Abstract
This paper describes simulations of feedback control of small disturbances in laminar Poiseuille flow. A polynomial-form spectral state-space model of the linearised flow with wall transpiration actuation and wall shear-stress measurements is generated, optimal controllers are synthesised, and closed-loop simulations are performed using an independent finite-volume Navier—Stokes solver. In addition, actuation via tangential wall transpiration is investigated, and LMI controllers, which minimise an upper bound on the peak transient energy growth, are synthesised and simulated.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Hogberg, M., Bewley, T.R.: Spatially localized convolution kernels for feedback control of transitional flows. In: Proc. 39th IEEE Conference on Decision and Control, Sydney, Australia, December 12-15 (2000) 3278-3283.
Kim, J.: Control of turbulent boundary layers, Physics of Fluids 15(5) (2003) 1093–1105.
Bewley, T.R., Liu, S.: Optimal and robust control and estimation of linear paths to transition. Journal of Fluid Mechanics 365 (1998) 305–349.
Schmid, P.J., Henningson, D.S.: Stability and Transition in Shear Flows, AppliedMathematical Sciences, Vol. 142. Springer-Verlag, New York (2001).
McKernan, J., Papadakis, G., Whidborne, J.F.: A linear state-space representation of plane Poiseuille flow for control design: A tutorial. The International Journal of Modelling, Identification and Control 1(4) (2006) 272–280.
McKernan, J.: Control of plane Poiseuille flow: A theoretical and computational investigation. PhD Thesis, Department of Aerospace Sciences, School of Engineering, Cranfield University (2006).
Whidborne, J.F., McKernan, J., Papadakis, G.: Minimal transient energy growth for plane Poiseuille flow. In: Proc. UKACC International Conference Control 2006 (ICC2006), August 30-September 1, Glasgow, UK (2006).
Butler, K.M., Farrell, B.F.: Three-dimensional optimal perturbations in viscous shear flow. Physics of Fluids 4(8) (1992) 1637–1650.
Reddy, S.C., Schmid, P.J., Baggett, J.S., Henningson, D.S.: On stability of streamwise streaks and transition thresholds in plane channel flows. Journal of Fluid Mechanics 365 (1998) 269–303.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer
About this paper
Cite this paper
McKernan, J., Whidborne, J.F., Papadakis, G. (2008). Simulations of Feedback Control of Early Transition in Poiseuille Flow. In: Morrison, J.F., Birch, D.M., Lavoie, P. (eds) IUTAM Symposium on Flow Control and MEMS. IUTAM Bookseries, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6858-4_40
Download citation
DOI: https://doi.org/10.1007/978-1-4020-6858-4_40
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-6857-7
Online ISBN: 978-1-4020-6858-4
eBook Packages: EngineeringEngineering (R0)