Mathematical Modeling of Non-Isothermal Flow of Thin Layer of Two-Phase Medium Permeable Surface

Processes of filtering two-phase media in filtration devices play an important role in various industries. Significant role in the process of filtering is the initial section of flow, which defines the basic parameters： the profile and value of the velocity, pressure gradients, concentration and dispersion of sediment particles, etc.. The problem is solved by the method of surfaces of equal cost, the results enabled to establish the influence of the input section on the filtering process.

Passive scalar characteristics along inertial particle trajectory in turbulent non-isothermal flows

The momentum and heat coupling between carrier fluid and particles are a complex and challenge topic in turbulent reactive gas-solid flow modeling.Most observations on this topic,either numerical or experimental,are based on Eulerian framework,which is not enough for developing the probability density function(PDF) model.In this paper,the instantous behavior and multi-particle statistics of passive scalar along inertial particle trajectory,in homogenous isotropic turbulence with a mean scalar gradient,are investigated by using the direct numerical simulation(DNS).The results show that St^1.0 particles are easy to aggregate in high strain and low vorticity regions in the fluid field,where the scalar dissipation is usually much higher than the mean value,and that every time they move across the cliff structures,the scalar change is much more intensive.Anyway,the self-correlation of scalar along particle trajectory is significantly different from the velocities observed by particle,for which the prefer-concentration effect is evident.The mechanical-to-thermal time scale ratio averaged along the particles,<r> p,is approximately two times smaller than that computed in the Eulerian frame r,and stays at nearly 1.77 with a weak dependence on particle inertia.

Numerical Simulation of the Non-isothermal Viscoelastic Flow Past a Confined Cylinder

A collocated finite volume method on unstructured meshes is introduced to simulate the viscoelastic flow of the polymer melt with viscous dissipation past a confined cylinder.The constitutive equation for the simulations is non-isothermal FENE-P model,which is derived from the molecular theories.The temperature effect on the macroscopic fields(e.g.,velocity,stress) and microscopic fields(e.g.,molecular orientation,deformation,stretch) is investigated by comparison of isothermal and non-isothermal situations.This investigation indicates that temperature rise caused by viscous dissipation should not be neglected since it has significant effect on the macroscopic and microscopic properties of the polymer melt.

Non-isothermal Crystallization and Thermal Transformation Behaviors of Plasma Sprayed Fe_(48)Cr_(15)Mo_(14)C_(15)B_(6)Y_(2)Amorphous Coating

The non-isothermal crystallization dynamic behavior and mechanism of plasma sprayed Fe_(48)Cr_(15)Mo_(14)C_(15)B_(6)Y_(2)coating were thoroughly studied.The phase transition and crystallization kinetics of the coating were elaborately investigated by differential scanning calorimetry(DSC),X-ray diffraction(XRD),scanning electron microscopy(SEM),and transmission electron microscopy(TEM).The findings reveal that the characteristic temperatures of the coating shift to an elevated temperature at a higher heating rate and the crystallization processes are thermally activated.The 3-rd step of crystallization processes is more susceptible to the continuously increased heating rate while the onset crystallization reaction is less sensitive to the continuously enhanced heating rate.Fe_(23)(C,B)_6 phase is inclined to precipitate than other crystal phases due to the substantial pre-generation ofα-Fe.The onset nucleation and growth ofα-Fe crystals is tough due to a higher onset apparent activation energy.Meanwhile,the transformation from Fe_(23)(C,B)_(6)to FeB is harder in comparison with the precipitation of other crystals.The most parts of the three crystallization processes are dominated by three-dimensional diffusion model due to the fact that most values of local Avrami exponent are higher than 2.5.

Evolution of mechanical properties,localized corrosion resistance and microstructure of a high purity Al-Zn-Mg-Cu alloy during non-isothermal aging

The evolution of mechanical properties,localized corrosion resistance of a high purity Al-Zn-Mg-Cu alloy during non-isothermal aging(NIA)was investigated by hardness test,electrical conductivity test,tensile test,intergranular corrosion test,exfoliation corrosion test,slow strain rate tensile test and electrochemical test,and the mechanism has been discussed based on microstructure examination by optical microscopy,electron back scattered diffraction,scanning electron microscopy and scanning transmission electron microscopy.The NIA treatment includes a heating stage from 40℃to 180℃with a rate of 20℃/h and a cooling stage from 180℃to 40℃with a rate of 10℃/h.The results show that the hardness and strength increase rapidly during the heating stage of NIA since the increasing temperature favors the nucleation and the growth of strengthening precipitates and promotes the transformation of Guinier-Preston(GPI)zones toη'phase.During the cooling stage,the sizes ofη'phase increase with a little change in the number density,leading to a further slight increase of the hardness and strength.As NIA proceeds,the corroded morphology in the alloy changes from a layering feature to a wavy feature,the maximum corrosion depth decreases,and the reason has been analyzed based on the microstructural and microchemical feature of precipitates at grain boundaries and subgrain boundaries.

Exploring the effect of cooling rate on non-isothermal crystallization of copolymer polypropylene by fast scanning calorimetry

Polypropylene is commonly used as a binder for ceramic injection molding,and rapid cooling is often encountered during processing.However,the crystallization behavior of polypropylene shows a strong dependence on cooling rate due to its semi-crystalline characteristics.Therefore,the influence of cooling rate on the quality of final product cannot be ignored.In this study,the fast differential scanning calorimetry(FSC)test was performed to study the influence of cooling rate on the non-isothermal crystallization behavior and non-isothermal crystallization kinetics of a copolymer polypropylene(PP BC03B).The results show that the crystallization temperatures and crystallinity decrease as the cooling rate increases.In addition,two exothermic peaks occur when cooling rate ranges from 30 to 300 K·s^(-1),indicating the formation of another crystal phase.Avrami,Ozawa and Mo equations were used to explore the non-isothermal crystallization kinetics,and it can be concluded that the Mo method is suitable for this study.

Simulation of faceted dendrite growth of non-isothermal alloy in forced flow by phase field method

Numerical simulation based on a new regularized phase field model was presented to simulate the dendritic shape of a non-isothermal alloy with strong anisotropy in a forced flow. The simulation results show that a crystal nucleus grows into a symmetric dendrite in a free flow and into an asymmetry dendrite in a forced flow. As the forced flow velocity is increased, both of the promoting effect on the upstream arm and the inhibiting effects on the downstream and perpendicular arms are intensified, and the perpendicular arm tilts to the upstream direction. With increasing the anisotropy value to 0.14, all of the dendrite arms tip velocities are gradually stabilized and finally reach their relative saturation values. In addition, the effects of an undercooling parameter and a forced compound flow on the faceted dendrite growth were also investigated.

Simulation of Non-Isothermal Turbulent Flows Through Circular Rings of Steel

This article is intended to examine the fluid flow patterns and heat transfer in a rectangular channel embedded with three semi-circular cylinders comprised of steel at the boundaries.Such an organization is used to generate the heat exchangers with tube and shell because of the production of more turbulence due to zigzag path which is in favor of rapid heat transformation.Because of little maintenance,the heat exchanger of such type is extensively used.Here,we generate simulation of flow and heat transfer using nonisothermal flow interface in the Comsol multiphysics 5.4 which executes the Reynolds averaged Navier stokes equation(RANS)model of the turbulent flow together with heat equation.Simulation is tested with Prandtl number(Pr=0.7)with inlet velocity magnitude in the range from 1 to 2 m/sec which generates the Reynolds number in the range of 2.2×10^(5) to 4.4×10^(5) with turbulence kinetic energy and the dissipation rate in ranges(3.75×10^(−3) to 1.5×10^(−2))and(3.73×10^(−3)−3×10^(−2))respectively.Two correlations available in the literature are used in order to check validity.The results are displayed through streamlines,surface plots,contour plots,isothermal lines,and graphs.It is concluded that by retaining such an arrangement a quick distribution of the temperature over the domain can be seen and also the velocity magnitude is increasing from 333.15%to a maximum of 514%.The temperature at the middle shows the consistency in value but declines immediately at the end.This process becomes faster with the decrease in inlet velocity magnitude.

Computational-Analysis of the Non-Isothermal Dynamics of the Gravity-Driven Flow of Viscoelastic-Fluid-Based Nanofluids Down an Inclined Plane

The paper explores the gravity-driven flow of the thin film of a viscoelastic-fluid-based nanofluids(VFBN)along an inclined plane under non-isothermal conditions and subjected to convective cooling at the free-surface.The Newton’s law of cooling is used to model the convective heat-exchange with the ambient at the free-surface.The Giesekus viscoelastic constitutive model,with appropriate modifications to account for non-isothermal effects,is employed to describe the polymeric effects.The unsteady and coupled non-linear partial differential equations(PDEs)describing the model problem are obtained and solved via efficient semi-implicit numerical schemes based on finite difference methods(FDM)implemented in Matlab.The response of the VFBN velocity,temperature,thermal-conductivity and polymeric-stresses to variations in the volume-fraction of embedded nanoparticles is investigated.It is shown that these quantities all increase as the nanoparticle volume-fraction becomes higher.

Modeling and simulation of non-isothermal three-phase flow for accurate prediction in underbalanced drilling

The present study aims at investigating the effect of temperature variation due to heat transfer between the formation and drilling fluids considering influx from the reservoir in the underbalanced drilling condition. Gas-liquid-solid three-phase flow model considering transient thermal interaction with the formation was applied to simulate wellbore fluid to calculate the wellbore temperature and pressure and analyze the influence of different parameters on fluid pressure and temperature distribution in annulus. The results show that the non-isothermal three-phase flow model with thermal consideration gives more accurate prediction of bottom-hole pressure(BHP) compared to other models considering geothermal temperature. Viscous dissipation, the heat produced by friction between the rotating drilling-string and well wall and drill bit drilling, and influx of oil and gas from reservoir have significant impact on the distribution of fluid temperature in the wellbore, which in turn affects the BHP. Bottom-hole fluid temperature decreases with increasing liquid flow rate, circulation time, and specific heat of liquid and gas but it increases with increasing in gas flow rate. It was found that BHP is strongly depended on the gas and liquid flow rates but it has weak dependence on the circulation time and specific heat of liquid and gas. BHP increase with increasing liquid flow rate and decreases with increasing gas flow rate.

Non-isothermal oxidation and ignition prediction of Ti-Cr alloys

The non-isothermal oxidation behavior and oxide scale microstructure of Ti-Cr alloy （0≤w（Cr）≤25%） were studied from room temperature to 1723 K by thermogravimetric analysis （TGA）, X-ray diffraction （XRD） and scanning electron microscopy （SEM）. The influencing mechanism of chromium on the oxidation resistance of Ti-Cr alloys was discussed. The results show that the oxidation resistance of the alloys decreases with Cr below a critical chromium content wC and increases above wC; above 1000 K, the oxidation kinetics obeys parabolic rule and titanium dominates the oxidation process; after oxidation, the oxygen-diffusing layer is present in the alloy matrix, the oxide scale is mainly composed of rutile whose internal layer is rich in chromium, and chromium oxides separated out from TiO2 near the alloy-oxide interface improve the oxidation resistance. Ignition of metals and alloys is a fast non-isothermal oxidation process and the oxidation mechanism of Ti-Cr alloys during ignition is predicted.

Non-isothermal retrogression kinetics for grain boundary precipitate of 7A55 aluminum alloy

The retrogression kinetics for grain boundary precipitate （GBP） of 7A55 aluminum alloy was investigated by transmission electron microscopy （TEM） observation. The results reveal that the coarsening behavior of GBP obeys “LSW” theory, namely, the cube of GBP average size has a linear dependence relation to retrogression time, and the coarsening rate accelerates at the elevated retrogression temperature. The GBP coarsening activation energy Qo of （115.2±1.3） kJ/mol is obtained subsequently. Taking the retrogression treatment schedule of 190℃, 45 min derived from AA7055 thin plate as reference, the non-isothermal retrogression model for GBP coarsening behavior is established based on “LSW”theory and “iso-kinetics” solution, which includes an Arrhenius form equation. After that, the average size of GBP r（t） is predicted successfully at any non-isothermal process T（t） when the initial size of GBP r0 is given. Finally, the universal characterization method for the microstructure homogeneity along the thickness direction of TA55 aluminum alloy thick plate is also set up.

Phase field simulation for non-isothermal solidification of multicomponent alloys coupled with thermodynamics database

In order to quantitively model the real solidification process of industrial multicomponent alloys, a non-isothermal phase field model was studied for multicomponent alloy fully coupled with thermodynamic and diffusion mobility database, which can accurately predict the phase equilibrium, solute diffusion coefficients, specific heat capacity and latent heat release in the whole system. The results show that these parameters are not constants and their values depend on local concentration and temperature. Quantitative simulation of solidification in multicomponent alloys is almost impossible without such parameters available. In this model, the interfacial region is assumed to be a mixture of solid and liquid with the same chemical potentials, but with different composition. The anti-trapping current is also considered in the model. And this model was successfully applied to industrial A1-Cu-Mg alloy for the free equiaxed dendrite solidification process.

Comparative analysis of isothermal and non-isothermal solidification of binary alloys using phase-field model

Based on the entropy function, a two-dimensional phase field model of binary alloys was established. Meanwhile, an explicit difference method with uniform grid was adopted to solve the phase field and solute field controlled equations. And the alternating direction implicit(ADI) algorithm for solving temperature field controlled equation was also employed to avoid the restriction of time step. Some characteristics of the Ni-Cu alloy were captured in the process of non-isothermal solidification, and the comparative analysis of the isothermal and the non-isothermal solidification was investigated. The simulation results indicate that the non-isothermal model is favorable to simulate the real solidification process of binary alloys, and when the thermal diffusivity decreases, the non-isothermal phase-field model is gradually consistent with the isothermal phase-field model.

Hydrogen desorption kinetics mechanism of Mg-Ni hydride under isothermal and non-isothermal conditions

The Mg-Ni hydride was prepared by hydriding combustion synthesis under a high magnetic field. The dehydriding kinetics of the hydrides was measured under the isothermal and non-isothermal conditions. A model was applied to analyzing the kinetics behavior of Mg-Ni hydride. The calculation results show that the theoretical value and the experimental data can reach a good agreement, especially in the case of non-isothermal dehydriding. The rate-controlling step is the diffusion of hydrogen atoms in the solid solution. The sample prepared under magnetic field of 6 T under the isothermal condition can reach the best performance. The similar tendency was observed under the non-isothermal condition and the reason was discussed.

Non-isothermal kinetic analysis of thermal dehydration of La_2(CO_3)_3·3.4H_2O in air

The single phase La2（CO3）3·3.4H2 O was synthesized by hydrothermal method. The thermal decomposition and intermediates and final solid products of La2（CO3）3·3.4H2O from 30 to 1000 °C were characterized by XRD, FTIR and DTA-TG. The kinetics of dehydration of La2（CO3）3·3.4H2O in the temperature range of 30-366 °C was investigated under non-isothermal conditions. Flynn-Wall-Ozawa and Friedman isoconversion methods were used to calculate the activation energy and analyze the reaction steps; multivariate non-linear regression program was applied to determine the most probable mechanism and the kinetic parameters. The results show that the thermal dehydration of La2（CO3）3·3.4H2O is a kind of three-step competitive reaction, and controlled by an n-order initial reaction followed by n-order competitive reaction（FnFnFn model）. The activation energy matching with the most probable model is close to value obtained by Friedman method. The fitting curves match the original TG-DTG curves very well.

4D-Flow MRI在肥厚型心肌病左室流出道血流评估中的价值探索

目的 探索四维血流(four-dimensional flow,4D-Flow)磁共振成像(magnetic resonance imaging,MRI)技术在左心室腔内应用的可行性。材料与方法 本研究为前瞻性、横断面研究,纳入2022年8月至2023年1月于我院接受心脏MRI检查的21例肥厚型心肌病患者,采用3.0 T MRI扫描仪进行二维血流(tow-dimensional flow,2D-Flow)及4D-Flow成像,收集患者一周内进行的超声心动图检查结果。采用组内相关系数(inter-class correlation coefficient,ICC)、变异系数(coefficients of variation,COV)及Bland-Altman分析比较2D-Flow、4D-Flow评估左室流出道峰值流速的可重复性及一致性,并通过Pearson相关性分析探究二者与超声心动图测量结果的关系。结果 2D-Flow和4D-Flow观察者内/观察者间的ICC分别为0.999/0.999和0.995/0.992,COV分别为0.5%/0.5%和2.4%/2.6%。4D-Flow与超声心动图的测量结果呈中度相关,相关系数r值为0.574(P=0.006),但一致性较差,ICC为0.375(P=0.013)。2D-Flow与4D-Flow和超声心动图间无显著的一致性及相关性。结论 4D-Flow技术能够可视化心腔内血流模式,对左室流出道峰值流速的测量具有高度可重复性,且与超声心动图的测量结果具有显著的一致性。

Simulation of Non-isothermal Injection Molding for a Non-Newtonian Fluid by Level Set Method

A non-isothermal injection molding process for a non-Newtonian viscous pseudoplastic fluid is simulated.A conservative interface capturing technique and the flow field solving method are coupled to perform a dynamic simulation.The validity of the numerical method is verified by a benchmark problem.The melt interface evolution versus time is captured and the physical quantities such as temperature,velocity and pressure at each time step are obtained with corresponding analysis.A"frozen skin"layer with the thickness increasing versus time during the injection process is found.The fact that the"frozen skin"layer can be reduced by increasing the injection velocity is numerically verified.The fountain flow phenomenon near the melt interface is also captured.Moreover,comparisons with the non-isothermal Newtonian case show that the curvatures of the interface arcs and the pressure contours near the horizontal mid-line of the cavity for the non-Newtonian pseudoplastic case is larger than that for the Newtonian case.The velocity profiles are different at different positions for the non-Newtonian pseudoplastic case,while in the case of Newtonian flow the velocity profiles are parabolic and almost the same at different positions.

Kinetics and Mechanism of Decomposition of Nano-sized Calcium Carbonate under Non-isothermal Condition

Experiments on thermal decomposition of nano-sized calcium carbonate were carried out in a thermo-gravimetric analyzer under non-isothermal condition of different heating rates (5 to 20K·min-1). The Coats and Redfern's equation was used to determine the apparent activation energy and the pre-exponential factors. The mechanism of thermal decomposition was evaluated using the master plots, Coats and Redfern's equation and the kinetic compensation law. It was found that the thermal decomposition property of nano-sized calcium carbonate was different from that of bulk calcite. Nano-sized calcium carbonate began to decompose at 640℃, which was 180℃lower than the reported value for calcite. The experimental results of kinetics were compatible with the mechanism of one-dimensional phase boundary movement. The apparent activation energy of nano-sized calcium carbonate was estimated to be 151kJ·mol-1 while the literature value for normal calcite was approximately 200kJ·mol-1. The order of magnitude of pre-exponential factors was estimated to be 10~9 s-1.

Cure Kinetics of DGEBA with Hyperbranched Poly(3-hydroxyphenyl) Phosphate as Curing Agent Studied by Non-isothermal DSC

The cure kinetics of diglycidyl ether of bisphenol A （DGEBA） with hyperbranched poly （3-hydroxyphenyl） phosphate（HHPP） as the curing agent was investigated by means of non-isothermal differential scanning calorimetry （DSC） at various heating rates. The results were compared with the corresponding results by using 1,3-dihydroxybenzene（DHB） as a model compound. The results show that HHPP can enhance the cure reaction of DGEBA, resulting in the decrease of the peak temperature of the curing curve as well as the decrease of the activation energy because of the flexible --P--O-- groups in the backbone of HHPP. However, both the activation energy of the cured polymer and the peak temperature of the curing curve are increased with DHB as a curing agent. The cure kinetics of the DGEBA/HHPP system was calculated by using the isoconversional method given by Malek. It was found that the two-parameter autocatalytic model（Sestak-Berggren equation） is the most adequate one to describe the cure kinetics of the studied System at various heating rates. The obtained non-isothermal DSC curves from the experimental data show the results being accordant with those theoretically calculated.