Turbulent cascade modeling of single and bubbly two-phase turbulent flows

Bolotnov, Igor A.; Lahey, R.T.; Drew, Donald A.; Jansen, Kenneth E.

doi:10.1016/j.ijmultiphaseflow.2008.06.006

Cited by 22 publications

(18 citation statements)

References 20 publications

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“…However, the behaviours reported previously for upward and downward flows are in agreement with the behaviour of the energy spectra shown in figure 14, as well as those reported in the literature (Lance & Bataille 1991;Bolotov et al 2008;Lelouvetel et al 2011). Figure 14 shows the energy spectra at the centreline (0 < r/R < 0.2) and close to the wall (0.8 < r/R < 1).…”

Section: Energy Spectrasupporting

confidence: 90%

“…These observations may explain the decrease in Π in upward flows, since there is less energy to transfer from large to small scales. In agreement with Lance & Bataille (1991) and Bolotov et al (2008), we observed that the slope of the dissipation range is approximately the same in bubbly flows as in single-phase flows, which explains the weak modifications of sgs .…”

Section: Energy Spectrasupporting

confidence: 89%

“…In figure 14, the discontinuous lines represent the −5/3 slope corresponding to the inertial range, in which large eddies transfer turbulent energy to small eddies (Pope 2000), and the dotted line represents a slope of −7/6. In an upward flow, the present results ( figure 14), the experimental results of Lance & Bataille (1991) and the numerical results of Bolotov et al (2008) show weak modifications in the magnitude of the spectrum, whereas, as reported in a previous study (Lelouvetel et al 2011), the spectrum exhibits significant modifications in downward flow. In an upward flow, figure 14(b) reveals a small decrease in the magnitude of the spectrum in the containing range and a modification of the −5/3 slope in the inertial range close to the wall.…”

Section: Energy Spectrasupporting

confidence: 87%

“…In an upward flow, figure 14(b) reveals a small decrease in the magnitude of the spectrum in the containing range and a modification of the −5/3 slope in the inertial range close to the wall. The results reported by Lance & Bataille (1991) and Bolotov et al (2008) also indicate that the slope of the inertial range becomes −7/6 in upward bubbly flows. These observations may explain the decrease in Π in upward flows, since there is less energy to transfer from large to small scales.…”

Section: Energy Spectramentioning

confidence: 76%

“…The results reported by Fujiwara et al (2004b) indicate that the turbulent kinetic energy (TKE) production rate and the TKE dissipation rate are not balanced in the case of a bubbly flow, suggesting that the presence of bubbles causes an interfacial transport of turbulent energy between bubbles and turbulent flow. Finally, Lance & Bataille (1991), Bunner & Tryggvason (2002) and Shawkat et al (2007) and Bolotov et al (2008) investigated the energy spectra in bubbly flows both experimentally and numerically and reported that, in contrast to the well-known −5/3 power law for a single-phase flow, the power law of the energy spectra in an upward bubbly flow becomes −8/3. This observation indicates a modification of the energy cascade, also observed by Mazzitelli et al (2003) in the case of microbubbles, in particular, a modification of the mechanisms of the energy transfer from large-scale eddies to small-scales eddies.…”

Section: Introductionmentioning

confidence: 99%

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Transport mechanisms of the turbulent energy cascade in upward/downward bubbly flows

et al. 2014

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The turbulent energy cascade in an upward or downward bubbly pipe flow with a Reynolds number of 1.5 × 10 4 was experimentally investigated in order to examine the effects of the flow direction on the turbulence modifications by bubbles. The bubble diameter was approximately 1 mm. The combination of a particle tracking velocimetry (PTV) system with Kolmogorov-order spatial and temporal resolutions and a shape projection imaging (SPI) system was used to simultaneously capture the liquid and bubble motions. The physical mechanisms of turbulence modification at each length scale, or in wavenumber space, were investigated by introducing a filtering-based scaling analysis, in which the filtering techniques derived from large eddy simulation (LES) were applied to the PTV measurements. The analysis can be used to examine the turbulent kinetic energy (TKE) exchange between bubbles and flows at each wavenumber. We observed significant differences in the flow statistics and turbulent energy budget of upward and downward flows, which are due to the sign of the relative velocity of bubbles. A negative relative velocity (downward flow) induces greater modifications in the energy budget than a positive relative velocity (upward flow), which suggests that the bubble-transport term of the turbulent energy is greater when the flow has to push down the bubbles. The flow provides more energy to the bubbles when it pushes them in the downward direction. The flow will also receive and dissipate more energy from the bubbles in a downward flow compared with an upward flow due to the greater transverse motion of the bubbles. The analysis introduced in the present study shows that the energy transfer from large to small scales is decreased in an upward flow and is increased in a downward flow. Similarly, the sign of the bubble term indicates that turbulent flow receives energy from bubbles in an upward flow, while it transfers energy to bubbles in a downward flow. We also observed that this energy transport is approximately 10 times larger in a downward flow than in an upward flow.

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Section: Energy Spectrasupporting

confidence: 90%

Section: Energy Spectrasupporting

confidence: 89%

Section: Energy Spectrasupporting

confidence: 87%

Section: Energy Spectramentioning

confidence: 76%

Section: Introductionmentioning

confidence: 99%

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Transport mechanisms of the turbulent energy cascade in upward/downward bubbly flows

et al. 2014

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Evaluation of linear autoregressive models for estimation of energy spectra in gappy turbulent velocity data

Lai

Socolofsky

2017

Limnology & Ocean Methods

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This paper deals with the problem of data interpolation in velocity time series measured by acoustic Doppler velocimeters and acoustic Doppler current profilers; the gap-filled data are often used to determine turbulent kinetic energy (TKE) dissipation using Kolmogorov's inertial subrange scaling. For the latter to estimate dissipation accurately, it is important that the interpolation scheme preserves the attributes, both spectral slope and component magnitudes, of the true energy spectrum. We show that this goal can be achieved using the simple zeroth-order sample and hold interpolation in situations where isolated data gaps, having durations shorter than the integral time scale of flow, occur. Its success is explained using the framework of stochastic autoregressive (AR) processes, which we also compare to the Langevin equation for the Lagrangian velocity of a turbulent flow field. We also demonstrate that linear interpolation is not appropriate because it can be interpreted as a nonstationary second order AR process, leading to erroneous conclusions for spectral slope and magnitude. When data dropouts occur in clusters, i.e., of durations longer than the integral time scale, we propose to use the first order AR process, of which sample and hold is its limiting case, for interpolation. The effectiveness of our proposal is tested and demonstrated with synthetic time series having a range of spectral slopes, from 27/6 to 28/3, and with experimental data measured in a turbulent channel flow. A comparison is also made with the more sophisticated proper orthogonal decomposition-based interpolation. The paper ends with a step-by-step procedure on using the proposed method in applications.

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Stability of concentrated suspensions under Couette and Poiseuille flow

Ahnert

Münch

Niethammer³

et al. 2018

J Eng Math

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The stability of two-dimensional Poiseuille flow and plane Couette flow for concentrated suspensions is investigated. Linear stability analysis of the two-phase flow model for both flow geometries shows the existence of a convectively driven instability with increasing growth rates of the unstable modes as the particle volume fraction of the suspension increases. In addition it is shown that there exists a bound for the particle phase viscosity below which the two-phase flow model may become ill-posed as the particle phase approaches its maximum packing fraction. The case of twodimensional Poiseuille flow gives rise to base state solutions that exhibit a jammed and unyielded region, due to shear-induced migration, as the maximum packing fraction is approached. The stability characteristics of the resulting Bingham-type flow is investigated and connections to the stability problem for the related classical Bingham-flow problem are discussed.

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Turbulent cascade modeling of single and bubbly two-phase turbulent flows

Cited by 22 publications

References 20 publications

Transport mechanisms of the turbulent energy cascade in upward/downward bubbly flows

Transport mechanisms of the turbulent energy cascade in upward/downward bubbly flows

Evaluation of linear autoregressive models for estimation of energy spectra in gappy turbulent velocity data

Stability of concentrated suspensions under Couette and Poiseuille flow

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