Z. Yang
OPEN ACCESS
Transition process in separated–reattached flows plays a key role in many practical engineering applications. Hence, accurately predicting transition is crucial since the transition location has a significant impact on the aerodynamic performance and a fundamental understanding of the instability mechanisms involved in transition process is required in order to make significant advances in engineering design and transition control, for example, to delay the turbulent phase where laminar flow characteristics are desirable (low friction drag) or to accelerate it where high mixing of turbulent flow are of interest (in a combustor). The current understanding of instabilities involved in the transition process in separated–reattached flows is far from complete and it is usually very difficult to theoretically and experimentally study the transition process since theoretical studies suffer from the limitation imposed by nonlinearity of the transition process at later stages and experimental studies are limited by temporal and spatial resolution; hence, a thorough description of the transition process is lacking. Nevertheless, significant progress has been made with the simulation tools, such as large eddy simulation (LES), which has shown improved predictive capabilities and can predict transition process accurately. This paper will first briefly present LES formalism followed by its applications to study the transition process in separated–reattached flows, reviewing our current understanding of several important phenomena associated with the transition process and focusing on the instabilities in particular.
instability, large eddy simulation, separated–reattached fl ows, transition process
[1] Langtry, R.B. & Menter, F.R., Transition modelling for general CFD applications inaeronautics. AIAA 2005-522, Reno, Nevada, 2005.
[2] Smagorinsky, J., General circulation experiments with the primitive equations: I – thebasic experiment. Monthly Weather Review, 91, pp. 99–164, 1963. doi: http://dx.doi.org/10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2
[3] Schmid, P.J. & Henningson, D.S., Stability and Transition in Shear Flows, Springer:New York, 2001. doi: http://dx.doi.org/10.1007/978-1-4613-0185-1
[4] Lesieur, M. & Metais, O., New trends in large eddy simulations of turbulence. AnnualReview of Fluid Mechanics, 28, pp. 45–82, 1996. doi: http://dx.doi.org/10.1146/annurev.fl .28.010196.000401
[5] Sagaut, P., Large Eddy Simulation for Incompressible Flows: An Introduction, 2nd edn,Springer: Berlin, 2003.
[6] Kajishima, T. & Nomachi, T., One-equation sub-grid scale model using dynamic procedurefor the energy production. Transaction of ASME, 73, pp. 368–373, 2006.
[7] Germano, P., Piomelli, U., Moin, P. & Cabot, W.H., A dynamic sub-grid scale eddyviscosity model. Physics of Fluids, 3(7), pp. 1760–1765, 1991. doi: http://dx.doi.org/10.1063/1.857955
[8] Lee, S., Lele, S. & Moin, P., Simulation of spatially evolving turbulence and theapplicability of Taylor’s hypothesis in compressible fl ow. Physics of Fluids A, 4,pp. 1521–1530, 1992. doi: http://dx.doi.org/10.1063/1.858425
[9] Druault, P., Lardeau, S., Bonnet, J.-P., Coiffet, F., Deville, J., Lamballais, E., et al.Generation of three-dimensional turbulent inlet conditions for large-eddy simulation.AIAA Journal, 42(3), pp. 447–456, 2004. doi: http://dx.doi.org/10.2514/1.3946
[10] Veloudis, I., Yang, Z., McGuirk, J.J., Page, G.J. & Spencer, A., Novel implementationand assessment of a digital fi lter based approach for the generation of large-eddysimulation inlet conditions. Journal of Flow, Turbulence and Combustion, 79, pp. 1–24,2007. doi: http://dx.doi.org/10.1007/s10494-006-9058-y
[11] Benhamadouche, S., Jarrin, N., Addad, Y. & Laurence, D., Synthetic turbulent infl owconditions based on a vortex method for large eddy simulation. Progress in ComputationalFluid Dynamics, 6(1–3), pp. 50–57, 2006. doi: http://dx.doi.org/10.1504/PCFD.2006.009482
[12] Tabor, G.R. & Baba-Ahmadi, M.H., Inlet conditions for large eddy simulation: areview. Computers & Fluids, 39, pp. 553–567, 2010. doi: http://dx.doi.org/10.1016/j.compfl uid.2009.10.007
[13] Ho, C.M. & Huerre, P., Perturbed free shear layers. Annual Review of Fluid Mechanics,16, pp. 365–424, 1984. doi: http://dx.doi.org/10.1146/annurev.fl .16.010184.002053
[14] Yang, Z. & Voke, P.R., Large-eddy simulation of boundary layer separation and transitionat a change of surface curvature. Journal of Fluid Mechanics, 439, pp. 305–333,2001. doi: http://dx.doi.org/10.1017/S0022112001004633
[15] Chandrasekhar, S., Hydrodynamic and Hydromagnetic Stability, Clarendon Press:Oxford, 1961.
[16] Abdalla, I.E. & Yang, Z., Numerical study of the instability mechanism in transitionalseparating-reattaching fl ow. International Journal of Heat and Fluid Flow, 25,pp. 593–605, 2004. doi: http://dx.doi.org/10.1016/j.ijheatfl uidfl ow.2004.01.004
[17] Roberts, S.K. & Yaras, M.I., Large-eddy simulation of transition in a separation bubble.ASME Journal of Fluids Engineering, 128, pp. 232–238, 2006. doi: http://dx.doi.org/10.1115/1.2170123
[18] McAuliffe, B.R. & Yaras, M.I., Numerical study of instability mechanisms leading totransition in separation bubbles. ASME Journal of Turbomachinery, 130, pp. 1–8, 2008.doi: http://dx.doi.org/10.1115/1.2750680
[19] Lang, M., Rist, U. & Wagner, S., Investigations on controlled transition developmentin a laminar separation bubble by means of LDA and PIV. Experiments in Fluids, 36,pp. 43–52, 2004. doi: http://dx.doi.org/10.1007/s00348-003-0625-x
[20] Roberts, S.K. & Yaras, M.I., Effects of periodic unsteadiness, free-stream turbulenceand fl ow Reynolds number on separation-bubble transition. ASME-GT2003-38626,2003.
[21] Volino, R.J. & Bohl, D.G., Separated fl ow transition mechanism and prediction withhigh and low free stream turbulence under low pressure turbine conditions. ASMEGT2004-53360, 2004.
[22] Metcalfe, R.W., Orszag, S.A., Brachet, M.E. & Riley, J.J., Secondary instability of atemporally growing mixing layer. Journal of Fluid Mechanics, 184, pp. 207–243, 1987.doi: http://dx.doi.org/10.1017/S0022112087002866
[23] Huang, L.S. & Ho, C.M., Small-scale transition in a plane mixing layer. Journalof Fluid Mechanics, 210, pp. 475–500, 1990. doi: http://dx.doi.org/10.1017/S0022112090001379
[24] Winant, C.D. & Browand, F.K., Vortex pairing: the mechanism of turbulent mixing- layergrowth at moderate Reynolds number. Journal of Fluid Mechanics, 63, pp. 237–255,1974. doi: http://dx.doi.org/10.1017/S0022112074001121
[25] Malkiel, E. & Mayle, R.E., Transition in a separation bubble. ASME Journal ofTurbomachinery, 118, pp. 752–759, 1996. doi: http://dx.doi.org/10.1115/1.2840931
[26] McAuliffe, B.R. & Yaras, M.I., Passive manipulation of separation-bubble transitionusing surface modifi cations. ASME Journal of Fluids Engineering, 131, pp. 021201:1–16, 2009.
[27] Yang, Z. & Abdalla, I.E., Effects of free-stream turbulence on large-scale coherentstructures of separated boundary layer transition. International Journal for NumericalMethods in Fluids, 49, pp. 331–348, 2005. doi: http://dx.doi.org/10.1002/fl d.1014
[28] Yang, Z & Abdalla, I.E., Effects of free-stream turbulence on a transitional separatedreattachedfl ow over a fl at plate with a sharp leading edge. International Journal of Heatand Fluid Flow, 30, pp. 1026–1035, 2009. doi: http://dx.doi.org/10.1016/j.ijheatfl uidflow.2009.04.010
[29] Kiya, M. & Sasaki, K., Structure of a turbulent separation bubble. Journal of FluidMechanics, 137, pp. 83–113, 1983. doi: http://dx.doi.org/10.1017/S002211208300230X
[30] Cherry, N.J., Hillier, R. & Latour, M.E.M.P., Unsteady measurements in a separatingand reattaching fl ow. Journal of Fluid Mechanics, 144, pp. 13–46, 1984. doi: http://dx.doi.org/10.1017/S002211208400149X
[31] Kiya, M. & Sasaki, K., Structure of large-scale vortices and unsteady reverse fl ow inthe reattaching zone of a turbulent separation bubble. Journal of Fluid Mechanics, 154,pp. 463–491, 1985. doi: http://dx.doi.org/10.1017/S0022112085001628
[32] Abdalla, I.E. & Yang, Z., Numerical study of a separated-reattached fl ow on a bluntplate. AIAA Journal, 43, pp. 2465–2474, 2005. doi: http://dx.doi.org/10.2514/1.1317
[33] Hussain, A.K.M.F., Coherent structures and turbulence. Journal of Fluid Mechanics,173, pp. 303–356, 1986. doi: http://dx.doi.org/10.1017/S0022112086001192
[34] Cantwell, B.J., Organised motion in turbulent fl ow. Annual Review of Fluid Mechanics,13, pp. 457–515, 1981. doi: http://dx.doi.org/10.1146/annurev.fl .13.010181.002325
[35] Kim, H.T., Kline, S.J. & Reynolds, W.C., The production of turbulence near a smoothwall in a turbulent boundary layer. Journal of Fluid Mechanics, 50, pp. 133–160, 1971.doi: http://dx.doi.org/10.1017/S0022112071002490
[36] Smith, C.R. & Metzler, S.P., The characteristics of low-speed streaks in the near-wallregion of a turbulent boundary layer. Journal of Fluid Mechanics, 129, pp. 27–54, 1983.doi: http://dx.doi.org/10.1017/S0022112083000634
[37] Yang, Z., Large-scale structures at various stages of separated boundary layer transition.International Journal of Numerical Methods in Fluids, 40, pp. 723–733, 2002.doi: http://dx.doi.org/10.1002/fl d.373
[38] Abdalla, I.E., Yang, Z. & Cook, M., Computational analysis and fl ow structure of atransitional separated-reattached fl ow over a surface mounted obstacle and a forwardfacingstep. International Journal of Computational Fluid Dynamics, 23, pp. 25–57,2009. doi: http://dx.doi.org/10.1080/10618560802566246