基于欧拉模型的泥沙冲刷数值模拟
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摘要
在使用欧拉模型进行泥沙定点冲刷的数值计算时,会产生不合理的床面波动和冲刷坑回填现象。为合理体现泥沙相在静止状态时的固体性质,并且反映水下泥沙堆积的特性,本文通过加载源项引入泥沙起动模型和水下休止角模型,修正了欧拉模型泥沙相的动量方程。数值计算结果分别和轴对称、平面泥沙冲刷实验比较,发现计算模型能较好获得轴对称冲刷的冲刷坑深度和宽度等形态参数;在连续冲刷的平面实验中,计算模型也能反应出泥沙相固态特征,准确捕捉不同时刻的冲刷坑内形态。数值计算得到的冲刷坑周围流体特征反映出水流不再使交界面的泥沙起动,克服了欧拉模型的不足。
In the numerical simulation of sediment scour using a Eulerian model,unreasonable wavy interface and scour hole backfill may be found. To reasonably simulate the solid and depositional properties of sediment in a static regime,and to reflect sediment accumulation characteristics underwater,the source term in the momentum equation of the sedimentation phase in a Eulerian model was modified. We added the source item to introduce the modeled incipient motion and the modeled underwater repose angle. The numerical calculation results were compared with the axisymmetric scouring and planar sediment scouring models. We found that,through this model configuration,we could obtain the parameters of the hole that is scouring asymmetrically,including depth and width. With our continuously scouring planar model,the solid property of sediment was represented correctly and the scour hole shapes at different moments were also well predicted. The flow characteristics around the scouring hole obtained in the simulation showed that sand around the boundary cannot be moved by flow,thereby overcoming the shortcomings of the Eulerian model.
In the numerical simulation of sediment scour using a Eulerian model,unreasonable wavy interface and scour hole backfill may be found. To reasonably simulate the solid and depositional properties of sediment in a static regime,and to reflect sediment accumulation characteristics underwater,the source term in the momentum equation of the sedimentation phase in a Eulerian model was modified. We added the source item to introduce the modeled incipient motion and the modeled underwater repose angle. The numerical calculation results were compared with the axisymmetric scouring and planar sediment scouring models. We found that,through this model configuration,we could obtain the parameters of the hole that is scouring asymmetrically,including depth and width. With our continuously scouring planar model,the solid property of sediment was represented correctly and the scour hole shapes at different moments were also well predicted. The flow characteristics around the scouring hole obtained in the simulation showed that sand around the boundary cannot be moved by flow,thereby overcoming the shortcomings of the Eulerian model.
引文
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[15]王喆,袁庆晴,马洪新,等.射流式挖沟机沟内流场数值计算与分析[J].哈尔滨工程大学学报,2015,36(3):292-296.WANG Zhe,YUAN Qingqing,MA Hongxin,et al. Numerical calculation and analysis of the flow field caused by a jetting trencher[J]. Journal of Harbin Engineering University,2015,36(3):292-296.
[16]钱宁,万兆惠.泥沙运动力学[M].北京:科学出版社,2003:247.
[2]ADERIBIGBE O O,RAJARATNAM N. Erosion of loose beds by submerged circular impinging vertical turbulent jets[J]. Journal of hydraulic research,1996,34(1):19-33.
[3]CHAKRAVARTI A,JAIN R K,KOTHYARI U C. Scour under submerged circular vertical jets in cohesionless sediments[J]. ISH journal of hydraulic engineering,2014,20(1):32-37.
[4]HOU Jiaoyi,ZHANG Lishan,GONG Yongjun,et al. Theoretical and experimental study of scour depth by submerged water jet[J]. Advances in mechanical engineering,2016,8(12):1-9.
[5]槐文信,王增武,钱忠东,等.二维垂向射流沙质河床冲刷的数值模拟[J].中国科学:技术科学,2012,42(1):72-81.HUAI Wenxin,WANG Zengwu,QIAN Zhongdong,et al.Numerical simulation of sandy bed erosion by 2D vertical jet[J]. Science China technological sciences, 2011,54(12):3265-3274.
[6]张芝永,拾兵.泥沙局部冲淤二维数值模拟仿真[J].哈尔滨工程大学,2013,34(2):145-150.ZHANG Zhiyong,SHI Bing. Two-dimensional numerical simulation on local mud&sand erosion and deposition[J].Journal of Harbin Engineering University,2013,34(2):145-150.
[7]钱忠东,胡晓清,槐文信,等.基于欧拉模型的淹没射流冲刷数值模拟[J].中国科学:技术科学,2011,41(4):419-425.QIAN Zhongdong,HU Xiaoqing,HUAI Wenxin,et al. Numerical simulation of sediment erosion by submerged jets using an Eulerian model[J]. Science China technological sciences,2010,53(12):3324–3330.
[8]VAN BANG D P,NGUYEN K D,ZAPATA M U,et al. A two-phase numerical model for the water injection dredging(WID)technology:an unified formulation for continuum mechanic[C]//11th International Conference on Hydroinformatics. New York,2014.
[9]NGUYEN C T,NGUYEN C T,BUI H H,et al. A new SPH-based approach to simulation of granular flows using viscous damping and stress regularisation[J]. Landslides,2017,14(1):69-81.
[10]KUANG S B,LAMARCHE C Q,CURTIS J S,et al. Discrete particle simulation of jet-induced cratering of a granular bed[J]. Powder technology,2013,239:319-336.
[11]CROSTA G B,DE BLASIO F V,DE CARO M,et al.Modes of propagation and deposition of granular flows onto an erodible substrate:experimental, analytical, and numerical study[J]. Landslides,2017,14(1):47-68.
[12]IONESCU I R,MANGENEY A,BOUCHUT F,et al. Viscoplastic modeling of granular column collapse with pressure-dependent rheology[J]. Journal of non-newtonian fluid mechanics,2015,219:1-18.
[13]MINATTI L,PARIS E. A SPH model for the simulation of free surface granular flows in a dense regime[J]. Applied mathematical modelling,2015,39(1):363-382.
[14]LAGRE P Y,STARON L,POPINET S. The granular column collapse as a continuum:validity of a two-dimensional Navier-Stokes model with aμ(I)-rheology[J].Journal of fluid mechanics,2011,686:378-408.
[15]王喆,袁庆晴,马洪新,等.射流式挖沟机沟内流场数值计算与分析[J].哈尔滨工程大学学报,2015,36(3):292-296.WANG Zhe,YUAN Qingqing,MA Hongxin,et al. Numerical calculation and analysis of the flow field caused by a jetting trencher[J]. Journal of Harbin Engineering University,2015,36(3):292-296.
[16]钱宁,万兆惠.泥沙运动力学[M].北京:科学出版社,2003:247.