Measurement System of Bubbly Flow Using Ultrasonic Velocity Profile Monitor and Video Data Processing Unit, (II)

The authors have developed a measurement system which is composed of an ultrasonic velocity profile monitor and a video data processing unit in order to clarify its multi-dimensional flow characteristics in bubbly flows and to offer a data base to validate numerical codes for multi-dimensional two-phase flow. In this paper, the measurement system was applied for bubbly countercurrent flows in a vertical rectangular channel. At first, both bubble and water velocity profiles and void fraction profiles in the channel were investigated statistically. Next, turbulence intensity in a continuous liquid phase was defined as a standard deviation of velocity fluctuation, and the two-phase multiplier profile of turbulence intensity in the channel was clarified as a ratio of the standard deviation of flow fluctuation in a bubbly countercurrent flow to that in a water single phase flow. Finally, the distribution parameter and drift velocity used in the drift flux model for bubbly countercurrent flows were calculated from the obtained velocity profiles of both phases and void fraction profile, and were compared with the correlation proposed for bubbly countercurrent flows.     

Measurement System of Bubbly Flow Using Ultrasonic Velocity Profile Monitor and Video Data Processing Unit, (III)

The authors have developed a new measurement system which consisted of an Ultrasonic Velocity Profile Monitor (UVP) and a Video Data Processing Unit (VDP) in order to clarify the two-dimensional flow characteristics in bubbly flows and to offer a data base to validate numerical codes for two-dimensional two-phase flow. In the present paper, the proposed measurement system is applied to fully developed bubbly cocurrent flows in a vertical rectangular channel. At first, both bubble and water velocity profiles and void fraction profiles in the channel were investigated statistically. In addition, the two-phase multiplier profile of turbulence intensity, which was defined as a ratio of the standard deviation of velocity fluctuation in a bubbly flow to that in a water single phase flow, were examined. Next, these flow characteristics were compared with those in bubbly countercurrent flows reported in our previous paper. Finally, concerning the drift flux model, the distribution parameter and drift velocity were obtained directly from both bubble and water velocity profiles and void fraction profiles, and their results were compared with those in bubbly countercurrent flows.     

Experimental and numerical studies of void fraction distribution in rectangular bubble columns

Bubbly flow is encountered in a wide variety of industrial applications ranging from flows in nuclear reactors to process flows in chemical reactors. The presence of a second phase, recirculating flow, instabilities of the gas plume and turbulence, complicate the hydrodynamics of bubble column reactors.This paper describes experimental and numerical results obtained in a rectangular bubble column 0.1 m wide and 0.02 m in depth. The bubble column was operated in the dispersed bubbly flow regime with gas superficial velocities up to 0.02 m/s. Images obtained from a high speed camera were used to observe the general flow pattern and have been processed to calculate bubble velocities, bubble turbulence parameters and bubble size distributions. Gas disengagement technique was used to obtain the volume averaged gas fraction over a range of superficial gas velocities. A wire mesh sensor was applied, to measure the local volume fraction at two different height positions. Numerical calculations were performed with an Eulerian–Eulerian two-fluid model approach using the commercial code CFX.The paper details the effect of various two-fluid model interfacial momentum transfer terms on the numerical results. The inclusion of a lift force was found to be necessary to obtain a global circulation pattern and local void distribution that was consistent with the experimental measurements. The nature of the drag force formulation was found to have significant effect on the quantitative volume averaged void fraction predictions.     

Experiment and numerical simulation of bubbly two-phase flow across horizontal and inclined rod bundles

Experimental and numerical analyses were carried out on vertically upward air-water bubbly two-phase flow behavior in both horizontal and inclined rod bundles with either in-line or staggered array. The inclination angle of the rod bundle varied from 0 to 60° with respect to the horizontal. The measured phase distributions indicated non-uniform characteristics, particularly in the direction of the rod axis when the rods were inclined. The mechanisms for this non-uniform phase distribution is supposed to be due to: (1) Bubble segregation phenomenon which depends on the bubble size and shape; (2) bubble entrainment by the large scale secondary flow induced by the pressure gradient in the horizontal direction which crosses the rod bundle; (3) effects of bubble entrapment by vortices generated in the wake behind the rods which travel upward along the rod axis; and (4) effect of bubble entrainment by local flows sliding up along the front surface of the rods. The liquid velocity and turbulence distributions were also measured and discussed. In these speculations, the mechanisms for bubble bouncing at the curved rod surface and turbulence production induced by a bubble were discussed, based on visual observations. Finally, the bubble behaviors in vertically upward bubbly two-phase flow across horizontal rod bundle were analyzed based on a particle tracking method (one-way coupling). The predicted bubble trajectories clearly indicated the bubble entrapment by vortices in the wake region.     

Application of LDA to bubbly flows

The fluctuating velocity field in an air–water bubble column (i.d. 15.2 cm) at a gas fraction of 25% is investigated using backscatter LDA. Since the interpretation of LDA signals in bubbly flows is not straight forward also experiments on a single bubble train are reported. It is discussed that in the latter case when using seeding the backscatter LDA measures predominantly the liquid velocity. No improvement from thresholding on the discrimination between gas and liquid was found. The bubble column experiments show that the radial averaged liquid velocity profile represents the well known gross scale circulation present in the column. More interesting, it is also seen that the fluctuating velocity field can be studied in great detail. The velocity probability density functions directly indicate high turbulence intensity. Low frequency fluctuations are observed in agreement with visual observations. The data rate is an exponential function of the distance from the column wall. This limits the possibilities of spectral analysis in the central part of the flow. However, close to the wall the mean data rate is sufficient to study the frequency contents of the signal. It is shown that the power spectral density function obeys a −5/3 power law and that the autocorrelation function is of similar shape as reported in literature on bubbly flows.     

Experimental and numerical investigation of counter-current stratified flows in horizontal channels

Counter-current flow regimes of air and water are investigated in the WENKA test facility at the Forschungszentrum Karlsruhe. With the fluorescent-particle image velocimetry (PIV) measurement technique, velocity and velocity fluctuations are measured up to the free surface. A statistical model is presented to correlate the measured void fraction with the turbulent kinetic energy calculated from the measured velocity fluctuations. The experimental data are used to develop a phase interaction model to simulate stratified flows. Two different approaches are compared for turbulence modelling. The Prandtl mixing length model and an extended k–ω model for the two-phase region are applied to supercritical flow conditions.     

Void distribution and bubble motion in bubbly flows in a 4×4 rod bundle. Part II: numerical simulation

Numerical simulations of bubbly flows in a four by four rod bundle are carried out using a multi-fluid model to examine effects of the numerical treatment of phase distribution and drag model. The transport equations of bubble number density and void fraction are used as the continuity equation of the gas phase. Two drag models are tested: one of them accounts for the bubble deformation (aspect ratio), whereas the other does not. The rod diameter, the rod pitch and the hydraulic diameter of the rod bundle are 10, 12.5 and 9.1 mm, respectively. The gas and liquid volume fluxes are J_G = 0.06 m/s and J_L = 0.9 and 1.5 m/s, respectively. The bubble diameter ranges from 1 to 5 mm. Comparisons between the numerical and measured data show that (1) the restriction on bubble lateral motion due to the presence of rods can be taken into account by using the transport equation of bubble number density, whereas that of the void fraction cannot deal with the restriction and causes large errors in the distribution of void fraction and (2) the reduction in the bubble-relative velocity near the wall is predictable by using the drag model accounting for the bubble deformation effect.     

Two phase flow 1D turbulence model for poly-disperse upward flow in a vertical pipe

A 1D test-solver was developed in recent years for modeling of two phase bubbly flows in pipe geometry. The solver considers a number of bubble classes and calculates bubble-size resolved void fraction profiles in the radial direction. A successful implementation was achieved regarding bubble forces models (non-drag forces). Discrepancies appeared when coalescence and breakup rates were significant. These rates depend upon local turbulence quantities, which are possible reason for discrepancies. Originally the test-solver is equipped by Sato model (Sato, Y., Sadatomi, M., Sekoguchi, K., 1981. Momentum and heat transfer in two-phase bubble flow. I. International Journal Multiphase Flow 7, 167–177 .) which accounts for turbulence via shear- and bubble-induced viscosities calculated out of empirical correlations. One equation for the turbulent kinetic energy was solved, while the dissipation rate was calculated out of a correlation. In order to improve calculation of the local turbulence parameters, a two-phase k– turbulence model was adopted instead. The account for the bubble-induced turbulence was made via a source term taken out of literature. Comparisons between new and old turbulence modeling against experimental data showed better agreement for the new model. The experiments covered a wide range of water and air superficial velocities for upward bubbly flow in two pipe's diameters: 50 and 200 mm. The main feature of the new model is providing more reliable values of turbulence parameters for application in coalescence and breakup models. A comparison with CFX 5.7 calculations in a 50 mm pipe showed better calculation results when the source term was considered in the k– equations. An implementation into CFX is planned.     

Numerical study of a bubble plume generated by bubble entrainment from an impinging jet

The current paper presents the prediction results of a bubbly flow under plunging jet conditions using multiphase mono- and poly-dispersed approaches. The models consider interfacial momentum transfer terms arising from drag, lift, and turbulent dispersion force for the different bubble sizes. The turbulence is modeled by an extended k–? model which accounts for bubble induced turbulence. Furthermore in case of a poly-dispersed air–water flow the bubble size distribution, bubble break-up and coalescence processes as well as different gas velocities in dependency on the bubble diameter are taken into account using the Inhomogeneous MUSIG model. This model is a generalized inhomogeneous multiple size group model based on the Eulerian modeling framework which was developed in the framework of a cooperative work between ANSYS-CFX and Forschungszentrum Dresden-Rossendorf (FZD). The latter is now implemented into the CFD code CFX.According to the correlation on the lateral lift force obtained by Tomiyama (1998); this force changes its sign in dependence on the bubble size. Consequently the entrained small bubbles are trapped below the jet. They can escape from the bubble plume only by turbulent fluctuations or by coalescence. If the size of the bubbles generated by coalescence exceeds the size at which the lift force changes its sign these large bubbles go out from the plume and rise to the surface.A turbulent model based on an additional source term for turbulence kinetic energy and turbulence eddy dissipation equation is compared to the common concept for modeling the turbulence quantities proposed by Sato et al. (1981). It has been found that the large bubble distribution is slightly affected by the turbulence modeling which affects particularly the bubble coalescence and break-up process.     

Numerical investigation of bubble wake properties in the moving liquid with LES model

Wake flow caused by the relative motions between bubble and liquid phase influences bubble motions and enhances turbulent properties in the liquid phase. This phenomenon has been stressed for a better understanding of bubbly flow. In this paper, large eddy simulation (LES) is performed to simulate a single bubble rising in the moving liquid, with volume of fluid (VOF) method to capture the interface movements between bubble and liquid phase. The simulation results are firstly compared with the numerical and experimental data from the literature. A good agreement demonstrated the capability of the employed computational fluid dynamics (CFD) approach to predict turbulent properties in the liquid phase and capture interface movement as well as its induced wake flow. Consequently, the dynamic behaviors of a single bubble rising in the moving liquid were investigated. An ensemble averaged has been employed to evaluate the velocity distribution composed by wake velocity and liquid velocity quantitatively as well as the velocity fluctuations enhanced by bubble motion. Their dependency was also evaluated based on a systematic CFD simulation which covers a wide range of liquid velocity. With comparisons of the single phase flow, the influence from the existence of bubble on turbulent properties was determined.     

Two fluid model for two-phase turbulent jets

Eulerian two-fluid models are widely used in nuclear reactor safety and CFD. In these models turbulent diffusion of a dispersed phase must be formulated in terms of the fluctuating interfacial force and the Reynolds stresses. The interfacial force is obtained using the probability distribution function approach by Reeks (1992). This paper is the first application of this force to a case of engineering interest outside homogeneous turbulence. An Eulerian multidimensional two-fluid model for a cylindrical two-phase dispersed particle jet is proposed and compared with experimental data. The averaged conservation equations of mass and momentum are solved for each phase and the turbulent kinetic energy equation is solved for the continuous phase. The turbulent diffusion force and the Reynolds stresses are constituted within the context of the k- model of turbulence. A dissipation term has been added to the k- model for the turbulence modulation by the particles. Once the constitutive relations have been defined, the two-fluid model is implemented in a computational fluid dynamics code. It is shown that when the particles are very small the model is consistent with a convection-diffusion equation for particle transport where the diffusivity is defined according to Taylor's model (Taylor, G.I., 1921. Diffusion by continuous movements. Proc. London Math. Society, A20, pp. 196–211). The two-fluid model is also compared against two experimental data sets. Good agreement between the model and the data is obtained. The sensitivity of the results to various turbulent mechanisms is discussed.     

Effect of flow-induced vibration on local flow parameters of two-phase flow

A preliminary study was conducted experimentally in order to investigate the effect of flow-induced vibration on flow structure in two-phase flow. Two kinds of experiments were performed, namely ‘reference’ (no vibration) and ‘vibration’ experiments. In the reference experiment, an experimental loop was fixed tightly by three structural supports, whereas the supports were loosen a little in the vibration experiment. In the vibration experiment vibration was induced by flowing two-phase mixture in the loop. For relatively low superficial liquid velocity, flow-induced vibration promoted the bubble coalescence but liquid turbulence energy enhanced by the vibration might not be enough to break up the bubble. This leaded to the marked increase of Sauter mean diameter, and the marked decrease of interfacial area concentration. Accordingly, flow-induced vibration changed the void fraction profile from ‘wall peak’ to ‘core peak’ or ‘transition’, which increased distribution parameter in the drift-flux model. For high superficial liquid velocity, shear-induced liquid turbulence generated by two-phase flow itself might be dominant for liquid turbulence enhanced by flow-induced vibration. Therefore, the effect of flow-induced vibration on local flow parameters was not marked as compared with that for low superficial liquid velocity. Since it is anticipated that flow structure change due to flow-induced vibration would affect the interfacial area concentration, namely interfacial transfer term, further study may be needed under the condition of controlled flow-induced vibration.     

Balance of Liquid-phase Turbulence Kinetic Energy Equation for Bubble-train Flow

In this paper the investigation of bubble-induced turbulence using direct numerical simulation (DNS) of bubbly two-phase flow is reported. DNS computations are performed for a bubble-driven liquid motion induced by a regular train of ellipsoidal bubbles rising through an initially stagnant liquid within a plane vertical channel. DNS data are used to evaluate balance terms in the balance equation for the liquid phase turbulence kinetic energy. The evaluation comprises single-phase-like terms (diffusion, dissipation and production) as well as the interfacial term. Special emphasis is placed on the procedure for evaluation of interfacial quantities. Quantitative analysis of the balance equation for the liquid phase turbulence kinetic energy shows the importance of the interfacial term which is the only source term. The DNS results are further used to validate closure assumptions employed in modelling of the liquid phase turbulence kinetic energy transport in gas-liquid bubbly flows. In this context, the performance of respective closure relations in the transport equation for liquid turbulence kinetic energy within the two-phase k—epsilon and the two-phase k—l model is evaluated.     

Computations of post-trip reactor core thermal hydraulics using a strain parameter turbulence model

Coolant flows in the cores of nuclear reactors consist of ascending vertical flows in a large number of parallel passages. Under post-trip conditions such heated turbulent flows may be modified strongly from the forced convection condition by the action of buoyancy, in particular exhibiting impaired levels of heat transfer with respect to corresponding forced convection cases. The heat transfer performance of these ‘mixed convection’ flows is investigated here using two physically distinct eddy viscosity turbulence models: the recent ‘strain parameter’ (or k––S) model of Cotton and Ismael [A strain parameter turbulence model and its application to homogeneous and thin shear flows. Int. J. Heat Fluid Flow 19 (1998) 326] is examined against the benchmark low-Reynolds-number k– model of Launder and Sharma [Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc. Lett. Heat Mass Transfer 1 (1974) 131]. Comparison is made with three sets of heat transfer data for ascending mixed convection flows, and it is demonstrated that both turbulence models are generally successful in resolving the Nusselt number distributions occurring along the lengths of mixed convection flow passages. The mechanisms by which the strain parameter model generates reduced turbulence levels, and hence impaired heat transfer rates, is explored in comparison with a fourth set of experimental data for mixed convection flow profiles.     

Experimental investigation and CFD simulation of horizontal stratified two-phase flow phenomena

For the investigation of stratified two-phase flow, two horizontal channels with rectangular cross-section were built at Forschungszentrum Dresden-Rossendorf (FZD). The channels allow the investigation of air/water co-current flows, especially the slug behaviour, at atmospheric pressure and room temperature. The test-sections are made of acrylic glass, so that optical techniques, like high-speed video observation or particle image velocimetry (PIV), can be applied for measurements. The rectangular cross-section was chosen to provide better observation possibilities. Moreover, dynamic pressure measurements were performed and synchronised with the high-speed camera system.CFD post-test simulations of stratified flows were performed using the code ANSYS CFX. The Euler–Euler two fluid model with the free surface option was applied on grids of minimum 4 × 10⁵ control volumes. The turbulence was modelled separately for each phase using the k–ω-based shear stress transport (SST) turbulence model. The results compare very well in terms of slug formation, velocity, and breaking. The qualitative agreement between calculation and experiment is encouraging and shows that CFD can be a useful tool in studying horizontal two-phase flow.     

PIV Measurement of Pressure Distributions about Single Bubbles

Measurements of velocity and pressure distributions around a bubble are of fundamental importance to model the forces acting on the bubbles and to verify detailed numerical methods for the prediction of flow in nuclear reactors. The measurements of velocity distributions around a bubble have been conducted to understand the interaction between liquid flow and bubbles. However there are few studies on pressure distributions around a bubble for the lack of measurement method. In this study, we developed a method for evaluating a pressure distribution by making use of velocity data obtained by a particle image velocimetry (PIV) or a particle tracking velocimetry (PTV), and applied it to laminar pipe flows, laminar flows around single particles and single bubbles in a pipe to examine its accuracy and applicability to the flow around single bubbles. As a result, we could confirm that the method can evaluate the pressure distribution in various laminar flows, provided that the velocity data possess a good quality and a flow of concern is two-dimensional. The proposed method therefore has a potential to provide the important information for modeling of the bubble motion and verification of CFD methods such as interface tracking and lattice Boltzmann methods.     

A turbulence model study for simulating flow inside tight lattice rod bundles

Performances of various turbulence models are evaluated for calculation of detailed coolant velocity distribution in a tight lattice fuel bundle. The individual models are briefly outlined and compared with respect to the prediction of wall shear stress and velocity field, for a fully developed flow inside a triangular lattice bundle. Comparisons clearly show the importance of proper modeling of the turbulence-driven secondary flows in subchannels. A quadratic k– model, which showed promising capability in this respect, is adjusted in its coefficients, and the adjusted model is applied to fully developed flow in an infinite triangular array, with various Reynolds numbers. The results show that the inclusion of adequate anisotropy modeling enables to accurately reproduce the wall shear stress distribution and velocity field in tight lattice fuel bundles.     

Effects of non-uniform inlet boundary conditions and lift force on prediction of phase distribution in upward bubbly flows with Fluent-IATE

This study investigates the profile effects of the boundary conditions in two-phase flows, such as the inlet void fraction, interfacial area concentration, and phase velocity, on the predictions of flow behaviors downstream. Simulations are performed for upward air-water bubbly flows in a 48.3-mm inner diameter pipe by employing Fluent's two-fluid model together with an interfacial area transport equation (IATE) model. The IATE was developed in the literature to model the interfacial area concentration by taking into account the bubble coalescence and disintegration, and phase change effects.In this study, two types of inlet boundary conditions are considered, one being a uniform-profile boundary condition in the radial direction with area-averaged experimentally measured values while the other being a non-uniform profile condition based on the actual measured profiles at the inlet. The numerical predictions of downstream profiles of the phase distributions indicate that the two types of boundary conditions yield similar results for the downstream flow behaviors for the bubbly flow conditions investigated. In addition, the results with and without the lift force demonstrated that the lift force is essential to obtain accurate lateral phase distribution.