Two-fluid Model Research Articles

Development of transient thermal-hydraulic analysis model for the two-phase loop thermosyphon

To comprehensively and accurately simulate and predict the flow and heat transfer characteristics of the two-phase loop thermosyphon (TPLT), a two-fluid two-phase model was developed. A six-equation set was formulated to account for two-phase flow, encompassing mass equations, momentum equations, and energy equations. The interactions between the fluids in terms of mass, momentum, and energy were also taken into account. To obtain numerical solutions for the partial differential equations within a staggered mesh framework, we employed the 2nd-order Lax-Wendroff scheme to obtain the discrete linear system, complemented by the inclusion of a flux limiter. The Semi-Implicit Method for Pressure-Linked Equation (SIMPLE) algorithm was employed to address the solution of the linear equation system. Data from a small-scale TPLT test was used to assess the accuracy and reliability of both the physical models and the numerical method proposed in this study. Simulations were performed under two working conditions of the thermosyphon with filling ratio of 45 % and 64 %. The simulation results exhibited good agreement with the experimental data, demonstrating the accuracy of the model. Furthermore, the model is capable of providing information on the complex two-phase flow inside the TPLT that cannot be measured experimentally.

A homogenized two-phase computational framework for meso- and macroscale blood flow simulations

Background and ObjectiveOwing to the complexity of physics linked with blood flow and its associated phenomena, appropriate modeling of the multi-constituent rheology of blood is of primary importance. To this effect, various kinds of computational fluid dynamic models have been developed, each with merits and limitations. However, when additional physics like thrombosis and embolization is included within the framework of these models, computationally efficient scalable translation becomes very difficult. Therefore, this paper presents a homogenized two-phase blood flow framework with similar characteristics to a single fluid model but retains the flow resolution of a classical two-fluid model. The presented framework is validated against four different sets of experiments. MethodsThe two-phase model of blood presented here is based on the classical diffusion-flux framework. Diffusion flux models are known to be less computationally expensive than two-fluid multiphase models since the numerical implementation resembles single-phase flow models. Diffusion flux models typically use empirical slip velocity correlations to resolve the motion between phases. However, such correlations do not exist for blood. Therefore, a modified slip velocity equation is proposed, derived rigorously from the two-fluid governing equations. An additional drag law for red blood cells (RBCs) as a function of volume fraction is evaluated using a previously published cell-resolved solver. A new hematocrit-dependent expression for lift force on RBCs is proposed. The final governing equations are discretized and solved using the open-source software OpenFOAM. ResultsThe framework is validated against four sets of experiments: (i) flow through a rectangular microchannel to validate RBC velocity profiles against experimental measurements and compare computed hematocrit distributions against previously reported simulation results (ii) flow through a sudden expansion microchannel for comparing experimentally obtained contours of hematocrit distributions and normalized cell-free region length obtained at different flowrates and inlet hematocrits, (iii) flow through two hyperbolic channels to evaluate model predictions of cell-free layer thickness, and (iv) flow through a microchannel that mimics crevices of a left ventricular assist device to predict hematocrit distributions observed experimentally. The simulation results exhibit good agreement with the results of all four experiments. ConclusionThe computational framework presented in this paper has the advantage of resolving the multiscale physics of blood flow while still leveraging numerical techniques used for solving single-phase flows. Therefore, it becomes an excellent candidate for addressing more complicated problems related to blood flow, such as modeling mechanical entrapment of RBCs within blood clots, predicting thrombus composition, and visualizing clot embolization.

Energy-stable discretization of the one-dimensional two-fluid model

In this paper we present a complete framework for the energy-stable simulation of stratified incompressible flow in channels, using the one-dimensional two-fluid model. Building on earlier energy-conserving work on the basic two-fluid model, our new framework includes diffusion, friction, and surface tension. We show that surface tension can be added in an energy-conserving manner, and that diffusion and friction have a strictly dissipative effect on the energy.We then propose spatial discretizations for these terms such that a semi-discrete model is obtained that has the same conservation properties as the continuous model. Additionally, we propose a new energy-stable advective flux scheme that is energy-conserving in smooth regions of the flow and strictly dissipative where sharp gradients appear. This is obtained by combining, using flux limiters, a previously developed energy-conserving advective flux with a novel first-order upwind scheme that is shown to be strictly dissipative.The complete framework, with diffusion, surface tension, and a bounded energy, is linearly stable to short wavelength perturbations, and exhibits nonlinear damping near shocks. The model yields smoothly converging numerical solutions, even under conditions for which the basic two-fluid model is ill-posed. With our explicit expressions for the dissipation rates, we are able to attribute the nonlinear damping to the different dissipation mechanisms, and compare their effects.

CFD verification of total pressure loss coefficient for gas-liquid two-phase flow

Traditionally, we design gas-liquid two-phase flow systems with pressure loss that is assumed by homogeneous flow. However, in real phenomena, the flow rate of water or air through a system cannot be correctly predicted unless we evaluate by the total pressure loss. there are currently few methods for measuring total pressure loss, and the value of total pressure loss is not yet clearly. Therefore, we devised a method to measure total pressure loss by pump Q-H characteristic and succeeded in measuring total pressure loss indirectly. We compared the test results with the analysis to clarify the prediction accuracy of the analysis using commercial codes. We apply three two-phase flow models for the simulation: a VOF model, a homogeneous flow model, and a two-fluid model. The simulation results of comparison between each fluid model indicated that the VOF model predicted with the best accuracy, with the error of 46% compared to the test results. This study provides a benchmark for the current commercial code, and the prediction accuracy of the different models provides a direction for future improvements in the analysis.

Effect of axial and radial components of the magnetic field on the electrostatic resistive instabilities in Hall thruster plasma

A two-fluid model is used to investigate the influence of the axial component of the magnetic field on the growth rate of electrostatic resistive instabilities with cross field electron transport in a Hall thruster. The axial component of the magnetic field plays an important role in instabilities. It provides additional confinement to electrons and ions near the channel axis. Also, it helps to protect the walls from the direct impacts of particles, thereby reducing erosion and extending the operational lifetime of the system. A fourth-order dispersion equation is derived using plasma perturbed densities into Poisson's equation to observe the various effects on the growing waves in plasma. It is observed that the growth rate and the real frequency increase with axial and radial components of the magnetic field, respectively. The order of the real frequency of the wave is found to be 106/s. For the fixed value of the azimuthal wavenumber (ky=500/m), the amplitude of the growth rate of the instability dropped to almost 40% if the axial component of the magnetic field is considered. Similarly, the amplitude of the real frequency increases by almost 74% (at ky=500/m) by incorporating the contribution of the axial component of the magnetic field. In addition, it is also observed that the amplitude of the growth rate increases with low values of radial and axial components of the magnetic field, but it decreases at the higher value of the magnetic field due to the resonance of electron cyclotron frequency with plasma frequency.

Volume average of two-fluid RANS equations and a priori estimation of subgrid terms on subcooled boiling experiments

A statistic-volume averaged two-fluid model, convenient for subchannel and system codes in nuclear industry, is established from RANS equations of Neptune_CFD code and leads to the appearance of subgrid terms. A database of simulations is made on experiments with flow representative of nuclear reactor cores with cylindrical (KIT) and subchannel (PSBT) configurations. The subgrid terms are then compared to the convection terms on the database of 82 test cases. Concerning momentum and energy equations, subgrid terms reach respectively 7.5% and 16% of convection terms. Overall, the comparison shows that dispersion terms are always greater than turbulence terms, but both remain in the same order of magnitude, and are not negligible compared to convection. Moreover, the geometry has an impact on the dispersion terms. This observation suggests that caution should be exercised when using correlation established on a different geometry.

Scaling and modeling of the heat transfer across the free surface of a thermocapillary liquid bridge

PurposeThis paper aims to derive a reduced-order model for the heat transfer across the interface between a millimetric thermocapillary liquid bridge from silicone oil and the surrounding ambient gas.Design/methodology/approachNumerical solutions for the two-fluid model are computed covering a wide parametric space, making a total of 2,800 numerical flow simulations. Based on the computed data, a reduced single-fluid model for the liquid phase is devised, in which the heat transfer between the liquid and the gas is modeled by Newton’s heat transfer law, albeit with a space-dependent Biot function Bi(z), instead of a constant Biot number Bi.FindingsAn explicit robust fit of Bi(z) is obtained covering the whole range of parameters considered. The single-fluid model together with the Biot function derived yields very accurate results at much lesser computational cost than the corresponding two-phase fully-coupled simulation required for the two-fluid model.Practical implicationsUsing this novel Biot function approach instead of a constant Biot number, the critical Reynolds number can be predicted much more accurately within single-phase linear stability solvers.Originality/valueThe Biot function for thermocapillary liquid bridges is derived from the full multiphase problem by a robust multi-stage fit procedure. The derived Biot function reproduces very well the theoretical boundary layer scalings.

Validation of a two-fluid turbulence model in comsol multiphysics for the problem of flow around aerodynamic profiles

The article presents a study of a two-fluid turbulence model in the Comsol Multiphysics software package for the problem of a subsonic flow around the DSMA661 and NACA 4412 airfoils with angles of attack of 0 and 13.87 degrees, respectively. In this paper, the finite element method is used for the numerical implementation of the turbulence equations. To stabilize the discretized equations, stabilization by the Galerkin least squares method was used. The results obtained are compared with the results of other RANS, LES, DES models and experimental data. It is shown that in the case of continuous flow around the DSMA661 airfoil, the results of the two-fluid model are very close to the SST results and are in good agreement with the experimental data. When flowing around the NACA 4412 airfoil, flow separation occurs and a recirculation zone appears. It is shown that in such cases the two-fluid model gives more accurate results than other turbulence models. Implementation of the Comsol Multiphysics software package showed good convergence, stability, and high accuracy of the two-fluid turbulence model.

Three-dimensional transient CFD simulation of lignite chemical looping gasification in a circulating fluidized bed

In this work, a full-loop 3D computational fluid dynamics (CFD) numerical simulation of the chemical looping gasification (CLG) process of lignite in a circulating fluidized bed (CFB) was performed using a two-fluid Eulerian-Eulerian model. The results showed that the CFD simulation effectively captured the axial and radial velocities of the particles. More radial flow occurred in the bottom part of the riser and inside the cyclone. The exothermic reaction became dominant within 7s, while the heat-absorbing reaction became dominant between 7 and 15s. The aggregation regions of syngas moved up with that of the high-temperature zone, and CO was the main contributor to the syngas. The particle size in the range of 175–225 μm was inversely proportional to the size of the average heat transfer coefficient (HTC) in the riser. Extremely small particle size saturated the bed, suppressing the HTC. The peak of the HTC was 387.7 W/(m2·K), which occurred in the upper-middle region of the riser and reached. The maximum HTC average value was 180.6 W/(m2·K). Finally, experimental data were used to verify the reliability of the model.

Error field penetration in J-TEXT tokamak based on two-fluid drift-MHD model

An externally generated resonant magnetic perturbation can induce complex non-ideal MHD responses in their resonant surfaces. We have studied the plasma responses using Fitzpatrick’s improved two-fluid model and program LAYER. We calculated the error field penetration threshold for J-TEXT. In addition, we find that the island width increases slightly as the error field amplitude increases when the error field amplitude is below the critical penetration value. However, the island width suddenly jumps to a large value because the shielding effect of the plasma against the error field disappears after the penetration. By scanning the natural mode frequency, we find that the shielding effect of the plasma decreases as the natural mode frequency decreases. Finally, we obtain the m/n = 2/1 penetration threshold scaling on density and temperature.

Towards Uncovering Dark Matter Effects on Neutron Star Properties: A Machine Learning Approach

Over the last few years, researchers have become increasingly interested in understanding how dark matter affects neutron stars, helping them to better understand complex astrophysical phenomena. In this paper, we delve deeper into this problem by using advanced machine learning techniques to find potential connections between dark matter and various neutron star characteristics. We employ Random Forest classifiers to analyze neutron star (NS) properties and investigate whether these stars exhibit characteristics indicative of dark matter admixture. Our dataset includes 32,000 sequences of simulated NS properties, each described by mass, radius, and tidal deformability, inferred using recent observations and theoretical models. We explore a two-fluid model for the NS, incorporating separate equations of state for nucleonic and dark matter, with the latter considering a fermionic dark matter scenario. Our classifiers are trained and validated in a variety of feature sets, including the tidal deformability for various masses. The performance of these classifiers is rigorously assessed using confusion matrices, which reveal that NS with admixed dark matter can be identified with approximately 17% probability of misclassification as nuclear matter NS. In particular, we find that additional tidal deformability data do not significantly improve the precision of our predictions. This article also delves into the potential of specific NS properties as indicators of the presence of dark matter. Radius measurements, especially at extreme mass values, emerge as particularly promising features. The insights gained from our study are pivotal for guiding future observational strategies and enhancing the detection capabilities of dark matter in NS. This study is the first to show that the radii of neutron stars at 1.4 and 2.07 solar masses, measured using NICER data from pulsars PSR J0030+0451 and PSR J0740+6620, strongly suggest that the presence of dark matter in a neutron star is more likely than only hadronic composition.

Two-group drift-flux model for dispersed gas-liquid flows in rod bundles

Interfacial transfer terms in gas-liquid two-phase flows are formulated as the product of interfacial area concentration (IAC) and flux. The interfacial area transport equation (IATE) is essential for obtaining IAC in transient and developing two-phase flows. Two-group IATE was developed to account for the difference in the interfacial drag force between two groups of bubbles, where spherical and distorted bubbles are categorized as group one, while cap, slug, and churn turbulent bubbles are categorized as group two. The rigorous two-group approach requires two-group gas momentum equations, resulting in one additional momentum equation in the two-fluid model. The mixture gas momentum equation is considered to avoid the additional momentum equation. The two-group drift-flux model is necessary to calculate the two-group gas velocity from the mixture velocity. The present study develops an approximation methodology to acquire subchannel average and rod bundle average two-group two-phase flow parameters based on the validated power law assumption and a limited number of local data. The two-group model is developed for the distribution parameter and drift velocity for dispersed two-phase flows in rod bundles. The total performance of the newly developed two-group drift-flux model is evaluated by two-phase flow data in rod bundles. The results show that the developed two-group drift-flux model could well predict two-group gas velocities in rod bundles. This model is useful for subchannel thermal hydraulic analysis codes as a complement to the conventional one-group drift-flux model.

Mapping GENERIC Hydrodynamics into Carter’s Multifluid Theory

We show that the GENERIC model for relativistic heat conduction is a multifluid of Carter; this allows one to compute the multifluid constitutive relations directly from the GENERIC formalism. As a quick application, we prove that in the limit of infinite heat conductivity, GENERIC heat conduction reduces to the relativistic two-fluid model for superfluidity. This surprising “crossover” is a consequence of relativistic causality: if diffusion happens too fast, all the diffusing charge cumulates on the surface of the light cone, and it eventually travels at the speed of light like a wave. Our analysis is non-perturbative and carried out in a fully non-linear regime.

CFD simulation of a circulating fluidized bed carbon capture system using a solid-supported amine sorbent

Carbon capture, utilization, and sequestration (CCS) is one of the key technologies to reduce the emission of carbon dioxide, including that from exiting flue gas of fossil fuel-fired power plants. In this study, the two-fluid model approach was used to simulate the hydrodynamics of the entire circulating fluidized bed (CFB) loop of the integrated carbonation and regeneration sections using the mass and momentum equations and constitutive relations for both the gas and solid phases. Then, the verified models of the non-reactive simulation of the CFB loop were combined with species, energy equations, and carbonation regeneration rate of reactions for both phases to simulate the entire circulating fluidized bed carbon capture unit. The predicted extent of CO2 capture in this system showed the potential of continuous carbon capture using amine-based solid sorbents through the circulating fluidized bed CO2 capture unit.

The Cauchy Problem for a Non-conservative Compressible Two-Fluid Model with Far Field Vacuum in Three Dimensions

The Cauchy Problem for a Non-conservative Compressible Two-Fluid Model with Far Field Vacuum in Three Dimensions

The effect of slip on the development of flow separation due to a bump in a channel based on a two-fluid turbulence model

In the paper, two-fluid turbulence model simulations were used to calculate the flow of a statistically two-dimensional turbulent boundary layer over a hump. In this work, the finite element method is used for the numerical implementation of the turbulence equations. Galerkin least squares (GLS) stabilization was used to stabilize the discretized equations. The results of the two fluid models were compared with experimental measurements by Matai, R., Durbin P. A. and the SST turbulence model which exists in the Comsol Multiphysics software package. The implementation of the Comsol Multiphysics software package showed the stability and good accuracy of the two-fluid turbulence model than the SST turbulence model.

Numerical simulation of the flow in a flat suddenly expanding channel based on a two-fluid turbulence model

The article presents the results of a numerical study of the flow structure in a flat channel in the zone of its sudden expansion in the form of a ledge. The calculations are based on the numerical solution of a system of non-stationary equations using a new two-fluid turbulence model. The results of the profiles of longitudinal velocity and turbulent stress in different sections of the channel before and after the ledge, as well as the change in the coefficient of friction for the lower wall of the channel depending on the distance after the ledge are obtained. For the difference approximation of the initial equations, the control volume method was used, and the relationship between velocities and pressure was found using the SIMPLEC procedure. In this case, the viscous terms were approximated by the central difference, and for convective terms, a second-order scheme of accuracy against the flow was used. To confirm the correctness of the numerical results, a comparison was made with experimental data from the NASA database for the Reynolds number Re=36000. And the influence of the calculated grid in the results of the study was also investigated.

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.

Improvement of the two-fluid momentum equation for turbulent bubbly flows

A two-fluid model is widely employed to predict gas–liquid two-phase flows. Conventional two-fluid equations, derived by assuming that all phases are interpenetrating continua, occasionally yield impractical results. For example, the bubble velocity is predicted to be higher than the water velocity for a horizontal fully developed bubbly flow. One solution for this irrational result is two-fluid momentum equations based on the motion of fluid particles. This study revisits the particle-motion-based two-fluid equations. Previously, it was validated only with respect to the difference between the bubble and liquid velocities. Recently, we observed an erroneous prediction of the void fraction distribution by the existing particle-motion-based momentum equations. This study, through rigorous analysis, discovered that this error could be resolved by neglecting the turbulent kinetic energy term in the particle-motion-based equation for the gas phase. Subsequently, the revised momentum equations were applied to the vertical and horizontal air–water bubbly flows. The conventional and revised momentum equations produced similar results for upward bubbly flows because the relative velocity between the bubble and water phases was mainly governed by buoyancy. For horizontal bubbly flows, the revised momentum equations led to a downward shift in the liquid velocity distributions, which was attributed to the modified momentum diffusion term. At a higher modification factor of turbulent dispersion, the velocity distributions exhibited an upward shift. We conclude that the optimization of physical models should be based on the revised two-fluid momentum equations.

Comparison of numerical results of turbulence models for the problem of heat transfer in turbulent molasses

The study introduces Malikov's two-fluid methodology along with the RSM turbulence model for simulating turbulent heat transfer phenomena. It elucidates that temperature fluctuations within turbulent flows arise from temperature differentials between the respective fluids. Leveraging the two-fluid paradigm, the researchers develop a mathematical framework to characterize turbulent heat transfer dynamics. This resultant turbulence model is then applied to analyze heat propagation in turbulent flows around a flat plate and in scenarios involving submerged jets. To validate the model's efficacy, numerical outcomes are juxtaposed against established RSM turbulence models and experimental findings. The comparative analysis reveals that the two-fluid turbulent transport model aptly captures the thermodynamic behaviors inherent in turbulent flows with exceptional precision.