层流和湍流

尼古拉兹（J.Nikuradse，1932）
层流
层流和湍流： 管内阻力损失
湍流
层流和湍流： 外流 External flow
层流和湍流： 边界层转捩 Boundary layer transition
转捩发生在Transition occurs when Turbulent boundary layer d grows faster
Re=2300 Re=11000
length scale : h (n 3 / e )1/4 velocity scale : uh (en )1/4 time scale : th (n / e )1/2
(uh /h) 1/th Reh huh /n 1
Andrey Kolmogorov and Kolmogorov microscopic scale
Turbulent flow: characterized by velocity fluctuations and highly disordered motion. 转捩过程不是突然发生的，而是在某些区域逐 渐开始，逐步发展
The transition from laminar to turbulent flow does not occur suddenly; rather, it occurs over some region in which the flow fluctuates between laminar and turbulent flows before it becomes fully turbulent.
turbulent湍流
湍流： 能量和运动尺度Scales of motion
Length scale L
长度尺度:L 脉动速度：uo 特征时间(turn over time): L/ uo 脉动能量uo2 能量耗散率e= uo2/(L/ uo )= uo3 /L 最小旋涡尺度h=(n3/e)1/4; L/h=(uoL/n) 3/4=Reo3/4 最小速度尺度v=(ne)1/4; Reh~1 最小时间尺度：t=(n/e)1/2;
Model equations for E() in the production range and dissipation range have been developed. We will not discuss
the theory behind them here.
The full spectrum is given by: Will not discuss fL and fh today.
British scientist Osborne Reynolds (1842–1912) discovered that the flow regime depends mainly on the ratio of inertial forces to viscous forces in the fluid.
Turbulence 2014
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湍流
管内流动 Internal flow 外流 External flow
雷诺实验 Reynolds Experiment
层流和湍流
层流：和缓、有序的运动
Laminar flow: characterized by smooth streamlines and highly ordered motion. 湍流：不断变化，无序运动
英国人雷诺提出转捩主要由惯性力和粘性力的比值决定 The ratio is called the Reynolds number雷诺数 and is expressed for
internal flow in a circular pipe as
层流和湍流：管内流动
湍流混合能力更强，流场内速度分布更均匀，低速区域较小 壁面附近，湍流速度梯度较大，壁面切应力较大 湍流度为标准差（脉动速度）除以平均速度 /U
湍流边界层厚度增长快 Turbulent boundary layer more effective in mixing 湍流边界层
混合效率高 Turbulent boundary layer more viscous drag
湍流边界层产生壁面切应力大
层流和湍流：边界层
laminar层流
E( ) Ce 2/3 5/3 f L fh
log E()
Energy containing
range
Inertial subrange
log
wk.baidu.com
Dissipation range
Richardson
L.F. Richardson (“Weather Prediction by Numerical Process.” Cambridge University Press, 1922) summarized this in the following often cited verse:
Big whirls have little whirls Which feed on their velocity; And little whirls have lesser whirls, And so on to viscosity
in the molecular sense.
Full spectrum E()
层流和湍流： Reynolds Number 雷诺数
The transition from laminar to turbulent flow depends on the geometry, surface roughness, flow velocity, surface temperature, and type of fluid, among other things. 转捩受到几何形状、表面粗糙度、 流动速度、表面温度、流体性质等因素影响