Page History

...

{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 

{latex}$\vec{v}^{\,}_r${latex}

 is the relative velocity (the velocity viewed from the moving frame) and 

{latex}$\vec{\omega}^{\,}${latex}

 is the angular velocity.

Note the additional terms for the Coriolis force (

{latex}$2 \vec{\omega}^{\,} \times \vec{v}^{\,}_r${latex}

) and the centripetal acceleration (

{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 

{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. 

...

This therefore proves that the velocity distribution at theta of 0 and 120 degrees are the same. If we denote theta_1 to represent one of the periodic boundaries for the 1/3 domain and theta_2 being the other boundary, then  

{latex}$\vec{v}^{\,}(r_i,\theta_1)=\vec{v}^{\,}(r_i,\theta_2)${latex}

.

The boundary conditions on the fluid domain are as follow:

...

Plugging in our angular velocity of -2.22 rad/s and using the blade length of 43.2 meters plus 1 meter to account for the distance from the root to the hub, we get

{latex}
\begin{equation*}
v
$$v=-2.22\ \mathrm{rad/s}\ \mathbf{\hat{k}} \times -44.2\ \mathrm{m}\ \mathbf{\hat{i}}
\end{equation*}
\begin{equation*}
v$$
$$v=98.1\ \mathrm{m/s}\ \mathbf{\hat{j}}$$
\end{equation*}
{latex}

...

Start-Up

Please follow along to start this project! It is recommended to have these videos run side by side with your ANSYS project, with the video taking 1/3 of the screen space and the ANSYS window taking 2/3 of the screen space. An even better method is to use two monitors. This would allow running both the tutorial videos and ANSYS in full-screen. For example, the tutorial would be opened up on your laptop and ANSYS would be running on a lab computer. If you use the Cornell lab computers then make sure to bring some earbuds!

...