Diffuser

Two outlet diffusers of a weather shaft with pit fans

A diffuser is a component used in machinery , power stations , ventilators , vehicles , aircraft and shipbuilding that slows gas / liquid flows and increases gas / liquid pressure. In hydropower plants, the diffuser is called a suction pipe . A diffuser is basically the reverse of a nozzle . It is used to "recover" kinetic energy in the pipe hydraulics . Diffusers are used technically to convert kinetic energy into pressure energy. To do this, the flow has to be decelerated. This is usually achieved by a continuous or discontinuous expansion of the flow cross-section, which can be implemented geometrically in different ways.

technical description

Difference between supersonic and subsonic

With a diffuser for subsonic flows , the flow cross-section always increases in the flow direction of the flowing medium.

In aerodynamics , the diffuser is used in supersonic aircraft , for example , to brake the air in the engine inlet of a turbine to subsonic speed, since the air is only allowed to flow around the blades of the rotors and stators in the subsonic range. Because if the blades of the rotors and stators in a jet drive reach supersonic speeds , the flow breaks down, the combustion chamber suffocates, the drive fails. In addition, shock waves run through the fluid and the rotor / stator blades, which can destroy the engine.

In the nozzle , which tapers in the direction of flow and which follows the engine, the air then accelerates again to supersonic speed.

If the flow medium itself is at supersonic speed and should it also remain at supersonic speed (for example in the air inlet of a pulse engine), then the nozzle must widen in the direction of flow, not taper. This paradoxical phenomenon is explained in the article nozzle .

In the hydrodynamics to influence the phenomenon of cavitation applied, as well as the aerodynamics in the region of the sound, the diffuser is a very complex to be calculated component.

In diffusers with an opening angle of (supercritical diffuser), dissipation occurs as the flow detaches from the diffuser wall, which leads to strong turbulence in the transition areas to the dead spaces. In the event of a sudden expansion of the cross-section ( ) one speaks of a " Carnotian shock loss", the corresponding diffuser is called a jump diffuser . In such a diffuser, the flow comes to rest again after a distance of about eight to ten times the large diameter. ${\ displaystyle \ alpha \ geq 8 \, ^ {\ circ}}$ ${\ displaystyle \ alpha = 90 \, ^ {\ circ}}$

The quality of a diffuser is described by the “diffuser efficiency” or the “pressure recovery number”. ${\ displaystyle \ eta _ {D}}$

Calculation for incompressible fluids ( Mach <0.3)

However, the effect of a diffuser is relatively manageable in the case of non-turbulent and non-viscous flows (that is, there are no eddies due to sudden changes in cross-section or the like and the friction losses of the medium on the walls can be neglected). Then the simplified Bernoulli equation applies

{\ displaystyle p + {\ frac {1} {2}} \ rho v ^ {2} = {\ text {constant}}}

.

It is the so-called static pressure acting on the outer walls of the diffuser, the density of the medium and its flow rate. (Note: The Bernoulli equation is simplified in that it does not take into account height differences.) As can be seen, the static pressure must decrease as the flow velocity increases. ${\ displaystyle p}$ ${\ displaystyle \ rho}$ ${\ displaystyle v}$ ${\ displaystyle p}$ ${\ displaystyle v}$

Since the same volume per unit of time must flow through a pipe with a variable cross-section at every point, it can be seen that the flow velocity in a cross- section is inversely proportional to the flow velocity in the cross-section to the ratio of the cross-section, so it must apply: ${\ displaystyle v_ {1}}$ ${\ displaystyle A_ {1}}$ ${\ displaystyle v_ {2}}$ ${\ displaystyle A_ {2}}$

{\ displaystyle {\ frac {v_ {1}} {v_ {2}}} = {\ frac {A_ {2}} {A_ {1}}}}

or.

{\ displaystyle v_ {2} = {\ frac {A_ {1}} {A_ {2}}} v_ {1}}

In addition, due to the above (simplified) Bernoulli equation:

{\ displaystyle p_ {1} + {\ frac {1} {2}} \ rho v_ {1} ^ {2} = {\ text {constant}} = p_ {2} + {\ frac {1} {2 }} \ rho v_ {2} ^ {2}}

Both together result in:

{\ displaystyle p_ {1} + {\ frac {1} {2}} \ rho v_ {1} ^ {2} = p_ {2} + {\ frac {1} {2}} \ rho \ left ({ \ frac {A_ {1}} {A_ {2}}} v_ {1} \ right) ^ {2}}

or transformed:

{\ displaystyle p_ {2} -p_ {1} = {\ frac {1} {2}} \ rho v_ {1} ^ {2} \ left (1- \ left ({\ frac {A_ {1}} {A_ {2}}} \ right) ^ {2} \ right)}

I.e. with increasing cross-section (diffuser:) the pressure increases (and the flow velocity decreases) and with decreasing cross-section (nozzle:) the pressure decreases (and the flow velocity increases). ${\ displaystyle A_ {2}> A_ {1}}$ ${\ displaystyle A_ {2} <A_ {1}}$

In the case of very narrow cross-sections or very viscous media, the friction losses must also be taken into account, as well as the turbulence that occurs in the case of suddenly changing cross-sections (see next section).

Mathematical description

Diffuser (schematic)

In the event of a sudden change in cross-section, the following applies to the loss figure defined in fluid mechanics : ${\ displaystyle \ xi}$

{\ displaystyle \ xi _ {D} = \ left (1 - {\ frac {A_ {1}} {A_ {2}}} \ right) ^ {2}}

With the loss figure and the extended Bernoullis theorem of the pipe hydraulics (consideration of dissipation) follows:

Energy law: ${\ displaystyle \ Delta p = p_ {1} -p_ {2} + {\ frac {\ rho} {2}} (w_ {1} ^ {2} -w_ {2} ^ {2}) = \ xi _ {D} {\ frac {\ rho} {2}} w_ {1} ^ {2}}$

Conservation of mass: for ${\ displaystyle w_ {1} = {\ frac {A_ {2}} {A_ {1}}} w_ {2}}$ ${\ displaystyle \ rho = {\ text {constant}}}$

{\ displaystyle p_ {1} -p_ {2} = {\ frac {\ rho} {2}} \ left (\ xi _ {D} w_ {1} ^ {2} - (w_ {1} ^ {2 } -w_ {2} ^ {2}) \ right) = {\ frac {\ rho} {2}} w_ {1} ^ {2} \ cdot \ left (\ xi _ {D} -1+ \ left ({\ frac {A_ {1}} {A_ {2}}} \ right) ^ {2} \ right)}

Technical application

Diffusers are used in high-speed, in particular supersonic, aircraft in order to achieve a defined gas pressure in the immediate intake area of the engines. In order to be able to set the optimal conditions, the diffuser is usually designed to be movable. Airplanes with a particularly large speed range, or where a long range is important, have complex diffusers with adjustable flaps and multiple variable cross-sections.

Diffusers are used in motorsport , often also in super sports cars and occasionally in sports cars . This creates a vacuum under the floor of the vehicle, which presses the vehicle against the ground and thus allows higher cornering speeds and also improves driving behavior at high speeds. The task of the diffuser is to increase the negative pressure under the vehicle back to the ambient pressure behind the vehicle. In many cases, such a diffuser is a wing close to the ground.

In hydrodynamics one finds the diffuser z. B. in pumps and water jet / jet engines as well as in fans in aerodynamics.

Diffusers can also be found in the field of aquaristics . There they serve the purpose of introducing gases such as carbon dioxide or oxygen into the water that are required for the life and growth of the fauna and flora in the aquarium . This happens through the "suction pipe effect", in that the flowing water inside the outflow line is sucked in by the negative pressure by means of a fresh air or gas supply line, mixed with the water and then fed into the basin. In particular, these diffusers are used during the use of algae control agents, medicines and / or in the event of a disproportion between the stock of plants and fish for additional and compensatory ventilation of the artificial habitat. It is disputed whether a diffuser is also useful for normal pool sizes.

Diffusers can be used to increase the flow rate from a vessel, which is known as the suction pipe effect . This was apparently already known in ancient Rome, because according to Sextus Iulius Frontinus it was forbidden there to connect a pipe with increasing diameter directly to a mouthpiece of the water pipe.

In the area of smaller wind turbines, there are repeated attempts to increase their effectiveness with the help of diffusers.

Web links

Wiktionary: Diffuser - explanations of meanings, word origins, synonyms, translations

Diffusers in wind energy

Individual evidence

↑ Peter Hakenesch: Flow of fluids. Chapter 4, Part 3. In: Slides for the lecture Fluid Mechanics. P. 45 , accessed on February 4, 2016 .
↑ Herbert Sprenger: Experimental investigations on straight and curved diffusers . Doctoral thesis approved by the Swiss Federal Institute of Technology in Zurich to obtain the title of Doctor in Technical Sciences. In: Messages from the Institute for Aerodynamics at the Swiss Federal Institute of Technology in Zurich . No. 27 . Leemann, Zurich, 2nd historical review, p. 8th f . ( ethz.ch [PDF; accessed on January 18, 2015]).

[Hakenesch-1] Peter Hakenesch: Flow of fluids. Chapter 4, Part 3. In: Slides for the lecture Fluid Mechanics. P. 45 , accessed on February 4, 2016 .

[2] Herbert Sprenger: Experimental investigations on straight and curved diffusers . Doctoral thesis approved by the Swiss Federal Institute of Technology in Zurich to obtain the title of Doctor in Technical Sciences. In: Messages from the Institute for Aerodynamics at the Swiss Federal Institute of Technology in Zurich . No. 27 . Leemann, Zurich, 2nd historical review, p. 8th f . ( ethz.ch [PDF; accessed on January 18, 2015]).