scholarly journals On bubble clustering and energy spectra in pseudo-turbulence

2010 ◽  
Vol 650 ◽  
pp. 287-306 ◽  
Author(s):  
JULIÁN MARTÍNEZ MERCADO ◽  
DANIEL CHEHATA GÓMEZ ◽  
DENNIS VAN GILS ◽  
CHAO SUN ◽  
DETLEF LOHSE
Keyword(s):  
Isotropic Turbulence ◽  
Liquid Velocity ◽  
Pair Correlation ◽  
Bubble Diameter ◽  
Three Dimensional ◽  
Radial Distance ◽  
Energy Spectra ◽  
Bubble Velocity ◽  
Vertical Orientation ◽  
Gaussian Form

Three-dimensional particle tracking velocimetry (PTV) and phase-sensitive constant temperature anemometry in pseudo-turbulence – i.e. flow solely driven by rising bubbles – were performed to investigate bubble clustering and to obtain the mean bubble rise velocity, distributions of bubble velocities and energy spectra at dilute gas concentrations (α ≤ 2.2 %). To characterize the clustering the pair correlation function G(r, θ) was calculated. The deformable bubbles with equivalent bubble diameter db = 4–5 mm were found to cluster within a radial distance of a few bubble radii with a preferred vertical orientation. This vertical alignment was present at both small and large scales. For small distances also some horizontal clustering was found. The large number of data points and the non-intrusiveness of PTV allowed well-converged probability density functions (PDFs) of the bubble velocity to be obtained. The PDFs had a non-Gaussian form for all velocity components and intermittency effects could be observed. The energy spectrum of the liquid velocity fluctuations decayed with a power law of −3.2, different from the ≈ −5/3 found for homogeneous isotropic turbulence, but close to the prediction −3 by Lance & Bataille (J. Fluid Mech., vol. 222, 1991, p. 95) for pseudo-turbulence.

On the rise of an ellipsoidal bubble in water: oscillatory paths and liquid-induced velocity

2001 ◽  
Vol 440 ◽  
pp. 235-268 ◽  
Author(s):  
KJETIL ELLINGSEN ◽  
FRÉDÉRIC RISSO
Keyword(s):  
Bubble Dynamics ◽  
Liquid Velocity ◽  
Bubble Diameter ◽  
Three Dimensional ◽  
Vertical Axis ◽  
Bubble Velocity ◽  
Velocity Magnitude ◽  
Axis Parallel ◽  
Wake Instability ◽  
Induced Velocity

This work is an experimental study of the rise of an air bubble in still water. For the bubble diameter considered, path oscillations develop in the absence of shape oscillations and the effect of surfactants is shown to be negligible. Both the three-dimensional motion of the bubble and the velocity induced in the liquid are investigated. After the initial acceleration stage, the bubble shape remains constant and similar to an oblate ellipsoid with its symmetry axis parallel to the bubble-centre velocity, and with constant velocity magnitude. The bubble motion combines path oscillations with slow trajectory displacements. (These displacements, which consist of horizontal drift and rotation about a vertical axis, are shown to have no influence on the oscillations). The bubble dynamics involve two unstable modes which have the same frequency and are π/2 out of phase. The primary mode develops first, leading to a plane zigzag trajectory. The secondary mode then grows, causing the trajectory to progressively change into a circular helix. Liquid-velocity measurements are taken up to 150 radii behind the bubble. The nature of the liquid flow field is analysed from systematic comparisons with potential theory and direct numerical simulations. The flow is potential in front of the bubble and a long wake develops behind. The wake structure is controlled by two mechanisms: the development of a quasi-steady wake that spreads around the non-rectilinear bubble trajectory; and the wake instability that generates unsteady vortices at the bubble rear. The velocities induced by the wake vortices are small compared to the bubble velocity and, except in the near wake, the flow is controlled by the quasi-steady wake.

The Influence of Gas and Liquid Flow Rates on the Transient Bubble Characteristics in a Liquid Cross-Flow

2011 ◽  
Author(s):  
Kamran Siddiqui ◽  
Wajid A. Chishty
Keyword(s):  
Inclination Angle ◽  
Liquid Flow ◽  
Liquid Velocity ◽  
Velocity Ratio ◽  
Bubble Diameter ◽  
Vertical Plane ◽  
Cross Flow ◽  
Bubble Velocity ◽  
Appreciable Effect ◽  
Flow Rates

The paper reports on an experimental study conducted to investigate the dynamics of gas bubbles when injected from an orifice that is subjected to a liquid cross-flow. The experiments were conducted over a range of gas and liquid flow rates and at various orientations of the liquid channel. An image processing algorithm was developed for the detection and characterization of the bubbles in both temporal and spatial coordinates. The transient behaviour of bubble dynamics at different channel orientations under different liquid and gas flow conditions are presented in the paper. Results show that the equivalent bubble diameter in the vertical plane decreased with increase in time as well as with increase in the gas-to-liquid velocity ratio. The channel inclination has no appreciable effect on the bubble diameter. The streamwise bubble velocity showed significant transient fluctuations, which diminished with an increase in the channel inclination angle. The fluctuations of the bubble vertical velocity were found to be unaffected by the channel inclination angle. The magnitudes of both streamwise and vertical velocities were influenced by the channel inclination, however, the trends were found to be opposite.

scholarly journals A Combined Numerical and Experimental Study of Hydrodynamics for an Air-Water External Loop Airlift Reactor

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Deify Law ◽  
Samuel T. Jones ◽  
Theodore J. Heindel ◽  
Francine Battaglia
Keyword(s):  
Liquid Velocity ◽  
Bubble Column ◽  
Bubble Diameter ◽  
Three Dimensional ◽  
Airlift Reactor ◽  
Cfd Modeling ◽  
Bubble Column Reactor ◽  
Ensemble Averaging ◽  
3D Simulations ◽  
External Loop

The external loop airlift reactor (ELALR) is a modified bubble column reactor that is composed of two vertical columns that are interconnected with two horizontal tubes and is often preferred over traditional bubble column reactors because they can operate over a wider range of conditions. In the present work, the gas-liquid flow dynamics in an ELALR was simulated using an Eulerian–Eulerian ensemble-averaging method in two-dimensional (2D) and three-dimensional (3D) coordinate systems. The computational fluid dynamics (CFD) simulations were compared to experimental measurements from a 10.2 cm diameter ELALR for superficial gas velocities ranging from 1 cm/s to 20 cm/s. The effect of specifying a mean bubble diameter to represent the gas phase in the CFD modeling was investigated, and 2D and 3D simulations were found to be in good agreement with the experimental data. The ELALR flow regimes were compared for the reactor operating in bubble column, closed vent, and open vent modes, and the 2D simulations qualitatively predicted the behavior of bubble growth in the downcomer. However, it was found that 3D simulations were necessary to capture the physics of the ELALR for gas holdup, bulk density differences, and riser superficial liquid velocity.

scholarly journals CFD Modeling of Gas-Liquid Bubbly Flow in Horizontal Pipes: Influence of Bubble Coalescence and Breakup

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
K. Ekambara ◽  
R. Sean Sanders ◽  
K. Nandakumar ◽  
J. H. Masliyah
Keyword(s):  
Volume Fraction ◽  
Liquid Velocity ◽  
Bubbly Flow ◽  
Bubble Diameter ◽  
Three Dimensional ◽  
Gas Bubbles ◽  
Bubbly Flows ◽  
Cfd Modeling ◽  
Horizontal Pipe ◽  
The Impact

Modelling of gas-liquid bubbly flows is achieved by coupling a population balance equation with the three-dimensional, two-fluid, hydrodynamic model. For gas-liquid bubbly flows, an average bubble number density transport equation has been incorporated in the CFD code CFX 5.7 to describe the temporal and spatial evolution of the gas bubbles population. The coalescence and breakage effects of the gas bubbles are modeled. The coalescence by the random collision driven by turbulence and wake entrainment is considered, while for bubble breakage, the impact of turbulent eddies is considered. Local spatial variations of the gas volume fraction, interfacial area concentration, Sauter mean bubble diameter, and liquid velocity are compared against experimental data in a horizontal pipe, covering a range of gas (0.25 to 1.34 m/s) and liquid (3.74 to 5.1 m/s) superficial velocities and average volume fractions (4% to 21%). The predicted local variations are in good agreement with the experimental measurements reported in the literature. Furthermore, the development of the flow pattern was examined at three different axial locations ofL/D= 25, 148, and 253. The first location is close to the entrance region where the flow is still developing, while the second and the third represent nearly fully developed bubbly flow patterns.

scholarly journals The on-axis magnetic well and Mercier's criterion for arbitrary stellarator geometries

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
P. Kim ◽  
R. Jorge ◽  
W. Dorland
Keyword(s):  
Magnetic Field ◽  
Original Work ◽  
Three Dimensional ◽  
Radial Distance ◽  
Analytical Form ◽  
One Dimensional ◽  
Modern Notation ◽  
Magnetic Well ◽  
First Time ◽  
Dimensional Integral

A simplified analytical form of the on-axis magnetic well and Mercier's criterion for interchange instabilities for arbitrary three-dimensional magnetic field geometries is derived. For this purpose, a near-axis expansion based on a direct coordinate approach is used by expressing the toroidal magnetic flux in terms of powers of the radial distance to the magnetic axis. For the first time, the magnetic well and Mercier's criterion are then written as a one-dimensional integral with respect to the axis arclength. When compared with the original work of Mercier, the derivation here is presented using modern notation and in a more streamlined manner that highlights essential steps. Finally, these expressions are verified numerically using several quasisymmetric and non-quasisymmetric stellarator configurations including Wendelstein 7-X.

scholarly journals Numerical and experimental study on turbulence statistics in a large fan-stirred combustion vessel

2021 ◽  
Vol 62 (5) ◽  
Author(s):  
M. E. Morsy ◽  
J. Yang
Keyword(s):  
Isotropic Turbulence ◽  
Burning Velocity ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Turbulence Models ◽  
Initial Pressure ◽  
Dynamics Modeling ◽  
Turbulence Statistics ◽  
Experimental Conditions ◽  
Measured Velocity

Abstract Particle image velocimetry (PIV) has become a popular non-intrusive tool for measuring various types of flows. However, when measuring three-dimensional flows with two-dimensional (2D) PIV, there are some uncertainties in the measured velocity field due to out-of-plane motion, which might alter turbulence statistics and distort the overall flow characteristics. In the present study, three different turbulence models are employed and compared. Mean and fluctuating fields obtained by three-dimensional computational fluid dynamics modeling are compared to experimental data. Turbulence statistics such as integral length scale, Taylor microscale, Kolmogorov scale, turbulence kinetic energy, dissipation rate, and velocity correlations are calculated at different experimental conditions (i.e., pressure, temperature, fan speed, etc.). A reasonably isotropic and homogeneous turbulence with large turbulence intensities is achieved in the central region extending to almost 45 mm radius. This radius decreases with increasing the initial pressure. The influence of the third dimension velocity component on the measured characteristics is negligible. This is a result of the axisymmetric features of the flow pattern in the current vessel. The results prove that the present vessel can be conveniently adopted for several turbulent combustion studies including mainly the determination of turbulent burning velocity for gaseous premixed flames in nearly homogeneous isotropic turbulence. Graphic abstract

Diesel Droplet Diffusion in Isotropic Turbulence With Digital Holographic Cinematography

2005 ◽  
Author(s):  
Balaji Gopalan ◽  
Edwin Malkiel ◽  
Jian Sheng ◽  
Joseph Katz
Keyword(s):  
Time Series ◽  
High Speed ◽  
Isotropic Turbulence ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Time History ◽  
Sample Volume ◽  
Velocity Autocorrelation Function ◽  
Digital Cameras ◽  
Velocity Autocorrelation

High-speed in-line digital holographic cinematography was used to investigate the diffusion of droplets in locally isotropic turbulence. Droplets of diesel fuel (0.3–0.9mm diameter, specific gravity of 0.85) were injected into a 37×37×37mm3 sample volume located in the center of a 160-liter tank. The turbulence was generated by 4 spinning grids, located symmetrically in the corners of the tank, and was characterized prior to the experiments. The sample volume was back illuminated with two perpendicular collimated beams of coherent laser light and time series of in-line holograms were recorded with two high-speed digital cameras at 500 frames/sec. Numerical reconstruction generated a time series of high-resolution images of the droplets throughout the sample volume. We developed an algorithm for automatically detecting the droplet trajectories from each view, for matching the two views to obtain the three-dimensional tracks, and for calculating the time history of velocity. We also measured the mean fluid motion using 2-D PIV. The data enabled us to calculate the Lagrangian velocity autocorrelation function.

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