Optical fibre probe measurements of bubbly flow in hydraulic jumps

This paper describes measurements of void fractions, bubble frequencies and bubble sizes in hydraulic jumps with Froude numbers 2.0, 2.4, 3.7 and 4.8. In each case data were obtained with a dual-tip optical fibre probe at a large number of points throughout the jump. Across the lower part of the flow, dominated by air entrainment into a region of turbulent shear, void fractions follow a Gaussian distribution. In the upper region, dominated by interactions with the free surface, the void fraction follows the form of an error function. The intersection between these two profiles provides a well-defined boundary between the two regions. Comparisons are made with measurements at higher Froude numbers [by Chanson, H., Brattberg, T., 2000. Experimental study of the air–water shear flow in a hydraulic jump. International Journal of Multiphase Flow 26, 583–607] revealing a very large measure of compatibility between the two sets of data.     

Bubbly flow measurements in hydraulic jumps with small inflow Froude numbers

The transition from supercritical to subcritical open channel flow is characterised by a strong dissipative mechanism called a hydraulic jump. A hydraulic jump is turbulent and associated with the development of large-scale turbulence and air entrainment. In the present study, some new physical experiments were conducted to characterise the bubbly flow region of hydraulic jumps with relatively small Froude numbers (2.4 < Fr₁ < 5.1) and relatively large Reynolds numbers (6.6 × 10⁴ < Re < 1.3 × 10⁵). The shape of the time-averaged free-surface profiles was well defined and the longitudinal profiles were in agreement with visual observations. The turbulent free-surface fluctuation profiles exhibited a peak of maximum intensity in the first half of the hydraulic jump roller, and the fluctuations exhibited some characteristic frequencies typically below 3 Hz. The air–water flow properties showed two characteristic regions: the shear layer region in the lower part of the flow and an upper free-surface region above. The air–water shear layer region was characterised by local maxima in terms of void fraction and bubble count rate. Other air–water flow characteristics were documented including the distributions of interfacial velocity and turbulence intensity. The probability distribution functions (PDF) of bubble chord time showed that the bubble chord times exhibited a broad spectrum, with a majority of bubble chord times between 0.5 and 2 ms. An analysis of the longitudinal air–water structure highlighted a significant proportion of bubbles travelling within a cluster structure.     

Local liquid velocity measurements in air-water bubbly flow

Local measurements of axial liquid velocity were performed for vertical upward air-water bubbly flow in a 101.6-mm inner-diameter round pipe by using a laser Doppler anemometer (LDA) and a hot-film anemometer (HFA). The data reduction approaches for both the LDA and HFA are discussed in detail. A threshold scheme with the information of local void fraction and velocity distribution in single-phase flow was applied to the LDA to approximately discriminate liquid velocity signals from those of the bubble interface velocity. Furthermore, a formulation was given to account for the effect of the bubble relative velocity on the liquid in the front and wake regions of the bubbles. For the HFA, an amplitude threshold scheme and a slope criterion were used to extract liquid velocity information. To reduce the measurement uncertainty, the experiments were performed in flow conditions where the area-averaged void fraction was less than 20%. The experimental results showed satisfactory agreement between the liquid volumetric flow rates calculated by area integration of the local liquid velocity and void fraction measurements, and the measured value by a magnetic flow meter. Also, the area-averaged relative velocity between the gas and liquid phases obtained from the current measurements agreed well with previous research.     

Turbulence structure of air-water bubbly flow—II. local properties

Microstructure was studied experimentally in air-water two-phase bubbly flow flowing upward in a vertical pipe of 60 mm diameter under atmospheric pressure. The results indicate that over a large portion of fully-developed bubbly flow the phases, the velocities of bubbles and water, and the ratio between the velocities of the phases have fairly flat radial profiles. In the wall region a maximum void fraction was observed. Spectra of the velocities of bubbles and water showed a Poisson distribution and a normal distribution function, respectively. The experimental evidence indicated a trend for the turbulent intensity to decrease first with increasing gas flow rate for constant water velocity and to increase again with a further increase in the gas flow rate. This phenomenon was more significant for a higher water velocity.     

Turbulence structure of air-water bubbly flow—I. measuring techniques

This paper, the first in a series describing our work on the turbulence structure of air-water bubbly flow, describes the principles of measurement and specially developed electronic instrumentation for determining various important local parameters, and the rates of turbulent transport of heat and bubbles in air-water two-phase bubbly flow. These instruments indicate the phase distribution, the bubble velocity and its spectrum, the water velocity and the turbulent intensity, and the turbulent dispersion coefficient of bubbles. Brief discussions are also presented on the accuracy of these techniques.     

Turbulence structure of air-water bubbly flow—III. transport properties

An experimental study of heat and bubble transport in turbulent air-water bubbly flow was carried out by means of tracer techniques. Helium tracer gas concentration data and temperature distributions were used to extract bubble and heat diffusivity information. The results indicated that the turbulent velocity components of the liquid phase play a predominant role in the turbulent transport process. A systematic increase of diffusivity of heat, ?_H, with quality and water velocity was observed. An empirical correlation for the diffusivity ratio ?_H,TP/?_H,SP is presented. The Péclet number, u′_covbar|dφ, for bubble dispersion can be approximated by 2.0, independent of the flow variables. The bubble-to-heat diffusivity ratio, φ/?_H, approaches unity with increasing quality and water velocity. Momentum transport is also discussed, based on a mixing length theory.     

Turbulence measurements in a swirling pipe flow

This paper reports laser-Doppler measurements of the mean flow and turbulence stresses in a swirling pipe flow. Experiments were carried out under well-controlled laboratory conditions in a refractive index-matched pipe flow facility. The results show pronounced asymmetry in mean and fluctuating quantities during the downstream decay of the swirl. Experimental data reveal that the swirl significantly modifies the anisotropy of turbulence and that it can induce explosive growth of the turbulent kinetic energy during its decay. Anisotropy invariant mapping of the turbulent stresses shows that the additional flow deformation imposed by initially strong swirling motion forces turbulence in the core region to tend towards the isotropic two-component state. When turbulence reaches this limiting state it induces rapid production of turbulent kinetic energy during the swirl decay.

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Light extinction technique for void fraction measurements in bubbly flow

 The analysis of the scattering induced by a dispersion of gas bubbles in a liquid medium on a collimated, monochromatic light beam, traversing the two-phase flow, allows for the direct measurement of the 2-D distribution of the line-average of the interfacial area density. The 2-D distribution of the line-average of the void fraction is deduced from that of the interfacial area density through an image processing algorithm. To demonstrate the technique, experiments are performed in a pool of water injected with air and illuminated with a CW argon ion laser. Since the bubble diameters range from a fraction of a millimeter to a few millimeters, the scattering processes are entirely in the Mie range. The limits of applicability of the technique and the measurement uncertainty are discussed. The results compare favorably with level-swell based measurements used as a reference. Received: 14 February 1997/Accepted: 4 February 1998     

Total pressure fluctuations and two-phase flow turbulence in hydraulic jumps

The large-scale turbulence and high air content in a hydraulic jump restrict the application of many traditional flow measurement techniques. This paper presents a physical modelling of hydraulic jump, where the total pressure and air–water flow properties were measured simultaneously with intrusive probes, namely a miniature pressure transducer and a dual-tip phase-detection probe, in the jump roller. The total pressure data were compared to theoretical values calculated based upon void fraction, water depth and flow velocity measured by the phase-detection probe. The successful comparison showed valid pressure measurement results in the turbulent shear region with constant flow direction. The roller region was characterised by hydrostatic pressure distributions, taking into account the void fraction distributions. The total pressure fluctuations were related to both velocity fluctuations in the air–water flow and free-surface dynamics above the roller, though the time scales of these motions differed substantially.     

Turbulence measurements in decaying swirl flow in a pipe

Turbulence in decaying swirl flow through a pipe is studied experimentally by using a single rotating inclined hot-wire probe and the results are presented in the form of profiles of the three mean velocities and the six components of the stress tensor. The results indicate that all the nine components are very weakly influenced by the Reynolds number, but strongly depend on the initial swirl. The swirling stream develops two regions of flow which are characterized by the variation of the tangential velocity and the Reynolds stresses. It was also found that the turbulence intensities are higher at the core and with the decay of the swirl their magnitudes reduce markedly at the core while they change slightly near the wall.Nomenclature A, A ₁–A ₄ constants in equations (1–9) - B constant in equation (10) - C constant in equations (1–9) - D pipe diameter - E hot-wire anemometer output voltage - e fluctuating component of anemometer voltage - k yaw parameter - R pipe radius - r radial coordinate - S _n swirl number, 2 ₀ ^R uwr ²dr/R2 ₀ ^R ur ² dr - (S _n )_in swirl number at inlet - T _m maximum moment of tangential velocity about axis, (W×Y)_max - U non-dimensional axial velocity, u/u _av - u, v, w time mean velocities in x, r and directions - u, v, w fluctuating components of velocity in x, r and directions - u _av average axial velocity - V non-dimensional radial velocity, v/u _av - v ₁ instantaneous velocity vector - v _x , v _y , v _z instantaneous velocity components in x, y and z directions - W non-dimensional tangential velocity, w/u _av - W _max maximum tangential velocity at a section - x axial coordinate - Y non-dimensional radius, r/R - Y ⁺ radius at which maximum tangential velocity occurs - probe angle - the angle between the wire axis and the instantaneous velocity vector - azimuthal angle of rotation of the probe about its axis     

Experimental assessment of scale effects affecting two-phase flow properties in hydraulic jumps

A hydraulic jump is the rapid transition from a supercritical to subcritical free-surface flow. It is characterised by strong turbulence and air bubble entrainment. New air–water flow properties were measured in hydraulic jumps with partially developed inflow conditions. The data set together with the earlier data of Chanson (Air bubble entrainment in hydraulic jumps. Similitude and scale effects, 119 p, 2006) yielded similar experiments conducted with identical inflow Froude numbers Fr ₁ = 5 and 8.5, but Reynolds numbers between 24,000 and 98,000. The comparative results showed some drastic scale effects in the smaller hydraulic jumps in terms of void fraction, bubble count rate and bubble chord time distributions. The present comparative analysis demonstrated quantitatively that dynamic similarity of two-phase flows in hydraulic jumps cannot be achieved with a Froude similitude. In experimental facilities with Reynolds numbers up to 10⁵, some viscous scale effects were observed in terms of the rate of entrained air and air–water interfacial area.     

Full-field bubbly flow velocity measurements using a multiframe particle tracking technique

The study is an examination of two-phase dispersed air bubble flow about a cylindrical conductor emitting a constant heat flux. The technique of Particle Image Velocimetry is utilized in order to obtain a full-field non-invasive measurement of the resulting bubbly flow velocity field. The employed approach utilizes a flow visualization technique in which the instantaneous velocity profile of a given flow field is determined by digitally recording particle or bubble images within the flow over multiple successive video frames and then conducting a completely computational analysis of the data. The use of particle tracking algorithms which perform a point-by-point matching of seed images from one frame to the next allows construction of particle or bubble pathlines and instantaneous velocity field. Results were initially obtained for a synthetically created flow field and a single phase liquid convective field seeded with flow-following tracer particles. The method was additionally extended to measurements within a gas/liquid system in which bubble rise velocities over a substantial two-dimensional flow area were determined in order to demonstrate the effectiveness of the developed digital data acquisition and analysis methodology.A version of this paper was presented at the 12th Symposium on Turbulence, University of Missouri-Rolla, 24–26 September, 1990     

Full-field bubbly flow velocity measurements by digital image pulsed laser velocimetry

Digital Pulsed Laser Velocimetry (DPLV) is a full-field, two dimensional, noninvasive, quantitative flow visualization technique. The technique described here includes the novel use of direct digitization of two-phase bubbly flow images using a high resolution imaging system. The image data is stored for further analysis by new image processing and analysis software developed for flow experiments.In the technique, ten consecutive frames of data separated by a time increment of 150 ms, are recorded. Each of these ten frames contains the images of bubbles at that one instant of time. A program smooths the instantaneous image and calculates bubble parameters. Another program matches the bubbles from each of the frames into tracks of bubbles through time. This program uses a statistical technique to determine the best possible path of the bubbles.The ability of pulsed laser velocimetry to capture simultaneous and quantitative rather than qualitative information along with these image processing techniques gives the experimentalist a powerful tool to perform flow visualization and analysis.     

Vortices in bubbly two-phase flow

The properties of a von Kármán vortex street are examined theoretically for bubbly flow around a rectangular obstacle. The time-dependent, two-dimensional Navier-Stokes equations describing each field are coupled through local pressure equilibration, a phenomenological momentum exchange term and a new representation of the virtual mass acceleration terms. Bubble fragmentation and coalescence are represented by the effect of relaxation to local Weber number equilibrium in a transport equation for the time and space variations of bubble-number density. Turbulence is represented by an eddy viscosity model. High-speed computer results for an air-water system agree well with published data for downstream gas accumulation in the vortices. Variations in Strouhal frequency with upstream void fraction are discussed in terms of bubble sublayer growth along the sides of the obstacle and the resulting movement of the flow separation streamline. Satellite eddy formation is observed, and the alteration of street characteristics by bubble migration is examined.     

Turbulence measurements in pipe flow using a nano-scale thermal anemometry probe

A new nano-scale thermal anemometry probe (NSTAP) has been developed using a novel procedure based on deep reactive ion etching. The performance of the new probe is shown to be superior to that of the previous design by Bailey (J Fluid Mech 663:160–179, 2010). It is then used to measure the streamwise velocity component of fully developed turbulent pipe flow, and the results are compared with data obtained using conventional hot-wire probes. The NSTAP agrees well with the hot-wire at low Reynolds numbers, but it is shown that it has better spatial resolution and frequency response. The data demonstrate that significant spatial filtering effects can be seen in the hot-wire data for probes as small as 7 viscous units in length.     

Free-surface fluctuations and turbulence in hydraulic jumps

A hydraulic jump is the highly turbulent transition between a high-velocity impinging flow and a turbulent roller. The jump flow is characterised by some substantial air bubble entrainment, spray and splashing. In the present study, the free-surface fluctuations and air-water properties of the hydraulic jump roller were investigated physically for relatively small Froude numbers (2.4 < Fr₁ < 5.1) and relatively large Reynolds numbers (6.6 × 10⁴ < Re < 1.3 × 10⁵). The shape of the mean free surface profile was well defined, and the time-averaged free-surface elevation corresponded to the upper free-surface, with the quantitative values being close to the equivalent clear-water depth. The turbulent fluctuation profiles exhibited a maximum in the first part of the hydraulic jump roller. The free-surface fluctuations presented some characteristic frequencies between 1.4 and 4 Hz. Some simultaneous free-surface measurements at a series of two closely located points yielded the free-surface length and time scales of free-surface fluctuations in terms of both longitudinal and transverse directions. The length scale data seemed to depend upon the inflow Froude number, while the time scale data showed no definite trend. Some simultaneous measurements of instantaneous void fraction and free-surface fluctuations exhibited different features depending upon the phase-detection probe sensor location in the different regions of the roller.     

Slip velocity measurements in an upward bubbly flow by combined LDA and electrodiffusional techniques

 An experimental technique for the measurement of the local slip velocity of spherical bubbles is reported. It is based on the measurement of the local liquid velocity by an electrodiffusional method, and the bubble velocity by a specially adapted LDA (Laser Doppler anemometer) with a short measuring volume. The bubble velocity is measured taking into account the shift between the bubble centre and the centre of the LDA measuring volume. The slip velocity is obtained by subtracting the liquid velocity from the bubble velocity at the point corresponding to the bubble centre. The technique is applicable for flows with high velocity gradients. Results of the slip velocity measurements in an upward bubbly flow at laminar pipe Reynolds numbers are presented. Received: 25 July 1996/Accepted: 13 April 1998     

Kinetic model of bubbly flow

A kinetic approach based on the approximate calculation of the fluid flow potential and formulation of Hamilton’s equations for generalized coordinates and momenta of bubbles is employed to describe processes of collective interaction of gas bubbles moving in an inviscid incompressible fluid. Kinetic equations governing the evolution of the distribution function of bubbles are derived. These equations are similar to Vlasov equations. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 130–138, September–October, 2000.     

Turbulence measurements in a flow generated by the collision of radially flowing wall jets

Early results of an experimental investigation of the abnormally high turbulence level and mixing layer growth rate characteristics found in the upwash regions of aircraft with vertical short takeoff and landing (V/STOL) flows in ground effect are presented. The upwash flow is formed from the collision of two opposing radially flowing wall jets. The wall jets are created in a unique way that allows the upwash to form without any interference due to the source jets. The objective of this work is to systematically characterize the development and structure of the flow. The upwash flow exhibits very large mixing rates compared to turbulent free or wall jet flows. A unique set of two component velocity profiles was taken in the upwash flow field. These measurements include several higher moment terms that appear in the turbulent kinetic energy equations, as well as length scales and intermittency determinations. Measurements were taken' along the axis connecting the two source jets as well as off this axis at six measurement stations above ground. The results provide detailed data on an important class of flows where none existed, and they are expected to significantly improve the computational empirical tools available for predicting V/STOL behavior near the ground.A version of this paper was presented at the 10th Symposium on Turbulence, University of Missouri-Rolla, September 22–24, 1986     

Turbulence kinetic energy budget in bubbly flows in a vertical duct

Understanding turbulence kinetic energy (TKE) budget in gas–liquid two-phase bubbly flows is indispensable to develop and improve turbulence models for the bubbly flows. In this study, a molecular tagging velocimetry based on photobleaching reaction was applied to turbulent bubbly flows with sub-millimeter bubbles in a vertical square duct to examine the applicability of the k–ε models to the bubbly flows. Effects of bubbles on TKE budget are discussed and a priori tests of the standard and low Reynolds number k–ε models are carried out to examine the applicability of these models to the bubbly flows. The conclusions obtained are as follows: (1) The photobleaching molecular tagging velocimetry is of use for validating turbulence models. (2) The bubbles increase the liquid velocity gradient in the near wall region, and therefore, enhance the production and dissipation rates of TKE. (3) The k–ε models can reasonably evaluate the production rate of TKE in the bubbly flows. (4) The modulations of diffusion due to the bubbles have different characteristics from the diffusion enhancement due to shear-induced turbulence. Hence, the k–ε models fail in evaluating the diffusion rate in the near wall region in the bubbly flows. (5) The k–ε models represent the trends of the production, dissipation, and diffusion rates of ε in the bubbly flow, although more accurate experimental data are required for quantitative validation of the ε equation.