re λ = 160 Re λ = 175 Re λ = 200 Re λ = 240 Mordant et al. 10 6 0 5 10 15 20 a/a rms Voth et al. 2002 Qureshi et al. 2008 Brown et al. 2008 Volk et al. 2011 Martinez et al. 2012 The microbubbles (D/η < 2) almost behave like tracers See talk by Tagawa on May 16 black line: Mordant, Carwford & Bodenschatz, Physica D, 193, 245 (2004) Martinez, Prakash, Tagawa, Sun & Lohse, Phys. Fluids (2012 in press)
Finite-size particles in turbulence 10 4 Heavy 10 2 Γ = ρ p /ρ f 10 0 10 0 10 2 10 4 Neutrally buoyant Light 10 0 10 1 Voth et al. 2002 Qureshi et al. 2008 Brown et al. 2008 Volk et al. 2011 Martinez et al. 2012 Present work D/η Our focus: Finite-sized bubbles Effects: Gravity + Finite-size Experiments + DNS with Faxén corrections
Experiments Active grid Flow direc+on Twente Water Tunnel Capillary Islands
Challenge 1: strong mean flow Systems with strong mean flow Moving camera with the flow Tracking duration is too short
Challenge 1I: strong deformation Bubble heavily deforms The deformation is stronger for a turbulent case Even for a single rising bubble Veldhuis, Biesheuvel & Lohse, Int. J. Multiphase Flow 35, 312 (2009). Ravelet, Colin, Risso, Phys. Fluids 23, 103301 (2011)
Challenge 1I: strong deformation 2ppm Triton X-100 surfactant Takagi & Matsumoto, Annu. Rev. Fluid Mech. 43, 615 (2011)
Challenge 1I: strong deformation Triton-X ~ 1 ppm deformation is reduced Bubble diameter: ~ 3mm effect on liquid is negligible, but changes the boundary condition on the bubble
Challenge III: detecting overlapping bubbles Circular Hough Transformation Detect circles with various radii in grayscale image via Hough Transform by Tao Peng, University of Maryland
Challenge III: detecting overlapping bubbles more than 90% of bubbles are detected in this image
Experiments vertical y x horizontal Moving camera follows bubbles Bubble detection using circular hough transform 2D PTV Polynomial fitted Trajectories
Bubble size versus Reynolds number (c) 2 PDF 1 D=2.50±0.21mm D=2.55±0.25mm D=2.70±0.28mm D=2.90±0.27mm D=3.15±0.30mm Re λ =230 Re λ =215 Re λ =195 Re λ =170 Re λ =145 0 0 1 2 3 4 5 D (mm)
Flow parameters V mean (ms 1 ) Re (µm) D/ St N data 0.20 145 431 7.3 1.34 20.3 10 6 0.30 170 325 8.9 2.36 21.8 10 6 0.40 195 265 10.2 3.54 18.34 10 6 0.50 215 227 11.2 4.84 9.03 10 6 0.60 230 200 12.5 6.25 4.68 10 6
Simulations: Faxén corrections dv dt = apple Du Dt V + 3 r 2 p ([u] s v) surface average [u] S =(4 r 2 p) 1 Z S u(x, t)d 2 x volume average apple Du Dt V =(4/3 r 3 p) 1 Z V Du Dt (x,t)d3 x Accounts for the nonuniformity of the flow at the particle scale Calzavarini, Volk, Bourgoin, Leveque, Pinton & Toschi, J. Fluid Mech. 630, 179 (2009)
Simulations: More refined particle model non-stokesian drag force history force It has been proved for neutrally buoyant particles simulations: Faxén correction to the added mass has a dominant role in the particle acceleration statistics even for particle size at the integral scale Calzavarinia, Volk, Lévêque, Pinton & Toschi Physica, D 241, 237 (2012)
Simulations: Faxén corrections dv dt = apple Du Dt V + 3 r 2 p ([u] s v) surface average [u] S =(4 r 2 p) 1 Z S u(x, t)d 2 x volume average apple Du Dt V =(4/3 r 3 p) 1 Z V Du Dt (x,t)d3 x Accounts for the nonuniformity of the flow at the particle scale Calzavarini, Volk, Bourgoin, Leveque, Pinton & Toschi, J. Fluid Mech. 630, 179 (2009)
Results: Velocity PDF
Velocity PDF: horizontal component y x 10 0 10 1 10 2 Re = 145; = 7.3 Re = 170; = 8.9 Re = 195; = 10.2 Re = 215; = 11.2 Re = 230; = 12.5 Gaussian fit 10 0 10 1 10 2 Re = 145; = 7.3 Re = 170; = 8.9 Re = 195; = 10.2 Re = 215; = 11.2 Re = 230; = 12.5 Gaussian fit PDF 10 3 PDF 10 3 10 4 10 4 10 5 10 5 10 6 8 6 4 2 0 2 4 6 8 v / v x x,rms PDFs are sub-gaussian with flatness values: 2.27-2.78 10 6 8 6 4 2 0 2 4 6 8 10 v y / v y,rms PDFs deviate from Gaussian profile with flatness values: 2.9-3.77
Results: acceleration PDF: gravity effect
Acceleration PDF: gravity effect 10 0 10 0 10 1 a x, Re λ =145 a y, Re λ =145 10 1 a x, Re λ =230 a y, Re λ =230 10 2 10 2 PDF 10 3 PDF 10 3 10 4 10 4 10 5 10 5 10 6 10 0 10 10 6 10 0 10 a/a rms a/a rms Clear difference in ax and ay Effect of gravity seen at low Reλ Gravity effect becomes weaker at high Reλ
Acceleration variances 3.0 2.0 <a x 2 > micro-bubbles <a y 2 > micro-bubbles <a z 2 > micro-bubbles <a 2 >/g 2 1.0 0.0 0 4 8 12 16 D/η variances: all components collapse for microbubbles (D/η <2)
Acceleration variances 3.0 2.0 Present <a 2 x > Present <a 2 y > <a 2 x > micro-bubbles <a 2 y > micro-bubbles <a 2 z > micro-bubbles a 2 y <a 2 >/g 2 1.0 a 2 x 0.0 0 4 8 12 16 D/η variances of finite-sized bubbles: different for horizontal and vertical components
Acceleration variances statistical effect of gravity is to add an offset on the vertical direction a 2 y = (a 0 y ± g) 2 a 0 y the vertical acceleration component in absence of gravity a 0 y =0 isotropy a 02 y = a 2 y g 2
Acceleration variances 3.0 2.0 Present <a 2 x > Present <a 2 y > <a 2 x > micro-bubbles <a 2 y > micro-bubbles <a 2 z > micro-bubbles a 2 y <a 2 >/g 2 1.0 a 2 x 0.0 0 4 8 12 16 D/η variances of finite-sized bubbles: different for horizontal and vertical components
Acceleration variances 3.0 Present <a x 2 > Present <a y 2 > - g 2 <a x 2 > micro-bubbles <a 2 >/g 2 2.0 1.0 <a y 2 > micro-bubbles <a z 2 > micro-bubbles a 02 y = a 2 y a 2 x g 2 0.0 0 4 8 12 16 D/η variances of finite-sized bubbles: statistical effect of gravity is just additive on the vertical direction (offset of a g 2 )
Results: normalized acceleration variance vs. size ratio
Normalized acceleration variances: DNS-Faxén 10 1 β 2 = 9 <a 2 >/<a f 2 > 10 0 10 1 10 2 10 0 10 1 D/η ϕ 9: theoretical upper bound from the added mass term for bubbles dv dt = apple Du Dt V + 3 r 2 p ([u] s v)
Normalized acceleration variances: DNS-Faxén 10 1 β 2 = 9 <a 2 >/<a f 2 > 10 0 10 1 DNS Faxen Γ=1 Re λ =75 DNS Faxen Γ=1 Re λ =180 10 2 10 0 10 1 D/η ϕ Neutrally buoyant particles: <a 2 >/<af 2 > as D/η
Normalized acceleration variances: DNS-Faxén 10 1 β 2 = 9 <a 2 >/<a f 2 > 10 0 10 1 DNS Point Γ=0 Re λ =180 DNS Faxen Γ=1 Re λ =75 DNS Faxen Γ=1 Re λ =180 10 2 10 0 10 1 D/η ϕ Point bubbles: <a 2 >/<af 2 > exceeds 9
Normalized acceleration variances: DNS-Faxén 10 1 β 2 = 9 <a 2 >/<a f 2 > 10 0 10 1 DNS Point Γ=0 Re λ =180 DNS Faxen Γ=0 Re λ =75 DNS Faxen Γ=0 Re λ =180 DNS Faxen Γ=1 Re λ =75 DNS Faxen Γ=1 Re λ =180 10 2 10 0 10 1 D/η ϕ Faxén bubbles: <a 2 >/<af 2 > less than 9 due to finite-size effect
Normalized acceleration variances: DNS vs. EXP 10 1 β 2 = 9 <a 2 >/<a f 2 > 10 0 10 1 10 2 DNS Point Γ=0 Re λ =180 DNS Faxen Γ=0 Re λ =75 DNS Faxen Γ=0 Re λ =180 Volk et al. 2008 DNS Faxen Γ=1 Re λ =75 DNS Faxen Γ=1 Re λ =180 10 0 10 1 D/η ϕ EXP <a x 2 > EXP <a y 2 >-g 2 Acceleration variances are about 5 ± 2 times of fluid tracers Less than 9 due to finite-size effects
Results: acceleration intermittency vs. size ratio (horizontal component)
Acceleration PDF 10 0 10 1 10 2 DNS Tracers ϕ = 2 Micro bubble ϕ=0.8 ϕ=1.7 EXP PDF 10 3 10 4 10 5 10 6 0 5 10 15 a/a rms microbubbles behave almost like tracers
Acceleration PDF 10 0 10 1 10 2 DNS Tracers ϕ = 2 Micro bubble ϕ=0.8 ϕ=1.7 EXP ϕ=7.3 PDF 10 3 10 4 10 5 10 6 0 5 10 15 a/a rms Finite-size effect: substantial decrease in intermittency
Acceleration PDF 10 0 10 1 10 2 DNS Tracers ϕ = 2 Micro bubble ϕ=0.8 ϕ=1.7 EXP ϕ=7.3 ϕ=8.9 PDF 10 3 10 4 10 5 10 6 0 5 10 15 a/a rms Finite-size effect: substantial decrease in intermittency
Acceleration PDF 10 0 10 1 10 2 DNS Tracers ϕ = 2 Micro bubble ϕ=0.8 ϕ=1.7 EXP ϕ=7.3 ϕ=8.9 ϕ=10.2 PDF 10 3 10 4 10 5 10 6 0 5 10 15 a/a rms Finite-size effect: substantial decrease in intermittency
Acceleration PDF 10 0 10 1 10 2 DNS Tracers ϕ = 2 Micro bubble ϕ=0.8 ϕ=1.7 EXP ϕ=7.3 ϕ=8.9 ϕ=10.2 PDF 10 3 10 4 ϕ=11.2 ϕ=12.5 10 5 10 6 0 5 10 15 a/a rms Finite-size effect: substantial decrease in intermittency
Acceleration PDF PDF 10 0 10 1 10 2 10 3 10 4 EXP ϕ=7.3 ϕ=8.9 ϕ=10.2 ϕ=11.2 ϕ=12.5 10 5 10 6 0 5 10 15 a/a rms EXP: intermittency as D/η
Acceleration PDF PDF 10 0 10 1 10 2 10 3 10 4 10 5 EXP ϕ=7.3 ϕ=8.9 ϕ=10.2 ϕ=11.2 ϕ=12.5 DNS ϕ = 8 ϕ = 16 ϕ = 32 ϕ = 48 10 6 0 5 10 15 a/a rms EXP: intermittency as D/η DNS: same trend; but a factor of 2-3 difference in D/η
Finite-sized bubbles: Summary Gravity increases <ay 2 > by an offset of g 2 reduces the intermittency of the ay PDF at low Re <ax 2 > and <ay 2 > ~ 5 ± 2 times <atracers 2 >: effect of finite size Acceleration PDF: intermittency as D/η Experiments are matched by DNS with Faxén corrections Thanks for your attention! particles in turbulence more details: Prakash et al. arxiv:1204.4108.