Free jet

(the opening angle was larger than shown in reality)

A free jet is a flow from a nozzle (diameter ) into the free environment without wall limitation. The fluid flowing out of the nozzle and the fluid of the surroundings have different speeds. A shear layer is created between them , from which a free jet develops. The surrounding fluid is sucked in and carried away. ${\displaystyle d_{0}}$

Division into areas

Downstream the free jet is divided into three areas.

• The undisturbed flow disappears within the conical core area ; it is dissolved from the edge by the sucked in fluid. In free jets with constant density, the length of the core is around five to eight and depends heavily on the initial turbulence in the nozzle. ${\displaystyle d_{0}}$

• In the transition zone , the speed profile approaches a self-similar shape. ${\displaystyle v_{x}(y)}$

• After about eight to 30 the similarity area begins , in which the self-similar free jet is fully developed. ${\displaystyle d_{0}}$

Similarity area

In the similarity area, the speed decreases hyperbolically with increasing axial distance from the nozzle opening : ${\displaystyle v_{x}(x)}$ ${\displaystyle x}$

${\displaystyle v(x)=v_{0}\cdot {\frac {d_{0}}{d(x)}}}$

with (see below) ${\displaystyle d(x)=0{,}32\cdot x}$

The speed decreases from the center of the jet outwards ( direction) in the form of a Gaussian bell curve . ${\displaystyle v_{x}(y)}$ ${\displaystyle y}$

The jet angle at which the speed has halved is calculated from:

${\displaystyle \tan(\Theta )\approx {\frac {0{,}32}{2}}}$

${\displaystyle \Leftrightarrow \Theta \approx 10^{\circ }}$

Here the streamlines of the sucked-in fluid have the minimum distance to the jet axis, their curvature is small.

The jet angle at which the speed has decreased to only 1% is about 18 °, i.e. approx. H. here is the just measurable edge of the free jet. ${\displaystyle \Theta }$

The fictitious free jet origin is behind the nozzle opening, i. H. at ${\displaystyle 0{,}6\cdot d_{0}}$ ${\displaystyle x=-0{,}6\cdot d_{0}.}$

The diameter and the mass flow of the free jet increase linearly: ${\displaystyle d(x)}$ ${\displaystyle {\dot {m}}(x)}$

${\displaystyle d(x)=0{,}32\cdot x}$

${\displaystyle {\dot {m}}(x)={\dot {m}}_{0}\cdot {\frac {d(x)}{d_{0}}}}$

The momentum and the static pressure are constant. ${\displaystyle I}$ ${\displaystyle p}$

Examples

• In the swimming pool , the fresh water flows into the pool from nozzles. The penetration depth is several meters. The spread of the free jet can be felt with the hands.
• A free jet is created behind the jet engine of a jet aircraft .
• In the injector of a Bunsen burner , the fuel gas flows out of a nozzle and is mixed with air by means of a free jet. Because of the different densities of air and gas , the mass flow changes by the factor . ${\displaystyle \rho _{\text{Luft}}}$ ${\displaystyle \rho _{\text{Gas}}}$ ${\displaystyle {\dot {m}}(x)}$ ${\displaystyle {\sqrt {\rho _{\text{Luft}}/\rho _{\text{Gas}}}}}$
• Propulsion of the rattle boat .

literature

• Hermann Schlichting, Klaus Gersten: boundary layer theory. 9th edition. Springer-Verlag, 1997, ISBN 3-540-55744-X .
• Piercristian Rinaldi: About the behavior of turbulent free jets in limited spaces (=  hydraulics and hydrology . No. 71 ). Techn. Univ., Chair and Laboratory for Hydraulics and Hydrology , Munich 2003, DNB  969250738 .

Individual evidence

1. ↑ JW Gauntner, JNB Livingood, P. Hrycak: Survey of literature on Flow characteristics of a single turbulent jet impinging on a flat plate. Lewis Research Center, Washington, DC: National Aeronautics and Space Administration, 1970. - NASA Technical Note. - TN D-5652
2. ↑ JO Hinze, BG Hegge Zijnen: Transfer of heat and matter in the turbulent mixing zone of an axially symmetrical jet. In: Applied Scientific Research 1. No. 1, 1949, pp. 435-461.
3. ^ PA Davidson: Turbulence: An Introduction for Scientists and Engineers. Oxford University Press, New York 2004.