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Equations Fluid
Show changesAlert about the upcoming downtime of the Wiki-Server
| ← Older revision | Revision as of 20:34, 17 April 2019 | ||
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| − | + | <div class="alert alert-danger" role="alert"> |
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| + | On the 24th of April 2019 the server will be (physically) moved to a new location. It will not be available during that time and unfortunately there will be no replacement server. The expected downtime will be from 8:00 CEST to 14:00. Sorry for any inconvenince this may cause |
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<!-- Server currently in read-only mode! Reason is that the server machine is moved to another office and in the mean-time a replacement server is used. As all edits on the replacement server would be lost this is turned off. Normal operations should resume on the 13th of December 2016. For updates see [https://twitter.com/ofwiki @ofwiki]. Sorry for any inconvenience this may cause --> |
<!-- Server currently in read-only mode! Reason is that the server machine is moved to another office and in the mean-time a replacement server is used. As all edits on the replacement server would be lost this is turned off. Normal operations should resume on the 13th of December 2016. For updates see [https://twitter.com/ofwiki @ofwiki]. Sorry for any inconvenience this may cause --> |
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<!-- <div style="font-size:111%; border:solid 2px; margin:0; padding:.1em; background:#f99;">It seems that some domains do not accept mails from the Wiki software. This is being investigated. If you don't get confirmation mails for passwords or so, please contact me [http://www.cfd-online.com/Forums/openfoam/60855-wiki.html here].</div> --> |
<!-- <div style="font-size:111%; border:solid 2px; margin:0; padding:.1em; background:#f99;">It seems that some domains do not accept mails from the Wiki software. This is being investigated. If you don't get confirmation mails for passwords or so, please contact me [http://www.cfd-online.com/Forums/openfoam/60855-wiki.html here].</div> --> |
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Equations Liquid Film
| ← Older revision | Revision as of 15:52, 17 April 2019 | ||
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<center><math> |
<center><math> |
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| − | \nabla \cdot |
+ |
\rho \nabla \cdot \bold {U_p} \delta = |
| − | \nabla \cdot |
+ |
\rho \nabla \cdot \left [ \bold {\frac { \bold { H[U] }}{A_P}} - \bold {\frac {\delta}{A_P}} \nabla \left ( {P_p} \delta - {P_u} \right ) + {\frac {\delta}{\bold A_P}}\rho g_t \right ] \delta |
</math></center> |
</math></center> |
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</td><td width="5%">(6)</td></tr></table> |
</td><td width="5%">(6)</td></tr></table> |
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| + | After applying the chain rule: |
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| + | <table width="70%"><tr><td> |
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| + | <center><math> |
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| + | |||
| + | \rho \nabla \cdot \bold {U_p} \delta = \rho \bold {U_p} \cdot \nabla \delta + \rho \delta \nabla |
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| + | \cdot \bold {U_p} = \rho \left [ \bold {\frac { \bold { H[U] }}{A_P}} - \bold {\frac {\delta}{A_P}} \nabla \left ( {P_p} \delta - {P_u} \right ) + {\frac {\delta}{\bold A_P}}\rho g_t \right ] \cdot \nabla \delta + |
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| + | \rho \nabla \cdot \left [ \bold {\frac { \bold { H[U] }}{A_P}} - \bold {\frac {\delta}{A_P}} \nabla \left ( {P_p} \delta - {P_u} \right ) + {\frac {\delta}{\bold A_P}}\rho g_t \right ] \delta |
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| + | </math></center> |
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| + | </td><td width="5%">(7)</td></tr></table> |
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| + | It is evident that the above equation still represents a non linear equation for the film thickness <math> \delta </math>. In order to solve the above equation, it has to be linearized and an iterative algorithm has to be applied. |
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And finally: |
And finally: |
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