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Research Papers: Natural and Mixed Convection

Experimental Investigation of Transitional Natural Convection in a Cube Using Particle Image Velocimetry—Part II: Turbulence Quantities and Proper Orthogonal Decomposition

[+] Author and Article Information
Marios D. Georgiou

Department of Mechanical Science
and Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: georgiou@illinois.edu

Aristides M. Bonanos

Energy, Environment and Water Center,
The Cyprus Institute,
Nicosia, Cyprus
e-mail: a.bonanos@cyi.ac.cy

John G. Georgiadis

Department of Mechanical Science and Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: georgia@illinois.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 28, 2016; final manuscript received June 29, 2016; published online September 20, 2016. Assoc. Editor: Andrey Kuznetsov.

J. Heat Transfer 139(1), 012503 (Sep 20, 2016) (10 pages) Paper No: HT-16-1315; doi: 10.1115/1.4034167 History: Received May 28, 2016; Revised June 29, 2016

An experimental investigation of transitional natural convection in an air filled cube was conducted in this research. The characteristic dimension of the enclosure was H = 0.35 m, and data were collected in the middle plane of the cavity. The Rayleigh number range examined was 5.0×107Ra3.4×108. In Part I, the authors presented the mean velocity profiles in the enclosure and conducted heat transfer measurements on the hot wall. An expression between Nu and Ra numbers was concluded and compared against other correlations available in literature. In the present work, the authors present a complete description of the flow in the enclosure by quantifying the low turbulence regime developed in the cavity. This was accomplished by estimating Reynolds stresses, turbulent kinetic energy, vorticity, and swirling strength. Proper orthogonal decomposition (POD) was employed to analyze the flow fields obtained from the experimental data and retain the most salient features of the flow field. This study attempts to close the gap of available experimental data in the literature and provide experimental benchmark data that can be used to validate CFD codes since the estimated error from particle image velocimetry (PIV) measurements is within 1–2%.

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References

Yang, K. , 1988, “ Transitions and Bifurcations in Laminar Buoyant Flows in Confined Enclosures,” ASME J. Heat Transfer, 110(4b), pp. 1191–1204. [CrossRef]
Tian, Y. , and Karayiannis, T. , 2000, “ Low Turbulence Natural Convection in an Air Filled Square Cavity. Part I: The Thermal and Fluid Flow Fields,” Int. J. Heat Mass Transfer, 43(6), pp. 849–866. [CrossRef]
Tian, Y. , and Karayiannis, T. , 2000, “ Low Turbulence Natural Convection in an Air Filled Square Cavity. Part II: The Turbulence Quantities,” Int. J. Heat Mass Transfer, 43(6), pp. 867–884. [CrossRef]
Davis, G. D. V. , 1983, “ Natural Convection of Air in a Square Cavity: A Bench Mark Numerical Solution,” Int. J. Numer. Methods Fluids, 3(3), pp. 249–264. [CrossRef]
Markatos, N. , and Pericleous, K. , 1984, “ Laminar and Turbulent Natural Convection in an Enclosed Cavity,” Int. J. Heat Mass Transfer, 27(5), pp. 755–772. [CrossRef]
Fusegi, T. , Hyun, J. , Kuwahara, K. , and Farouk, B. , 1991, “ A Numerical Study of Three-Dimensional Natural Convection in a Differentially Heated Cubical Enclosure,” Int. J. Heat Mass Transfer, 34(6), pp. 1543–1557. [CrossRef]
Henkes, R. , and Hoogendoorn, C. , 1990, “ On the Stability of the Natural Convection Flow in a Square Cavity Heated From the Side,” Appl. Sci. Res., 47(3), pp. 195–220. [CrossRef]
Paolucci, S. , and Chenoweth, D. R. , 1989, “ Transition to Chaos in a Differentially Heated Vertical Cavity,” J. Fluid Mech., 201, pp. 379–410. [CrossRef]
Ravi, M. , Henkes, R. , and Hoogendoorn, C. , 1994, “ On the High-Rayleigh-Number Structure of Steady Laminar Natural-Convection Flow in a Square Enclosure,” J. Fluid Mech., 262, pp. 325–351. [CrossRef]
Janssen, R. , and Henkes, R. , 1995, “ Influence of Prandt1 Number on Instability Mechanisms and Transition in a Differentially Heated Square Cavity,” J. Fluid Mech., 290, pp. 319–344. [CrossRef]
Henkes, R. , and Le Quéré, P. , 1996, “ Three-Dimensional Transition of Natural Convection Flows,” J. Fluid Mech., 319, pp. 281–303. [CrossRef]
Ibrahim, A. , Saury, D. , and Lemonnier, D. , 2013, “ Coupling of Turbulent Natural Convection With Radiation in an Air-Filled Differentially-Heated Cavity at Ra=1.5×109,” Comput. Fluids, 88, pp. 115–125. [CrossRef]
Xin, S. , Salat, J. , Joubert, P. , Sergent, A. , Penot, F. , and Quéré, P. L. , 2013, “ Resolving the Stratification Discrepancy of Turbulent Natural Convection in Differentially Heated Air-Filled Cavities. Part III: A Full Convection–Conduction–Surface Radiation Coupling,” Int. J. Heat Fluid Flow, 42, pp. 33–48. [CrossRef]
TSI, 2012, “ Insight 4G: Data Acquisition, Analysis, and Display Software Platform User Guide,” TSI, Inc., Shoreview, MN.
Kahler, C. , Sammler, B. , and Kompenhans, J. , 2004, “ Generation and Control of Tracer Particles for Optical Flow Investigations in Air,” Particle Image Velocimetry: Recent Improvements, Springer, Berlin, pp. 417–426.
Pope, S. B. , 2000, Turbulent Flows, Cambridge University Press, Cambridge, UK.
Wu, Y. , and Christensen, K. T. , 2006, “ Population Trends of Spanwise Vortices in Wall Turbulence,” J. Fluid Mech., 568, pp. 55–76. [CrossRef]
Kriegseis, J. , Dehler, T. , Gnirß, M. , and Tropea, C. , 2010, “ Common-Base Proper Orthogonal Decomposition as a Means of Quantitative Data Comparison,” Meas. Sci. Technol., 21(8), p. 085403. [CrossRef]
Holmes, P. , Lumley, J. L. , and Berkooz, G. , 1998, Turbulence, Coherent Structures, Dynamical Systems and Symmetry, Cambridge University Press, Cambridge, UK.

Figures

Grahic Jump Location
Fig. 1

Experimental setup schematic: The main components of the experiment are the test cavity and the 2D-PIV system

Grahic Jump Location
Fig. 3

〈v2〉 Reynolds stress in the vertical direction as developed in the enclosure: (a) Ra = 5.08 × 107, (b) Ra = 1.50 × 108, (c) Ra = 2.25 × 108, and (d) Ra = 3.40 × 108

Grahic Jump Location
Fig. 2

〈u2〉 Reynolds stress in the horizontal direction as developed in the enclosure: (a) Ra = 5.08 × 107, (b) Ra = 1.50 × 108, and (c) Ra = 3.40 × 108

Grahic Jump Location
Fig. 7

Swirling strength Λci developed in the enclosure: (a) Ra = 5.08 × 107, (b) Ra = 1.50 × 108, and (c) Ra = 3.40 × 108

Grahic Jump Location
Fig. 4

〈uv〉 shear stress developed in the enclosure: (a) Ra = 5.08 × 107, (b) Ra = 1.50 × 108, and (c) Ra = 3.40 × 108

Grahic Jump Location
Fig. 8

Total energy as a function of number of modes

Grahic Jump Location
Fig. 9

Cumulative energy as a function of number of modes

Grahic Jump Location
Fig. 10

First spatial eigenmode in the x-direction as a function of Rayleigh number: (a) Ra = 5.08 × 107, (b) Ra = 7.34 × 107, (c) Ra = 9.42 × 108, (d) Ra = 1.50 × 108, (e) Ra = 1.81 × 108, (f) Ra = 2.00 × 108, (g) Ra = 2.25 × 108, and (h) Ra = 3.40 × 108

Grahic Jump Location
Fig. 5

Turbulent kinetic energy (TKE) developed in the enclosure: (a) Ra = 5.08 × 107, (b) Ra = 1.50 × 108, and (c) Ra = 3.40 × 108

Grahic Jump Location
Fig. 6

Vorticity ω developed in the enclosure: (a) Ra = 5.08 × 107, (b) Ra = 1.50 × 108, and (c) Ra = 3.40 × 108

Grahic Jump Location
Fig. 11

First spatial eigenmode in the y-direction as a function of Rayleigh number: (a) Ra = 5.08 × 107, (b) Ra = 7.34 × 107, (c) Ra = 9.42 × 108, (d) Ra = 1.50 × 108, (e) Ra = 1.81 × 108, (f) Ra = 2.00 × 108, (g) Ra = 2.25 × 108, and (h) Ra = 3.40 × 108

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