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DOE OSTI2021

Comprehensive framework for data-driven model form discovery of the closure laws in thermal-hydraulics codes

The two-phase two-fluid model is a basis of many thermal-hydraulics codes used in design, licensing, and safety considerations of nuclear power plants. Thermal-hydraulics codes rely on the closure laws to close the system of conservation equations and describe the interactions between phases. These laws, derived from years of experimental investigations, are semi-empirical correlations that lack generality and have a limited range of applicability. Increase of computational power, availability of new experiments, and development of high-fidelity simulations has increased the number of validation data. The discrepancies between the code predictions and the validation data are a great source of knowledge. Missing physics that are not included in the model but are important for the considered phenomena can be discovered by propagating the information from the experimental results through the model. Furthermore, physics-discovered data-driven model form (P3DM) methodology integrates available integral effect tests and separate effects tests to determine the necessary corrections to the model form of the closure laws. In contrast to existing calibration techniques, the methodology modifies the functional form of the closure laws. Based on the functional form of the correction, the missing physics that were not included in the original model can be discovered. The methodology provides the alternative to the machine learning approach, in which the model is discovered in the form of the intractable black-box relation. In this work, the methodology was applied to the CTF subchannel code to improve the prediction of the two-phase flow phenomena.

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NASA NTRS1983

Ponderomotive force in a warm two-fluid plasma

A general expression for the ponderomotive force of electromagnetic field with slowly varying amplitude in a warm plasma is obtained in the collisionless two-fluid model. Compared to the existing expression obtained for a cold and stationary plasma, this result contains two additional terms for the general case. One of them is involved with the density gradient and the wavenumber derivative of the dielectric tensor of a plasma. Thus, for an inhomogeneous plasma, it accounts for the effects of spatial dispersion, hence of finite temperature of the plasma. The other term is proportional to the time derivative of the density and the frequency derivative of the dielectric tensor, and is nonzero unless the plasma is stationary or nondispersive. Inclusion of these new terms in the ponderomotive force will enable self-consistent analysis of the general behavior of nonlinear waves with finite wavelengths in a warm plasma.

Lee, N. C.↗

NASA NTRS1989

The modelling of heat, mass and solute transport in solidification systems

The aim of this paper is to explore the range of possible one-phase models of binary alloy solidification. Starting from a general two-phase description, based on the two-fluid model, three limiting cases are identified which result in one-phase models of binary systems. Each of these models can be readily implemented in standard single phase flow numerical codes. Differences between predictions from these models are examined. In particular, the effects of the models on the predicted macro-segregation patterns are evaluated.

Voller, V. R.↗

NASA NTRS1974

Four photon parametric amplification

An analysis is presented describing four-photon parametric amplification in an unbiased Josephson junction. Central to the theory is the model of the Josephson effect as a nonlinear inductance. Linear, small signal analysis is applied to the two-fluid model of the Josephson junction. The gain, gain-bandwidth product, high frequency limit, and effective noise temperature are calculated for a cavity reflection amplifier. The analysis is extended to multiple (series-connected) junctions and subharmonic pumping.

Parrish, P. T.↗

DOE OSTI2022

Development of machine learning framework for interface force closures based on bubble tracking data

Interfacial force closures in the two-fluid model play a critical role for the predictive capabilities of void fraction distribution. However, the practices of interfacial force modeling have long been challenged by the inherent physical complexity of the two-phase flows. The rapidly expanding computational capabilities in the recent years have made high-fidelity data from the interface-captured direct numerical simulation become more available, and hence potential for data-driven interfacial force modeling has prevailed. In this work, we established a data-driven modeling framework integrated to the HZDR multiphase Eulerian-Eulerian framework for computational fluid dynamics simulations. The data-driven framework is verified in a benchmark problem, where a feedforward neural network managed to capture the non-linear mapping between bubble Reynolds number and drag coefficient and reproduce the void distribution resulting from the baseline model in the test case. The second focus is on utilizing the bubble tracking data set to form a closure for the bubble drag in the turbulent bubbly flow, in which the drag coefficient is set to be correlated with the bubble Reynolds number and the Eötvös number. Pseudo-steady state filtering in the Frenet Frame was carried out to obtain the drag coefficient from the turbulent bubbly flow data. The performance of the data-driven drag model is also examined through a case study, where improvement of model’s prediction near-wall is regarded necessary. In conclusion, discussion and further plans of investigation are provided.

42 ENGINEERING↗

DOE OSTI2022

A two-fluid single-column model of turbulent shallow convection. Part II: Single-column model formulation and numerics

The two-fluid single-column model of Thuburn et al. (Quart. J. R. Meteorol. Soc., 2019, 145, 1535–1550) is extended to include moisture and horizontal wind shear. Turbulent kinetic energy is introduced as a prognostic variable, dependence on a diagnosed boundary-layer height is removed, and subfilter fluxes are approximated using a two-fluid version of a Mellor–Yamada scheme. Three mechanisms for entrainment and detrainment processes are introduced, which represent entrainment of unstable air at the surface, forced detrainment of air at the top of the boundary/cloud layers, and turbulent mixing that relaxes the convective fluid to a reference profile. A semi-implicit Eulerian discretization replaces the semi-implicit semi-Lagrangian implementation of Thuburn et al. (Quart. J. R. Meteorol. Soc., 2019, 145, 1535–1550) to improve numerical stability and conservation. The equations for the implicit time step are solved using a quasi-Newton method, which is shown to perform well in numerical tests for conservation and convergence. The two-fluid single-column model presented in this article will be applied to simulations of shallow cumulus convection in Part III.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1972

Solar wind for a magnetized plasma with tensor plasma pressure.

A solar wind model for a magnetized solar wind is presented using one-fluid hydromagnetic equations with generalized polytrope equations of state for the two tensor components of the plasma pressure. Fluid and magnetic field variables are calculated at the Earth using certain boundary conditions at the Sun. The azimuthal velocity agrees with observed values and explains the considerable loss of angular momentum from the Sun by the solar wind. The results are good for most variables but suggest that a two-fluid model with electrons at higher temperatures and smaller temperature anisotropy ratios than the ions would give improved agreement for some quantities.

Tan, M.↗

DOE OSTI2022

Perovskite Sorbent Oxygen Separation Modeling with MFiX

This document chronicles the development and implementation of computational kinetic rate models that capture absorption and desorption characteristics of the National Energy Technology Laboratory (NETL) developed perovskite, Sr 1-x Ca x FeO 3-δ . Two paths to create accurate kinetic rates were followed: (1) an isothermal rate approach where thermogravimetric (TGA) data are recast as oxygen capacities through a pseudo-second order Lagergren equation (He et al., 2009); and (2) a more traditional Arrhenius approach where experimental data are fit with a power law model to derive associate activation energies (Bulfin et al., 2020a). For reference, the mathematics and associate experimental strategies that support these derivations are included in this report. In addition, computational fluid dynamics (CFD) models were developed to utilize both kinetic rate formulations and applied to simulate oxygen uptake and release in small scale scenarios. The program Multiphase Flow with interphase eXchanges (MFiX) was used to create: (1) discrete element method (DEM) simulations of a single tube of granular perovskite experiencing isothermal O 2 -absorption; and desorption and (2) two-fluid-model (TFM) non-isothermal simulations of perovskite O 2 -absorption and desorption tubes that share a wall. Conjugate heat transfer between steel walled tubes and the perovskite bed were managed with user-defined functions. As the project moves to simulating larger scale devices that will require more robust conjugate heat transfer methods, developed kinetic rates and associate methodologies have been recast for use in the ANSYS Fluent CFD program.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Theory-based scaling laws of near and far scrape-off layer widths in single-null L-mode discharges

Abstract Theory-based scaling laws of the near and far scrape-off layer (SOL) widths are analytically derived for L-mode diverted tokamak discharges by using a two-fluid model. The near SOL pressure and density decay lengths are obtained by leveraging a balance among the power source, perpendicular turbulent transport across the separatrix, and parallel losses at the vessel wall, while the far SOL pressure and density decay lengths are derived by using a model of intermittent transport mediated by filaments. The analytical estimates of the pressure decay length in the near SOL is then compared to the results of three-dimensional, flux-driven, global, two-fluid turbulence simulations of L-mode diverted tokamak plasmas, and validated against experimental measurements taken from an experimental multi-machine database of divertor heat flux profiles, showing in both cases a very good agreement. Analogously, the theoretical scaling law for the pressure decay length in the far SOL is compared to simulation results and to experimental measurements in TCV L-mode discharges, pointing out the need of a large multi-machine database for the far SOL decay lengths.

Physics↗

NASA NTRS1988

Confined turbulent fluid-particle flow modeling using multiple-realization particle trajectory schemes

A multiple-realization particle trajectory scheme has been developed and applied to the numerical prediction of confined turbulent fluid-particle flows. The example flows investigated include the vertical pipe upflow experimental data of Tsuji et al. and the experimental data of Leavitt for a coaxial jet flow, comprising a particle-laden central jet and a clean annular jet, into a large recirculation chamber. The results obtained from the numerical scheme agree well with the experimental data, lending confidence to the modeling approach. The multiple-realization particle trajectory turbulent flow modeling scheme is believed to be a more elegant and accurate approach to the extension of single-particle hydrodynamics to dilute multi-particle systems than the more commonly employed two-fluid modeling approach. It is also better able to incorporate additional force items such as lift, virtual mass and Bassett history terms directly into the particle equation of motion as appropriate. This makes it a suitable candidate for particle migration studies and an extension to situations involving liquid particulate phases with possible propulsion applications, such as in spray combustion, follows naturally.

Adeniji-Fashola, A. A.↗

DOE OSTI2026

A filter-dependent granular temperature model from large-scale CFD-DEM data

The computational study of strongly-coupled, gas–solid flows at scales relevant to most environmental and engineering applications requires the use of ‘coarse-grained’ methodologies such as the two-fluid model, particle-in-cell approach or the multiphase Reynolds Averaged Navier–Stokes equations. While these strategies enable computations at desirable length- and time-scales, they rely heavily on models to capture important flow physics that occur at scales smaller than the mesh. To date, the models that do exist are based on a limited set of flow conditions, such as very dilute particle phase. To this end, we leverage a large-scale repository of CFD-DEM data to develop filter-size dependent models for the mean variance in particle volume fraction, a quantity commonly used to assess the degree of clustering, and the granular temperature, a key quantity for accurately predicting gas–solid flows. In conclusion, because of its filter-size dependence, the granular temperature model can be directly translated to coarse-grained approaches and tied directly to grid size.

AMReX↗

DOE OSTI2024

Effects of alpha-ion stopping on ignition and ignition criteria in inertial confinement fusion experiments

With the advent of ignited plasmas at the National Ignition Facility (NIF), alpha physics has become a driving factor in theoretical understanding and experimental behavior. In this communication, we explore aspects of direct alpha-ion heating through comparison of the consequences from the one-fluid and two-fluid models in the hydrodynamic approach. We show that the case with all alpha energy deposited in electrons raises the ignition criteria by ∼4 keV or ∼0.2 g/cm2 in the hotspot relative to the case with all alpha energy deposited in ions. In the case of the recently ignited NIF implosion, 30% of the 3.5 MeV α energy is deposited into the DT fuel ions, for which there is negligible difference between the one-fluid and two-fluid ignition criteria. However, changes in the ion stopping fraction through profile effects and alternate stopping power models could lead to ignition curve shifts of ∼1 keV.

Physics↗

NASA NTRS1989

Rarefied-continuum gas dynamics transition for SUMS project

This program is to develop an analytic method for reducing SUMS data for the determination of the undisturbed atmosphere conditions ahead of the shuttle along its descending trajectory. It is divided into an internal flow problem, an external flow problem and their matching conditions. Since the existing method of Direct Simulation Monte Carlo (DSMC) failed completely for the internal flow problem, the emphasis is on the internal flow of a highly non-equilibrium, rarefied air through a short tube of a diameter much less than the gaseous mean free path. A two fluid model analysis of this internal flow problem has been developed and studied with typical results illustrated. A computer program for such an analysis and a technical paper published in Lecture Notes in Physics No. 323 (1989) are included as Appendices 3 and 4. A proposal for in situ determination of the surface accommodation coefficients sigma sub t and sigma e is included in Appendix 5 because of their importance in quantitative data reduction. A two fluid formulation for the external flow problem is included as Appendix 6 and a review article for AIAA on Hypersonic propulsion, much dependent on ambient atmospheric density, is also included as Appendix 7.

Cheng, Sin-I↗

DOE OSTI2024

HL-2A's ELM cycle simulations by integrating BOUT++'s drift MHD and transport code

A new integrating model has been developed to couple tokamak edge multiscale magnetohydrodynamic (MHD) events and transport simulations, such as edge-localized mode (ELM) cycles. As a proof of principle, we first start from a set of three-field two-fluid model equations, which includes the pressure, current, and vorticity. Here, the equations are separated into the slowly evolving part of the axisymmetric component by taking a time average of the axisymmetric component. The time-averaged fluxes, which are quadratic in fluctuating quantities, act as driven terms for the time-averaged axisymmetric quantities that determine the plasma transport, and therefore the large-scale evolution of the plasma profiles. Then the HL-2A's ELM cycles are simulated using the model. Good agreements of ELM size and pedestal recovery time have been achieved for the solutions obtained from the coupled simulation compared with experiment. For one ELM cycle simulation, the coupled code can achieve a speedup of a factor of up to 30 over standalone code.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2004

Effects of Kinetic Processes in Shaping Io's Global Plasma Environment: A 3D Hybrid Model

The global dynamics of the ionized and neutral components in the environment of Io plays an important role in the interaction of Jupiter's corotating magnetospheric plasma with Io. The stationary simulation of this problem was done in the MHD and the electrodynamics approaches. One of the main significant results from the simplified two-fluid model simulations was a production of the structure of the double-peak in the magnetic field signature of the I0 flyby that could not be explained by standard MHD models. In this paper, we develop a method of kinetic ion simulation. This method employs the fluid description for electrons and neutrals whereas for ions multilevel, drift-kinetic and particle, approaches are used. We also take into account charge-exchange and photoionization processes. Our model provides much more accurate description for ion dynamics and allows us to take into account the realistic anisotropic ion distribution that cannot be done in fluid simulations. The first results of such simulation of the dynamics of ions in the Io's environment are discussed in this paper.

Lipatov, Alexander S.↗

NASA NTRS2006

Effects of Kinetic Processes in Shaping Io's Global Plasma Environment: A 3D Hybrid Model

The global dynamics of the ionized and neutral gases in the environment of Io plays an important role in the interaction of Jupiter s corotating magnetospheric plasma with Io. Stationary simulations of this problem have already been done using the magnetohydrodynamics (MHD) and the electrodynamics approaches. One of the major results of recent simplified two-fluid model simulations [Saur, J., Neubauer, F.M., Strobel, D.F., Summers, M.E., 2002. J. Geophys. Res. 107 (SMP5), 1-18] was the production of the structure of the double-peak in the magnetic field signature of the Io flyby. These could not be explained before by standard MHD models. In this paper, we present a hybrid simulation for Io with kinetic ions and fluid electrons. This method employs a fluid description for electrons and neutrals, whereas for ions a particle approach is used. We also take into account charge-exchange and photoionization processes and solve self-consistently for electric and magnetic fields. Our model may provide a much more accurate description for the ion dynamics than previous approaches and allows us to account for the realistic anisotropic ion velocity distribution that cannot be done in fluid simulations with isotropic temperatures. The first results of such a simulation of the dynamics of ions in Io s environment are discussed in this paper. Comparison with the Galileo IO flyby results shows that this approach provides an accurate physical basis for the interaction and can therefore naturally reproduce all the observed salient features.

Lipatov, Alexander S.↗

NASA NTRS1975

Multifluids description of dynamics of upper atmosphere

A multifluids model to investigate ionospheric dynamics was established on kinetic theory. Its resultant equations are used to examine the following dynamic problems in the gamma region of 80-2000 Km of the ionosphere: (1) propagation of acoustic modes in the 500-2,000 Km of the ionosphere (two fluid model); (2) the relation between the cross field plasma drift instabilities and type I and type II ionospheric irregularities; and (3) time dependent neutral wind structure and horizontal pressure gradient.

Wu, S. T.↗

DOE OSTI2021

Deterministic Calibration of MFiX-PIC, Part 1: Settling Bed

The Particle-in-cell (PIC) numerical approach for modeling granular solids in fluid flow has gained significant interest in recent years. Valued for its often shorter time-to-solution, the PIC formulation relies on modeling statistical groupings of particles called parcels in cooperation with a solids stress model to affect local solids velocity. This is in contrast to the discrete element model (DEM) where every particle in a system is modelled individually and directly coupled to local solids velocity through Newtonian mechanics. The U.S. Department of Energy (DOE), National Energy Technology Laboratory (NETL) develops and maintains Multiphase Flow with Interphase eXchanges (MFiX), a collection of open-source computational fluid dynamics (CFD) solvers. Included in the MFiX suite are traditional two-fluid model (TFM) and DEM solvers, and a recently added PIC solver (NETL, 2021). In general, PIC methodologies offer an accuracy trade-off in lieu of computational speed; and therefore, it is important to assess the credibility of MFiX-PIC simulations. For this purpose, a systematic verification, validation and uncertainty quantification (VVUQ) effort was initiated at NETL to assess the new PIC solver

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