PROPER ORTHOGONAL DECOMPOSITION: A TOOL TO STUDY THE UNDERLYING PHYSICS OF TURBULENCE
DOI:
https://doi.org/10.11113/jt.v79.11890Keywords:
POD, turbulent channel, energy dynamics, coherent structures, stratificationAbstract
Wall bounded turbulence have been investigated by many authors to understand the underlying physics, experimentally as well as numerically with different techniques and methods. Enormous studies are reported in the literature in the field of turbulence to get the insight of near wall structure in a broad spectrum of Reynolds number. To recognize the contribution of different turbulent scales in a flow a well-known technique, Proper Orthogonal decomposition (POD) is used. Dynamical behaviour of coherent structure in a turbulent channel flow submitted to high temperature gradient is investigated via proper orthogonal decomposition (POD). The turbulent data is generated using thermal large eddy simulation (TLES) of channel flow at Re = 180 for two values of temperature ratio between hot and cold wall. The POD technique is applied to fluctuating part of the velocity to study the temporal evolution of the most energetic modes. It is observed that dominant flow structures are elongated in streamwise direction which further distorted due to the interaction with bean shaped propagating modes. The plotted average energy E(t) as a function of non-dimensional time shows a constant level of fluctuating energy with one little peak at t+ = 1000, all other smaller spikes are showing constant fluctuations about mean line. This behavior at  quantitatively describe the role of temperature stratification which stabilizes the roll mode energy and prevent them from breakup into smaller scales thus affects the interaction process during turbulent burst event resulting in a chugging or relaminarizing phenomenon. It is observed that thermal stratification decreases the bursting rate by slowing the breaking mechanism of streamwise elongated modes to larger number of bean shaped modes which results in relaminarization of the flow near hot wall.
References
Robinson, S. K. 1991. Coherent Motions in the Turbulent Boundary Layer. Annu. Rev. Fluid Mech. 23: 601-639.
Kasagi, N., Sumitani, Y., and Lida, O. 1995. Kinematics of the Quasi-coherent Vortical Structure in Near-wall Turbulence. Int. J. Heat & Fluid Flow. 16: 2-10.
Kravchenko, A. G., Choi, H., and Moin, P. 1993. On the Relation of Near-wall Streamwise Vortices to Wall Skin Friction in Turbulent Boundary Layers. Phys. Fluids A. 12: 3307-3309.
Kline, S. J., Reynolds, W. C., Schraub, F. A., and Runstadler, P. W. 1967. The Structure of Turbulent Boundary Layers. J. Fluid Mech. 30: 741-773.
Hamilton, J. M., Kim J., and Waleffe, F. 1995. Regeneration Mechanisms of Near-wall Turbulence Structures. J. Fluid Mech. 287: 317-348.
Perry, A. E., and Chong, M. S. 1991. A Description of Eddying Motions and flow Patterns Using Critical-point Concepts. Annu. Rev. Fluid Mech. 19: 125-155.
Zhou, J., Adrian, R. J., Balachandar, S., and Kendall, T. M. 1999. Mechanisms for Generating Coherent Packets of Hairpin Vortices in Channel flow. J. Fluid Mech. 387: 353-396.
Jeong, J. and Hussain, F. 1995. On the Deï¬nition of a Vortex. J. Fluid Mech. 285: 69-94.
Lumley, J. L. 1971. Stochastic Tools in Turbulence. 1st ed. Academic Press, New York, NY.
Sirovich, L. 1987. Turbulence and the Dynamics of Coherent Structures. Part I: Coherent Structures. Part II: Symmetries and Transformations. Part III: Dynamics and Scaling. Q. Appl. Math. 45: 561-590.
Berkooz, G., Holmes, P., and Lumley, J. L. 1993. The Proper Orthogonal Decomposition in the Analysis of Turbulent flows. Annu. Rev. Fluid Mech. 25: 539-575.
Sirovich, L., Kirby, M., and Winter, M. 1990. An Eigenfunction Approach to Large Scale Transitional Structures in Jet flow. Phys. Fluids A. 2: 127-136.
Ball, K. S., Sirovich, L., and Keefe, L. R. 1991. Dynamical Eigenfunction Decomposition of Turbulent Channel Flow. Int. J. Numer. Meth. Fluids. 12: 585-604.
Webber, G. A., Handler, R. A., and Sirovich, L. 1997. The Karhunen–Lo´Eve Decomposition of Minimal Channel Fow. Phys. Fluids. 9: 1054-1066.
Jim´enez J. and Moin P. 1991. The Minimal FLow Unit in Near-wall Turbulence. J. Fluid Mech. 225: 213-240.
Yahya, S. M., Anwer S. F., and Sanghi, S. 2013. Phenomenological and Statistical Analyses of Turbulence in Forced Convection with Temperature-Dependent Viscosity Under Non-Boussinesq Condition. Eur. Phys. J. E. 36: 120.
Lumley, J. L., and Poje, A. 1997. Low-dimensional Models for flows with Density Fluctuations. Phys. Fluids. 9: 2023-2031.
Deane, A. E., and Sirovich, L. 1991. A Computational Study of Rayleighbenard Convection. Part I. Rayleigh-number Scaling. J. Fluid Mech. 222: 231-250.
Webber, G. A., Handler, R. A., and Sirovich, L. 2002. Energy Dynamics in a Turbulent Channel Flow using the Karhunen-Loeve Approach. Int. J. Numer. Meth. Fluids. 40: 1381-1400.
Duggleby, A., Ball, K. S., and Paul, M. R. 2007. Dynamics of Propagating Turbulent Pipe Flow Structures. Part II: Relaminarization. arXiv:physics/0608259 [physics.u-dyn] 0608: 1-20.
Downloads
Published
Issue
Section
License
Copyright of articles that appear in Jurnal Teknologi belongs exclusively to Penerbit Universiti Teknologi Malaysia (Penerbit UTM Press). This copyright covers the rights to reproduce the article, including reprints, electronic reproductions, or any other reproductions of similar nature.
