Global solvability of a non-conservative compressible generic two-fluid model

We report temperature-dependent optical response measurements of YBa2Cu3O7−δ thin films in the visible spectral range under cryogenic conditions. We observe a sharp increase in transmittance near the superconducting transition temperature (Tc), followed by a saturation of transmittance within a few kelvins below Tc. This increase in transmittance is accompanied by a corresponding decrease in reflectance as the temperature drops below Tc; both quantities track the superconducting phase transition. Changes in transmittance are found to be wavelength dependent, with the maximum variation occurring at 633 nm and minimal at 450 nm. These observations establish a correlation between the variation in optical response and the superconducting phase transition in the visible regime. The results of our experiment highlight the potential for using non-contact optical measurements in the visible range to determine Tc. The effect can be explained using the two-fluid model, which can account for the observed temperature and wavelength dependence of the transmittance of the superconducting thin films.

An implicit numerical method for the three-dimensional two-fluid model with large phase changes in pressurized water reactors

Stability and instability of a generic compressible two-fluid model with equal pressures

Abstract Divertor concepts which are capable to handle the power exhaust of tokamaks remain a critical component on the path towards a magnetic confinement fusion reactor. One approach to circumvent the strong localization of the power deposition onto the divertor plates is by shaping the magnetic field topology in the vicinity of the divertor, resulting in so-called Advanced Divertor Configurations (ADCs). The present work investigates the heat flux mitigation via divertor flux expansion, which offers a two-fold merit: the parallel heat flux density decreases due to an increase of the wetted area, and the divertor profile might be broadened further due to enhanced turbulent E × B transport. For this purpose, turbulence simulations across the edge and scrape-off layer of ASDEX Upgrade (AUG) in attached L-mode conditions are performed with the GRILLIX code, which implements an electromagnetic, transcollisional, full- f , two-fluid plasma model coupled to diffusive neutrals. The simulations scan the currents of the recently installed in-vessel coils in the upper divertor of AUG leading to an approximately linear decrease of the magnetic shear around the X -point and a strongly non-linear increase of the divertor flux expansion. Realistic divertor heat flux profiles are obtained and the expected influence of the flux expansion is recovered. Additionally, a small contribution to the peak heat flux reduction due to increased turbulent radial E × B transport is observed and explained.

The famous two-fluid model of finite-temperature superfluids has been recently extended to describe the mixed classical-superfluid dynamics of the newly discovered supersolid phase of matter. We show that for rigidly rotating supersolids one can derive a more appropriate single-fluid model, in which the seemingly classical and superfluid contributions to the motion emerge from a spatially varying phase of the global wave function. That allows one to design experimental protocols to excite and detect the peculiar rotation dynamics of annular supersolids, including partially quantized supercurrents, in which each atom brings less than ℏ units of angular momentum. Our results are valid for a more general class of density-modulated superfluids.

Abstract Synergetic effects of diamagnetic flow and E × B shear flow on neoclassical tearing modes (NTMs) are numerically investigated by using a two-fluid four-field model. Such seed islands are driven by the boundary perturbation rather than through core seed islands. Firstly, in the single-helicity simulations, the initial equilibrium includes the 3/2 mode with negative Δ′. The boundary perturbation can induce a driven-reconnection on the 3/2 rational surface with island width as w ∼ Ψ a 1 / 2 , where Ψ a is the boundary perturbation amplitude. When the 3/2 island widths exceed a critical value (equivalently seed island), the 3/2 NTM is triggered with a much larger island width. It is found that when diamagnetic flow is greater than a threshold δ w , the 3/2 mode cannot enter the NTM phase, but still keeps in the driven-reconnection saturation state. A strong positive scaling δ w ∝ Ψ a 1.15 is obtained. Further increasing diamagnetic flow accelerates the early island growth due to the excitation of drift tearing mode, but reduces the saturation of the driven-reconnection. The E × B shear flow can effectively enhance or offset the suppressing effect of the diamagnetic flow depending on their co- or counter-direction. Secondly, in the multiple-helicity simulations, an extra 2/1 mode with positive Δ′ is added in the system. The 3/2 mode enters quickly the nonlinear NTM saturation due to the boundary drive, but the early growth of 2/1 mode is slow. When the 2/1 mode reaches saturation, it can suppress the 3/2 NTM to a lower level saturation. It is found that the diamagnetic flow can keep the 3/2 mode in the driven-reconnection saturation, but raise the 2/1 mode saturation. The increase of 2/1 islands can trigger the 3/2 NTM with larger 3/2 islands on the 3/2 rational surfaces. The simultaneous growth of both 2/1 and 3/2 islands generates a wider flattened region of the pressure, significantly reducing the drive of bootstrap current for the 3/2 NTM. As a result, the 3/2 NTM returns to a very low driven-reconnection level or is completely stabilized. Moreover, the synergetic effects of diamagnetic flow and E × B shear flow with fixed and unfixed profiles are also studied, and the Poincaré plots of magnetic topology evolution are illustrated to clearly understand the interaction between multiple-helicity islands.

Plasma flow in force-free magnetospheres: Two-fluid model near pulsars and black holes

Laminar dispersion force effects on two-fluid modelling and simulation of bubble column hydrodynamics

The exact position and the value of the hot-spot temperature in a transformer could be estimated by calculation using computational fluid dynamics. However, this approach requires the usage of significant computational resources. In this paper, a review on some recent investigations on this topic is made, focusing thereby primarily on the investigation in which the field distribution of the dependent variables is taken into consideration in a conjugate heat transfer problem. Still, the determination of the hot-spot temperature in the transformer is an open problem. Furthermore, a review on some fundamental aspects related to the heat transfer in the transformer was made, and some new approaches for the calculation of heat transfer in the transformer were proposed: smoothed-particle hydrodynamics, two-fluid model and the application of T-Flows computational software. Thus, the smoothed-particle hydrodynamics is found as a convenient approach, since it is traditionally related to laminar flow, that is present in the transformer; the two-fluid model significantly saves the computational resources, while the application of the computational software T-Flows is free and extremely powerful for computation of conjugate heat transfer and parallel computation. The conducted research defined the guidelines for the future work in numerical modelling of heat transfer in transformers.

During BOUT++ simulations for edge-localized modes (ELMs), the electric potential is generally calculated using the flute-ordering one-dimensional Laplace solver. However, it is not valid for the toroidal axisymmetric (i.e., toroidal mode number n = 0) component, leading to the limitation on evolving n = 0 electric field and parallel current. Recently, to evolve the n = 0 electric field and plasma current, Seto et al. [Phys. Plasmas 26, 052507 (2019)] have adopted the two-dimensional Laplace solver to calculate the n = 0 electric potential and indicate the ELM evolution can be significantly affected. In this work, based on the EAST upper single null equilibrium, ELM simulation using BOUT++ six-field two-fluid model with n = 0 electric field and parallel current evolution is performed. Compared to the case with fixed n = 0 parallel current (∼5%) and net-drift-flow-free n = 0 electric field (∼7%), the simulated ELM size is significantly reduced (∼2%) and more consistent with the small ELM observed in experiment. Further analysis indicates that the reduction of simulated ELM size is mainly because: (1) the decrease in the n = 0 parallel current density during the nonlinear phase leads to the reduction of instability drive, causing smaller initial crash; (2) the relatively strong radial electric field shear suppresses the turbulence transport.

Hydrogen-based direct reduction (H-DR) represents an environmentally benign and energy-efficient alternative in ironmaking that has significant industrial potential. This study reviews the current status of H-DR shaft furnaces and accompanying hydrogen-rich reforming technologies (steam and autothermal reforming), assessing the three dominant numerical frameworks used to analyze these processes: (i) porous medium continuum models, (ii) the Eulerian two-fluid model (TFMs), and (iii) coupled computational fluid dynamics (CFD)–discrete element method (DEM) models. The respective trade-offs in terms of computational cost and model accuracy are critically compared. Recent progress is evaluated from an engineering standpoint in four key areas: optimization of the pellet bed structure and gas distribution, thermal control of the reduction zone, sensitivity analysis of operating parameters, and industrial-scale model validation. Current limitations in predictive accuracy, computational efficiency, and plant-level transferability are identified, and possible mitigation strategies are discussed. Looking forward, high-fidelity multi-physics coupling, advanced mesoscale descriptions, AI-accelerated surrogate models, and rigorous uncertainty quantification can facilitate effective scalable and intelligent application of hydrogen-based shaft furnace simulations.

This study addresses three-dimensional modeling of the thermal interaction between the core melt and the melt localization device (trap) during a severe accident at a nuclear power plant. An optimized configuration for filling the localization device with sacrificial material is proposed. The calculations incorporate the Reynolds-averaged Navier–Stokes equations, numerical solutions of the heat conduction equation, and a two-fluid interface dynamics model, enabling simultaneous consideration of turbulent flow within the liquid phases, the moving boundary of the melting sacrificial material (Stefan problem), and stratification with inversion. The analysis proceeds in three consecutive stages. The first stage models the melting of the sacrificial material; the second simulates the stratification of layers; the third evaluates heat transfer after stratification. Based on the results, an optimal filling configuration for the trap is developed. The study presents detailed volumetric temperature distributions throughout all three stages, the heat flux distribution on the trap walls, and the maximum thickness of the melted shell caused by intense thermal interaction. Comparison between three-dimensional simulations and similar two-dimensional studies demonstrates that 3D modeling more accurately captures the characteristic timing of solidification and subsequent melting processes. The advantages of the proposed approach over existing methods are highlighted. Its applicability for designing and optimizing melt localization devices is shown, and prospects for future development are discussed, including incorporating chemical reactions and adapting the model to other reactor types. The data convincingly suggest that the adopted configuration has significant potential to extend the period during which effective mitigation of severe accident consequences at nuclear power plants can be maintained.

This study explores the use of computational simulations to analyze the reduction processes of iron oxide powders in fluidized beds. Iron powders are employed as energy carriers; that is, they can be oxidized to release energy and subsequently reduced using renewable energy sources, enabling a closed-loop, carbon-free energy cycle—a clean alternative to fossil fuels. To simulate this process, the Two-Fluid Model (TFM) with the Kinetic Theory of Granular Flow (KTGF) for closure is adopted. This work presents the initial steps in scaling up the computational modeling of such systems, which are typically studied using Lagrangian techniques to capture particle interactions and reaction details. To achieve this, a multiphase (gas-solid) flow involving multiple reacting species is modeled and solved using the OpenFOAM suite. Among the challenges of the study are the complex temperature-dependent reactive dynamics between hydrogen and iron oxides, as well as particle sintering at elevated temperatures. The results demonstrate the capability of the TFM-KTGF approach to capture complex thermochemical phenomena. This represents an initial step toward developing an efficient computational tool for modeling pilot-scale metal fuel fluidization units within a reasonable computational time. Such tools can support the design and optimization of these processes, leading to improved efficiency and reduced operational costs.

Objective: The objective of this study is to develop and assess a numerical tool based on the one-dimensional two-fluid model for supporting flow-assurance strategies in oil pipelines. The research aims to enhance the predictive capability of transient gas–liquid flows by incorporating high-order advective schemes, addressing limitations commonly found in commercial simulators (e.g., ALFAsim, LedaFlow and OLGA), which predominantly rely on first-order numerical formulations. Theoretical Framework: The study is grounded in multiphase flow theory and the classical two-fluid four-equation single-pressure model. Concepts related to hyperbolicity, interfacial pressure modeling, and numerical flux limiting techniques are central to the investigation, providing a robust basis for understanding how discretization strategies influence flow predictions and operational decision-making. Method: A finite-volume formulation with a staggered grid is applied to discretize the governing equations. Several high-order schemes, such as Second-Order Upwind and TVD limiters, are implemented to evaluate their accuracy in solving convective terms. The water faucet benchmark is used to test stability and convergence under transient flow conditions. Results and Discussion: The findings show that incorporating an interfacial pressure difference term ensures the hyperbolicity of the model and prevents non-physical oscillations, even on refined grids. High-order schemes yield sharper interfaces and reduced numerical diffusion when compared to first-order formulations. Research Implications: The results highlight the potential of advanced numerical strategies to support flow-assurance analysis, risk mitigation, and operational planning in offshore pipeline systems, improving reliability in the oil and gas sector. Originality/Value: This study contributes to the literature by demonstrating the applicability of high-order numerical schemes within the one-dimensional two-fluid model to enhance the predictive reliability of transient gas-liquid flows in oil pipelines. Unlike widely used commercial simulators (such as ALFAsim, LedaFlow, OLGA, among others), which predominantly rely on first-order methods for advective transport, this research introduces and evaluates higher-order formulations capable of reducing numerical diffusion and improving interface resolution. The relevance of this work lies in its potential to strengthen flow-assurance analysis, inform risk mitigation strategies, and support more sustainable operational practices in the oil and gas sector.

Branched horizontal wells are widely applied in oil and gas development. However, their complex structures make cuttings transport and deposition problems more pronounced. In this study, a three-dimensional branched wellbore model was established based on an intelligent drilling and completion simulation system. A computational fluid dynamics (CFD) approach, incorporating the Eulerian–Eulerian two-fluid model and the kinetic theory of granular flow, was employed to investigate the effects of wellbore diameter, eccentricity, curvature, flow rate, and rheological parameters on cuttings transport behavior. Results from the steady-state simulations indicate that increasing the wellbore diameter and eccentricity intensifies cuttings deposition at the connection section, with the lower-region concentration rising significantly as the eccentricity increases from 0% to 60%. A larger curvature enhances local flow disturbance but reduces the overall cuttings transport efficiency. Increasing the flow rate improves hole cleaning but may promote cuttings accumulation near the bottom of the main wellbore. As the flow behavior index increases from 0.4 to 0.8, the average cuttings concentration rises from 0.0996 to 0.1008, and the pressure drop increases from 1,010,894 Pa to 1,042,880 Pa, indicating improved transport capacity but higher energy consumption. Experimental results are consistent with the numerical simulation trends, confirming the model’s reliability. This study provides both theoretical and experimental support for optimizing complex wellbore structures and drilling fluid parameters.

To tackle flow safety challenges arising from paraffin deposition in low-temperature shale oil multiphase conveying systems, this study establishes a multi-physics coupled model for predicting wax layer growth. The proposed modeling framework integrates a steady-state two-fluid model with thermodynamic equilibrium equations and a kinetics mechanism describing paraffin deposition. This mechanism explicitly accounts for molecular diffusion effects, deposit layer porosity, and shear stripping phenomena. The resultant integrated model facilitates comprehensive prediction of flow regimes, temperature profiles, pressure gradients, and wax layer thickness distribution within multiphase pipelines. Validation against experimental measurements and OLGA simulation results confirms the model's accuracy. Furthermore, the influence of operating temperature and fluid flow rate on the required pigging cycles is investigated. This model provides a robust theoretical foundation for ensuring the safe operation of multiphase pipelines transporting waxy shale oils.

Abstract This paper presents an improved version of the Spalding two-fluid turbulence model developed by Malikov. The model is applied to numerically simulate turbulent flows past one and two square cylinders at a Reynolds number of Re = 47,000. The SIMPLE algorithm with a semi-implicit scheme and second-order accuracy is used to solve the equations. The code developed by the authors was tested on a two-dimensional benchmark problem of flow past a single square cylinder and then applied to crossflow past two square cylinders located side by side. The ratio of the distance between the cylinders, T/d, varied from 0 to 5, which allowed us to identify three characteristic flow regimes: single, slot (interference), and antiphase synchronous. The simulation results were compared with experimental data and showed good agreement in terms of pressure distribution, vortex wake structure, and aerodynamic force coefficients. Comparison with RANS and LES models confirmed that Malikov’s model provides comparable accuracy with significantly lower computational costs.

A number of important physics effects on the stability of relatively high-n (n is the toroidal mode number) peeling-ballooning modes (PBMs) are investigated based on an equilibrium reconstructed from a NSTX discharge, utilizing extended magnetohydrodynamic (MHD) eigenvalue solvers. For a given toroidal mode number n, multiple branches of instabilities are computed, with the total number of unstable branches roughly linearly scaling with n. Most of the unstable branches are located in the plasma core region, but edge-localized branches, i.e., PBMs, are also identified at higher n-numbers. For the single-fluid-wise most unstable PBM with n=19, stabilizing/destabilizing effects due to various physics beyond ideal MHD are systematically investigated. Plasma toroidal flow is found to be weakly stabilizing. Local flow shear is generally stabilizing as well, with the degree of stabilization depending on the initial growth rate (without flow shear) of the mode. The plasma resistivity can strongly destabilize the PBM within the single-fluid framework. Anisotropic thermal transport, strong parallel sound wave damping, as well as two-fluid effects are all stabilizing to the mode. In particular, diamagnetic stabilization (within the two-fluid model) is found to be very strong for this mode.

The study of magnetically confined plasma involves complex physics spanning disparate time and length scales, requiring simulation strategies ranging from magnetohydrodynamics (MHD) to particle-based formulations. Single-fluid MHD simulations, although computationally efficient, fail to capture important small-scale phenomena. Conversely, particle-based formulations, while accurate, are prohibitively expensive for large-scale simulations. To bridge this gap, the two-fluid MHD model with a generalized Ohm’s law (GOL) retains the small-scale physics present in kinetic approaches while benefitting from the efficient computational techniques used in standard MHD. Nevertheless, existing two-fluid GOL formulations can still be computationally demanding due to stiff source terms and time step restrictions imposed by the wave speed of Maxwell’s equations. Overcoming these problems without sacrificing accuracy remains challenging. This work presents a novel combination of implicit and explicit algorithms to reduce computational cost while retaining accuracy. Key novel features include an implicit Maxwell solver that eliminates time step restrictions imposed by the speed of light and a locally implicit treatment of stiff source terms, substantially improving stability and enabling larger time steps. A centered monotone finite volume scheme (FORCE-α) provides an accurate solution for propagating waveforms at a lower cost compared to Riemann problem-based methods. The resulting algorithms are highly parallelized and are tested against benchmarks that have known numerical solutions in one and two space dimensions.