Comparative numerical study of single and two-phase models of nanofluid heat transfer in wavy channel

The main purpose of this study is to survey numerically comparison of two- phase and single phase of heat transfer and flow field of copper-water nanofluid in a wavy channel. The computational fluid dynamics （CFD） prediction is used for heat transfer and flow prediction of the single phase and three different two-phase models （mixture, volume of fluid （VOF）, and Eulerian）. The heat transfer coefficient, temperature, and velocity distributions are investigated. The results show that the differences between the temperature fie].d in the single phase and two-phase models are greater than those in the hydrodynamic tleld. Also, it is found that the heat transfer coefficient predicted by the single phase model is enhanced by increasing the volume fraction of nanoparticles for all Reynolds numbers; while for the two-phase models, when the Reynolds number is low, increasing the volume fraction of nanoparticles will enhance the heat transfer coefficient in the front and the middle of the wavy channel, but gradually decrease along the wavy channel.

GLOBAL EXISTENCE OF CLASSICAL SOLUTION FOR A VISCOUS LIQUID-GAS TWO-PHASE MODEL WITH MASS-DEPENDENT VISCOSITY AND VACUUM

In this work, we obtain the global existence and uniqueness of classical solu-tions to a viscous liquid-gas two-phase model with mass-dependent viscosity and vacuum in one dimension, where the initial vacuum is allowed. We get the upper and lower bounds of gas and liquid masses n and m by the continuity methods which we use to study the compressible Navier-Stokes equations.

The Fermion Representation of the Phase Model

In this paper,we give a Fermion representation of the Phase model.We find that the states in the phase model can be described by Maya diagrams,and operators can be described by Fermions.We calculate the rule of multiplications of Young diagrams in N×M box by Fermions,and also calculate the relations in the Phase model by Fermions.

3-Phase Modeling for the Origin of Chinese Lithium-Rich Brines

There are significantly different origins and mineralizations among various lithium-rich brines of the world.As for Clayton Valley,Nevada,the data and interpretations recently presented suggest that the model

Stability analysis of unsaturated soil slope during rainfall infiltration using coupled liquid-gas-solid three-phase model

Generally, most soil slope failures are induced by rainfall infiltration, a process that involves interactions between the liquid phase, gas phase,and solid skeleton in an unsaturated soil slope. In this study, a loosely coupled liquid-gas-solid three-phase model, linking two numerical codes,TOUGH2/EOS3, which is used for water-air two-phase flow analysis, and FLAC^(3D), which is used for mechanical analysis, was established. The model was validated through a documented water drainage experiment over a sandy column and a comparison of the results with measured data and simulated results from other researchers. The proposed model was used to investigate the features of water-air two-phase flow and stress fields in an unsaturated soil slope during rainfall infiltration. The slope stability analysis was then performed based on the simulated water-air two-phase seepage and stress fields on a given slip surface. The results show that the safety factor for the given slip surface decreases first, then increases, and later decreases until the rainfall stops. Subsequently, a sudden rise occurs. After that, the safety factor decreases continually and reaches its lowest value, and then increases slowly to a steady value. The lowest value does not occur when the rainfall stops, indicating a delayed effect of the safety factor. The variations of the safety factor for the given slip surface are therefore caused by a combination of pore-air pressure, matric suction, normal stress, and net normal stress.

A quasi single-phase model for debris flows and its comparison with a two-phase model

A depth-averaged quasi single-phase mixture model is proposed for debris flows over inclined bed slopes based on the shallow water hydrosediment-morphodynamic theory with multi grain sizes. The stresses due to fluctuations are incorporated based on analogy to turbulent flows, as estimated using the depth-averaged k-? turbulence model and a modification component. A fully conservative numerical algorithm, using wellbalanced slope limited centred scheme, is deployed to solve the governing equations. The present quasi single-phase model using four closure relationships for the bed shear stresses is evaluated against USGS experimental debris flow and compared with traditional quasi single-phase models and a recent physically enhanced two-phase model. It is found that the present quasi single-phase model performs much better than the traditional models, and is attractive in terms of computational cost while the two-phase model performs even better appreciably.

Sensitivity analysis of a dense discrete phase model for 3D simulations of a tapered fluidized bed

This study aims to conduct a sensitivity analysis of closure models and modeling parameters for the Dense Discrete Phase Modeling(DDPM)approach in order to investigate the hydrodynamics of a 3D lab-scale Tapered Fluidized Bed(TFB).The closure models and model parameters under investigation include the gas-solid drag force,viscous models,particle-particle interaction models,restitution coefficient,specularity coefficient,and rebound coefficient.The primary objective of this sensitivity analysis is to optimize the numerical model's performance.The numerical results,in terms of axial and lateral Solid Volume Fraction(SVF)profiles obtained from the sensitivity analysis,indicate that the drag force and restitution coefficient significantly influence the hydrodynamics of the TFB.Properly selecting these parameters could result in the improved performance of the numerical model.However,the sensitivity of turbulence models,particle-particle interaction models,specularity coefficient,and rebound coefficient has a lesser impact on the hydrodynamics results.This work concludes with the recommendation of a set of closure models and modeling parameters that offer the most accurate prediction of the hydrodynamics of the TFB.

Bifurcation Analysis Reveals Solution Structures of Phase Field Models

The phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems.Here,we develop a new analytical approach based on the bifurcation analysis to explore the mathematical solution structure of phase field models.Revealing such solution structures not only is of great mathematical interest but also may provide guidance to experimentally or computationally uncover new morphological evolution phenomena in materials undergoing electronic and structural phase transitions.To elucidate the idea,we apply this analytical approach to three representative phase field equations:the Allen-Cahn equation,the Cahn-Hilliard equation,and the Allen-Cahn-Ohta-Kawasaki system.The solution structures of these three phase field equations are also verified numerically by the homotopy continuation method.

Phase field model for electric-thermal coupled discharge breakdown of polyimide nanocomposites under high frequency electrical stress

In contrast to conventional transformers, power electronic transformers, as an integral component of new energy power system, are often subjected to high-frequency and transient electrical stresses, leading to heightened concerns regarding insulation failures. Meanwhile, the underlying mechanism behind discharge breakdown failure and nanofiller enhancement under high-frequency electrical stress remains unclear. An electric-thermal coupled discharge breakdown phase field model was constructed to study the evolution of the breakdown path in polyimide nanocomposite insulation subjected to high-frequency stress. The investigation focused on analyzing the effect of various factors, including frequency, temperature, and nanofiller shape, on the breakdown path of Polyimide(PI) composites. Additionally, it elucidated the enhancement mechanism of nano-modified composite insulation at the mesoscopic scale. The results indicated that with increasing frequency and temperature, the discharge breakdown path demonstrates accelerated development, accompanied by a gradual dominance of Joule heat energy. This enhancement is attributed to the dispersed electric field distribution and the hindering effect of the nanosheets. The research findings offer a theoretical foundation and methodological framework to inform the optimal design and performance management of new insulating materials utilized in high-frequency power equipment.

Application of different CFD multiphase models to investigate effects of baffles and nanoparticles on heat transfer enhancement

In this work, the effect of baffles in a pipe on heat transfer enhancement was studied using computa- tional fluid dynamics （CFD） in the presence of Al2O3 nanoparticles which are dispersed into water. Fluid flow through the horizontal tube with uniform heat flux was simulated numerically and three dimensional governing partial differential equations were solved. To find an accurate model for CFD simulations, the results obtained by the single phase were compared with those obtained by three different multiphase models including Eulerian, mixture and volume of fluid （VOF） at Reynolds numbers in range of 600 to 3000, and two different nanoparticle concentrations （1% and 1.6%）. It was found that multi- phase models could better predict the heat transfer in nanofluids. The effect of baffles on heat transfer of nanofluid flow was also investigated through a baffled geometry. The numerical results show that at Reynolds numbers in the range of 600 to 2100, the heat transfer of nanofluid flowing in the geometry without baffle is greater than that of water flowing through a tube with baffle, whereas the difference between these effects （nanofluid and baffle） decreases with increasing the Reynolds number. At higher Reynolds numbers （2100-3000） the baffle has a greater effect on heat transfer enhancement than the nanofluid.

Thermodynamic consistent phase field model for sintering process with multiphase powders

A thermodynamic consistent phase field model is developed to describe the sintering process with multiphase powders. In this model, the interface region is assumed to be a mixture of different phases with the same chemical potential, but with different compositions. The interface diffusion and boundary diffusion are also considered in the model. As an example, the model is applied to the sintering process with Fe-Cu powders. The free energy of each phase is described by the well-developed thermodynamic models, together with the published optimized parameters. The microstructure and solute distribution during the sintering process can both be obtained quantitively.

Comparative study of two fluid model and dense discrete phase model for simulations of gas-solid hydrodynamics in circulating fluidized beds

Computational fluid dynamics(CFD)has become a valuable tool to study the complex gas-solid hydrodynamics in the circulating fluidized bed(CFB).Based on the two fluid model(TFM)under the Eulerian-Eulerian framework and the dense discrete phase model(DDPM)under the Eulerian-Lagrangian framework,this work conducts the comparative study of the gas-solid hydrodynamics in a CFB riser by these two different models.Results show that DDPM could be used to predict gas-solid hydrodynamics in the circulating fluidized bed,and there are differences between TFM and DDPM,especially in the radial distribution profiles of solid phase.Sensitivity analysis results show that the gas-solid drag model exhibits significant effects on the results for both the two models.The specularity coefficient and the restitution coefficient in the TFM,as well as the reflection coefficient and the parcel number in the DDPM,exhibit less impact on the simulated results.

Numerical analysis and experimental validation of hydrodynamics of a thin bubbling fluidized bed for various particle-size distributions using a three-dimensional dense discrete phase model

A dense discrete phase model combined with the kinetic theory of granular flows was used to study the bubbling characteristics and segregation of poly-dispersed particle mixtures in a thin fluidized bed.Our simulations showed that in using the hybrid Eulerian-Lagrangian method,the common use of one computational cell in the thickness direction of the thin bed does not predict wall friction correctly.Instead,a three-cell discretization of the thickness direction does predict the wall friction well but six cells were needed to prevent overprediction of the bed expansion.The change in specularity factor(SF)of the model not only affected the predictions of the velocity of particles,but also had a considerable impact on their flow pattern.A decrease in SF,which decreases wall friction,showed an over-prediction in the size of bubbles,particle velocities,and void fraction of the bed,and led to a shift in the circulation center toward the bottom of the bed.The segregation of the Geldart B particles was studied in the narrow range from 400 to 600μm with a standard deviation less than 10%of the average diameter.Simulations showed that large particles accumulated close to the distributor at the bottom of the bed and the center of the bed,but small particles moved towards the wall and top surface.The decrease in the mean particle size and spread in shape of the distribution improves mixing by up to 30%at a superficial gas velocity of around 2.5 times the minimum fluidization velocity.Log-normal mixtures with a small proportion of large particles had the most uniform distribution with a thin layer of jetsam forming at the bottom of the bed.Finally,experimental verification of the segregation and mixing of polydisperse particles with narrow size distribution is suggested.

Coupled Model of Two-phase Debris Flow,Sediment Transport and Morphological Evolution

The volume fraction of the solid and liquid phase of debris flows, which evolves simultaneously across terrains, largely determines the dynamic property of debris flows. The entrainment process significantly influences the amplitude of the volume fraction. In this paper, we present a depth-averaged two-phase debris-flow model describing the simultaneous evolution of the phase velocity and depth, the solid and fluid volume fractions and the bed morphological evolution. The model employs the Mohr–Coulomb plasticity for the solid stress, and the fluid stress is modeled as a Newtonian viscous stress. The interfacial momentum transfer includes viscous drag and buoyancy. A new extended entrainment rate formula that satisfies the boundary momentum jump condition （Iverson and Ouyang, 2015） is presented. In this formula, the basal traction stress is a function of the solid volume fraction and can take advantage of both the Coulomb and velocity-dependent friction models. A finite volume method using Roe’s Riemann approximation is suggested to solve the equations. Three computational cases are conducted and compared with experiments or previous results. The results show that the current computational model and framework are robust and suitable for capturing the characteristics of debris flows.

A phase model for point spread function estimation in ground-based astronomy

In ground-based astronomy, images of objects in outer space are acquired via ground-based tele- scopes. However, the imaging system is generally interfered by atmospheric turbulence and hence images so acquired are blurred with unknown point spread function （PSF）. To restore the observed images, aberration of the wavefront at the telescope＇s aperture, i.e., the phase, is utilized to derive the PSF. However, the phase is not readily available. Instead, its gradients can be collected by wavefront sensors. Thus the usual approach is to use regularization methods to reconstruct high-resolution phase gradients and then use them to recover the phase in high accuracy. Here, we develop a model that reconstructs the phase directly. The proposed model uses the tight frame regularization and it can be solved efficiently by the Douglas-Rachford alternating direction method of multipliers whose convergence has been well established. Numerical results illustrate that our new model is efficient and gives more accurate estimation for the PSF.

Experimental and numerical investigation of liquid-solid binary fluidized beds： Radioactive particle tracking technique and dense discrete phase model simulations

Liquid-solid binary fluidized beds are widely used in many industries. However, the flow behavior of such beds is not well understood due to the lack of accurate experimental and numerical data. In the current study, the behavior of monodisperse and binary liquid-solid fluidized beds of the same density but dif- ferent sizes is investigated using radioactive particle tracking （RPT） technique and a dense discrete phase model （DDPM）. Experiments and simulations are performed in monodisperse fluidized beds containing two different sizes of glass beads （0.6 and I mm） and a binary fluidized bed of the same particles for vari- ous bed compositions. The results show that both RPT and DDPM can predict the mixing and segregation pattern in liquid-solid binary fluidized beds. The mean velocity predictions of DDPM are in good agree- ment with the experimental findings for both monodisperse and binary fluidized beds. However, the axial root mean square velocity predictions are only reasonable for bigger particles. Particle-particle interac- tions are found to be critical for predicting the flow behavior of solids in liquid-solid binary fluidized beds.

Modified surface tension model for free surface flow with single-phase lattice Boltzmann method

A single-phase lattice Boltzmann model with modified surface tension is developed in this paper to solve the problem of high-density-ratio free surface flow.The computational efficiency and accuracy are both enhanced.The restriction to the relaxation factor （which needs to be smaller than 1） is circumvented by the new surface tension algebra,due to its rational physical nature compared with the treatment of Xing,Buther and Yang in their paper （Comp.Mater.Sci.,2007,39（2）：282-290）.The proposed stable surface tension scheme is applied to simulate the free deformation of a square droplet with surface tension effect and the process of a droplet impinging on a liquid film.The numerical solution for free deformation of a droplet agrees well with thermodynamic principles,and also achieves high accuracy in comparison with Xing,et al.＇s model.Three typical impinging modes are successfully obtained with the new scheme,and another particular mode found by Wang and Chen is also successfully simulated.The evolutions of liquid crown agree well with the power law related to time.

Global Existence of Solutions for Baer-Nunziato Two-Phase Flow Model in a Bounded Domain

In this paper, we study the global existence and uniqueness of strong solutions for the Baer-Nunziato two-phase flow model in a bounded domain with a no-slip boundary. The global existence and uniqueness of strong solutions are obtained when the initial value is near the equilibrium state in H2 (Ω). Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.

Analytical method for softness abrasive flow field based on discrete phase model

Aiming at the problem of difficult contact finishing for mini structural surface in course of mould manufacturing,a new no-tool precision machining method based on soft abrasive flow machining (SAFM) was proposed. It allocated restrained component near surface machined,constituted restrained abrasive flow passage,and made the surface become a segment of passage wall. It could control turbulence abrasive flow in restrained passage,realize micro cutting for passage wall,and utilize the irregular motion of abrasive flow to eliminate the mono-directional marks on machined surfaces,and the precision could reach the specular level. A two-phase dynamic model of abrasive flow oriented to SAFM combined with discrete phase model (DPM) was established,the law of two-phase flow motion and the related physical parameters was obtained by corresponding numerical simulation method,and the mechanism of precision machining in SAFM was discussed. Simulation results show that the abrasive flow machining process mainly appears as translation of ablating location with the influence by granular pressure,and as the variation of machining efficiency with the influence by near-wall particle velocity. Thus via control of the inlet velocity and its corresponding machining time,it is supposed to work out the machining process according to the machining requirements by using the Preston equation to seek the relationship among velocity,pressure and material removing rate. By tracking near-wall particles,it can be confirmed that the movement of near-wall abrasive particles is similar to stream-wise vortices. The cutting traces on workpiece surfaces assume disorderly arrangement,so the feasibility of the SAFM method can be reaffirmed.

Phase field modeling of dendrite growth

Single dendrite and multi-dendrite growth for Al-2 mol pct Si alloy during isothermal solidification are simulated by phase field method. In the case of single equiaxed dendrite growth, the secondary and the necking phenomenon can be observed. For multi-dendrite growth, there exists the competitive growth among the dendrites during solidification. As solidification proceeds, growing and coarsening of the primary arms occurs, together with the branching and coarsening of the secondary arms. When the diffusion fields of dendrite tips come into contact with those of the branches growing from the neighboring dendrites, the dendrites stop growing and being to ripen and thicken.