Multicomponent Simulations Research Articles

A diffuse-interface method for reducing spurious pressure oscillations in multicomponent transcritical flow simulations

Spurious pressure oscillations are a numerical instability that is commonly observed in multiphase and multicomponent flow problems near the critical point. A diffuse-interface model has been created to simulate transcritical mixing in multispecies and multiphase systems where spurious pressure oscillations pose a serious challenge in achieving convergence. To reduce the spurious pressure oscillations, three methods have been proposed and implemented in the present paper: (1) artificially thickening the interface between different species, (2) reconstruction of the primitive variables in the characteristics space, and (3) developing a hybrid method (HY) that switches between quasi-conservative (QC) double-flux (DF) and the classical fully-conservative numerical procedures based on the changes in the effective specific heat ratio and the effective reference internal energy. The cases considered include (1) a transcritical shock tube problem between nitrogen and n-dodecane, (2) a near-critical shock-droplet interaction, and (3) the transcritical Spray A benchmark case of Engine Combustion Network (ECN) that represents the injection of n-dodecane into a high-pressure and high-temperature nitrogen environment. Characteristic-wise reconstruction of the primitive variables in our proposed fully-conservative method tends to reduce the spurious pressure oscillations compared to primitive-wise reconstruction including the reconstruction of the speed of sound. The HY model is found to effectively reduce the magnitude of the spurious pressure oscillations, the loss of energy conservation, and provides more accurate results for all tested cases. The artificial thickening of the interface between different species is found to reduce spurious pressure oscillations and reduce energy conservation loss when used in conjunction with a QC method (HY or DF).

Surrogate Model for Multi-Component Diffusion of Uranium through Opalinus Clay on the Host Rock Scale

Multi-component (MC) diffusion simulations enable a process based and more precise approach to calculate transport and sorption compared to the commonly used single-component (SC) models following Fick’s law. The MC approach takes into account the interaction of chemical species in the porewater with the diffuse double layer (DDL) adhering clay mineral surfaces. We studied the shaly, sandy and carbonate-rich facies of the Opalinus Clay. High clay contents dominate diffusion and sorption of uranium. The MC simulations show shorter diffusion lengths than the SC models due to anion exclusion from the DDL. This hampers diffusion of the predominant species CaUO2(CO3)32−. On the one side, species concentrations and ionic strengths of the porewater and on the other side surface charge of the clay minerals control the composition and behaviour of the DDL. For some instances, it amplifies the diffusion of uranium. We developed a workflow to transfer computationally intensive MC simulations to SC models via calibrated effective diffusion and distribution coefficients. Simulations for one million years depict maximum uranium diffusion lengths between 10 m and 35 m. With respect to the minimum requirement of a thickness of 100 m, the Opalinus Clay seems to be a suitable host rock for nuclear waste repositories.

Compositional Modeling of Dimethyl Ether–CO2 Mixed Solvent for Enhanced Oil Recovery

Dimethyl ether (DME) is a compound first introduced by Shell as a chemical solvent for enhanced oil recovery (EOR). This study aims to investigate the efficiency of EOR using the minimum miscible pressure (MMP) and viscous gravity number when a mixed solvent of CO2 and DME is injected. Adding DME to the CO2 water-alternating-gas process reduces the MMP and viscous gravity number. Reduction in MMP results in miscible conditions at lower pressures, which has a favorable effect on oil swelling and viscosity reduction, leading to improved mobility of the oil. In addition, the viscous gravity number decreases, increasing the sweep efficiency by 26.6%. Numerical studies were conducted through a series of multi-phase, multi-component simulations. At a DME content of 25%, the MMP decreased by 30.1% and the viscous gravity number decreased by 66.4% compared with the injection of CO2 only. As a result, the maximum oil recovery rate increased by 31% with simultaneous injection of DME and CO2 compared with only using CO2.

Intrinsic Nano-Diffusion-Couple for Studying High Temperature Diffusion in Compositionally Complex Superalloys

We present a new approach for the quantitative study of high-temperature diffusion in compositionally complex superalloys on the nano-scale. As key element, the approach utilizes the γ/γ'-microstructure itself as intrinsic nano-diffusion-couple. By establishing equilibrium at one temperature followed by annealing at a different temperature, well-defined transient states are generated which are studied using analytical transmission electron microscopy (TEM). We demonstrate this approach for a high-performance multi-component superalloy. The temporal evolution of element concentrations is consistently revealed for γ- and γ'-forming elements and is compared to multi-component diffusion simulations. Excellent agreement is obtained for Ni, Co, and Cr whereas diffusion of Al and, in particular, Re lacks behind in the experiment. Finally, it is demonstrated that transient states can also be captured by in-situ TEM using chip-based heating devices. The nano-diffusion-couple approach offers great opportunities for diffusion studies in compositionally complex superalloys and might be extended to other two-phase multicomponent systems.

A shock-stable modification of the HLLC Riemann solver with reduced numerical dissipation

The purpose of this paper is twofold. First, the application of high-order methods in combination with the popular HLLC Riemann solver demonstrates that the grid-aligned shock instability can strongly affect simulation results when the grid resolution is increased. Beyond the well-documented two-dimensional behavior, the problem is particularly troublesome with three-dimensional simulations. Hence, there is a need for shock-stable modifications of HLLC-type solvers for high-speed flow simulations.Second, the paper provides a stabilization of the popular HLLC flux based on a recently proposed mechanism for grid aligned-shock instabilities Fleischmann et al. (2020) [8]. The instability was found to be triggered by an inappropriate scaling of acoustic and advection dissipation for local low Mach numbers. These low Mach numbers occur during the calculation of fluxes in transverse direction of the shock propagation, where the local velocity component vanishes. A centralized formulation of the HLLC flux is provided for this purpose, which allows for a simple reduction of nonlinear signal speeds. In contrast to other shock-stable versions of the HLLC flux, the resulting HLLC-LM flux reduces the inherent numerical dissipation of the scheme.The robustness of the proposed scheme is tested for a comprehensive range of cases involving strong shock waves. Three-dimensional single- and multi-component simulations are performed with high-order methods to demonstrate that the HLLC-LM flux also copes with latest challenges of compressible high-speed computational fluid dynamics.

Combining thermodynamics with tensor completion techniques to enable multicomponent microstructure prediction

Multicomponent alloys show intricate microstructure evolution, providing materials engineers with a nearly inexhaustible variety of solutions to enhance material properties. Multicomponent microstructure evolution simulations are indispensable to exploit these opportunities. These simulations, however, require the handling of high-dimensional and prohibitively large data sets of thermodynamic quantities, of which the size grows exponentially with the number of elements in the alloy, making it virtually impossible to handle the effects of four or more elements. In this paper, we introduce the use of tensor completion for high-dimensional data sets in materials science as a general and elegant solution to this problem. We show that we can obtain an accurate representation of the composition dependence of high-dimensional thermodynamic quantities, and that the decomposed tensor representation can be evaluated very efficiently in microstructure simulations. This realization enables true multicomponent thermodynamic and microstructure modeling for alloy design.

Comparison of finite volume and lattice Boltzmann methods for multicomponent flow simulations

AbstractIn pseudopotential lattice Boltzmann (LB) models for simulating multicomponent flows, interaction forces between the components of a mixture lead to phase separation and interfacial tension. At the macroscopic scale, such LB models solve an advection‐diffusion equation for each component and the Navier‐Stokes equations for the fluid mixture. In this paper, the computational efficiency of the LB method is compared with a finite volume (FV) solver for the same macroscopic‐scale equations for a binary system in a two dimensional domain. The FV implementation replicates the phase separation of the LB model. Differences in the interfacial tension are due to truncation of the Taylor series expansion of the LB interaction force in the FV version. While the computations required to update the domain for each timestep can be completed faster with the FV approach, a smaller timestep is required to achieve stability, which negates the improvement in processing speed. The FV implementation, however, allows independent variation of model parameters, which is not possible in LB. For example, the viscosity can be changed without affecting interfacial tension or the extent of phase separation. Furthermore, it is possible to obtain low interfacial tensions without suppressing phase separation with the FV formulation. The significance of changing the diffusion rate of components on the deformation of a droplet in shear is also demonstrated. For three‐dimensional simulations, the finite volume approach is expected to be faster than LB and would benefit from the demonstrated flexibility in specifying model parameters.

Complex multicomponent real-fluid thermodynamic model for high-pressure Diesel fuel injection

The Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) has been coupled with Vapor-Liquid Equilibrium (VLE) calculations in a density-based solver of the Navier-Stokes equations to perform multicomponent two-phase simulations of Diesel injections at high-pressure conditions. This molecular-based EoS requires three empirically determined but well-known parameters to model the properties of a specific component, and thus, there is no need for extensive model calibration, as is typically the case when the NIST (REFPROP) library is utilised. PC-SAFT can handle flexibly the thermodynamic properties of multi-component mixtures for which the NIST (REFPROP) library supports only limited component combinations. Moreover, complex hydrocarbon mixtures can be modelled as a single pseudo-component knowing its number averaged molecular weight (MW) and hydrogen-to-carbon (HN/CN) ratio. Published molecular dynamic simulations have been utilised to demonstrate that the developed algorithm properly captures the VLE interface at high-pressure conditions. Several advection test cases and shock tube problems were performed to validate the numerical framework using analytical and exact solutions. Additionally, two-dimensional simulations of n-dodecane and Diesel injections into nitrogen are included to demonstrate the multidimensional, multispecies and multiphase capability of the numerical framework.

A modified Monod rate law for predicting variable S isotope fractionation as a function of sulfate reduction rate

Abstract Microbial sulfate reduction is associated with characteristic S isotope partitioning, which can aid in determining the rate of this ubiquitous reactive pathway in a wide variety of reducing environments. Here we introduce a new simple yet predictive model that expands the range of environmental conditions over which this functional relationship can be applied through the use of a modified Monod rate expression constrained by a novel set of experiments. A series of continuously-fed batch reactors containing an equivilant biomass of Desulfovibrio vulgaris, a sulfate reducing bacteria, were subjected to differing continuous mass addition rates of formate to precisely control the rate of sulfate reduction via electron donor limitation. Based on growth yield calculations, additional biomass accumulation was negligible. The isotopic composition (δ34S) of the residual sulfate pool was measured through time for each experiment. This approach resulted in five steady state reduction rates of 2.06, 1.22, 0.83, 0.52 and 0.28 μmol * h−1 that enriched the unreacted sulfate in 34S by unique characteristic enrichment factors (αobs) of 0.9976, 0.9962, 0.9938, 0.9924 and 0.9903, respectively. This relationship was used to calibrate a new coupled set of isotope-specific Monod rate laws that have been modified to incorporate (1) a minimum (α1) and maximum (α2) fractionation factor and (2) a rate-controlling electron donor factor (DF). Application of these parameters in the updated model reproduce most of our data and simulate realistic shifts in the observed fractionation factor (αobs) as a function of reduction rate in an electron donor limited system. The model was applied to our current dataset as well as three previous studies, which collectively provide a broad range in both rates and αobs, and support validation across substantially different conditions. We show that this approach offers a reasonable approximation to more detailed microbial reactive network models, while still maintaining sufficient simplicity and versatility to allow incorporation into multi-component reactive transport simulations. Thus, the current study provides a foundation for accurate simulation of the relationship between αobs and sulfate reduction rates in open, transient, and through-flowing systems.

Application of an Equilibrium-Phase Spray Model to Multicomponent Gasoline Direct Injection

An Equilibrium Phase (EP) spray model has been recently proposed for modeling high-pressure diesel fuel injection, which is based on jet theory and a phase equilibrium assumption. In this approach, the non-equilibrium processes of drop breakup, collision and surface vaporization are neglected, assuming that spray vaporization is a mixing-controlled equilibrium process. A liquid-jet model and a gas-jet model are also intro-duced to improve grid-independency. In the current study, the EP model is applied in simulations of multi-hole gasoline direct injection (GDI). The model is validated at ambient densities from 3 to 9 kg/m3 and ambient temperatures from 400 K to 900 K, for two different GDI injectors, i.e. the Engine Combustion Network (ECN) Spray G injector and a GM injector. Iso-octane is used as the surrogate in consistency with available experi-ments. The results show good agreement in terms of liquid/vapor penetration, shape of the vapor envelope, and the velocity evolution along the injector centerline. Then, a 10-component gasoline surrogate fuel is used to demonstrate the capability of this model for multi-component spray simulations, which is essential for engine combustion and emission predictions.

Toward Optimizing LNAPL Remediation

AbstractOptimizing the remediation of light nonaqueous phase liquids (LNAPLs) to achieve an acceptable endpoint status for a site is not trivial. Recently, Sookhak Lari, Johnston, et al. (2018, https://doi.org/10.1016/j.jhazmat.2017.11.006), Sookhak Lari, Rayner, and Davis (2018, https://doi.org/10.1016/j.jenvman.2018.07.041) conducted three‐dimensional multiphase, multicomponent simulations to address LNAPL remediation endpoints for a single recovery well. However, optimized LNAPL remediation for multiple wells is not addressed in the literature. In the first part of this paper, we establish a matrix of 10 simulation scenarios to show the sensitivity of the remedial endpoint (i.e., what is feasibly achieved) to several parameters including viscosity and partitioning attributes of the LNAPL, heterogeneity of the formation, and the location and number of the recovery wells. While this addresses the variability of LNAPL removal from the subsurface and is valuable in its own right, it does not address the optimal removal of LNAPL. We address this in the second part of the paper by linking a genetic algorithm to TMVOC‐MP to allow, for example, the assessment of the optimal number and location of LNAPL recovery wells in a field‐scale problem. Using supercomputing facilities and within 49 genetic algorithm generations, each including 150 members, highly optimized answers to different objective functions were obtained. For the first time, such a multiphase, multicomponent optimization tool promises the possibility of optimizing LNAPL remediation at field scale to achieve practicable endpoint conditions, within computational affordability.

Development of a less-dissipative hybrid AUSMD scheme for multi-component flow simulations

In this study, a less-dissipative hybrid AUSMD scheme considering the linearized approximated solution around the material interfaces of compressible multi-component flows is proposed. A high-resolution reconstruction scheme, so-called MUSCL + THINC, has been devised by combining the MUSCL method with the Tangent of Hyperbola for Interface Capturing technique (THINC) under the boundary variation diminishing concept, which is used to determine the cell-interface values to evaluate the AUSMD flux. Several perfect gas and multi-component flow problems are selected as the benchmark test cases. The flow models we use here are the perfect gas Euler equations and the multi-phase five-equation flow model. We compared the proposed MUSCL + THINC-type AUSMD scheme with the original MUSCL-type AUSMD scheme to verify its capability of capturing shock waves, expansion fans, and material interfaces, which are identified as a well-defined sharp jump in volume fraction. Numerical results of all benchmark tests show that the MUSCL + THINC-type AUSMD solver is superior to the original MUSCL-type AUSMD in resolving shock waves, expansion fans, and interfaces. In particular, the solution quality for expansion fans and interfaces on coarse grids is greatly improved by the MUSCL + THINC-type AUSMD scheme.

Mach number effect on the instability of a planar interface subjected to a rippled shock

The Richtmyer-Meshkov (RM) instability of a planar interface (${\mathrm{N}}_{2}\ensuremath{-}{\mathrm{SF}}_{6}$) subjected to a sinusoidal rippled shock, as the variant of a sinusoidal interface impinged by a planar shock, is investigated through high-order compressible multicomponent hydrodynamic simulations. The rippled shock is generated by a planar shock penetrating through a single-mode interface ($\mathrm{He}\ensuremath{-}{\mathrm{N}}_{2}$), and its propagation characteristic agrees reasonably with Bates' analytical solution. Evolution of the flat contact surface impacted by the rippled shock is found to be heavily dependent on the rippled shock phase, and it can be well explained by the impulsive perturbation and continuous perturbation regimes. Various rippled shocks with different Mach numbers ranging from 1.15 to 1.80 are considered. It is found that the influence of the shock strength on the instability growth behaves differently for rippled shocks at different phases. In the case that the shock-interface collision happens when the rippled shock amplitude vanishes for the first time, as the shock strength increases, the impulsive perturbation (i.e., amplitude growth caused by the impulsive shock impact) plays an increasingly more important role in the instability growth than the continuous perturbation (i.e., amplitude growth induced by the disturbed postshock pressure field). In contrast, in the case that the impingement occurs when the rippled shock amplitude becomes zero for the second time, the instability development contributed by the impulsive perturbation is a certain percentage of the total instability growth regardless of the shock strength. The role of the impulsive perturbation in the present nonstandard RM instability within the single-mode framework can be reasonably predicted by an empirical formula combined with the model of Ishizaki et al. [Phys. Rev. E 53, R5592 (1996)].

Chemo-elastic phase-field simulation of the cooperative growth of mutually-accommodating Widmanstätten plates

A comprehensive understanding of the phase transformations is of primary importance to optimize the properties of a material. In the present study, a novel and thermodynamically consistent chemo-elastic multiphase-field model is formulated to simulate phase transformations which yield unique needle-like patterns, referred to as Widmanstätten structure. Owing to the critical role of the curvature in the growth of the Widmanstätten structure, the model is devised to recover the sharp interface solutions, despite the introduction of a diffuse interface. This condition is fulfilled by formulating the chemical and the elastic driving force based on the grand potential density and the mechanical jump conditions, respectively. Additionally, to render a quantitative chemical driving force, parameters from CALPHAD-database (TCFE8) are incorporated. The current work, through the multicomponent multiphase-field simulations, shows that at high temperatures, when the chemical driving force is insufficient to actuate the growth of a plate, the Widmanstätten structure evolves by the co-operative growth of self-accommodating plates. Furthermore, the growth of a single Widmanstätten plate at low temperature is also simulated, and the growth kinetics of the transformations are verified through existing analytical predictions.

A multimass correction for multicomponent fluid flow simulation using smoothed particle hydrodynamics

SummaryIn multicomponent fluid flow simulations using smoothed particle hydrodynamics, the Lagrangian particles used are mostly of equal mass. This is preferred over multimass particle setup (particles with different values of mass), as it resolves the fluid interfaces comparatively better. But the flip side of using uniform mass particle setup is that it may not be computationally economical in situations with large‐density ratios. Hence, using multimass particle setup is both economical and perhaps inevitable. An attractive feature of multimass particle setup is that it allows uniform resolution in regions with different values of density. To take advantage of the multimass setup, it is therefore imperative to reduce the error associated with its usage. In this work, we present suitable multimass correction terms and assess its effectiveness using the ∇h–smooth particle hydrodynamics scheme. Standard benchmark problems, viz, shock tube test, triple‐point shock test, Rayleigh‐Taylor instability, and Kelvin‐Helmholtz instability were solved with multimass particle setup, where significant improvements could be achieved in resolving the associated contact discontinuities.

Coupling discrete and continuum concentration particle models for multiscale and hybrid molecular-continuum simulations.

Hybrid molecular-continuum simulation techniques afford a number of advantages for problems in the rapidly burgeoning area of nanoscale engineering and technology, though they are typically quite complex to implement and limited to single-component fluid systems. We describe an approach for modeling multicomponent hydrodynamic problems spanning multiple length scales when using particle-based descriptions for both the finely resolved (e.g., molecular dynamics) and coarse-grained (e.g., continuum) subregions within an overall simulation domain. This technique is based on the multiscale methodology previously developed for mesoscale binary fluids [N. D. Petsev, L. G. Leal, and M. S. Shell, J. Chem. Phys. 144, 084115 (2016)], simulated using a particle-based continuum method known as smoothed dissipative particle dynamics. An important application of this approach is the ability to perform coupled molecular dynamics (MD) and continuum modeling of molecularly miscible binary mixtures. In order to validate this technique, we investigate multicomponent hybrid MD-continuum simulations at equilibrium, as well as non-equilibrium cases featuring concentration gradients.

High-order spectral volume scheme for multi-component flows using non-oscillatory kinetic flux

Abstract In this paper, an arbitrary high-order compact method is developed for compressible multi-component flows with a stiffened gas equations of state (EOS). The main contribution is combining the high-order, conservative, compact spectral volume scheme (SV) with the non-oscillatory kinetic scheme (NOK) to solve the quasi-conservative extended Euler equations of compressible multi-component flows. The new scheme consists of two parts: the conservative part and the non-conservative part. The original high order compact SV scheme is used to discretize the conservative part directly. In order to treat the equation of state of the stiffened gas, the NOK scheme is utilized to compute the numerical flux. Then, careful analysis is made to satisfy the necessary condition to avoid unphysical oscillation near the material interfaces. After that, a high-order compact scheme for the non-conservative part is obtained. This new scheme has the following advantages for numerical simulations of compressible multi-component stiffened gas: high order accuracy with compact stencil and oscillation-free near the material interfaces. Numerical tests demonstrate the good performance and the efficiency of the new scheme for multi-component flow simulations.

A computational assessment of representative sampling of soil gas using existing groundwater monitoring wells screened across the water table

Representative sampling is of great importance to decision making regarding contaminant site risks and remedial effectiveness. A focus here is whether existing groundwater monitoring wells screened across the water table can be sampled to yield representative indicators of soil gas composition. For the first time, we provide multi-phase, multi-component computational simulations to address this. We simulated high and low gas extractions rate strategies to sample the gas phase over short and extended screening intervals across the water table. We investigated the options against a field data set representative of typical hydrocarbon vapour profiles, inclusive of major gases, oxygen and carbon dioxide. We also evaluated the sampling options for uniform and non-uniform multi-component gasoline LNAPL distributions, including hazardous chemicals. Less sensitivity to the sampling option was observed for depth-wise increasing concentration profiles with a near-constant concentration across the screen. Significant discrepancy between the ratio of different compounds in the sample and in-situ (real) values was observed for high-rate gas extraction (particularly for an extended-screen). Low-rate gas extraction provided satisfactory results for all the scenarios. Shorter screening slightly improved the accuracy of this option. Graphical representations are provided to allow assessment of the applicability of each sampling option for various site conditions.

The influence of mixing on stable isotope ratios in porous media: A revised Rayleigh model

AbstractFor an irreversible reaction, the Rayleigh or distillation‐type relationship between stable isotope enrichment and reactant concentration is compromised if fluid samples are characterized by a range of water ages or different extents of reaction progress. Such mixed samples are rarely avoided in the standard methods of sampling fluid from natural porous media. As a result, application of a Rayleigh model to stable isotope ratios measured in aquifers commonly requires a diminished or effective fractionation factor relative to the intrinsic value obtained in the absence of transport effects. Thus, quantitative application of intrinsic parameter values to a fractionating reaction occurring in porous media flow requires revision to the functional form of the relationship between reactant concentration and isotope fractionation. Here we derive a series of analytical solutions for the relationship between fractionation and flow subject to nonuniform fluid travel time distributions. These solutions are unique from previous approaches in that they avoid the use of a dispersion coefficient. The results are demonstrated against multicomponent reactive transport simulations of stable isotope fractionation in homogeneous and spatially correlated heterogeneous flow fields, and applied to a data set of stable chromium (Cr) isotope enrichment obtained from a contaminated aquifer. We show that the flux‐weighted isotope ratio of a solute is more sensitive to the effects of physical heterogeneity than solute concentrations. Our results support an updated functional form of the traditional Rayleigh model that describes the relationship between reactant concentration and isotope fractionation and is valid for a mixed‐fluid sample.

The effect of gme topology on multicomponent adsorption in zeolitic imidazolate frameworks.

We employ a simulation approach to study the adsorption of single, binary and ternary mixtures on eight gme Zeolitic Imidazolate Frameworks (ZIFs) at 298 K. Four adsorbate fluids were considered; carbon dioxide, methane, nitrogen and water. We compute the high pressure adsorption density profiles inside the micropore channels of each crystal. The profiles are compared directly for the different structures and adsorbate components and used to highlight the influence of the imidazolate ligands on pure and competitive adsorption. ZIFs with long ligands reveal an additional, accessible to the fluid space detected for the first time. This is a wedged volume on one direction of the pore walls, shaped thus because the long ligands tilt in order to be connected. We estimate the pressure required for water to become the dominating competing adsorbate within different crystal cavities. The simulated data for CO2 adsorption in ZIF69 strongly correlate with a set of Raman spectroscopy intensity values that correspond to the same adsorbate-adsorbent system.