Multicomponent Flow Research Articles

Developing PDE-constrained optimal control of multicomponent contamination flows in porous media

This paper develops a robust and efficient PDE-constrained optimal control model for multicomponent pollutions in porous media, which takes into account nonlinear multi-component contamination flows of groundwater. The objective of the pollution optimal control is to identify the optimal injection rates from the top part boundary of domain, which can minimize the least squares error between the concentrations that are simulated and the allowable observed concentrations at observation sites, combining with the affection of costs associated with reducing emissions at injection locations. To discrete the constrained governing system of nonlinear multi-component flows, the splitting improved upwind finite difference scheme is developed for multicomponent PDEs system involving nonlinear chemical reactions of multicomponent pollutants and the pollutant injected rates on the upper part boundary. We employ the differential evolution (DE) optimization algorithm to solve the optimization. We numerically demonstrate the effectiveness of our model by analyzing the flow simulation on a simple geometric aquifer and identifying the optimal injection rates by minimizing the concentration derivation and the abatement costs. We also investigate the simulation of the contamination flow in a more realistic-shaped aquifer, which further validates our model's robustness and efficacy. The developed PDE-constrained control model and algorithm can be applied to applications of groundwater pollution control.

Benchmark Simulation of Laminar Reactive Micromixing Using Lattice Boltzmann Methods

Micromixers are chemical processing devices with complex flow patterns applied for both mixing and reaction of chemical species. In current research, laminar reacting multicomponent flows are considered. Despite the laminar streaming regime (e.g., Re = 186), there exist secondary flow microstructures. For this setup, accurate predictions of those structures are possible with a large-eddy simulation on a fine mesh resolving till the Batchelor microscales. Utilizing the open-source lattice Boltzmann method (LBM) framework, OpenLB, a benchmark simulation of the reacting micromixer, is re-established with new, more precise computation results. In this context, a Schmidt-number-based stabilization method for LBM-discretized reactive advection–diffusion equations by laminar secondary flow structures is used. A convergence study is performed, which is also a novelty. All computations have been performed on the high-performance computing cluster HoreKa using up to 160 NVIDIA A100 graphics processing units.

CFD investigation on flowing and discharging characteristics of airborne Halon 1301 fire-extinguishing agent at varied altitudes

To investigate the functioning mechanism of cruise altitude on transportation and discharging dynamics of onboard fire-extinguishants, a numerical model coupling the vaporization and flowing process is established for the Halon 1301-N2 multi-component two-phase flow inside the onboard fire-extinguishing system based on computational fluid dynamics. Flowing and transportation parameters are simulated and compared for Halon 1301 at 0 m, 3000 m, 6000 m and 12000 m. Moreover, the peak discharging fluid pressure, velocity and density are also analyzed to evaluate the impact of altitude on discharging dynamics of Halon 1301. Notably, the maximum discharging velocity at 3000 m, 6000 m and 12000 m are reduced by 4%, 9% and 15% relative to that at 0 m; the maximum discharging fluid pressure and density at 12000 m are respectively reduced by 32% and 12% relative to those at 0 m. High altitude is unraveled to inhibit the vaporization of Halon 1301 and lower the discharging efficiency at the pipeline outlet, consequently lowering the diffusion efficiency and effective concentration of Halon 1301 in the protected area and further weakening the fire-suppression effectiveness. The unveiled insights afford guidance for the optimization of fire-extinguishing systems to improve the fire-fighting capability of airplanes at high altitudes.

High-order finite volume methods for solving compressible multicomponent flows

High-order finite volume methods for solving compressible multicomponent flows

High-order finite volume method for solving compressible multicomponent flows with Mie–Grüneisen equation of state

In this paper, we propose a new high-order finite volume method for solving the multicomponent fluids problem with Mie–Grüneisen EOS. Firstly, based on the cell averages of conservative variables, we develop a procedure to reconstruct the cell averages of the primitive variables in a high-order manner. Secondly, the high-order reconstructions employed in computing numerical fluxes are implemented in a characteristic-wise manner to reduce numerical oscillations as much as possible and obtain high-resolution results. Thirdly, advection equation within the governing system is rewritten in a conservative form with a source term to enhance the scheme’s performance. We utilize integration by parts and high-order numerical integration techniques to handle the source terms. Finally, all variables are evolved by using Runge–Kutta time discretization. All steps are carefully designed to maintain the equilibrium of pressure and velocity for the interface-only problem, which is crucial in designing a high-resolution scheme and adapting to more complex multicomponent problems. We have performed extensive numerical tests for both one- and two-dimensional problems to verify our scheme’s high resolution and accuracy.

Adaptation of the Low Dissipation Low Dispersion Scheme for Reactive Multicomponent Flows on Unstructured Grids Using Density-Based Solvers

Abstract The low dissipation low dispersion (LD2) second-order accurate scheme is effective for scale-resolving simulations in finite volume computational fluid dynamics (CFD) solvers, thanks to its combination of a skew-symmetric split form for convective terms and matrix-valued artificial dissipation fluxes. However, reactive flow simulations face challenges due to steep gradients and varying gas properties. This study replaces the skew-symmetric scheme with the kinetic energy and entropy preserving (KEEP) scheme, utilizing quadratic and cubic split forms for convective terms, enhancing stability. The nonsmooth fluid interfaces in reactive flow simulations necessitate upwind fluxes for reactive scalars to limit total variation (TV), also requiring upwind fluxes for the mixture-dependent internal energy fluxes. Other convective terms use central discretizations from the KEEP scheme, leveraging LD2’s spatial reconstruction to minimize dispersive errors. Numerical assessments show this approach reduces spurious pressure oscillations in single and multicomponent flows. The absolute flux Jacobian for dissipation flux calculation is efficiently computed using an expanded Turkel’s approach for thermally perfect gas mixtures. Partial pressure derivatives are approximated when using the flamelet generated manifolds (FGM) combustion model. The proposed scheme is evaluated through scale-resolving simulations of the Cambridge burner flame SWB1 on an unstructured grid using the density-based solver TRACE, employing both finite rate chemistry (FRC) and FGM combustion models. Comparative analysis with the all-speed SLAU2 scheme shows the superior performance of the proposed scheme in handling turbulent reactive multicomponent flows.

A free-energy based multiple-distribution-function lattice Boltzmann method for multi-component and multi-phase flows

This study presents the development of a multiple-distribution-function lattice Boltzmann model (MDF-LBM) for the accurate simulation of multi-component and multi-phase flow. The model is based on the diffuse interface theory and free energy model, which enable the derivation of hydrodynamic equations for the system. These equations comprise a Cahn-Hilliard (CH) type mass balance equation, which accounts for cross diffusion terms for each species, and a momentum balance equation. By establishing a relationship between the total chemical potential and the general pressure, the momentum balance equation is reformulated in a potential form. This potential form, together with the CH type mass balance equation, is then utilized to construct the MDF-LBM as a coupled convection–diffusion system. Numerical simulations demonstrate that the proposed MDF-LBM accurately captures phase behavior and ensures mass conservation. Additionally, the calculated interface tension exhibits good agreement with experimental data obtained from laboratory studies.

Modelling and simulation on compressible multi-component gas-liquid flows with chemical reaction and phase transition effects

In this paper, mathematical models and numerical algorithm are conducted for simulating compressible two-phase multi-component reactive flows, coupling with the finite-rate-based chemistry and the instantaneous-equilibrium phase transition model. Distinctive from previous multi-component two-phase governing equations, all volume fraction transport equations, with non-conservative characteristics, of gaseous components are substituted with a thermal equilibrium assumption inside the gaseous mixture for closure. Moreover, based on the temperature polynomial (NASA-7) fitted gas properties and the stiffened gas equation of state (SG-EOS) described liquid properties, the instantaneous-equilibrium phase transition model is re-derived, and the solving strategy of the transient phase transition model is detailly provided using an algebraical approach rather than the iterative process. Having included these elements, the proposed model is validated on three canonical tests, first for pure reactive flows, second for pure two-phase flows, and third for complex compressible multi-component two-phase reactive flows with phase transition effects: hydrogen-oxygen detonation interacting with a water droplet. The cases have well demonstrated the proposed model capability and the expected fluid physics in both the multiphase and reactive flows are reproduced.

Artificial neural network aided vapor–liquid equilibrium model for multi-component high-pressure transcritical flows with phase change

In this work, an artificial neural network (ANN) aided vapor–liquid equilibrium (VLE) model is developed and coupled with a fully compressible computational fluid dynamics (CFD) solver to simulate the transcritical processes occurring in high-pressure liquid-fueled propulsion systems. The ANN is trained in Python using TensorFlow, optimized for inference using Open Neural Network Exchange Runtime, and coupled with a C++ based CFD solver. This plug-and-play model/methodology can be used to convert any multi-component CFD solver to simulate transcritical processes using only open-source packages, without the need of in-house VLE model development. The solver is then used to study high-pressure transcritical shock-droplet interaction in both two- and four-component systems and a turbulent temporal mixing layer (TML), where both qualitative and quantitative agreement (maximum relative error less than 5%) is shown with respect to results based on both direct evaluation and the state-of-the-art in situ adaptive tabulation (ISAT) method. The ANN method showed a 6 times speed-up over the direct evaluation and a 2.2-time speed-up over the ISAT method for the two-component shock-droplet interaction case. The ANN method is faster than the ISAT method by 12 times for the four-component shock-droplet interaction. A 7 times speed-up is observed for the TML case for the ANN method compared to the ISAT method while achieving a data compression factor of 2881. The ANN method also shows intrinsic load balancing, unlike traditional VLE solvers. A strong parallel scalability of this ANN method with the number of processors was observed for all the three test cases. Code repository for 0D VLE solvers, and C++ ANN interface—https://github.com/UMN-CRFEL/ANN_VLE.git.

Analysis of the effect of probe structure on sampling accuracy in supersonic airflow

The accuracy of the sampling of the gas components has a significant impact on the measurement of various performance parameters in the combustion chamber of an aero-engine. This paper examines the accuracy of a six-point gas sampling probe when used in supersonic airflow. A numerical simulation method of component transport and fluid-solid coupling is employed to construct a three-dimensional probe multi-component gas flow characteristic solution model. Three kinds of probes with 28°, 30° and 32° angles and structure-modified conical probes were established, and the influence law of probe structure on gas sampling accuracy was analyzed. The results of the study demonstrate that the 28° and structurally modified conical probes yield a more effective improvement in sampling accuracy in comparison to the original 30° structure. The test data of the test bench are in good agreement with the simulation results, thereby demonstrating the reliability and accuracy of the sampling probe following structural modification.

Pore scale modeling on microbial hydrogen consumption and mass transfer of multicomponent gas flow in underground hydrogen storage of depleted reservoir

As first effort in literature, this study proposed a mathematical model for microbial hydrogen consumption of underground hydrogen storage in the depleted reservoir, considering phase-change mechanism in growth-decay of bio-film, methanogen reaction, and mass transfer in the multicomponent flow. Effects of the growth-decay mechanisms of methanogens on pore structure, permeability and gas components, were simulated and analyzed in 2D and 3D porous models. The results indicated that: 1) The potential risk of the clogging of the pore space by microbial community was confirmed. 2) The initial volume fraction of microbial saturation (VFm) has a great effect on the growth and decay mechanism of methanogen which adopts the hydrogen as the energy source. 3) The optimized decay coefficient of the biomass could be achieved to decrease the loss of hydrogen and its purity. 4) The reduction rate of porosity and normalized permeability (KN) was believed to be related to decay-growth mechanism of microbials and the pore structure. The model with a lower porosity would lead to a higher saturation of biofilm-water layer (BWL), as well as a higher reduction of the porosity. The required time to reach the maximum BWL was the same, when assuming the growth process of methanogen was homogeneous and isotopic.

Giant Effect of CO2 Injection on Multiphase Fluid Adsorption and Shale Gas Production: Evidence from Molecular Dynamics.

Carbon dioxide (CO2) injection in unconventional gas-bearing shale reservoirs is a promising method for enhancing methane recovery efficiency and mitigating greenhouse gas emissions. The majority of methane is adsorbed within the micropores and nanopores (≤50 nm) of shale, which possess extensive surface areas and abundant adsorption sites for the sequestration system. To comprehensively discover the underlying mechanism of enhanced gas recovery (EGR) through CO2 injection, molecular dynamics (MD) provides a promising way for establishing the shale models to address the multiphase, multicomponent fluid flow behaviors in shale nanopores. This study proposes an innovative method for building a more practical shale matrix model that approaches natural underground environments. The grand canonical Monte Carlo (GCMC) method elucidates gas adsorption and sequestration processes in shale gas reservoirs under various subsurface conditions. The findings reveal that previously overlooked pore slits have a significant impact on both gas adsorption and recovery efficiency. Based on the simulation comparisons of absolute and excess uptakes inside the kerogen matrix and the shale slits, it demonstrates that nanopores within the kerogen matrix dominate the gas adsorption while slits dominate the gas storage. Regarding multiphase, multicomponent fluid flow in shale nanopores, moisture negatively influences gas adsorption and carbon storage while promoting methane recovery efficiency by CO2 injection. Additionally, saline solution and ethane further impede gas adsorption while facilitating displacement. Overall, this work elucidates the substantial effect of CO2 injection on fluid transport in shale formations and advances the comprehensive understanding of microscopic gas flow and recovery mechanisms with atomic precision for low-carbon energy development.

A Volume-of-Fluid method for multicomponent droplet evaporation with Robin boundary conditions

We propose a numerical method tailored to perform interface-resolved simulations of evaporating multicomponent two-phase flows. The novelty of the method lies in the use of Robin boundary conditions to couple the transport equations for the vaporized species in the gas phase and the transport equations of the same species in the liquid phase. The Robin boundary condition is implemented with the cost-effective procedure proposed by Chai et al. [1] and consists of two steps: (1) calculating the normal derivative of the mass fraction fields in cells adjacent to the interface through the reconstruction of a linear polynomial system, and (2) extrapolating the normal derivative and the ghost value in the normal direction using a linear partial differential equation. This methodology yields a second-order accurate solution for the Poisson equation with a Robin boundary condition and a first-order accurate solution for the Stefan problem. The overall methodology is implemented in an efficient two-fluid solver, which includes a Volume-of-Fluid (VoF) approach for the interface representation, a divergence-free extension of the liquid velocity field onto the entire domain to transport the VoF, and the temperature equation to include thermal effects. We demonstrate the convergence of the numerical method to the analytical solution for multicomponent isothermal evaporation and observe good overall computational performance for simulating non-isothermal evaporating two-fluid flows in two and three dimensions.

IMAGING OF BUBBLY FLOW USING ULTRASOUND

Flow measurement is a vital ‎issue in instrumentation and has been applied in the various industries. The characteristics of a single phase regime has been extensively researched. On the other hand obtaining the characteristics of a multi-component flow is more complex and traditional equipment do not provide ‎reliable results. As such, tomography utilizing non-invasive ‎transducers is getting attention in the industries because it does not invade the flow. Ultrasonic tomography is among the methods which is suitable for flow containing bubbles. In this project, 16 ultrasonic transducers are placed around a flow pipe. Five different phantoms representing solid flow are placed in the pipe. The flow is imaged using the linear back projection algorithm. The results show that the system was able to image the phantoms which are placed at different locations.

Modelling of Multicomponent Fluid Flow in Deforming and Reacting Porous Rock

We propose a coupled hydro-chemo-mechanical model and its 1D numerical implementation. We demonstrate its application to model filtration of a multicomponent fluid in deforming and reacting host rocks, considering changes in the densities, phase proportions and chemical compositions of coexisting phases. We presented 1D numerical implementation on the example of soapstone formation from serpentinite during H₂O-СО2 fluid filtration with low concentration of СО2 coupled with viscous deformation of mineral matrix, considering MgO-SiO2-H₂O-СО2 system. The numerical results show porosity wave propagation by viscous (de)compaction mechanism accompanied with the formation of an elongated zone with higher filtration properties. After the formation of such a channel, the formation and propagation of reaction fronts occurs associated with the transformation of the mineral composition of the original rock. During H2O-CO2 fluid filtration, starting from 1 weight percent of dissolved CO2, carbonization of hydrated serpentinite starts, specifically antigorite transforms to magnesite and talc.

Numerical modeling of the non-equilibrium condensation in multi-component flows through the high expansion ratio nozzles

Excessive flow expansion in the thruster nozzles reduces the flow temperature and pressure. This provides conditions for the condensation phenomena in the nozzle, which can affect the thrust performance of thrusters. In this paper, the condensation effect of water components in the decomposition products of hydrogen peroxide in a typical thruster nozzle is modeled. To describe the state and properties of the real gas mixture, the Peng-Robinson equation of state is used. Moreover, the effects of H2O2 concentration and nozzle profile on the condensation and nozzle performance parameters are studied. The results show that by more flow expansion and crossing the saturated state of condensable components, the thrust coefficient improves up to 6%. This improvement decreases by increasing the H2O2 concentration in the reaction chamber for a fixed nozzle expansion ratio. Due to the small growth of droplets during the free molecular regime of the droplet growth in the high-speed flow, the non-equilibrium condensation continues until the nozzle outflow. In addition, although all the profiles have the same expansion ratio for nucleation start, increasing the nozzle length results in larger nano-droplets, more liquid mass fraction formation up to 4%, and moving the Wilson point to the further upstream sections in the nozzle.

Unfolding of shocked hydrodynamic instability at SF[formula omitted] elliptical interface: Physical insights from numerical simulations

The Richtmyer–Meshkov (RM) instability widely exists in variety of industrial and scientific applications, such as in inertial confinement fusion, astrophysics explosions, supersonic combustion, bubble dynamics and cavitation. This study investigates the unfolding physical phenomena of RM instability at SF6 elliptical bubbles using numerical simulations. In contrast to cylindrical bubble, both shocked horizontal/vertical-aligned elliptical bubbles with different aspect ratios are considered, emphasizing the aspect ratio effects on flow morphology, complex wave patterns, interface deformation, vorticity generation, and interface features. For this purpose, a two-dimensional system of compressible Navier–Stokes-Fourier equations for multicomponent flows are solved using by a mixed modal discontinuous Galerkin method. Numerical simulations illustrate that the aspect ratio of elliptical bubbles have a significant influence on the vortex dynamics and the associated RM instability flows in contrast to the cylindrical bubble. In horizontal-aligned elliptical bubbles, some additional complex waves pattern, including inward jet and secondary vortex rings are observed. While, in vertical-aligned elliptical bubbles, the interface between two primary vortex rings is always vertical and has a “hippocampus” appearance due to the enhancement of downstream velocity. The baroclinic vorticity due to misalignment of density and pressure gradients at interface affects the bubble deformation and induces the Kelvin–Helmholtz instability, which leads to turbulent mixing. It is observed that the complexity of the vorticity fields is enhanced with increasing aspect ratios. Further, these aspect ratio effects result in integral diagnostic of important spatially integrated fields, and various interface features.

The divergence-free velocity formulation of the consistent Navier-Stokes Cahn-Hilliard model with non-matching densities, divergence-conforming discretization, and benchmarks

The prototypical diffuse-interface model that describes multi-component flows is the Navier-Stokes Cahn-Hilliard model (NSCH). Over the last decades many NSCH models have appeared that claim to describe the same physical phenomena, yet are distinct from one another. In a recent article [M.F.P. ten Eikelder, K.G. van der Zee, I. Akkerman, and D. Schillinger, Math. Mod. Meth. Appl. S. 33, pp 175-221, 2023.] we have established a unified framework of virtually all NSCH models. The framework reveals that there is only a single consistent NSCH model that naturally emanates from the underlying mixture theory. In the current article we present, verify and validate this novel consistent NSCH model by means of numerical simulation. To this purpose we discretize a divergence-free velocity formulation of the consistent NSCH model using divergence-conforming isogeometric spaces. We compare computations of our consistent model to results of existing models from literature. The predictive capability of the numerical methodology is demonstrated via three-dimensional computations of a rising bubble and the contraction of a liquid filament that compare well with experimental data.

High viscosity ratio multicomponent flow simulations in porous media using a pseudo-potential central moment lattice Boltzmann method

Multicomponent Immiscible flows within porous media are a pivotal concern in engineering applications, especially in contexts such as oil reservoirs, which exhibit a broad spectrum of properties, including varying viscosities. The precise characterization of flow dynamics, particularly when confronted with a dynamic contact interface within intricate and heterogeneous structures, has remained a significant challenge in the field. This study employs an enhanced Pseudo-potential Central Moment Lattice Boltzmann Method to simulate multicomponent immiscible flows within porous media. The model is implemented through an in-house CUDA code (called Dena) to leverage the parallel processing capabilities of the Lattice Boltzmann Method. In order to assess the accuracy and effectiveness of this method, several test cases are examined, including the Capillary Intrusion Test, the Fingering Process, and the Drainage Process within a real porous medium. Comparative analysis against analytical and experimental results substantiates the model's capabilities and accuracy. Furthermore, the impact of viscosity ratio variations among different flow components within porous media is investigated. With the developed approach, it is possible to span a range of viscosity ratios up to 2132. The findings underscore the model's stability and accuracy in simulating high-viscosity ratio multicomponent fluid flows within porous media.

SIMMER code two-fluid model well-posedness and stability for simulating liquid metal (lead–lithium eutectic), water vapor, and non-condensable gases multi-component multi-phase flows

Liquid metals are employed as a coolant in liquid metal fast reactors (LMFR) and are considered breeders and coolants for future power-producing fusion reactors. The interaction of liquid metals with other coolants, such as air and water, is one of the possible occurrences in liquid metal-cooled reactors. Although the SIMMER-III computer code is currently in the validation and verification phase, it is a prospective candidate code for correctly investigating possible accidents. This study aims to determine the stability and well-posedness of the SIMMER-III code Eulerian-Eulerian two-fluid model (TFM) under any such accident scenario. This work also considers the influence of the virtual mass force and diffusion forces in momentum on TFM stability in accelerated liquid metal, steam, and non-condensable gaseous flows throughout all flow regimes. The characteristics method is used to assess the ill-posed nature of TFM for all types of accidents and accident scenarios in a hypothetical simplified system model with several components (Lead–Lithium, non-condensable gases, and water vapor). It has been discovered that the analysis findings vary from the air and water two-component two-phase flows (characteristics roots spectrum and error growth rate patterns) and are particularly sensitive to the diffusion and virtual mass coefficients. This is because liquid metals have a higher density than liquid water and steam, resulting in strong virtual mass forces and weak diffusion forces in liquid-metal and gas two-phase flows. Because of the extensive range of possible interactions between fluxes of different components, producing an accurate representation of diffusion in multi-component mixtures is difficult. Because of this, it is strongly suggested that the virtual mass coefficient and diffusion coefficients be handled more accurately for these kinds of flows. The values of these coefficients significantly affect how accurate proposed TFM predictions are, but there hasn't been much research on how to estimate them. The study also sheds light on the model's accuracy and highlights the areas where the model's predictions will be mathematically trustworthy.