# Laminar flow

Laminar flow

The laminar flow ( lat. Lamina "plate"), also laminar flow , is a movement of liquids and gases in which no visible turbulence (eddies / cross flows) occurs in a transition area between two different flow velocities ( hydrodynamic boundary layer ) that spreads perpendicular to the direction of flow : The fluid flows in layers that do not mix with each other. In this case (with constant flow velocity over time) it is mostly a stationary flow .

Colloquially, a flow that follows the course of a wall or a profile is sometimes referred to as laminar flow . In technical terms, however, this phenomenon is a trained or attached current.

## properties

Formation of a laminar boundary layer on a flat surface. Here Re x is smaller than Re crit  ≈ 10 5 for each x . The plate length x must therefore be finite.

To illustrate the difference between laminar flow and turbulent flow, the physicist Osborne Reynolds carried out an experiment in coloring a water flow in a pipeline in 1883 and found that the turbulence in the pipeline only occurs above a certain flow velocity. The Reynolds number Re is used as an assessment criterion . This is defined as follows:

${\ displaystyle \ mathrm {Re}: = {\ frac {v \ cdot l} {\ nu}} = {\ frac {v \ cdot l \ cdot \ rho} {\ eta}}}$,

where the amount of a characteristic flow velocity , a characteristic length and the kinematic viscosity or (or also ) the dynamic viscosity and the density of the flowing fluid is. ${\ displaystyle v}$${\ displaystyle l}$${\ displaystyle \ nu}$${\ displaystyle \ eta}$${\ displaystyle \ mu}$${\ displaystyle \ rho}$

Above a critical value , the laminar flow becomes unstable to small disturbances. For example, this value is around for pipe flow ${\ displaystyle \ mathrm {Re_ {krit}}}$

${\ displaystyle \ mathrm {Re_ {krit}} = {\ frac {v _ {\ mathrm {m}} \ cdot d} {\ nu}} \ approx 2320}$

where is the mean flow velocity and is to be used as the characteristic length of the pipe diameter . The critical Reynolds number is given for overflow plates ${\ displaystyle v_ {m}}$${\ displaystyle d}$

${\ displaystyle \ mathrm {Re_ {krit}} = {\ frac {v_ {0} \ cdot x} {\ nu}} \ approx 10 ^ {5}}$.

Here is the distance from the front edge to the rear edge of the plate and the speed of the undisturbed flow. ${\ displaystyle x}$${\ displaystyle v_ {0}}$

If the flow in a pipe is laminar, the Hagen-Poiseuille law applies . It describes the volume flow through the pipe depending on the inner radius of the pipe. ${\ displaystyle {\ tfrac {\ mathrm {d} V} {\ mathrm {d} t}}}$

## Cause of the onset of turbulence

Principle of a vortex ring
Creation of eddies in an initially laminar flow
Smoke rings as a torus rotating in itself

The primary cause of the laminar flow, which becomes unstable and then turbulent after a certain value, is the fact that the flow field of such a flow is not vortex-free in the mathematical sense even before that . There means freedom from eddy u. a. that one moves along a closed curve, e.g. B. in a circle, moving body neither gains nor loses energy - in the picture on the left, however, a particle that moves quickly to the right in the middle of the flow and then slowly back to the left along the wall would be permanently supplied with energy leads to the formation of the vortices drawn: If there are disturbances in the area around the particle, which is practically always the case, these are fanned by the supply of energy until the initially ordered movement (stratified flow ) finally changes into a disordered turbulent flow . ${\ displaystyle \ mathrm {Re_ {krit}}}$

A well-known example of this effect is the formation of smoke rings (see fig.), In which the ambient air takes on the role of the stationary vessel wall. It now does not blow too quickly into the center of a small smoke cloud formed in front of the mouth (power supply), deforms it to a rotating itself in the torus (vortex ring English vortex ring ), the well-known smoke ring.

## Occurrence in nature and technology

Special wing profile for researching laminar flow in aviation

Laminar flows occur in nature, for example in the groundwater and in the bloodstream on, are in technical applications but rather the exception, such as the micro-process technology , where one already makes this phenomenon to Use. Fire brigades sometimes use flow straighteners for long hose lengths, as they allow considerably longer hose lengths to be used (important e.g. in case of high-rise fires).

Flow straighteners have also been increasingly used for modern water features and fountains in recent years (as of 2014). For so-called water sausages , d. H. jumping water jets, they are even an essential requirement.

Laminar boundary layers usually have less wall friction than turbulent boundary layers, especially in the area of ​​the critical Reynolds number. For this reason, so-called laminar profiles are used in glider construction , for example , which, due to their shape, have a long laminar run length (the distance between the leading edge and the laminar / turbulent transition point) in order to achieve low flow resistances. The lengthening of the laminar boundary layer is achieved by designing the profile in which the transition to a turbulent boundary layer flow is delayed as long as possible. Laminar profiles, however, are intolerant of too large an angle of attack, which leads to a stall .

In turbulent flow, so-called riblets can reduce frictional resistance, as can the small depressions called dimples on the surface of golf balls .

### Laminar flow

Flow principle "laminar flow clean room"

When describing technical facilities, one occasionally comes across the English-language term laminar flow . This is generally understood to mean a (mostly vertical) directed, low-turbulence air flow. A low-turbulence flow generated in this way swirls around obstacles such as machines or tables. In safety workbenches , laminar flow conditions are created using special systems that have fans, filters and air distributors (so-called laminarizers). The room through which there is no return flow has a defined clean room quality (depending on the filters used), since only sterile air remains in the room or possible particles are blown away in a directed manner.

In industry, low-turbulence (quasi-laminar) flows are used wherever product contamination by particles in the air is to be avoided. The air flow reduces the turbulence of existing particles and removes them through the air flow directed downwards. This makes them interesting for applications in which the increased risk of particle formation (e.g. due to friction between moving parts) has to be compensated, e.g. B. when filling pharmaceuticals. Typical examples are clean rooms in semiconductor technology , medicine and pharmacy.

Another application are workstations that work with powders that are basically explosive (powders made from organic materials such as flour). Due to the laminar flow, these powders cannot spread in the air and reach the status of an explosive air-solid mixture.

An essential innovation of the Pharmacy Operating Regulations 2005 ABO is that the production of sterile drugs - especially eye drops or drugs to be administered parenterally - must be carried out in the laboratory using a laminar flow or an isolator according to the state of the art, unless the production is done in one own sterile room.