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{latex}
\begin{equation*}
\nabla \cdot (\rho \vec{v}^{\,}_r \vec{v}^{\,}_r)+\rho(2 \vec{\omega}^{\,} \times \vec{v}^{\,}_r+\vec{\omega}^{\,} \times \vec{\omega}^{\,} \times \vec{r}^{\,})=-\nabla p +\nabla \cdot \overline{\overline{\tau}}_r
\end{equation*}
{latex} |
Where
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{latex}$\vec{v}^{\,}_r${latex} |
is the relative velocity (the velocity viewed from the moving frame) and
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{latex}$\vec{\omega}^{\,}${latex} |
is the angular velocity.
Note the additional terms for the Coriolis force (
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{latex}$2 \vec{\omega}^{\,} \times \vec{v}^{\,}_r${latex} |
) and the centripetal acceleration (
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{latex}$\vec{\omega}^{\,} \times \vec{\omega}^{\,} \times \vec{r}^{\,}${latex} |
) in the Navier-Stokes equations. In Fluent, we'll turn on the additional terms for a moving frame of reference and input
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{latex}$\vec{\omega}^{\,}= -2.22 \mathbf{\hat{k}}${latex} |
.
For more information about flows in a moving frame of reference, visit ANSYS Help View > Fluent > Theory Guide > 2. Flow in a Moving Frame of Reference and ANSYS Help Viewer > Fluent > User's Guide > 9. Modeling Flows with Moving Reference Frames.
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{latex}
$$v=-2.22\ \mathrm{rad/s}\ \mathbf{\hat{k}} \times -44.2\ \mathrm{m}\ \mathbf{\hat{i}}
$$
$$v=98.1\ \mathrm{m/s}\ \mathbf{\hat{j}}$$
{latex} |
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