基于尾流振子模型涡激振动数值模拟的加权显隐交替计算数值方法  

Weighted explicit-implicit alternating method for numerical simulation of vortex-induced vibration based on wake oscillator model

作　　者：马宁[1,2] 王宴滨[3] 贾光燕 崔振轩 刘耀斌 MA Ning;WANG Yanbin;JIA Guangyan;CUI Zhenxuan;LIU Yaobin(School of Science,China University of Petroleum(Beijing),Beijing 102249,China;State Key Laboratory of Petroleum Resources and Engineering,China University of Petroleum(Beijing),Beijing 102249,China;College of Petroleum Engineering,China University of Petroleum(Beijing),Beijing 102249,China)

机构地区：[1]中国石油大学(北京)理学院,北京102249 [2]中国石油大学(北京)油气资源与工程全国重点实验室,北京102249 [3]中国石油大学(北京)石油工程学院,北京102249

出　　处：《中国石油大学学报(自然科学版)》2025年第2期159-166,共8页Journal of China University of Petroleum(Edition of Natural Science)

基　　金：国家自然科学基金优秀青年基金项目(52322110);北京市科技新星计划项目(20230484341);中国石油大学(北京)油气资源与工程全国重点实验室课题(PRE/DX-2404)。

摘　　要：采用尾流振子模型对柔性圆柱体建立振动控制耦合方程,以实现立管涡激振动(VIV)行为的准确预测和分析。鉴于方程的非线性、耦合性以及偏微分特征,提出一种新算法,即加权显隐交替计算数值方法,并对4种不同长径比的立管进行数值模拟。结果表明:该方法在提升计算效率的同时,也增强数值稳定性;不同的空间和时间步长对差分格式稳定性以及计算速度存在影响,应灵活地调整这些参数以获得最佳的模拟效果;不同加权系数组合的数值解的精度对加权系数的选择并不敏感,选择计算简单且稳定性好的加权系数即可;深海立管的振动行为呈现出明显的方向性特征,这一行为是由行波和驻波的共同作用所引导;行波主要对立管的中部区域产生影响,而驻波则主要作用于立管的两端;随着立管长径比的增加,行波的影响逐渐向立管中上部分迁移,并且它控制的区间长度也随之增大,同时驻波对立管下端的影响变得越发显著,参与涡激振动的模态数量也相应增加。Using the wake oscillator model,a vibration control coupling equation was established for the flexible cylinder to achieve accurate prediction and analysis of the vortex-induced vibration(VIV)behavior of the riser.Due to the nonlinearity,coupling,and partial differential nature of the equations,a new numerical method-weighted explicit-implicit alternating method was proposed.Then this method was applied to perform numerical simulations of risers with four different aspect ratios.The results show that the method can enhance numerical stability while improve computational efficiency.By analyzing various combinations of spatial step and time step sizes,it is found that they have an impact on the stability of difference schemes as well as computational speed.These parameters should be adjusted flexibly to achieve the best simulation results.Analysis of different weighting coefficient combinations shows that the precision of the numerical solution is not sensitive to the choice of weighting coefficients.Then,computationally efficient and stability-optimized coefficients are selected.The vibration behavior of deep-sea risers exhibits significant directional characteristics,which are guided by the combined effects of traveling waves and standing waves.Traveling waves primarily affect the central region of the riser,while standing waves predominantly influence the two ends of the riser.As the aspect ratio of the riser increases,the influence of traveling waves gradually shifts towards the upper-middle section,and the length of the affected region also increases.Meanwhile,the influence of standing waves at the lower end of the riser becomes more pronounced,and the number of modes participating in vortex-induced vibration also increases.

关 键 词：加权显隐交替计算 非线性耦合偏微分方程 涡激振动 数值模拟 

分 类 号：O241.82[理学—计算数学]