CFD airfoil profile drag calculation using far-field wake analysis
Le Roux, V.
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With the ever increasing cost of experimental data and the ultimate decrease of project lifespan from design to implementation it has become the aerodynamicist?s main priority to design and model new ideas with precise accuracy. There is thus no room for discrepancies that arise between various computational fluid dynamic simulation packages. However, as we live in a realistic world these discrepancies do turn up from time to time, and it is the sole purpose of engineers to minimize and ultimately eliminate these discrepancies. In the field of CFD simulations the main discrepancies that give rise to never-ending headaches are those found when comparing the experimental drag to the drag predicted by simulation software implementing panel codes and the near-field method – in other words the differences in drag predicted by the Squire-Young model, the near-field model and the far-field, also referred to as the “wake rake model”. One such example of differences between drag predicted by the Squire-Young model and the near-field model can be seen in Figure 1, Chapter 1 where two aerofoils were analysed at a Reynolds number of 1 million and a Mach number of 0. In Figure 1 it can clearly be seen that for the XFOIL simulation with 120 panels there is a clear distinction between the performance of the ST1 and OPT110 aerofoils. As for the Star-CCM+ simulation set-up with a fine mesh and the SST k – w, turbulence and the y – e transition model, the results show that both aerofoils have similar performance characteristics. One of the main reasons for these discrepancies can be ascribed to the over-sensitivity of the pressure drag component to the level of grid refinement used in the simulation. The reason why drag accuracy is sensitive to grid definition is because an inadequate grid at positions of high curvature means that the boundary layer in these portions of the model is not accurately solved. These inaccuracies are then superimposed when the near-field method surface integrates these erroneously solved flow variables to find the profile drag. Historically the far-field methods implemented by experimentalists have hinted at a solution to solve this overdependence of drag on the level of grid refinement. This is because rather than using the locally solved flow variables that can be contaminated by spurious drag, the far-field method uses a momentum deficit at the far-downstream wake to calculate the total profile drag. Although this method potentially solves the discrepancies between the near-field and far-field method, a concise procedure to implement the far-field method to a converged viscous unstructured grid study has not yet been developed. Thus the main theme of this thesis is to address the problem of discrepancies arising in the drag predicted by the near-field and far-field method. In this thesis reliable methods of far-field drag extraction from a 2-D viscous unstructured CFD study will be developed and validated. To validate the performance of the proposed far-field methods against the performance of the panel code XFOIL and the near-field method of Star-CCM+, it was, in the first place, necessary to acquire reliable experimental data. The aerofoil data was acquired from the UIUC low-speed subsonic wind tunnel. Experiments were conducted in 1996, 1997 and 2002 respectively (Selig & McGranahan, 2003). The simulations for our own validation purposes were conducted between Reynolds numbers of 400 000 and 500 000 and can be regarded as low Reynolds number simulations. The aerofoils used in this thesis were the E231, S834 and FX 63-137 profiles designed for small wind turbine applications. As a first objective the performance of XFOIL was validated with regard to the UIUC low-speed subsonic wind tunnel experimental data for the three above mentioned aerofoils. This was done in two phases: I. The first was to analyse the reliability of the standard XFOIL simulation against our benchmark wind tunnel data. II. The second was to confirm the performance of a new proposed geometry importation method, aimed to rectify the problem of XFOIL to over predict lift and under predict drag in high separation areas. The results of the XFOIL validation phase carried out in preparation for this thesis are discussed in Chapter 3, and the newly proposed method of geometry importation to non-linearly cluster aerofoil panel nodes more densely in areas of high interest, appear in Appendix B. The main objective of this thesis is to report on the development, implementation and validation of various far-field drag extraction methods incorporated into a converged unstructured grid CFD simulation. Chapter 4 deals with the development and Chapter 5 with the implementation of these far-field drag extraction methods. Tables 22, 27 and 30 Chapter 5 show some promising results in favour of the proposed far-field method above the near-field method for drag calculation. In these tables the maximum drag count error (for angle of attack range simulated) of the near-field and various far-field methods are displayed with regard to experimental data. The reason why the various proposed far-field methods of drag prediction exhibit such a significant improvement over the accuracy of the drag prediction of the near-field method is due to a reduced sensitivity to spurious drag. In the cases investigated the far-field method has a reduced sensitivity to the mesh refinement in areas of high curvature. For this reason the validity of the pressure drag calculation is conserved to a higher degree. As artificial spurious drag is implicitly added to the pressure drag term of the near-field method, it can clearly be seen from the figures in Chapter 5 and Chapter 6 that the far-field drag extraction yields profile drag values lower than the near-field method, and are ultimately closer to the experimental values.
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