水泥3D打印喷头中浆体的流动分析
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摘要
针对水泥浆体在流经水泥3D打印样机喷头结构时沾黏、流动性差的问题,提出一种基于多松弛参数格子玻尔兹曼方法(MRT-LBM)的模型,研究幂律流体在单螺杆机构中的流动特性.采用MRT-LBM修正模型,对水泥浆体在喷头中的流动情况进行数值模拟,得到水泥浆体在喷头装置内不同位置处的速度分布情况,为水泥3D打印喷头结构提出改进方案.通过已有理论解的泊肃叶流对修正后的MRT-LBM模型进行详细论述,并将解析解与MRT-LBM修正模型得到的结果进行对比,验证分段幂律模型的可行性.最后,改变晶格节点的数量(10～500),计算实验结果与理论结果的相对误差,结果表明修正后的MRT-LBM模型是稳定的.
A model based on multiple-relaxation time lattice Boltzmann method(MRT-LBM) was proposed to study the flow characteristics of power-law fluid in single screw mechanism, aiming at the problem of poor adhesion and fluidity of cement slurry when flowing through the nozzle structure of cement 3 D printing prototype. The cement paste flow in the printing nozzle was numerically simulated by the modified MRT-LBM model; the cement paste velocity distribution in different positions was obtained, which can help optimize the nozzle structure. the modified MRT-LBM model was discussed in detail by Poiseuille flow with theoretical solution, and the analytical solution was compared with the results obtained by the modified MRT-LBM model to verify the correctness of the truncated power-law model. Finally, the relative error between the experimental results and theoretical results was calculated when the number of lattice nodes changes from 10 to 50, which indicates that the modified MRT-LBM model is stable.
A model based on multiple-relaxation time lattice Boltzmann method(MRT-LBM) was proposed to study the flow characteristics of power-law fluid in single screw mechanism, aiming at the problem of poor adhesion and fluidity of cement slurry when flowing through the nozzle structure of cement 3 D printing prototype. The cement paste flow in the printing nozzle was numerically simulated by the modified MRT-LBM model; the cement paste velocity distribution in different positions was obtained, which can help optimize the nozzle structure. the modified MRT-LBM model was discussed in detail by Poiseuille flow with theoretical solution, and the analytical solution was compared with the results obtained by the modified MRT-LBM model to verify the correctness of the truncated power-law model. Finally, the relative error between the experimental results and theoretical results was calculated when the number of lattice nodes changes from 10 to 50, which indicates that the modified MRT-LBM model is stable.
引文
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[2]覃亚伟,骆汉宾,车海潮,徐捷.基于挤出固化的建筑3D打印装置设计及验证[J].土木工程与管理学报,2016,33(1):54-60.TAN Ya-wei,LUO Han-bin,CHE Hai-chao,et al.Design and verification of 3D printing device based on extrusion solidification[J].Civil engineering and management,2016,33(1):54-60.
[3]CHEN H,CHEN S,MATTHAEUS W H.Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method[J].Physical Review A,1992,45(8):R5339.
[4]QIAN Y H,D'HUMIèRES D,LALLEMAND P.Lattice BGK models for Navier-Stokes equation[J].EPL(Europhysics Letters),1992,17(6):479-484.
[5]AHARONOV E,ROTHMAN D H.Non-Newtonian flow(through porous media):A lattice-Boltzmann method[J].Geophysical Research Letters,2013,20(8):679-682.
[6]BOEK E S,CHIN J,COVENEY P V.Lattice Boltzmann simulation of the flow of non-Newtonian fluids in porous media[J].International Journal of Modern Physics B,2003,17(1/2):99-102.
[7]MALASPINAS O,COURBEBAISSE G,DEVILLEM O.Simulation of a generalized Newtonian fluid by the lattice Boltzmann method[J].International Journal of Modern Physics C,2009,18(12):1939-1949.
[8]D'HUMIèRES D.Multiple-relaxation-time lattice Boltzmann models in three dimensions[J].Philosophical Transactions,2002,360(1792):437.
[9]CHAI Z H,SHI B C,GUO Z L,et al.Multiplerelaxation-time lattice Boltzmann model for generalized Newtonian fluid flows[J].Journal of Non-Newtonian Fluid Mechanics,2011,166(5):332-342.
[10]FALLAH K,KHAYAT M,BORGHEI M H,et al.Multiple-relaxation-time lattice Boltzmann simulation of non-Newtonian flows past a rotating circular cylinder[J].Journal of Non-Newtonian Fluid Mechanics,2012,177:1-14.
[11]蔺喜强,张涛,霍亮,等.水泥基建筑3D打印材料的制备及应用研究[J].混凝土,2016(6):141-144.LIN Xin-qaing,ZHANG Tao,HUO Liang,et al.Study on the preparation and application of 3Dprinted materials for cement building[J].Concrete,2016(6):141-144.
[12]乔星宇,李韵通,潘宁.3D打印建筑混凝土配合比设计研究[J].现代装饰理论,2016(6):240-241.QIAO Xin-yu,LI Yun-tong,PAN Ning.Research on design of concrete mix proportion of 3D printed building[J].Modern decoration theory,2016(6):240-241.
[13]BANNISTER C E.Rheological evaluation of cement slurries:methods and models[C]//SPE Annual Technical Conference and Exhibition.[S.l.]:Society of Petroleum Engineers,1980:59-66.
[14]阮文军.注浆扩散与浆液若干基本性能研究[J].岩土工程学报,2005(1):69-73.RUAN Wen-jun.Study on the basic properties of grouting diffusion and slurry[J].Journal of Geotechnical Engineering,2005(1):69-73.
[15]LALLEMAND P,LUO L S.Theory of the lattice boltzmann method:dispersion,dissipation,isotropy,galilean invariance,and stability[J].Physical Review E Statistical Physics Plasmas Fluids and Related Interdisciplinary Topics,2000,61(6 Pt A):6546-6562.
[16]BOYD J,BUICK J,GREEN S.A second-order accurate lattice Boltzmann non-Newtonian flow model[J].Journal of Physics A General Physics,2006,3950(46):14241-14247.
[17]BUICK J M,COSGROVE J A.Numerical simulation of the flow field in the mixing section of a screw extruder by the lattice Boltzmann model[J].Chemical Engineering Science,2006,61(10):3323-3326.
[18]GIRIMAJI S.Lattice Boltzmann method:fundamentals and engineering applications with computer codes[J].AIAA Journal,2013,51(4):398-404.
[19]NIU X D,SHU C,CHEW Y T,et al.Investigation of stability and hydrodynamics of different lattice Boltzmann models[J].Journal of Statistical Physics,2004,117(3/4):665-680.
[20]BEHREND O,HARRIS R,WARREN P B.Hydrodynamic behavior of lattice Boltzmann and lattice Bhatnagar-Gross-Krook models[J].Physical Review E,1994,50(6):4586.