Coefficient Ke Research Articles

Removal of Low-Content Impurities from Pure Al by Supergravity Combined with Semi-Solid Method

Recently, the purification technology for high-purity aluminum (Al) has become the focus and difficulty of the majority of researchers. In this study, a novel approach for removing iron (Fe) impurities from pure Al via combining the supergravity field and semi-solid refining was proposed. Various separation temperatures (T), holding times (th), and separation times (ts) were applied within a gravitational field to explore their impact on the purification process and its underlying mechanisms. The optimal conditions were achieved at T = 653 °C, th = 40 min, ts = 3 min, and a gravity coefficient G = 1000, with the loss rate of purified Al reaching up to 4.1% and the removal rate of Fe reaching 81.9%. The Fe content in pure Al was reduced from 0.32 wt.% to 0.06 wt.%. Moreover, the purified mechanism of supergravity in a semi-solid method was reported for the first time. It was concluded that supergravity could decrease the value of the effective distribution coefficient (ke), thereby promoting the continuous migration of Fe impurities at the solidification interface into the liquid phase. The Fe-rich phase in the Al melt was completely filtered to the lower part of the crucible in the supergravity field, completing the further purification of the pure Al.

Development of viscosity models of concentrated suspensions: Contribution of particle-size and shape indices

Blending cementitious powders marks multiple morphological features which dictate the rheology of cement-based suspensions. Models, whether theoretical or empirical, unveiled the convolution in describing the consequence of particles’ morphology on the rheology of cement-based suspensions. The viscosity of various cement suspensions designed with different liquid-to-binder ratios was examined. Models, for instance, Krieger–Dougherty and Mooney, were implemented to foresee the relative viscosity of the employed suspensions in terms of the coupled physical properties and dry relative solid fraction. The coefficient kE and intrinsic viscosity (η) are in good agreement with particle-size indices, including fineness index (SSA × Gs) and particle-size ratio (d502/SSA). In addition, the current models were adjusted with a focus on new coupled-physical properties, including static (αR × αS), dynamic (αF × cohesion), and total flowability (ftotal) indices. This resulted in significant improvement in the precision of determining the viscosity of concentrated cement-based suspensions.

Analytical model for concrete-filled double skin tube columns with different cross-sectional shapes under axial compression

The existing theoretical analysis models of concrete-filled double skin tube (CFDST) columns are limited to the analysis of CFDST columns with circular outer and inner tubes (CC-CFDST). The purpose of this paper is to propose a unified model for CFDST columns with different cross-sectional shapes, including CFDST columns with rectangular outer and inner tubes (RR-CFDST), CFDST columns with square outer and inner tubes (SS-CFDST), CFDST columns with square outer and circular inner tubes (SC-CFDST), CFDST columns with circular outer and square inner tubes (CS-CFDST), CC-CFDST columns. The CFDST columns with different shapes (original columns) are replaced with equivalent CC-CFDST columns by assuming that they have the same cross-sectional areas of the inner and outer steel tubes and concrete. The difference in mechanical properties between the original column and the equivalent column is attributed to the difference in the confining effect of the steel tube on the core concrete caused by the different shape, which is considered by the shape effect coefficient ke. The proposed model is verified by collected experimental data of CFDST columns with different cross-sectional shapes. The mean value and coefficient of variation of the ratio of the calculated bearing capacity to the experimental bearing capacity are 1.006 and 0.119, respectively. The results show that the proposed model can predict the axial compression bearing capacity and load–deflection curves of CFDST columns accurately.

Kinetic Modeling of Heat and Mass Transfer During Deep Fat Frying of Churro

The effect of deep fat frying temperatures, ranging from 160 to 190 oC, on frying parameters including the heat transfer coefficient (he), mass transfer coefficient (ke) and effective moisture diffusivity (De) were investigated during deep fat frying of churro that is fried dough pastry. Therefore experimental studies were conducted for both heat and mass transfer phenomena and mathematical model was developed for simultaneous transfer by using Newman technique for churro actual geometry (3-D cylindrical shape). Fourier’s and Fick’s laws were applied for computation of coefficients of heat and mass transfer. The he coefficients were 437.360-93.535 W/m2K in the temperatures range of 160 to 190 oC. However, the value of ke and De increased by an increase in oil temperature during frying. The maximum values were determined as 17.36 x10-5 m/s and 2.48 x10-5 m2/s at 190 oC for ke and De, respectively. Model and experimental data had good agreement and the transfer coefficients followed the first order kinetic model with high R2 and low RMSE values. There was found an Arrhenius equation between the effective moisture diffusivity and deep fat frying temperature, so the value of activation energy was calculated as 63.546 kj/mol.

3D mathematical modeling of external mass transfer effect in high-rate adsorption process

The effect of external mass transfer on the high-rate adsorption system was evaluated in the present study. In the experimental section, the removal of methyl orange (MO) was carried out by using surfactant modified chitosan-clinoptilolite at specific conditions such as the optimum adsorbent dosage of 11 g L−1, solution pH of 3.5, contact time of about 3 min and constant temperature of 30 °C. The characterization of adsorbent showed the porosity value of 0.064 and the BET surface area of 10.5 m2 g−1. These features of adsorbent established the high-rate adsorption process in which the shape of decay curves is not smooth and the concentration of adsorbate falls quickly. In high-rate adsorption processes, the external mass transfer mechanism has a significant effect on total mass transfer at early time of adsorption. The pore volume and surface diffusion model (PVSDM) were applied for predicting MO concentration decay curves. This model and its parameters could not estimate properly the concentration of MO at the early time of the adsorption process. To overcome this problem, in addition to optimization of surface diffusion coefficient (Ds), the external mass transfer coefficient (ke) was optimized and the effect of those parameters was studied in three dimensions. The optimization provided a better agreement between the model and experimental data in such a way to reduce the error rate. To show better the effect of external mass transfer, Biot number (between (2.15 and 24.05) × 10−3) was applied and it revealed that the adsorption mechanism was controlled by external mass transport. The high external surface area illustrated that in all values of ke and initial concentration of MO, surface diffusion is the dominant mechanism in intraparticle diffusion and the low porosity of adsorbent limited the penetration of adsorbate species into the adsorbent cavities, whereby the pore volume diffusion could be considered negligible.

Mathematical model of an asynchronous machine in real coordinates of state

A mathematical description of an asynchronous machine with unreduced parameters in the space of real phase coordinates is given. When studying an asynchronous motor in a dual power supply system with controlled converters in rotor and stator circuits, there is a need for an AM model without parameters, in which the processes in the stator and rotor circuits will correspond to reality in magnitude. In addition, such a model is necessary when analyzing the energy parameters of the whole electric drive controlled by the rotor. To observe real processes in the stator and rotor, the model should be designed in separate spatial coordinate systems. In reference books for AM with a wound rotor (WR), as a rule, the real parameters (resistances, currents and voltages) of the stator and rotor and the voltage reduction coefficient ( ke ) are given. Bringing currents and resistances (inductances) is carried out by coefficients ki=ke and kr=ke2 respectively. Let's consider the description of the machine without reduction of parameters. For the convenience of further consideration, let's introduce the general value of the mutual inductance.
 We obtain an equation for the electromagnetic moment in real coordinates. Let's design a model in the MATLAB dynamic modeling environment using vector-matrix representation. Matrix algebraic operations with vector variables are implemented by Matlab Fn blocks, which are the calls to userdefined functions described in the form of M-files. The content of Matlab Fn functions is considered. On the model, the processes of starting of an AM with a phase rotor of AK-52-6 type were. Shows the graphs of start-up transients. The processes in the obtained model coincided with the results of modeling of this engine in the model with the coordinates reduced to the rotor. Thus, the energy processes described by this model correspond to the processes to the model with the given parameters, and the processes of currents and flux linkages changing of the stator and rotor are real.
 The model designed in the MATLAB/Simulink dynamic modeling environment can be used to study double-powered asynchronous electric drives.

Revealing the influence of high magnetic field on the solute distribution during directional solidification of Al-Cu alloy

The effect of the high magnetic field (MF) on the distribution of solute concentration during directional solidification of Al-Cu alloy under low growth speed was experimentally investigated. The amount of non-equilibrium eutectic is quantified via X-ray computed tomography (XCT) and demonstrated to reduce with the application of MF. Further, experimental results reveal that the MF alleviates the microsegregation and increases the average Cu concentration in solid solution, leading to the increases of the effective partition coefficient ke. It was also found that Cu concentration in solid solution increases continuously with the increasing intensity of MF, following the strengthening of micro-hardness. The change of ke under the MF is demonstrated to attribute to the thermoelectric magnetic convection (TEMC) in the mushy zone and the thermoelectric magnetic force (TEMF) acting on the solid. The TEMC is supposed to cause secondary convection owing to the inequality in flow velocities of circulation in different positions of dendrite stem. And the vacancies created by the proliferation and movement of dislocations induced by TEMF in the matrix is supposed to be able to capture solute atoms and thus enhance the solute concentration in the solid solution.

Study on the effective distribution coefficient of impurity separation in the preparation of high purity aluminum

Effective distribution coefficient (ke) plays an important role in zone melting purification but has never been systematically calculated as an important parameter. A novel analysis method for impurity separation separating from Al using determination of impurities (Si, Fe, Cu, Zn) content and calculation of ke has been investigated. Experimental results show that the impurity separation effect was significantly improved due to the ke closely approximating the equilibrium distribution coefficient (k0) via optimization of purification times and speed of the melting zone. When the times of purification were increased from 15 to 20 times, the ke values of Si, Fe, Cu, and Zn at the sample (No. 3) were 0.603, 0.702, 0.364, and 0.502, respectively. Correspondingly, the removal rate of impurities of Si, Fe, Cu, and Zn increased by 6.25%, 1%, 10.49%, and 27.58%, respectively. The effect on the ke of Cu and Fe is more significant at the sample (No. 3) when the melting zone speed is changed. The removal rates of Fe and Cu in the sample are 99.0% and 94.75% when the melting zone speed was 1/3 mm/min, and, correspondingly, the removal rates of Si and Zn were 81.7% and 88.51%, respectively. The Al content at sample position No. 3 is more than 999994.59 ppm when the sample was purified 15 times at a speed of 0.5 mm/min, which meets the standard of 5N high purity aluminum.

Experimental study on heat transfer process in boilers to predict thermal strain/stress distribution and deformation risk of membrane walls

As boilers are designed with higher parameters and larger capacity, deformation failure caused by thermal stress seriously threatens the safety of heating surfaces, especially membrane walls. In this paper, thermal strain/stress distribution on membrane walls, and its relationship with heat transfer process in the furnace were experimentally investigated in a laboratory-scaled arch-fired boiler. Tension strain and compression stress were detected on membrane walls, with definite directionality decided by wall structure. The measured high stress and high temperature zones coincided well with the location of deformation failure in the prototype boiler. Temperature on membrane walls links the heat transfer process and strain/stress distribution. A high level of wall temperature enhanced the directionality of strain/stress, while dispersive temperature gradient weakened such directionality. Additionally, significant correlations were found between wall temperature and corresponding thermal strain/stress. By defining constraint coefficients (β1, β2) and stress coefficients (ke, kτ), a model was proposed to quantitatively predict the strain/stress distribution on membrane walls. It provides a way to reduce the deformation risk of membrane walls via improving heat transfer process. Furtherly, the temperature-strain/stress correlations found in the arch-fired boiler were validated in another wall-fired boiler, thus provide great value in safety precaution to various boiler types.

Quantitative comparison of evaluation indices for asphalt–filler interaction ability within filler critical volume fraction

Asphalt–filler interaction plays a key role in the performances of asphalt mastic and asphalt mixture. However, the current studies ignore the filler critical volume fraction that has significant effects on asphalt–filler interaction ability. There is also lacking quantitative comparison of evaluation indices within filler critical volume fraction. In this study, two kinds of virgin asphalt binders and three kinds of mineral fillers were selected to fabricate asphalt mastics, and the dynamic shear rheological properties of virgin asphalt binders and asphalt mastics were measured, and the interaction evaluation indices complex viscosity coefficient Δη*, intrinsic viscosity [η], complex modulus coefficient ΔG*, K-B-G*, Einstein coefficient KE, L-A-δ and K-B-δ were quantitatively compared. The results indicate that complex viscosity coefficient Δη* and intrinsic viscosity [η] are not suitable for evaluation of asphalt–filler interaction ability. ΔG* and K-B-G* can evaluate the differences of asphalt and different fillers interaction ability based on the same kind of asphalt binder. Nevertheless, ΔG* and K-B-G* cannot differentiate the effects of asphalt binder on asphalt–filler interaction ability well. Although Einstein coefficient KE can evaluate asphalt–filler interaction ability, the Einstein coefficient KE is fitting results, and cannot distinguish the interaction ability under different filler volume fractions. L-A-δ and K-B-δ can differentiate the interaction ability of different asphalt binders and fillers well, and also the sensitivity factors of index K-B-δ are greater than L-A-δ. Therefore, K-B-δ is the most suitable for evaluating asphalt and filler interaction ability. Based on the evaluation index K-B-δ, asphalt–filler interaction ability increases initially and decreases afterwards with an increase in filler concentration within filler critical volume fraction.

Estimation of Knudsen diffusion coefficients from tracer experiments conducted with a binary gas system and a porous medium

A previous study has reported that Knudsen diffusion coefficients obtained by tracer experiments conducted with a binary gas system and a porous medium are consistently smaller than those obtained by permeability experiments conducted with a single-gas system and a porous medium. To date, however, that study is the only one in which tracer experiments have been conducted with a binary gas system. Therefore, to confirm this difference in Knudsen diffusion coefficients, we used a method we had developed previously to conduct tracer experiments with a binary carbon dioxide–nitrogen gas system and five porous media with permeability coefficients ranging from 10−13 to 10−11 m2. The results showed that the Knudsen diffusion coefficient of N2 (DN2) (cm2/s) was related to the effective permeability coefficient ke (m2) as DN2 = 7.39 × 107ke0.767. Thus, the Knudsen diffusion coefficients of N2 obtained by our tracer experiments were consistently 1/27 of those obtained by permeability experiments conducted with many porous media and air by other researchers. By using an inversion simulation to fit the advection–diffusion equation to the distribution of concentrations at observation points calculated by mathematically solving the equation, we confirmed that the method used to obtain the Knudsen diffusion coefficient in this study yielded accurate values. Moreover, because the Knudsen diffusion coefficient did not differ when columns with two different lengths, 900 and 1500 mm, were used, this column property did not influence the flow of gas in the column. The equation of the dusty gas model already includes obstruction factors for Knudsen diffusion and molecular diffusion, which relate to medium heterogeneity and tortuosity and depend only on the structure of the porous medium. Furthermore, there is no need to take account of any additional correction factor for molecular diffusion except the obstruction factor because molecular diffusion is only treated in a multicomponent gas system. Thus, molecular diffusion considers only the obstruction factor related to tortuosity. Therefore, we introduced a correction factor for a multicomponent gas system into the DGM equation, multiplying the Knudsen diffusion coefficient, which includes the obstruction factor related to tortuosity, by this correction factor. From the present experimental results, the value of this correction factor was 1/27, and it depended only on the structure of the gas system in the porous medium.

Predicting Secondary-Dendrite Arm Spacing of the Al-4.5wt%Cu Alloy During Unidirectional Solidification

Mechanical properties and performance of metallic materials depend on their microstructures. In order to develop engineering materials that match prescribed criteria and to enable design with multifunctional materials, it is essential to be able to predict their microstructural patterns, such as size, shape, and spacing of the dendritic structures observed in solidified metals. In the cases of metallic alloys, which present dendritic structure, the mechanical properties of foundry products depend mainly on the primary- and secondary-arm. Therefore, it is important, in a computational simulation of the solidification processes, to use reliable methods to correlate the thermal parameters with secondary-dendrite arm spacing. This study presents a numerical model for prediction of secondary-arm spacing as a function of thermal parameters (cooling rates and local solidification time). Spacing of the arms for a binary alloy is numerically predicted using a phase-field model. Secondary dendrites calculated by phase-field model, they are similar to the ones found in experiments investigation of solidification in Al-Cu alloys. Arm spacing predicted in the present work, when compared with the experimental results, showed good agreement. Its estimation takes place at the late stage of growth. The effect of physical properties (partition coefficient (ke), diffusion in the liquid (DL) and diffusion in the solid phase (DS)) on secondary-arm spacing is systematically investigated by phase-field model. With the help of numerical results for Al-4.5wt%Cu alloy, the applicability of the phase-field model to the estimation of secondary-dendrite arm spacing during unidirectional solidification is demonstrated.

Evaluation indices of asphalt–filler interaction ability and the filler critical volume fraction based on the complex modulus

The asphalt–filler interaction plays a significant role in the performances of asphalt mastics and mixtures, and the asphalt–filler interaction ability could be evaluated by the rheological properties. In this paper, two kinds of matrix asphalt binders and six kinds of fillers were selected to prepare asphalt mastic with different filler volume fractions, and the dynamic shear rheological properties of asphalt mastics were measured and analysed. The filler critical volume fraction which is the transition point from “diluted region” to “concentrated region” for asphalt mastic was defined and determined according to the variation of asphalt mastic’s complex modulus with filler volume fractions. In the “diluted region”, the asphalt–filler interaction plays a dominant role in the increasing of complex modulus. However, the interaction between filler particles plays a dominant role in the “concentrated region”. Then, the complex modulus coefficient ΔG*, the Einstein coefficient KE and the coefficient K−B−G* were applied to evaluate the asphalt–filler interaction ability in the range of the filler critical volume fraction. It indicated that the three evaluation indices had good consistency for characterising the asphalt–filler interaction ability, but the coefficient K−B−G* had the best sensitivity. So the coefficient K−B−G* can significantly distinguish the interaction ability between asphalt binder and different fillers.

A novel hybrid model combining continuum local nonequilibrium and discrete variables methods for solute trapping during rapid alloy solidification

A novel hybrid model, which combines the advantages of micro-scale discrete approach and continuum local nonequilibrium diffusion model (LNDM), has been developed to describe solute trapping and solute drag during rapid alloy solidification with non-sharp interface. The model treats the solid-liquid interface as a region with well-defined borders, which consists of n interatomic (discrete) layers. The continuum LNDM, which is presented in Acta Mater. 93 (2015) 256–263, as well as in earlier publications, describes local nonequilibrium solute diffusion in a much wider bulk liquid region. The solute partition coefficient and the solute drag energy are studied as functions of the interface velocity, the interface width and other parameters. The model predicts that the abrupt transition to partitionless and dragless solidification occurs independently of the interface width and the equilibrium partition coefficient KE at a finite interface velocity VD. The complete solute trapping velocity VD is a purely diffusion parameter, whereas the mid-transition velocity between KE and the complete solute trapping K = 1 depends on the interface width and KE.

A mathematical model for the transfer of soil solutes to runoff under water scouring

The transfer of nutrients from soil to runoff often causes unexpected pollution in water bodies. In this study, a mathematical model that relates to the detachment of soil particles by water flow and the degree of mixing between overland flow and soil nutrients was proposed. The model assumes that the mixing depth is an integral of average water flow depth, and it was evaluated by experiments with three water inflow rates to bare soil surfaces and to surfaces with eight treatments of different stone coverages. The model predicted outflow rates were compared with the experimentally observed data to test the accuracy of the infiltration parameters obtained by curve fitting the models to the data. Further analysis showed that the comprehensive mixing coefficient (ke) was linearly correlated with Reynolds' number Re (R2>0.9), and this relationship was verified by comparing the simulated potassium concentration and cumulative mass with observed data, respectively. The best performance with the bias error analysis (Nash Sutcliffe coefficient of efficiency (NS), relative error (RE) and the coefficient of determination (R2)) showed that the predicted data by the proposed model was in good agreement with the measured data. Thus the model can be used to guide soil-water and fertilization management to minimize nutrient runoff from cropland.

Dual crop coefficient of common bean in Tangará da Serra, Mato Grosso

ABSTRACT This study aimed to determine the dual crop coefficient of common bean ( Phaseolus vulgaris L.) for Tangará da Serra-MT, Brazil. The study used the FAO-56 dual kc method, dividing the kc into soil evaporation coefficient (ke), determined in microlysimeters, and basal crop coefficient (kcb), determined in weighing lysimeters. The study was conducted from July 10 (sowing) to October 6, 2014 (harvest), using the common bean cultivar 'BRS Estilo' and a sprinkler irrigation system with a coefficient of uniformity greater than 80%. The total rainfall and irrigation during the crop cycle (84 days) was 524.8 mm; the potential evapotranspiration (ETo) estimated for the period was 327.9 mm, whereas the crop evapotranspiration (ETc) accumulated during the cycle, determined in lysimeters, was equal to 477.5 mm. The kcb values determined for the initial, full development and final stages were 0.32, 1.10 and 0.81, respectively, while for ke, the respective values were 0.85, 0.40 and 0.53.

A mathematical model for distribution of calcium in silicon by vacuum directional solidification

Calcium is one of the main impurity elements in silicon. The removal of calcium strongly affects the quality of the polycrystalline silicon ingot produced by a vacuum directional solidification method. Based on the considerations of the theory of segregation, mass transfer and evaporation during vacuum directional solidification process, a mathematical model for calcium distribution in silicon was proposed and it can be used to explain the removal mechanism. In order to confirm the mathematical model, an industrial scale experiment on UMG-Si with an initial purity of 99.98 wt. % was performed. Since the reaction temperature strongly influences both the evaporation and segregation of calcium, the dependences of effective segregation coefficient (keff) and the evaporation coefficient (kE) on temperature were carefully investigated. The results showed that the proposed mathematical model was highly consistent with the experimental data and the calcium removal efficiency mainly relied on the evaporation step.

Defining the mutual coupling of capacitive power transfer for wireless power transfer

Capacitive power transfer (CPT) based on electric field coupling has been proposed recently as an alternative technology for wireless power transfer, and a good understanding of the capacitive coupling is of great importance in the design and evaluation of CPT systems. A new term named capacitive coupling coefficient kE is introduced to provide a quantitative measure of the coupling condition between the coupling plates. The term is derived by modelling the capacitive coupling plates based on electric charge balance, and its physical meaning is explained clearly in relation to the equivalent primary/secondary and mutual capacitances, which is also experimentally demonstrated by comparing two CPT systems with different cross-coupling configurations.

Study of kinetics in the biosorption of lead onto native and chemically treated olive stone

In this research, olive stone was used as precursor for the development of new biosorbents for lead ions. Chemical treatments were analyzed in terms of their effects on physical–chemical properties and kinetics of lead removal. A kinetic study of the biosorption of lead ions by olive stone was analyzed according to six different kinetic models (pseudo first, pseudo second, pseudo n-order, Elovich, solid diffusion and double exponential models). The biosorption kinetic data were successfully described with pseudo-nth order and double exponential models for all biosorbents. The double exponential model allowed estimating the values of external and internal mass transfer coefficients. The values of external mass transfer coefficient (ke) ranged from 42.62×10−6 to 508.3×10−6mmin−1 and the internal mass transfer coefficient (ki) from 3.76×10−6 to 73.4×10−6mmin−1. On the other hand, the analysis of experimental data showed that chemical treatments of the biomass led to increase biosorption capacity of the native biomass.

Influence of the film thickness on structural and optical properties of CdTe thin films electrodeposited on stainless steel substrates

CdTe thin films of different thicknesses were deposited by electrodeposition on stainless steel substrates (SS). The dependence of structural and optical properties on film thickness was evaluated for thicknesses in the range 0.17–1.5 μm. When the film is very thin the crystallites lack preferred orientation, however, thicker films showed preference for (111) plane. The results show that structural parameters such as crystallite size, lattice constant, dislocation density and strain show a noticeable dependence on film thickness, however, the variation is significant only when the film thickness is below 0.8 μm. The films were successfully transferred on to glass substrates for optical studies. Optical parameter such as absorption coefficient (α), band gap (Eg), refractive index (n), extinction coefficient (ke), real (ɛr) and imaginary (ɛi) parts of the dielectric constant were studied. The results indicate that all the optical parameters strongly depend on film thickness.