Reconstruction of the Most Energetic Modes in a Fully Developed Turbulent Channel Flow with Density Variation

Proper orthogonal decomposition (POD) is used to reconstruct spatio-temporal data of a fully developed turbulent channel flow with density variation at Reynolds number of 150, based on the friction velocity and the channel half-width, and Prandtl number of 0.71. To apply POD to the fully developed turbulent channel flow with density variation, the flow field (velocities, density, and temperature) is scaled by the corresponding root mean square values (rms) so that the flow field becomes dimensionless. A five-vector POD problem is solved numerically. The reconstructed second-order moments of velocity, temperature, and density from POD eigenfunctions compare favorably to the original Direct Numerical Simulation (DNS) data.

• Elteyeb Eljack
• Takashi Ohta

• Pattern Recognition
• POD
• Coherent Structures
• Low dimensional modelling.

[1] Lumley, J. L. (1967) The Structure of Inhomogeneous Turbulent Flows.
In Atmospheric Turbulence and Radio Wave Propagation (A.M. Yaglom
and V.I. Takarski, eds.), pp. 166-178. Moscow: Nauka.
[2] Lumley, J. L. (1972) Stochastic Tools in Turbulence. New York: Academic
Press.
[3] Lumley, J. L. (1981) Coherent Structures in Turbulence. In Transition and
Turbulence (R.E. Meyer, ed.), pp. 215-242. New York: Academic Press.
[4] Sirovich, L. (1987) Turbulence and the Dynamics of Coherent Structures,
parts I-III., Q. Appl. Maths XLV (3), pp. 561-590.
[5] Holmes, P. Lumley, J. L. and Berkooz, G. (1996) Turbulence, Coherent
Structures, Dynamical Systems and Symmetry, Cambridge University
Press.
[6] Hasan Nadeem and Sanghi Sanjeev (2007) Proper Orthogonal Decomposition
and Low-dimensional Modelling of Thermally Driven Twodimensional
Flow in a Horizontal Rotating Cylinder, J. Fluid Mech. Vol.
573, pp. 265-295.
[7] Lumley, J. L. and Poje, A. (1997) Low-dimensional Models for Flows
with Density Fluctuations, Phys. Fluids 9, pp. 2023-2031.
[8] Ohta, T. Mizobata, K. and Kajishima, T. (2006) Influence of Density
Fluctuation on DNS of Turbulent Channel Flow in The Presence of
Temperature Stratification, In Proc. of The 5th Int. Symp. on Turbulence,
Heat and Mass Transfer - Dubrovnik, Croatia, September 25-29.
[9] Ohta, T. Nakamura, K. Mizobata, K. and Kajishima, T. (2007) DNS of
Turbulent Channel Flow with Density Variation Under Some Conditions
of Unstable Stratification, In Proc. of HT2007 ASME-JSME Thermal
Engineering Summer Heat Transfer Conference, July 8-12, Vancouver,
British Columbia, Canada.