This article is concerned with the numerical investigation of one-dimensional population balance models for batch crystallization process with fines dissolution.In batch crystallization,dissolution of smaller unwanted...This article is concerned with the numerical investigation of one-dimensional population balance models for batch crystallization process with fines dissolution.In batch crystallization,dissolution of smaller unwanted nuclei below some critical size is of vital importance as it improves the quality of product.The crystal growth rates for both size-independent and size-dependent cases are considered.A delay in recycle pipe is also included in the model.The space–time conservation element and solution element method,originally derived for non-reacting flows,is used to solve the model.This scheme has already been applied to a range of PDEs,mainly in the area of fluid mechanics.The numerical results are compared with those obtained from the Koren scheme,showing that the proposed scheme is more efficient.展开更多
The objective of the work is focused on predictions of microsegregation,solidification speed,dendritic arm spacings and dendrite morphology by phase-field model.The numerical results were compared with experimental da...The objective of the work is focused on predictions of microsegregation,solidification speed,dendritic arm spacings and dendrite morphology by phase-field model.The numerical results were compared with experimental data.The experimental values for cooling rates and effective partition coefficient were adopted during calculations.The results of microsegregation through phase-field model show excellent agreement with the experimental data.Such excellent agreement is because cooling rates,effective partition coefficient and back-diffusion of solute are considered in the model.For solidification speed,the calculation results show good agreement with the experimental data.Tertiary dendritic arm spacing calculated with phase-field model is compared with experimental data.The results show good agreement between them.The dendrite arm spacing varies with position because high cooling rates are responsible for the refinement effect on microstructure.Finally,two-dimensional simulation produced a dendrite that is similar to that found in the experiment.展开更多
Let V be a hyperbolic 5-dimensional indefinite space. W is the infinite Weyl group of an irreducible root system. The principal aim of this paper is to classify all crystallgraphic groups associated with W up to conju...Let V be a hyperbolic 5-dimensional indefinite space. W is the infinite Weyl group of an irreducible root system. The principal aim of this paper is to classify all crystallgraphic groups associated with W up to conjugation in the affine group A(V).展开更多
Sn-36%Ni peritectie alloys were directionally solidified at different growth rates under a constant temperature gradient （20 K/mm）, the dependences of microstructural characteristic length scales on the growth rate ...Sn-36%Ni peritectie alloys were directionally solidified at different growth rates under a constant temperature gradient （20 K/mm）, the dependences of microstructural characteristic length scales on the growth rate were investigated. Experimental results are presented, including primary and higher order dendrite arm spacings 21, 22, 23 and dendrite tip radius R of primary NisSn2 phase. Comparisons between the theoretical predictions and the experimental results show that, for the primary dendrites, 21=335.882v-0.21, which is in agreement with the Kurz-Fisher model; for the secondary dendrites, λ2=44.957v-0.277, which is consistent with the Bouchard-Kirkaldy model; for the tertiary dendrites, λ3=40.512v-0.274; for the dendrite tip radius, R=22.7v-0.36. The experimental results also show that the 21/22 changes greatly with increasing growth rate while the 21/23 has no significant change, indicating that tertiary dendrite arms have a more similar growth characteristics to primary dendrites compared with secondary dendrites. The λ1/R ranges from 2 to 2.3 with the increase of growth rate. Key words： Sn-Ni alloy; directional solidification; dendrite arm spacing; dendrite tip radius展开更多
A combined numerical model of thermal field and the primary dendrite arm spacing （PDAS） was proposed to correlate the process parameters and PDAS in laser welding of Cu and A1. The solidification parameters simulate...A combined numerical model of thermal field and the primary dendrite arm spacing （PDAS） was proposed to correlate the process parameters and PDAS in laser welding of Cu and A1. The solidification parameters simulated by the finite volume method with commercial software ANASYS FLUENT were applied in the PDAS model to predict the dendrite arm spacing of fusion zone. Dendrite was also examined by the metallographic method to validate the model. Results indicate that the calculated PDAS agrees with metallographic measurements reasonably, especially the Hunt model. PDAS increases apparently with increasing laser power while decreases slightly with increasing welding speed. Increasing laser power increases the secondary dendrite and increasing welding speed increases the microporosity in dendrite.展开更多
The results of struvite reaction crystallization from diluted water solutions of phosphates （V） （0.20 mass% of PO43-） by means of magnesium and ammonium ions are presented. Continuous FB MSZ crystallizer with jet ...The results of struvite reaction crystallization from diluted water solutions of phosphates （V） （0.20 mass% of PO43-） by means of magnesium and ammonium ions are presented. Continuous FB MSZ crystallizer with jet pump driven by compressed air was used. Influence of pH and mean residence time of suspension on the crystal product quality was determined. Increase in pH from 9 to 11 resulted that mean crystal size decreased nearly two-time： from 27.1 to 15.1μm for mean residence time of suspension 900 s. Elongation of this time from 900 to 3,600 s influenced struvite crystal size advantageously-it increased from 27.1 to 41.2 μm at pH 9. From the population density distributions nucleation and growth rates of struvite were calculated based on the simplest SIG model of mass crystallization kinetics in MSMPR crystallizer. Linear growth rate ofstruvite crystals decreased nearly two-time with the increase in environment pH from 9 to 11, and more than 2.5-time with the elongation of mean residence time of crystal suspension in a crystallizer from 900 to 3,600 s from 1.34× 10-8 m/s （pH 9, τ= 900 s） to 2.60×10-9 m/s （pH 11, τ= 3,600 s）.展开更多
We present an analytical analysis of the spatial resolution of quantum ghost imaging implemented by entangled photons from a general, spontaneously parametric, down-conversion process. We find that the resolution is a...We present an analytical analysis of the spatial resolution of quantum ghost imaging implemented by entangled photons from a general, spontaneously parametric, down-conversion process. We find that the resolution is affected by both the pump beam waist and the nonlinear crystal length. Hence, we determined a method to improve the resolution for a certain imaging setup. It should be noted that the resolution is not uniquely related to the degree of entanglement of the photon pair since the resolution can be optimized for a certain degree of entanglement. For certain types of Einstein-Podolsky-Rosen(EPR) states——namely the momentum-correlated or momentum-positively correlated states——the resolution exhibits a simpler relationship with the pump beam waist and crystal length. Further, a vivid numerical simulation of ghost imaging is presented for different types of EPR states,which supports our analysis. This work discusses applicable references to the applications of quantum ghost imaging.展开更多
文摘This article is concerned with the numerical investigation of one-dimensional population balance models for batch crystallization process with fines dissolution.In batch crystallization,dissolution of smaller unwanted nuclei below some critical size is of vital importance as it improves the quality of product.The crystal growth rates for both size-independent and size-dependent cases are considered.A delay in recycle pipe is also included in the model.The space–time conservation element and solution element method,originally derived for non-reacting flows,is used to solve the model.This scheme has already been applied to a range of PDEs,mainly in the area of fluid mechanics.The numerical results are compared with those obtained from the Koren scheme,showing that the proposed scheme is more efficient.
基金FAPERJ(Fundacao de Amparo a Pesquisa do Estado do Rio de Janeiro,APQ#1:E-26/010.001942/2019)CNPq(Conselho Nacional de Desenvolvimento Cientifico e Tecnologico)for their financial support。
文摘The objective of the work is focused on predictions of microsegregation,solidification speed,dendritic arm spacings and dendrite morphology by phase-field model.The numerical results were compared with experimental data.The experimental values for cooling rates and effective partition coefficient were adopted during calculations.The results of microsegregation through phase-field model show excellent agreement with the experimental data.Such excellent agreement is because cooling rates,effective partition coefficient and back-diffusion of solute are considered in the model.For solidification speed,the calculation results show good agreement with the experimental data.Tertiary dendritic arm spacing calculated with phase-field model is compared with experimental data.The results show good agreement between them.The dendrite arm spacing varies with position because high cooling rates are responsible for the refinement effect on microstructure.Finally,two-dimensional simulation produced a dendrite that is similar to that found in the experiment.
文摘Let V be a hyperbolic 5-dimensional indefinite space. W is the infinite Weyl group of an irreducible root system. The principal aim of this paper is to classify all crystallgraphic groups associated with W up to conjugation in the affine group A(V).
基金Projects （51071062, 51271068, 51274077） supported by the National Natural Science Foundation of China Project （2011 -P03） supported by Open Fund of State Key Laboratory of Mold and Die Technology of Huazhong University of Science and Technology, China+1 种基金 Project （HIT. NSRIF. 2013002） supported by the Fundamental Research Funds for the Central Universities, China Project （2011CB610406） supported by the National Basic Research Program of China
文摘Sn-36%Ni peritectie alloys were directionally solidified at different growth rates under a constant temperature gradient （20 K/mm）, the dependences of microstructural characteristic length scales on the growth rate were investigated. Experimental results are presented, including primary and higher order dendrite arm spacings 21, 22, 23 and dendrite tip radius R of primary NisSn2 phase. Comparisons between the theoretical predictions and the experimental results show that, for the primary dendrites, 21=335.882v-0.21, which is in agreement with the Kurz-Fisher model; for the secondary dendrites, λ2=44.957v-0.277, which is consistent with the Bouchard-Kirkaldy model; for the tertiary dendrites, λ3=40.512v-0.274; for the dendrite tip radius, R=22.7v-0.36. The experimental results also show that the 21/22 changes greatly with increasing growth rate while the 21/23 has no significant change, indicating that tertiary dendrite arms have a more similar growth characteristics to primary dendrites compared with secondary dendrites. The λ1/R ranges from 2 to 2.3 with the increase of growth rate. Key words： Sn-Ni alloy; directional solidification; dendrite arm spacing; dendrite tip radius
基金Supported by the National Natural Science Foundation of China(No.50975195)
文摘A combined numerical model of thermal field and the primary dendrite arm spacing （PDAS） was proposed to correlate the process parameters and PDAS in laser welding of Cu and A1. The solidification parameters simulated by the finite volume method with commercial software ANASYS FLUENT were applied in the PDAS model to predict the dendrite arm spacing of fusion zone. Dendrite was also examined by the metallographic method to validate the model. Results indicate that the calculated PDAS agrees with metallographic measurements reasonably, especially the Hunt model. PDAS increases apparently with increasing laser power while decreases slightly with increasing welding speed. Increasing laser power increases the secondary dendrite and increasing welding speed increases the microporosity in dendrite.
文摘The results of struvite reaction crystallization from diluted water solutions of phosphates （V） （0.20 mass% of PO43-） by means of magnesium and ammonium ions are presented. Continuous FB MSZ crystallizer with jet pump driven by compressed air was used. Influence of pH and mean residence time of suspension on the crystal product quality was determined. Increase in pH from 9 to 11 resulted that mean crystal size decreased nearly two-time： from 27.1 to 15.1μm for mean residence time of suspension 900 s. Elongation of this time from 900 to 3,600 s influenced struvite crystal size advantageously-it increased from 27.1 to 41.2 μm at pH 9. From the population density distributions nucleation and growth rates of struvite were calculated based on the simplest SIG model of mass crystallization kinetics in MSMPR crystallizer. Linear growth rate ofstruvite crystals decreased nearly two-time with the increase in environment pH from 9 to 11, and more than 2.5-time with the elongation of mean residence time of crystal suspension in a crystallizer from 900 to 3,600 s from 1.34× 10-8 m/s （pH 9, τ= 900 s） to 2.60×10-9 m/s （pH 11, τ= 3,600 s）.
基金supported by the National Natural Science Foundation of China(Grant Nos.11174121,11321063,91121001,and 91321312)the National Program on Key Basic Research Project(Grant No.2012CB921802)
文摘We present an analytical analysis of the spatial resolution of quantum ghost imaging implemented by entangled photons from a general, spontaneously parametric, down-conversion process. We find that the resolution is affected by both the pump beam waist and the nonlinear crystal length. Hence, we determined a method to improve the resolution for a certain imaging setup. It should be noted that the resolution is not uniquely related to the degree of entanglement of the photon pair since the resolution can be optimized for a certain degree of entanglement. For certain types of Einstein-Podolsky-Rosen(EPR) states——namely the momentum-correlated or momentum-positively correlated states——the resolution exhibits a simpler relationship with the pump beam waist and crystal length. Further, a vivid numerical simulation of ghost imaging is presented for different types of EPR states,which supports our analysis. This work discusses applicable references to the applications of quantum ghost imaging.
