https://cfd-online.com/W/index.php?title=Shuai-Agarwal_turbulence_Model&feed=atom&action=historyShuai-Agarwal turbulence Model - Revision history2024-03-29T06:17:41ZRevision history for this page on the wikiMediaWiki 1.16.5https://cfd-online.com/W/index.php?title=Shuai-Agarwal_turbulence_Model&diff=25498&oldid=prevRamesh Agarwal: /* Shuai – Agarwal One Equation k-kL Turbulence Model */2021-04-10T19:43:37Z<p><span class="autocomment">Shuai – Agarwal One Equation k-kL Turbulence Model</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Shuai – Agarwal One Equation k-kL Turbulence Model ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Shuai – Agarwal One Equation k-kL Turbulence Model ==</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>'''The turbulent viscosity is given by:'''</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>'''The turbulent <ins class="diffchange diffchange-inline">kinematic </ins>viscosity is 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>:<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: #ffa; color:black; font-size: smaller;"><div>P=\frac{\tau_{ij}}{\rho} \frac{\partial u_{i}}{\partial <del class="diffchange diffchange-inline">y</del>}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>P=\frac{\tau_{ij}}{\rho} \frac{\partial u_{i}}{\partial <ins class="diffchange diffchange-inline">x_{j}</ins>}</div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>S_{i j}=\frac{1}{2}\left(\frac{\partial u_{i}}{\partial <del class="diffchange diffchange-inline">y</del>} + \frac{\partial u_{j}}{\partial <del class="diffchange diffchange-inline">x</del>} \right)</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>S_{i j}=\frac{1}{2}\left(\frac{\partial u_{i}}{\partial <ins class="diffchange diffchange-inline">x_{j}</ins>} + \frac{\partial u_{j}}{\partial <ins class="diffchange diffchange-inline">x_{i}</ins>} \right)</div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>'''The <del class="diffchange diffchange-inline">parameter </del>of the model are:'''</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>'''The <ins class="diffchange diffchange-inline">parameters </ins>of the model are:'''</div></td></tr>
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</table>Ramesh Agarwalhttps://cfd-online.com/W/index.php?title=Shuai-Agarwal_turbulence_Model&diff=25497&oldid=prevRamesh Agarwal: /* Introduction */2021-04-10T19:19:25Z<p><span class="autocomment">Introduction</span></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: #ffa; color:black; font-size: smaller;"><div>One-equation k-kL turbulence model was developed from two-equation k-kL closure of Abdol-Hamid et al<del class="diffchange diffchange-inline">. [1]</del>. Improvements to the original formulation of one-equation k-kL model (AIAA 2019-1879) were made by optimizing the model constants. The new improved model has been validated by simulating several benchmark canonical wall-bounded turbulent flows with small regions of separation from NASA TMR (https://turbmodels.larc.nasa.gov/). The model needs further investigations by the scientific community to evaluate its potential.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>One-equation k-kL turbulence model was developed from two-equation k-kL closure of Abdol-Hamid et al. Improvements to the original formulation of one-equation k-kL model (AIAA 2019-1879) were made by optimizing the model constants <ins class="diffchange diffchange-inline">(AIAA 2020-1075)</ins>. The new improved model has been validated by simulating several benchmark canonical wall-bounded turbulent flows with small regions of separation from NASA TMR (https://turbmodels.larc.nasa.gov/). The model needs further investigations by the scientific community to evaluate its potential.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Shuai – Agarwal One Equation k-kL Turbulence Model ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Shuai – Agarwal One Equation k-kL Turbulence Model ==</div></td></tr>
</table>Ramesh Agarwalhttps://cfd-online.com/W/index.php?title=Shuai-Agarwal_turbulence_Model&diff=25493&oldid=prevLin.zhenghao: Created page with "== Introduction == One-equation k-kL turbulence model was developed from two-equation k-kL closure of Abdol-Hamid et al. [1]. Improvements to the original formulation of one-equa..."2021-04-08T02:58:50Z<p>Created page with "== Introduction == One-equation k-kL turbulence model was developed from two-equation k-kL closure of Abdol-Hamid et al. [1]. Improvements to the original formulation of one-equa..."</p>
<p><b>New page</b></p><div>== Introduction ==<br />
One-equation k-kL turbulence model was developed from two-equation k-kL closure of Abdol-Hamid et al. [1]. Improvements to the original formulation of one-equation k-kL model (AIAA 2019-1879) were made by optimizing the model constants. The new improved model has been validated by simulating several benchmark canonical wall-bounded turbulent flows with small regions of separation from NASA TMR (https://turbmodels.larc.nasa.gov/). The model needs further investigations by the scientific community to evaluate its potential.<br />
<br />
==Shuai – Agarwal One Equation k-kL Turbulence Model ==<br />
'''The turbulent viscosity is given by:'''<br />
<br />
:<math><br />
v_{t}=C_{\mu}^{1/4} \frac{kL}{{k}^{1/2}}<br />
</math><br />
<br />
'''The final form of the new Shuai-Agarwal one-equation k-kL model is obtained as: '''<br />
<br />
:<math><br />
\frac{D v_{t}}{D t}=a_{1}\left(C_{\phi 1}-\frac{1}{2}\right) \frac{P}{S}+\left(\frac{1}{2} a_{1}-\frac{C_{\phi 2}}{\sqrt{a_{1}}}\right) v_{t} S+\frac{v v_{t}\left(1-6 f_{\phi}\right)}{d^{2}}+\frac{\sigma}{2 }\frac{v_{t}}{S} \frac{\partial v_{t}}{\partial x_{i}} \frac{\partial S}{\partial x_{i}}+\frac{3 \sigma}{4} \frac{\partial v_{t}}{\partial x_{i}} \frac{\partial v_{t}}{\partial x_{i}}-\frac{\sigma}{4} \frac{\partial S}{\partial x_{i}} \frac{\partial S}{\partial x_{i}} \frac{v_{t}^{2}}{S^{2}}+\frac{\partial}{\partial x_{i}}\left(\left(\sigma v_{t}+v\right) \frac{\partial v_{t}}{\partial x_{i}}\right)<br />
</math><br />
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<br />
'''Where <math>P</math> is the production term:'''<br />
<br />
:<math><br />
P=\frac{\tau_{ij}}{\rho} \frac{\partial u_{i}}{\partial y}<br />
</math><br />
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<br />
:<math><br />
{\tau_{ij}}={\mu_{t}} \left(2S_{i j}-\frac{2}{3} \frac{\partial u_{k}}{\partial x_{k}}{\delta_{i j}}\right)-\frac{2}{3} {\rho}{\delta_{i j}}<br />
</math><br />
<br />
<br />
:<math><br />
S_{i j}=\frac{1}{2}\left(\frac{\partial u_{i}}{\partial y} + \frac{\partial u_{j}}{\partial x} \right)<br />
</math><br />
<br />
<br />
'''The following Bradshaw relation is used to express the relationship between <math>v_{t}</math> and k and kL:'''<br />
<br />
:<math><br />
v_{t}|\frac{\partial u}{\partial y}|=C_{\mu}^{\frac{1}{2}}{k}<br />
</math><br />
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'''The parameter of the model are:'''<br />
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:<math><br />
C_{\phi 1}=\left(\zeta_{1}-\zeta_{2}\left(\frac{\sqrt{\nu_{t}}}{L_{k} \sqrt{S}}\right)^{2}\right)<br />
</math><br />
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:<math><br />
C_{\phi 2}={\zeta_{3}}<br />
</math><br />
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:<math><br />
L_{v k}=\kappa\left|\frac{U^{\prime}}{U^{\prime \prime}}\right|<br />
</math><br />
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:<math><br />
U^{\prime}=\sqrt{2}{S_{ij}}{S_{ij}}<br />
</math><br />
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:<math><br />
U^{\prime \prime}=\sqrt{\left(\frac{\partial^{2} u}{\partial x^{2}}+\frac{\partial^{2} u}{\partial y^{2}}+\frac{\partial^{2} u}{\partial z^{2}}\right)^{2}+\left(\frac{\partial^{2} v}{\partial x^{2}}+\frac{\partial^{2} v}{\partial y^{2}}+\frac{\partial^{2} v}{\partial z^{2}}\right)^{2}+\left(\frac{\partial^{2} w}{\partial x^{2}}+\frac{\partial^{2} w}{\partial y^{2}}+\frac{\partial^{2} w}{\partial z^{2}}\right)^{2}}<br />
</math><br />
<br />
:<math><br />
L_{v k , max}=C_{1 2}{\kappa}{d}{f_{p}}<br />
</math><br />
<br />
:<math><br />
L_{v k , min}=\frac{\sqrt{v_{t}}}{{C_{11}}{\sqrt{S}}}<br />
</math><br />
<br />
:<math><br />
f_{p}={min}{[max(\frac{P}{{\rho}{v_{t}}{S^{2}}} , 0.5) {,}{1.0}]}<br />
</math><br />
<br />
:<math><br />
f_{\phi}=\frac{1+C_{d1}{\epsilon}}{1+\epsilon^{4}}<br />
</math><br />
<br />
:<math><br />
\epsilon=\frac{d \sqrt{0.3\frac{{v_{t}}{S}}{a_{1}}}}{20v}<br />
</math><br />
<br />
:<math><br />
\zeta_{2}=\zeta_{1}-\frac{\zeta_{3}}{C_{\mu}^{\frac{3}{4}}}+\frac{\kappa^{2}\sigma}{ C_{\mu}^{\frac{1}{2}}}<br />
</math><br />
<br />
'''The model constants are:'''<br />
<br />
:<math><br />
\zeta_{1}=1.5<br />
</math><br />
<br />
:<math><br />
\zeta_{2}=0.95<br />
</math><br />
<br />
:<math><br />
\zeta_{3}=0.16<br />
</math><br />
<br />
:<math><br />
\kappa=0.41<br />
</math><br />
<br />
:<math><br />
a_{1}=\sqrt{C_{\mu}}=0.3<br />
</math><br />
<br />
:<math><br />
C_{11}=10.0<br />
</math><br />
<br />
:<math><br />
C_{12}=1.3<br />
</math><br />
<br />
:<math><br />
C_{d1}=4.7<br />
</math><br />
<br />
:<math><br />
\sigma=0.6<br />
</math><br />
<br />
==References==<br />
*{{reference-paper|author= S. Shuai and R. K. Agarwal|year=2020| title=A New Improved One-Equation Turbulence Model Based on k-kL Closure|rest= AIAA Paper 2020-1075, January 2020}}<br />
*{{reference-paper|author= K. S. Abdol-Hamid, J. R. Carlson, and C. L. Rumsey|year=2016|title= Verification and Validation of the k-kL Turbulence Model in FUN3D and CFL3D Codes|rest= AIAA 2016-3941, 2016}}<br />
[[Category:Turbulence models]]</div>Lin.zhenghao