On the turbulence modelling of bubble plumes

Applied Mathematical Modelling, 2017

Traditional Reynolds-averaged Navier-Stokes (RANS) approaches to turbulence modelling, such as the k-ϵ model, has some well-known shortcomings when modelling transient flow phenomena. To mitigate this, a filtered URANS model has been derived where turbulent structures larger than a given filter size (typically grid size) is captured by the flow equations and smaller structures are modelled according to a modified k-ϵ model. This modelling approach is also known as a VLES model (Very Large Eddy Scale model), and provides more details of the transient turbulence than the k-ϵ model at little extra computational cost.

World Water & Environmental Resources Congress 2003, 2003

This paper discusses different issues that appear when characterizing turbulence in two-phase, air-water flows, in relatively deep containers. The flows correspond to bubble plumes with relatively large bubble diameters. Results of velocity time series obtained with the help of Acoustic Doppler Velocimeters (ADVs) are presented and analyzed. The post-processing of those signals is discussed in detail, presenting a methodology to separate air velocity from water velocity using ADV. Turbulence statistics, obtained from the time series, are also presented. Specifically, spatial distributions for the turbulent kinetic energy are analyzed. An interpretation of the behavior of the plume in the tank is also provided.

This paper presents an analysis of measurements of mean flow and turbulence statistics in bubble plumes conducted in a large experimental tank (digester) at a wastewater treatment plant. Profiles of dissipation rates of turbulent kinetic energy are presented for the first time, together with distributions for the turbulent kinetic energy and Kolmogorov length scales. Dissipation rates obtained from time velocity series and SCAMP measurements are also compared.

This paper presents an integral model to evaluate the impact of gas transfer on the hydrodynamics of bubble plumes. The model is based on the Gaussian type self-similarity and functional relationships for the entrainment coeffi cient and factor of momentum amplifi cation due to turbulence. The impact of mass transfer on bubble plume hydrodynamics is investigated considering different bubble sizes, gas fl ow rates and water depths. The results revealed a relevant impact when fi ne bubbles are considered, even for moderate water depths. Additionally, model simulations indicate that for weak bubble plumes (i.e., with relatively low fl ow rates and large depths and slip velocities), both dissolution and turbulence can affect plume hydrodynamics, which demonstrates the importance of taking the momentum amplifi cation factor relationship into account. For deeper water conditions, simulations of bubble dissolution/decompression using the present model and classical models available in the literature resulted in a very good agreement for both aeration and oxygenation processes. Sensitivity analysis showed that the water depth, followed by the bubble size and the fl ow rate are the most important parameters that affect plume hydrodynamics. Lastly, dimensionless correlations are proposed to assess the impact of mass transfer on plume hydrodynamics, including both the aeration and oxygenation modes.

2002

Complex, 3D mixing of single-and multi-phase flows, in particular by injection of gas and creation of bubble plumes, occurs in a number of situations of interest in energy technology, process and environmental engineering, etc. For all these applications, the ...

Journal of Fluid Mechanics, 1993

Bubble plumes in a linearly stratified ambient fluid are studied. Four well-defined flow regions were observed: an upward-moving bubble core, an inner plume consisting of a mixture of bubbles and relatively dense fluid, an annular downdraught and beyond that a horizontal intrusion flow. Depending on the gas flow rate with respect to the stratification, three types of intrusions were documented. At large gas flow rates a single intrusion was observed. As the gas flow rate was decreased, the buoyancy flux was insufficient to carry the lower fluid to the surface and a stack of intrusions were formed. At very low gas flow rates the intrusions became unsteady. The transition between these three regimes was observed to occur at critical values of the pararnetersN3H4/(QBg), Q B g / (4~a~u~ H) , and H/H,, where N is the buoyancy frequency, H is the water depth, HT is equal to H+H,, H A being the atmospheric pressure head, Q B is the gas flow rate at the bottom, g the acceleration due to gravity, a the entrainment coefficient and us the differential between the bubble and the average water velocity commonly called the slip velocity. The height between intrusions was found to scale with the Ozmidov length (QBg/P)i, the plunge point entrainment with the inner plume volume flux (Q, g)gN-f and the radial distance to the plunge point with (Qog/Ns)i, where Q, is the gas flow rate at the free surface. These results were used to construct a double annular plume model which was used to investigate the efficiency of conversion of the input bubble energy to potential energy of the stratification; the efficiency was found to first increase, reach a maximum, then decrease with decreasing gas flow rate. This agreed well with the results from the laboratory experiments.

International Journal of Multiphase Flow, 2002

1) A short review is given of some of the important publications on air-bubble plumes. Two main ways of modelling, using either the entrainment assumption, or the energy balance principle, are presented and briefly compared.

Computers & Fluids, 2005

The results of large eddy simulations (LES) of turbulent bubbly wake flows are presented. The LES technique was applied together with the Lagrangian particle dynamics method and a random flow generation (RFG) technique to the cases of a two-phase bubbly mixing layer and the high-Reynolds number bubbly ship-wake flows. The validation was performed on the experimental data for the bubbly mixing layer. Instantaneous distributions and probability density functions of bubbles in the wake were obtained using a joint LES/RFG approach. Separate estimates of bubble decay due to dissolution and buoyancy effects were obtained. The analysis of bubble agglomeration effects was done on the basis of experimental data for a turbulent vortex to satisfy one-way coupling that is used in this study.

Experiments in Fluids, 2006

Flow turbulence generated by a bubble plume in a large tank is characterized. Two different turbulence mechanisms contributing to the mixing and transport process are identified on velocity signals recorded outside of the bubble-plume core: a macro-scale process governed by the wandering motion of the bubble-plume; and an intermediate-and micro-scale process represented by the Kolmogorov power spectrum. A methodology is presented to characterize the different processes and their contributions to the turbulence parameters. The results help to understand the bubbleplume phenomenon and provide a basis to validate numerical models of bubble-plumes used in the design of combined-sewer-overflow reservoirs.

Chemical Engineering …, 2009

A large-eddy simulation of gas–liquid flow in a large scale bubble plume is presented. The Euler-Euler approach is used to describe the equations of motion of the two phase flow. The sub-grid scale modeling is based on the Smagorinsky kernel. All the non-drag forces (turbulent dispersion force (only for RANS), virtual mass force, lift force) and drag force are incorporated in the model. Overall, predictions are in good agreement with the experimental data at higher measurement levels but discrepancies are observed in the region near the injector. The axial mean liquid velocity and gas velocity at all the measurement levels exhibit the expected Gaussian profiles and plume spreading. The predictions of gas void fraction, axial gas and liquid velocity are in good agreement with the experimental data except near the injector. Further, the detailed comparison of LES and RANS predictions along with experimental data is presented and discussed.

Chemical Engineering Journal, 2018

Direct numerical simulations (DNS) provide a description of turbulent flow fields at every point in space and time. Since every statistical quantity can be computed, this data should be useful for the development of closure models. In this paper, models for bubbly turbulent flows, in a two-fluid framework, are investigated using DNS data. A

Physics of Fluids, 1998

Direct numerical simulations ͑DNS͒ of bubble-laden isotropic decaying turbulence are performed using the two-fluid approach ͑TF͒ instead of the Eulerian-Lagrangian approach ͑EL͒. The motivation for the study is that EL requires considerable computational resources, especially for the case of two-way coupling, where the instantaneous trajectories of a large number of individual bubbles need to be computed. The TF formulation is developed by spatially averaging the instantaneous equations of the carrier flow and bubble phase over a scale of the order of the Kolmogorov length scale, which, in our case, is much larger than the bubble diameter. On that scale, the bubbles are treated as a continuum ͑without molecular diffusivity͒ characterized by the bubble phase velocity field and concentration ͑volume fraction͒. The bubble concentration, C, is assumed small enough (Cр10 Ϫ3) to neglect the bubble-bubble interactions. As a test case, direct simulation of a bubble-laden Taylor-Green vortex with one-way coupling is performed with a bubble response time of the order of the flow time scale ͑inverse of the mean vorticity͒. This simple flow allows a direct examination of the effects of the preferential accumulation of bubbles in the high-enstrophy regions of the flow on the accuracy of the two-fluid formulation. The temporal development of the maximum bubble concentration obtained from DNS agrees well with the analytical solution. DNS of the bubble-laden decaying turbulence are also performed for both cases of one-way and two-way coupling. Here, the bubble diameter and response time are much smaller than the Kolmogorov length and time scales, respectively. In this case, as expected, the effects of the preferential accumulation of the bubbles are not pronounced. The results also show that the bubble-laden flow is analogous to a stratified flow with an effective density ϭ(1ϪC) f. Thus, due to the two-way interaction between the bubbles and carrier flow, the turbulence decay is enhanced with stable stratification, and reduced with unstable stratification.

Physics of Fluids, 2007

The dynamics and dispersion of small air bubbles in isotropic turbulence are analyzed computationally. The flow field is simulated using a pseudo-spectral code, while the bubble dynamics are analyzed by integration of a Lagrangian equation of motion that accounts for buoyancy, added mass, pressure, drag, and lift forces. Probability density functions (pdfs) of bubble velocities, lift and drag forces, and of field velocities and vorticities along bubble trajectories are used to analyze bubble dynamics. Lagrangian bubble trajectories are also employed to determine dispersion characteristics, following the theoretical development of Cushman and Moroni . Consistent with available experimental data, bubble rise velocities are increasingly suppressed with increasing turbulence intensity. The analysis also reveals that the vertical bubble velocities are characterized by asymmetric pdfs that are positive or negative-skewed dependent upon the non-dimensional turbulence intensity and the Taylor length scale. The role of the lift force in moving the bubbles to the down-flow side of turbulent eddies, and consequently retarding their rise, is consistently observed in all analysis. The dispersion of 40 µm bubbles and transition to Fickian behavior is shown to be weakly affected by the turbulence level. Larger, 400 µm bubbles are shown to be more sensitive to turbulence level with transition to Fickian behavior delayed in low turbulence fields.

International Journal of Multiphase Flow, 2006

An extensive study of the most important hydrodynamic characteristics of fairly large-scale bubble plumes was conducted using several measurement techniques and a variety of tools to analyze the data. Particle image velocimetry (PIV), double-tip optical probes (OP) and photographic techniques were extensively applied to measure bubble and liquid velocities, void-fraction and bubble sizes. PIV measurements in a vertical plane crossing the centre of the injector provided the instantaneous velocity fields for both phases, as well as hydrodynamic parameters, such as the movement of the axis of the plume and its instantaneous shape. Statistical studies were performed using image processing to determine the distribution of the apparent instantaneous plume diameter and centreline position. An important finding was that there is little instantaneous spreading of the bubble plume core; the spreading of the time-averaged plume width (as measured from the time-averaged void-fraction and time-averaged liquid velocity fields) is largely due to plume meandering and oscillations. The liquid-phase stress tensor distributions obtained from the instantaneous velocity data indicate that, for the continuous phase, these stresses scale linearly with the local void-fraction in the range of 0.5% < a < 2.5%. The bubbles were found to be ellipsoidal, with shape factor e % 0.5.