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Active control of transonic buffet flow

Published online by Cambridge University Press:  05 July 2017

Chuanqiang Gao ,
Weiwei Zhang Open the ORCID record for Weiwei Zhang [Opens in a new window] ,
Jiaqing Kou ,
Yilang Liu  and
Zhengyin Ye
Chuanqiang Gao
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China
Weiwei Zhang*
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China
Jiaqing Kou
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China
Yilang Liu
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China
Zhengyin Ye
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China
*
†Email address for correspondence: aeroelastic@nwpu.edu.cn
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Abstract

Transonic buffet is a phenomenon of aerodynamic instability with shock wave motions which occurs at certain combinations of Mach number and mean angle of attack, and which limits the aircraft flight envelope. The objective of this study is to develop a modelling method for unstable flow with oscillating shock waves and moving boundaries, and to perform model-based feedback control of the two-dimensional buffet flow by means of trailing-edge flap oscillations. System identification based on the ARX algorithm is first used to derive a linear model of the input–output dynamics between the flap rotation (the control input) and the lift and pitching moment coefficients (system outputs). The model features a pair of unstable complex-conjugate poles at the characteristic buffet frequency. An appropriate reduced-order model (ROM) with a lower dimension is further obtained by a balanced truncation method that keeps the pair of unstable poles in the unstable subspace but truncates the dynamics in the stable subspace. Based on this balanced ROM, two kinds of feedback control are designed by pole assignment and linear quadratic methods respectively. These independent designs, however, result in similar suboptimal static output feedback control laws. When introduced in numerical simulations, they are both able to completely suppress the buffet instability. Furthermore, the resulting controllers are even able to stabilize buffet flows with nonlinear disturbances and in off-design flow conditions, thus implying their robustness. The analysis of the feedback control laws indicates that parameters (frequency and phase) corresponding to the ‘anti-resonance’ of the linear input–output model are vital for optimal control. The best performance is obtained when the control operates close to the ‘anti-resonance’, which is supported by the optimal frequency and the phase of the open-loop control as well as by the optimal phase of the closed-loop control.

JFM classification

Compressible Flows: Compressible Flows Flow Control: Flow Control Nonlinear Dynamical Systems: Low-dimensional models
Type
Papers
Information
Journal of Fluid Mechanics , Volume 824 , 10 August 2017 , pp. 312 - 351
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Copyright
© 2017 Cambridge University Press 

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References

Ahuja, S. & Rowley, C. W. 2010 Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators. J. Fluid Mech. 645, 447–478.Google Scholar
Åkervik, E., Brandt, L., Henningson, D. S., Hoepffner, J., Marxen, O. & Schlatter, P. 2006 Steady solutions of the Navier–Stokes equations by selective frequency damping. Phys. Fluids 18, 68102.Google Scholar
Akhtar, I., Borggaard, J., Burns, J. A., Imtiza, H. & Zietsman, L. 2015 Using functional gains for effective sensor location in flow control: a reduced-order modeling approach. J. Fluid Mech. 781, 622–656.CrossRefGoogle Scholar
Bagheri, S., Henningson, D. S., Hoepffner, J. & Schmid, P. J. 2009 Input–output analysis and control design applied to a linear model of spatially developing flows. Appl. Mech. Rev. 62, 020803.CrossRefGoogle Scholar
Barbagallo, A., Sipp, D. & Schmid, P. J. 2009 Closed-loop control of an open cavity flow using reduced-order models. J. Fluid Mech. 641, 1–50.Google Scholar
Barbagallo, A., Sipp, D. & Schmid, P. J. 2011 Input–output measures for model reduction and closed-loop control: application to global modes. J. Fluid Mech. 685, 23–53.Google Scholar
Belson, B. A., Semeraro, O., Rowley, C. W. & Henningson, D. S. 2013 Feedback control of instabilities in the two-dimensional Blasius boundary layer: the role of sensors and actuators. Phys. Fluids 25, 054106.Google Scholar
Brunton, S. L., Dawson, S. T. M. & Rowley, C. W. 2014 State-space model identification and feedback control of unsteady aerodynamic forces. J. Fluids Struct. 50, 253–270.CrossRefGoogle Scholar
Brunton, S. L. & Noack, B. R. 2015 Closed-loop turbulence control: progress and challenges. Appl. Mech. Rev. 67, 050801.CrossRefGoogle Scholar
Carini, M., Pralits, J. O. & Luchini, P. 2015 Feedback control of vortex shedding using a full-order optimal compensator. J. Fluids Struct. 53, 15–25.Google Scholar
Caruana, D., Mignosi, A. & Corrège, M. 2005 Buffet and buffeting control in transonic flow. Aerosp. Sci. Technol. 9 (7), 605–616.Google Scholar
Caruana, D., Mignosi, A. & Robitaillié, C. 2003 Separated flow and buffeting control. Flow Turbul. Combust. 71, 221–245.Google Scholar
Choi, H., Jeon, W. P. & Kim, J. 2008 Control of flow over a bluff body. Annu. Rev. Fluid Mech. 40, 113–139.Google Scholar
Crouch, J. D., Garbaruk, A., Magidov, D. & Travin, A. 2009 Origin of transonic buffet on aerofoils. J. Fluid Mech. 628, 357–369.Google Scholar
Dandois, J. 2016 Experimental study of transonic buffet phenomenon on a 3D swept wing. Phys. Fluids 28, 016101.CrossRefGoogle Scholar
Dandois, J., Lepage, A., Dor, J. & Molton, P. 2014 Open and closed-loop control of transonic buffet on 3D turbulent wings using fluidic devices. Comptes Rendus Mecanique 342, 425–436.Google Scholar
Davison, E. J. & Wang, S. H. 1975 On pole assignment in linear multivariable systems using output feedback. IEEE Trans. Autom. Control 20 (4), 516–518.Google Scholar
Doerffer, P., Hirsch, C. & Dussauge, J. P. 2011 NACA0012 with aileron. In Unsteady Effects of Shock Wave Induced Separation, pp. 101–131. Springer.Google Scholar
Dowell, E. H. & Hall, K. C. 2001 Modeling of fluid–structure interaction. Annu. Rev. Fluid Mech. 33, 445–490.Google Scholar
Eastwood, J. & Jarrett, J. 2012 Toward designing with three-dimensional bumps for lift/drag improvement and buffet alleviation. AIAA J. 50 (12), 2882–2898.CrossRefGoogle Scholar
Fabbiane, N., Semeraro, O., Simon, B. & Henningson, D. S. 2014 Adaptive and model-based control theory applied to convectively unstable flows. Appl. Mech. Rev. 66, 060801.Google Scholar
Fabbiane, N., Simon, B., Fischer, F., Grundmann, S., Bagheri, S. & Henningson, D. S. 2015 On the role of adaptivity for robust laminar flow control. J. Fluid Mech. Rapids 767, R1.Google Scholar
Flinois, T. & Morgans, A. S. 2016 Feedback control of unstable flows: a direct modelling approach using the eigensystem realisation algorithm. J. Fluid Mech. 793, 41–78.Google Scholar
Flinois, T. L. B., Morgans, A. S. & Schmid, P. J. 2015 Projection-free approximate balanced truncation of large unstable systems. Phys. Rev. E 92, 023012.Google Scholar
Franke, M. 2014 Eigenvalue assignment by static output feedback – on a new solvability condition and the computation of low gain feedback matrices. Intl J. Control 87 (1), 64–75.Google Scholar
Gao, C. Q., Zhang, W. W., Li, X. T., Liu, Y. L., Quan, J. G., Ye, Z. Y. & Jiang, Y. W. 2017 Mechanism of frequency lock-in in transonic buffeting flow. J. Fluid Mech. 818, 528–561.Google Scholar
Gao, C. Q., Zhang, W. W., Liu, Y. L., Ye, Z. Y. & Jiang, Y. W. 2015 Numerical study on the correlation of transonic single-degree-of-freedom flutter and buffet. Sci. China – Phys. Mech. Astron. 58, 084701.Google Scholar
Gao, C. Q., Zhang, W. W. & Ye, Z. Y. 2016a A new viewpoint on the mechanism of transonic single-degree-of-freedom flutter. Aerosp. Sci. Technol. 52, 144–156.Google Scholar
Gao, C. Q., Zhang, W. W. & Ye, Z. Y. 2016b Numerical study on closed-loop control of transonic buffet suppression by trailing edge flap. Comput. Fluids 132, 32–45.Google Scholar
Gautier, N. & Aider, J. L. 2014 Feed-forward control of a perturbed backward-facing step flow. J. Fluid Mech. 756, 181–196.Google Scholar
Gautier, N., Aider, J. L., Duriez, T., Noack, B. R., Segond, M. & Abel, M. 2015 Closed-loop separation control using machine learning. J. Fluid Mech. 770, 442–457.Google Scholar
Guzman, I. J., Sipp, D. & Schmid, P. J. 2014 A dynamic observer to capture and control perturbation energy in noise amplifiers. J. Fluid Mech. 758, 728–753.Google Scholar
He, G., Wang, J. & Pan, C. 2013 Initial growth of a disturbance in a boundary layer influenced by a circular cylinder wake. J. Fluid Mech. 718, 116–130.CrossRefGoogle Scholar
He, S., Yang, Z. C. & Gu, Y. S. 2014 Transonic limit cycle oscillation analysis using aerodynamic describe functions and superposition principle. AIAA J. 52 (7), 1393–1403.Google Scholar
Hervé, A., Sipp, D., Schmid, P. J. & Samuelides, M. 2012 A physics-based approach to flow control using system identification. J. Fluid Mech. 702, 26–58.CrossRefGoogle Scholar
Huang, J., Xiao, Z. & Liu, J. 2012 Simulation of shock wave buffet and its suppression on an OAT15A supercritical airfoil by IDDES. Sci. China – Phys. Mech. Astron. 55 (2), 260–271.CrossRefGoogle Scholar
Huang, S. C. & Kim, J. 2008 Control and system identification of a separated flow. Phys. Fluids 20, 101509.Google Scholar
Illingworth, S., Morgans, A. & Rowley, C. 2012 Feedback control of cavity flow oscillations using simple linear models. J. Fluid Mech. 709, 223–248.CrossRefGoogle Scholar
Iovnovich, M. & Raveh, D. E. 2012 Reynolds-averaged Navier–Stokes study of the shock-buffet instability mechanism. AIAA J. 50 (4), 880–890.Google Scholar
Jacquin, L., Molton, P. & Deck, S. 2009 Experimental study of shock oscillation over a transonic supercritical profile. AIAA J. 47 (9), 1985–1994.Google Scholar
Jordi, B. E., Cotter, C. J. & Sherwin, S. J. 2014 Encapsulated formulation of the selective frequency damping method. Phys. Fluids 26, 034101.Google Scholar
Jovanović, M. R., Schmid, P. J. & Nichols, J. W. 2014 Sparsity-promoting dynamic mode decomposition. Phys. Fluids 26, 024103.CrossRefGoogle Scholar
Juillet, F., Schmid, P. J. & Huerre, P. 2013 Control of amplifier flows using subspace identification techniques. J. Fluid Mech. 725, 522–565.CrossRefGoogle Scholar
Kim, J. & Bewley, T. R. 2007 A linear systems approach to flow control. Annu. Rev. Fluid Mech. 39, 383–417.Google Scholar
Kimura, H. 1977 A further result on the problem of pole assignment by output feedback. IEEE Trans. Autom. Control 22, 458–463.CrossRefGoogle Scholar
Kou, J. Q. & Zhang, W. W. 2017a An improved criterion to select dominant modes from dynamic mode decomposition. Eur. J. Mech. (B/Fluids) 62, 109–129.Google Scholar
Kou, J. Q. & Zhang, W. W. 2017b Layered reduced-order models for nonlinear aerodynamics and aeroelasticity. J. Fluids Struct. 68, 174–193.Google Scholar
Kou, J. Q., Zhang, W. W. & Yin, M. L. 2016 Novel Wiener models with a time-delayed nonlinear block and their identification. Nonlinear Dyn. 85 (4), 2389–2404.Google Scholar
Lee, B. H. K. 2001 Self-sustained shock oscillations on airfoils at transonic speeds. Prog. Aerosp. Sci. 37 (2), 147–196.Google Scholar
Li, J. & Zhang, W. W. 2016 The performance of proper orthogonal decomposition in discontinuous flows. Theor. Appl. Mech. Lett. 6, 236–243.Google Scholar
Liu, Y., Wang, G., Zhu, S. B. & Ye, Z. Y.2016a Numerical study of transonic shock buffet instability mechanism. AIAA Paper 2016-4386.CrossRefGoogle Scholar
Liu, Y. L., Zhang, W. W., Jiang, Y. W. & Ye, Z. Y. 2016b A high-order finite volume method on unstructured grids using RBF reconstruction. Comput. Maths Applics. 72, 1096–1117.Google Scholar
Ma, Z., Ahuja, S. & Rowley, C. W. 2011 Reduced order models for control of fluids using the eigensystem realization algorithm. Theor. Comput. Fluid Mech. 25, 233–247.Google Scholar
McCormick, D. 1993 Shock/boundary-layer interaction control with vortex generators and passive cavity. AIAA J. 31 (1), 91–96.CrossRefGoogle Scholar
Moore, B. C. 1981 Principal component analysis in linear systems: controllability, observability, and model reduction. IEEE Trans. Autom. Control 26, 17–32.CrossRefGoogle Scholar
Ogawa, H., Babinsky, H. & Pätzold, M. 2008 Shock-wave/boundary-layer interaction control using three-dimensional bumps for transonic wings. AIAA J. 46 (6), 1442–1452.Google Scholar
Piatak, D. J., Sekula, M. K., Rausch, R. D., Florance, J. R. & Ivanco, T. G.2015 Overview of the space launch system transonic buffet environment test program. AIAA Paper 2015-0557.Google Scholar
Rowley, C., Williams, D. & Colonius, T. 2006 Linear models for control of cavity flow oscillations. J. Fluid Mech. 547, 317–330.Google Scholar
Rowley, C. W. 2005 Model reduction for fluids using balanced proper orthogonal decomposition. Intl J. Bifurcation Chaos 15, 997–1013.Google Scholar
Rowley, C. W., Mezić, I., Bagheri, S., Schlatter, P. & Henningson, D. S. 2009 Spectral analysis of nonlinear flows. J. Fluid Mech. 641, 115–128.Google Scholar
Samimy, M., Debiasi, M., Caraballo, E., Serrani, A., Yuan, X., Little, J. & Myatt, J. H. 2007 Feedback control of subsonic cavity flows using reduced-order models. J. Fluid Mech. 579, 315–346.Google Scholar
Sartor, F., Mettot, C., Bur, R. & Sipp, D. 2015b Unsteadiness in transonic shock-wave/boundary-layer interactions: experimental investigation and global stability analysis. J. Fluid Mech. 781, 550–577.Google Scholar
Sartor, F., Mettot, C. & Sipp, D. 2015a Stability, receptivity, and sensitivity analyses of buffeting transonic flow over a profile. AIAA J. 53 (7), 1980–1993.Google Scholar
Schmid, P. J. 2010 Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 5–28.CrossRefGoogle Scholar
Scholz, P., Casper, M., Ortmanns, J., Kähler, C. J. & Radespiel, R. 2008 Leading-edge separation control by means of pulsed vortex generator jets. AIAA J. 46 (4), 836–847.Google Scholar
Semeraro, O., Bagheri, S., Brandt, L. & Henningson, D. S. 2011 Feedback control of three-dimensional optimal disturbances using reduced-order models. J. Fluid Mech. 677, 63–102.Google Scholar
Semeraro, O., Pralits, J. O., Rowley, C. W. & Henningson, D. S. 2013 Riccati-less approach for optimal control and estimation: an application to two-dimensional boundary layers. J. Fluid Mech. 731, 394–417.Google Scholar
Siegel, S. G., Seidel, J., Fagley, C., Luchtenburg, D. M., Cohen, K. & Mclaughlin, T. 2008 Low-dimensional modelling of a transient cylinder wake using double proper orthogonal decomposition. J. Fluid Mech. 610, 1–42.Google Scholar
Sipp, D. 2012 Open-loop control of cavity oscillations with harmonic forcings. J. Fluid Mech. 708, 439–468.Google Scholar
Spalart, P. & Allmaras, S.1992 A one-equation turbulence model for aerodynamic flows. AIAA Paper 92-0439.Google Scholar
Tian, Y., Liu, P. Q. & Li, Z. 2014 Multi-objective optimization of shock control bump on a supercritical wing. Sci. China – Tech. Sci. 57 (1), 192–202.Google Scholar
Titchener, N. & Babinsky, H. 2013 Shock wave/boundary-layer interaction control using a combination of vortex generators and bleed. AIAA J. 51 (5), 1221–1233.Google Scholar
Wang, G., Mian, H. H. & Ye, Z. Y. 2015 Improved point selection method for hybrid-unstructured mesh deformation using radial basis functions. AIAA J. 53 (4), 1016–1025.Google Scholar
Weller, J., Camarri, S. & Iollo, A. 2009 Feedback control by low-order modeling of the laminar flow past a bluff body. J. Fluid Mech. 634, 405–418.Google Scholar
Zhang, W. W., Gao, C. Q., Liu, Y. L., Ye, Z. Y. & Jiang, Y. W. 2015a The interaction between transonic buffet and flutter. Nonlinear Dyn. 82, 1851–1865.Google Scholar
Zhang, W. W., Li, X. T., Ye, Z. Y. & Jiang, Y. W. 2015b Mechanism of frequency lock-in in vortex-induced vibrations at low Reynolds numbers. J. Fluid Mech. 783, 72–102.Google Scholar
Zhou, K., Salomon, G. & Wu, E. 1999 Balanced realization and model reduction for unstable systems. Intl J. Robust Nonlinear Control 9 (3), 183–198.Google Scholar
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This movie shows the closed-loop control by LQ method in Figure 26.

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