In the present study, the main focus is to explore the Couette effect on turbulent secondary
structures by simulating the turbulent Poiseuille, Couette-Poiseuille and Couette flows
inside a square duct where the bulk Reynolds number is kept around 10000. Both the
Smagorinsky model with Van Direst damping function and the dynamic Smagorinsky model
employed here predict the mean and turbulence quantities well by comparisons with DNS
data. The present numerical method was validated by computing the Poiseuille flow, which
was then used as base to explore influences of the moving wall on Couette-Poiseuille flows.
The turbulence generated secondary flow is modified by the presence of the top moving
wall, where the symmetric vortex pattern vanishes. It is interesting to note that a linear
relation exits between the angle and the parameter r = Ww=Wbulk, and change in slope
occurs at r » 1:5. Near the moving wall due to the reduction of the streamwise velocity
fluctuation at the moving wall, turbulence structure gradually moves towards a rod-like
axi-symmetric turbulence as r increases. As the wall velocity increases further for r > 1:5,
the rod like structure disappears, and turbulence reverts to the disk like structure. The
near wall structures are first visualized by the instantaneous velocity field in one cross-plane
of the square duct after the flow has achieved fully developed state. Along the top moving
wall, the low mean shear rate suppresses the generation of these turbulent structures.
Therefore, near the top corners the ejection events from the side walls are the dominant
structures.
The present numerical procedures are capable of simulating complex turbulent wall-
bounded flows. It is demonstrated that the present results have shown the influence of
top moving wall on the turbulent levels and anisotropic. Scientifically, results of this
prediction have great reference value for researchers concerning turbulent duct flows or
turbulence modeling. Finally, this work will allow the industry to benefit from the design
and optimization.

[1] Deardor®, J. W., 1970, "A numerical study of three-dimensional turbulent
channel flow at large Reynolds numbers," J. Fluid Mech., Vol. 41, pp. 453-480.
[2] Smagorinsky, J., 1963, "General Circulation Experiments with the Primitive
Equations. I. The Basic Experiments," Monthly Weather Review, Vol. 91, pp.
99-164.
[3] Van Driest, E. R., 1956, "On turbulent flow near a wall," J. Aerospace Science,
Vol. 23, pp. 1007-1012.
[4] Germano, M., Piomelli, U., Moin, P., and Cabot, W. H., A., 1991, "A dynamic
subgrid-scale eddy viscosity model," Phys. Fluids, Vol. 3, pp. 1760-1765.
[5] Moin, P., Squires, K., Cabot, W. H. and Lee, S., A., 1991, "A dynamic subgrid-
scale model for compressible turbulence and scalar transport" Phys. Fluids,
Vol. 3, pp. 2746-2757.
[6] Lilly, D. K., A., 1991, "A dynamic subgrid-scale eddy viscosity model," Phys.
Fluids, Vol. 4, pp. 633-635.
[7] Zang, Y., Street, R. L. and Kose®, J. R., A, 1993, "A dynamic mixed subgrid-
scale and its application to turbulent recirculating flows" Phys. Fluids, Vol. 5,
pp. 3186-3196.
[8] Ghosal, S., Lund, T. S., Moin, P., and Akselvoll, K., 1995, "A dynamic
localization model for large-eddy simulation of turbulent flows," J. Fluid Mech.,
Vol. 286, pp. 229-255.
[9] Piomelli, U. and Liu, A., 1995, "Large eddy simulation of rotating channel
°ows using a localized dynamic midel" Phys. Fluids, Vol. 7, pp. 839-848.
[10] Cabot, W., 1995, "Large-eddy simulations with wall models," In: Annual
Research Briefs. Center for Turbulence Research, Stanford, pp. 41-50.
[11] Meneveau, C., Lund, T. S., and Cabot, W. H., 1996, "A Lagrangian dynamic
subgrid scale model of turbulence" J. Fluid Mech, Vol. 319, pp. 353-385.
[12] Prandtl, L., 1926, "Uber die ausgebildete turbulenz," Verh. 2nd Intl. Kong.
Fur Tech. Mech., Zurich,[English translation NACA Tech. Memo. 435.
[13] Salinas vazquez, M. and Metais, O., 2002, "Large eddy simulation of the
turbulent flow through a heated square duct," J. Fluid Mech., Vol. 453, pp.
201-238.
[14] Winkler, C.M., Rani, Sarma L. and Vanka, S.P., 2005, "Preferential
concentration of particles in a fully developed turbulent square duct flow,"
Int. J. Multiphase Flow, Vol. 30, pp. 27-50.
[15] Nikuradse, J., 1930, "Turbulente stromung in nicht-kreisformigen Rohren,"
Ing. Arch., Vol. 1, pp. 306-332.
[16] Chorin, A. J., 1968, "Numerical solution of the Navier-Stokes equations,"
Mathematics of Computation, Vol. 22, pp. 745-762.
[17] Choi, H. and Moin, P. A., 1994, "Effects of the Computational Time Step on
Numerical Solutions of Turbulent Flow," J. Comput. Phys, Vol. 113, pp. 1-4.
[18] Kim, J. and Moin, P., 1987, "Application of a fractional-step method to
incompressible Navie-Stokes equations," J. Comput. Phys. Vol. 177, pp. 133-
166.
[19] Launder, B. E. and Ying, W. M., 1973, "Prediction of flow and heat transfer
in ducts of square cross-section," Heat and Fluid Flow, Vol. 3, pp. 115-121.
[20] Peter, L. O'Sullivan, iringen, S. and Huser, A., N., 1999, "DNS/LES of
turbulent flow in a square duct: A priori evaluation of subgrid models ," Lecture
Notes in Physics, pp. 290-301.
[21] Salvetti, M. V. and Banerjee, S., 1995, "A periori tests of new dynamic sub-
grid scale model for finite difference large eddy simulation." Phy. Fl, Vol. 7,
pp. 2831-2847.
[22] Brogolia, R., Pascarelli, A. and Piomelli, U., 2003, "Large eddy simulations of
ducts with a free surface", J. Fluid Mech, Vol. 484, pp. 223-253
[23] Abe, H., Kawamura, H. and Matsuo, Y., 2001, "Direct numerical simulation
of a fully developed turbulent channel with respect to the Reynolds number
dependence," ASME., Vol.123, pp. 382-393.
[24] Moser, R. D., Kim, J. and Mansour, N. N., 1999, "Direct numerical simulation
of turbulent channel °ow up to Re¿ = 590," J. Fluid Mech., Vol. 177, pp.
943-945.
[25] Wei, T. and Willmarth, W. W., 1989, "Reynolds-number effects on the
structure of a turbulent channel flow," J. Fluid Mech., Vol.204, pp. 57-95.
[26] Kuroda, A., Kasagi, N. and Hirata, M., 1993, "Direct numerical simulation of
turbulent plane CouetteVPoiseuille flows: Effect of mean shear rate on the near
wall turbulence structures," Proceeding of the 9th Symposium on Turbulent
Shear Flow, Kyoto, Japan, pp.8.4.1-8.4.6.
[27] Huser, A. and Biringen, S., 1993, "Direct numerical simulation of turbulent
flow in a square duct," J. Fluid Mech., Vol. 257, pp. 65-95.
[28] Huser, A., Biringen, S. and Hatay, F. F., 1994, "Direct numerical simulation of
turbulent flow in a square duct: Reynolds-stress budgets," Physics of Fluids,
Vol. 6, pp. 3144-3152.
[29] Iwamoto, K., Suzuki, Y. and Kasagi, N., N, 2002, "Reynolds Number Effect
on Wall Turbulence. Toward Effective Feedback Control." International J. of
Heat and Fluid Flow, Vol. 23, pp. 678-689.
[30] Madabhushi, R. K. and Vanka, S. P., 1991, "Large eddy simulation of
turbulencedriven secondary flow in a square duct," Phyics of Fluids A, Vol.
3, pp. 2734-2745.
[31] Gavrilakis, S., 1992, "Numerical simulation of low-Reynolds-number turbulent
°ow through a straight square duct," J. Fluid Mech., Vol. 244, pp. 101-129.
[32] Lumley, J. L., 1978, "Computational modeling of turbulent flows," Advances
in Applied Mechanics, Vol. 18, pp. 123-176.
[33] Lee, M. J. and Reynolds, W. C., 1985, "Numerical experiments on the structure
of homogeneous turbulence," Report TF-24, Thermoscience Division, Stanford
University.
[34] Antonia, R. A., Danh, H. Q. and Prabhu, A., 1977, "Response of turbulent
boundary layer to a step change of heat flux," J. Fluid Mech., Vol. 99, pp.
153-177.
[35] Salinas Vazquez, M., Vicente Rodriguez, W. and Issa, R., 2005, "Effects of
ridged walls on the heat transfer in a heated square duct," Int. J. Heat and
Mass Transfer, Vol. 48, pp. 2050-2063.