Turbulent flows

We generally differentiate between a laminar and a turbulent flow state. If the flow velocity is very small, the flow will be laminar, and if the flow velocity exceeds a certain boundary value, the flow becomes turbulent. The figure to the right shows this transition from a “well-ordered” laminar state to a seemingly stochastic and “chaotic” turbulent state for pipe flow. This experiment has already been done by Reynolds around 1860. Reynolds had then shown that the transition from laminar to turbulent can be described by the dimension-less Reynolds-number:

, with u being the “typical“ velocity, L being the „typical“ long measure and

being the

kinematical viscosity. The characteristic length L is used for the description of fluid-transport processes (hydrodynamics, mass transport, heat transport, etc.) in so-called dimensionless index numbers, such as the Reynolds-number or Prandtl-number. It has the dimension of a length, but describes the three-dimensional geometry of a reference system. In simplified terms we apply for the characteristic length in the Reynolds number the diameter if there is a pipe flow or the water depth if we have an open channel flow.

The critical Reynolds number for pipe flow is about 580, so that for example the flow within a pipe with the diameter D=0,20 m is turbulent if the flow velocity is greater than ~ 3 mm/s. This observation makes clear that most of the flows with technical relevance are turbulent. One of the few exceptions is for example human blood vessels that have laminar flow as a general rule (…maybe except for the aorta).

 

 

Reynold’s experiment showing the transition from laminar to turbulent pipe flow, taken from [*1].

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Module
Hydrodynamics of Floods
Source

TUHH

References

*1 Van Dyke (1982)

Downloads

Skript Environmental Hydraulic Simulation:

Turbulent flow

Further Information

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