Channel flow

Flow profile in a fluid channel
1: laminar
2: turbulent

A channel flow is understood as the flow between two infinitely extended flat plates at a distance . ${\ displaystyle L}$

Your Reynolds number is usually given as:

{\ displaystyle \ mathrm {Re} = {\ frac {{\ overline {u}} _ {cl} \ cdot L} {\ nu}}}

With

the channel center speed and ${\ displaystyle {\ overline {u}} _ {cl}}$
the kinematic viscosity . ${\ displaystyle \ nu}$

In the laminar case ( ) a parabolic profile is formed. For higher Reynolds numbers ( ), the flow changes into a turbulent channel flow, with the mean flow profile becoming more box-shaped. The flow resistance then increases compared to the laminar case, since the additional turbulent shear stresses ensure greater momentum transport in the lateral direction (hereinafter: "y-direction"). ${\ displaystyle \ mathrm {Re} <2300}$ ${\ displaystyle \ mathrm {Re}> 2300}$

The wall shear stress indicates the force per area with which the panels must be held:

{\ displaystyle \ tau _ {wand} = \ eta \ cdot {\ frac {\ partial u (y)} {\ partial y}}}

With

the dynamic viscosity . ${\ displaystyle \ eta}$

Usually, all values in the vicinity of the wall (rms values, wall clearances ) are related to the wall shear stress velocity :

{\ displaystyle u _ {\ tau} = {\ sqrt {\ nu \ cdot {\ frac {\ partial u (y)} {\ partial y}}}}}

.

This system of units is called "+ units" (read: plus units ). In the fully developed turbulent channel flow z. B. the maximum turbulence production at instead. ${\ displaystyle y ^ {+} = 12}$

If you want to calculate the flow profile in a channel, you can use the universal wall law for the fully developed turbulent channel flow to z. B. to calculate the wall friction .

literature

Hermann Schlichting, Klaus Gersten, Egon Krause, Herbert, jun. Oertel: boundary layer theory . Springer, Berlin 2006, ISBN 3-540-23004-1 .