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DOE OSTI2019

The Importance of Viscous and Interfacial Forces in the Hydrodynamics of the Top-Submerged-Lance Furnace

The purpose of this work is to focus on the hydrodynamics of a Top-Submerged-Lance (TSL) smelting furnace, understanding how liquid properties and operational parameters act on key factors of a TSL process, such as splashing, mixing, mass transfer area, and bubble development. A deep knowledge of all those aspects is needed since they all influence the smelting reaction rates; hence the efficiency of the reactor. The characterization and scaling of the TSL gas injection are commonly based on the modified Froude number, the ratio of dynamic and gravitational forces. Detailed literature research reveals a potential weakness of this approach, since it does not consider the effects of viscosity and surface tension. To investigate this question an extensive parametric study was performed applying computational fluid dynamics to cold and non-reactive flows, which provided a broad overview of the physics of the flow. The analysis was performed on fluid dynamic properties (liquid density, liquid viscosity, surface tension) and operational variables (gas volume flow, lance immersion depth). The coupled Level Set—Volume of Fluid model, available in the commercial solver ANSYS Fluent{sup ®}, was used to resolve the gas–liquid interface in the multiphase flow. The results of the work underscore the significance of the viscous and interfacial forces for gas injection in smelting slags, confirming the incompleteness of applying only the Froude number to describe such flows.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Assessment of model parameters in MFiX particle-in-cell approach

The limitations in numerical treatment of solids-phase in conventional methods like Discrete Element Model and Two-Fluid Model have facilitated the development of alternative techniques such as Particle-In-Cell (PIC). However, a number of parameters are involved in PIC due to its empiricism. In this work, global sensitivity analysis of PIC model parameters is performed under three distinct operating regimes common in chemical engineering applications, viz. settling bed, bubbling fluidized bed and circulating fluidized bed. Simulations were performed using the PIC method in Multiphase Flow with Interphase eXchanges (MFiX) developed by National Energy Technology Laboratory (NETL). A non-intrusive uncertainty quantification (UQ) based approach is applied using Nodeworks to first construct an adequate surrogate model and then identify the most influential parameters in each case. This knowledge will aid in developing an effective design of experiments and determine optimal parameters through techniques such as deterministic or statistical calibration.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2023

Model-parallel Fourier neural operators as learned surrogates for large-scale parametric PDEs

Fourier neural operators (FNOs) are a recently introduced neural network architecture for learning solution operators of partial differential equations (PDEs), which have been shown to perform significantly better than comparable deep learning approaches. Once trained, FNOs can achieve speed-ups of multiple orders of magnitude over conventional numerical PDE solvers. However, due to the high dimensionality of their input data and network weights, FNOs have so far only been applied to two-dimensional or small three-dimensional problems. To remove this limited problem-size barrier, we propose a model-parallel version of FNOs based on domain-decomposition of both the input data and network weights. Here, we demonstrate that our model-parallel FNO is able to predict time-varying PDE solutions of over 2.6 billion variables on Perlmutter using up to 512 A100 GPUs and show an example of training a distributed FNO on the Azure cloud for simulating multiphase CO 2 dynamics in the Earth’s subsurface.

58 GEOSCIENCES↗

DOE OSTI2022

Experimental measurements of gas-particle flows in large-scale strippers

Measurements of gas–solid particle flow in a large-scale stripper unit are reported. The experiments target industrial (pilot) scale measurements of gas-particle flow that can be used to validate numerical methods for modeling multiphase flows, such as computational fluid dynamics coupled to the discrete element method (CFD-DEM). Specifically, experiments were performed with Geldart Group B (533 µm) glass beads in a stripper unit. In general, previous CFD-DEM validation datasets were performed in benchtop experimental systems and limited to O(10 5 ) particles. Here, in this work, the number of particles in the isolated section of the stripper is O(10 7 ) for all tests. Measurements are reported for a ~2 m tall section of the ~1 m diameter stripper. Radial mass flux profiles measured at five axial positions and three axial pressure drop measurements are reported for six operating conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

A particle resolved simulation approach for studying shock interactions with moving, colliding solid particles

This work applies a new combination of techniques for the fully resolved simulation of compressible, gas–particle multiphase flows. Here, the adaptive wavelet collocation method is used to dynamically, and efficiently, adapt the computational grid to localized flow features and the particles. A characteristic-based volume penalization method that imposes arbitrary Dirichlet, Neumann, or Robin-type immersed boundary conditions, is used to enforce the no-slip condition at particle surfaces. A hard-sphere collision model is applied to capture the particle–particle collisions. Proof of concept test cases are presented, showcasing the dynamic grid adaptation and fully resolved two-way coupling between the phases that is possible with this approach. Results for a shock-driven single cylinder under viscous and inviscid conditions are presented along with a demonstration of a shock interacting with a cloud of randomly distributed cylinders and spheres.

42 ENGINEERING↗

DOE OSTI2018

Application of LES-CFD for predicting pulverized-coal working conditions after installation of NOx control system

The upcoming environmental requirements outlined at the 2017 European Commission Integrated Pollution Prevention and Control (IPPC) are becoming more and more strict in comparison to the existing standards – IED 2010/75/EU. Questions arise about changes in boiler operating conditions after the adoption of the regulations to fulfill specified emission limits. Of initial concern is the question of which technology to pursue in order to reach the specified level of NOx emissions at 150 mg/Nm 3 @6%O 2 . By introducing an air staging technique the NOx limit can be partially achieved; however these changes affect the boiler operation in a detrimental way. In order to investigate impact of de-NOx installation on the temperature and heat flux distribution, numerical techniques can be used. In order to determine the impact of the changes in the boiler operation, here this paper presents the application of an advanced, multiphase open-source code Arches, developed at the University of Utah for modeling pulverized-coal combustion using Large-Eddy Simulation (LES). Numerical simulations showed the effect on the boiler's working parameters e.g., heat-transfer rate, temperature distribution, species concentration, and NOx emission before and after proposed modifications.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2018

Next generation modeling of microbial souring – Parameterization through genomic information

Biogenesis of hydrogen sulfide (H 2 S) (microbial souring) has detrimental impacts on oil production operations and can cause health and safety problems. Understanding the processes that control the rates and patterns of sulfate reduction is crucial in developing a predictive understanding of reservoir souring and associated mitigation processes. This work demonstrates an approach to utilize genomic information to constrain the biological parameters needed for modeling souring, providing a pathway for using microbial data derived from oil reservoir studies. Minimum generation times were calculated based on codon usage bias and optimal growth temperatures based on the frequency of amino acids. We show how these derived parameters can be used in a simplified multiphase reactive transport model by simulating the injection of cold (30 °C) seawater into a 70 °C reservoir, modeling the shift in sulfate reducing microorganisms (SRM) community composition, sulfate and sulfide concentrations through time and space. Finally, we explore the question of necessary model complexity by comparing results using different numbers of SRM. Simulations showed that the kinetics of a SRM community consisting of twenty-five SRM could be adequately represented by a reduced community consisting of nine SRM with parameter values derived from the mean and standard deviations of the original SRM.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

A coupled thermo-hydro-mechanical model for simulating leakoff-dominated hydraulic fracturing with application to geologic carbon storage

A potential risk of injecting CO2 into storage reservoirs with marginal permeability (≲ 10 mD (1 mD = 10 –15 m 2 )) is that commercial injection rates could induce fracturing of the reservoir and/or the caprock. Such fracturing is essentially fluid-driven fracturing in the leakoff-dominated regime. Recent studies suggested that fracturing, if contained within the lower portion of the caprock complex, could substantially improve the injectivity without compromising the overall seal integrity. Modeling this phenomenon entails complex coupled interactions among the fluids, the fracture, the reservoir, and the caprock. Here, we develop a simple method to capture all these interplays in high fidelity by sequentially coupling a hydraulic fracturing module with a coupled thermal-hydrological-mechanical (THM) model for nonisothermal multiphase flow. The model was made numerically tractable by taking advantage of self-stabilizing features of leakoff-dominated fracturing. The model is validated against the PKN solution in the leakoff-dominated regime. Moreover, we employ the model to study thermo-poromechanical responses of a fluid-driven fracture in a field-scale carbon storage reservoir that is loosely based on the In Salah project's Krechba reservoir. The model reveals complex yet intriguing behaviors of the reservoir-caprock-fluid system with fracturing induced by cold CO 2 injection. We also study the effects of the in situ stress contrast between the reservoir and caprock and thermal contraction on the vertical containment of the fracture. The proposed model proves effective in simulating practical problems on length and time scales relevant to geological carbon storage.

58 GEOSCIENCES↗

DOE OSTI2021

Mathematical modeling of novel porous transport layer architectures for proton exchange membrane electrolysis cells

Thin foil based porous transport layers (PTLs) that contain highly structured pore arrays have shown promise as anode PTLs in proton exchange membrane electrolysis cells. These novel PTLs, fabricated with advanced manufacturing techniques, produce thin, tunable, multifunctional layers with reduced flow and interfacial resistances and high thermal and electric conductivities. To further optimize their design, it is important to understand their fundamental impact on the transport of protons, electrons, and liquid/vapor mixtures in the electrode. In this work, we develop a two-dimensional multiphysics model to simulate the coupled electrochemistry and multiphase transport in an electrolysis cell operated with the novel PTL architecture. The results show that larger pores improve access of water to the anode catalyst layer, which is beneficial for both the oxygen evolution reaction and membrane hydration. Larger pore sizes also improve oxygen gas transport from the catalyst layer, because generated oxygen gas is forced to travel in-plane through the anode catalyst layer until it reaches a pore opening that is connected to a channel. The discussed results confirm that the proposed thin foil based PTLs are fundamentally different from conventional PTLs, such as felts or layered meshes. The model developed in this work also provides generalizable insight into fundamental PEMEC phenomena, such as the competition between liquid and gas phase transport, membrane hydration and water management, and nonuniform electrochemical reactions, which are processes relevant to all PEMEC designs.

25 ENERGY STORAGE↗

DOE OSTI2020

A simple and effective five-equation two-phase numerical model for liquid-vapor phase transition in cavitating flows

Numerical difficulties, notably the non-monotonic behavior of the Wood speed of sound and the volume fraction positivity, associated with the reduced five-equation two-phase flow model of Kapila et al. (2001) [A.K. Kapila, R. Menikoff, J.B. Bdzil, S.F. Son, D.S. Stewart, 2001. Two-phase modeling of deflagration-to-detonation transition in granular materials: reduced equations, Physics of Fluids 13(10), 3002–3024] have been resolved in the past through the introduction of a frozen speed of sound and an algebraic approach for mechanical relaxation afforded by a pressure non-equilibrium six-equation model proposed by [R. Saurel, F. Petitpas, R.A. Berry, 2009. Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixture, J. Comput. Phys. 228, 1678–1712]. By contrast, it is explored and demonstrated in this work that these difficulties can in fact still be resolved within the numerical scheme for solving the reduced five-equation model by numerically replacing the Wood speed of sound for the estimates of wave speeds in the approximate Riemann solver HLLC with the monotonic mixture speed of sound for a transport five-equation model. For shock interface (artificial mixture separating pure or nearly pure fluids) interaction problems, with the apparent advantage of monotonic behavior of the speed of sound in the interface, the effect of the numerical replacement is also confined to the interface. Differences other than the behavior of the speed of sound within the interface in the solutions due to the replacement diminish with increasing resolution when reasonable solution can be obtained with Wood speed of sound. For cavitating/expansion problems in physical fluid mixture, it is pointed out and explained why acoustics in the numerical solutions still propagate at the Wood speed of sound (therefore consistent with the reduced five-equation model) even though in some cases a much higher speed of sound like the numerical replacement above for solving the reduced five-equation model or the frozen speed of sound for solving a six-equation model is used for the estimates of wave speeds in the HLLC scheme. A variant of the five-equation two-phase flow model by Saurel et al. (2008) [R. Saurel, F. Petitpas, R. Abgrall, 2008. Modelling phase transition in metastable liquids: application to cavitating and flashing flows, J. Fluid Mech. 607, 313–350] is then constructed for liquid-vapor phase transition in cavitating flows. The relaxation toward thermo-chemical equilibrium during phase transition is achieved by solving a simple system of algebraic equations for the equilibrium state variables for better efficiency, following Pelanti and Shyue (2014) [M. Pelanti, K.-M. Shyue, 2014. A mixture-energy-consistent six-equation two-phase numerical model for fluid with interfaces, cavitation and evaporation waves. J. Comput. Phys. 259, 331–357]. Therefore, the current model retains both the simplicity afforded by the five-equation model and the efficiency of the algebraic relaxation solver. An alternative algebraic approach for handling the non-conservative term (the so-called K∇ · u term) in the reduced five-equation model for mechanical equilibrium of a liquid-vapor mixture is also explored by enforcing the thermal equilibrium at the same time. Finally, numerical results of sample tests in both one and two dimensions in the literature as well as that in three dimensions demonstrate the effectiveness and ability of the proposed model to simulate cavitating flows. An interesting mechanism of shock generation by acoustics in water due to phase transition is then found by the numerical simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension

Shock waves are often used in experiments to create a shear flow across liquid droplets to study secondary atomization. Similar behavior occurs inside of supersonic combustors (scramjets) under startup conditions, but it is challenging to study these conditions experimentally. In order to investigate this phenomenon further, a numerical approach is developed to simulate compressible multiphase flows under the effects of surface tension forces. The flow field is solved via the compressible multicomponent Euler equations (i.e., the five equation model) discretized with the finite volume method on a uniform Cartesian grid. The solver utilizes a total variation diminishing (TVD) third-order Runge–Kutta method for time-marching and second order TVD spatial reconstruction. Surface tension is incorporated using the Continuum Surface Force (CSF) model. Fluxes are upwinded with a modified Harten–Lax–van Leer Contact (HLLC) approximate Riemann solver. An interface compression scheme is employed to counter numerical diffusion of the interface. The present work includes modifications to both the HLLC solver and the interface compression scheme to account for capillary force terms and the associated pressure jump across the gas–liquid interface. A simple method for numerically computing the interface curvature is developed and an acoustic scaling of the surface tension coefficient is proposed for the non-dimensionalization of the model. The model captures the surface tension induced pressure jump exactly if the exact curvature is known and is further verified with an oscillating elliptical droplet and Mach 1.47 and 3 shock-droplet interaction problems. The general characteristics of secondary atomization at a range of Weber numbers are also captured in a series of simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Predicting the performance uncertainty of a 1-MW pilot-scale carbon capture system after hierarchical laboratory-scale calibration and validation

A challenging problem in designing pilot-scale carbon capture systems is to predict, with uncertainty, the adsorber performance and capture efficiency under various operating conditions where no direct experimental data exist. Motivated by this challenge, we previously proposed a hierarchical framework in which relevant parameters of physical models were sequentially calibrated from different laboratory-scale carbon capture unit (C2U) experiments. Specifically, three models of increasing complexity were identified based on the fundamental physical and chemical processes of the sorbent-based carbon capture technology. Results from the corresponding laboratory experiments were used to statistically calibrate the physical model parameters while quantifying some of their inherent uncertainty. The parameter distributions obtained from laboratory-scale C2U calibration runs are used in this study to facilitate prediction at a larger scale where no corresponding experimental results are available. In this paper, we first describe the multiphase reactive flow model for a sorbent-based 1-MW carbon capture system then analyze results from an ensemble of simulations with the upscaled model. The simulation results are used to quantify uncertainty regarding the design’s predicted efficiency in carbon capture. In particular, we determine the minimum gas flow rate necessary to achieve 90% capture efficiency with 95% confidence.

bubbling bed↗

DOE OSTI2022

Additively manufactured multiplexed inertial coalescence filters

Multiphase flows often pose a significant challenge to the efficient and reliable design of thermofluidic systems. This paper describes multiplexed inertial coalescence filters composed of parallel helical pathways, designed to capture fine droplets (<40 µm) through inertial separation while maintaining a low pressure drop (<400 Pa). Filtration efficiencies for 7 µm and 30 µm droplets were characterized for varying flow conditions, with complete capture observed above a threshold flow rate. Models for filtration efficiency and pressure drop were developed and validated against experimental results to allow system design and optimization, enabled by the tunable additive manufacturing approach used to fabricate the filters. Filter quality factor was computed for varying droplet sizes, showcasing exceptional quality factor when compared to state-of-the-art filters documented in the literature. In conclusion, this multiplexed inertial coalescence filtration approach could find use in dehumidification systems, fog harvesting, chemical reactors, and microgravity droplet capture.

3D Printing↗

DOE OSTI2025

Accurate models of the added mass force of a uniform random distribution of spherical particles or bubbles

The added mass force resulting from the acceleration of a body in a fluid is of fundamental and practical interest in dispersed multiphase flows. Euler–Lagrange (EL) and Euler–Euler (EE) simulations require closure terms for the added mass force in order to accurately couple the conserved variables between phases. Presently, a more thorough understanding of the added mass force in a multi-particle system is developed based on potential flow resulting in a resistance matrix formulation analogous to Stokesian dynamics. This formulation is then used to generate a dataset of added mass resistance matrices for large systems of randomly generated particles. This methodology is used to create a volume fraction corrected binary model for predicting the added mass force in large systems as well as generate statistics of the added mass force in such systems. This work provides clarification to the theory of the added mass force for particle clouds, and modelling options that may be implemented in existing EL and EE codes.

42 ENGINEERING↗

DOE OSTI2025

Three-Dimensional Bubble Fluidics in Architected Porous Media

Gas bubble flows in porous media often exhibit complex and seemingly unpredictable behaviors that are difficult to control. This lack of control limits the ability to design effective devices which manage multiphase flows. Here, we show how the design of 3D printed pores can deterministically control the flow path of an injected gas stream. Open cell structures can be designed to shape the gas/liquid interface with fidelity to control how the two phases are distributed throughout a porous material. The distributed gas volume is free to interact physically and chemically with the surrounding liquid phase, an effect we exploit to create a logical control gate to redirect flows within a lattice. This also allows us to design architectures for reactive capture and aerating bioreactors, resulting in patterned boundaries which can make more effective use of the liquid and gas reagents.

3D microfluidics↗

DOE OSTI2021

Modeling the Size Distribution and Chemical Composition of Secondary Organic Aerosols during the Reactive Uptake of Isoprene-Derived Epoxydiols under Low-Humidity Condition

Reactive uptake of isoprene epoxydiols (IEPOX), which are isoprene oxidation products, onto acidic sulfate aerosols is recognized to be an important mechanism for the formation of isoprene-derived secondary organic aerosol (SOA). While a mechanistic understanding of IEPOX-SOA formation exists, several processes affecting their formation remain uncertain. Evaluating mechanistic IEPOX-SOA models with controlled laboratory experiments under longer atmospherically relevant timescales is critical. Here, we implement our latest understanding of IEPOX-SOA formation within a box model to simulate the measured reactive uptake of IEPOX on polydisperse ammonium bisulfate seed aerosols within an environmental Teflon chamber. The model is evaluated with single-particle measurements of size distribution, volume, density, and composition of aerosols due to IEPOX-SOA formation at timescales of hours. Additionally, we find that the model can simulate the growth of particles due to IEPOX multiphase chemistry, as reflected in increases of the mean particle size and volume concentrations, and a shift of number size distribution to larger sizes. The model also predicts the observed evolution of particle number mean diameter and total volume concentrations at the end of the experiment. We show that in addition to self-limiting effects of IEPOX-SOA coatings, accounting for the molar balance between inorganic and organic sulfate and mass accommodation coefficient of IEPOX are important parameters governing modeling of IEPOX-SOA formation. Thus, models which do not account for the molar sulfate balance and/or diffusion limitations within IEPOX-SOA coatings are likely to predict too high IEPOX-SOA formation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Inertial dynamics of an interface with interfacial mass flux: Stability and flow fields’ structure, inertial stabilization mechanism, degeneracy of Landau’s solution, effect of energy fluctuations, and chemistry-induced instabilities

This work focuses on the long-standing problem of inertial dynamics of an interface with interfacial mass flux and reports new mechanisms for the interface stabilization and destabilization. The interface is a phase boundary separating fluids of different densities and having interfacial mass flux. To analyze the interface dynamics from a far field, we develop and apply the general matrix method to rigorously solve the boundary value problem involving the governing equations in the fluid bulk and the boundary conditions at the interface and at the outside boundaries of the domain. We find the fundamental solutions for the linearized system of equations and analyze the interplay of interface stability with flow fields’ structure by directly linking rigorous mathematical attributes to physical observables. We find that the interface is stable when the dynamics conserves the fluxes of mass, momentum, and energy; the stabilization is due to an inertial mechanism causing small oscillations of the interface velocity. In the classic Landau’s dynamics, the postulate of perfect constancy of the interface velocity leads to the development of Landau–Darrieus instability. This destabilization is also linked to the imbalance of the perturbed energy at the interface. The classic Landau’s solution is found to have degeneracy; lifting of the degeneracy may lead to singularity and self-similar dynamics. Our results compare well with traditional theories of combustion and propose new experiments to study the dynamics of the interface and the flow fields in combustible systems. We further conduct reactive molecular dynamics simulations to elucidate the complexity of chemical processes, to study the destabilizing effect of energy fluctuations on the interface stability, and to illustrate the chemistry-induced instabilities. In summary, we identify the extreme sensitivity of the interface dynamics to the interfacial boundary conditions, including the formal properties of fundamental solutions and the qualitative and quantitative properties of the flow fields. This provides new opportunities for studies, diagnostics, and control of multiphase flows in a broad range of processes in nature and technology.

42 ENGINEERING↗

DOE OSTI2020

A numerical study of particle jetting in a dense particle bed driven by an air-blast

In this work, the particle jetting behavior in a blast-driven dense particle bed is studied at early times. Four-way coupled Euler–Lagrange simulations are performed using a high-order discontinuous Galerkin spectral element solver coupled with a high-order Lagrangian particle solver, wherein the inter-particle collisions are resolved using a discrete element method collision model. Following the experiments of Rodriguez et al. [“Formation of particle jetting in a cylindrical shock tube,” Shock Waves 23(6), 619–634 (2013)] and the simulations of Osnes et al. [“Numerical simulation of particle jet formation induced by shock wave acceleration in a Hele-Shaw cell,” Shock Waves 28(3), 451–461 (2018)], the simulations are performed in a quasi-two-dimensional cylindrical geometry (Hele-Shaw cell). Parametric studies are carried out to assess the impact of the coefficient of restitution and the strength of the incident shock on the particle jetting behavior. The deposition of vorticity through a multiphase (gas–particle) analog of Richtmyer–Meshkov instability is observed to play a crucial role in channeling the particles into well-defined jets at the outer edge of the particle bed. This is confirmed by the presence of vortex pairs around the outer jets. Furthermore, the effect of the relaxation of the relative velocity between the two phases on the vorticity generation is explored by analyzing the correlation between the radial velocity of particles and the radial velocity of the gas at the particle location.

42 ENGINEERING↗