Rotor Flow Analysis using Animplicit Harmonic Balance Method

Authors: D. Im, S. Choi, H. Kwon, S. H. Park, J. H. Kwon

Abstract:

This paper is an extension of a previous work where a diagonally implicit harmonic balance method was developed and applied to simulate oscillatory motions of pitching airfoil and wing. A more detailed study on the accuracy, convergence, and the efficiency of the method is carried out in the current paperby varying the number of harmonics in the solution approximation. As the main advantage of the method is itsusage for the design optimization of the unsteady problems, its application to more practical case of rotor flow analysis during forward flight is carried out and compared with flight test data and time-accurate computation results.

Keywords: Design optimization, Implicit harmonic balancemethod, number of harmonics, rotor flows

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1062380

References:

[1] Im, D., Kwon, J. H., and Park, S. H., "Periodic Unsteady Flow Analysis Using a Diagonally Implicit Harmonic Balance Method", submitted to the AIAA Journal, Jan. 2011
[2] Choi, S., and Datta, A., "CFD Prediction of Rotor Loads Using Time- Spectral Method and ExactFluid-Structure Interface", 26th AIAA Applied Aerodynamics Conference, Aug. 2008, Honolulu,Hawaii.
[3] Choi, S., and Datta, A., "CFD Prediction of Rotor Loads Using Time- Spectral Method and ExactFluid-Structure Interface", (accepted for Journal of American Helicopter Society, under revision.)
[4] Ekici, K., Hall, K.C. and Dowell, E.H., "Computationally Fast Harmonic Balance Methods for Unsteady Aerodynamic Predictions of Helicopter Rotors," Journal of Computational Physics, Vol.227, 2008, pp. 6206- 6225
[5] Choi, S., Potsdam, M., Lee, K., Iaccarino, G., and Alonso, J. J., "Helicopter Rotor Design Usinga Time-Spectral and Adjoint-Based Method", 12th AIAA/ISSMO Multidisciplinary Analysis andOptimization Conference, Sep. 2008, British Columbia, Canada.
[6] Gopinath, A.K. and Jameson, A., "Time Spectral Method for Periodic Unsteady Computations over Two- and Three- Dimensional Bodies," 43rd AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2005-1220, Reno, NV, January 10-13, 2005.
[7] McMullen, M., Jameson, A., and Alonso, J., "Demonstration of Nonlinear Frequnecy Domain Methods," AIAA Journal Vol.44, No.7, 2006,pp. 1428-1435
[8] Dawson, S., Marcolini, M., Booth, E., Straub, F. K., Hassan, A. A., Tadghighi,H. and Kelly, H., "Wind Tunnel Test of An Active Flap Rotor: BVI Noise andVibration Reduction," paper presented at the 51st Annual Forum of theAmerican Helicopter Society, May 1995.
[9] A. R. Piziali "An experimental investigation of 2D and 3D oscillating wing aerodynamcis for a range of angles of attack including stall," NASA TM 4632, 1994
[10] Hall, K.C., Thomas, J.P., and Clark, W.S., "Computation of Unsteady Nonlinear Flows in Cascades Using a Harmonic Balance Technique," AIAA Journal, Vol. 40, No. 5, 2002, pp. 879-886,
[11] Thomas, J.P., Custer, C.H., Dowell, E.H. and Hall, K.C., "Unsteady Flow Computation Using a Harmonic Balance Approach Implemented about the OVERFLOW 2 Flow Solver," 19thAIAA Computational Fluid Dynamics Conference,AIAA Paper 2009-4270, San Antonio, TX, June, 2009.
[12] Pulliam, T.H. andChaussee, D.S., "A Diagonal Form of an Implicit Approximate-Factorization Algorithm," Journal of Computational Physics, Vol.39, 1981, pp. 347-363
[13] Jameson, A., "Time Dependent Calculations Using Multigrid with Applications to Unsteady Flows Past Airfoils and Wings," AIAA 10th CFD Conference, AIAA Paper 91-1596 , June, 1991
[14] Park, S.H. and Kwon, J.H., "Implementation of Turbulence Models in an Implicit Multigrid Method," AIAA Journal, Vol.42, No.7, 2004, pp. 1348-1357