Verification & Validation

Verification

Two important verifications that can be made to check whether the simulation correctly solved the model is to see if mass is balance and if the pressure on the blade has converged. Both have been inspected in the previous section. 

Check iterations

Another essential condition to verify is whether a sufficient number of iterations were performed in obtaining the solution (i.e if the solution converged). The figure below shows how the solution behaves after 3000 iterations. As you can see, the residuals do not change much between 1500 and 3000 iterations. This is why 1500 iterations was deemed appropriate for the sake of this tutorial, considering the reduction in solving time. The solution, however, does appear to converges better after 3000 iterations. 

Check mesh refinement

Finally, it is crucial to perform a mesh refinement study. A finer mesh can help achieve a more precise solution of the model but is more computationally expensive. A CFD analyst thus has to gauge what mesh size will provide a decently accurate solution at a reasonable computing cost. This is of course very dependent on the desired accuracy of results and the application of the project. 

The following table demonstrates how the results change with a greater number of cells. It is quite clear that the mesh created in the tutorial (which has around 350,000 cells) is not fine enough to obtain a sufficiently accurate solution. 

Convergence of the numerical solution is represented by a negligible change in power coefficient from an approximately four-fold increase in number of elements in the mesh. The mesh was refined by adjusting global and local mesh controls: relevance center, face sizing, inflation and sphere of influence. To obtain a mesh of 7.7 million elements (right-most data point in the plot), the relevance center was set to fine; the face size was set to 0.05m; for inflation, the number of layers was increased to 10 at a growth rate of 1.2; for the sphere of influence, the radius was set to 50m and element size was set to 1m.

Check that the domain is sufficiently large

Compare blade tip velocities

The blade tip velocity was found to be 98.05 m/s in CFD-Post. This is basically identical to result obtain from hand-calculations which was 98.10 m/s. Great!

Compare power coefficients

Back in the Pre-Analysis section, we had predicted the power coefficient to be around 0.3. As seen on the convergence plot above, the numerical results do agree well with this value considering a sufficient number of elements in the mesh. For example, using a mesh of 2 million cells, the power coefficient becomes 38% as opposed to the 30% from hand-calculations. These match up quite well considering the many assumptions used in the simple 1D momentum theory. 

At last, we should keep in mind that power coefficient must lie under the Betz limit of 16/27=59.2% for a non-shrouded rotor. Our numerical results correctly fall below this limit. 

Validation

We currently do not have the experimental data to validate our results.

Acknowledgments

This tutorial is made under great help and support from:

• Dr. Rajesh Bhaskaran, Cornell University, 
• Sean Harvey, ANSYS.Inc
• Guang Wu, ANSYS.Inc

Also a big thank you to Robert Zhang (M.Eng) for his help with integrating this tutorial in the wind power class at Cornell University. 

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