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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

## Abstract

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 $5.0×107≤Ra≤3.4×108$. 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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## Figures

Fig. 1

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

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

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

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

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

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

Fig. 6

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

Fig. 8

Total energy as a function of number of modes

Fig. 9

Cumulative energy as a function of number of modes

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

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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