Multiphase Flow Code Research Articles

Development of parameter-free, two-fluid, viscous multiphase flow solver for cough-droplet simulations

Multiphase flows arise in various fields that involve complicated phenomena. Studies have shown that COVID-19 can occur via air microdroplets, and breathing jets with microdroplets turn into turbulent cloud or puffs in cases of coughing and sneezing (Bourouiba et al., 2014). Microdroplets are upturned by buoyancy in the turbulent cloud and transported without falling. Furthermore, they float in air for hours and can be transported over long distances (Mittal et al., 2020). This scenario also involves a mixed phase flow of air and droplets. To simulate these phenomena, a numerical model assuming mechanical and thermal non-equilibrium multiphase flow is required to predict the range of turbulent cloud transport. In this study, to better simulate the turbulent cloud trajectories, a viscosity term is added to a two-phase flow six-equation model (two-fluid modeling or effective-fluid modeling, EFM) developed by Liou et al. (2008). It is a development of a parameter-free, viscous multiphase flow code, based on a single-phase compressible finite-volume solver (Kitamura et al., 2013). This solver is validated in the Poiseuille flow and laminar-flat-plate problem with an isothermal wall through a comparison with the analytical solutions. A detailed simulation of coughing is performed. The location of the turbulent cloud upturned by buoyancy is compared with the data of past studies.

A corotational finite element approach coupled to a discrete forcing method to solve hyperelastic deformation induced by two-phase flow

Fluid–structure interaction is an ever occurring phenomenon in engineering. In power plants for instance, fuel rods, tubes in steam generator or cooling towers may deform under the extreme load caused by the fluid flowing around them. It may also be valuable to study this kind of interaction during pipelines installation or for wind generating structures. If the deformation is sufficiently important as to influence the fluid behaviour, the problem must be tackled as a whole. Therefore, fluids and structures cannot be processed separately. In this work, a fluid–structure interaction method taking into account the large deformation of simple geometry is developed in neptune_cfd, a 3D multiphase flow code based on Eulerian–Eulerian approach with a single pressure. The solid structures are geometrically non-linear elastic beams in plane strain. The coupling interface is tracked with a discrete forcing method based on a time and space dependent porosity method. The latter is updated several times for each time steps in order to ensure convergence.The present formulation is checked on a semi-analytical problem and validated for a dam break over a flexible plate with experimental confrontation and comparison.

On water-ingression during top-flooding of corium melts

In the course of severe accident in a nuclear power plant, the corium mixture may flow down in the reactor pit and start a thermal attack of the basemat concrete. A simple way to terminate the melt progression may be to add water on top of it. Among the various physical processes that may participate in the quenching, water may penetrate into the solidified corium through cracks generated by the thermal stress during the solidification.The present paper aims at providing a clarification of the process though an analysis of the few dedicated experimental data available using proto-typical corium, namely the SSWICS 1-7 experiments. At first, a general reminder and analysis of the data is given. Then, the thermal-hydraulic aspects are investigated through the construction of a dedicated heat flux correlation and its use via the experimentally measured post-test permeabilities. The analysis is supported by 1D and 2D evaluations with the multiphase flow code MC3D-PREMIX, slightly modified for the purpose. It is concluded that the heat flux drastically decreases with the amount of added concrete material. Furthermore, 2D border effects are investigated and their importance highlighted in view of the experimental results analysed. These effects should explain the absence of observation of water ingression heat flux in the cases with large concrete amounts. Following, the paper proposes a model for the created permeability. Due to the complexity of the process and to the large uncertainties of the needed material properties in the considered situation with very high temperatures, a semi-empirical model is derived.Lastly, the model is adapted to the situation with internal decay heat, although no open experimental data is available to precisely support any model. A complete modeling is out of the scope of the paper, hence the focus is to provide hints for a first analysis of the impact of decay heat on its coolability.

CFD-DEM simulation of Small-Scale Challenge Problem 1 with EMMS bubble-based structure-dependent drag coefficient

In this study, the energy minimization multi-scale (EMMS)/Bubbling model is coupled with the computational fluid dynamics/discrete element method (CFD-DEM) model via a structure-dependent drag coefficient to simulate the National Energy Technology Laboratory (NETL) small-scale challenge problem using the open-source multiphase flow code MFIX. The numerical predictions are compared against particle velocity measurements obtained from high-speed particle image velocimetry (HSPIV) and differential pressure measurements. The drag-reduction effect of the EMMS bubble-based drag coefficient is observed to significantly improve predictions of the horizontal particle velocity and granular temperature when compared to several other drag coefficients tested; however, the vertical particle velocity and pressure fluctuation characteristic predictions are degraded. The drag-reduction effect is characterized by a reduction in the sizes of slugs or voids, as identified through spectral decomposition of the pressure fluctuations. Overall, this study shows great promise in employing drag coefficients, developed via multi-scale approaches (such as the EMMS paradigm), in CFD-DEM models.

Comparison between hydrostatic and total pressure simulations of dam-break flows

ABSTRACT Shallow water models are commonly used to simulate dam-break flow; however, shallow water equations usually assume a hydrostatic pressure assumption that can limit model applications. Dam-break flow can also be solved by total pressure formulation with Navier–Stokes equations, that are computationally more expensive but can deal with a wider range of problems. We propose a multiphase flow code with second-order precision, called SuLi-LS. This code uses the Level Set methodology and can consider total pressure or hydrostatic pressure assumption in Navier–Stokes solution. To analyse the differences between hydrostatic and total pressure, we compared SuLi-LS results with experimental cases. The comparison shows that total pressure consideration provides accurate results for the dam-break flow problems, and it is a considerably better approach than considering hydrostatic pressure assumption. We found that hydrostatic pressure assumption can be valid for dam-break flows in which there is an underlying water bed.

Three‐dimensional numerical simulation of upflow bubbling fluidized bed in opaque tube under high flux solar heating

Solid particles can be used as a heat transfer medium in concentrated solar power plants to operate at higher temperature and achieve higher heat conversion efficiency than using the current solar heat transfer fluids that only work below 600°C. Among various particle circulation concepts, the dense particle suspension (DPS) flow in tubes, also called upflow bubbling fluidized bed (UBFB), was studied in the frame of the CSP2 FP7 European project. The DPS capacity to extract heat from a tube absorber exposed to concentrated solar radiation was demonstrated and the first values of the tube wall‐to‐DPS heat transfer coefficient were measured. A stable outlet temperature of 750°C was reached with a metallic tube, and a particle reflux in the near tube wall region was evidenced. In this article, the UBFB behavior is studied using the multiphase flow code NEPTUNE_CFD. Hydrodynamics of SiC Geldart A‐type particles and heat transfer imposed by a thermal flux at the wall are coupled in two‐dimensional unsteady numerical simulations. The convective/diffusive heat transfer between the gas and dispersed phase, and the inter‐particle radiative transfer (Rosseland approximation) are accounted for. Simulations and experiments are compared here and the temperature influence on the DPS flow is analyzed. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3857–3867, 2018

Determination of PVC powder drying kinetics at particle scale: Experimental study and modeling

ABSTRACTAn original experimental method is used to determine drying kinetic at particle scale. The particle scale kinetics was obtained by immersion of a small mass of wet polyvinyl chloride (PVC) particles (cake) in a batch dense fluidized bed containing inert hot particles (glass bead). The results are summarized here and prove clearly that the PVC drying is controlled by a competition between internal and external transfers. The drying kinetic was described by a particle scale model taking into account the convective–diffusive (mass transfer) and the convective–evaporative (heat transfer) phenomena. To validate this model with the experimental data, the experimental fluidized bed dryer is modeled following two different approaches: a perfect stirred reactor model and a 3D numerical simulation using the multiphase flow code NEPTUNE_CFD. The aim of this 3D simulation is to simulate the phenomena occurring, at local scale, in a dense fluidized bed dryer and to show the limitations of the perfect stirred reactor model.

Code verification for multiphase flows using the method of manufactured solutions

Code verification is the process of ensuring, to the extent possible, that there are no algorithm deficiencies and coding mistakes (bugs) in a scientific computing simulation. Order of accuracy testing using the Method of Manufactured Solutions (MMS) is a rigorous technique that is employed here for code verification of the main components of an open-source, multiphase flow code – MFIX. Code verification is performed here on 2D and 3D, uniform and stretched meshes for incompressible, steady and unsteady, single-phase and two-phase flows using the two-fluid model of MFIX. Currently, the algebraic gas-solid exchange terms are neglected as these can be verified via techniques such as unit-testing. The no-slip wall, free-slip wall, and pressure outflow boundary conditions are verified. Temporal orders of accuracy for first-order and second-order time-marching schemes during unsteady simulations are also assessed. The presence of a modified SIMPLE-based algorithm in the code requires the velocity field to be divergence free in case of the single-phase incompressible model. Similarly, the volume fraction weighted velocity field must be divergence-free for the two-phase incompressible model. A newly-developed curl-based manufactured solution is used to generate manufactured solutions that satisfy the divergence-free constraint during the verification of the single-phase and two-phase incompressible governing equations. Manufactured solutions with constraints due to boundary conditions as well as due to divergence-free flow are derived in order to verify the boundary conditions.

Heat transfer partitioning model of film boiling of particle cluster in a liquid pool: implementation in a CFD code

In the present work an effective heat transfer partitioning model of three phase (particles, liquid and vapour) flow and thermal interaction have been developed by a multi-fluid approach under film boiling condition. The in-house multiphase flow code is based on finite volume method of discretization and SIMPLE-based pressure correction algorithm. From consideration of mass, momentum and energy balance across the liquid–vapour interface, the vapour bubble generated from the vapour film have been modeled and incorporated in the code. Different interaction terms between each phase are incorporated depending upon the flow regime. The code is validated with in-house and available experimental results. Finally the effect of relevant parameters on void generation under film boiling condition of particles is estimated.

European activities on crosscutting thermal-hydraulic phenomena for innovative nuclear systems

Thermal-hydraulics is recognized as a key scientific subject in the development of innovative reactor systems. In Europe, a consortium is established consisting of 24 institutions of universities, research centers and nuclear industries with the main objectives to identify and to perform research activities on important crosscutting thermal-hydraulic issues encountered in various innovative nuclear systems. For this purpose the large-scale integrated research project THINS (Thermal-Hydraulics of Innovative Nuclear Systems) is launched in the 7th Framework Programme FP7 of European Union. The main topics considered in the THINS project are (a) advanced reactor core thermal-hydraulics, (b) single phase mixed convection, (c) single phase turbulence, (d) multiphase flow, and (e) numerical code coupling and qualification. The main objectives of the project are:•Generation of a data base for the development and validation of new models and codes describing the selected crosscutting thermal-hydraulic phenomena.•Development of new physical models and modeling approaches for more accurate description of the crosscutting thermal-hydraulic phenomena.•Improvement of the numerical engineering tools for the design analysis of the innovative nuclear systems.This paper describes the technical tasks and methodologies applied to achieve the objectives. Main results achieved so far are summarized. This paper serves also as a guidance of this special issue.

Modeling blast waves, gas and particles dispersion in urban and hilly ground areas

The numerical simulation of shock and blast waves as well as particles dispersion in highly heterogeneous media such as cities, urban places, industrial plants and part of countries is addressed. Examples of phenomena under study are chemical gas products dispersion from damaged vessels, gas dispersion in urban places under explosion conditions, shock wave propagation in urban environment. A three-dimensional simulation multiphase flow code (HI2LO) is developed in this aim. To simplify the consideration of complex geometries, a heterogeneous discrete formulation is developed. When dealing with large scale domains, such as countries, the topography is considered with the help of elevation data. Meteorological conditions are also considered, in particular regarding complex temperature and wind profiles. Heat and mass transfers on sub-scale objects, such as buildings, trees and other obstacles are considered as well. Particles motion is addressed through a new turbulence model involving a single parameter to describe accurately plumes. Validations against experiments in basic situations are presented as well as examples of industrial and environmental computations.

The Effect of Stress on Flow and Transport in Fractured Rock Masses Using an Extended Multiple Interacting Continua Method with Crack Tensor Theory

We present an extended multiple interacting continua (Ex-MINC) model of fractured rock masses that uses Oda’s crack tensor theory to upscale the hydraulic and mechanical properties. The Ex-MINC concept includes separate connected continua representing active fractures, inactive fractures, and matrix to represent the fracture-matrix system. The crack tensor theory was used to calculate the stress-dependent permeability tensor and compliance tensor for individual grid blocks. By doing this, we transformed a discrete fracture network model into a grid-based continuum model. The Ex-MINC model was verified against an existing analytical solution, and the entire Ex-MINC/crack tensor model approach was applied to a benchmark test (BMT) related to coupled stress, fluid flow, and transport through a 20-×20-m model domain of heavily fractured media. This BMT was part of the international DECOVALEX project for the development of coupled models and their validation, thus providing us with the opportunity to compare our results with the results of independent models. We conducted the coupled hydraulic and mechanical modeling with TOUGH-FLAC, a simulator based on the TOUGH2 multiphase flow code and the FLAC3D geomechanical code. The results of our simulations were generally consistent with the results of the other independent modeling approaches and showed how inactive fractures impeded solute transport through the fractured system by providing an additional fracture surface area as an avenue for increasing fracture matrix diffusion.

Evaluating the performance of parallel subsurface simulators: An illustrative example with PFLOTRAN.

[1] To better inform the subsurface scientist on the expected performance of parallel simulators, this work investigates performance of the reactive multiphase flow and multicomponent biogeochemical transport code PFLOTRAN as it is applied to several realistic modeling scenarios run on the Jaguar supercomputer. After a brief introduction to the code's parallel layout and code design, PFLOTRAN's parallel performance (measured through strong and weak scalability analyses) is evaluated in the context of conceptual model layout, software and algorithmic design, and known hardware limitations. PFLOTRAN scales well (with regard to strong scaling) for three realistic problem scenarios: (1) in situ leaching of copper from a mineral ore deposit within a 5-spot flow regime, (2) transient flow and solute transport within a regional doublet, and (3) a real-world problem involving uranium surface complexation within a heterogeneous and extremely dynamic variably saturated flow field. Weak scalability is discussed in detail for the regional doublet problem, and several difficulties with its interpretation are noted.

A method for incorporating equilibrium chemical reactions into multiphase flow models for CO2 storage

CO2 injection and storage in deep saline aquifers involves many coupled processes, including multiphase flow, heat and mass transport, rock deformation and mineral precipitation and dissolution. Coupling is especially critical in carbonate aquifers, where minerals will tend to dissolve in response to the dissolution of CO2 into the brine. The resulting neutralization will drive further dissolution of both CO2 and calcite. This suggests that large cavities may be formed and that proper simulation may require full coupling of reactive transport and multiphase flow. We show that solving the latter may suffice whenever two requirements are met: (1) all reactions can be assumed to occur in equilibrium and (2) the chemical system can be calculated as a function of the state variables of the multiphase flow model (i.e., liquid and gas pressure, and temperature). We redefine the components of multiphase flow codes (traditionally, water and CO2), so that they are conservative for all reactions of the chemical system. This requires modifying the traditional constitutive relationships of the multiphase flow codes, but yields the concentrations of all species and all reaction rates by simply performing speciation and mass balance calculations at the end of each time step. We applied this method to the H2O–CO2–Na–Cl–CaCO3 system, so as to model CO2 injection into a carbonate aquifer containing brine. Results were very similar to those obtained with traditional formulations, which implies that full coupling of reactive transport and multi-phase flow is not really needed for this kind of systems, but the resulting simplifications may make it advisable even for cases where the above requirements are not met. Regarding the behavior of carbonate rocks, we find that porosity development near the injection well is small because of the low solubility of calcite. Moreover, dissolution concentrates at the front of the advancing CO2 plume because the brine below the plume tends to reach high CO2 concentrations quite rapidly. We conclude that carbonate dissolution needs not to be feared.

OpenGeoSys-ChemApp: a coupled simulator for reactive transport in multiphase systems and application to CO2 storage formation in Northern Germany

Sequestration of CO2 into a deep geological reservoir causes a complex interaction of different processes such as multiphase flow, phase transition, multicomponent transport, and geochemical reactions between dissolved CO2 and the mineral matrix of the porous medium. A prognosis of the reservoir behaviour and the feedback from large-scale geochemical alterations require efficient process-based numerical models. For this purpose, the multiphase flow and multicomponent transport code OpenGeoSys-Eclipse have been coupled to the geochemical model ChemApp. The newly developed coupled simulator was successfully verified for correctness and accuracy of the implemented reaction module by benchmarking tests. The code was then applied to assess the impact of geochemical reactions during CO2 sequestration at a hypothetical but typical Bunter sandstone formation in the Northern German Basin. Injection and spreading of 1.48 × 107 t of CO2 in an anticline structure of the reservoir were simulated over a period of 20 years of injection plus 80 years of post-injection time. Equilibrium geochemical calculations performed by ChemApp show only a low reactivity to the geochemical system. The increased acidity of the aqueous solution results in dissolution of small amounts of calcite, anhydrite, and quartz. Geochemical alterations of the mineral phase composition result in slight increases in porosity and permeability, which locally may reach up to +0.02 and 0.1 %, respectively.

Back-Calculated Soil–Water Characteristic Curve From Fluid Flow Data

Abstract The soil–water characteristic curve (SWCC) is a fundamental property of an unsaturated soil that is used to predict multiphase flow and transport through porous media. Direct measurement of the SWCC using conventional testing devices is time consuming. A methodology with which to estimate the SWCC is proposed in this paper based on the recorded data of transient fluid flow into soil during a 50 g centrifugal test. An inverse analysis was performed to fit the numerical simulation results, obtained using a finite element multiphase flow code NAPL simulator, to the centrifugal model test data. For the numerical simulations, several sets of representative SWCC parameters of the modeled soil were assumed. Based on an optimization scheme, the parameters that produced the best match between measured and simulated data were selected, and the SWCC for the soil was predicted. To validate the proposed method, the predicted SWCC was compared with that obtained via a conventional test. The comparison showed that the SWCC obtained via inverse analysis with a van Genuchten model parameter set of α = 0.4 m−1 and η = 3 compared relatively well to the measured one. Thus this new method, based on inverse analysis of the fluid flow data from centrifugal modeling, could be used as a reliable, indirect technique for predicting field SWCCs.

Magnitude and Duration of Temperature Changes in Geological Storage of Carbon Dioxide

Injecting carbon dioxide for storage can lead to substantial cooling of the reservoir that lasts for many years. This paper compares temperature data from the first stage of the CO2CRC Otway Project with theoretical results. Solutions are given for one-dimensional models of vertical and spherical heat diffusion and a radial model of lateral heat transport, and used to delineate the extent to which vertical heat transport follows spherical or linear equations. Solutions are also presented for two-dimensional radial simulations of CO2 injection with the non-isothermal multiphase flow code TOUGH2, to allow for the dependence of the thermal conductivity on CO2 saturation. Finally the size and duration of the temperature perturbation resulting from larger-scale CO2 injection projects are calculated.

Towards unified drag laws for inertial flow through fibrous materials

We give a comprehensive survey of published experimental, numerical and theoretical work on the drag law correlations for fluidized beds and flow through porous media, together with an attempt of systematization. Ranges of validity as well as limitations of commonly used relations (i.e. the Ergun and Forchheimer relations for laminar and inertial flows) are studied for a wide range of porosities. The pressure gradient is linear in superficial velocity, U for low Reynolds numbers, Re, referred to as Darcy’s law. Here, we focus on the non-linear contribution of inertia to the transport of momentum at the pore scale, and explain why there are different non-linear corrections on the market.From our fully resolved finite element (FE) results, for both ordered and random fibre arrays, (i) the weak inertia correction to the linear Darcy relation is third power in U, up to small Re∼1–5. When attempting to fit our data with a particularly simple relation, (ii) a non-integer power law performs astonishingly well up to the moderate Re∼30. However, for randomly distributed arrays, (iii) a quadratic correction performs quite well as used in the Forchheimer (or Ergun) equation, from small to moderate Re.Finally, as main result, the macroscopic properties of random, fibrous porous media are related to their microstructure (arrangement) and porosity. All results (Re<30) up to astonishingly large porosity, ε∼0.9, scale with Reg, i.e., the gap Reynolds number that is based on the average second nearest neighbour (surface to surface) distances. This universal result is given as analytical closure relation, which can readily be incorporated into existing (non)commercial multi-phase flow codes. In the transition regime, the universal curve actually can be fitted with a non-integer power law (better than ∼1% deviation), but also allows to define a critical Regc∼1, below which the third power correction holds and above which a correction with second power fits the data considerably better.

Development and implementation of a polydispersed multiphase flow model in OpenFOAM

Abstract The two-phase flow solver implemented in the open-source OpenFOAM code was extended to a multiphase flow formulation ( n dispersed and one continuous phases) and then coupled to the population balance equation (PBE) solution by the Direct Quadrature Method of Moments (DQMOM), originating a polydispersed multiphase flow solver. Although each dispersed phase has its own velocity field, the present implementation considers only the interfacial momentum exchange between the continuous and the dispersed phases. The multiphase flow formulation was described and the details of the PBE–CFD coupling algorithms in OpenFOAM were provided. The implementation of the multiphase flow code was verified and evaluated against the original OpenFOAM two-phase flow solver for flow through a 2D backward facing step, using simplified breakage and aggregation kernels. The computational cost of both codes were compared for serial and parallel simulations.

Academic validation of multi-phase flow codes

Transport equations solved in the multiphase codes are more complex than those in single phase codes. The origin of this difference is mainly due to the complex interactions between the different length and time scales involved in the different phenomena. It is therefore difficult to estimate the potentialities of the numerics in multiphase codes without the help of computational results. For the validation, simple situations relevant for two phase phenomena are chosen. They must be as simple as possible, mainly with single effects and related to the scope of codes devoted to safety analysis. Cases in which one physical phenomenon is uppermost are preferred. Heuristic criteria which must be fulfilled by the computational results are then defined on the basis of our experience in multiphase flow computational analysis. They are illustrated with results from benchmarks. The way each criterion is fulfilled in a given calculation and its relative importance are underlined. This approach enables to separate the numerical and physical part of the results. The results allow to exhibit a correct behavior of the numerical method of the SIMMER-IV code, developed jointly by JAEA (Japan), FzK (Germany), and CEA (France). More generally, the approach is convenient to investigate the potentialities of new developed codes. It allows to avoid unwanted effects like “black box” ones, when unexpected results are obtained in non-academic situations.