On the Receptivity of Pipe Poiseuille Flow With a Bump on the Wall Under the Periodical Pressure
-
摘要: 采用渐近分析方法,建立了在周期压力驱动下,完全发展的圆管Poiseuille流当管壁存在局部不规则几何形状时的感受性问题模型．通过特征函数的双正交系统，应用Chebyshev配点法进行数值求解．通过算例计算，获得周期压力和矩形突起激发起的流体系统中的各种空间发展模态以及相应的感受性系数．从计算和分析可以知道，在流场的不同发展阶段不同的模态起着主导作用，这与在试验中观察到的扰动流场在不同位置的特性是一致的．
-
关键词:
- Poiseuille流 /
- 双正交系统 /
- 特征函数 /
- 感受性
Abstract: Asymptotic method was a dopted to obtain a receptivity model for a pipe Poiseuille flow under periodical pressure, the wall of the pipe with a bump. Bi-orthogonal eigen-function systems and Chebyshev collocation method were used to resolve the problem. Various spatial modes and the receptivity coefficients were obtained. The results show that different modes dominate the flow in different stages, which is comparable with the phenomena observed in experiments.-
Key words:
- Poiseuille flow /
- bi-orthogonal /
- eigen-function /
- receptivity
-
[1] Reynold O. An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels[J].Philos Trans Roy Soc London,1883,174(3)：935—1023. doi: 10.1098/rstl.1883.0029 [2] Tatsumi T. Stability of the laminar inlet-flow prior to the formation of Poiseuille regime,Part Ⅱ[J].J Phys Soc Japan,1952,7(2)：495—516. doi: 10.1143/JPSJ.7.495 [3] Wygnanski I，Champagne F H.On transition in a pipe flow[J].J Fluid Mech，1973,59(1)：281—306. doi: 10.1017/S0022112073001576 [4] Tumin A M.Receptivity of pipe Poiseuille flow[J].J Fluid Mech,1996,315(1)：119—135. doi: 10.1017/S0022112096002364 [5] Tumin A M，Fedorov A V. Instability wave excitation by a localized vibrator in boundary layer[J].J Appl Mech Tech Phys,1984,25(3)：867—887. [6] Salwen H.Expansion in spatial or temporal eigenmodes of the linearized Navier-Stokes equations[J].Bull Amer Phys Soc,1979,24(1)：74—88. [7] Schensted I V.Contributions to the theory of hydrodynamic stability[D].PhD dissertation. University of Michigan，1960. [8] Salwen H，Grosch C E.The continuous spectrum of the Orr-Sommerfeld equation—Part 2： Eigenfunction expansion[J].J Fluid Mech,1981,104(2)：445—463. doi: 10.1017/S0022112081002991 [9] Hill D C. Adjoint systems and their role in the receptivity problem for boundary layers[J].J Fluid Mech,1995,292(1)：183—203. doi: 10.1017/S0022112095001480 [10] Leite R J.An experiment investigation of the stability of Poiseuille flow[J].J Fluid Mech,1959,5(1)：81—97. doi: 10.1017/S0022112059000076 -
点击查看大图
计量
- 文章访问数: 2022
- HTML全文浏览量: 83
- PDF下载量: 469
- 被引次数: 0
下载:
