A theory for turbulent pipe and channel flows
A theory for turbulent pipe and channel flows
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湍流管道和渠道流动理论
DOI：
10.1017/s0022112000001385
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发表时间：
2000
影响因子：
3.7
通讯作者：
W. George
中科院分区：
文献类型：
--
作者：
M. Wosnik;L. Castillo;W. George
提出了一种充分发展的湍流管道和通道流理论，该理论将经典分析扩展到包括有限雷诺数的影响。有限雷诺数下这些流动的适当缩放是使用雷诺平均纳维-斯托克斯方程从尺寸和物理考虑因素得出的。在无限雷诺数的限制下，它们分别简化为熟悉的壁面定律和速度赤字定律。事实上，两个缩放轮廓都描述了雷诺数有限值的整个流动，但减少到内部和外部轮廓，用于确定它们在“重叠”区域中的函数形式，该区域都保留在极限内。该重叠区域对应于恒定雷诺剪应力区域（大约 30 < y+ < 0.1R+，其中 R+ = u*R/v）。该重叠区域中的轮廓是对数的，但在变量 y + a 中，其中 a 是偏移量。与经典理论不同，加性参数 Bi、Bo 和对数系数 1/κ 取决于 R+。然而，它们是渐近常数，并且通过约束方程联系起来。相应的摩擦定律也是对数的，并且完全由速度剖面参数决定，反之亦然。还有人认为，在重叠区域底部附近存在一个中间层，其边界大约为 30 < y+ < 300，其中惯性主导湍流的能量和耗散范围之间没有必要的尺度分离。因此，雷诺应力和平均流量保留雷诺数依赖性，即使明确包含粘度的项在单点雷诺平均方程中可以忽略不计。一个简单的湍流模型表明，偏移参数 a 考虑了中间层，因此 y 中的对数行为仅适用于 y+ > 300 之外，远远超出了通常寻求的范围。仔细检查了来自超级管道实验和通道流 DNS 的实验数据，结果表明在 1.8 × 102 < R+ < 5.3 × 105 的整个范围内与新理论非常一致。所有参数的雷诺数依赖性和摩擦定律可以通过单个经验函数 H = A/(ln R+)α 确定，对于 α > 0，就像边界层一样。随着雷诺数的增加，参数的雷诺数依赖性减小得非常缓慢，并且仅当 R+ [Gt ] 105 时才达到渐近行为。
A theory for fully developed turbulent pipe and channel flows is proposed which extends the classical analysis to include the effects of finite Reynolds number. The proper scaling for these flows at finite Reynolds number is developed from dimensional and physical considerations using the Reynolds-averaged Navier–Stokes equations. In the limit of infinite Reynolds number, these reduce to the familiar law of the wall and velocity deficit law respectively. The fact that both scaled profiles describe the entire flow for finite values of Reynolds number but reduce to inner and outer profiles is used to determine their functional forms in the ‘overlap’ region which both retain in the limit. This overlap region corresponds to the constant, Reynolds shear stress region (30 < y+ < 0.1R+ approximately, where R+ = u*R/v). The profiles in this overlap region are logarithmic, but in the variable y + a where a is an offset. Unlike the classical theory, the additive parameters, Bi, Bo, and log coefficient, 1/κ, depend on R+. They are asymptotically constant, however, and are linked by a constraint equation. The corresponding friction law is also logarithmic and entirely determined by the velocity profile parameters, or vice versa. It is also argued that there exists a mesolayer near the bottom of the overlap region approximately bounded by 30 < y+ < 300 where there is not the necessary scale separation between the energy and dissipation ranges for inertially dominated turbulence. As a consequence, the Reynolds stress and mean flow retain a Reynolds number dependence, even though the terms explicitly containing the viscosity are negligible in the single-point Reynolds-averaged equations. A simple turbulence model shows that the offset parameter a accounts for the mesolayer, and because of it a logarithmic behaviour in y applies only beyond y+ > 300, well outside where it has commonly been sought. The experimental data from the superpipe experiment and DNS of channel flow are carefully examined and shown to be in excellent agreement with the new theory over the entire range 1.8 × 102 < R+ < 5.3 × 105. The Reynolds number dependence of all the parameters and the friction law can be determined from the single empirical function, H = A/(ln R+)α for α > 0, just as for boundary layers. The Reynolds number dependence of the parameters diminishes very slowly with increasing Reynolds number, and the asymptotic behaviour is reached only when R+ [Gt ] 105.