Mean velocity, spreading and entrainment characteristics of weak bubble plumes in unstratified and stationary water

2019 ◽  
Vol 874 ◽  
pp. 102-130 ◽  
Author(s):  
Binbin Wang ◽  
Chris C. K. Lai ◽  
Scott A. Socolofsky
Keyword(s):  
Diffusion Coefficient ◽  
Lateral Spreading ◽  
Liquid Volume ◽  
Bubble Plume ◽  
Mean Flow ◽  
Unified Framework ◽  
Mean Velocity ◽  
Turbulent Diffusion Coefficient ◽  
Bubble Plumes ◽  
The Mean

In this paper we present an experimental and theoretical study of weak bubble plumes in unstratified and stationary water. We define a weak bubble plume as one that spreads slower than the linear rate of a classic plume. This work focuses on the characteristics of the mean flow in the plume, including centreline velocity, plume spreading and entrainment of ambient water. A new theory based on diffusive spreading instead of an entrainment hypothesis is used to describe the lateral spreading of the bubbles and the associated plume. The new theory is supported by the experimental data. With the measured data of liquid volume fluxes and the new theory, we conclude that the weak bubble plume is a decreasing entrainment process, with the entrainment coefficient $\unicode[STIX]{x1D6FC}$ in the weak bubble plume decreasing with height $z$, following $\unicode[STIX]{x1D6FC}\sim z^{-1/2}$, and taking on values much smaller than those in a classic bubble plume. An additional non-dimensional diffusion coefficient, $\hat{E_{t}}\sim E_{t}U_{s}^{2}/B_{0}$, is also needed to describe the evolution of the volume and kinematic momentum fluxes for the mean flow in the weak bubble plume. Here, $E_{t}$ is the effective turbulent diffusion coefficient, $U_{s}$ is the terminal rise velocity of the bubbles, and $B_{0}$ is the kinematic buoyancy flux of the source. Finally, we provide a unified framework for the mean flow characteristics, including volume flux, momentum flux and plume spreading for the classic and weak bubble plumes, which also provides insight on the transition from classic to weak bubble plume behaviour.

The structure of a highly decelerated axisymmetric turbulent boundary layer

2021 ◽  
Vol 929 ◽  
Author(s):  
N. Agastya Balantrapu ◽  
Christopher Hickling ◽  
W. Nathan Alexander ◽  
William Devenport
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Shear Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Large Scale ◽  
Convection Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean

Experiments were performed over a body of revolution at a length-based Reynolds number of 1.9 million. While the lateral curvature parameters are moderate ( $\delta /r_s < 2, r_s^+>500$ , where $\delta$ is the boundary layer thickness and r s is the radius of curvature), the pressure gradient is increasingly adverse ( $\beta _{C} \in [5 \text {--} 18]$ where $\beta_{C}$ is Clauser’s pressure gradient parameter), representative of vehicle-relevant conditions. The mean flow in the outer regions of this fully attached boundary layer displays some properties of a free-shear layer, with the mean-velocity and turbulence intensity profiles attaining self-similarity with the ‘embedded shear layer’ scaling (Schatzman & Thomas, J. Fluid Mech., vol. 815, 2017, pp. 592–642). Spectral analysis of the streamwise turbulence revealed that, as the mean flow decelerates, the large-scale motions energize across the boundary layer, growing proportionally with the boundary layer thickness. When scaled with the shear layer parameters, the distribution of the energy in the low-frequency region is approximately self-similar, emphasizing the role of the embedded shear layer in the large-scale motions. The correlation structure of the boundary layer is discussed at length to supply information towards the development of turbulence and aeroacoustic models. One major finding is that the estimation of integral turbulence length scales from single-point measurements, via Taylor's hypothesis, requires significant corrections to the convection velocity in the inner 50 % of the boundary layer. The apparent convection velocity (estimated from the ratio of integral length scale to the time scale), is approximately 40 % greater than the local mean velocity, suggesting the turbulence is convected much faster than previously thought. Closer to the wall even higher corrections are required.

A Mean Flow Model for Polymer and Fiber Turbulent Drag Reduction

2005 ◽  
Vol 15 (6) ◽  
pp. 370-389 ◽  
Author(s):  
Anshuman Roy ◽  
Ronald G. Larson
Keyword(s):  
Drag Reduction ◽  
Weissenberg Number ◽  
Extensional Viscosity ◽  
Mean Flow ◽  
Dimensionless Numbers ◽  
Zero Shear Viscosity ◽  
Mean Velocity ◽  
Fiber Concentration ◽  
Turbulent Drag ◽  
The Mean

Abstract We present a one-parameter model that fits quantitatively the mean velocity profiles from experiments and numerical simulations of drag-reduced wall-bounded flows of dilute solutions of polymers and non-Brownian fibers in the low and modest drag reduction regime. The model is based on a viscous mechanism of drag reduction, in which either extended polymers or non-Brownian fibers increase the extensional viscosity of the fluid and thereby suppress both small and large turbulent eddies and reduce momentum transfer to the wall, resulting in drag reduction. Our model provides a rheological interpretation of the upward parallel shift S+ in the mean velocity profile upon addition of polymer, observed by Virk. We show that Virk’s correlations for the dependence on polymer molecular weight and concentration of the onset wall shear stress and slope increment on the Prandtl-Karman plot can be translated to two dimensionless numbers, namely an onset Weissenberg number and an asymptotic Trouton ratio of maximum extensional viscosity to zero-shear viscosity. We believe that our model, while simple, captures the essential features of drag reduction that are universal to flexible polymers and fibers, and, unlike the Virk phenomenology, can easily be extended to flows with inhomogeneous polymer or fiber concentration fields.

scholarly journals On the streamwise evolution of turbulent boundary layers in arbitrary pressure gradients

2002 ◽  
Vol 461 ◽  
pp. 61-91 ◽  
Author(s):  
A. E. PERRY ◽  
IVAN MARUSIC ◽  
M. B. JONES
Keyword(s):  
Boundary Layers ◽  
Scaling Laws ◽  
Power Spectra ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Stream Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
The Mean

A new approach to the classic closure problem for turbulent boundary layers is presented. This involves, first, using the well-known mean-flow scaling laws such as the log law of the wall and the law of the wake of Coles (1956) together with the mean continuity and the mean momentum differential and integral equations. The important parameters governing the flow in the general non-equilibrium case are identified and are used for establishing a framework for closure. Initially closure is achieved here empirically and the potential for achieving closure in the future using the wall-wake attached eddy model of Perry & Marusic (1995) is outlined. Comparisons are made with experiments covering adverse-pressure-gradient flows in relaxing and developing states and flows approaching equilibrium sink flow. Mean velocity profiles, total shear stress and Reynolds stress profiles can be computed for different streamwise stations, given an initial upstream mean velocity profile and the streamwise variation of free-stream velocity. The attached eddy model of Perry & Marusic (1995) can then be utilized, with some refinement, to compute the remaining unknown quantities such as Reynolds normal stresses and associated spectra and cross-power spectra in the fully turbulent part of the flow.

Optical studies on the turbulent motion of solid particles in a pipe flow

1991 ◽  
Vol 231 ◽  
pp. 665-688 ◽  
Author(s):  
James B. Young ◽  
Thomas J. Hanratty
Keyword(s):  
Diffusion Coefficient ◽  
Particle Velocity ◽  
Turbulent Diffusion ◽  
Slip Velocity ◽  
Rate Of Change ◽  
Solid Particles ◽  
Mean Square ◽  
Turbulent Diffusion Coefficient ◽  
Fluid Turbulence ◽  
The Mean

An extension of an axial viewing optical technique (first used by Lee, Adrian & Hanratty) is described which allows the determination of the turbulence characteristics of solid particles being transported by water in a pipe. Measurements are presented of the mean radial velocity, the mean rate of change radial velocity, the mean-square of the radial and circumferential fluctuations, the Eulerian turbulent diffusion coefficient, and the Lagrangian turbulent diffusion coefficient. A particular focus is to explore the influence of slip velocity for particles which have small time constants. It is found that with increasing slip velocity the magnitude of the turbulent velocity fluctuations remains unchanged but that the turbulent diffusivity decreases. The measurements of the average rate of change of particle velocity are consistent with the notion that particles move from regions of high fluid turbulence to regions of low fluid turbulence. Measurements of the root-mean-square of the fluctuations of the rate of change of particle velocity allow an estimation of the average magnitude of the particle slip in a highly turbulent flow, which needs to be known to analyse the motion of particles not experiencing a Stokes drag.

On the stability of an inviscid shear layer which is periodic in space and time

1967 ◽  
Vol 27 (4) ◽  
pp. 657-689 ◽  
Author(s):  
R. E. Kelly
Keyword(s):  
Growth Rate ◽  
Shear Layer ◽  
Finite Amplitude ◽  
Periodic Component ◽  
Periodic Flow ◽  
Flow Profile ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean ◽  
The Stability

In experiments concerning the instability of free shear layers, oscillations have been observed in the downstream flow which have a frequency exactly half that of the dominant oscillation closer to the origin of the layer. The present analysis indicates that the phenomenon is due to a secondary instability associated with the nearly periodic flow which arises from the finite-amplitude growth of the fundamental disturbance.At first, however, the stability of inviscid shear flows, consisting of a non-zero mean component, together with a component periodic in the direction of flow and with time, is investigated fairly generally. It is found that the periodic component can serve as a means by which waves with twice the wavelength of the periodic component can be reinforced. The dependence of the growth rate of the subharmonic wave upon the amplitude of the periodic component is found for the case when the mean flow profile is of the hyperbolic-tangent type. In order that the subharmonic growth rate may exceed that of the most unstable disturbance associated with the mean flow, the amplitude of the streamwise component of the periodic flow is required to be about 12 % of the mean velocity difference across the shear layer. This represents order-of-magnitude agreement with experiment.Other possibilities of interaction between disturbances and the periodic flow are discussed, and the concluding section contains a discussion of the interactions on the basis of the energy equation.

scholarly journals WKB theory for rapid distortion of inhomogeneous turbulence

1999 ◽  
Vol 390 ◽  
pp. 325-348 ◽  
Author(s):  
S. NAZARENKO ◽  
N. K.-R. KEVLAHAN ◽  
B. DUBRULLE
Keyword(s):  
Large Scale ◽  
Isotropic Turbulence ◽  
Two Dimensional ◽  
Turbulent Spot ◽  
Mean Flow ◽  
Mean Velocity ◽  
Inhomogeneous Turbulence ◽  
Large Scale Vortex ◽  
The Mean ◽  
Mean Strain

A WKB method is used to extend RDT (rapid distortion theory) to initially inhomogeneous turbulence and unsteady mean flows. The WKB equations describe turbulence wavepackets which are transported by the mean velocity and have wavenumbers which evolve due to the mean strain. The turbulence also modifies the mean flow and generates large-scale vorticity via the averaged Reynolds stress tensor. The theory is applied to Taylor's four-roller flow in order to explain the experimentally observed reduction in the mean strain. The strain reduction occurs due to the formation of a large-scale vortex quadrupole structure from the turbulent spot confined by the four rollers. Both turbulence inhomogeneity and three-dimensionality are shown to be important for this effect. If the initially isotropic turbulence is either homogeneous in space or two-dimensional, it has no effect on the large-scale strain. Furthermore, the turbulent kinetic energy is conserved in the two-dimensional case, which has important consequences for the theory of two-dimensional turbulence. The analytical and numerical results presented here are in good qualitative agreement with experiment.

Effect of an Azimuthal Mean Flow On the Structure and Stability of Thermoacoustic Modes in an Annular Combustor Model with Electroacoustic Feedback

2020 ◽  
Author(s):  
Sylvain C. Humbert ◽  
Jonas Moeck ◽  
Alessandro Orchini ◽  
Christian Oliver Paschereit
Keyword(s):  
Mach Number ◽  
Initial Conditions ◽  
Mean Flow ◽  
Final State ◽  
Mean Velocity ◽  
Acoustic Damping ◽  
Annular Combustor ◽  
The Mean ◽  
High Mach ◽  
The Stability

Abstract Thermoacoustic oscillations in axisymmetric annular combustors are generally coupled by degenerate azimuthal modes, which can be of standing or spinning nature. Symmetry breaking due to the presence of a mean azimuthal flow splits the degenerate thermoacoustic eigenvalues, resulting in pairs of counter-spinning modes with close but distinct frequencies and growth rates. In this study, experiments have been performed using an annular system where the thermoacoustic feedback due to the flames is mimicked by twelve identical electroacoustic feedback loops. The mean azimuthal flow is generated by fans. We investigate the standing/spinning nature of the oscillations as a function of the Mach number for two types of initial states, and how the stability of the system is affected by the mean azimuthal flow. It is found that spinning, standing or mixed modes can be encountered at very low Mach number, but increasing the mean velocity promotes one spinning direction. At sufficiently high Mach number, spinning modes are observed in the limit cycle oscillations. In some cases, the initial conditions have a significant impact on the final state of the system. It is found that the presence of a mean azimuthal flow increases the acoustic damping. This has a beneficial effect on stability: it often reduces the amplitude of the self-sustained oscillations, and can even suppress them in some cases. However, we observe that the suppression of a mode due to the mean flow may destabilize another one. We discuss our findings in relation with an existing low-order model.

scholarly journals Energy-consistent entrainment relations for jets and plumes

2015 ◽  
Vol 782 ◽  
pp. 333-355 ◽  
Author(s):  
Maarten van Reeuwijk ◽  
John Craske
Keyword(s):  
Kinetic Energy ◽  
Richardson Number ◽  
Turbulence Kinetic Energy ◽  
Mean Flow ◽  
Unified Framework ◽  
First Order ◽  
Entrainment Coefficient ◽  
The Mean ◽  
Flow Turbulence ◽  
Pure Plume

We discuss energetic restrictions on the entrainment coefficient${\it\alpha}$for axisymmetric jets and plumes. The resulting entrainment relation includes contributions from the mean flow, turbulence and pressure, fundamentally linking${\it\alpha}$to the production of turbulence kinetic energy, the plume Richardson number$\mathit{Ri}$and the profile coefficients associated with the shape of the buoyancy and velocity profiles. This entrainment relation generalises the work by Kaminskiet al. (J. Fluid Mech., vol. 526, 2005, pp. 361–376) and Fox (J. Geophys. Res., vol. 75, 1970, pp. 6818–6835). The energetic viewpoint provides a unified framework with which to analyse the classical entrainment models implied by the plume theories of Mortonet al.(Proc. R. Soc. Lond.A, vol. 234, 1955, pp. 1–23) and Priestley & Ball (Q. J. R. Meteorol. Soc., vol. 81, 1954, pp. 144–157). Data for pure jets and plumes in unstratified environments indicate that to first order the physics is captured by the Priestley and Ball entrainment model, implying that (1) the profile coefficient associated with the production of turbulence kinetic energy has approximately the same value for pure plumes and jets, (2) the value of${\it\alpha}$for a pure plume is roughly a factor of$5/3$larger than for a jet and (3) the enhanced entrainment coefficient in plumes is primarily associated with the behaviour of the mean flow and not with buoyancy-enhanced turbulence. Theoretical suggestions are made on how entrainment can be systematically studied by creating constant-$\mathit{Ri}$flows in a numerical simulation or laboratory experiment.

Measurements with a pulsed-wire and a hot-wire anemometer in the highly turbulent wake of a normal flat plate

1976 ◽  
Vol 77 (3) ◽  
pp. 473-497 ◽  
Author(s):  
L. J. S. Bradbury
Keyword(s):  
Turbulent Flow ◽  
Flat Plate ◽  
Flow Direction ◽  
Operating Conditions ◽  
Turbulent Intensity ◽  
Hot Wire ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean ◽  
Better Than

This paper describes an investigation into the response of both the pulsed-wire anemometer and the hot-wire anemometer in a highly turbulent flow. The first part of the paper is concerned with a theoretical study of some aspects of the response of these instruments in a highly turbulent flow. It is shown that, under normal operating conditions, the pulsed-wire anemometer should give mean velocity and longitudinal turbulent intensity estimates to an accuracy of better than 10% without any restriction on turbulence level. However, to attain this accuracy in measurements of turbulent intensities normal to the mean flow direction, there is a lower limit on the turbulent intensity of about 50%. An analysis is then carried out of the behaviour of the hot-wire anemometer in a highly turbulent flow. It is found that the large errors that are known to develop are very sensitive to the precise structure of the turbulence, so that even qualitative use of hot-wire data in such flows is not feasible. Some brief comments on the possibility of improving the accuracy of the hot-wire anemometer are then given.The second half of the paper describes some comparative measurements in the highly turbulent flow immediately downstream of a normal flat plate. It is shown that, although it is not possible to interpret the hot-wire results on their own, it is possible to calculate the hot-wire response with a surprising degree of accuracy using the results from the pulsed-wire anemometer. This provides a rather indirect but none the less welcome check on the accuracy of the pulsed-wire results, which, in this very highly turbulent flow, have a certain interest in their own right.

A vortex-street model of the flow in the similarity region of a two-dimensional free turbulent jet

1982 ◽  
Vol 123 ◽  
pp. 523-535 ◽  
Author(s):  
J. W. Oler ◽  
V. W. Goldschmidt
Keyword(s):  
Experimental Data ◽  
Reynolds Stress ◽  
Turbulent Jet ◽  
Vortex Street ◽  
Two Dimensional ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Core ◽  
The Mean ◽  
Similarity Relationships

The mean-velocity profiles and entrainment rates in the similarity region of a two-dimensional jet are generated by a simple superposition of Rankine vortices arranged to represent a vortex street. The spacings between the vortex centres, their two-dimensional offsets from the centreline, as well as the core radii and circulation strengths, are all governed by similarity relationships and based upon experimental data.Major details of the mean flow field such as the axial and lateral mean-velocity components and the magnitude of the Reynolds stress are properly determined by the model. The sign of the Reynolds stress is, however, not properly predicted.

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