Pre-Analysis & Start-Up

Pre-Analysis

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

• Mathematical model: (e.g.: We'll look at the governing equations + boundary conditions and the assumptions contained within the mathematical model.)
• Numerical solution procedure in ANSYS: (e.g.: We'll briefly overview the solution strategy used by ANSYS and contrast it to the hand calculation approach.)
• Hand-calculations of expected results: (e.g.: We'll use an analytical solution of the mathematical model to predict the expected stress field from ANSYS. 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 solved here are the conservation of mass and the conservation of momentum (Navier-Stokes equations), taken in a frame of reference moving with the turbine:

• Conservation of Mass:
  
• Navier-Stokes equations, simplified for constant angular velocity
  
  where:
   and 

FLUENT will solve this in a moving frame of reference. This is a good simplification, because with it we don't have to deal with moving mesh. (yet! Keep checking for future tutorials on that!)

Note that we're solving a turbulent problem, and we will assume k-epsilon model with default FLUENT values

Boundary Conditions

The boundary conditions are:

• Inlet (far-field): constant velocity in the x-direction of 10m/s, with turbulent intensity of 5% and turbulent viscosity ratio of 1.
• Outlet (far-field): absolute pressure of 101325 Pa, or 1 atm, with same turbulent parameters as above. 
• Blades: wall, so no velocity. (No-slip condition).

Numerical Solution Procedure in ANSYS

FLUENT will follow the Finite-Volume Method and will divide the domain into multiple control volumes or "cells".
From the integral form of the governing equations, it will perform a control volume balance for each each and write algebric nonlinear equations for them, and then linearize these equations..
Next, it will solve iteratively this equations and stop the iteration when the Residuals are below a certain specified tolerance.

Velocity, pressure, angular velocity and turbulence parameter k are calculated in the cell centers, after inverting the matrix of the system of algebric equations in cell-center values.
With these values, the post-process tool will derive everything else that we might want, like wall shear, etc.

Hand-Calculations of Expected Results

Calculate Cp?

We expect large vortices downstream the turbine?

Start-Up

Go to Step 2: Geometry

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