# Energy spectra in turbulent bubbly flows

Vivek N. Prakash, J. Martinez Mercado, Leen van Wijngaarden, E. Mancilla, Y. Tagawa, Detlef Lohse, Chao Sun

21 Citations (Scopus)

### Abstract

We conduct experiments in a turbulent bubbly flow to study the nature of the transition between the classical $-5/3$−5/3 energy spectrum scaling for a single-phase turbulent flow and the $-3$−3 scaling for a swarm of bubbles rising in a quiescent liquid and of bubble-dominated turbulence. The bubblance parameter (Lance & Bataille J. Fluid Mech., vol. 222, 1991, pp. 95–118; Rensen et al., J. Fluid Mech., vol. 538, 2005, pp. 153–187), which measures the ratio of the bubble-induced kinetic energy to the kinetic energy induced by the turbulent liquid fluctuations before bubble injection, is often used to characterise bubbly flow. We vary the bubblance parameter from $b=\infty$b=∞ (pseudoturbulence) to $b=0$b=0 (single-phase flow) over 2–3 orders of magnitude (0.01–5) to study its effect on the turbulent energy spectrum and fluctuations in liquid velocity. The probability density functions (PDFs) of the fluctuations in liquid velocity show deviations from the Gaussian profile for $b>0$b>0, i.e. when bubbles are present in the system. The PDFs are asymmetric with higher probability in the positive tails. The energy spectra are found to follow the $-3$−3 scaling at length scales smaller than the size of the bubbles for bubbly flows. This $-3$−3 spectrum scaling holds not only in the well-established case of pseudoturbulence, but surprisingly in all cases where bubbles are present in the system ($b>0$b>0). Therefore, it is a generic feature of turbulent bubbly flows, and the bubblance parameter is probably not a suitable parameter to characterise the energy spectrum in bubbly turbulent flows. The physical reason is that the energy input by the bubbles passes over only to higher wavenumbers, and the energy production due to the bubbles can be directly balanced by the viscous dissipation in the bubble wakes as suggested by Lance & Bataille (1991). In addition, we provide an alternative explanation by balancing the energy production of the bubbles with viscous dissipation in the Fourier space.
Original language English 174-190 17 Journal of fluid mechanics 791 https://doi.org/10.1017/jfm.2016.49 Published - 15 Feb 2016

### Fingerprint

turbulent flow
Turbulent flow
energy spectra
bubbles
Bubbles (in fluids)
Liquids
Kinetic energy
Probability density function
Fluids
scaling
Turbulence
liquids
probability density functions
dissipation
kinetic energy
single-phase flow
fluids
Experiments
wakes
energy

### Cite this

Prakash, V. N., Martinez Mercado, J., van Wijngaarden, L., Mancilla, E., Tagawa, Y., Lohse, D., & Sun, C. (2016). Energy spectra in turbulent bubbly flows. Journal of fluid mechanics, 791, 174-190. https://doi.org/10.1017/jfm.2016.49
Prakash, Vivek N. ; Martinez Mercado, J. ; van Wijngaarden, Leen ; Mancilla, E. ; Tagawa, Y. ; Lohse, Detlef ; Sun, Chao. / Energy spectra in turbulent bubbly flows. In: Journal of fluid mechanics. 2016 ; Vol. 791. pp. 174-190.
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abstract = "We conduct experiments in a turbulent bubbly flow to study the nature of the transition between the classical $-5/3$−5/3 energy spectrum scaling for a single-phase turbulent flow and the $-3$−3 scaling for a swarm of bubbles rising in a quiescent liquid and of bubble-dominated turbulence. The bubblance parameter (Lance & Bataille J. Fluid Mech., vol. 222, 1991, pp. 95–118; Rensen et al., J. Fluid Mech., vol. 538, 2005, pp. 153–187), which measures the ratio of the bubble-induced kinetic energy to the kinetic energy induced by the turbulent liquid fluctuations before bubble injection, is often used to characterise bubbly flow. We vary the bubblance parameter from $b=\infty$b=∞ (pseudoturbulence) to $b=0$b=0 (single-phase flow) over 2–3 orders of magnitude (0.01–5) to study its effect on the turbulent energy spectrum and fluctuations in liquid velocity. The probability density functions (PDFs) of the fluctuations in liquid velocity show deviations from the Gaussian profile for $b>0$b>0, i.e. when bubbles are present in the system. The PDFs are asymmetric with higher probability in the positive tails. The energy spectra are found to follow the $-3$−3 scaling at length scales smaller than the size of the bubbles for bubbly flows. This $-3$−3 spectrum scaling holds not only in the well-established case of pseudoturbulence, but surprisingly in all cases where bubbles are present in the system ($b>0$b>0). Therefore, it is a generic feature of turbulent bubbly flows, and the bubblance parameter is probably not a suitable parameter to characterise the energy spectrum in bubbly turbulent flows. The physical reason is that the energy input by the bubbles passes over only to higher wavenumbers, and the energy production due to the bubbles can be directly balanced by the viscous dissipation in the bubble wakes as suggested by Lance & Bataille (1991). In addition, we provide an alternative explanation by balancing the energy production of the bubbles with viscous dissipation in the Fourier space.",
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Prakash, VN, Martinez Mercado, J, van Wijngaarden, L, Mancilla, E, Tagawa, Y, Lohse, D & Sun, C 2016, 'Energy spectra in turbulent bubbly flows' Journal of fluid mechanics, vol. 791, pp. 174-190. https://doi.org/10.1017/jfm.2016.49

Energy spectra in turbulent bubbly flows. / Prakash, Vivek N.; Martinez Mercado, J.; van Wijngaarden, Leen; Mancilla, E.; Tagawa, Y.; Lohse, Detlef; Sun, Chao.

In: Journal of fluid mechanics, Vol. 791, 15.02.2016, p. 174-190.

TY - JOUR

T1 - Energy spectra in turbulent bubbly flows

AU - Prakash, Vivek N.

AU - van Wijngaarden, Leen

AU - Mancilla, E.

AU - Tagawa, Y.

AU - Lohse, Detlef

AU - Sun, Chao

PY - 2016/2/15

Y1 - 2016/2/15

N2 - We conduct experiments in a turbulent bubbly flow to study the nature of the transition between the classical $-5/3$−5/3 energy spectrum scaling for a single-phase turbulent flow and the $-3$−3 scaling for a swarm of bubbles rising in a quiescent liquid and of bubble-dominated turbulence. The bubblance parameter (Lance & Bataille J. Fluid Mech., vol. 222, 1991, pp. 95–118; Rensen et al., J. Fluid Mech., vol. 538, 2005, pp. 153–187), which measures the ratio of the bubble-induced kinetic energy to the kinetic energy induced by the turbulent liquid fluctuations before bubble injection, is often used to characterise bubbly flow. We vary the bubblance parameter from $b=\infty$b=∞ (pseudoturbulence) to $b=0$b=0 (single-phase flow) over 2–3 orders of magnitude (0.01–5) to study its effect on the turbulent energy spectrum and fluctuations in liquid velocity. The probability density functions (PDFs) of the fluctuations in liquid velocity show deviations from the Gaussian profile for $b>0$b>0, i.e. when bubbles are present in the system. The PDFs are asymmetric with higher probability in the positive tails. The energy spectra are found to follow the $-3$−3 scaling at length scales smaller than the size of the bubbles for bubbly flows. This $-3$−3 spectrum scaling holds not only in the well-established case of pseudoturbulence, but surprisingly in all cases where bubbles are present in the system ($b>0$b>0). Therefore, it is a generic feature of turbulent bubbly flows, and the bubblance parameter is probably not a suitable parameter to characterise the energy spectrum in bubbly turbulent flows. The physical reason is that the energy input by the bubbles passes over only to higher wavenumbers, and the energy production due to the bubbles can be directly balanced by the viscous dissipation in the bubble wakes as suggested by Lance & Bataille (1991). In addition, we provide an alternative explanation by balancing the energy production of the bubbles with viscous dissipation in the Fourier space.

AB - We conduct experiments in a turbulent bubbly flow to study the nature of the transition between the classical $-5/3$−5/3 energy spectrum scaling for a single-phase turbulent flow and the $-3$−3 scaling for a swarm of bubbles rising in a quiescent liquid and of bubble-dominated turbulence. The bubblance parameter (Lance & Bataille J. Fluid Mech., vol. 222, 1991, pp. 95–118; Rensen et al., J. Fluid Mech., vol. 538, 2005, pp. 153–187), which measures the ratio of the bubble-induced kinetic energy to the kinetic energy induced by the turbulent liquid fluctuations before bubble injection, is often used to characterise bubbly flow. We vary the bubblance parameter from $b=\infty$b=∞ (pseudoturbulence) to $b=0$b=0 (single-phase flow) over 2–3 orders of magnitude (0.01–5) to study its effect on the turbulent energy spectrum and fluctuations in liquid velocity. The probability density functions (PDFs) of the fluctuations in liquid velocity show deviations from the Gaussian profile for $b>0$b>0, i.e. when bubbles are present in the system. The PDFs are asymmetric with higher probability in the positive tails. The energy spectra are found to follow the $-3$−3 scaling at length scales smaller than the size of the bubbles for bubbly flows. This $-3$−3 spectrum scaling holds not only in the well-established case of pseudoturbulence, but surprisingly in all cases where bubbles are present in the system ($b>0$b>0). Therefore, it is a generic feature of turbulent bubbly flows, and the bubblance parameter is probably not a suitable parameter to characterise the energy spectrum in bubbly turbulent flows. The physical reason is that the energy input by the bubbles passes over only to higher wavenumbers, and the energy production due to the bubbles can be directly balanced by the viscous dissipation in the bubble wakes as suggested by Lance & Bataille (1991). In addition, we provide an alternative explanation by balancing the energy production of the bubbles with viscous dissipation in the Fourier space.

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DO - 10.1017/jfm.2016.49

M3 - Article

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EP - 190

JO - Journal of fluid mechanics

JF - Journal of fluid mechanics

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Prakash VN, Martinez Mercado J, van Wijngaarden L, Mancilla E, Tagawa Y, Lohse D et al. Energy spectra in turbulent bubbly flows. Journal of fluid mechanics. 2016 Feb 15;791:174-190. https://doi.org/10.1017/jfm.2016.49