# Stratford's separation criterion

(Difference between revisions)
 Revision as of 08:42, 13 February 2008 (view source)Jola (Talk | contribs) (not finished yet)← Older edit Revision as of 12:15, 13 February 2008 (view source)Jola (Talk | contribs) (still not finished)Newer edit → Line 1: Line 1: - Stratford's separation criteria is an old classical analytical way to assess if a boundary layer is likely to separate or not. Stratford's criteria says that from the start of the pressure recovery (max velocity and minimum static pressure) the boundary layer is on the verge of separation when: + Stratford's separation criteria is an old classical analytical way to assess if a turbulent boundary layer is likely to separate or not. Stratford's criteria says that from the start of the pressure recovery where the max velocity and the minimum static pressure is obtained the boundary layer is on the verge of separation when: $[itex] Line 5: Line 5:$ [/itex] - Where + This formula is only valid as long as $C'_p < \frac{4}{7}$. - $C'_p$ is the canonical pressure distribution defined by: + *$C'_p$ is the canonical pressure distribution defined by: :$C'_p = 1 - \left( \frac{U}{U_{max}} \right) ^ 2$ :$C'_p = 1 - \left( \frac{U}{U_{max}} \right) ^ 2$ :$U$ is the local velocity and $U_{max}$ is the maximum velocity at the start of the pressure recovery. :$U$ is the local velocity and $U_{max}$ is the maximum velocity at the start of the pressure recovery. - $x'$ is the effective length of the boundary layer. Note that computing $x'$ can be a bit tricky. If the boundary layer is first accelerated up to the start of the recovery a turbulent boundary layer can be assumed to have the followig effective length: + *$k$ is a constant which Stratford used the following values for: + :$+ k = + \begin{cases} + 0.35 & \mbox{if } \frac{d^2p}{dx^2} \le 0 \mbox{ (concave recovery)} \\ + 0.39 & \mbox{if } \frac{d^2p}{dx^2} > 0 \mbox{ (convex recovery)} + \end{cases} +$ + + *$x'$ is the effective length of the boundary layer. Note that computing $x'$ can be a bit tricky. If the boundary layer is first accelerated up to the start of the recovery a turbulent boundary layer can be assumed to have the followig effective length: + + Stratford's separation criteria is known to be conservative. It will most likely predict a bit too early separation.

## Revision as of 12:15, 13 February 2008

Stratford's separation criteria is an old classical analytical way to assess if a turbulent boundary layer is likely to separate or not. Stratford's criteria says that from the start of the pressure recovery where the max velocity and the minimum static pressure is obtained the boundary layer is on the verge of separation when:

$C'_p \cdot \sqrt{x' \frac{dC'_p}{dx}} = k \cdot \left( \frac{Re}{10^6} \right) ^ {0.1}$

This formula is only valid as long as $C'_p < \frac{4}{7}$.

• $C'_p$ is the canonical pressure distribution defined by:
$C'_p = 1 - \left( \frac{U}{U_{max}} \right) ^ 2$
$U$ is the local velocity and $U_{max}$ is the maximum velocity at the start of the pressure recovery.
• $k$ is a constant which Stratford used the following values for:
$k = \begin{cases} 0.35 & \mbox{if } \frac{d^2p}{dx^2} \le 0 \mbox{ (concave recovery)} \\ 0.39 & \mbox{if } \frac{d^2p}{dx^2} > 0 \mbox{ (convex recovery)} \end{cases}$
• $x'$ is the effective length of the boundary layer. Note that computing $x'$ can be a bit tricky. If the boundary layer is first accelerated up to the start of the recovery a turbulent boundary layer can be assumed to have the followig effective length:

Stratford's separation criteria is known to be conservative. It will most likely predict a bit too early separation.