Global modes in a confined impinging jet: application to heat transfer and control
Tóm tắt
We investigate the stability and control of a plane, laminar jet impinging on a flat plate in a channel, a geometry used to cool down a hot wall with a cold air jet in many industrial configurations. The global stability analysis indicates that, even for a strong confinement, the two-dimensional (2-D) steady flow is unstable to three-dimensional (3-D), steady perturbations. In the simplest limit case where dilatation effects are neglected, we show that the development of the instability induces a significant spanwise modulation of the heat flux at the impacted wall. To control the leading global mode, we propose adjoint-based 3-D harmonic and 2-D steady forcing in the bulk or at the wall. We show for instance that the unstable mode is controllable using a spanwise uniform blowing at the upper wall, in a specific domain corresponding to the footprint of the upper recirculating bubble. These techniques are applied to a novel open-loop control, in which we introduce into the flow a small airfoil, modelled by the lift force it exerts on the flow.
Tài liệu tham khảo
Barkley D., Gomes M., Henderson R.: Three-dimensional instability in flow over a backward-facing step. J. Fluid Mech. 473, 167–190 (2002)
Bayly B.: Three-dimensional centrifugal-type instabilities in inviscid two-dimensional flows. Phys. Fluids 31, 56–64 (1988)
Bottaro A., Corbett P., Luchini P.: The effect of base flow variation on flow stability. J. Fluid Mech. 476, 293–302 (2003)
Chiriac V., Ortega A.: A numerical study of the unsteady flow and heat transfer in a transitional confined slot jet impinging on an isothermal surface. Int. J. Heat Mass Transf. 45, 1237–1248 (2002)
Chomaz J.M.: Global instabilities in spatially developing flows: non-normality and nonlinearity. Ann. Rev. Fluid Mech. 37, 357–392 (2005)
Chomaz J.M., Huerre P., Redekopp L.: The effect of nonlinearity and forcing on global modes. In: Coulet, P., Huerre, P. (eds) New Trends in Nonlinear Dynamcs and Pattern-Forming Phenomena: The Geometry of Nonequilibrium. NATO ASI Series B, vol. 237, pp. 259–274. Plenum, New York (1990)
Davis T.A.: A column pre-ordering strategy for the unsymmetric-pattern multifrontal method. ACM Trans. Math. Softw. 30(2), 165–195 (2004)
Ehrenstein U., Gallaire F.: On two-dimensional temporal modes in spatially evolving open flows: the flat-plate boundary layer. J. Fluid Mech. 536, 209–218 (2005)
Gallaire F., Marquillie M., Ehrenstein U.: Three-dimensional transverse instabilities in detached boundary layers. J. Fluid Mech. 571, 221–233 (2007)
Giannetti, F., Luchini, P.: Receptivity of the circular cylinder’s first instability. In: Proceedings of the 5th European Fluid Mechanics Conference, Toulouse (2003)
Giannetti F., Luchini P.: Structural sensitivity of the first instability of the cylinder wake. J. Fluid Mech. 581, 167–197 (2007)
Hill, D.: A theoretical approach for analyzing the restabilization of wakes. Technical Report 103858, NASA (1992)
Lee H., Yoon H., Ha M.: A numerical investigation on the fluid flow and heat transfer in the confined impinging slot jet in the low reynolds number region for different channel heights. Int. J. Heat Mass Transf. 51, 4055–4068 (2008)
Lifschitz A., Hameiri E.: Local stability conditions in fluid dynamics. Phys. Fluids A 3, 2644–2651 (1991)
Luchini, P., Giannetti, F., Pralits, J.: Structural sensitivity of linear and nonlinear global modes. AIAA Paper 2008-4227 (2008)
Marquet O., Sipp D., Jacquin L.: Sensitivity analysis and passive control of the cylinder flow. J. Fluid Mech. 615, 221–252 (2008)
Marquet, O., Sipp, D., Jacquin, L., Chomaz, J.M.: Multiple timescale and sensitivity analysis for the passive control of the cylinder flow. AIAA Paper 2008-4228 (2008)
Martin A.: Heat and mass transfer between impinging gas jets and solid surfaces. Adv. Heat Transf. 13, 1–60 (1977)
Schmid P., Henningson D.: On the stability of a falling liquid curtain. J. Fluid Mech. 463, 163–171 (2002)
Sipp D., Jacquin L.: Three-dimensional centrifugal-type instabilities of two-dimensional flows in rotating systems. Phys. Fluids 12, 1740–1748 (2000)
Varieras, D.: Étude de l’écoulement et du transfert de chaleur en situation de jet plan confiné. Ph.D. thesis, Université Paul Sabatier—Toulouse III (2000)
Varieras D., Brancher P., Giovannini A.: Self-sustained oscillations of a confined impinging jet. Flow Turb. Comb. 78, 1–15 (2007)