Kinematic stability and simulations of the variational two-fluid model for slug flow

The two-fluid short-wave theory (TF-SWT) mode of the one-dimensional two-fluid model (TFM) [A. Clausse and M. Lopez de Bertodano, "Natural modes of the two-fluid model of two-phase flow,"Phys. Fluids 33, 033324 (2021)] showed that the incompressible kinematic and Kelvin-Helmholtz instabilities are the source of the long-standing ill-posed question. Here, the stability of the short wave mode is analyzed to obtain an unstable incompressible well-posed TFM for vertical slug flow, where inertial coupling and drag play the key role. Then, a computational method is implemented to perform non-linear simulations of slug waves. Linear stability analyses, i.e., characteristics and dispersion, of a variational TF-SWT for vertical slug flows are presented. The current TFM is constituted with a lumped-parameter model of inertial coupling between the Taylor bubble and the liquid. A characteristic analysis shows that this conservative model is parabolic, and it provides a base upon which other models can be constructed, including short-wave damping mechanisms, like vortex dynamics. The dispersion analysis shows that depending on the interfacial drag, the problem can be kinematic unstable. A new kinematic condition in terms of the inertial coupling and the interfacial drag is derived that is consistent with previous theoretical and experimental results. The material waves, which are predicted by linear stability theory, then develop into nonlinear slug waveforms that are captured by the numerical simulations. These and the horizontal stratified flow waves of previous research illustrate the TFM capability to model interfacial structures that behave like waves. Otherwise, when the physics of the TF-SWT waves is ignored, the model is ill-posed.Fil: Clausse, Alejandro. Comisión Nacional de Energía Atómica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; Argentina. Pontificia Universidad Católica Argentina "Santa María de los Buenos Aires"; ArgentinaFil: Chetty, K.. Purdue University. School Of Nuclear Engineering; Estados UnidosFil: Buchanan, J.. Naval Nuclear Laboratory; Estados UnidosFil: Ram, R.. Purdue University. School Of Nuclear Engineering; Estados UnidosFil: Lopez de Bertodano, M.. Purdue University. School Of Nuclear Engineering; Estados Unido

Chaos in wavy-stratified fluid-fluid flow

We perform a nonlinear analysis of a fluid-fluid wavy-stratified flow using a simplified two-fluid model (TFM), i.e., the fixed-flux model (FFM), which is an adaptation of the shallow water theory for the two-layer problem. Linear analysis using the perturbation method illustrates the short-wave physics leading to the Kelvin-Helmholtz instability (KHI). The interface dynamics are chaotic, and analysis beyond the onset of instability is required to understand the nonlinear evolution of waves. The two-equation FFM solver based on a higher-order spatiotemporal finite difference scheme is used in the current simulations. The solution methodology is verified, and the results are compared with the measurements from a laboratory-scale experiment. The finite-time Lyapunov exponent (FTLE) based on simulations is comparable and slightly higher than the autocorrelation function decay rate, consistent with previous findings. Furthermore, the FTLE is observed to be a strong function of the angle of inclination, while the root mean square of the interface height exhibits a square-root dependence. It is demonstrated that this simple 1-D FFM captures the essential chaotic features of the interface dynamics. This study also adds to a growing body of work indicating that a TFM with appropriate short wavelength physics is well-behaved and chaotic beyond the KHI.Fil: Vaidheeswaran, Avinash. National Energy Technology Laboratory; Estados Unidos. West Virginia University Research Corporation; Estados UnidosFil: Clausse, Alejandro. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Grupo de Plasmas Densos Magnetizados. Provincia de Buenos Aires. Gobernación. Comision de Investigaciones Científicas. Grupo de Plasmas Densos Magnetizados; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; ArgentinaFil: Fullmer, William D.. National Energy Technology Laboratory; Estados Unidos. Leidos; Estados UnidosFil: Marino, Raúl. Universidad Nacional de Cuyo. Facultad de Ciencias Exactas y Naturales; ArgentinaFil: López de Bertodano, Martín. Purdue University. School Of Nuclear Engineering; Estados Unido

Coleccion de los tratados de paz, alianza, neutralidad, garantia ... hechos por los pueblos, reyes y principes de España con los pueblos, reyes, principes, republicas y demás potencias de Europa... : desde antes del establecimiento de la monarchia gothica hasta el feliz reynado del Rey N.S.D. Fernando VI...

ct03

Multiphase turbulence in bubbly flows: RANS simulations

The ability of a two-fluid Eulerian–Eulerian computational multiphase fluid dynamic model to predict bubbly air–water flows is studied. Upward and downward pipe flows are considered and a database of 19 experiments from 6 different literature sources is used to assess the accuracy of the model, with the aim of evaluating our ability to predict these kinds of flows and to contribute to ongoing efforts to develop more advanced simulation tools. The particular focus in the work described is on the prediction of multiphase turbulence due to its relevance in the modelling of bubbly flows in general, including bubble coalescence and break-up, and boiling at a wall. Overall, a satisfactory accuracy is obtained in the prediction of liquid velocities and void fraction distributions in all conditions, including upward and downward flows, and wall-peaked and core-peaked void profiles, when values of the bubble diameter are specified from experimental data. Due to its importance for the correct prediction of the turbulence level in these flows, a bubble-induced turbulence model is introduced, starting from an existing formulation. Source terms due to drag are included in the turbulence kinetic energy and the turbulence energy dissipation rate equations of the k-ε turbulence model, and optimisation of the turbulence source gives velocity fluctuation predictions in agreement with data. After comparisons with data, improvement in the predictions of other turbulence models is also demonstrated, with a Reynolds stress formulation based on the SSG (Speziale et al., 1991) pressure–strain model and the same bubble-induced turbulence model accurately predicting the two-phase flows and the anisotropy of the turbulence field. The same database is also exploited to evaluate different drag models and the advantages of including the effect of the bubble aspect ratio. Following experimental evidence, the model of Tomiyama et al. (2002) is used which assumes that the bubble shape is closer to spherical near a wall and employs a correlation to calculate the aspect ratio. An increase in the drag coefficient due to the higher aspect ratio increases the accuracy of calculated velocity profiles in the near-wall region, even if additional validation is still required due to the possible loss of accuracy in the pipe centre

Numerical and experimental investigations for insulation particle transport phenomena in water flow

The investigation of insulation debris generation, transport and sedimentation becomes more important with regard to reactor safety research for pressurized and boiling water reactors, when considering the long-term behaviour of emergency core coolant systems during all types of loss of coolant accidents (LOCA). The insulation debris released near the break during a LOCA incident consists of a mixture of a disparate particle population that varies with size, shape, consistency and other properties. Some fractions of the released insulation debris can be transported into the reactor sump, where it may perturb or impinge on the emergency core cooling systems. Open questions of generic interest are for example the particle load on strainers and corresponding pressure-drop, the sedimentation of the insulation debris in a water pool, its possible re-suspension and transport in the sump water flow. A joint research project on such questions is being performed in cooperation with the University of Applied Science Zittau/Görlitz and the Forschungszentrum Dresden-Rossendorf. The project deals with the experimental investigation and the development of computational fluid dynamic (CFD) models for the description of particle transport phenomena in coolant flow. While the experiments are performed at the University Zittau/Görlitz, the theoretical work is concentrated at Forschungszentrum Dresden-Rossendorf. In the present paper, the basic concepts for computational fluid dynamic (CFD) modelling are described and experimental results are presented. Further experiments are designed and feasibility studies were performed

Influence of multiphase turbulence modelling on interfacial momentum transfer in two-fluid Eulerian-Eulerian CFD models of bubbly flows

Eulerian-Eulerian two-fluid computational fluid dynamic (CFD) models are increasingly used to predict bubbly flows at an industrial scale. In these approaches, interface transfer is modelled with closure models and correlations. Normally, the lateral void fraction distribution is considered to mainly result from a balance between the lift and wall lubrication forces. However, and despite the numerous models available that achieve, at least in pipe flows, a reasonable predictive accuracy, agreement on a broadly applicable and accurate modelling approach has not yet been reached. Additionally, the impact of turbulence modelling on the lateral void fraction distribution has not, in general, been examined in detail. In this work, an elliptic blending Reynolds stress model (EB-RSM), capable of resolving the turbulence field in the near-wall region and improved to account for the contribution of bubble-induced turbulence, is evaluated against best-practice k-ε and high-Reynolds second-moment turbulence closures. Lift and wall lubrication forces are initially deliberately neglected in the EB-RSM. Comparisons for flows in pipes and a square duct show that the EB-RSM reproduces the lateral void fraction distribution, including the peak in the void fraction in the near-wall region, and reaches an accuracy comparable to the other two models noted above. In rod bundles, even if none of the models considered performs with sufficient accuracy, the EB-RSM detects features of the flow that are not predicted by the other two approaches. Overall, the results demonstrate a much more prominent role of the turbulence structure and the induced cross-sectional pressure field on the lateral void fraction distribution than is normally considered. These effects need to be accounted for if more physically-consistent modelling of bubbly flows is to be achieved. The lift force is added to the EB-RSM in the final part of the paper, to provide a two-fluid formulation that can be used as the basis for additional developments aimed at improving the accuracy and general applicability of two-fluid CFD models

RANS simulation of bubble coalescence and break-up in bubbly two-phase flows

In bubbly flows, the bubble size distribution dictates the interfacial area available for the interphase transfer processes and, therefore, understanding the behaviour and the average features of the bubble population is crucial for the prediction of these kinds of flows. In this work, by means of the STAR-CCM+ code, the Sγ population balance model is coupled with an Eulerian–Eulerian two-fluid approach and tested against data on upward bubbly pipe flows. The Sγ model, based on the moments of the bubble size distribution, tracks the evolution of the bubble sizes due to bubble break-up and bubble coalescence. Good accuracy for the average bubble diameter, the velocity and the void fraction radial profiles is achieved with a modified coalescence source. Numerical results show that better predictions are obtained when these flows are considered to be coalescence dominated, but, nevertheless, additional knowledge is required to progress in the development of coalescence and break-up models that include all the possible responsible mechanisms. In this regard, there is a requirement for experimental data that will allow validation of both the predicted bubble diameter distribution and the intensity of the turbulence in the continuous phase which has a significant impact on coalescence and break-up models. An advanced version of the model, that includes a Reynolds stress turbulence formulation and two groups of bubbles to account for the opposite behaviour of spherical bubbles, which accumulate close to the pipe wall, and cap bubbles, that migrate towards the pipe centre, is proposed. The Reynolds stress model is found to better handle the interactions between the turbulence and the interphase forces, and the use of only two bubble groups seems sufficient to describe the whole bubble spectrum and the bubbly flow regime up to the transition to slug flow

Measurement of air distribution and void fraction of an upwards air-water flow using electrical resistance tomography and a wire-mesh sensor

Measurements on an upwards air-water flow are reported that were obtained simultaneously with a dual-plane electrical resistance tomograph (ERT) and a wire-mesh sensor (WMS). The ultimate measurement target of both ERT and WMS is the same, the electrical conductivity of the medium. The ERT is a non-intrusive device whereas the WMS requires a net of wires that physically crosses the flow. This paper presents comparisons between the results obtained simultaneously from the ERT and the WMS for evaluation and calibration of the ERT. The length of the vertical testing pipeline section is 3 m with an internal diameter of 50 mm. Two distinct sets of air-water flow rate scenarios, bubble and slug regimes, were produced in the experiments. The fast impedance camera ERT recorded the data at an approximate time resolution of 896 frames per second (fps) per plane in contrast with the 1024 fps of the wire-mesh sensor WMS200. The set-up of the experiment was based on well established knowledge of air-water upwards flow, particularly the specific flow regimes and wall peak effects. The local air void fraction profiles and the overall air void fraction were produced from two systems to establish consistency for comparison of the data accuracy. Conventional bulk flow measurements in air mass and electromagnetic flow metering, as well as pressure and temperature, were employed, which brought the necessary calibration to the flow measurements. The results show that the profiles generated from the two systems have a certain level of inconsistency, particularly in a wall peak and a core peak from the ERT and WMS respectively, whereas the two tomography instruments achieve good agreement on the overall air void fraction for bubble flow. For slug flow, when the void fraction is over 30%, the ERT underestimates the void fraction, but a linear relation between ERT and WMS is still observed

A CFD-DEM solver to model bubbly flow. Part I: Model development and assessment in upward vertical pipes

[EN] In the computational modeling of two-phase flow, many uncertainties are usually faced in simulations and validations with experiments. This has traditionally made it difficult to provide a general method to predict the two-phase flow characteristics for any geometry and condition, even for bubbly flow regimes. Thus, we focus our research on studying in depth the bubbly flow modeling and validation from a critical point of view. The conditions are intentionally limited to scenarios where coalescence and breakup can be neglected, to concentrate on the study of bubble dynamics and its interaction with the main fluid. This study required the development of a solver for bubbly flow with higher resolution level than TFM and a new methodology to obtain the data from the simulation. Part I shows the development of a solver based on the CFD-DEM formulation. The motion of each bubble is computed individually with this solver and aspects as inhomogeneity, nonlinearity of the interfacial forces, bubble-wall interactions and turbulence effects in interfacial forces are taken into account. To develop the solver, several features that are not usually required for traditional CFD-DEM simulations but are relevant for bubbly flow in pipes, have been included. Models for the assignment of void fraction into the grid, seeding of bubbles at the inlet, pressure change influence on the bubble size and turbulence effects on both phases have been assessed and compared with experiments for an upward vertical pipe scenario. Finally, the bubble path for bubbles of different size have been investigated and the interfacial forces analyzed. (C) 2017 Elsevier Ltd. All rights reserved.The authors sincerely thank the ''Plan Nacional de I + D+ i" for funding the project MODEXFLAT ENE2013-48565-C2-1-P and ENE2013-48565-C2-2-P.Peña-Monferrer, C.; Monrós Andreu, G.; Chiva Vicent, S.; Martinez-Cuenca, R.; Muñoz-Cobo, JL. (2018). A CFD-DEM solver to model bubbly flow. Part I: Model development and assessment in upward vertical pipes. Chemical Engineering Science. 176:524-545. https://doi.org/10.1016/j.ces.2017.11.005S52454517