Terms Of Momentum Transfer Research Articles

Flow characteristics of dispersed two-phase flows in an 8 × 8 rod bundle

Two-phase flows in rod bundles or tube bundles appear in heat transfer systems. The bundle-average (or one-dimensional) void fraction is a critical parameter in overall system design, performance evaluation, and safety assessment. Accurate bundle-average void fraction prediction requires a precise interfacial momentum transfer term formulated using the distribution parameter and drift velocity, two essential drift-flux parameters in the drift-flux model. The currently utilized modeling approach is based on the distribution parameter and drift velocity determined together through drift-flux plots. This results in possible compensation errors between the distribution parameter and drift velocity in the model validation process. The independent validation of the constitutive equations for the distribution parameter and drift velocity has been challenging due to experimental difficulty in measuring detailed two-phase flow structures in rod bundles. The present study proposes an approximation methodology to obtain subchannel average two-phase flow parameters using local two-phase flow data measured at two local points: the subchannel center and minimum gap center in a rod bundle. The distributions of subchannel average two-phase flow parameters are invaluable in benchmarking subchannel analysis codes. Comprehensive subchannel average void fraction and gas velocity mappings are given to discuss the effects of gas and liquid velocities, pressure, spacer grid, and developing length on the two-phase flow characteristics in the rod bundle. The bundle-average distribution parameter values calculated by subchannel average two-phase flow parameters are used for independent validation of the constitutive equations of the distribution parameter. The bundle-average drift velocity values back-calculated using the distribution parameter values are also used for independent validation of the constitutive equation of the drift velocity.

Correlated Product Distributions in the Photodissociation of à State NO-CH4 and NO-N2 van der Waals Complexes.

This paper reports correlated product distributions for dissociation of the van der Waals complexes NO-CH4 and NO-N2 on their à state surfaces, providing detailed data sets against which calculations can be benchmarked. NO-CH4 dissociation strongly favors small changes in the CH4 angular momentum, with ΔJ = 0 and 1 providing the bulk of the products. Conversely, the associated NO products show little constraint in terms of the rotational angular momentum transfer, with the full range of energetically accessible angular momentum states populated, although the distributions show minima. The lack of angular momentum transfer to methane accompanied by broad, structured, angular momentum transfer to NO gives the NO-CH4 dissociation some qualitative similarities to NO-Rg complex dissociation. In contrast, for NO-N2, the cluster of highest probability products corresponds to high N2 angular momentum and low NO angular momentum, with a sharp drop in the probability for populating the highest energetically accessible J states. For both the NO and N2 products, there appears to be a constraint limiting angular momentum transfer at the highest energetically accessible rotational states. Both complexes show product distributions that include a component attributed to excitation from warm complexes, which provides insight into their internal energies. Interestingly, for NO-N2, the 44,475 cm-1 photolysis translational energy release distribution for N = 8 extends to energies beyond those accessible from the highest bound X̃ states. This indicates either that there are long-lived (>100 μs) states above the X̃ state binding energy or that there is another mechanism that also contributes to this distribution.

On turbulence and interfacial momentum transfer in dispersed gas-liquid flows: Contribution of bubbly flow experiments under microgravity conditions

The major focus of the present work is to develop an adequate closure model for the turbulent contribution of the interfacial momentum transfer term in turbulent bubbly flow. For this purpose, numerical simulations have been conducted on bubbly pipe flows under microgravity conditions. With no buoyancy effect, the average interfacial forces are negligible due to the small interphase relative motion. In these conditions, the distribution and the dynamics of bubbles are mainly controlled by the turbulence effects. Based on a phenomenological approach, a new closure for the turbulent interfacial momentum transfer is developed within Eulerian two-fluid modelling based on the averaging of the added mass force. The turbulent terms thus obtained comprises a non-linear term and a convective acceleration term associated with the drift velocity. The two-fluid model with the proposed interfacial momentum transfer closure and an original three-equation turbulence model for bubbly flows has been implemented in a 3D CFD code and applied to pipe bubbly flow under microgravity conditions. When compared to conventional two-fluid closures, the turbulent contribution of the added mass force proved to be a relevant closure that provides a substantial improvement in predicting the void fraction distribution and the bubbles’ dynamics.

All-regime two-phase flow modeling using a novel four-field large interface simulation approach

Two-phase flows may occur in many regimes, ranging from dispersed flow, slug or plug flow to stratified flow. To capture all those regimes with a monolithic approach, a so-called all-regime two-phase model should be developed. This paper presents such an all-regime two-phase modeling approach called Four-Field Large Interface Simulation (FF-LIS), in which we consistently consider two phases (gas and liquid) which can both be either resolved or sub-grid, resulting in four fields. The efficacy of this approach hinges on the accuracy with which the inter-scale mass, momentum and energy transfer terms between dispersed and resolved regimes are captured. In this paper, we introduce three phenomenological mechanisms to control the inter-scale transfer: absorption, break-up and coalescence. The separation of multiphase scales allows for the explicit modeling of transfer between them, whereas other methods often rely on an algebraic regime map in which transfer between scales is accounted for implicitly. We apply FF-LIS to the simulation of both bubbly and fully resolved single bubble flow, as a way of validating FF-LIS in those two two-phase limits. Next, the transfer terms are illustrated by simulation of bubbles rising in a column. As the bubble concentration increases, it is shown that a transfer from sub-grid to resolved occurs. Finally, we apply FF-LIS to the simulation of two-phase horizontal pipe flow in which the several flow regimes, depending on the superficial velocities, are recovered, and to the simulation of a plunging jet in which FF-LIS is shown to produce an entrained bubble plume. FF-LIS presents a computational platform for faithful two-phase resolved and sub-grid simulation of relevant real-world two-phase problems, and allows two-phase modelers for the explicit control on what can be resolved, and what should be sub-grid.

Electromagnetic form factors of the Ω− baryon in the spacelike and timelike regions

We present complete calculations of the electromagnetic form factors of the $\Omega^-$ in the spacelike region and in the timelike region. The four elastic form factors: electric charge ($G_{E0}$), magnetic dipole ($G_{M1}$), electric quadrupole ($G_{E2}$) and magnetic octupole ($G_{M3}$), are estimated within the covariant spectator quark model, in terms of the square momentum transfer $q^2$. The free parameters of the $\Omega^-$ wave function, including a $S$-wave state and two independent $D$-wave states radial wave functions and the admixture coefficients are fixed by the comparison with the lattice QCD data in the spacelike region ($Q^2=-q^2 \le 0$) and with the recent $e^+ e^- \to \Omega^- \bar \Omega^+$ data from CLEO in the timelike region ($q^2 > 0$). The estimates in the timelike region for square momentum transfer $q^2 \ge 4 M_\Omega^2$ are based on large-$q^2$ asymptotic relations ($M_\Omega$ is the $\Omega^-$ mass). We examine also the impact of the large-$Q^2$ correlations between different form factors and analyze the possible solutions. The electric quadrupole and the magnetic octupole moments of the $\Omega^-$, and the $e^+ e^- \to \Omega^- \bar \Omega^+$ integrated cross sections for very large $q^2$ are estimated based on the model results.

Development of a novel two-phase flow solver for nuclear reactor analysis: algorithms, verification and implementation in OpenFOAM

A porous medium-based representation of nuclear reactors and complex engineering systems more in general can significantly reduce simulation and modelling costs, while preserving a reasonable degree of accuracy via regime map-based correlations for modelling physical interactions. This paper presents a segregated algorithm for the simulation of dispersed two phase flows in such systems treated as porous media in an Eulerian framework. The global algorithm pertaining to the coupling between the mass, momentum and energy conservation equations solution is discussed and implemented via the finite volume OpenFOAM programming library. In the context of pressure–velocity coupling, a novel implementation of the Partial Elimination Algorithm for the treatment of the inter-phase momentum transfer term is developed. It is found to perform better than existing implementations for a number of cases with important momentum coupling between phases. A conclusive verification of the overall solution algorithm is performed with the Method of Manufactured Solutions and order-of-accuracy testing. From an implementation perspective, the performance of the algorithm in parallel strong scaling up to 4096 cores is assessed and proves to be in line with OpenFOAM-based code standards.

Drift-flux parameter modeling of vertical downward gas–liquid two-phase flows for interfacial drag force formulation

The two-fluid model has been adopted as a platform of nuclear thermal–hydraulic system analysis code because it can treat the mechanical and thermal non-equilibrium between phases through the interfacial transfer terms. Precise modeling of the area-averaged interfacial drag force in the interfacial momentum transfer term is essential in predicting void fraction accurately. The drift-flux parameters, such as the distribution parameter and drift velocity, play an essential role in formulating the area-averaged interfacial drag force. This study aims at developing a drift-flux correlation with a wide application range for vertical downward two-phase flows. First, over 1200 experimental void fraction data of vertical downward two-phase flows were collected from 13 sources. Then, the existing correlations of the distribution parameter and drift velocity were reviewed and examined. Finally, a new drift-flux correlation was developed based on a large amount of experimental data and state-of-the-art knowledge of two-phase flow behaviors. The comparison between the experimental and calculated void fractions by the newly-developed correlation demonstrated that the new correlation could achieve superior performance to the existing correlations. More than 93% of the predicted void fractions were predicted within ± 20% error with the mean relative deviation and mean absolute relative deviation of 0.609% and 9.93%, respectively.

Shoaling Waves Interacting with an Orthogonal Current

In the present work, an experimental investigation on the hydrodynamics of shoaling waves superposed on a steady orthogonal current is carried out. An experimental campaign in a wave tank has been performed, with waves and current interacting at a right angle over a sloping planar beach. Velocity data have been gathered during the experiments in order to investigate mean, phase and turbulent flow. A detailed preliminary analysis of the time- and space-variability of the experiments is presented. Results show that a complex interaction between waves and current occurs as the wave shoals, in terms of sheer production, momentum transfer and turbulent mixing. Superposition of waves determines a shear increase at the bottom due to an enhanced turbulence mixing, nonetheless as depth decreases and the current velocity consequently increases, shoaling waves may be less efficient in enhancing shear at the bottom. Moreover, the superposition of waves determines the current to oscillate around its mean velocity value. Nevertheless, as wave shoals and simultaneously current velocity increases with decreasing depth, waves and current oscillatory motion experience a phase lag, as a response of the larger momentum of the current to the changing of the shoaling waves acceleration distribution along the wave phase. Moreover, the turbulent bursting events of the combined flow in proximity of the bed have been investigated by means of quadrant analysis, showing an increase of the turbulent ejections and sweeps due to the superposition of the shoaling waves.

Effect of interfacial drag force model on code prediction for upward adiabatic two-phase bubbly flow in vertical channels

Accurate modeling of the interfacial drag force is one of the keys to predicting thermo-fluid parameters using one-dimensional nuclear thermal-hydraulic system analysis code architected through the two-fluid model. The interfacial drag force appears in the interfacial momentum transfer term and governs the velocity slip or the relative velocity between gas and liquid phases. The most straightforward method to model the interfacial drag force is to model the force through the drag law (drag law approach). A drag coefficient and interfacial area concentration should be given to close the interfacial drag force model. Among them, the modeling of the interfacial area concentration has been one of the weakest links in the interfacial drag force modeling due to the lack of reliable data covering a wide test condition including prototypic nuclear reactor conditions and lack of physically sound interfacial area model. To avoid a considerable uncertainty in the prediction of the interfacial area concentration, Andersen and Chu (1982) proposed the interfacial drag force model using the drift-flux parameters (Andersen approach). The Andersen approach is practical for the simulation of a slow transient flow and a steady flow. Major system analysis codes such as USNRC TRACE have adopted the Andersen approach in the interfacial drag force modeling. Some attempts to improve the code performance have been considered using the drag law approach with the interfacial area transport equation. The dynamic modeling of the interfacial area concentration has the potential to improve the prediction accuracy of the interfacial area concentration in a transient flow and developing flow. Due to the importance of the improved interfacial drag force modeling, the implementation and evaluation of the interfacial area transport equation in USNRC TRACE code has been performed by Talley et al. (2011, 2013). The study claimed that the introduction of the interfacial area transport equation into the TRACE code improved the code performance in an adiabatic bubbly flow analysis significantly. The present study assessed the code calculation made by Talley et al. (2011) and identified several issues in the code calculation results. The present study analytically demonstrated that the drag law approach became identical with the Andersen approach for the distorted particle regime (or a major bubble shape regime in bubbly flow) due to the balancing-out of the interfacial area concentration (or bubble size) in the numerator and denominator of the interfacial drag force formulation. The code calculation using TRAC code endorsed the analytical assessment of the insignificant or no merit of the interfacial area transport equation in the code performance of the adiabatic bubbly flow analysis. The present study also pointed out the inconsistency of the code calculation made by Talley et al. (2011).

Comparison of the experimental and numerical analyses of silver nanofluid under influence of strong magnetic field

Purpose Nanofluids’ properties made them interesting for various areas like engineering, medicine or cosmetology. Discussed here, research pertains to specific problem of heat transfer enhancement with application of the magnetic field. The main idea was to transfer high heat rates with utilization of nanofluids including metallic non-ferrous particles. The expectation was based on changed nanofluid properties. However, the results of experimental analysis did not meet it. The heat transfer effect was smaller than in the case of base fluid. The only way to understand the process was to involve the computational fluid dynamics, which could help to clarify this issue. The purpose of this research is deep understanding of the external magnetic field effect on the nanofluids heat transfer. Design/methodology/approach In presented experimental and numerical studies, the water and silver nanofluids were considered. From the numerical point of view, three approaches to model the nanofluid in the strong magnetic field were used: single-phase Euler, Euler–Euler and Euler–Lagrange. In two-phase approach, the momentum transfer equations for individual phases were coupled through the interphase momentum transfer term expressing the volume force exerted by one phase on the second one. Findings Therefore, the results of numerical simulation predicted decrease of convection heat transfer for nanofluid with respect to pure water, which agreed with the experimental results. The experimental and numerical results are in good agreement with each other, which confirms the right choice of two-phase approach in analysis of nanofluid thermo-magnetic convection. Originality/value The Euler–Lagrange exhibit the best matching with the experimental results.

Single ionization of helium by fast proton impact in different kinematical regimes

We present ultrahigh-resolution data on fully differential cross sections for single ionization of helium induced by 1 MeV proton impact. In the present work we explore a different regime of kinematic conditions in terms of momentum transfer and electron energies than previously published data. These data are compared with different theoretical calculations. Reasonable agreement between the first Born approximation and experiment is obtained in the kinematic regime close to the Bethe ridge. Far from this region the calculated binary peak is shifted with respect to experiment. In order to resolve this problem, we analyze several theoretical mechanisms beyond the customary first Born approximation theory. These mechanisms include the 3C model (three Coulomb functions), effective charges, off-shell pair $T$ matrices instead of pair potentials, and semiclassical postcollision interaction. We find that a combination of the 3C model with a semiclassical postcollision interaction effect may explain the observed discrepancy.

Performance analysis and quantitative design of a flow‐guiding sieve tray by computational fluid dynamics

AbstractAn evolution of the traditional sieve tray, the flow‐guiding sieve tray (FGST), has been utilized in many separation processes, especially for handling viscous systems. The objectives of this work are to optimize the design process of FGSTs and realize the full potential of their separation performance. A computation fluid dynamic (CFD) model that incorporated the modified interphase momentum transfer term was developed. Simulated measures of hydrodynamic performance, such as pressure drop, weeping, entrainment, and clear liquid height agree well with the experimental data, thus verifying the accuracy and reliability of the CFD model established in this work. Furthermore, based on the obtained hydrodynamic parameters, a quantitative model for designing flow‐guiding holes was established and validated by modifying an experimental FGST (diameter 476 mm) and reconstructing an industrial sieve‐tray tower (diameter 1,200 mm). The hydrodynamic parameters and quantitative model are of vital importance for better design and further modification of FGST.

Large eddy simulations of the turbulent flows of twin parallel jets

Turbulent jet interactions play a significant role in terms of momentum and heat transfer. For example, in next generation nuclear reactors, high temperature flow mixing in the lower plenum and mixing fluctuations in the coolant may influence power oscillations. Thus, the estimation of the mixing condition needs to be accurate. Recent benchmark experiments using particle image velocimetry (PIV) technique provided high-fidelity experimental data that could be used in comparative studies. In the present study, large eddy simulation (LES) numerical methodology is used on a parallel jet system and validated with benchmark PIV experiments. The results indicate good agreement in terms of the merging point and time averaged velocity profile. Spectral analyses via Welch’s power spectral density functions are used to analyze frequency information in turbulence jets. The proper orthogonal decomposition (POD) analysis method is applied using a snapshot method. The POD analysis indicates vortex structures similar to those in the benchmark PIV experiment.

CFD simulation of sieve-fixed valve tray hydrodynamics

In this work, the sieve-fixed valve (SFV) tray was designed by adding flow-guiding and sieve holes on the valve caps of the original trapezoid valve (OTV). A computational fluid dynamics (CFD) model of three-dimensional two-phase flow was developed to describe the flow structure of SFV tray. Based on the experimental clear liquid height, the modified correlation of Bennett was adopted for liquid–gas interaction and the ga–liquid momentum transfer term MGL was also obtained. To demonstrate the function of flow-guiding hole and sieve hole, the hydrodynamics of the OTV and SFV trays including pressure drop, weeping, entrainment and clear liquid height were experimented and compared. What’s more, local information such as velocity profile and flow field around the valves were simulated. CFD results showed that the new valve tray with flow-guiding holes was capable of promoting liquid flow and homogenizing liquid flow. This study proved that CFD research can test modification of devices, and provide information which could not be obtained by experiment. The CFD method tends to be a necessary part for designing and modifying new distillation internals.

A generic framework for multi-field two-phase flow based on the two-fluid model

Multiphase computational fluid dynamics (MCFD) simulation based on the two-fluid model has emerged as a valuable tool for a wide range of engineering applications. The classical two-field, two-fluid model treats each phase as a whole, which may introduce considerable uncertainties when a phase is comprised of significantly different forms, e.g., liquid droplets and liquid film, and/or vapor bubbles and continuous vapor core. This uncertainty becomes particularly important for resolving the multi-dimensional distribution of different fields in CFD applications. In relation to this, a multi-field model is necessary to mechanistically model a wide range of two-phase flow regimes. In this paper, a generic and rigorous multi-field two-fluid framework is derived based on the local instant formulation of the mass, momentum and energy conservation equations for single-phase fluids. The averaged field conservation equations and interfacial jump conditions are obtained from the local instantaneous formulation through a derivation with minimal assumptions. Based on this framework, a six-field two-fluid model is proposed as a practical model for typical two-phase flows in industrial systems, in which the flow regimes may span from bubbly to annular. These six fields include: continuous liquid, two dispersed liquid fields, continuous gas, and two dispersed gas fields. The field boundaries and different types of closure relations required to close the model are briefly discussed. The relationship between the momentum transfer terms in the Eulerian two-fluid model and the particle forces have been established by introducing a statistical averaging and the equation of motion for a single particle.

New Method of Rigorous Modeling and CFD Simulation for Methanol—Steam Reforming in Packed-Bed Reactors

A comprehensive dynamic mathematical model was developed to analyze methanol−steam reforming in catalytic packed-bed reactor. The contributions of all molecular and convective terms of momentum, heat, and mass transfer were taken into consideration, with the inclusion of effectiveness factor. Effects of two predominant parameters: particle size and the wall heat flux on the reactor performance for the methanol−steam reforming were examined. It was revealed that by increasing the average particle size from 700 to 3200 µm, which corresponded to porosity values of 0.4 and 0.6, the effectiveness factor decreased by nearly 80% and subsequently the overall methanol conversion decreased by around 74%. Besides, through a set of organized simulation runs, it was discovered that with increasing the dimensionless wall heat flux from 0 to 0.2 Wm−1 K−1, the methanol conversion was enhanced by 87%.

Model predictions for the wide-angle x-ray scatter signals of healthy and malignant breast duct biopsies.

Wide-angle x-ray scatter (WAXS) could potentially be used to diagnose ductal carcinoma in situ (DCIS) in breast biopsies. The regions of interest were assumed to consist of fibroglandular tissue and epithelial cells and the model assumed that biopsies with DCIS would have a higher concentration of the latter. The scattered number of photons from a 2-mm diameter column of tissue was simulated using a 110-kV beam and selectively added in terms of momentum transfer. For a 1-min exposure, specificities and sensitivities of unity were obtained for biopsies 2- to 20-mm thick. The impact of sample and tumor cell layer thicknesses was studied. For example, a biopsy erroneously estimated to be 8mm would be correctly diagnosed if its actual thickness was between 7.3 and 8.7mm. An 8-mm thick malignant biopsy can be correctly diagnosed provided the malignant cell layer thickness is [Formula: see text]. WAXS methods could become a diagnostic tool for DCIS within breast biopsies.

Numerical simulations of drop size evolution in a horizontal pipeline

A population balance model using a standard method of moments (S−γ) in an Eulerian–Eulerian framework has been used for oil and brine two-phase flow simulations in pipelines. Results have been compared to both numerical and experimental data from the literature. The effects of the forces constituting the momentum transfer term at the interphase between droplets and the continuous phase (drag, lift, turbulent dispersion and virtual mass), turbulence modelling, break-up and coalescence parameters are analysed; they are shown to be important for droplet mean diameter evolution. It has been demonstrated that a correct combination of models and parameters improves (47% for the best case) simulated results when compared to experimental data. Interactions between the different components of the whole model are discussed and their corresponding effects on the droplet diameter predictions are explained. In particular, the addition of the lift force tends to push the droplet toward the walls of the computational domain where turbulence and shear stress are the strongest, therefore leading to an increased break-up rate. Based on the findings of this study, recommendations for further population balance-based modelling with a standard method of moments are provided.

Multiple Size Group Modeling of Polydispersed Bubbly Flow in the Mold: An Analysis of Turbulence and Interfacial Force Models

An inhomogeneous Multiple Size Group (MUSIG) model based on the Eulerian–Eulerian approach has been developed to describe the polydispersed bubbly flow inside the continuous-casting mold. A laboratory scale mold has been simulated using four different turbulence closure models (modified k − ɛ, RNG k − ɛ, k − ω, and SST) with the purpose of critically comparing their predictions of bubble Sauter mean diameter distribution with previous experimental data. Furthermore, the influences of all the interfacial momentum transfer terms including drag force, lift force, virtual mass force, wall lubrication force, and turbulent dispersion force are investigated. The breakup and coalescence effects of the bubbles are modeled according to the bubble breakup by the impact of turbulent eddies while for bubble coalescence by the random collisions driven by turbulence and wake entrainment. It has been found that the modified k − ɛ model shows better agreement than other models in predicting the bubble Sauter mean diameter profiles. Further, simulations have also been performed to understand the sensitivity of different interfacial forces. The appropriate drag force coefficient, lift force coefficient, virtual mass force coefficient, and turbulent dispersion force coefficient are chosen in accordance with measurements of water model experiments. However, the wall lubrication force does not have much effect on the current polydispersed bubbly flow system. Finally, the MUSIG model is then used to estimate the argon bubble diameter in the molten steel of the mold. The argon bubble Sauter mean diameter generated in molten steel is predicted to be larger than air bubbles in water for the similar conditions.

Numerical prediction of dispersed turbulent liquid–solid flows in vertical pipes

ABSTRACTA mathematical model for the simulation of dispersed turbulent liquid–solid flows in vertical pipes is presented. The model is based on the Eulerian–Eulerian approach and solves the averaged mass and momentum conservation equations for both phases, coupled by means of interfacial momentum transfer terms. Its distinctive feature is the modelling of interphase friction and turbulence modulation. In particular, specific source terms which generalize some existing correlations originally developed for gas–solid flows are introduced in the conservation equations for the turbulent kinetic energy of the fluid and its dissipation rate to account for turbulence modulation. By comparison with experimental data available in the literature for different flow conditions, the model revealed that it is capable of reproducing the main features of the flow. Moreover, it proved capable of predicting the effect of particle size on turbulence modulation in liquid–solid flows.