In this numerical study, the flow obtained behind a trailing edge separating two streams of different velocities is studied by means of direct numerical simulation. The main originality of this work is that the splitter plate itself is included in the computational domain using an immersed boundary method. The influence of the trailing-edge shape is considered through the analysis of the destabilizing mechanisms and their resulting effect on the spatial development of the flow. The streamwise evolution of the different flows is found to be very different for each of the configurations considered, both in terms of mean quantities and flow dynamics. Present results suggest that the wake component, which dominates the flow close to the trailing edge, is still influential further downstream, as already observed in pure wake flows but only conjectured in mixing layer. A detailed analysis of the vortex dynamics is proposed using instantaneous visualizations, statistical/stability analysis considerations, and proper orthogonal decomposition in order to better understand how the transition regime from the wake to the mixing layer occurs and why it can influence the self-similarity, in a region where no wake influence can be locally detected.
REFERENCES
1.
J. -M.
Chomaz
, “Global instabilities in spatially developing flows: Non-normality and nonlinearity
,” Annu. Rev. Fluid Mech.
37
, 357
(2005
).2.
P.
Huerre
and P. A.
Monkewitz
, “Local and global instabilities in spatially developing flows
,” Annu. Rev. Fluid Mech.
22
, 473
(1990
).3.
W. K.
George
, “The self-preservation of turbulent flows and its relation to initial conditions and coherent structures
,” in Advances in Turbulence
, edited by W. K.
George
and R.
Arndt
(Hemisphere
, New York
, 1989
), pp. 39
–73
.4.
M.
Lesieur
, Turbulence in Fluids
, 4th ed. (Springer
, New York
, 2008
).5.
J.
Mathew
, I.
Mahle
, and R.
Friedrich
, “Effects of compressibility and heat release on entrainment processes in mixing layers
,” J. Turbul.
9
, 14
(2009
).6.
M.
Rogers
and R.
Moser
, “Direct simulation of a self-similar turbulent mixing layer
,” Phys. Fluids
6
, 903
(1994
).7.
N. D.
Sandham
and R. D.
Sandberg
, “Direct numerical simulation of the early development of a turbulent mixing layer downstream of a splitter plate
,” J. Turbul.
10
, 1
(2009
).8.
G.
Brown
and A.
Roshko
, “On density effects and large structure in turbulent mixing layers
,” J. Fluid Mech.
64
, 775
(1974
).9.
R. D.
Metha
, “Effect of velocity ratio on plane mixing layer development: Influence of the splitter plate wake
,” Exp. Fluids
10
, 194
(1991
).10.
P.
Comte
, J. H.
Silvestrini
, and P.
Bégou
, “Streamwise vortices in large-eddy simulations of mixing layers
,” Eur. J. Mech. B/Fluids
17
, 615
(1998
).11.
Y.
Wang
, M.
Tanahashia
, and T.
Miyauch
, “Coherent fine scale eddies in turbulence transition of spatially-developing mixing layer
,” Int. J. Heat Fluid Flow
28
, 1280
(2007
).12.
C.
Braud
, D.
Heitz
, G.
Arroyo
, L.
Perret
, J.
Delville
, and J. -P.
Bonnet
, “Low-dimensional analysis, using POD, for two mixing layer-wake interactions
,” Int. J. Heat Fluid Flow
25
, 351
(2004
).13.
S.
Laizet
and E.
Lamballais
, “Direct-numerical simulation of the splitting-plate downstream-shape influence upon a mixing layer
,” C. R. Acad. Sci., Ser. IIb: Mec., Phys., Chim., Astron.
334
, 454
(2006
).14.
L.
Perret
, J.
Delville
, and J. -P.
Bonnet
, “Investigation of the large scale structures in the turbulent mixing layer downstream a thick plate
,” Proceedings of the Third International Symposium on Turbulence and Shear Flow Phenomena
, Sendai, Japan, 2003
.15.
D.
Wallace
and L. G.
Redekopp
, “Linear instability characteristics of wake-shear layers
,” Phys. Fluids A
4
, 189
(1992
).16.
D. A.
Hammond
and L. G.
Redekopp
, “Global dynamics of symmetric and asymmetric wakes
,” J. Fluid Mech.
331
, 231
(1997
).17.
B.
Dziomba
and H. E.
Fiedler
, “Effect of initial conditions on two-dimensional free shear layers
,” J. Fluid Mech.
152
, 419
(1985
).18.
S.
Laizet
and J. C.
Vassilicos
, “Multiscale generation of turbulence
,” Journal of Multiscale Modelling
1
, 177
(2009
).19.
E.
Lamballais
, J.
Silvestrini
, and S.
Laizet
, “Direct numerical simulation of a separation bubble on a rounded finite-width leading edge
,” Int. J. Heat Fluid Flow
29
, 612
(2008
).20.
E.
Laurendeau
, P.
Jordan
, J. P.
Bonnet
, J.
Delville
, P.
Parnaudeau
, and E.
Lamballais
, “Subsonic jet noise reduction by fluidic control: The interaction region and the global effect
,” Phys. Fluids
20
, 101519
(2008
).21.
P.
Parnaudeau
, J.
Carlier
, D.
Heitz
, and E.
Lamballais
, “Experimental and numerical studies of the flow over a circular cylinder at Reynolds number 3900
,” Phys. Fluids
20
, 085101
(2008
).22.
S.
Laizet
and E.
Lamballais
, “Direct numerical simulation of a spatially evolving flow from an asymmetric wake to a mixing layer
,” Direct and Large-Eddy Simulation VI
(Springer
, Poitiers
, 2006
).23.
S.
Laizet
and E.
Lamballais
, “High-order compact schemes for incompressible flows: A simple and efficient method with quasi-spectral accuracy
,” J. Comput. Phys.
228
, 5989
(2009
).24.
P.
Parnaudeau
, E.
Lamballais
, D.
Heitz
, and J. H.
Silvestrini
, “Combination of the immersed boundary method with compact schemes for DNS of flows in complex geometry
,” Direct and Large-Eddy Simulation V
(Springer
, Munich
, 2003
).25.
P.
Holmes
, J. L.
Lumley
, and G.
Berkooz
, Turbulence, Coherent Structures, Dynamical Systems and Symmetry
(Cambridge University Press
, Cambridge
, 1996
).26.
J.
Delville
, “Characterization of the organization in shear layers via the proper orthogonal decomposition
,” Appl. Sci. Res.
53
, 263
(1994
).27.
L.
Sirovich
, “Turbulence and the dynamics of coherent structures. Part 1: Coherent structures
,” Q. J. Mech. Appl. Math.
45
, 561
(1987
).28.
M.
Rajaee
, S. K. F.
Karlsson
, and L.
Sirovich
, “Low-dimensional description of free-shear-flow coherent structures and their dynamical behaviour
,” J. Fluid Mech.
258
, 1
(1994
).29.
L.
Sirovich
, K. S.
Ball
, and L. R.
Keefe
, “Plane waves and structures in turbulence channel flow
,” Phys. Fluids A
2
, 2217
(1990
).30.
F. K.
Browand
and T. R.
Troutt
, “A note on spanwise structure in the two-dimensional mixing layer
,” J. Fluid Mech.
93
, 325
(1980
).31.
P.
Comte
, M.
Lesieur
, and E.
Lamballais
, “Large- and small-scale stirring of vorticity and a passive scalar in a 3-D temporal mixing layer
,” Phys. Fluids A
4
, 2761
(1992
).© 2010 American Institute of Physics.
2010
American Institute of Physics
You do not currently have access to this content.
