Shear layer

The shear layer (engl. Mixing layer or shear layer ) referred to in the fluid mechanics of the transition region between the two rectified currents at different speeds.

For a more precise delimitation from the wall-bound boundary layer , a free shear layer is often used .

Basics

Sketch of a free shear layer of the thickness behind a flow profile (free flow velocities U ₁ and U ₂ ). ${\displaystyle \delta }$

Due to the friction, there is no abrupt transition between two parallel flows of different speeds, but a shear layer is formed, the speed profile of which is S-shaped (see picture). The thickness of the shear layer is determined in the laminar case ${\displaystyle \delta }$

${\displaystyle \delta ={\frac {\Delta u}{\left.\partial u/\partial y\right|_{{\text{max}},y}}}}$

With

• the speed difference and ${\displaystyle \Delta u=U_{1}-U_{2}}$
• the maximum of the velocity gradient perpendicular to the direction of flow . ${\displaystyle \partial u/\partial y}$ ${\displaystyle x}$

Analogous to the wall-bound boundary layer, the thickness of the laminar shear layer in the downstream direction increases with the root of the run length  : ${\displaystyle x}$

${\displaystyle \delta \sim {\sqrt {x/Re}}}$

Here Re denotes the Reynolds number .

Due to this spatial growth of the shear layer, there is a small velocity component in the y-direction, with a displacement effect in the area of ​​the fast flow and a suction of fluid in the area of ​​the slow flow.

In compressible flows, the friction within the shear layer leads to a higher temperature and thus to a lower density within the shear layer, since the pressure is constant.

Shear layers are always unstable due to the turning point in the velocity profile (see linear stability theory ). Usually this is a convective instability, but in the case of opposing free flow velocities an absolute instability also occurs. The strong inflation rates in a shear layer lead to a rolling up of eddies , which are referred to as Kelvin-Helmholtz instability .

Occur

Free shear layers occur in nature and in technical applications. In nature, examples can be found in meteorology and astrophysics , in the technical field with boundary layer separation and with free jets . In jet engines , for example, a shear layer forms between the exhaust gas jet and the ambient air , the strong turbulence of which is a main source of noise in aircraft engines.

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  Shear layer in the atmosphere , made visible by clouds .

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  Vortex structures in a shear layer, calculated using DNA .

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  Shear layer when peeling off a profile .

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  Shear layer on the exhaust jet of a jet aircraft .

literature

• Tim Colonius, Sanjiva Lele, Parviz Moin : Sound generation in a mixing layer. In: Journal of Fluid Mechanics. Vol. 330, 1997, pp. 375-409, doi : 10.1017 / S0022112096003928 .
• Hermann Schlichting , Klaus Gersten : boundary layer theory . 9th, completely revised and expanded edition. Springer, Berlin et al. 1997, ISBN 3-540-55744-X .
• Frank M. White: Viscous fluid flow. 2nd edition. McGraw-Hill, New York NY et al. 1991, ISBN 0-07-069712-4 .

Web links

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