The Influence of Radial Area Variation on Wind Turbines to the Axial Induction Factor


Improvements in the aerodynamic design will lead to more efficiency of wind turbines and higher power production. In the present study, a 3D parametric gas turbine blade geometry building code, 3DBGB, has been modified in order to include wind turbine design capabilities. This approach enables greater flexibility of the design along with the ability to design more complex geometries with relative ease. The NREL NASA Phase VI wind turbine was considered as a test case for validation and as a baseline by which modified designs could be compared. The design parameters were translated into 3DBGB input to create a 3D model of the wind turbine which can also be imported into any CAD program. Design modifications included replacing the airfoil section and modifying the thickness to chord ratio as a function of span. These models were imported into a high-fidelity CFD package, Fine/TURBO by NUMECA. Fine/TURBO is a specialized CFD platform for turbo-machinery analysis. A code-geomturbo was used to convert the 3D model of the wind turbine into the native format used to define geometries in the Fine/TURBO meshing tool, AutoGrid. The CFD results were post processed using a 3D force analysis code. The radial force variations were found to play a measurable role in the performance of wind turbine blades. The radial component of the blade surface area as it varies in span is the dominant contributor of the radial forces. Through the radial momentum equation, this radial force variation is responsible for creating the streamline curvature that leads to the expansion of the streamtube (slipstream) that is responsible for slowing the wind velocity ahead of the wind turbine leading edge, which is quantified as the axial induction factor. These same radial forces also play a role in changing the slipstream for propellers. Through the design modifications, simulated with CFD and post-processed appropriately, this connection with the radial component of area to the radial forces to the axial induction factor, and finally the wind turbine power is demonstrated. The results from the CFD analysis and 3D force analysis are presented. For the case presented, the power increases by 5.6% due to changes in airfoil thickness only.

Share and Cite:

Sairam, K. and Turner, M. (2014) The Influence of Radial Area Variation on Wind Turbines to the Axial Induction Factor. Energy and Power Engineering, 6, 401-418. doi: 10.4236/epe.2014.611034.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Appalachian State University-North Carolina Wind Energy.
[2] Manwell, J.F. and McGowan, J.G. and Rogers, A.L. (2002) Wind Energy Explained: Theory, Design and Application of Wind Energy. 1st Edition, John Wiley and Sons, Inc., Hoboken.
[3] Dey, S. (2011) Wind Turbine Blade Design System-Aerodynamic and Structural Analysis. Master’s thesis, University of Cincinnati, Cincinnati.
[4] Drela, M. and Youngren, H. XFOIL-Subsonic Airfoil Development System.
[5] Park, K., Turner, M.G., Siddappaji, K. and Dey, S. and Merchant, A. (2011) Optimization of a 3-Stage Booster Part 1: The Axisymmetric Multi-Disciplinary Optimization Approach to Compressor Design. ASME Proceedings, Paper No. GT2011-46569, 1413-1422.
[6] Siddappaji, K. (2012) Parametric 3D Blade Geometry Modeliing Tool for Turbomachinery Systems. Master’s Thesis, University of Cincinnati, Cincinnati.
[7] Siddappaji, K., Turner, M.G., Dey, S., Park, K. and Merchant, A. (2011) Optimization of a 3-Stage Booster-Part 2: The Parametric 3D Blade Geometry Modeling Tool. ASME Proceedings, Paper No. GT2011-46664, 1431-1443.
[8] Giguere, P. and Selig, M.S. (1999) Design of a Tapered and Twisted Blade for the NREL Combined Experiment Rotor. Technical report, NREL/SR-500-26173.
[9] Numeca.
[10] Numeca User Manuals.
[12] Novak, R.A. (1967) Streamline Curvature Computing Procedures for Fluid-Flow Problems. Journal of Engineering for Gas Turbines and Power, 89, 478-490.
[13] Betz, A. (1926) Windenergie und ihre ausnutzung durch wind-muhlen: Vandenhoeckund ruprecht.
[14] Smith Jr., L.H. (1966) The Radial-Equilibrium Equation of Turbomachinery. Journal of Engineering for Gas Turbines and Power, 88, 1-12.
[15] Sairam, K. (2013) The Influence of Radial Area Variation on Wind Turbines to the Axial Induction Factor. Master’s Thesis, University of Cincinnati, Cincinnati.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.