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{latex}
\begin{equation*}
\vec{v}^{\,}(r_1,\theta) = \vec{v}^{\,}(r_1,\theta_1 - 120n)
\end{equation*}
{latex}

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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:

Inlet: Velocity of 12 m/s with turbulent intensity of 5% and turbulent viscosity ratio of 10 

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Side Boundaries: Periodic

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Numerical Solution Procedure in ANSYS

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This huge set of algebraic equations is inverted through an iterative process. The matrix to be inverted is huge but sparse. 

Solver: Pressure-based

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In FLUENT, we will use the pressure-based solver. 

Hand-Calculations of Expected Results

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