# Stratford's separation criterion

(Difference between revisions)
 Revision as of 17:54, 14 February 2008 (view source)Jola (Talk | contribs) (still more to add)← Older edit Revision as of 18:15, 14 February 2008 (view source)Jola (Talk | contribs) (First version finished)Newer edit → Line 1: Line 1: - 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: + Stratford's separation criterion 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: $[itex] Line 24: Line 24: :[itex]x' = \int_0^{x^{turb}_{rec}} \left( \frac{U}{U_{max}} \right) ^ 3 dx + (x - x^{turb}_{rec})$ :$x' = \int_0^{x^{turb}_{rec}} \left( \frac{U}{U_{max}} \right) ^ 3 dx + (x - x^{turb}_{rec})$ Note that this is only valid if the approaching boundary layer can be assumed to be fully turbulent. If the boundary layer is laminar, or undergoes transition, a different approximations needs to be done. Note that this is only valid if the approaching boundary layer can be assumed to be fully turbulent. If the boundary layer is laminar, or undergoes transition, a different approximations needs to be done. + + *$Re = \frac{U_{max} \cdot x'}{\nu}$ + The Reynolds number above is based on the effective length of the bounday layer $x'$ and the  maximum velocity $U_{max}$ at the start of the recovery. Stratford's separation criteria is known to be conservative. It will most likely predict a bit too early separation. Stratford's separation criteria is known to be conservative. It will most likely predict a bit too early separation.

## Revision as of 18:15, 14 February 2008

Stratford's separation criterion 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 and is assumed to be turbulent all the time a turbulent boundary layer can be assumed to have the followig effective length:
$x' = \int_0^{x^{turb}_{rec}} \left( \frac{U}{U_{max}} \right) ^ 3 dx + (x - x^{turb}_{rec})$

Note that this is only valid if the approaching boundary layer can be assumed to be fully turbulent. If the boundary layer is laminar, or undergoes transition, a different approximations needs to be done.

• $Re = \frac{U_{max} \cdot x'}{\nu}$

The Reynolds number above is based on the effective length of the bounday layer $x'$ and the maximum velocity $U_{max}$ at the start of the recovery.

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