https://cfd-online.com/W/index.php?title=Stratford%27s_separation_criterion&feed=atom&action=historyStratford's separation criterion - Revision history2024-03-28T14:33:46ZRevision history for this page on the wikiMediaWiki 1.16.5https://cfd-online.com/W/index.php?title=Stratford%27s_separation_criterion&diff=22672&oldid=prevJola: Formatting improvements2013-12-11T11:10:31Z<p>Formatting improvements</p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>For <math>C'_p > \frac{4}{7}</math> (velocity ratios <math>\frac{U_{max}}{U} > 1.53</math>) Stratford successfully used the following formula to compute <math>C'_p</math>:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>For <math>C'_p > \frac{4}{7}</math> (velocity ratios <math>\frac{U_{max}}{U} > 1.53</math>) Stratford successfully used the following formula to compute <math>C'_p</math>:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><math>C'_p = 1 - \frac{a}{\sqrt{x' + b}}</math>, for <math>C'_p > \frac{4}{7}</math> where the constants a and b are chosen so that the slope and value of <math>C'_p</math> match at <math>C'_p = \frac{4}{7}</math> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><math>C'_p = 1 - \frac{a}{\sqrt{x' + b}}</math>, for <math>C'_p > \frac{4}{7}</math> where the constants <ins class="diffchange diffchange-inline"><math></ins>a<ins class="diffchange diffchange-inline"></math> </ins>and <ins class="diffchange diffchange-inline"><math></ins>b<ins class="diffchange diffchange-inline"></math> </ins>are chosen so that the slope and value of <math>C'_p</math> match at <math>C'_p = \frac{4}{7}</math> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>To compute <math>a</math> and b for <math>x'_{C'_p = 4/7}</math> the following formulas can be deduced:</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>To compute <math>a</math> and <ins class="diffchange diffchange-inline"><math></ins>b<ins class="diffchange diffchange-inline"></math> </ins>for <math>x'_{C'_p = 4/7}</math> the following formulas can be deduced:</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math>b = \frac{3}{14 \cdot \frac{dC'_p}{dx'}|_{C'_p=4/7}} - x'_{C'_p=4/7}</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math>b = \frac{3}{14 \cdot \frac{dC'_p}{dx'}|_{C'_p=4/7}} - x'_{C'_p=4/7}</math></div></td></tr>
</table>Jolahttps://cfd-online.com/W/index.php?title=Stratford%27s_separation_criterion&diff=22671&oldid=prevJola: Added formulas for a and b for C'_p > 4/72013-12-11T11:08:19Z<p>Added formulas for a and b for C'_p > 4/7</p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math>C'_p = 1 - \frac{a}{\sqrt{x' + b}}</math>, for <math>C'_p > \frac{4}{7}</math> where the constants a and b are chosen so that the slope and value of <math>C'_p</math> match at <math>C'_p = \frac{4}{7}</math> </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math>C'_p = 1 - \frac{a}{\sqrt{x' + b}}</math>, for <math>C'_p > \frac{4}{7}</math> where the constants a and b are chosen so that the slope and value of <math>C'_p</math> match at <math>C'_p = \frac{4}{7}</math> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">To compute <math>a</math> and b for <math>x'_{C'_p = 4/7}</math> the following formulas can be deduced:</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><math>b = \frac{3}{14 \cdot \frac{dC'_p}{dx'}|_{C'_p=4/7}} - x'_{C'_p=4/7}</math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><math>a = \frac{3}{7} \sqrt{x'_{C'_p=4/7} + b}</math></ins></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Stratford's separation criteria is known to be conservative. It will most likely predict a bit too early separation.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Stratford's separation criteria is known to be conservative. It will most likely predict a bit too early separation.</div></td></tr>
</table>Jolahttps://cfd-online.com/W/index.php?title=Stratford%27s_separation_criterion&diff=22669&oldid=prevJola: Added formula for C'p > 4/72013-12-11T09:50:57Z<p>Added formula for C'p > 4/7</p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*<math>Re = \frac{U_{max} \cdot x'}{\nu}</math> </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*<math>Re = \frac{U_{max} \cdot x'}{\nu}</math> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The Reynolds number above is based on the effective length of the bounday layer <math>x'</math> and the maximum velocity <math>U_{max}</math> at the start of the recovery.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The Reynolds number above is based on the effective length of the bounday layer <math>x'</math> and the maximum velocity <math>U_{max}</math> at the start of the recovery.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">For <math>C'_p > \frac{4}{7}</math> (velocity ratios <math>\frac{U_{max}}{U} > 1.53</math>) Stratford successfully used the following formula to compute <math>C'_p</math>:</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><math>C'_p = 1 - \frac{a}{\sqrt{x' + b}}</math>, for <math>C'_p > \frac{4}{7}</math> where the constants a and b are chosen so that the slope and value of <math>C'_p</math> match at <math>C'_p = \frac{4}{7}</math> </ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Stratford's separation criteria is known to be conservative. It will most likely predict a bit too early separation.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Stratford's separation criteria is known to be conservative. It will most likely predict a bit too early separation.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*{{reference-paper|author=Cebeci, T., Mosinskis, G. J., and Smith A. M. O|year=1972|title=Calculation of Separation Points in Incompressible Turbulent Flows|rest=Journal of Aircraft, Vol. 9., Sept. 1972, p. 618-624}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*{{reference-paper|author=Cebeci, T., Mosinskis, G. J., and Smith A. M. O|year=1972|title=Calculation of Separation Points in Incompressible Turbulent Flows|rest=Journal of Aircraft, Vol. 9., Sept. 1972, p. 618-624}}</div></td></tr>
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<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">== External Links ==</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* http://adg.stanford.edu/aa200b/blayers/turbseparation.html</ins></div></td></tr>
</table>Jolahttps://cfd-online.com/W/index.php?title=Stratford%27s_separation_criterion&diff=8910&oldid=prevJola at 18:41, 14 February 20082008-02-14T18:41:15Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== References ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== References ==</div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>*{{reference-paper|author=Stratford, B. S.|year=1959|title=The Prediction of Separation of the Turbulent Boundary Layer|rest=Journal of Fluid Mechanics, Vol. 5, pp. 1-16<del class="diffchange diffchange-inline">.</del>}}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>*{{reference-paper|author=Stratford, B. S.|year=1959|title=The Prediction of Separation of the Turbulent Boundary Layer|rest=Journal of Fluid Mechanics, Vol. 5, pp. 1-16}}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>*{{reference-paper|author=Cebeci, T., Mosinskis, G. J., and Smith A. M. O|year=1972|title=Calculation of Separation Points in Incompressible Turbulent Flows|rest=Journal of Aircraft, Vol. 9., Sept. 1972, p. 618-624<del class="diffchange diffchange-inline">.</del>}}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>*{{reference-paper|author=Cebeci, T., Mosinskis, G. J., and Smith A. M. O|year=1972|title=Calculation of Separation Points in Incompressible Turbulent Flows|rest=Journal of Aircraft, Vol. 9., Sept. 1972, p. 618-624}}</div></td></tr>
</table>Jolahttps://cfd-online.com/W/index.php?title=Stratford%27s_separation_criterion&diff=8909&oldid=prevJola: Added a couple of references and an alternative constant from Cebeci-Smith2008-02-14T18:40:45Z<p>Added a couple of references and an alternative constant from Cebeci-Smith</p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\end{cases}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\end{cases}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Other researcers have used other values. Cebeci-Smith for example used <math>k = 0.5</math>, which is a bit less conservative than Statford's original values.</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*<math>x'</math> is the effective length of the boundary layer. Note that computing <math>x'</math> 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:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*<math>x'</math> is the effective length of the boundary layer. Note that computing <math>x'</math> 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:</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Stratford's separation criteria is known to be conservative. It will most likely predict a bit too early separation.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Stratford's separation criteria is known to be conservative. It will most likely predict a bit too early separation.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">== References ==</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">*{{reference-paper|author=Stratford, B. S.|year=1959|title=The Prediction of Separation of the Turbulent Boundary Layer|rest=Journal of Fluid Mechanics, Vol. 5, pp. 1-16.}}</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">*{{reference-paper|author=Cebeci, T., Mosinskis, G. J., and Smith A. M. O|year=1972|title=Calculation of Separation Points in Incompressible Turbulent Flows|rest=Journal of Aircraft, Vol. 9., Sept. 1972, p. 618-624.}}</ins></div></td></tr>
</table>Jolahttps://cfd-online.com/W/index.php?title=Stratford%27s_separation_criterion&diff=8908&oldid=prevJola: First version finished2008-02-14T18:15:41Z<p>First version finished</p>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Stratford's separation <del class="diffchange diffchange-inline">criteria </del>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:</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Stratford's separation <ins class="diffchange diffchange-inline">criterion </ins>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:</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>x' = \int_0^{x^{turb}_{rec}} \left( \frac{U}{U_{max}} \right) ^ 3 dx + (x - x^{turb}_{rec})</math> </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>x' = \int_0^{x^{turb}_{rec}} \left( \frac{U}{U_{max}} \right) ^ 3 dx + (x - x^{turb}_{rec})</math> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>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.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>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.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">*<math>Re = \frac{U_{max} \cdot x'}{\nu}</math> </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">The Reynolds number above is based on the effective length of the bounday layer <math>x'</math> and the maximum velocity <math>U_{max}</math> at the start of the recovery.</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Stratford's separation criteria is known to be conservative. It will most likely predict a bit too early separation.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Stratford's separation criteria is known to be conservative. It will most likely predict a bit too early separation.</div></td></tr>
</table>Jolahttps://cfd-online.com/W/index.php?title=Stratford%27s_separation_criterion&diff=8907&oldid=prevJola: still more to add2008-02-14T17:54:23Z<p>still more to add</p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 17:54, 14 February 2008</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>*<math>x'</math> is the effective length of the boundary layer. Note that computing <math>x'</math> 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:</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>*<math>x'</math> is the effective length of the boundary layer. Note that computing <math>x'</math> can be a bit tricky. If the boundary layer is first accelerated up to the start of the recovery <ins class="diffchange diffchange-inline">and is assumed to be turbulent all the time </ins>a turbulent boundary layer can be assumed to have the followig effective length:</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">:<math>x' = \int_0^{x^{turb}_{rec}} \left( \frac{U}{U_{max}} \right) ^ 3 dx + (x - x^{turb}_{rec})</math> </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">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.</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Stratford's separation criteria is known to be conservative. It will most likely predict a bit too early separation.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Stratford's separation criteria is known to be conservative. It will most likely predict a bit too early separation.</div></td></tr>
</table>Jolahttps://cfd-online.com/W/index.php?title=Stratford%27s_separation_criterion&diff=8904&oldid=prevJola: Stratford's separation criteria moved to Stratford's separation criterion: Incorrect title2008-02-13T18:20:21Z<p><a href="/Wiki/Stratford%27s_separation_criteria" class="mw-redirect" title="Stratford's separation criteria">Stratford's separation criteria</a> moved to <a href="/Wiki/Stratford%27s_separation_criterion" title="Stratford's separation criterion">Stratford's separation criterion</a>: Incorrect title</p>
<table style="background-color: white; color:black;">
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<td colspan='1' style="background-color: white; color:black;">← Older revision</td>
<td colspan='1' style="background-color: white; color:black;">Revision as of 18:20, 13 February 2008</td>
</tr></table>Jolahttps://cfd-online.com/W/index.php?title=Stratford%27s_separation_criterion&diff=8901&oldid=prevJola: still not finished2008-02-13T12:15:43Z<p>still not finished</p>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>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 <del class="diffchange diffchange-inline">(</del>max velocity and minimum static pressure<del class="diffchange diffchange-inline">) </del>the boundary layer is on the verge of separation when:</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Stratford's separation criteria is an old classical analytical way to assess if a <ins class="diffchange diffchange-inline">turbulent </ins>boundary layer is likely to separate or not. Stratford's criteria says that from the start of the pressure recovery <ins class="diffchange diffchange-inline">where the </ins>max velocity and <ins class="diffchange diffchange-inline">the </ins>minimum static pressure <ins class="diffchange diffchange-inline">is obtained </ins>the boundary layer is on the verge of separation when:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">Where</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">This formula is only valid as long as <math>C'_p < \frac{4}{7}</math>.</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><math>C'_p</math> is the canonical pressure distribution defined by:</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">*</ins><math>C'_p</math> is the canonical pressure distribution defined by:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>C'_p = 1 - \left( \frac{U}{U_{max}} \right) ^ 2</math> </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>C'_p = 1 - \left( \frac{U}{U_{max}} \right) ^ 2</math> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>U</math> is the local velocity and <math>U_{max}</math> is the maximum velocity at the start of the pressure recovery.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>U</math> is the local velocity and <math>U_{max}</math> is the maximum velocity at the start of the pressure recovery.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><math>x'</math> is the effective length of the boundary layer. Note that computing <math>x'</math> 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:</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">*<math>k</math> is a constant which Stratford used the following values for:</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">:<math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">k =</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">\begin{cases}</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">0.35 & \mbox{if } \frac{d^2p}{dx^2} \le 0 \mbox{ (concave recovery)} \\ </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">0.39 & \mbox{if } \frac{d^2p}{dx^2} > 0 \mbox{ (convex recovery)}</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">\end{cases}</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline"></math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">*</ins><math>x'</math> is the effective length of the boundary layer. Note that computing <math>x'</math> 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:</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">Stratford's separation criteria is known to be conservative. It will most likely predict a bit too early separation.</ins></div></td></tr>
</table>Jolahttps://cfd-online.com/W/index.php?title=Stratford%27s_separation_criterion&diff=8900&oldid=prevJola: not finished yet2008-02-13T08:42:28Z<p>not finished yet</p>
<p><b>New page</b></p><div>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:<br />
<br />
<math><br />
C'_p \cdot \sqrt{x' \frac{dC'_p}{dx}} = k \cdot \left( \frac{Re}{10^6} \right) ^ {0.1}<br />
</math><br />
<br />
Where<br />
<br />
<math>C'_p</math> is the canonical pressure distribution defined by:<br />
<br />
:<math>C'_p = 1 - \left( \frac{U}{U_{max}} \right) ^ 2</math> <br />
:<math>U</math> is the local velocity and <math>U_{max}</math> is the maximum velocity at the start of the pressure recovery.<br />
<br />
<math>x'</math> is the effective length of the boundary layer. Note that computing <math>x'</math> 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:</div>Jola