Based on the stability analysis with no linearization and expansion, it is argued that instability in the lattice BGK model is originated from the linear relaxation hypothesis of collision in the model. The hypothesis...Based on the stability analysis with no linearization and expansion, it is argued that instability in the lattice BGK model is originated from the linear relaxation hypothesis of collision in the model. The hypothesis stands up only when the deviation from the local equilibrium is weak. In this case the computation is absolutely stable for real fluids. But for flows of high Reynolds number, this hypothesis is violated and then instability takes place physically. By performing a transformation a quantified stability criteria is put forward without those approximation. From the criteria a sufficient condition for stability can be obtained and serve as an estimation of the limited Reynolds number as high as possible.展开更多
In the present study, the influence of natural convection on the lamellar eutectic growth is determined by a phase-field-lattice Boltzmann study for Al-Cu eutectic alloy. The mass difference resulting from concentrati...In the present study, the influence of natural convection on the lamellar eutectic growth is determined by a phase-field-lattice Boltzmann study for Al-Cu eutectic alloy. The mass difference resulting from concentration difference led to the fluid flow, and a robust parallel and adaptive mesh refinement algorithm was employed to improve the computational efficiency without any compromising accuracy. Results show that the existence of natural convection would affect the growth undercooling and thus control the interface shape by adjusting the lamellar width. In particular, by alternating the magnitude of the solute expansion coefficient, the strength of the natural convection is changed. Corresponding microstructure patterns are discussed and compared with those under no-convection conditions.展开更多
The problem of the mixed convection in a cubic cavity is studied with lattice Boltzmann method. A multiple-relaxation-time lattice Boltzmann model for incompressible flow in the cubic cavity and another thermal lattic...The problem of the mixed convection in a cubic cavity is studied with lattice Boltzmann method. A multiple-relaxation-time lattice Boltzmann model for incompressible flow in the cubic cavity and another thermal lattice Boltzmann model for solving energy/temperature equation are proposed. The present models are first validated through a comparison with some available results, and then, we present a detailed parameter study on the mixed convection in the cubic cavity. The numerical results show that the flow and the Reynolds and Richardson numbers. temperature patterns change greatly with variations of展开更多
Natural convection in a square cavity at high Rayleigh numbers is simulated by multiple relaxation time(MRT)lattice Boltzmann method(LBM)with a separate distribution function to solve the temperature.The Rayleigh numb...Natural convection in a square cavity at high Rayleigh numbers is simulated by multiple relaxation time(MRT)lattice Boltzmann method(LBM)with a separate distribution function to solve the temperature.The Rayleigh numbers examined here range from Ra=103 to Ra=10^(8).For Rayleigh numbers below 10^(8),the flow remains stationary and transition occurs beyond Ra=2×10^(8).Unsteady results at higher Rayleigh numbers(Ra=10^(9) and Ra=10^(10))are also investigated.To the best of our knowledge,this is the first accurate study which involves the high Rayleigh numbers Ra=10^(9),10^(10).展开更多
The thermosolutal convection can alter segregation pattern,change dendrite morphology and even cause freckles formation in alloy solidification.In this work,the multiphase-field model was coupled with lattice Boltzman...The thermosolutal convection can alter segregation pattern,change dendrite morphology and even cause freckles formation in alloy solidification.In this work,the multiphase-field model was coupled with lattice Boltzmann method to simulate the dendrite growth under melt convection in superalloy solidification.In the isothermal solidification simulations,zero and normal gravitational accelerations were applied to investigate the effects of gravity on the dendrite morphology and the magnitude of melt flow.The solute distribution of each alloy component along with the dendrite tip velocity during solidification was obtained,and the natural convection has been confirmed to affect the microsegregation pattern and the dendrite growth velocity.In the directional solidification simulations,two typical temperature gradients were applied,and the dendrite morphology and fluid velocity in the mushy zone during solidification were analyzed.It is found that the freckles will form when the average fluid velocity in the mushy zone exceeds the withdraw velocity.展开更多
A Coupled Lattice Bhatnagar Gross Krook （CLBGK） model was proposed with a robust boundary scheme to model the Bossinesq incompressible flows. The LBGK method is a powerful approach, but is also computationally deman...A Coupled Lattice Bhatnagar Gross Krook （CLBGK） model was proposed with a robust boundary scheme to model the Bossinesq incompressible flows. The LBGK method is a powerful approach, but is also computationally demanding. Therefore, parallel computing was implemented, and the codes were run on the parallel computer “Lenovo DeepComp 1800” with 24 nodes written in C＋＋ using the Message Passing Interface （MPI） library. Numerical results for natural convection in a cavity with the Rayleigh number （ Ra ） ranging from 10^6 to 4× 10^10 were presented, and found to agree well with the previous work. And with the increase of the resolution rate, the accuracy has been greatly improved. In addition, new models were set up by applying different equilibriums to the CLBGK model to simulate the same problem, which all yield sound results.展开更多
A two-dimensional coupled model of the cellular automaton(CA)and the lattice Boltzmann method(LBM)was developed to simulate the solute dendrite growth of Fe-C-Mn-S alloy in the presence of forced convection.The model ...A two-dimensional coupled model of the cellular automaton(CA)and the lattice Boltzmann method(LBM)was developed to simulate the solute dendrite growth of Fe-C-Mn-S alloy in the presence of forced convection.The model describes the transport phenomenon by the evolution of moving pseudo-particles distribution functions and utilizes the LBM to solve fluid flow and solute transport under forced convection numerically.Based on the solute field calculated by the CA technique,the dynamics of dendrite growth were determined by the previously proposed local solute balance method.The accuracy of the forced convection dendrite growth model was verified by comparing the CA-LBM model with Lipton-Glicksman-Kurz analytical model.It is revealed that the dendrite symmetry structure is destroyed compared to free diffusion,and the upstream arm is more developed than the downstream arm of the dendrite.The enriched solute segregates more at the downstream side than at the upstream side of the dendrite.The length of the upstream dendrite arm increases firstly and then becomes stable with the increase in the flow velocity,the dendrite necking is restrained,and the vertical dendrite arm becomes longer.展开更多
文摘Based on the stability analysis with no linearization and expansion, it is argued that instability in the lattice BGK model is originated from the linear relaxation hypothesis of collision in the model. The hypothesis stands up only when the deviation from the local equilibrium is weak. In this case the computation is absolutely stable for real fluids. But for flows of high Reynolds number, this hypothesis is violated and then instability takes place physically. By performing a transformation a quantified stability criteria is put forward without those approximation. From the criteria a sufficient condition for stability can be obtained and serve as an estimation of the limited Reynolds number as high as possible.
基金supported by the National Natural Science Foundation of China[grant number U1537202]the TsinghuaGeneral Motor International collaboration project[grant number 20153000354]+1 种基金the UK Royal Society through the Newton International Fellowship Schemethe National Laboratory for Information Science and Technology in Tsinghua University for access to supercomputing facilities
文摘In the present study, the influence of natural convection on the lamellar eutectic growth is determined by a phase-field-lattice Boltzmann study for Al-Cu eutectic alloy. The mass difference resulting from concentration difference led to the fluid flow, and a robust parallel and adaptive mesh refinement algorithm was employed to improve the computational efficiency without any compromising accuracy. Results show that the existence of natural convection would affect the growth undercooling and thus control the interface shape by adjusting the lamellar width. In particular, by alternating the magnitude of the solute expansion coefficient, the strength of the natural convection is changed. Corresponding microstructure patterns are discussed and compared with those under no-convection conditions.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 60773195 and 51006040
文摘The problem of the mixed convection in a cubic cavity is studied with lattice Boltzmann method. A multiple-relaxation-time lattice Boltzmann model for incompressible flow in the cubic cavity and another thermal lattice Boltzmann model for solving energy/temperature equation are proposed. The present models are first validated through a comparison with some available results, and then, we present a detailed parameter study on the mixed convection in the cubic cavity. The numerical results show that the flow and the Reynolds and Richardson numbers. temperature patterns change greatly with variations of
文摘Natural convection in a square cavity at high Rayleigh numbers is simulated by multiple relaxation time(MRT)lattice Boltzmann method(LBM)with a separate distribution function to solve the temperature.The Rayleigh numbers examined here range from Ra=103 to Ra=10^(8).For Rayleigh numbers below 10^(8),the flow remains stationary and transition occurs beyond Ra=2×10^(8).Unsteady results at higher Rayleigh numbers(Ra=10^(9) and Ra=10^(10))are also investigated.To the best of our knowledge,this is the first accurate study which involves the high Rayleigh numbers Ra=10^(9),10^(10).
基金financially supported by the National Key Research and Development Program of China(No.2017YFB0701503)the National Science and Technology Major Project(No.2017ZX04014001)the National Natural Science Foundation of China(No.51374137).
文摘The thermosolutal convection can alter segregation pattern,change dendrite morphology and even cause freckles formation in alloy solidification.In this work,the multiphase-field model was coupled with lattice Boltzmann method to simulate the dendrite growth under melt convection in superalloy solidification.In the isothermal solidification simulations,zero and normal gravitational accelerations were applied to investigate the effects of gravity on the dendrite morphology and the magnitude of melt flow.The solute distribution of each alloy component along with the dendrite tip velocity during solidification was obtained,and the natural convection has been confirmed to affect the microsegregation pattern and the dendrite growth velocity.In the directional solidification simulations,two typical temperature gradients were applied,and the dendrite morphology and fluid velocity in the mushy zone during solidification were analyzed.It is found that the freckles will form when the average fluid velocity in the mushy zone exceeds the withdraw velocity.
文摘A Coupled Lattice Bhatnagar Gross Krook （CLBGK） model was proposed with a robust boundary scheme to model the Bossinesq incompressible flows. The LBGK method is a powerful approach, but is also computationally demanding. Therefore, parallel computing was implemented, and the codes were run on the parallel computer “Lenovo DeepComp 1800” with 24 nodes written in C＋＋ using the Message Passing Interface （MPI） library. Numerical results for natural convection in a cavity with the Rayleigh number （ Ra ） ranging from 10^6 to 4× 10^10 were presented, and found to agree well with the previous work. And with the increase of the resolution rate, the accuracy has been greatly improved. In addition, new models were set up by applying different equilibriums to the CLBGK model to simulate the same problem, which all yield sound results.
基金funded by the National Natural Science Foundation of China(Grant Nos.52074071 and U1660204)Fundamental Research Funds for the Central Universities of China(Grant No.N172502006)Liaoning Revitalization Talents Program(Grant No.XLYC1802032).
文摘A two-dimensional coupled model of the cellular automaton(CA)and the lattice Boltzmann method(LBM)was developed to simulate the solute dendrite growth of Fe-C-Mn-S alloy in the presence of forced convection.The model describes the transport phenomenon by the evolution of moving pseudo-particles distribution functions and utilizes the LBM to solve fluid flow and solute transport under forced convection numerically.Based on the solute field calculated by the CA technique,the dynamics of dendrite growth were determined by the previously proposed local solute balance method.The accuracy of the forced convection dendrite growth model was verified by comparing the CA-LBM model with Lipton-Glicksman-Kurz analytical model.It is revealed that the dendrite symmetry structure is destroyed compared to free diffusion,and the upstream arm is more developed than the downstream arm of the dendrite.The enriched solute segregates more at the downstream side than at the upstream side of the dendrite.The length of the upstream dendrite arm increases firstly and then becomes stable with the increase in the flow velocity,the dendrite necking is restrained,and the vertical dendrite arm becomes longer.
