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Pre-Analysis & Start-Up

Pre-Analysis

In the Pre-Analysis step, we'll review the following:

Mathematical

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Mathematical Model 

Governing Equations

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This form of the Navier Stokes equations has additional terms, namely the centripetal acceleration term and the Coriolis term. The equations that we will use looks look as followfollows:

Conservation of mass:

{latex}
\begin{equation*}
\frac{\partial \rho}{\partial t}+\nabla \cdot \rho \vec{v}^{\,}_r =0
\end{equation*}
{latex}

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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. 

Important: We use the Reynolds Averaged form of continuity and momentum and use the SST k-omega turbulence model to close the equation set. 

Boundary Conditions

We model only 1/3 of the full domain using periodicity assumptions:

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

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

Outlet: Pressure of 1 atm 

Blade: No-slip

Side Boundaries: Periodic

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

Hand-Calculations of Expected Results

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