An Improved Three-Dimensional Non-Equilibrium Mixing Pool Model

This paper presents an improved three-dimensional non-equilibrium mixing pool model.It is a simplified form of the original model and is more practical for applications.The simulation re-sults show that the industrial scale distillation tray columns can be described closely by the improvedmodel.The effects of model parameters,such as the number of mixing pools,the point efficiencyand flow pattern,on separation are analyzed quantitatively.

Numerical simulation of anode heat transfer of nitrogen arc utilizing two-temperature chemical non-equilibrium model

A detailed understanding of anode heat transfer is important for the optimization of arc processing technology.In this paper,a two-temperature chemical non-equilibrium model considering the collisionless space charge sheath is developed to investigate the anode heat transfer of nitrogen free-burning arc.The temperature,total heat flux and different heat flux components are analyzed in detail under different arc currents and anode materials.It is found that the arc current can affect the parameter distributions of anode region by changing plasma characteristics in arc column.As the arc current increases from 100 A to 200 A,the total anode heat flux increases,however,the maximum electron condensation heat flux decreases due to the arc expansion.The anode materials have a significant effect on the temperature and heat flux distributions in the anode region.The total heat flux on thoriated tungsten anode is lower than that on copper anode,while the maximum temperature is higher.The power transferred to thoriated tungsten anode,ranked in descending order,is heat flux from heavy-species,electron condensation heat,heat flux from electrons and ion recombination heat.However,the electron condensation heat makes the largest contribution for power transferred to copper anode.

Numerical investigation on the flow characteristics of a reverse-polarity plasma torch by two-temperature thermal non-equilibrium modelling

A two-temperature(2 T)thermal non-equilibrium model is developed to address the thermal nonequilibrium phenomenon that inevitably exists in the reverse-polarity plasma torch(RPT)and applied to numerically investigate the plasma flow characteristics inside and outside the RPT.Then,a detailed comparison of the results of the 2 T model with those of the local thermal equilibrium(LTE)model is presented.Furthermore,the temperature of the plasma jet generated by a RPT and the RPT’s voltage are experimentally measured to compare and validate the result obtained by different models.The differences of the measured excitation temperature and the arc voltage between the 2 T model and experimental measurement are less than 13%and 8%,respectively,in all operating cases,validating the effectiveness of the 2 T model.The LTE model overestimates the velocity and temperature distribution of the RPT and its plasma jet,showing that thermal non-equilibrium phenomena cannot be neglected in the numerical modelling of the RPT.Unlike other common hot cathode plasma torches,the thermal non-equilibrium phenomenon is found even in the arc core of the RPT,due to the strong cooling effect caused by the big gas flow rate.

Radiative heat transfer analysis of a concave porous fin under the local thermal non-equilibrium condition:application of the clique polynomial method and physics-informed neural networks

The heat transfer through a concave permeable fin is analyzed by the local thermal non-equilibrium(LTNE)model.The governing dimensional temperature equations for the solid and fluid phases of the porous extended surface are modeled,and then are nondimensionalized by suitable dimensionless terms.Further,the obtained nondimensional equations are solved by the clique polynomial method(CPM).The effects of several dimensionless parameters on the fin's thermal profiles are shown by graphical illustrations.Additionally,the current study implements deep neural structures to solve physics-governed coupled equations,and the best-suited hyperparameters are attained by comparison with various network combinations.The results of the CPM and physicsinformed neural network(PINN)exhibit good agreement,signifying that both methods effectively solve the thermal modeling problem.

Three-Temperature Model Applied to Thermochemical Non-Equilibrium Reentry Flows in 2D—Seven Species

In this work, a study involving the fully coupled Euler and Navier-Stokes reactive equations is performed. These equations, in conservative and finite volume contexts, employing structured spatial discretization, on a condition of thermochemical non-equilibrium, are analyzed. High-order studies are accomplished using the Spectral method of Streett, Zang, and Hussaini. The high enthalpy hypersonic flows around a circumference, around a reentry capsule, along a blunt body, and along a double ellipse in two-dimensions are simulated. The Van Leer, Liou and Steffen Jr., and Steger and Warming flux vector splitting algorithms are applied to execute the numerical experiments. Three temperatures, which are the translational-rotational temperature, the vibrational temperature, and the electron temperature, are used to accomplish the numerical comparisons. Excellent results were obtained with minimum errors inferior to 6.0%. The key contribution of this work is the correct implementation of a three temperature model coupled with the implementation of three algorithms to perform the numerical simulations, as well the description of energy exchange mechanisms to perform more realistic simulations.

Two-Dimensional Mathematical Model of Tidal Current and Sediment for Oujiang Estuary and Wenzhou Bay

A 2-D mathematical model of tidal current and sediment has been developed for the Oujiang Estuary and the Wenzhou Bay. This model accomodates complicated features including multiple islands, existence of turbidity, and significant differ-ence in size distribution of bed material. The governing equations for non-uniform suspended load and bed load transport are presented in a boundary-fitted orthogonal curvilinear coordinate system. The numerical solution procedures along with their initial conditions, boundary conditions, and movable boundary technique are presented. Strategies for computation of the critical condition of deposition or erosion, sediment transport capacity, non-uniform bed load discharge, etc. are suggested. The model verification computation shows that, the tidal levels computed from the model are in good agreement with the field data at the 18 tidal gauge stations. The computed velocities and flow directions also agree well with the values measured along the totally 52 synchronously observed verticals distributed over 8 cross sections. The coraputed tidal water throughputs through the Huangda'ao cross section are close to the measured data. And the computed values of bed deformation from Yangfushan to the estuary outfall and in the outer-sea area are in good agreement with the data observed from 1986 to 1992. The changes of tidal volumes through the estuary, velocities in different channels and the bed form due to the influence of the reclamation project on the Wenzhou shoal are predicted by means of this model.

Physics-based analysis and simulation model of electromagnetic interference induced soft logic upset in CMOS inverter

The instantaneous reversible soft logic upset induced by the electromagnetic interference（EMI） severely affects the performances and reliabilities of complementary metal–oxide–semiconductor（CMOS） inverters. This kind of soft logic upset is investigated in theory and simulation. Physics-based analysis is performed, and the result shows that the upset is caused by the non-equilibrium carrier accumulation in channels, which can ultimately lead to an abnormal turn-on of specific metal–oxide–semiconductor field-effect transistor（MOSFET） in CMOS inverter. Then a soft logic upset simulation model is introduced. Using this model, analysis of upset characteristic reveals an increasing susceptibility under higher injection powers, which accords well with experimental results, and the influences of EMI frequency and device size are studied respectively using the same model. The research indicates that in a range from L waveband to C waveband, lower interference frequency and smaller device size are more likely to be affected by the soft logic upset.

Direct modeling for computational fluid dynamics

All fluid dynamic equations are valid under their modeling scales, such as the particle mean free path and mean collision time scale of the Boltzmann equation and the hydrodynamic scale of the Navier-Stokes （NS） equations. The current computational fluid dynamics （CFD） focuses on the numerical solution of partial differential equations （PDEs）, and its aim is to get the accurate solution of these governing equations. Under such a CFD practice, it is hard to develop a unified scheme that covers flow physics from kinetic to hydrodynamic scales continuously because there is no such governing equation which could make a smooth transition from the Boltzmann to the NS modeling. The study of fluid dynamics needs to go beyond the traditional numer- ical partial differential equations. The emerging engineering applications, such as air-vehicle design for near-space flight and flow and heat transfer in micro-devices, do require fur- ther expansion of the concept of gas dynamics to a larger domain of physical reality, rather than the traditional dis- tinguishable governing equations. At the current stage, the non-equilibrium flow physics has not yet been well explored or clearly understood due to the lack of appropriate tools. Unfortunately, under the current numerical PDE approach, it is hard to develop such a meaningful tool due to the absence of valid PDEs. In order to construct multiscale and multiphysics simulation methods similar to the modeling process of con- structing the Boltzmann or the NS governing equations, the development of a numerical algorithm should be based on the first principle of physical modeling. In this paper, instead of following the traditional numerical PDE path, we introduce direct modeling as a principle for CFD algorithm develop- ment. Since all computations are conducted in a discretized space with limited cell resolution, the flow physics to be mod- eled has to be done in the mesh size and time step scales. Here, the CFD is more or less a direct construction of dis- crete numerical evolution equations, where the mesh size and time step will play dynamic roles in the modeling process. With the variation of the ratio between mesh size and local particle mean free path, the scheme will capture flow physics from the kinetic particle transport and collision to the hydro- dynamic wave propagation. Based on the direct modeling, a continuous dynamics of flow motion will be captured in the unified gas-kinetic scheme. This scheme can be faithfully used to study the unexplored non-equilibrium flow physics in the transition regime.

Non-equilibrium ignition criterion for magnetized deuterium–tritium fuel

In this paper, non-equilibrium ignition conditions for magnetized cylindrical deuterium–tritium plasma in the presence of an axial magnetic field have been investigated. It is expected that temperature imbalance between ions and electrons as well as the axial magnetic field will relax the threshold of ignition conditions.Therefore, ignition conditions for this model are derived numerically involving the energy balance equation at the stagnation point. It has been derived using parametric space including electron and ion temperature(T_e, T_i), areal density(q R), and seed magnetic field-dependent free parameters of B/q, mB, and BR. For B/ρ < 10~6 G cm^3 g^(-1),mB < 4 × 10~4 G cm g^(-1), and BR <3 × 10~5 G cm, the minimum fuel areal density exceeds between ρR >0.002 g cm^(-2), ρR> 0.25 g cm^(-2), and ρR > 0.02 g cm^(-2),respectively. The practical equilibrium conditions also addressed which is in good agreement with the corresponding one-temperature magnetized mode proposed in previous studies. Moreover, it has been shown that the typical criterion of BR ≥(6.13–4.64) × 10~5 G cm would be expectable. It is also confirmed that the minimum product of areal density times fuel temperature in equilibrium model is located in the range of T = 6–8 keV for all these free parameters, depending on the magnitude of the magnetic field. This is the entry point for the non-equilibrium model consistent with equilibrium model.

The role of velocity derivative skewness in understanding non-equilibrium turbulence

The turbulence governed by the Navier-Stokes equation is paramount in many physical processes.However,it has been considered as a challenging problem due to its inherent nonlinearity,non-equilibrium,and complexity.Herein,we review the connections between the velocity derivative skewness Sk and the non-equilibrium properties of turbulence.Sk,a reasonable candidate for describing the non-equilibrium turbulence,which varies during the non-equilibrium procedure.A lot of experimental or numerical evidences have shown that the perturbation of energy spectrum,which associated with the excitation of large scales,results in an obvious variation of Sk,and Sk is a negative value in this rapid energy decay process.The variation of positive Sk is closely related to the perturbation of transfer spectrum,and this corresponds to the backward energy transfer process.In addition,the skewness characterizes the production(or reduction)rate of enstrophy due to vortex stretching(or compression).Using the transport equation of turbulent energy dissipation rate and enstrophy,it is possible to establish a theoretical connection between skewness and the non-equilibrium turbulence.It is expected that this work could trigger the rapid advancement of the future studies of non-equilibrium turbulence,and also the improvement of turbulence models.

Non-equilibrium turbulent phenomena in transitional flat plate boundary-layer flows

Many recent laboratory experiments and numerical simulations support a non-equilibrium dissipation scaling in decaying turbulence before it reaches an equilibrium state.By analyzing a direct numerical simulation(DNS)database of a transitional boundary-layer flow,we show that the transition region and the non-equilibrium turbulence region,which are located in different streamwise zones,present different non-equilibrium scalings.Moreover,in the wall-normal direction,the viscous sublayer,log layer,and outer layer show different non-equilibrium phenomena which differ from those in grid-generated turbulence and transitional channel flows.These findings are expected to shed light on the modelling of various types of non-equilibrium turbulent flows.

Simulation of MEG Packed Distillation Column Using an Equilibrium Stage Model-Case Study on Operating Parameters of Farsa Petrochemical Company： Assaluyeh-lran

Two types of equilibrium and non-equilibrium stage models are generally used to simulate the mass transfer of packed distillation column. Using non-equilibrium model requires the calculation of mass transfer coefficients, thus, usually equilibrium-based methods are preferred to be used for simulations of distillation columns. In this paper, packed column distillation of production of Mono Ethylene Glycol in FARSA SHIMI Company （Assaluyeh-Iran）＇s Ethylene Glycol portion has been simulated through using the equilibrium model and solving the related equations. The simulation has been carried out in the MATLAB environment. The column also has been simulated in the Aspen Hysys and Aspen Plus ver. 2006.5 environments. Then, the output has been compared with software results, designing and operating data of the underlying columns which demonstrate good consistency with the model. Having the model validated, the effect of some operating parameters has been analyzed through the model.

The second-order dynamic phase transition and Lee-Yang zeros in Eggers urn model

A second-order dynamic phase transition in a non-equilibrium Eggers urn model for the separation of sand is studied. The order parameter, the susceptibility and the stationary probability distribution have been calculated. By applying the Lee-Yang zeros method of equilibrium phase transitions, we study the distributions of the effective partition function zeros and obtain the same result for the model. Thus, the Lee-Yang theory can be applied to a more general non-equilibrium system.

Analyzing Heat Extraction and Sustainability of EGS with a Novel Model

We investigate the subsurface heat exchange process in EGS （enhanced geothermal systems） with a previously developed novel model. This model treats the porous heat reservoir as an equivalent porous medium of a single porosity. However, it considers local thermal non-equilibrium between solid rock matrix and fluid flowing in the factures and employs two energy conservation equations to describe heat transfer in the rock matrix and in the fractures, respectively, enabling the modeling and analyses of convective heat exchange in the heat reservoir. Another salient feature of this model is its capability of simulating the complete subsurface heat exchange process in EGS. The EGS subsurface geometry of interest physically consists of multiple domains： open channels for injection and production wells, the artificial heat reservoir, and the rocks enclosing the heat reservoir, while computationally we treat it as a single-domain of multiple sub-regions associated with different sets of characteristic properties （porosity and permeability, etc.）. This circumvents typical difficulties about matching boundary conditions between sub-domains in traditional multi-domain approaches and facilitates numerical implementation and simulation of the complete subsurface heat exchange process. This model is used to perform a comprehensive parametric study with respect to an imaginary doublet EGS. Effects of several parameters, including the permeability of heat reservoir, heat exchange coefficient in the heat reservoir, the specific area of fractures in the heat reservoir, and thermal compensation from surrounding rocks, on the heat extraction efficiency and EGS lifetime are analyzed.

An Improved k-Equation Turbulence Model

LRN （low-Reynolds number） modifications to the NR （Norris-Reynolds） k-equation turbulence model are proposed and evaluated. The k and e that render the hybrid time scale are determined using the k-transport equation together with the Bradshaw and other algebraic relations. The eddy-viscosity coefficient Cμ and the empirical damping function are constructed such as to preserve the anisotropic characteristics of turbulence for application to non-equilibrium turbulent flows. The MNR （modified NR） model is applied to calculate two well-documented flows, yielding predictions in good agreement with the DNS （direct numerical simulation） and experimental data. Comparisons demonstrate that the MNR model offers a significant improvement over the original NR model and competitiveness with the Spalart-Allmaras one-equation turbulence model. The performance evaluation dictates that unlike the original NR model, the MNR model can be employed as a single-equation model instead of associating it with the two-layer model of turbulence.

90Sr在微风化二长花岗岩中迁移实验及模拟研究

采用加压的方式,利用动态柱实验方法,通过3H、90Sr在微风化二长花岗岩中的穿透曲线,研究了90Sr在微风化二长花岗岩中的迁移规律,获得90Sr在微风化二长花岗岩中的迁移参数。实验中控制流速为1 mL/h,3H总活度为10^(4)Bq,迁移实验进行了120 h,3H浓度峰值出现在8.0 h,活度浓度峰值为213.4 kBq/L,穿透曲线无明显拖尾现象;90Sr总活度为5×10^(4)Bq,迁移实验进行了132 d,90Sr浓度峰值出现在27.4 d,活度浓度峰值为46.26 kBq/L,浓度下降阶段呈现明显的拖尾现象。利用数值模拟方法,基于3H的穿透曲线计算得到微风化二长花岗岩的垂向弥散度为3.03 cm;对比了平衡模型、双点吸附模型、两区模型、双点吸附两区模型四种模型下90Sr在微风化二长花岗岩中的迁移拟合结果,发现四种模型拟合结果相差较大,其中双点吸附两区模型通过引入非流动区含水量、溶质交换一级速率系数、非平衡吸附一级速率系数等参数能够更好地描述核素在微风化二长花岗岩介质迁移过程中的拖尾现象。结果表明:90Sr在微风化二长花岗岩中的吸附分配系数为1.23 mL/g,溶质交换一级速率系数为0.227/d,非平衡吸附一级速率系数为0.118/d。

砂岩含水介质中铀的吸附和迁移行为研究

地浸铀矿山退役后,含水层中残留的含铀浸出液随着地下水的运动向下游迁移扩散,存在对周边地下水污染的风险。本文设计了若干组批实验和柱实验,研究铀在北方某地浸铀矿山砂岩含水介质中的吸附和迁移行为。实验结果表明,砂岩对铀的吸附在12 h以内达到平衡,铀初始浓度越高,砂岩的铀吸附容量越大;砂岩对铀的吸附为吸热反应,温度升高有利于吸附反应的进行。溶液pH值和共存HCO_(3)^(-)浓度会对铀的吸附作用产生强烈的影响:pH值在7左右时,铀的吸附量最高;HCO_(3)^(-)浓度越高,铀的吸附量越低。这些影响是通过改变溶液中铀的络合形态和砂岩矿物表面的电荷性质实现的。柱实验表明,pH值、铀浓度、流速和HCO_(3)^(-)浓度是影响铀在饱和砂岩含水介质中迁移的重要因素。pH值≤7时,pH值越高,砂岩柱越不易被铀穿透;而铀浓度、流速、HCO_(3)^(-)浓度越高,砂岩柱越易被铀穿透。两点非平衡模型可以很好地拟合不同条件下铀在砂岩柱中的迁移过程。批实验获得的分配系数是柱实验的1.1~6.6倍。通过对比实验条件、含水层特性和地下水化学特征,确定分配系数为48.1 mL/g时,较适合描述研究区内砂岩含水层中的铀迁移。上述认识为地浸铀矿山地下水铀的反应运移过程和天然自净化机理提供了理论依据。

On the Liquid-Vapor Phase-Change Interface Conditions for Numerical Simulation of Violent Separated Flows

Numerous models have been proposed in the literature to include phase change into numerical simulations of two-phase flows.This review paper presents the modeling options that have been taken in order to obtain a model for violent separated flows with application to sloshing wave impacts.A relaxation model based on linear non-equilibrium thermodynamics has been chosen to compute the rate of phase change.The integration in the system of partial differential equations is done through a non-conservative advection term.For each of these modelling choices,some alternative models from the literature are presented and discussed.The theoretical framework for all phase change model(conservation equations and entropy growth)is also summarized.

Molecular Simulations of Water Transport Resistance in Polyamide RO Membranes: Interfacial and Interior Contributions

Understanding the transport resistance of water molecules in polyamide(PA)reverse osmosis(RO)membranes at the molecular level is of great importance in guiding the design,preparation,and applications of these membranes.In this work,we use molecular simulation to calculate the total transport resistance by dividing it into two contributions:the interior part and the interfacial part.The interior resistance is dependent on the thickness of the PA layer,while the interfacial resistance is not.Simulation based on the 5 nm PA layer reveals that interfacial resistance is the dominating contribution(>62%)to the total resistance.However,for real-world RO membranes with a 200 nm PA layer,interfacial resistance plays a minor role,with a contribution below 10%.This implies that there is a risk of inaccuracy when using the typical method to estimate the transport resistance of RO membranes,as this method involves simply multiplying the total transport resistance of the simulated value based on a membrane with a 5 nm PA layer.Furthermore,both the interfacial resistance and the interior resistance are dependent on the chemistry of the PA layer.Our simulation reveals that decreasing the number of residual carboxyl groups in the PA layer leads to decreased interior resistance;therefore,the water permeability can be improved at no cost of ion rejection,which is in excellent agreement with the experimental results.

Non-equilibrium model for catalytic distillation process

A new improved tri-diagonal method was developed for the non-equilibrium stage model of the catalytic distillation by coupling consumptive reaction coefficient.The reactions in the distillation column were divided into generative reaction and consumptive reac-tion.The non-equilibrium stage model was introduced for the catalytic distillation process of the dimethyl car-bonate(DMC)synthesis by urea methanolysis over solid based catalyst,and the improved tri-diagonal method was used to solve the model equations.Comparison of pre-dicted results with experiment data shows that the mean relative error of the yield of DMC was 3.78%under dif-ferent conditions such as different operating pressures and reaction temperatures.The improved tri-diagonal matrix method could avoid the negative values of the liquid com-positions during the calculations and restrain the fluc-tuation of compositions by slowing down the variations of the values in the iteration.The modeling results show that the improved tri-diagonal method was appropriate for system containing a wide range of boiling point com-ponents and a different rate of reactions.