Measuring microbubble clustering in turbulent flow

Transcription

1 Slide 1 Measuring microbubble clustering in turbulent flow Enrico Calzavarini University of Twente The Netherlands In collaboration with T. H van den Berg, S. Luther, F. Toschi, D. Lohse

2 Slide 2 Motivation Disperse multiphase turbulent flows - Modifications of the turbulent flow field spectra modification drag reduction - Characterization of preferential concentrations mixing or segregation

3 Physics of Fluid Group, University of Twente, The Netherlands. Slide 3 Microbubbles in Twente Water Channel ceramic plates (microbubble production) active grid (turbulence generation) hot-film (test section) Fluid: Uz= 0.22 m/s Reλ = 200 η = 10-4 m L 103 η Measurement section 2m 2m reservoir Flow direction elbow pump Bubbles: Radius = 100 µm ( η) Reb 1 gas fraction: 0 0.3% Experimental set-up details: Rensen, J. M., Luther, S. & Lohse, D. J. Fluid Mech. 538, (2005)

4 Effect of microbubbles on energy spectrum Slide 4 Dissipative spectra D(k)=2n k2 E(k) by hot-wire measurements single-phase 0.1% 0.3% our microbubble experiments Van den Berg, Luther and Lohse Energy spectra in microbubbly turbulence Phys. Fluids 18, (2006). E(k) ~ k -8/3 D(k) ~ k -2/3 Lance & Bataille (1991) Not observed for microbubbles!

5 Effect of microbubbles on energy spectrum Slide 5 Same features obtained in numerics (Eulerian-Lagrangian): Enhancement at small scales Reduction at large scales single-phase 0.1% 0.3% our numerics Mazzitelli, I., Lohse, D. & Toschi, F. (2003 ) The effect of microbubbles on developedturbulence. Phys. Fluids 15, L5. our microbubble experiments

6 Slide 6 Bubble clustering 1) Are microbubbles clustered in the flow? 2) How to characterize it? Statistical analysis of the experimental single-point hot-wire data 3) Is this again consistent with numerical simulations?

7 Slide 7 Bubble detection by hot-wire microbubbles do not break-up but bounce on the probe time derivative A typical signal hot wire size d b Temporal resolution

8 Slide 8 Our data set: Two samples: a) T tot = # bubbles Re λ = 206 void fraction b) T tot = Re λ = 180 Stokes = τ b / τ η 0.01 d b /η 0.5 From time to space domain via Taylor hypothesis:

9 Slide 9 Two statistical tests for bubble clustering

10 Slide 10 First statistical test: Pdf( r) Probability density function of distance intervals between bubbles For homogeneous bubbles: ρ= N b / ( T tot U) exponential distribution mean rate of bubbles per unit length For Δr L ( Pdf tail ) fit: Concentration factor:

11 Slide 11 Pdf( r) Log pdf(δr) exponential fit compensated plot Log pdf(δr) exponential fit (b) fit (a) C = 10% C = 19% - Re + Clustering increases with Re

12 Slide 12 Test against random sample Pdf( r) (b) (a) Exponential distribution, same time-length, same mean rate of experimental samples

13 Slide 13 Second statistical test: Coarse grained analysis of counted bubbles over a given space window Coarse grained central moments Scale dependent Kurtosis and Skewness For homogeneous (Poisson) statistics:

14 Slide 14 K(r) and S(r) K(r) (b) K(r) (a) 500 η - Re η Our spatial resolution: a) b) Deviation from Poisson statistics starts at r min up to 500 η

15 Slide 15 Numerical simulations Eulerian-Lagrangian DNS isotropic homogeneous turbulent flow one-way coupling a) Re λ = 95 b) Re λ = 91 N b =10 5, void fraction 2.5% St=0.1 d b /η 1 From flow visualization St=0.1 We use numerical single-point probes as in experiment

16 Slide 16 Pdf( r) (numerics) (b) (a) C = 29% C = 37% - Re + Clustering increases with Re

17 Slide 17 K(r) and S(r) (numerics) (b) (a) η - Re + η Deviation from Poisson statistics starts at η up to 50 η

18 Slide 18 Conclusions 1) Our single -point hot-wire experimental records of microbubbles in turbulence display clustering 2) Fraction of bubbles trapped ~ 10 % 3) Scale dependent deviation from Poisson distribution from η up to O(100η) 4) Clustering increase with Reynolds. 5) Similar qualitative features in DNS, although stronger concentrations observed. Microbubble clustering in turbulent flow, E. Calzavarini, T. H. van den Berg, S. Luther, F. Toschi and D. Lohse, preprint on Arxiv: physics/