# Turbulent Natural Convection in a Square Cavity with a Circular Cylinder

## Abstract

In this paper, numerical simulations of high Rayleigh number flows (10 ^{8}-10 ^{10}) were conducted to investigate the turbulent fluid flow and thermal characteristics of natural convection induced by a centrally placed hot cylinder in a cold square enclosure. The effect of the aspect ratio (radius of the cylinder to the side of the cavity) was investigated for three values (0.1, 0.2, and 0.3) for each Rayleigh number. Effects of turbulence induced by the high Rayleigh number (>10 ^{7}) were computed by using the unsteady k-ω model. A spectral-element method with high polynomial order (high resolution) was used to solve the system of unsteady time-averaged equations of continuity, momentum, and energy, along with the turbulence equations. Detailed comparison with other numerical work is presented. Contours of velocity, temperature, and turbulence quantities are presented for various high Rayleigh numbers. Also presented is the influence of the Rayleigh number on the local Nusselt number on the centrally placed hot cylinder and the cold enclosure walls. Time-marching results show that the steady-state solutions can be obtained even for high Rayleigh numbers considered in this study. The results also show that the average and peak Nusselt numbers roughly double for each order of magnitudemore »

- Authors:

- Argonne National Lab. (ANL), Argonne, IL (United States)

- Publication Date:

- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1339154

- Grant/Contract Number:
- AC02-06CH11357

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Thermophysics and Heat Transfer

- Additional Journal Information:
- Journal Volume: 30; Journal Issue: 4; Journal ID: ISSN 0887-8722

- Publisher:
- American Institute of Aeronautics and Astronautics, Inc.

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; natural convection; high Rayleigh number; turbulence; k-ω model

### Citation Formats

```
Aithal, S. M..
```*Turbulent Natural Convection in a Square Cavity with a Circular Cylinder*. United States: N. p., 2016.
Web. doi:10.2514/1.T4873.

```
Aithal, S. M..
```*Turbulent Natural Convection in a Square Cavity with a Circular Cylinder*. United States. doi:10.2514/1.T4873.

```
Aithal, S. M.. Tue .
"Turbulent Natural Convection in a Square Cavity with a Circular Cylinder". United States.
doi:10.2514/1.T4873. https://www.osti.gov/servlets/purl/1339154.
```

```
@article{osti_1339154,
```

title = {Turbulent Natural Convection in a Square Cavity with a Circular Cylinder},

author = {Aithal, S. M.},

abstractNote = {In this paper, numerical simulations of high Rayleigh number flows (108-1010) were conducted to investigate the turbulent fluid flow and thermal characteristics of natural convection induced by a centrally placed hot cylinder in a cold square enclosure. The effect of the aspect ratio (radius of the cylinder to the side of the cavity) was investigated for three values (0.1, 0.2, and 0.3) for each Rayleigh number. Effects of turbulence induced by the high Rayleigh number (>107) were computed by using the unsteady k-ω model. A spectral-element method with high polynomial order (high resolution) was used to solve the system of unsteady time-averaged equations of continuity, momentum, and energy, along with the turbulence equations. Detailed comparison with other numerical work is presented. Contours of velocity, temperature, and turbulence quantities are presented for various high Rayleigh numbers. Also presented is the influence of the Rayleigh number on the local Nusselt number on the centrally placed hot cylinder and the cold enclosure walls. Time-marching results show that the steady-state solutions can be obtained even for high Rayleigh numbers considered in this study. The results also show that the average and peak Nusselt numbers roughly double for each order of magnitude increase of the Rayleigh number for all radii considered. Finally, a correlation for the average Nusselt number as a function of Rayleigh number and aspect ratio is also presented.},

doi = {10.2514/1.T4873},

journal = {Journal of Thermophysics and Heat Transfer},

number = 4,

volume = 30,

place = {United States},

year = {Tue Jul 19 00:00:00 EDT 2016},

month = {Tue Jul 19 00:00:00 EDT 2016}

}

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