Multicomponent Flow Research Articles

Different-Scale Simulation of Flows in Porous Media

The paper considers the development of algorithms for an adequate description of processes of different scales in porous media. The choice of a computational technique is determined by the reference size of the problem being solved. Models of porous medium flow under Darcy’s law, neglecting the medium microstructure, are used for the simulation at macro-scale. While at micro-scale, a direct description of fluid flow in porous channels with complex geometry by means of gas dynamic equations is used. In the first case the proposed model of non-isothermal multiphase multicomponent flow in a porous medium includes the mass balance and total energy conservation equations modified by analogy to the known quasi-gas dynamic equations. The model features are the introduction of minimal reference scales in space and in time and the change of the system type from parabolic to hyperbolic to increase the stability of explicit difference schemes applied for approximation. In the second case the dimensionless form of the quasi-gas dynamic system with pressure decomposition, developed by the authors earlier, is adapted to the simulation of flows in the pore space. The fictitious domain method is proposed to reproduce the core microstructure. The developed approaches have been verified by test predictions.

Mesoscale modelling of droplets' self-assembly in microfluidic channels.

A recently proposed mesoscale approach for the simulation of multicomponent flows with near-contact interactions is employed to investigate the early stage formation and clustering statistics of soft flowing crystals in microfluidic channels. Specifically, we first demonstrate the ability of the aforementioned mesoscale model to accurately reproduce main mechanisms leading to the formation of two basic droplet patterns (triangular and hexagonal), in close agreement with experimental evidence. Next, we quantitatively evaluate the device-scale clustering efficiency of the crystal formation process by introducing a new orientational order parameter, based on the Delaunay triangulation and Voronoi diagrams analysis of the droplet patterns. The mesoscale computational approach employed in this work proves to be an efficient tool to shed new light on the complex dynamics of dense emulsions, from short-scale thin-film hydrodynamics, all the way up to global structure formation and statistics of the resulting droplets ensembles.

Lbmpy: Automatic code generation for efficient parallel lattice Boltzmann methods

Lattice Boltzmann methods are a popular mesoscopic alternative to classical computational fluid dynamics based on the macroscopic equations of continuum mechanics. Many variants of lattice Boltzmann methods have been developed that vary in complexity, accuracy, and computational cost. Extensions are available to simulate multi-phase, multi-component, turbulent, and non-Newtonian flows. In this work we present lbmpy, a code generation package that supports a wide variety of different lattice Boltzmann methods. Additionally, lbmpy provides a generic development environment for new schemes. A high-level domain-specific language allows the user to formulate, extend and test various lattice Boltzmann methods. In all cases, the lattice Boltzmann method can be specified in symbolic form. Transformations that operate on this symbolic representation yield highly efficient compute kernels. This is achieved by automatically parallelizing the methods, and by various application-specific automatized steps that optimize the resulting code. This pipeline of transformations can be applied to a wide range of lattice Boltzmann variants, including single- and two-relaxation-time schemes, multi-relaxation-time methods, as well as the more advanced cumulant methods, and entropically stabilized methods. lbmpy can be integrated into high-performance computing frameworks to enable massively parallel, distributed simulations. This is demonstrated using the waLBerla multiphysics package to conduct scaling experiments on the SuperMUC-NG supercomputing system on up to 147 456 compute cores.

On a modified pseudopotential lattice Boltzmann model for multicomponent flows

This paper presents a pseudopotential lattice Boltzmann model for multicomponent flows involving large viscosity ratios. Firstly, a rigorous Chapman–Enskog analysis is conducted to show that previous models cannot recover the correct governing equation with a single-relaxation-time scheme when the viscosity ratio is not unity. Then, based on this analysis, we established a modified model to obtain the correct governing equation by introducing a system relaxation time into the evolution equation. Finally, we validated the modified model by conducting a two-phase cocurrent (Poiseuille) flow with single-relaxation-time and multiple-relaxation-times schemes. The numerical results show that the present model enormously improves the range of the accessible viscosity ratio. For the single-relaxation-time scheme, the viscosity ratio ranges from 1∕250 to 250 with a fourth order isotropy. For the multiple-relaxation-times scheme, the viscosity ratio is numerically stable and accurate for viscosity ratios between 1∕1000 to 1000 with fourth order isotropy.

A theory of generalised solutions for ideal gas mixtures with Maxwell-Stefan diffusion

<p style='text-indent:20px;'>After the pioneering work by Giovangigli on mathematics of multicomponent flows, several attempts were made to introduce global weak solutions for the PDEs describing the dynamics of fluid mixtures. While the incompressible case with constant density was enlighted well enough due to results by Chen and Jüngel (isothermal case), or Marion and Temam, some open questions remain for the weak solution theory of gas mixtures with their corresponding equations of mixed parabolic–hyperbolic type. For instance, Mucha, Pokorny and Zatorska showed the possibility to stabilise the hyperbolic component by means of the Bresch-Desjardins technique and a regularisation of pressure preventing vacuum. The result by Dreyer, Druet, Gajewski and Guhlke avoids <i>ex machina</i> stabilisations, but the mathematical assumption that the Onsager matrix is uniformly positive on certain subspaces leads, in the dilute limit, to infinite diffusion velocities which are not compatible with the Maxwell-Stefan form of diffusion fluxes. In this paper, we prove the existence of global weak solutions for isothermal and ideal compressible mixtures with natural diffusion. The main new tool is an asymptotic condition imposed at low pressure on the binary Maxwell-Stefan diffusivities, which compensates possibly extreme behaviour of weak solutions in the rarefied regime.</p>

Numerical Modeling of Transcritical and Supercritical Fuel Injections Using a Multi-Component Two-Phase Flow Model

In the present numerical study, implicit large eddy simulations (LES) of non-reacting multi-components mixing processes of cryogenic nitrogen and n-dodecane fuel injections under transcritical and supercritical conditions are carried out, using a modified reacting flow solver, originally available in the open source software OpenFOAM®. To this end, the Peng-Robinson (PR) cubic equation of state (EOS) is considered and the solver is modified to account for the real-fluid thermodynamics. At high pressure conditions, the variable transport properties such as dynamic viscosity and thermal conductivity are accurately computed using the Chung transport model. To deal with the multicomponent species mixing, molar averaged homogeneous classical mixing rules are used. For the velocity-pressure coupling, a PIMPLE based compressible algorithm is employed. For both cryogenic and non-cryogenic fuel injections, qualitative and quantitative analyses are performed, and the results show significant effects of the chamber pressure on the mixing processes and entrainment rates. The capability of the proposed numerical model to handle multicomponent species mixing with real-fluid thermophysical properties is demonstrated, in both supercritical and transcritical regimes.

Eulerian-Lagrangian modelling of detonative combustion in two-phase gas-droplet mixtures with OpenFOAM: Validations and verifications

A hybrid Eulerian-Lagrangian solver RYrhoCentralFoam is developed based on OpenFOAM® to simulate detonative combustion in two-phase gas-liquid mixtures. For Eulerian gas phase, RYrhoCentralFoam enjoys second order of accuracy in time and space discretizations and is based on finite volume method on polyhedral cells. The following developments are made based on the standard compressible flow solver rhoCentralFoam in OpenFOAM®: (1) multi-component species transport, (2) detailed fuel chemistry for gas phase combustion, and (3) Lagrangian solver for gas-droplet two-phase flows and sub-models for liquid droplets. To extensively verify and validate the developments and implementations of the solver and models, a series of benchmark cases are studied, including non-reacting multi-component gaseous flows, purely gaseous detonations, and two-phase gas-droplet mixtures. The results show that the RYrhoCentralFoam solver can accurately predict the flow discontinuities (e.g. shock wave and expansion wave), molecular diffusion, auto-ignition and shock-induced ignition. Also, the RYrhoCentralFoam solver can accurately simulate gaseous detonation propagation for different fuels (e.g. hydrogen and methane), about propagation speed, detonation frontal structures and cell size. Sub-models related to the droplet phase are verified and/or validated against analytical and experimental data. It is also found that the RYrhoCentralFoam solver is able to capture the main quantities and features of the gas-droplet two-phase detonations, including detonation propagation speed, interphase interactions and detonation frontal structures. As our future work, RYrhoCentralFoam solver can also be extended for simulating two-phase detonations in dense droplet sprays.

Is multicomponent environmental flow management always better than the fixed minimum flows for a river ecosystem?

AbstractEnvironmental flows (e‐flows) management is a basic task in reservoir operation. A simple approach for managing e‐flows is to maintain a fixed minimum flow, which releases at least a constant amount of water to sustain daily streamflow. Then e‐flows management becomes increasingly more sophisticated. Newer approaches include multicomponent e‐flow management, which provides different flows during different periods. This management approach produces a better flow regime than the fixed minimum flows because it more closely resembles the natural flow regime. However, in addition to e‐flow management strategies, flow regimes are also influenced by reservoir capacity, reservoir inflow, and water supply. The effects of these three variables on flow regime alteration have been rarely studied. To compare the effects of different reservoir capacities, reservoir inflows, and water supply quantities on flow regime alteration, we developed a hypothetical reservoir system for use in numerical experiments. In addition to the fixed minimum flows, we tested the effects of three other widely used e‐flow management strategies on flow regime alteration: the fraction of inflow, flow components, and four‐period release approaches. The range of variability approach is adopted to evaluate the flow regime alteration. The results show that the flow regime alteration decreases with increasing reservoir inflows and increases with increasing water supply quantity for all of the four e‐flow management strategies. We found that for certain values of reservoir capacity, reservoir inflow sequence, or water supply, the simple fixed minimum flows approach may produce the same results as the more sophisticated approaches.

Numerical Simulation of Solid Combustion in Microporous Particles.

In the present study, direct numerical simulations for smoldering in simplified geometries are performed for multicomponent and dilatable flows. The reactant gas is passing inside an array of permeable and microporous cylinders. The chemical reaction takes place within the grains. For the sake of simplicity, the smoldering is treated as a single step chemical reaction. We define a Darcy-Brinkman model to deal with the multi-scale nature of this problem. Varying the flow rate, and carbon content, we can investigate the response of our model, and try to compare with existing solutions or available experimental investigations. Thus, the ability of the Darcy Brinkman approach to capture such situations of porous particles combustion will be checked. The numerical model sensitivity to the inner grain permeability is also investigated.

Smooth formulation for isothermal compositional simulation with improved nonlinear convergence

Compositional simulation is challenging, because of highly nonlinear couplings between multi-component flow in porous media with thermodynamic phase behavior. The coupled nonlinear system is commonly solved by the fully-implicit scheme. Various compositional formulations have been proposed. However, severe convergence issues of Newton solvers can arise under the conventional formulations. Crossing phase boundaries produces kinks in discretized equations, and subsequently causing oscillations or even divergence of Newton iterations.The objective of this work is to develop a smooth formulation that removes all the property switches and discontinuities associated with phase changes. We show that it can be very difficult and costly to smooth the conservation equations directly. Therefore, we first reformulate the coupled system, so that the discontinuities are transferred to the phase equilibrium model. In this way a single and concise non-smooth equation is achieved and then a smoothing approximation can be made. The new formulation with a smoothing parameter provides smooth transitions of variables across all the phase regimes. In addition, we employ a continuation method where the solution progressively evolves toward the target system.We evaluate the efficiency of the new smooth formulation and the continuation method using several complex problems. Compared to the standard natural formulation, the developed formulation and method exhibit superior nonlinear convergence behaviors. The continuation method leads to smooth and stable iterative performance, with a negligible impact on solution accuracy. Moreover, it works robustly for a wide range of flow conditions without parameter tuning.

Improved phase-field models of melting and dissolution in multi-component flows.

We develop and analyse the first second-order phase-field model to combine melting and dissolution in multi-component flows. This provides a simple and accurate way to simulate challenging phase-change problems in existing codes. Phase-field models simplify computation by describing separate regions using a smoothed phase field. The phase field eliminates the need for complicated discretizations that track the moving phase boundary. However, standard phase-field models are only first-order accurate. They often incur an error proportional to the thickness of the diffuse interface. We eliminate this dominant error by developing a general framework for asymptotic analysis of diffuse-interface methods in arbitrary geometries. With this framework, we can consistently unify previous second-order phase-field models of melting and dissolution and the volume-penalty method for fluid-solid interaction. We finally validate second-order convergence of our model in two comprehensive benchmark problems using the open-source spectral code Dedalus.

Liutex-based analysis of drag force and vortex in two-phase flow past 2-D square obstacle using LBM on GPU

The two-phase flow past a square is a ubiquitous phenomenon widely encountered in industries and engineering, where the interaction of disparate phases coupled with the influence of the solid is rather complicated. In this context, the flow characteristics and the vortex field are investigated to reveal the mechanisms of the two-phase drag and the vortex variation. The lattice Boltzmann method (LBM) is utilized to study the multi-component two-phase flow. The computation implemented on the GPU is remarkably accelerated thanks to the natural parallelism of the LBM. The process of the two-phase flow past a square is thoroughly examined. The drag and lift forces, including the total force and the components caused by the dispersed phase and the continuous phase, respectively, are obtained, and their variation mechanisms are explained. Meanwhile, the vortex-identification approaches based on the Liutex as well as the traditional methods are compared. The relationship between the bubble breakup and coalescence processes and the extremums of different vortex identification variables is analyzed.

Numerical Simulation of the Solid Particle Sedimentation and Bed Formation Behaviors Using a Hybrid Method

In the safety analysis of sodium-cooled fast reactors, numerical simulations of various thermal-hydraulic phenomena with multicomponent and multiphase flows in core disruptive accidents (CDAs) are regarded as particularly difficult. In the material relocation phase of CDAs, core debris settle down on a core support structure and/or an in-vessel retention device and form a debris bed. The bed’s shape is crucial for the subsequent relocation of the molten core and heat removal capability as well as re-criticality. In this study, a hybrid numerical simulation method, coupling the multi-fluid model of the three-dimensional fast reactor safety analysis code SIMMER-IV with the discrete element method (DEM), was applied to analyze the sedimentation and bed formation behaviors of core debris. Three-dimensional simulations were performed and compared with results obtained in a series of particle sedimentation experiments. The present simulation predicts the sedimentation behavior of mixed particles with different properties as well as homogeneous particles. The simulation results on bed shapes and particle distribution in the bed agree well with experimental measurements. They demonstrate the practicality of the present hybrid method to solid particle sedimentation and bed formation behaviors of mixed as well as homogeneous particles.

A simple ghost fluid method for compressible multicomponent flows with capillary effects

A novel way of implementing surface tension effects in sharp-interface compressible flow models is proposed, aiming to address problems where liquid compressibility and capillarity are both important. The method is built on the principles of the grid-aligned formulation for ghost fluid techniques. In this approach, the Riemann problems at the interface are formulated along the grid rather than in a normal-to-the-interface direction; the method is thus simpler. The performance of the method is thoroughly examined following implementation in a well-established front tracking framework.

Oil displacement by multicomponent slug injection: An analytical solution for Langmuir adsorption isotherm

Injection of water containing dissolved chemical components is one of the most important enhanced oil recovery (EOR) techniques. This problem can be modeled by an (n+1)×(n+1) system of hyperbolic partial differential equations representing the conservation of water and chemical components. In this paper we present the solution to the problem of oil displacement by a water slug containing n dissolved chemicals driven by pure water. It is considered that the chemicals can be adsorbed by the rock following Langmuir adsorption isotherm. The solution for any number of dissolved chemicals was obtained from a generalization of the case where three polymers are dissolved in the slug. To build the solution we first introduced a potential function replacing time as an independent variable. This procedure splits the original system of equations into a one-phase purely chromatographic problem and a scalar hyperbolic equation. The one-phase problem was solved using multicomponent chromatography theory, and its solution was used to solve the scalar equation. Both solution procedures are based on the method of characteristics. Finally, the solution of the scalar equation was mapped onto the space-time plane. The concentration solution shows the development of a complete chromatographic cycle in the porous media, and due to the separation of the chemicals, water banks appear in the water saturation solution. These results are new and present important insights for two-phase multicomponent flows in porous media.

Stability of a (2G) Coated, Thin-Film YBaCuO 123 Superconductor: Intermediate Summary

This paper summarises results obtained with stability calculations of thin films and multi-filamentary superconductors. In a series of papers, all the contributions have been published in this journal. We now extend our previous investigations to the temporal aspect of the internal heat transfer and to the material homogeneity problem. Within multi-component heat transfer (solid conduction, radiation), the standard theory of radiative transfer in a coated, thin-film, YBaCuO3 123 superconductor correctly treats the energetic aspects of radiation propagation; this is the actual core of stability models. But a rigorous solution of the temporal aspect still is missing. It is the study of this aspect that would provide a new access to the physics of superconductor stability, in particular if after a disturbance the system is already close to a phase transition. A matrix formulation, using a combination of Monte Carlo and radiative transfer calculations, is suggested to circumvent the temporal solid conduction/radiative transfer problem in multi-component heat flow. As an important result, quench is not an event that proceeds instantaneously. Instead, it is a process the speed of which decreases the more, the closer the superconductor temperature approaches critical temperature until the residual number of electron pairs becomes too small to support critical current. The stability of superconductors and thermal fluctuations might reflect a common background: the relaxation time of the density of electron pairs after disturbances.

A conservative discontinuous Galerkin discretization for the chemically reacting Navier-Stokes equations

We present a detailed description and verification of a discontinuous Galerkin finite element method (DG) for the multi-component chemically reacting compressible Navier-Stokes equations that retains the desirable properties of DG, namely discrete conservation and high-order accuracy in smooth regions of the flow. Pressure equilibrium between adjacent elements is maintained through the consistent evaluation of the thermodynamics model and the resulting weak form, as well as the proper choice of nodal basis. As such, the discretization does not generate unphysical pressure oscillations in smooth regions of the flow or at material interfaces where the temperature is continuous. Additionally, we present an hp-adaptive DG method for solving systems of ordinary differential equations, DGODE, which is used to resolve the temporal evolution of the species concentrations due to stiff chemical reactions. The coupled solver is applied to several challenging test problems including multi-component shocked flows as well as chemically reacting detonations, deflagrations, and shear flows with detailed kinetics. We demonstrate that the discretization does not produce unphysical pressure oscillations and, when applicable, we verify that it maintains discrete conservation. The solver is also shown to reproduce the expected temperature and species profiles throughout a detonation as well as the expected two-dimensional cellular detonation structure. We also demonstrate that the solver can produce accurate, high-order, approximations of temperature and species profiles without artificial stabilization for the case of a one-dimensional pre-mixed flame. Finally, high-order solutions of two- and three-dimensional multi-component chemically reacting shear flows, computed without any additional stabilization, are presented.

Axisymmetric flows on the torus geometry

Abstract

An experimental investigation into ignition and combustion of groups of slurry fuel droplets containing high concentrations of water

In this study, the main ignition and combustion characteristics have been compared for droplet groups of a coal-water slurry containing petrochemicals (CWSP), as well as oil, surrounded by water droplets. Thus, in a combustion chamber, we simulated the ignition and combustion conditions of a heterogeneous fuel aerosol that can be formed when jets of different liquids cross or when multi-component flows delaminate. It was shown that a decrease in the distance between droplets (from 10 mm to 2 mm, i.e. to the typical fuel droplet size) reduces the gas-phase and heterogeneous ignition delay times of oil and CWSP by 30% on average. The evaporation times of water droplets decrease by approximately 25%, if the distance between them increases in the combustion chamber. It was established that the ignition delay times of oil and coal-water slurry containing petrochemicals increased by 20–40% and 40–70%, respectively, when a combustible liquid droplet was in the center with six water droplets around it. The experimental results are a database for the development of efficient technologies of injecting multi-component fuel into combustion chambers.

A 6M digital twin for modeling and simulation in subsurface reservoirs

A 6M digital twin for modeling and simulation in subsurface reservoirs