Fluid Mechanics and Flight Mechanics

Modal analysis of transonic buffet based on POD and DMD method

  • KOU Jiaqing ,
  • ZHANG Weiwei ,
  • GAO Chuanqiang
Expand
  • School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China

Received date: 2015-11-02

  Revised date: 2015-11-26

  Online published: 2016-01-11

Supported by

National Natural Science Foundation of China (11572252); Program for New Century Excellent Talents in University (NCET-13-0478)

Abstract

Transonic buffet is due to the self-sustained oscillations of shock wave in the unsteady transonic flow, which induces the forced periodically motion of the structure. For aircraft in transonic flow, this phenomenon exists commonly, leading to negative effects on the structural strength and fatigue life. Analysis based on mode decomposition is an effective tool for developing buffet control design. In this paper, two typical mode analysis methods, i.e., proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), are utilized for analyzing the transonic buffet of the OAT15A airfoil. Two techniques are compared by studying the frequency of dominant modes, pressure distributions on the surface and the errors of flow construction. Results indicate that because of the consideration of frequency characteristics in DMD, the critical stable characteristics and dominant frequency of transonic buffet are well captured. Besides, DMD method accurately mimic the time evolutions of flow variables near the shock wave. Although POD method provides relatively small errors for flow reconstruction, it performs worse than DMD near the shock wave region, because of the poorer approximation of pressure evolution in time.

Cite this article

KOU Jiaqing , ZHANG Weiwei , GAO Chuanqiang . Modal analysis of transonic buffet based on POD and DMD method[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2016 , 37(9) : 2679 -2689 . DOI: 10.7527/S1000-6893.2016.0003

References

[1] 张伟伟,高传强,叶正寅. 机翼跨声速抖振研究进展[J]. 航空学报, 2015, 36(4): 1056-1075. ZHANG W W, GAO C Q, YE Z Y. Research advances of wing/airfoil transonic buffet[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(4): 1056-1075 (in Chinese).
[2] LEE B H K. Oscillatory shock motion caused by transonic shock boundary-layer interaction[J]. AIAA Journal, 1990, 28(5): 942-944.
[3] MCDEVITT J B, OKUNO A F. Static and dynamic pressure measurements on a NACA 0012 airfoil in the Ames High Reynolds Number Facility: NASA TP-2485[R]. Washington, D.C.: NASA, 1985.
[4] JACQUIN L, MOLTON P, DECK S, et al. Experimental study of shock oscillation over a transonic supercritical profile[J]. AIAA Journal, 2009, 47(9): 1985-1994.
[5] GAO C Q, ZHANG W W, LIU Y L, et al. Numerical study on the correlation of transonic single-degree-of-freedom flutter and buffet[J]. Science China Physics, Mechanics and Astronomy, 2015, 58(8): 084701-1-084701-12.
[6] DECK S. Numerical simulation of transonic buffet over a supercritical airfoil[J]. AIAA Journal, 2005, 43(7): 1556-1566.
[7] CHEN L W, XU C Y, LU X Y. Numerical investigation of the compressible flow past an aerofoil[J]. Journal of Fluid Mechanics, 2010, 643(1): 97-126.
[8] LEE B H K. Self-sustained shock oscillations on airfoils at transonic speeds[J]. Progress in Aerospace Sciences, 2001, 37(2): 147-196.
[9] 张伟伟, 叶正寅. 基于CFD的气动力建模及其在气动弹性中的应用[J]. 力学进展, 2008, 38(1): 77-86. ZHANG W W, YE Z Y. On unsteady aerodynamic modeling based on CFD technique and its applications on aeroelastic analysis[J]. Advances in Mechanics, 2008, 38(1): 77-86 (in Chinese).
[10] ZHANG W W, YE Z Y. Effect of control surface on airfoil flutter in transonic flow[J]. Acta Astronautica, 2010, 66(7-8): 999-1007.
[11] ZHANG W W, LI X T, YE Z Y, et al. Mechanism of frequency lock-in in vortex-induced vibrations at low Reynolds numbers[J]. Journal of Fluid Mechanics, 2015, 783(1): 72-102.
[12] 寇家庆, 张伟伟, 叶正寅. 基于分层思路的动态非线性气动力建模方法[J]. 航空学报, 2015, 36(12): 3785-3797. KOU J Q, ZHANG W W, YE Z Y. Dynamic nonlinear aerodynamics modeling method based on layered model[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(12): 3785-3797 (in Chinese).
[13] ZHANG W W, WANG B B, YE Z Y, et al. Efficient method for limit cycle flutter analysis by nonlinear aerodynamic reduced-order models[J]. AIAA Journal, 2012, 50(5): 1019-1028.
[14] KOU J Q, ZHANG W W. An approach to enhance the generalization capability of nonlinear aerodynamic reduced-order models[J]. Aerospace Science and Technology, 2016, 49(1): 197-208.
[15] NOACK B R, AFANASIEV K, MORZYNSKI M, et al. A hierarchy of low-dimensional models for the transient and post-transient cylinder wake[J]. Journal of Fluid Mechanics, 2003, 497(1): 335-363.
[16] ROWLEY C W. Model reduction for fluids, using balanced proper orthogonal decomposition[J]. International Journal of Bifurcation and Chaos, 2005, 15(3): 997-1013.
[17] ROWLEY C W, MEZI? I, BAGHERI S, et al. Spectral analysis of nonlinear flows[J]. Journal of Fluid Mechanics, 2009, 641(1): 115-127.
[18] SCHMID P J. Dynamic mode decomposition of numerical and experimental data[J]. Journal of Fluid Mechanics, 2010, 656(1): 5-128.
[19] 李静, 张伟伟, 李新涛. 失稳初期的低雷诺数圆柱绕流POD-Galerkin建模方法研究[J]. 西北工业大学学报, 2015, 33(4): 596-602. LI J, ZHANG W W, LI X T. Researching method of building flow field of initial development stage of low Reynolds number flow past a circular cylinder[J]. Journal of Northwestern Polytechnical University, 2015, 33(4): 596-602 (in Chinese).
[20] WAN Z H, ZHOU L, WANG B F, et al. Dynamic mode decomposition of forced spatially developed transitional jets[J]. European Journal of Mechanics B/Fluids, 2015, 51(1): 16-26
[21] 潘翀, 陈皇, 王晋军. 复杂流场的动力学模态分解[C]//第八届全国实验流体力学学术会议论文集. 广州: 中国科学院南海海洋研究所, 2010: 77-82. PAN C, CHEN H, WANG J J. Dynamical mode decomposition of complex flow field[C]//8th National Conference on Experimental Fluid Mechanics. Guangzhou: South China Sea Institute of Oceanology, 2010: 77-82 (in Chinese).
[22] MARIAPPAN S, GARDNER A D, RICHTER K, et al. Analysis of dynamic stall using dynamic mode decomposition technique[J]. AIAA Journal, 2014, 52(11): 2427-2439.
[23] MOHAN A T, GAITONDE D V, VISBAL M R. Model reduction and analysis of deep dynamic stall on a plunging airfoil using dynamic mode decomposition: AIAA-2015-1058[R]. Reston: AIAA, 2015.
[24] CHEN K K, TU J H, ROWLEY C W. Variants of dynamic mode decomposition: Boundary condition, Koopman, and Fourier analyses[J]. Journal of Nonlinear Science, 2012, 22(6): 887-915.
[25] WYNN A, PEARSON D, GANAPATHISUBRAMANI B, et al. Optimal mode decomposition for unsteady flows[J]. Journal of Fluid Mechanics, 2013, 733(1): 473-503.
[26] JOVANOVI? M R, SCHMID P J, NICHOLS J W. Sparsity-promoting dynamic mode decomposition[J]. Physics of Fluids, 2014, 26(2): 024103-1-024103-22.
[27] TU J H, ROWLEY C W, LUCHTENBERG D M, et al. On dynamic mode decomposition: Theory and applications [J]. Journal of Computational Dynamics, 2014, 1(2): 391-421.
[28] BRUNET V. Computational study of buffet phenomenon with unsteady RANS equations: AIAA-2003-3679[R]. Reston: AIAA, 2003.

Outlines

/