# Primary and secondary instabilities in a glass-melting surface

## Abstract

The transition from steady laminar to chaotic convection in a glass-melting furnace specified by upper surface temperature distribution has been studied by direct numerical analysis of two- and three-dimensional time dependent Navier-Stokes equations. Thermal instability of the convection roll may take place when the modified Rayleigh number Ra{sub m} is larger than 9.71 {times} 10{sup 4}. It is shown that the basic flow patterns in a glass-melting furnace are steady laminar, unsteady periodic, quasi-periodic, and chaotic flow. The instabilities have the characteristic (viscous diffusion, {tau}{sub d} = H{sup 2}/{nu}{sub 0}) timescales observed in the typical transitions. Through primary (2-D) and secondary (3-D) instability analyses, the fundamental unsteady feature in a glass-melting furnace is well defined as an unsteady periodic or a weak chaotic flow with typical periods of 1--3 times {tau}{sub d}. The results strongly imply the possibility of unsteady or chaotic flow in glass melters.

- Authors:

- Hanyang Univ., Seoul (Korea, Republic of). School of Mechanical Engineering
- KAIST, Taejon (Korea, Republic of). Dept. of Mechanical Engineering

- Publication Date:

- OSTI Identifier:
- 687496

- Resource Type:
- Journal Article

- Journal Name:
- Numerical Heat Transfer. Part A, Applications

- Additional Journal Information:
- Journal Volume: 36; Journal Issue: 3; Other Information: PBD: 27 Aug 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATION; GLASS INDUSTRY; FURNACES; TRANSITION FLOW; TEMPERATURE DISTRIBUTION; NUMERICAL ANALYSIS; CONVECTION; INSTABILITY; UNSTEADY FLOW

### Citation Formats

```
Lim, K.O., Lee, K.S., and Song, T.H.
```*Primary and secondary instabilities in a glass-melting surface*. United States: N. p., 1999.
Web.

```
Lim, K.O., Lee, K.S., & Song, T.H.
```*Primary and secondary instabilities in a glass-melting surface*. United States.

```
Lim, K.O., Lee, K.S., and Song, T.H. Fri .
"Primary and secondary instabilities in a glass-melting surface". United States.
```

```
@article{osti_687496,
```

title = {Primary and secondary instabilities in a glass-melting surface},

author = {Lim, K.O. and Lee, K.S. and Song, T.H.},

abstractNote = {The transition from steady laminar to chaotic convection in a glass-melting furnace specified by upper surface temperature distribution has been studied by direct numerical analysis of two- and three-dimensional time dependent Navier-Stokes equations. Thermal instability of the convection roll may take place when the modified Rayleigh number Ra{sub m} is larger than 9.71 {times} 10{sup 4}. It is shown that the basic flow patterns in a glass-melting furnace are steady laminar, unsteady periodic, quasi-periodic, and chaotic flow. The instabilities have the characteristic (viscous diffusion, {tau}{sub d} = H{sup 2}/{nu}{sub 0}) timescales observed in the typical transitions. Through primary (2-D) and secondary (3-D) instability analyses, the fundamental unsteady feature in a glass-melting furnace is well defined as an unsteady periodic or a weak chaotic flow with typical periods of 1--3 times {tau}{sub d}. The results strongly imply the possibility of unsteady or chaotic flow in glass melters.},

doi = {},

journal = {Numerical Heat Transfer. Part A, Applications},

number = 3,

volume = 36,

place = {United States},

year = {1999},

month = {8}

}