The optimal transient growth process of perturbations driven by the pressure gradient is studied in a turbulent pipe flow. A new computational method is proposed, based on the projection operators which project the go...The optimal transient growth process of perturbations driven by the pressure gradient is studied in a turbulent pipe flow. A new computational method is proposed, based on the projection operators which project the governing equations onto the sub- space spanned by the radial vorticity and radial velocity. The method is validated by comparing with the previous studies. Two peaks of the maximum transient growth am- plification curve are found at different Reynolds numbers ranging from 20 000 to 250 000. The optimal flow structures are obtained and compared with the experiments and DNS results. The location of the outer peak is at the azimuthal wave number n = 1, while the location of the inner peak is varying with the Reynolds number. It is observed that the velocity streaks in the buffer layer with a spacing of 100δv are the most amplified flow structures. Finally, we consider the optimal transient growth time and its dependence on the azimuthal wave length. It shows a self-similar behavior for perturbations of different scales in the optimal transient growth process.展开更多
经典的特征线法(method of characteristics,MOC)因其简单方便,边界条件易于耦合求解,常应用于有压管道瞬变流方程的数值求解.对于复杂管道系统,受库朗数限制,该方法往往需要进行波速调整或插值求解,可能出现严重的累积误差和数值耗散....经典的特征线法(method of characteristics,MOC)因其简单方便,边界条件易于耦合求解,常应用于有压管道瞬变流方程的数值求解.对于复杂管道系统,受库朗数限制,该方法往往需要进行波速调整或插值求解,可能出现严重的累积误差和数值耗散.有限体积法Godunov格式(Godunov type scheme,GTS)对管道内部库朗数具有良好的鲁棒性,但边界条件采用精确黎曼不变量方法,处理复杂.同时,以往水锤计算通常仅考虑稳态摩阻,低估了瞬变压力的衰减.文章提出并推导了考虑动态摩阻的GTS-MOC耦合模型,使用二阶GTS计算管道内部控制体,在复杂边界处采用耦合GTS-MOC方法处理.首先,针对串联管和分叉管边界条件,对精确黎曼不变量方法和MOC方法进行了理论分析.推导结果表明,在马赫数(Ma)较小的管道瞬变流求解中,两种边界处理方法结果一致,与实验结果对比分析,验证了耦合格式求解的准确性.最后,将耦合格式分别与GTS和MOC进行比较.结果证明,耦合格式可以达到和GTS相同的精度,同时,串联管道系统中MOC线性插值法和波速调整法均存在数值耗散且随时间增加更明显,耦合格式结果具有准确性和稳定性,与精确解更吻合.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11322221,11132005,and 11490551)
文摘The optimal transient growth process of perturbations driven by the pressure gradient is studied in a turbulent pipe flow. A new computational method is proposed, based on the projection operators which project the governing equations onto the sub- space spanned by the radial vorticity and radial velocity. The method is validated by comparing with the previous studies. Two peaks of the maximum transient growth am- plification curve are found at different Reynolds numbers ranging from 20 000 to 250 000. The optimal flow structures are obtained and compared with the experiments and DNS results. The location of the outer peak is at the azimuthal wave number n = 1, while the location of the inner peak is varying with the Reynolds number. It is observed that the velocity streaks in the buffer layer with a spacing of 100δv are the most amplified flow structures. Finally, we consider the optimal transient growth time and its dependence on the azimuthal wave length. It shows a self-similar behavior for perturbations of different scales in the optimal transient growth process.
文摘经典的特征线法(method of characteristics,MOC)因其简单方便,边界条件易于耦合求解,常应用于有压管道瞬变流方程的数值求解.对于复杂管道系统,受库朗数限制,该方法往往需要进行波速调整或插值求解,可能出现严重的累积误差和数值耗散.有限体积法Godunov格式(Godunov type scheme,GTS)对管道内部库朗数具有良好的鲁棒性,但边界条件采用精确黎曼不变量方法,处理复杂.同时,以往水锤计算通常仅考虑稳态摩阻,低估了瞬变压力的衰减.文章提出并推导了考虑动态摩阻的GTS-MOC耦合模型,使用二阶GTS计算管道内部控制体,在复杂边界处采用耦合GTS-MOC方法处理.首先,针对串联管和分叉管边界条件,对精确黎曼不变量方法和MOC方法进行了理论分析.推导结果表明,在马赫数(Ma)较小的管道瞬变流求解中,两种边界处理方法结果一致,与实验结果对比分析,验证了耦合格式求解的准确性.最后,将耦合格式分别与GTS和MOC进行比较.结果证明,耦合格式可以达到和GTS相同的精度,同时,串联管道系统中MOC线性插值法和波速调整法均存在数值耗散且随时间增加更明显,耦合格式结果具有准确性和稳定性,与精确解更吻合.
