| 应用变分法计算三角形截面毛管中的流动 |
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| 引用本文： | 杨二龙,李东亮,高玉鑫,李欢,贾聚全.应用变分法计算三角形截面毛管中的流动[J].数学的实践与认识,2014(18). |
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| 作者姓名： | 杨二龙 李东亮 高玉鑫 李欢 贾聚全 |
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| 作者单位： | 东北石油大学教育部提高油气采收率重点实验室; |
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| 基金项目： | 国家自然科学基金重点项目“低渗透油层提高驱油效率的机理研究”(50634020)和国家自然科学基金青年科学基金“微观孔隙内原油活化条件的动力学机理研究”(51104030);黑龙江省教育厅科学技术研究项目“高含水期剩余油启动条件的微观机理研究”(12521059) |
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| 摘 要： | 以三角形截面管道中的流动为研究对象,在前人研究的基础上,进一步研究了牛顿流体和幂律流体在截面为三角形毛管中的流动,应用变分方法求出了毛管内速度分布的近似解,并通过对整个毛管进行积分,求出了类似泊肃叶定律的不同毛管内的流量与压差的定量关系.同时,又应用Matlab中的Pdetool工具对不同截面毛管中的层流流动进行了数值求解.变分结果、数值结果与有关文献解析解、数值解进行了对比,又进一步分析了幂律指数和截面形状对综合阻力系数、等效渗透率及流量-压差关系的影响.
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| 关 键 词： | 变分法 速度分布 综合阻力系数 幂律指数 |
Application of The Variational Method to Calculate the Flow of a Triangular Cross Section Pipe |
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| Abstract: | Take the flow of a triangular cross section pipe as the research object,on the basis of predecessors' conclusion,further studied on the the flow of a triangular cross section pipe of Newtonian fluid and power-law fluid,variational method is applied to solve the approximate solutions of velocity distribution inside tubular billet,and through the study of the integration of the capillary,find out the similar poiseuille's law of discharge and differential pressure quantitative relationship in different tubular billet.Again at the same time,the application of Pdetool in Matlab tools on laminar flow numerical solution of different cross section of wool tube.Compared variational results,the numerical results with the analytical solution and numerical solution of the relevant literature,and further analyzes the influence of the powerlaw index and cross section shape on the comprehensive resistance coefficient,the equivalent permeability and relations between rate of flow and differential pressure. |
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| Keywords: | variational method the velocity distribution comprehensive resistance coefficient power-law index |
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