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Cebeci-Smith model - Revision history
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Peter: Reverted edits by RicgeTcnac (Talk) to last version by Merrifj
2008-12-18T12:13:12Z
<p>Reverted edits by <a href="/Wiki/Special:Contributions/RicgeTcnac" title="Special:Contributions/RicgeTcnac">RicgeTcnac</a> (<a href="/W/index.php?title=User_talk:RicgeTcnac&action=edit&redlink=1" class="new" title="User talk:RicgeTcnac (page does not exist)">Talk</a>) to last version by <a href="/W/index.php?title=User:Merrifj&action=edit&redlink=1" class="new" title="User:Merrifj (page does not exist)">Merrifj</a></p>
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<td colspan='2' style="background-color: white; color:black;">← Older revision</td>
<td colspan='2' style="background-color: white; color:black;">Revision as of 12:13, 18 December 2008</td>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">letoaloucotr</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{Turbulence modeling}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{Turbulence modeling}}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The Cebeci-Smith [[#References|[Smith and Cebeci (1967)]]] is a two-layer algebraic 0-equation model which gives the eddy viscosity, <math>\mu_t</math>, as a function of the local boundary layer velocity profile. The model is suitable for high-speed flows with thin attached boundary-layers, typically present in aerospace applications. Like the [[Baldwin-Lomax model]], this model is not suitable for cases with large separated regions and significant curvature/rotation effects. Unlike the [[Baldwin-Lomax model]], this model requires the determination of of a boundary layer edge.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The Cebeci-Smith [[#References|[Smith and Cebeci (1967)]]] is a two-layer algebraic 0-equation model which gives the eddy viscosity, <math>\mu_t</math>, as a function of the local boundary layer velocity profile. The model is suitable for high-speed flows with thin attached boundary-layers, typically present in aerospace applications. Like the [[Baldwin-Lomax model]], this model is not suitable for cases with large separated regions and significant curvature/rotation effects. Unlike the [[Baldwin-Lomax model]], this model requires the determination of of a boundary layer edge.</div></td></tr>
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Peter
https://cfd-online.com/W/index.php?title=Cebeci-Smith_model&diff=9493&oldid=prev
RicgeTcnac: labaserdrond
2008-12-18T12:06:59Z
<p>labaserdrond</p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 12:06, 18 December 2008</td>
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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;">letoaloucotr</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{Turbulence modeling}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{Turbulence modeling}}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The Cebeci-Smith [[#References|[Smith and Cebeci (1967)]]] is a two-layer algebraic 0-equation model which gives the eddy viscosity, <math>\mu_t</math>, as a function of the local boundary layer velocity profile. The model is suitable for high-speed flows with thin attached boundary-layers, typically present in aerospace applications. Like the [[Baldwin-Lomax model]], this model is not suitable for cases with large separated regions and significant curvature/rotation effects. Unlike the [[Baldwin-Lomax model]], this model requires the determination of of a boundary layer edge.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The Cebeci-Smith [[#References|[Smith and Cebeci (1967)]]] is a two-layer algebraic 0-equation model which gives the eddy viscosity, <math>\mu_t</math>, as a function of the local boundary layer velocity profile. The model is suitable for high-speed flows with thin attached boundary-layers, typically present in aerospace applications. Like the [[Baldwin-Lomax model]], this model is not suitable for cases with large separated regions and significant curvature/rotation effects. Unlike the [[Baldwin-Lomax model]], this model requires the determination of of a boundary layer edge.</div></td></tr>
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RicgeTcnac
https://cfd-online.com/W/index.php?title=Cebeci-Smith_model&diff=9135&oldid=prev
Merrifj: /* Equations */
2008-06-11T15:18:33Z
<p><span class="autocomment">Equations</span></p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 15:18, 11 June 2008</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><table width="70%"><tr><td></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><table width="70%"><tr><td></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 class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>{\mu_t}_{inner} = \rho l^2 <del class="diffchange diffchange-inline">l </del>\left[\left(</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>{\mu_t}_{inner} = \rho l^2 \left[\left(</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> \frac{\partial U}{\partial y}\right)^2 +</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> \frac{\partial U}{\partial y}\right)^2 +</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> \left(\frac{\partial V}{\partial x}\right)^2</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> \left(\frac{\partial V}{\partial x}\right)^2</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></td><td width="5%">(6)</td></tr></table></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></td><td width="5%">(6)</td></tr></table></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>where <math>\alpha=0.0168</math><del class="diffchange diffchange-inline">, </del><math>\delta_v^*</math> is the velocity thickness given by </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>where <math>\alpha=0.0168</math> <ins class="diffchange diffchange-inline">and </ins><math>\delta_v^*</math> is the velocity thickness given 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><table width="70%"><tr><td></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><table width="70%"><tr><td></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 class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>\delta_v^* = \int_0^\delta (1-U/U_e)dy<del class="diffchange diffchange-inline">,</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>\delta_v^* = \int_0^\delta (1-U/U_e)dy<ins class="diffchange diffchange-inline">.</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></td><td width="5%">(7)</td></tr></table></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></td><td width="5%">(7)</td></tr></table></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">and </del><math>F_{KLEB}</math> is the Klebanoff intermittency function given by</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><math>F_{KLEB}</math> is the Klebanoff intermittency function given by</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><table width="100%"><tr><td></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><table width="100%"><tr><td></div></td></tr>
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Merrifj
https://cfd-online.com/W/index.php?title=Cebeci-Smith_model&diff=8246&oldid=prev
Shweta: /* Equations */
2007-09-17T17:23:28Z
<p><span class="autocomment">Equations</span></p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 17:23, 17 September 2007</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> \right]^{-1}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> \right]^{-1}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></td><td width="5%">(8)</td></tr></table></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></td><td width="5%">(8)</td></tr></table></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Model variants ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Model variants ==</div></td></tr>
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Shweta
https://cfd-online.com/W/index.php?title=Cebeci-Smith_model&diff=7703&oldid=prev
Jola at 09:41, 12 June 2007
2007-06-12T09:41:22Z
<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>where <math>y_{crossover}</math> is the smallest distance from the surface where <math>{\mu_t}_{inner}</math> is equal to <math>{\mu_t}_{outer}</math>:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>where <math>y_{crossover}</math> is the smallest distance from the surface where <math>{\mu_t}_{inner}</math> is equal to <math>{\mu_t}_{outer}</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><table width="<del class="diffchange diffchange-inline">100</del>%"><tr><td></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><table width="<ins class="diffchange diffchange-inline">70</ins>%"><tr><td></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 class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>y_{crossover} = MIN(y) \ : \ {\mu_t}_{inner} = {\mu_t}_{outer}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>y_{crossover} = MIN(y) \ : \ {\mu_t}_{inner} = {\mu_t}_{outer}</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The inner region is given</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The inner region is given</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><table width="<del class="diffchange diffchange-inline">100</del>%"><tr><td></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><table width="<ins class="diffchange diffchange-inline">70</ins>%"><tr><td></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 class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{\mu_t}_{inner} = \rho l^2 l \left[\left(</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{\mu_t}_{inner} = \rho l^2 l \left[\left(</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>where</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>where</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><table width="<del class="diffchange diffchange-inline">100</del>%"><tr><td></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><table width="<ins class="diffchange diffchange-inline">70</ins>%"><tr><td></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 class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>l = \kappa y \left( 1 - e^{\frac{-y^+}{A^+}} \right)</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>l = \kappa y \left( 1 - e^{\frac{-y^+}{A^+}} \right)</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>with the constant <math>\kappa = 0.4</math> and</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>with the constant <math>\kappa = 0.4</math> and</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><table width="<del class="diffchange diffchange-inline">100</del>%"><tr><td></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><table width="<ins class="diffchange diffchange-inline">70</ins>%"><tr><td></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 class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>A^+ = 26\left[1+y\frac{dP/dx}{\rho u_\tau^2}\right]^{-1/2}.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>A^+ = 26\left[1+y\frac{dP/dx}{\rho u_\tau^2}\right]^{-1/2}.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The outer region is given by:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The outer region is given 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: #ffa; color:black; font-size: smaller;"><div><table width="<del class="diffchange diffchange-inline">100</del>%"><tr><td></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><table width="<ins class="diffchange diffchange-inline">70</ins>%"><tr><td></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 class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{\mu_t}_{outer} = \alpha \rho U_e \delta_v^* F_{KLEB}(y;\delta),</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{\mu_t}_{outer} = \alpha \rho U_e \delta_v^* F_{KLEB}(y;\delta),</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>where <math>\alpha=0.0168</math>, <math>\delta_v^*</math> is the velocity thickness given by </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>where <math>\alpha=0.0168</math>, <math>\delta_v^*</math> is the velocity thickness given 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: #ffa; color:black; font-size: smaller;"><div><table width="<del class="diffchange diffchange-inline">100</del>%"><tr><td></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><table width="<ins class="diffchange diffchange-inline">70</ins>%"><tr><td></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 class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\delta_v^* = \int_0^\delta (1-U/U_e)dy,</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\delta_v^* = \int_0^\delta (1-U/U_e)dy,</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Category:Turbulence models]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Category:Turbulence models]]</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;">{{stub}}</ins></div></td></tr>
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Jola
https://cfd-online.com/W/index.php?title=Cebeci-Smith_model&diff=7702&oldid=prev
Jola at 09:39, 12 June 2007
2007-06-12T09:39:17Z
<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Equations ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Equations ==</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><table width="<del class="diffchange diffchange-inline">100</del>%"><tr><td></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><table width="<ins class="diffchange diffchange-inline">70</ins>%"><tr><td></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 class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\mu_t =</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\mu_t =</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\begin{cases}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\begin{cases}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{\mu_t}_{inner} & \mbox{if } y \le y_{crossover} \\ </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{\mu_t}_{inner} & \mbox{if } y \le y_{crossover} \\ </div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>{\mu_t}_{outer} & \mbox{if} y > y_{crossover}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>{\mu_t}_{outer} & \mbox{if } y > y_{crossover}</div></td></tr>
<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></td><td width="5%">(1)</td></tr></table></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></td><td width="5%">(1)</td></tr></table></div></td></tr>
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Jola
https://cfd-online.com/W/index.php?title=Cebeci-Smith_model&diff=7700&oldid=prev
Jola at 09:36, 12 June 2007
2007-06-12T09:36:23Z
<p></p>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">== Introduction ==</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">{{Turbulence modeling}}</ins></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The Cebeci-Smith [[#References|[Smith and Cebeci (1967)]]] is a two-layer algebraic 0-equation model which gives the eddy viscosity, <math>\mu_t</math>, as a function of the local boundary layer velocity profile. The model is suitable for high-speed flows with thin attached boundary-layers, typically present in aerospace applications. Like the [[Baldwin-Lomax model]], this model is not suitable for cases with large separated regions and significant curvature/rotation effects. Unlike the [[Baldwin-Lomax model]], this model requires the determination of of a boundary layer edge.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The Cebeci-Smith [[#References|[Smith and Cebeci (1967)]]] is a two-layer algebraic 0-equation model which gives the eddy viscosity, <math>\mu_t</math>, as a function of the local boundary layer velocity profile. The model is suitable for high-speed flows with thin attached boundary-layers, typically present in aerospace applications. Like the [[Baldwin-Lomax model]], this model is not suitable for cases with large separated regions and significant curvature/rotation effects. Unlike the [[Baldwin-Lomax model]], this model requires the determination of of a boundary layer edge.</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>
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Jola
https://cfd-online.com/W/index.php?title=Cebeci-Smith_model&diff=6370&oldid=prev
Littleandy: Category added
2006-10-04T07:51:31Z
<p>Category added</p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* {{reference-paper|author=Smith, A.M.O. and Cebeci, T. |year=1967|title=Numerical solution of the turbulent boundary layer equations|rest=Douglas aircraft division report DAC 33735}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* {{reference-paper|author=Smith, A.M.O. and Cebeci, T. |year=1967|title=Numerical solution of the turbulent boundary layer equations|rest=Douglas aircraft division report DAC 33735}}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* {{reference-book|author=Wilcox, D.C. |year=1998|title=Turbulence Modeling for CFD|rest=ISBN 1-928729-10-X, 2nd Ed., DCW Industries, Inc.}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* {{reference-book|author=Wilcox, D.C. |year=1998|title=Turbulence Modeling for CFD|rest=ISBN 1-928729-10-X, 2nd Ed., DCW Industries, Inc.}}</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;">[[Category:Turbulence models]]</ins></div></td></tr>
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Littleandy
https://cfd-online.com/W/index.php?title=Cebeci-Smith_model&diff=5534&oldid=prev
Jasond: further clean-up, still needs work
2006-05-06T15:25:02Z
<p>further clean-up, still needs work</p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Introduction ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Introduction ==</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>The Cebeci-Smith [[#References|[<del class="diffchange diffchange-inline">Cebeci and </del>Smith (1967)]]] is a two-layer algebraic 0-equation model which gives the eddy viscosity, <math>\mu_t</math>, as a function of the local boundary layer velocity profile. The model is suitable for high-speed flows with thin attached boundary-layers, typically present in aerospace applications. Like the [[Baldwin-Lomax model]], this model is not suitable for cases with large separated regions and significant curvature/rotation effects <del class="diffchange diffchange-inline">(see below)</del>. Unlike the [[Baldwin-Lomax model]], this model requires the determination of of a boundary layer edge.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>The Cebeci-Smith [[#References|[Smith <ins class="diffchange diffchange-inline">and Cebeci </ins>(1967)]]] is a two-layer algebraic 0-equation model which gives the eddy viscosity, <math>\mu_t</math>, as a function of the local boundary layer velocity profile. The model is suitable for high-speed flows with thin attached boundary-layers, typically present in aerospace applications. Like the [[Baldwin-Lomax model]], this model is not suitable for cases with large separated regions and significant curvature/rotation effects. Unlike the [[Baldwin-Lomax model]], this model requires the determination of of a boundary layer edge.</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>== Equations ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Equations ==</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></td><td width="5%">(2)</td></tr></table></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></td><td width="5%">(2)</td></tr></table></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>The inner region is given <del class="diffchange diffchange-inline">by the Prandtl - Van Driest formula:</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>The inner region is given</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><table width="100%"><tr><td></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><table width="100%"><tr><td></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 class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>{\mu_t}_{inner} = \rho l^2 \left<del class="diffchange diffchange-inline">| </del>\<del class="diffchange diffchange-inline">Omega </del>\right<del class="diffchange diffchange-inline">|</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>{\mu_t}_{inner} = \rho l^2 <ins class="diffchange diffchange-inline">l </ins>\left<ins class="diffchange diffchange-inline">[</ins>\<ins class="diffchange diffchange-inline">left(</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"> \frac{\partial U}{\partial y}\right)^2 +</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"> \left(\frac{\partial V}{\partial x}\right)^2</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>\right<ins class="diffchange diffchange-inline">]^{1/2},</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></td><td width="5%">(3)</td></tr></table></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></td><td width="5%">(3)</td></tr></table></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>
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<td colspan="2" class="diff-lineno">Line 38:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></td><td width="5%">(4)</td></tr></table></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></td><td width="5%">(4)</td></tr></table></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"><table width="100%"><tr><td></del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">with the constant </ins><math>\kappa = 0.4</math> <ins class="diffchange diffchange-inline">and</ins></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">:</del><math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>\kappa = 0.4<del class="diffchange diffchange-inline">, A^+ = 26\left[1+y\frac{dP/dx}{\rho u_\tau^2}\right]^{-1/2}</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div></math><del class="diffchange diffchange-inline"></td><td width="5%">(5)</td></tr></table></del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></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><table width="100%"><tr><td></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><table width="100%"><tr><td></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 class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>\left<del class="diffchange diffchange-inline">| </del>\<del class="diffchange diffchange-inline">Omega </del>\<del class="diffchange diffchange-inline">right| = </del>\<del class="diffchange diffchange-inline">sqrt{</del>2 <del class="diffchange diffchange-inline">\Omega_{ij</del>} \<del class="diffchange diffchange-inline">Omega_</del>{<del class="diffchange diffchange-inline">ij}</del>}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">A^+ = 26</ins>\left<ins class="diffchange diffchange-inline">[1+y</ins>\<ins class="diffchange diffchange-inline">frac{dP/dx}{</ins>\<ins class="diffchange diffchange-inline">rho u_</ins>\<ins class="diffchange diffchange-inline">tau^</ins>2}\<ins class="diffchange diffchange-inline">right]^</ins>{<ins class="diffchange diffchange-inline">-1/2</ins>}<ins class="diffchange diffchange-inline">.</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></td><td width="5%">(5)</td></tr></table></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></td><td width="5%">(5)</td></tr></table></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"><table width="100%"><tr><td></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">:<math></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">\Omega_{ij} = \frac{1}{2}</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">\left(</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"> \frac{\partial u_i}{\partial x_j} -</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"> \frac{\partial u_j}{\partial x_i}</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">\right)</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"></math></td><td width="5%">(6)</td></tr></table></del></div></td><td colspan="2"> </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>The outer region is given by:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The outer region is given by:</div></td></tr>
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<td colspan="2" class="diff-lineno">Line 50:</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 class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{\mu_t}_{outer} = \alpha \rho U_e \delta_v^* F_{KLEB}(y;\delta),</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{\mu_t}_{outer} = \alpha \rho U_e \delta_v^* F_{KLEB}(y;\delta),</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div></math></td><td width="5%">(<del class="diffchange diffchange-inline">7</del>)</td></tr></table></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></math></td><td width="5%">(<ins class="diffchange diffchange-inline">6</ins>)</td></tr></table></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>where <math>\alpha=0.0168</math>, <math>\delta_v^*</math> is the velocity thickness given by </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>where <math>\alpha=0.0168</math>, <math>\delta_v^*</math> is the velocity thickness given by </div></td></tr>
<tr><td colspan="2" class="diff-lineno">Line 66:</td>
<td colspan="2" class="diff-lineno">Line 57:</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 class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\delta_v^* = \int_0^\delta (1-U/U_e)dy,</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\delta_v^* = \int_0^\delta (1-U/U_e)dy,</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div></math></td><td width="5%">(<del class="diffchange diffchange-inline">8</del>)</td></tr></table></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></math></td><td width="5%">(<ins class="diffchange diffchange-inline">7</ins>)</td></tr></table></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>and <math>F_{KLEB}</math> is the Klebanoff intermittency function given by</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>and <math>F_{KLEB}</math> is the Klebanoff intermittency function given by</div></td></tr>
<tr><td colspan="2" class="diff-lineno">Line 74:</td>
<td colspan="2" class="diff-lineno">Line 65:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>F_{KLEB}(y;\delta) = \left[1 + 5.5 \left( \frac{y}{\delta} \right)^6</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>F_{KLEB}(y;\delta) = \left[1 + 5.5 \left( \frac{y}{\delta} \right)^6</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> \right]^{-1}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> \right]^{-1}</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div></math></td><td width="5%">(<del class="diffchange diffchange-inline">10</del>)</td></tr></table></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></math></td><td width="5%">(<ins class="diffchange diffchange-inline">8</ins>)</td></tr></table></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;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td colspan="2" class="diff-lineno">Line 88:</td>
<td colspan="2" class="diff-lineno">Line 79:</td></tr>
<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>
<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"><b></del>Smith, A.M.O. and Cebeci, T.<del class="diffchange diffchange-inline"></b> </del>Numerical solution of the turbulent boundary layer equations<del class="diffchange diffchange-inline">, </del>Douglas aircraft division report DAC 33735<del class="diffchange diffchange-inline">.</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>* <ins class="diffchange diffchange-inline">{{reference-paper|author=</ins>Smith, A.M.O. and Cebeci, T. <ins class="diffchange diffchange-inline">|year=1967|title=</ins>Numerical solution of the turbulent boundary layer equations<ins class="diffchange diffchange-inline">|rest=</ins>Douglas aircraft division report DAC 33735<ins class="diffchange diffchange-inline">}}</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* {{reference-book|author=Wilcox, D.C. |year=1998|title=Turbulence Modeling for CFD|rest=ISBN 1-928729-10-X, 2nd Ed., DCW Industries, Inc.}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* {{reference-book|author=Wilcox, D.C. |year=1998|title=Turbulence Modeling for CFD|rest=ISBN 1-928729-10-X, 2nd Ed., DCW Industries, Inc.}}</div></td></tr>
</table>
Jasond
https://cfd-online.com/W/index.php?title=Cebeci-Smith_model&diff=5528&oldid=prev
Jasond: Copied from B-L model, still pretty rough
2006-05-05T18:22:54Z
<p>Copied from B-L model, still pretty rough</p>
<table style="background-color: white; color:black;">
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<col class='diff-marker' />
<col class='diff-content' />
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<td colspan='2' style="background-color: white; color:black;">← Older revision</td>
<td colspan='2' style="background-color: white; color:black;">Revision as of 18:22, 5 May 2006</td>
</tr><tr><td colspan="2" class="diff-lineno">Line 1:</td>
<td colspan="2" class="diff-lineno">Line 1:</td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>== <del class="diffchange diffchange-inline">References </del>==</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>== <ins class="diffchange diffchange-inline">Introduction </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><del class="diffchange diffchange-inline">*<b></del>Smith<del class="diffchange diffchange-inline">, A.M.O. and </del>Cebeci, <del class="diffchange diffchange-inline">T.</del></<del class="diffchange diffchange-inline">b</del>> <del class="diffchange diffchange-inline">Numerical solution </del>of the <del class="diffchange diffchange-inline">turbulent </del>boundary layer <del class="diffchange diffchange-inline">equations</del>, <del class="diffchange diffchange-inline">Douglas aircraft division report DAC 33735</del>.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">The Cebeci-</ins>Smith <ins class="diffchange diffchange-inline">[[#References|[</ins>Cebeci <ins class="diffchange diffchange-inline">and Smith (1967)]]] is a two-layer algebraic 0-equation model which gives the eddy viscosity</ins>, <ins class="diffchange diffchange-inline"><math>\mu_t</ins></<ins class="diffchange diffchange-inline">math</ins>><ins class="diffchange diffchange-inline">, as a function </ins>of the <ins class="diffchange diffchange-inline">local </ins>boundary layer <ins class="diffchange diffchange-inline">velocity profile. The model is suitable for high-speed flows with thin attached boundary-layers</ins>, <ins class="diffchange diffchange-inline">typically present in aerospace applications. Like the [[Baldwin-Lomax model]], this model is not suitable for cases with large separated regions and significant curvature/rotation effects (see below). Unlike the [[Baldwin-Lomax model]], this model requires the determination of of a boundary layer edge</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 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;">== Equations ==</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>----</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline"><table width="100%"><tr><td></ins></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><<del class="diffchange diffchange-inline">i</del>> <del class="diffchange diffchange-inline">Return to [</del>[<del class="diffchange diffchange-inline">Turbulence modeling]</del>] </<del class="diffchange diffchange-inline">i</del>></div></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">\mu_t =</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">{\mu_t}_{inner} & \mbox{if } y \le y_{crossover} \\ </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">{\mu_t}_{outer} & \mbox{if} y > y_{crossover}</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></td><td width="5%">(1)</td></tr></table></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">where <math>y_{crossover}</math> is the smallest distance from the surface where <math>{\mu_t}_{inner}</math> is equal to <math>{\mu_t}_{outer}</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"><table width="100%"><tr><td></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">y_{crossover} = MIN(y) \ : \ {\mu_t}_{inner} = {\mu_t}_{outer}</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></td><td width="5%">(2)</td></tr></table></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">The inner region is given by the Prandtl </ins>- <ins class="diffchange diffchange-inline">Van Driest formula:</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"><table width="100%"><tr><td></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">{\mu_t}_{inner} = \rho l^2 \left| \Omega \right|</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></td><td width="5%">(3)</td></tr></table></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">where</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"><table width="100%"><tr><td></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">l = \kappa y \left( 1 </ins>- <ins class="diffchange diffchange-inline">e^{\frac{</ins>-<ins class="diffchange diffchange-inline">y^+}{A^+}} \right)</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></td><td width="5%">(4)</td></tr></table></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"><table width="100%"><tr><td></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">\kappa = 0.4, A^+ = 26\left[1+y\frac{dP/dx}{\rho u_\tau^2}\right]^{</ins>-<ins class="diffchange diffchange-inline">1/2}</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>><ins class="diffchange diffchange-inline"></td><td width="5%">(5)</td></tr></table></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"><table width="100%"><tr><td></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">\left| \Omega \right| = \sqrt{2 \Omega_{ij} \Omega_{ij}}</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></td><td width="5%">(5)</td></tr></table></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"><table width="100%"><tr><td></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">\Omega_{ij} = \frac{1}{2}</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">\left(</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"> \frac{\partial u_i}{\partial x_j} -</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"> \frac{\partial u_j}{\partial x_i}</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">\right)</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></td><td width="5%">(6)</td></tr></table></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">The outer region is given by:</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"><table width="100%"><tr><td></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">{\mu_t}_{outer} = \alpha \rho U_e \delta_v^* F_{KLEB}(y;\delta),</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></td><td width="5%">(7)</td></tr></table></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">where <math>\alpha=0.0168</math>, <math>\delta_v^*</math> is the velocity thickness given by </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"><table width="100%"><tr><td></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">\delta_v^* = \int_0^\delta (1-U/U_e)dy,</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></td><td width="5%">(8)</td></tr></table></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">and <math>F_{KLEB}</math> is the Klebanoff intermittency function given by</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"><table width="100%"><tr><td></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">F_{KLEB}(y;\delta) = \left</ins>[<ins class="diffchange diffchange-inline">1 + 5.5 \left( \frac{y}{\delta} \right)^6</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"> \right</ins>]<ins class="diffchange diffchange-inline">^{-1}</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>><ins class="diffchange diffchange-inline"></td><td width="5%">(10)</td></tr></table></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> </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">== Model variants ==</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> </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">== Performance, applicability and limitations ==</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> </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">== Implementation issues ==</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> </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">== 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> </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">*<b>Smith, A.M.O. and Cebeci, T.</b> Numerical solution of the turbulent boundary layer equations, Douglas aircraft division report DAC 33735.</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">* {{reference-book|author=Wilcox, D.C. |year=1998|title=Turbulence Modeling for CFD|rest=ISBN 1-928729-10-X, 2nd Ed., DCW Industries, Inc.}}</ins></div></td></tr>
</table>
Jasond