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Pre-Analysis & Start-Up
Pre-Analysis
In the Pre-Analysis step, we'll review the following:
- Mathematical model: We'll look at the governing equations + boundary conditions and the assumptions contained within the mathematical model.
- Numerical solution procedure in ANSYS: We'll briefly overview the solution strategy used by ANSYS and contrast it to the hand calculation approach.
- Hand-calculations of expected results: We'll use an analytical solution of the mathematical model to predict the expected particle velocity at the blade tip. We'll pay close attention to additional assumptions that have to be made in order to obtain an analytical solution.
Mathematical Model
Governing Equations
The governing equations are the continuity and Navier-Stokes equations. These equations are written in a steady rotating frame of reference. This has the advantage of making our simulation not require a moving mesh.
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 as follow:
Conservation of mass:
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\begin
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\frac
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+\nabla \cdot \rho \vec
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^
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_r =0
\end
Conservation of Momentum (Navier-Stokes):
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\begin
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\nabla \cdot (\rho \vec
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^
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_r \vec
^
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_r)+\rho(2 \vec
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^
\times \vec
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^
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_r+\vec
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^
\times \vec
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^
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\times \vec
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^
)=-\nabla p +\nabla \cdot \overline{\overline{\tau}}_r
\end
Where
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$vec
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^
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_r)$
is the relative velocity (the velocity viewed from the moving frame) and
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$vec
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^
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)$
is the angular velocity. 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.
Under Construction
Numerical Solution Procedure in ANSYS
Under Construction
Hand-Calculations of Expected Results
One simple hand-calculation that we can do now before even starting our simulation is to find theoretical wind velocity at the tip. We can then later compare our answer with what we get from our simulation to verify that they agree.
The velocity, v, on the blade should follow the formula
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\begin
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v=r \times \omega_{}
\end
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\begin
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\mathbf{m \ddot
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+ k x =0}
\end
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\begin
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m \ddot
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+ k x =0
\end
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\begin
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\boldsymbol{m \ddot
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+ k x =0}
\end
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
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\begin
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v=-2.22\ \mathrm
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\ \mathbf{\hat{k}} \times -44.2\ \mathrm
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\ \mathbf{\hat{i}}
\end
\begin
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v=98.1\ \mathrm
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\ \mathbf{\hat{j}}
\end
Start-Up
*Insert video
It will cover:
-Opening ANSYS
-Setting up the project schematic for the geometry and the Fluid flow, naming them.
Under Construction