Reduced Order Nonlinear Navier-Stokes Models for Synthetic Jets

[+] Author and Article Information
Othon K. Rediniotis, Jeonghwan Ko

Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843-3141

Andrew J. Kurdila

Department of Aerospace Engineering, Mechanics and Engineering Science, University of Florida, Gainesville, FL 32611-6250e-mail: ajk@aero.ufl.edu

J. Fluids Eng 124(2), 433-443 (May 28, 2002) (11 pages) doi:10.1115/1.1467598 History: Received October 15, 1999; Revised October 15, 2001; Online May 28, 2002
Copyright © 2002 by ASME
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Amitay M., Smith B. L., and Glezer A., 1998, “Aerodynamic Flow Control Using Synthetic Jet Technology,” AIAA Paper No. 98-0208, 36th Aerospace Sciences Meeting & Exhibit, Reno, NV.
Smith, D., Amitay, M., Kibens, V., Parekh, D., and Glezer, A., 1998, “Modifications of Lifting Body Aerodynamics Using Synthetic Jet Actuators,” AIAA Paper No. 98-0209, 36th Aerospace Sciences Meeting & Exhibit, Reno, NV.
Seifert, A. and Pack, L., 1999, “Oscillatory Excitation of Unsteady Compressible Flows over Airfoils at Flight Reynolds Number,” AIAA Paper No. 99-0925.
Joshi,  S. S., Speyer,  J. L., and Kim,  J., 1997, “A Systems Theory Approach to the Feedback Stabilization of Infinitesimal and Finite-Amplitude Disturbances in Plane Poiseuille Flow,” J. Fluid Mech., 332, pp. 157–184.
Gilarranz, J., Singh, K., Ko, J., Rediniotis, O. K., and Kurdila, A. J., 1997, “High Frame-Rate, High Resolution Cinematographic Particle Image Velocimetry,” AIAA Paper 97-0495.
Isidori, A., 1989, Nonlinear Control Systems, Springer-Verlag.
Krstic, M., Kanellakopoulos, I., Kokotovic, P., 1995, Nonlinear and Adaptive Control Design, Wiley, New York.
Sheen,  J.-J., and Bishop,  R. H., 1994, “Adaptive Nonlinear Control of Spacecraft,” J. Astronaut. Sci., 42(4), pp. 451–472.
Ko, J., Kurdila, A. J., and Strganac, T. W., 1997, “Nonlinear Control of a Prototypical Wing Section with Torsional Nonlinearity,” J. Guid. Control Dyn., 20 (6).
Cuvelier, P., 1976, “Optimal Control of a System Governed by the Navier-Stokes Equations Coupled with the Heat Equations,” in W. Eckhaus, ed., New Developments in Differential Equations, North-Holland, Amsterdam, pp. 81–98.
Gunzburger,  M., and Lee,  H. C., 1994, “Analysis, Approximation, and Computation of a Coupled Solid/Fluid Temperature Control Problem,” Comput. Methods Appl. Mech. Eng., 118, pp. 133–152.
Burns, J. A., and Ou, Y., 1994, “Feedback Control of the Driven Cavity Problem Using LQR Designs,” Proceedings of the 33rd Conference on Decision and Control, pp. 289–294, Lake Buena Vista, FL, Dec.
Banks, H. T., and Ito, K., 1994 “Structural Actuator Control of Fluid/Structure Interactions,” Proceedings of the 33rd Conference on Decision and Control, Lake Buena Vista, FL, pp. 283–288.
Desai,  M., and Ito,  K., 1994, “Optimal Control of Navier-Stokes Equations,” SIAM J. Control Optim., 32(5), pp. 1428–1446.
Ito,  K., and Kang,  S., 1994, “A Dissipative Feedback Control Synthesis for Systems Arising in Fluid Dynamics,” SIAM J. Control Optim., 32(3), pp. 831–854.
Ravindran,  S. S., and Hou,  L. S., 1998, “A Penalized Neumann Control Approach for Solving an Optimal Dirichlet Control Problem for the Navier-Stokes Equations,” SIAM J. Control Optim., 36(5), pp. 1795–1814.
Hou,  L. S., and Yan,  Y., 1997, “Dynamics for Controlled Navier-Stokes Systems with Distributed Controls,” SIAM J. Control Optim., 35(2), pp. 654–677.
Fattorini,  H. O., and Sritharan,  S. S., 1992, “Existence of Optimal Controls for Viscous Flow Problems,” Proc. R. Soc. London, Ser. A, 439, pp. 81–102.
Fattorini,  H. O., and Sritharam,  S. S., 1995, “Optimal Chattering Controls for Viscous Flow,” Nonlinear Analysis, Theory & Applications, 25(8), pp. 763–797.
Fursikov,  A. V., Gunzburger,  M. D., and Hou,  L. S., 1998, “Boundary Value Problems and Optimal Boundary Control for the Navier-Stokes System: The Two Dimensional Case,” SIAM J. Control Optim., 36(3), pp. 852–894, May.
Joslin, R. D., Gunzburger, M. D., Nicolaides, R. A., Erlehbacher, G., and Hussaini, M. Y., 1997, “Self-Contained Automated Methodology for Optimal Flow Control,” AIAA J., 35 (5).
Joslin, R. D., 1997, “Direct Numerical Simulation of Evolution and Control of Linear and Nonlinear Disturbances in Three Dimensional Attachment Line Boundary Layers,” NASA Technical Paper 3623.
Wygnanski, I., 1997, “Boundary Layer and Flow Control by Periodic Addition of Momentum,” 4th AIAA Shear Flow Control Conference,” Snowmass Village, CO, June 29–July 2, AIAA Paper No. 97-2117.
Trujillo, S. M., Bogard, D. G., and Ball, K. S., 1997, “Turbulent Boundary Layer Drag Reduction Using an Oscillating Wall,” 28th AIAA Fluid Dynamics Conference, 4th AIAA Shear Flow Control Conference, Snowmass Village, CO, June 29–July 2, AIAA Paper No. 97-1870.
Bewley, T. R., Moin, P., and Temam, R., 1997, “Optimal and Robust Approaches for Linear and Nonlinear Regulation Problems in Fluid Mechanics,” 28th AIAA Fluid Dynamics Conference, 4th AIAA Shear Flow Control Conference, Snowmass Village, CO, June 29–July 2, AIAA Paper No. 97-1872.
Cho, Y., Agarwal, R. K., and Nho, K., 1997, “Neural Network Approaches to Some Model Flow Control Problems,” 4th AIAA Shear Flow Conference, Snowmass Village, CO, June 29–July 2.
Aubry,  N., Holmes,  P., Lumley,  J. L., and Stone,  E., 1988, “The Dynamics of Coherent Structures in the Wall Region of a Turbulent Boundary Layer,” J. Fluid Mech., 192, pp. 115–173.
Ly,  H. V., and Tran,  H. T., 1998, “Proper Orthogonal Decomposition for Flow Calculations and Optimal Control in a Horizontal CVD Reactor,” Technical Report, Center for Research in Scientific Computation, North Carolina State University.
Corke,  T. C., Glauser,  M. N., and Berkooz,  G., 1994, “Utilizing Low Dimensional Dynamical Systems Models to Guide Control Experiments,” Appl. Mech. Rev., 47(6), Part 2, June, pp. 132–138.
Ito,  K., and Ravindran,  S. S., 1996 “Reduced Basis Method for Flow Control,” Technical Report CRSC-TR96-25, Center for Research in Scientific Computation, North Carolina State University.
Ito,  K., and Ravindran,  S. S., 1997 “A reduced basis method for control problems governed by PDEs,” Technical Report CRSC-TR-97-1, Center for Research in Scientific Computation, North Carolina State University.
Craig, R. R., 1981, Structural Dynamics, Wiley, New York.
Skelton, R. E., 1988, Dynamic Systems and Control, Wiley, New York.
Tang, D., Conner, M., and Dowell, E., 1997, “A Reduced Order Finite State Aerodynamic Model and Its Application to a Nonlinear Aeroelastic System,” preprint.
Elezgaray, J., Berkooz, G., Dankowicz, H., Holmes, P., and Myers, M., 1997, “Local Models and Large Scale Statistics of the Kuramoto-Sivashinsky Equation,” Wavelets and Multiscale Methods for Partial Differential Equations, W. Dahmen, A. Kurdila, and P. Oswald, eds., Academic Press.
Wickerhauser, M. V., Farge, M., Goirand, E., Wesfreid, E., and Cubillo, E., 1994, “Efficiency Comparison of Wavelet Packet and Adapted Local Cosine Bases for Compression of a Two Dimensional Turbulent Flow,” Wavelets: Theory, Algorithms, and Applications, Chui, C., Montefusco, L., and Puccio, L., eds., Academic Press, pp. 509–532.
Ko,  J., Kurdila,  A. J., Gilarranz,  J. L., and Rediniotis,  O. K., 1998, “Particle Image Velocimetry via Wavelet Analysis,” AIAA J., 36(8), pp. 1451–1459.
Ko, J., Kurdila, A. J., and Rediniotis, O. K., 1999, “Divergence Free Bases and Multiresolution Methods for Reduced-Order Flow Modeling,” AIAA J., in review.
Gunzburger, M. D., 1989, Finite Element Methods for Viscous Incompressible Flows: A Guide to Theory, Practice, and Algorithms, Academic Press, Boston, MA.
Temam, R., 1977, Navier-Stokes Equations, North-Holland Publishing Company.
Leove, M., 1945, “Functions Aleatoire de Second Ordre,” Compte Rend. Acad. Sci. (Paris).
Karhunen, K., 1946, “Zur Spektral Theorie Stochasticher Prozesse,” Ann. Acad. Sci. Fennicae, Ser. A1, Math. Phys., 37 .
Ball,  K. S., Sirovich,  L., and Keefe,  L. R., 1991, “Dynamical Eigenfunction Decomposition of Turbulent Channel Flow,” Int. J. Numer. Methods Fluids, 12, pp. 585–604.
Berkooz,  G., Holmes,  P., and Lumley,  J. L., 1993, “The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows,” Annu. Rev. Fluid Mech., 25, pp. 539–575.
Greenblatt, D. and Wygnanski, I., 1998, “Dynamic Stall Control By Oscillatory Forcing,” AIAA 98-0676.
Greenblatt, D., Darabi, A., Nishri, B., and Wygnanski, I., 1998, “Separation Control By Periodic Addition of Momentum with Particular Emphasis on Dynamic Stall,” Proceedings Heli Japan 98, Paper T3-4, American Helicopter Society.
Reichert,  R. S., Hatay,  F. F., Biringen,  S., and Huser,  A., 1994, “Proper Orthogonal Decomposition Applied to Turbulent Flow in a Square Duct,” J. Phys. Fluids, 6(9), pp. 3086–3092.
Seifert,  A., Bachat,  T., Koss,  D., Shepshelovich,  M., Wygnanski,  I., 1993, “Oscillatory Blowing: A Tool to Delay Boundary-Layer Separation,” AIAA J., 31(11), pp. 2052–2060.


Grahic Jump Location
Computational domain for the simulation
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Eigenvalue distribution
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Energy distribution for eigenvalues
Grahic Jump Location
The first four POD modes
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Projection error for different number of modeS
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Comparison of amplitudes for each mode: (a) first mode, (b) second mode, (c) third mode, (d) fourth mode
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Comparison of flow field (left—FIDAP, right—Galerkin): (a) t/T=0.025, (b) t/T=0.275, (c) t/T=0.525, (d) t/T=0.775




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