Harmonic balance methods applied to computational fluid dynamics problems

International Journal of Computational Fluid Dynamics

Volumn 27, Issue 2, 2013, Pages 52-67

  Hall, Kenneth C ^a   Ekici, Kivanc ^b   Thomas, Jeffrey P ^a   Dowell, Earl H ^a  

^a Duke University   (United States)

^b University of Tennessee   (United States)

Author keywords

computational fluid dynamics; harmonic balance; numerical stability; rotorcraft; turbomachinery; unsteady aerodynamics and aeroelasticity

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS MODELS; COURANT-FRIEDRICHS-LEWY; HARMONIC BALANCE; HARMONIC BALANCE ANALYSIS; HARMONIC BALANCE METHOD; NON-DIMENSIONAL PARAMETERS; ROTORCRAFT; UNSTEADY AERODYNAMICS;

AERODYNAMICS; COMPUTATIONAL FLUID DYNAMICS; CONVERGENCE OF NUMERICAL METHODS; PLATES (STRUCTURAL COMPONENTS); TURBOMACHINERY;

AEROELASTICITY;

EID: 84875833202     PISSN: 10618562     EISSN: 10290257     Source Type: Journal    
DOI: 10.1080/10618562.2012.742512     Document Type: Review

References (51)

1. Allen, C.B. 2004. An unsteady multiblock multigrid scheme for lifting forward flight rotor simulation. International Journal for Numerical Methods in Fluids, 45(9): 973-984. doi:10.1002/fld.711
2. Breard, C. Acoustic propagation and radiation modeling of lined duct with linear and non-linear frequency-domain solver. AIAA Paper 2003-3265.
3. Butsuntorn, N. and Jameson, A. Time spectral method for rotorcraft flow. AIAA Paper 2008-0403.
4. Caradonna, F.X. and Tung, C. 1981. Experimental and analytical studies of a model helicopter rotor in Hover, Moffett Field, CA: NASA Ames Research Center. Technical Manual NASA TM-81232
5. Chen, T., Vasanthakumar, P. and He, L. 2001. Analysis of unsteady blade row interaction using nonlinear harmonic approach. Journal of Propulsion and Power, 17(3): 651-658. doi:10.2514/2.5792
6. Choi, S. Validation study of aerodynamic analysis tools for design optimization of helicopter rotors. AIAA Paper 2007-3929.
7. Clark, W.S. 1992. Prediction of unsteady flows in turbomachinery using the linearized Euler equations on deforming grids, Durham, NC: Duke University. Thesis (Masters)
8. Clark, W.S. and Hall, K.C. 2000. A time-linearized Navier-Stokes analysis of stall flutter. Journal of Turbomachinery, 122: 467-476. doi:10.1115/1.1303073
9. Custer, C.H. Unsteady simulation of a 1.5 stage turbine using an implicitly coupled nonlinear harmonic balance method. ASME Paper GT2012-69690.
10. Davis, R.L. Prediction of 3-D unsteady flow in multi-stage turbomachinery using an implicit dual time-step approach. AIAA Paper 96-2565.
11. Ekici, K. and Hall, K.C. Nonlinear analysis of unsteady flows in multistage turbomachines using the harmonic balance technique. AIAA Paper 2006-422.
12. Ekici, K. and Hall, K.C. 2007. Nonlinear analysis of unsteady flows in multistage turbomachines using harmonic balance. AIAA Journal, 45(5): 1047-1057. doi:10.2514/1.22888
13. Ekici, K. and Hall, K.C. 2008. Nonlinear frequency-domain analysis of unsteady flows in turbomachinery with multiple excitation frequencies. AIAA Journal, 46(8): 1912-1920. doi:10.2514/1.26006
14. Ekici, K. and Hall, K.C. 2011. Harmonic balance analysis of limit cylce oscillations in turbomachinery. AIAA Journal, 49(7): 1478-1487. doi:10.2514/1.J050858
15. Ekici, K., Hall, K.C. and Dowell, E.H. 2008. Computationally fast harmonic balance methods for unsteady aerodynamic predictions of helicopter rotors. Journal of Computational Physics, 227(12): 6206-6225. doi:10.1016/j.jcp.2008.02.028
16. Ekici, K., Hall, K.C. and Kielb, R.E. 2010. Harmonic balance analysis of blade row interactions in a transonic compressor. Journal of Propulsion and Power, 26(2): 335-343. doi:10.2514/1.43879
17. Gentilli, N.C. 2010. Efficient solution of unsteady nonlinear flows using a multiple zone harmonic balance technique, Durham, NC: Duke University. Thesis (Masters)
18. Gerolymos, G.A., Michon, G. and Neubauer, J. 2002. Analysis and application of chorochronic periodicity in turbomachinery rotor/stator interaction computations. Journal of Propulsion and Power, 18(6): 1139-1152. doi:10.2514/2.6065
19. Gopinath, A. Three-dimensional unsteady multi-stage turbomachinery simulations using the harmonic balance technique. AIAA Paper 2007-0892.
20. Hall, K. and Clark, W. 1993. Linearized Euler predictions of unsteady aerodynamic loads in cascades. AIAA Journal, 31(3): 540-550. doi:10.2514/3.11363
21. Hall, K.C. 1998. "Computation of unsteady nonlinear flows in cascades using a harmonic balance technique". In Kerrebrock symposium-a symposium in honor of Professor Jack L. Kerrebrock's 70th birthday, Cambridge, MA: MIT.
22. Hall, K.C. and Crawley, E.F. 1989. Calculation of unsteady flows in turbomachinery using the linearized Euler equations. AIAA Journal, 27(6): 777-787. doi:10.2514/3.10178
23. Hall, K.C., Thomas, J.P. and Clark, W.S. Computation of unsteady nonlinear flows in cascades using a harmonic balance technique. 9th international symposium on unsteady aerodynamics, aeroacoustics and aeroelasticity of turbomachines.
24. Hall, K.C., Thomas, J.P. and Clark, W.S. 2002. Computation of unsteady nonlinear flows in cascades using a harmonic balance technique. AIAA Journal, 40(5): 879-886. doi:10.2514/3.15137
25. He, L. 2010. Fourier methods for turbomachinery applications. Progress in Aerospace Sciences, 46(8): 329-341. doi:10.1016/j.paerosci.2010.04.001
26. He, L. 2002. Analysis of rotor-rotor and stator-stator interferences in multi-stage turbomachines. Journal of Turbomachinery, 124(4): 564-571. doi:10.1115/1.1508382
27. He, L. and Denton, J.D. 1994. Three-dimensional time-marching inviscid and viscous solutions for unsteady flows around vibrating blades. Journal of Turbomachinery, 116(3): 469-476. doi:10.1115/1.2929436
28. He, L. and Ning, W. 1998. Efficient approach for analysis of unsteady viscous flows in turbomachines. AIAA Journal, 36(11): 2005-2012. doi:10.2514/2.328
29. Kielb, R. 2006. Non-synchronous vibration of turbomachinery airfoils, Durham, NC: Department of Mechanical Engineering and Materials Science. Technical report
30. Kumar, M. and Murthy, V.R. Analysis of flow around multibladed rotor using CFD in the frequency domain. AIAA Paper 2007-3806.
31. McMullen, M., Jameson, A. and Alonso, J. 2006. Demonstration of nonlinear frequency domain methods. AIAA Journal, 44(7): 1428-1435. doi:10.2514/1.15127
32. McMullen, M., Jameson, A. and Alonso, J.J. Acceleration of convergence to a periodic steady state in turbomachinery flows. AIAA Paper 2001-152.
33. McMullen, M., Jameson, A. and Alonso, J.J. Application of a non-linear frequency domain solver to the Euler and Navier-Stokes equations. AIAA Paper 2002-120.
34. Nadarajah, S., McMullen, M. and Jameson, A. Optimal control of unsteady flows using time accurate and non-linear frequency domain methods. AIAA Paper 2003-3875.
35. Richman, M. and Fleeter, S. Navier-Stokes simulation of IGV-rotor-stator interactions in a transonic compressor. AIAA Paper 2000-3379.
36. Ronch, A.D. Linear frequency domain and harmonic balance predictions of dynamic derivatives. AIAA Paper 2010-4699.
37. Sicot, F., Dufour, G. and Gourdain, N. 2012. A time-domain harmonic balance method for rotor/stator interactions. Journal of Turbomachinery, 134(1): 011001-1-011001-011001-1-01100113-011001-13. doi:10.1115/1.4003210
38. Sicot, F., Puigt, G. and Montagnac, M. 2008. Block-Jacobi implicit algorithms for the time spectral method. AIAA Journal, 46(12): 3080-3089. doi:10.2514/1.36792
39. Thomas, J.P., Dowell, E.H. and Hall, K.C. 2002. Nonlinear inviscid aerodynamic effects on transonic divergence, flutter, and limit-cycle oscillations. AIAA Journal, 40(4): 638-646. doi:10.2514/2.1720
40. Thomas, J.P., Hall, K.C. and Dowell, E.H. A harmonic balance approach for modeling nonlinear aeroelastic behavior of wings in transonic viscous flow. AIAA Paper 2003-1924.
41. Thomas, J.P., Hall, K.C. and Dowell, E.H. 2005a. Discrete adjoint approach for modeling unsteady aerodynamic design sensitivities. AIAA Journal, 43(9): 1931-1936. doi:10.2514/1.731
42. Thomas, J.P. Modeling limit cycle oscillation behavior of the F-16 fighter using a harmonic balance approach. AIAA Paper 2004-1696.
43. Thomas, J.P. Further investigation of modeling limit cycle oscillation behavior of the f-16 fighter using a harmonic balance approach. AIAA Paper 2005-1917.
44. Thomas, J. Unsteady flow computation using a harmonic balance approach implemented about the OVERFLOW 2 flow solver. AIAA Paper 2009-4270.
45. van der Weide, E., Gopinath, A. and Jameson, A. Turbomachinery applications with the time spectral method. AIAA Paper 2005-4905.
46. Vilmin, S. Unsteady flow modeling across the rotor/stator interface using the nonlinear harmonic method. ASME Paper GT2006-90210.
47. Weiss, J.M., Subramanian, V. and Hall, K.C. Simulation of unsteady turbomachinery flows using an implicitly coupled nonlinear harmonic balance method. ASME Paper GT2011-46367.
48. Welch, G., Milanovic, I. and Zaman, K. Application of harmonic balance technique to synthetic jets in cross-flow. AIAA Paper 2005-1111.
49. Woodgate, M.A. and Badcock, K.J. 2009. Implicit harmonic balance solver for transonic flow with forced motions. AIAA Journal, 47(4): 893-901. doi:10.2514/1.36311
50. Woodgate, M.A. and Barakos, G.N. Implicit CFD methods for fast analysis of rotor flows. AIAA Paper 2012-0421.
51. Yang, Z., Mavriplis, D. and Sitaraman, J. Prediction of helicopter maneuver loads using BDF/time spectral method on unstructured meshes. AIAA Paper 2011-1122.