On bubble clustering and energy spectra in pseudo-turbulence

3D-Particle Tracking (3D-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 ($\alpha \leq2.2$%). To characterize the clustering the pair correlation function $G(r,\theta)$ was calculated. The deformable bubbles with equivalent bubble diameter $d_b=4-5$ 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 to obtain well-converged Probability Density Functions (PDFs) of the bubble velocity. 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 $\approx -5/3$ found for homogeneous isotropic turbulence, but close to the prediction -3 by \cite{lance} for pseudo-turbulence

Energy spectra in turbulent bubbly flows

We conduct experiments in a turbulent bubbly flow to study the nature of the transition between the classical $-$5/3 energy spectrum scaling for a single-phase turbulent flow and the $-$3 scaling for a swarm of bubbles rising in a quiescent liquid and of bubble-dominated turbulence. The bubblance parameter, 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 the bubbly flow. We vary the bubblance parameter from $b = \infty$ (pseudo-turbulence) to $b = 0$ (single-phase flow) over 2-3 orders of magnitude ($0.01 - 5$) to study its effect on the turbulent energy spectrum and liquid velocity fluctuations. The probability density functions (PDFs) of the liquid velocity fluctuations show deviations from the Gaussian profile for $b > 0$, 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 scaling at length scales smaller than the size of the bubbles for bubbly flows. This $-$3 spectrum scaling holds not only in the well-established case of pseudo-turbulence, but surprisingly in all cases where bubbles are present in the system ($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 wave numbers, 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.Comment: J. Fluid Mech. (in press

The Aerodynamic Loads On A Flat Plate Between Parallel Walls Due To Rotational Flow Disturbances

In the thesis the effects of rotational flow disturbances on a body placed in an inviscid, incompressible fluid stream and in particular the case of a flat plate situated midway between two parallel planes were studied. A single vortex approaching the flat plate was first considered and then expanded to simulate the effects of pseudo-turbulence on the flat plate.;The finite-element and finite-difference numerical methods were evaluated in the thesis and arguments were made in support of using the finite-difference approach rather than the finite-element approach. The fact that the finite-difference technique was used for the particular flow problems studied in the thesis does not detract from the usefulness of finite-element methods for other flow problems particularly when further research has been made on variational methods applied to the non-linear fluid flow equations.;Theory for a Rotational Channel Vortex was developed and used to provide the upstream boundary conditions to the solution for the unsteady flow over a semi-infinite and then a finite flat plate. Also, new techniques were introduced in the thesis to predict the internal and external boundary conditions. It was found during the study that several methods were available to predict the boundary conditions on the flat plate but it was shown to be most important to select the appropriate method to formulate the correct boundary conditions on a body immersed in an unsteady rotational flow. The use of pseudo-turbulence models to simulate the approaching flow was also considered and it was shown that the loading on the plate could be determined using this approach. For instance the results showed that it was possible to predict the instantaneous unsteady loads on the flat plate from a particular approaching pseudo-turbulence with a particular power spectral density of the velocity fluctuations

An experimental study of wall-injected flows in a rectangular cylinder

An experimental investigation of the flow inside a rectangular cylinder with air injected continuously along the wall is performed. This kind of flow is a two-dimensional approximation of what happens inside a solid rocket motor, where the lateral grain burns expelling exhaust gas or in processes with air filtration or devices to attain uniform flows. We propose a brief derivation of some analytical solutions and a comparison between these solutions and experimental data, which are obtained using the Particle Image Velocimetry (PIV) technique, in order to provide a global reconstruction of the flowfield. The flow, which enters orthogonal to the injecting wall, turns suddenly its direction being pushed towards the exit of the chamber. Under the incompressible and inviscid flow hypothesis, two analytical solutions are reported and compared. The first one, known as Hart-McClure solution, is irrotational and the injection velocity is non-perpendicular to the injecting wall. The other one, due to Taylor and Culick, has non-zero vorticity and constant, vertical injection velocity. The comparison with laminar solutions is useful to assess whether transition to turbulence is reached and how the disturbance thrown in by the porous injection influences and modifies those solutions

The evolution of energy in flow driven by rising bubbles

We investigate by direct numerical simulations the flow that rising bubbles cause in an originally quiescent fluid. We employ the Eulerian-Lagrangian method with two-way coupling and periodic boundary conditions. In order to be able to treat up to 288000 bubbles, the following approximations and simplifications had to be introduced: (i) The bubbles were treated as point-particles, thus (ii) disregarding the near-field interactions among them, and (iii) effective force models for the lift and the drag forces were used. In particular, the lift coefficient was assumed to be 1/2, independent of the bubble Reynolds number and the local flow field. The results suggest that large scale motions are generated, owing to an inverse energy cascade from the small to the large scales. However, as the Taylor-Reynolds number is only in the range of 1, the corresponding scaling of the energy spectrum with an exponent of -5/3 cannot develop over a pronounced range. In the long term, the property of local energy transfer, characteristic of real turbulence, is lost and the input of energy equals the viscous dissipation at all scales. Due to the lack of strong vortices the bubbles spread rather uniformly in the flow. The mechanism for uniform spreading is as follows: Rising bubbles induce a velocity field behind them that acts on the following bubbles. Owing to the shear, those bubbles experience a lift force which make them spread to the left or right, thus preventing the formation of vertical bubble clusters and therefore of efficient forcing. Indeed, when the lift is artifically put to zero in the simulations, the flow is forced much more efficiently and a more pronounced energy accumulates at large scales is achieved.Comment: 9 pages, 7 figure

Kolmogorov turbulence co-exists with pseudo-turbulence in buoyancy-driven bubbly flows

We investigate spectral properties of buoyancy driven bubbly flows. Using high-resolution numerical simulations and phenomenology of homogeneous turbulence, we identify the relevant energy transfer mechanisms. We find: (a) At high enough Galilei number (ratio of the buoyancy to viscous forces) the kinetic energy spectrum shows the Kolmogorov scaling with a power law exponent $-5/3$ for the range of scales between the bubble diameter and the dissipation scale ($\eta$). (b) For scales smaller than $\eta$, the physics of pseudo-turbulence is recovered

Microbubbly drag reduction in Taylor-Couette flow in the wavy vortex regime

We investigate the effect of microbubbles on Taylor-Couette flow by means of direct numerical simulations. We employ an Eulerian-Lagrangian approach with a gas-fluid coupling based on the point-force approximation. Added mass, drag, lift, and gravity are taken into account in the modeling of the motion of the individual bubble. We find that very dilute suspensions of small non-deformable bubbles (volume void fraction below 1%, zero Weber number and bubble Reynolds number <10) induce a robust statistically steady drag reduction (up to 20%) in the so called wavy vortex flow regime (Re = 600-2500). The Reynolds number dependence of the normalized torque (the so-called Torque Reduction Ratio (TRR) which corresponds to the drag reduction) is consistent with a recent series of experimental measurements performed by Murai et al. (J. Phys. 14, 143 (2005)). Our analysis suggests that the physical mechanism for the torque reduction in this regime is due to the local axial forcing, induced by rising bubbles, that is able to break the highly dissipative Taylor wavy vortices in the system. We finally show that the lift force acting on the bubble is crucial in this process. When neglecting it, the bubbles preferentially accumulate near the inner cylinder and the bulk flow is less efficiently modified.Comment: 21 pages, 13 figures, extended and revised versio

The clustering morphology of freely rising deformable bubbles

We investigate the clustering morphology of a swarm of freely rising deformable bubbles. A three-dimensional Vorono\"i analysis enables us to quantitatively distinguish between two typical clustering configurations: preferential clustering and a grid-like structure. The bubble data is obtained from direct numerical simulations (DNS) using the front-tracking method. It is found that the bubble deformation, represented by the aspect ratio \chi, plays a significant role in determining which type of clustering is realized: Nearly spherical bubbles with \chi <~ 1.015 form a grid-like structure, while more deformed bubbles show preferential clustering. Remarkably, this criteria for the clustering morphology holds for different diameters of the bubbles, surface tension, and viscosity of the liquid in the studied parameter regime. The mechanism of this clustering behavior is connected to the amount of vorticity generated at the bubble surfaces.Comment: 10 pages, 5 figure

Fluctuations and massive separation in three-dimensional shock-wave/boundary-layer interactions

Shock-wave unsteadiness was observed in rapidly compressed supersonic turbulent boundary layer flows with significant separation. A Mach 2.85 shock-wave/turbulent boundary layer flow was set up over a series of cylinder-flare bodies in the High Reynolds Number Channel 1. The transition from fully attached to fully separated flow was studied using axisymmetric flares with increasing compression angles. In the second phase, the 30 deg flare was inclined relative to the cylinder axis, so that the effect on a separated flow of increasing 3 dimensionality could be observed. Two 3-D separated cases are examined. A simple conditional sampling technique is applied to the data to group them according to an associated shock position. Mean velocities and turbulent kinetic energies, computed from the conditionally samples data, are compared to those from the unsorted data and to computed values. Three basic questions were addressed: can conditional sampling be used to provide snapshots of the flow; are averaged turbulence quantities dominated by the bimodal nature of the interaction; and is the shock unsteadiness really important to computational accuracy