Void Fraction Profiles Research Articles

Determination of Flow Patterns in Vertical Upward Two-Phase Flow Channel via Void Fraction Profile

Two-phase flow happens widely in the industrial plants and certain equipment. This paper attempts to study the characteristics of two-phase flow in a vertical piping system. This was achieved by comparing the void fraction, in the working fluid, by employing Constant Electric Current Method (CECM) with the actual observation using high-speed camera. The experiment requires a complete set of two-phase flow system information and was conducted based on various flow conditions. In order to carry out this experiment, the two-phase flow loop was constructed using a specific experimental apparatus and components. The flow channels were constructed using three pipes with three different inner diameters of 21.0 mm, 47.0 mm and 95.0 mm. The flow direction was vertical upward co-current flow with liquid superficial velocity range of 0.025 m/s to 3.0 m/s and gas superficial velocity range of 0.025 m/s to 3.0 m/s, depending on the size of the pipe. The flow pattern investigation focuses on experimental work, which was based on systematic observation and measurements using a high-speed camera and some measuring apparatus. The void fraction measurement using the CECM sensor was integrated into two-phase flow system with constant electric current running in the pipe and data acquisition system controlled virtually via LabVIEW software. Both result of the flow pattern and void fraction graph were then compared to determine the type of flow pattern from the void fraction graph. Information from the previous studies and experiments were collected and the assumption of any theoretical simplifications were used as a reference. According to the result, the flow pattern in pipe can be easily determined using CECM.

Three dimensional void distribution measurement of salt-water pool-boiling in 5 × 5 bundle geometry with X-ray CT system

Boiling of sea water may occur in a pressure vessel of light water (nuclear) reactors to flood the nuclear fuel as an accident management procedure. Another salt water is borated water, which will be injected into the reactor core as a neutron absorber to avoid recriticality. Boiling behavior of such salt water including these mixtures is a key to gain the confidence of accident strategy to cool down the reactor core during accidental conditions. Pool boiling experiments were conducted with a simulated 5 × 5 fuel-rod bundle with three different fluids: water, condensed (two and half times higher concentration) sea water and its mixture solution of sea water and borated water. Three-dimensional void-fraction distributions in the rod bundles were quantified by the high-energy X-ray CT system with a linear accelerator. There are no significant differences in void fraction distributions between condensed sea water and mixture solution. The void-fraction has a peak at the center on horizontal plane for all the fluids. The two salt-waters shift boiling incipience toward downstream and decrease void swell level so that vertical void-fraction profiles of the salt waters are steeper than that of water. This is because created bubbles in the salt waters were smaller than those in water. The spacer has a mixing effect to increase void fraction at upstream of the spacer and homogenize the void fraction on the horizontal plane.

Multiple Wire-Mesh Sensors Applied to the Characterization of Two-Phase Flow inside a Cyclonic Flow Distribution System.

Wire-mesh sensors are used to determine the phase fraction of gas–liquid two-phase flow in many industrial applications. In this paper, we report the use of the sensor to study the flow behavior inside an offshore oil and gas industry device for subsea phase separation. The study focused on the behavior of gas–liquid slug flow inside a flow distribution device with four outlets, which is part of the subsea phase separator system. The void fraction profile and the flow symmetry across the outlets were investigated using tomographic wire-mesh sensors and a camera. Results showed an ascendant liquid film in the cyclonic chamber with the gas phase at the center of the pipe generating a symmetrical flow. Dispersed bubbles coalesced into a gas vortex due to the centrifugal force inside the cyclonic chamber. The behavior favored the separation of smaller bubbles from the liquid bulk, which was an important parameter for gas-liquid separator sizing. The void fraction analysis of the outlets showed an even flow distribution with less than 10% difference, which was a satisfactorily result that may contribute to a reduction on the subsea gas–liquid separators size. From the outcomes of this study, detailed information regarding this type of flow distribution system was extracted. Thereby, wire-mesh sensors were successfully applied to investigate a new type of equipment for the offshore oil and gas industry.

Direct comparison of shadowgraphy and x-ray imaging for void fraction determination

A quantitative analysis of two imaging modalities, shadowgraphy and x-ray imaging, is presented in the framework of void fraction determination. The need for this arises from the fact that shadowgraphs are sometimes utilized to quantify void fraction profiles, which is an unproven method. Time-averaged x-ray images are used to evaluate the performance of the time-averaged shadowgraphs. The case of a cavitating flow through an axisymmetric converging-diverging nozzle (‘venturi’) is considered, for three separate cavitation numbers. The complex nature of the cavitating flow through the venturi manifests itself in the occurrence of three distinct regimes: a swarm of tiny bubbles; a large, coalesced cavity near the wall; and a drifting/collapsing cavity. The flow regime governs the performance of shadowgraphy for void fraction determination, with two of the three regimes deemed acceptable for shadowgraphy. The quantitative comparison exemplifies that sole reliance on shadowgraphy may lead one to draw improper conclusions on the void fraction distributions, even at a qualitative level.

MP-PIC modeling of CFB risers with homogeneous and heterogeneous drag models

In this paper, the MP-PIC (multiphase particle-in-cell) approach is used for three-dimensional (3D) modeling of the gas-solid flows in two types of circulating fluidized bed (CFB) risers with Geldart group A and B particles by incorporating the homogeneous and heterogeneous drag force models in the MP-PIC method, respectively. First, the effects of the three important simulation parameters, namely, the grid cell number, numerical particle-parcel size and time step, are investigated. Having determined the appropriate values for the three parameters, the hydrodynamic characteristics predicted by different drag force models are rigorously analyzed. The homogeneous drag models considered are the six models, the Wen-Yu, Wenyu-Ergun, Syamlal-O’Brien, Gidaspow, HKL, and BVK models, while the four heterogeneous models considered are Sarkar and EMMS-based models (EMMS-Yang, EMMS-Matrix and EMMS-QL). For the riser 1 with the Geldart A particles, all the six homogeneous models predict extremely high solid fluxes and inconsistent void fraction distributions compared with experimental results. The heterogeneous Sarkar and EMMS-based models can effectively improve the simulation accuracy and predict a typical core-annulus flow structure. The lately-developed EMMS-QL model produces the most accurate solid flux. For the riser 2 with the Geldart B particles, both the heterogeneous and homogeneous drag force models can predict a reasonable flow structure. Further, there are no significant differences in the void fraction and velocity profiles due to the choice of a drag force model over the other. These drag force models also successfully capture the meso-scale local particle clusters. Of these drag-force models, the Wenyu-Ergun drag-forec model predicts comparatively accurate solid flux. Generally, MP-PIC combined with heterogeneous Sarkar and EMMS-based drag force models reasonably improve the simulation accuracy for the Geldart A particles, while these heterogeneous models have no superiority over the homogeneous drag models for the Geldart B particles.

Eulerian modelling of turbulent bubbly flow based on a baseline closure concept

Abstract A unified set of closures have been applied to simulating different configurations and fluids, i.e. pipe flow and bubble column, air/water and air/liquid metal. The simulated velocity, void fraction and turbulence profiles were compared with the measured ones. Starting from the baseline model for poly-disperse flows the present work is intended to prove the performance of a recently published model for bubble-induced turbulence, which was established on the basis of physical analyses and direct numerical simulation data. The model is shown to work well under various conditions without any need of tuning, and significant improvement in the prediction of turbulence parameters in comparison to other models is demonstrated. This is a great step towards developing the baseline closure concept. Finally, a brief discussion on the further development and future work regarding Eulerian closure models was given.

Direct numerical simulation study of end effects and D/d ratio on mass transfer in packed beds

Direct Numerical Simulation (DNS) was performed to investigate the end effects on mass transfer in a packed bed for Reynolds number (Re) ≤ 100. The system considered in this study was naphthalene-air with a Schmidt number (Sc) ∼ 2.52. The location of the spheres’ centers in a randomly packed bed were obtained from Discrete Element Method – Computational Fluid Dynamics (DEM-CFD) simulations. The influence of the confining wall on how packed bed ends affect mass transfer was studied by examining the axial void fraction profile with varying ratio of the column diameter to the particle sphere diameter (D/d). Overall, it was found that the confining wall has a significant impact. The ‘local’ mass transfer coefficient was calculated based on the obtained DNS results and the probability distribution curve and the spatial distribution of the computed ‘local’ Sherwood numbers as function of the ratio X/L (ratio of the height of the active part of the bed to the total height of the bed) were developed to quantify the end effects on mass transfer within packed beds. For a packed bed with no wall effects (D/d = 11), it was found that the end effects can be eliminated by replacing the active particles located at ∼2 sphere diameters from the entrance and ∼1 sphere diameter from the exit by inert particles.

Estimation of porosity and void fraction profiles in a packed bed of spheres using X-ray radiography

Two-phase flow through porous media must be well understood to develop a severe accident analysis code not only for light water reactor but also sodium-cooled fast reactor. When a core disruptive accident occurs in sodium-cooled fast reactor, the fuel inside the core become melted and interacts with the coolant. As a result, gas-liquid two-phase flow will be formed in the debris bed, which may have porous nature depending on the cooling process. In such condition, the local porosity and its distribution are very important to characterize two-phase flow field in the porous media. In this study, X-ray radiography was applied to measure the local porosity in the packed bed of spheres. The radial profiles were estimated from the chordal profiles measured by the X-ray method and compared with the previous porosity model. In addition, the void fraction radial profiles were also obtained in air-water two-phase flow.

Large-scale laboratory observation of flow properties in plunging breaking waves

A plunging breaking wave of 1-m height was generated in a very large wave tank of 5 m in width, 5 m in depth, and 300 m in length filled with freshwater. The surface velocities in the highly aerated region of the breaking wave were measured using bubble image velocimetry (BIV), while the void fraction profiles were measured using fiber optic reflectometers (FOR). The internal velocities below the aerated region were also measured using an array of acoustic Doppler velocimeters (ADV). A wavelet-based technique was used to detect vortical structures at the free surface and estimate their length scales. The measured surface velocity fields were decomposed into wave induced and turbulence induced components to investigate the temporal and spatial evolution of mean kinetic energy and turbulent kinetic energy. It was found that turbulence is advected and diffused mainly following the phase speed of the breaking wave, rather than from the wave group velocity during the first splash-up process. The internal velocity measurements below the aerated regions show that turbulent kinetic energy decreases exponentially as the depth increases. Since scale effects under breaking waves with turbulence and air entrainment are less understood, results in flow kinematics, turbulence, and void fraction in the present study were compared with that in Lim et al. (2015) which investigated small scale plunging breaking waves with a 0.2-m wave height. It was found that flow kinematics and some dynamic properties such as void fraction and turbulent kinetic energy can be well represented between different physical scales if the traditional Froude scaling law is applied. Other dynamic properties, including bubble number and size distributions, seem to be significantly affected by the physical scales.

Bubble Force Balance Formula for Low Reynolds Number Bubbly Flows in Pipes and Channels: Comparison of Wall Force Models

Abstract In recent work, we investigated analytically low Reynolds number bubbly flows in pipes. We showed that the distribution of bubbles results from a balance between lift, dispersion and wall forces, and exhibited an analytical expression for this void fraction profile. We then performed a comparison of this analytical Bubble Force Balance Formula (BFBF) with an experiment from the literature. Antal’s model was used for the wall force. The objective of the present work is to compare and assess the three main wall force models in the literature: Antal’s, Tomiyama’s and Frank’s models. We begin by deriving two new BFBF, respectively with Tomiyama’s and Frank’s forces. We can see that the choice of the model impacts the velocity with which the analytical void fraction profile goes to zero at the wall. We then compare our three analytical profiles with experimental measurements and DNS simulations of laminar flows from the literature. We restrict ourselves to the near-wall region. The choice of Antal’s wall force model yields the best agreement. The data is also used to estimate the dispersion coefficient at the wall. Interestingly, we obtain the same order of magnitude with the three wall force models.

Phase distribution characteristics of bubbly flow in 5 × 5 vertical rod bundles with mixing vane spacer grids

In order to predict the thermal–hydraulic parameters in nuclear reactor accurately, it is essential to reveal the phase distribution characteristics, the mechanisms of phase interactions and the effects of the mixing vane spacer grid (MVSG) in rod bundles, based on which the drift-flux model and interfacial area transport equation could be developed further. The profiles of local two phase flow parameters could give an insight into these phenomena. Therefore, the adiabatic air–water upward two-phase flow experiments are performed to measure local parameters in 5 × 5 rod bundles with mixing vane spacer grids (MVSGs) under different bubbly flow conditions. The miniaturized four-sensor conductivity probe (MFSCP) has been developed to measure local two-phase flow parameters, such as void fraction, interfacial area concentration (IAC), bubble velocity and bubble chord length. The detail local parameters are measured and analyzed in the bubbly flow. Typical wall peaks for void fraction are identified and the bubble velocity profiles have a reverse phase position with void fraction profiles. The mixing vane spacer grid (MVSG) plays an important role in phase distribution in rod bundles: the skewed peaks of void fraction is associated with the direction of mixing vanes; a larger value of area-averaged void fraction is induced at the downstream of MVSG; compared with other factors, the MVSG plays a leading role in interfacial area transportation. Moreover, the dissipation length of MVSG is less than 19.4 L/D for current bubbly flow conditions.

Effect of Microbubble Gas Saturation on Near-Wall Turbulence and Drag Reduction

The article presents results of an experimental study of the effect of gravitational orientation of the flow along its lower/upper solid boundaries on reduction of turbulent drag and void fraction profiles with injection of gas through a porous channel wall. The shear stress on the wall was measured in the Reynolds number range Rex = (0.23–1.1) × 107 by floating element transducers; the void fraction profile was determined using a fiber-optic sensor. The void fraction in the inner (near-wall) region of the boundary layer was shown to be a key parameter for turbulent drag reduction. The size of the inner region depends on the gas flow rate, the fluid velocity, the distance downstream of the gas generator, and the gravitational orientation of the wall.

Development of one-dimensional two-fluid model with consideration of void fraction covariance effect

ABSTRACT Accurate evaluation of gas-liquid two-phase flow behavior within rod bundle geometry is crucial for the safety assessment of the nuclear power plants. In safety assessment codes, two-phase flow in rod bundle geometry has been treated as a one-dimensional flow. In order to obtain the reliable one-dimensional two-fluid model, it is essential to utilize proper area-averaged models for governing equations and constitutive relations. The area-averaged interfacial drag term utilized to evaluate two-phase interfacial drag force is typically given by the drift-flux parameters which consider the velocity profile in two-phase flow fields. However, in a rigorous sense, the covariance due to void fraction profile is ignored in traditional formulations. In this paper, the rigorous formulation of one-dimensional momentum equation was derived by taking consideration of void fraction covariance, and a new set of one-dimensional momentum equation and constitutive relations for interfacial drag was proposed. The newly obtained set of formulations was embedded into TRAC-BF1 code and numerical simulation was performed to compare against the traditional model without covariance. It was found that effect of covariance was almost negligible for steady-state adiabatic conditions, but for high void fraction condition with added perturbation, the traditional model underpredicted the damping ratio at around 8%.

Estimate of void fraction and air entrainment flux in hydraulic jump using Froude number

Hydraulic jumps are induced in hydraulic facilities for the purposes of energy dissipation or flow aeration. Presently there is no means for a simple estimate of void fraction distribution and air entrainment flux, without detailed physical modelling. This paper presents a semi-theoretical model to simulate the void fraction and velocity distributions in hydraulic jumps characterized by partially-developed inflow conditions. Relationships were established between the inflow Froude number, jump roller length and key parameters that determine the full expression of void fraction and velocity profiles. The proposed model enables accurate prediction of void fraction, longitudinal velocity, and air flux using the inflow Froude number. The results indicated considerable air flux contribution of free-surface aeration, in addition to the singular air entrainment at the jump toe, for moderate to large Froude numbers. A Froude number between 8 and 9 tended to achieve highest aeration rate with maximum total air flux in the roller.

Transition flow regime on stepped spillways: air–water flow characteristics and step-cavity fluctuations

Stepped spillways are man-made hydraulic structures designed to control the release of flow and to achieve a high energy dissipation. The flow pattern for a given stepped chute geometry can be distinguished into different regimes. Herein, the transition flow regime occurs at a range of intermediate discharges and is characterised by strong hydrodynamic fluctuations and intense splashing next to the free-surface. Up to date, only minimal experimental data is available for the transition flow. As this flow regime is likely to occur on stepped spillways designed for skimming flow operation, a knowledge of the transition flow characteristics is important to ensure safe operation. The present article investigates the hydraulics of the transition flow regime on a laboratory spillway, presenting a detailed characterisation of air–water flow properties and an image-based analysis of pool depth fluctuations within successive step-cavities. The results show two different void fraction and turbulence intensity profiles, indicating the existence of an upper and a lower transition flow sub-regime. The image-based analysis suggests the presence of a rapidly and a gradually varied flow region downstream of the inception point for both sub-regimes, whereas full equilibrium flow was not reached in the physical model. Overall, the study contributes towards improving the characterisation of the transition flow by assembling analytical solutions for different two-phase flow parameters, including void fraction, interfacial velocity and step-cavity pool height.

Assessment of CFD-DEM solution error against computational cell size for flows through a fixed-bed of binary-sized particles

Computational cell size is a crucial factor for accuracy in Computational Fluid Dynamics (CFD) - Discrete Element Method (DEM) simulations of particle-fluid interactions. In the present study, we investigate how simulation results change with computational cell size and mixture composition, for calculation of drag force over a fixed bed containing a binary-sized particle mixture. To investigate the complex solution convergence behavior, the simulation results are examined for several definitions of dimensionless computational cell size. Several regimes of consistent behavior, across three investigated mixtures, are identified and a consistently optimal cell size range is identified. We find that both the difference between simulated solution results and published experimental results, and the standard deviation of the void fraction profile, show consistent trends when plotted against the dimensionless computational cell size based on the Sauter-mean particle diameter. Grid-refinement studies are performed across all grid solutions, and the Grid Convergence Index (GCI) is analyzed as a predictor for the grid solution error. Correlations between simulation error and GCI are not strong, likely because of incongruence of the solution trends with typical asymptotic convergence. Alternatively, a correlation between change in solution value on successively refined grids and finer-grid solution error is shown to be adequate for the current results.

Effect of wall wettability condition on drift-flux parameters in lead–bismuth two-phase flow in circular and annular bubble columns

ABSTRACT Lead–bismuth two-phase flow in a cylindrical vessel and annulus was experimentally investigated by varying the surface wettability of the vessel wall. The test section used in this study was a cylindrical stainless vessel with/without inner sleeve to change the hydraulic diameter. Volume-averaged void fraction was measured by varying the surface wettability of the test section, which was enhanced by using a soldering flux. Measured void fraction was compared with existing two-phase flow correlations and with one-dimensional theoretical simulations assuming one-dimensional drift-flux model. From experimental results, measured distribution parameters of the lead–bismuth two-phase flow are much larger than that of ordinary two-phase flow regardless of the surface wettability. In the present work, the one-dimensional analysis was carried out for the cylindrical vessel to reproduce the distribution parameter. From the simulation results, predicted value for the cylindrical vessel showed good agreement with experimental results. However, in annulus, the distribution parameters in annulus were underestimated by the present model. It was suggested that, in case of annulus, steeper void fraction profile might be formed near the inner surface for poor wettability condition.

Void fraction measurements of bubbly flow in a horizontal 90° bend using wire mesh sensors

Wire mesh sensors were used to investigate the void fraction distribution of two-phase gas-liquid bubbly flow in a 50.8 mm diameter horizontal test section containing a 90° bend. The 90° bend had a radius of curvature of 76.2 mm, and its inlet was installed at an axial distance of one hundred pipe diameters from the test section's inlet. Wire mesh sensors measurements were recorded at axial locations of 97.5, 112.8, and 130.8 pipe diameters from the air-water inlet, which included axial locations both upstream and downstream of the 90° bend. Deionised water and compressed air were used as the working fluids, with the bubbly flow regime achieved at superficial liquid velocities ranging from 3.50 m/s to 5.42 m/s and superficial gas velocities, referenced at atmospheric conditions, ranging from 0.10 to 1.25 m/s. The effects of the 90° bend, as well as superficial gas and liquid velocities, on the void fraction distribution were parametrically investigated. Extensive measurements of the area-averaged, time-averaged, and bulk-averaged void fraction are reported for a total of 27 individual test cases. Radial profiles of the time-averaged void fraction are presented for all test cases along both vertical and horizontal axes. Results demonstrated the effects of superficial liquid and gas velocities on phase distribution before and after the bend. Statistical techniques were applied to discretize a transitional bubbly-slug flow pattern into constituent small bubble and large bubble flow patterns.

A more fundamental wall lubrication force from turbulent dispersion regularization for multiphase CFD applications

Accurate prediction of the gas volume fraction distribution in the near-wall region is critical for the simulation of bubbly flows. Resolving the near-wall gas profile remains a considerable challenge for multiphase computational fluid dynamics (M-CFD) simulations based on the Eulerian–Eulerian framework, where the coupling of interfacial momentum exchange through closure relations for lift and turbulent dispersion leads to a non-physical gas accumulation in the wall-layer cells. Wall lubrication models have been developed in an attempt to remedy this behavior by providing an artificial force to move the void fraction profile away from the wall. Currently, such models suffer from a severe lack of generality, being characterized by overspecified formulations that are highly dependent on tunable coefficients; moreover, their application often leads to dramatic overcorrections of the void fraction profile, resulting in the first few wall-layer cells being unphysically devoid of the gas phase. Here, we propose a new wall lubrication model that is derived through regularization of turbulent dispersion in the near-wall region to account for the decreasing cross-sectional area of the bubbles. This novel approach is assessed via simulation of experiments from the Liu and Bankoff database using a custom modified version of the twoPhaseEulerFoam solver in OpenFOAM v3.0.1. Comparison with the original model of Antal et al. (1991) and a mesh sensitivity study demonstrate the model's strong performance in volume fraction prediction in addition to its ability to scale well with varying thicknesses of the first wall-layer. This methodology is entirely general and can be used to derive a wall lubrication model from any turbulence dispersion model and assumed void fraction profile. The approach could further be extended for application to multi-group bubble size models.

The effects of nanoparticles on the lift force and drag force on bubbles in nanofluids: A two-fluid model study

Bubbly flows of air-water and air-nanofluid were investigated numerically using the two-fluid model. Through comparing the predicted bubble velocity and void fraction profiles against the experimental data, the classic two-fluid model, which has been widely validated for two-phase flows of pure liquids, was found to be inapplicable to those of nanofluids because of the empirical nature of the interfacial force formulation. The roles of interfacial forces were believed to be significantly altered in nanofluids rather than in pure liquids due to the spontaneous phenomenon of nanoparticle adsorption at bubble interfaces. Because of the nanoparticle layer, bubbles submerged in nanofluids would partially behave like a rigid sphere and develop a rotation movement. A slanted wake could be induced behind the bubble, generating a lateral Magnus force pointing towards the pipe centre and consequently making the positive-to-negative reversion of lift force occur at a smaller bubble diameter. Meanwhile, the slanted wake would also make bubbles in the viscous regime experience a drag force similar to that in the distorted regime, which makes the viscous-to-distorted transition point occur at a smaller bubble Reynolds number. It was recommended that the most important task when modelling bubbly flows of nanofluids using the two-fluid model is to reformulate the interfacial forces accounting for the effects of nanoparticle adsorption.