cases:case079

# Turbulent Natural Convection in an Enclosed Tall Cavity

Experiments have been undertaken to investigate the natural convection of air in a tall differentially heated rectangular cavity (2.18 m high by 0.076 m wide by 0.52 m in depth, shown diagrammatically in the figure 1). They were performed with temperature differentials between the vertical plates of 19.6 and 39.9 C, giving Rayleigh numbers based on the cavity width of $0.86\times 10^6$ and $1.43\times 10^6$. Under these conditions the flow in the core of the cavity is fully turbulent and property variations with temperature are comparatively small.

Fig. 1: Cavity geometry and sample mean temperature profiles

A previously used experimental rig of Dafa'Alla and Betts (1996) was modified, by fitting partially conducting top and bottom walls and outer guard channels, to provide boundary conditions which avoid the inadequately defined sharp changes in temperature gradient and other problems associated with insufficient insulation on nominally adiabatic walls. Mean and turbulent velocity and temperature variations within the cavity have been measured, by LDA and thermocouples. The temperature and flow fields were found to be closely two-dimensional, except close to the front and back walls, and anti-symmetric across the diagonal of the cavity. The partially conducting roof and floor provide locally unstable thermal stratification in the wall jet flows there, which enhances the turbulence as the flow moves towards the temperature controlled plates.

The main measurement results consist of profiles of mean and rms velocity and temperature across the channel at a number of heights, on the mid-span plane (where 2-dimensionality of the flow is good). A number of profiles are also provided at other spanwise locations, allowing 2-dimensionality to be assessed. Further profiles are provided across some of the near-wall layers close to the top and side walls, as well as temperature profiles across the spanwise front and back walls.

A few velocity time series are also provided.

Sample plots of selected quantities are available.

Compressed archives of the files can be downloaded from the links below, or files can be retrieved individually from the tables.

#### Lower Rayleigh Number: $Ra = 8.6 \times 10^5$

Profiles across the centre of the cavity ($z=0$), at various heights $y/H$:

Profiles across the cavity at $z=130$ and $z=230$ mm, for various heights $y/H$:

Profiles at $z=130$ mm Profiles at $z=230$ mm
Vertical Velocity Temperature Temperature
Mean $V$
Rms $v'$
Mean $T$
Rms $t'$
Mean $T$
Rms $t'$
$y/H=0.05$ mv_z130_05_lo.dat
fvv_z130_05_lo.dat
mt_z130_05_lo.dat
ftt_z130_05_lo.dat
mt_z230_05_lo.dat
ftt_z230_05_lo.dat
$y/H=0.50$ mv_z130_50_lo.dat
fvv_z130_50_lo.dat
mt_z130_50_lo.dat
ftt_z130_50_lo.dat
mt_z230_50_lo.dat
ftt_z230_50_lo.dat
$y/H=0.95$ mv_z130_95_lo.dat
fvv_z130_95_lo.dat
mt_z130_95_lo.dat
ftt_z130_95_lo.dat
mt_z230_95_lo.dat
ftt_z230_95_lo.dat

Near-wall profiles normal to the front perspex wall, at $y/H=0.511$ and various $x$ positions across the cavity:

Temperature
Mean $T$
Rms $t'$
$x=19.05$ mm mt_y511_19_lo.dat
ftt_y511_19_lo.dat
$x=38.1$ mm mt_y511_38_lo.dat
ftt_y511_38_lo.dat
$x=57.15$ mm mt_y511_57_lo.dat
ftt_y511_57_lo.dat

Near-wall profiles normal to the top wall, at $z=0$ and $130$ mm for various $x$ positions across the cavity:

Profiles at $z=0$ mm Profiles at $z=130$ mm
Temperature Horizontal Velocity Temperature Horizontal Velocity
Mean $T$
Rms $t'$
Mean $U$
Rms $u'$
Mean $T$
Rms $t'$
Mean $U$
Rms $u'$
$x=19.05$ mm mt_vtz0_19_lo.dat
ftt_vtz0_19_lo.dat
$x=38.1$ mm mt_vtz0_38_lo.dat
ftt_vtz0_38_lo.dat
mu_vtz0_38_lo.dat
fuu_vtz0_38_lo.dat
mt_vtz130_38_lo.dat
ftt_vtz130_38_lo.dat
mu_vtz130_38_lo.dat
fuu_vtz130_38_lo.dat
$x=57.15$ mm mt_vtz0_57_lo.dat
ftt_vtz0_57_lo.dat

Near-wall profiles normal to the bottom wall, at $z=0$ and $130$ mm for various $x$ positions across the cavity:

Profiles at $z=0$ mm Profiles at $z=130$ mm
Temperature Horizontal Velocity Temperature Horizontal Velocity
Mean $T$
Rms $t'$
Mean $U$
Rms $u'$
Mean $T$
Rms $t'$
Mean $U$
Rms $u'$
$x=19.05$ mm mt_vbz0_19_lo.dat
ftt_vbz0_19_lo.dat
$x=38.1$ mm mt_vbz0_38_lo.dat
ftt_vbz0_38_lo.dat
mu_vbz0_38_lo.dat
fuu_vbz0_38_lo.dat
mt_vbz130_38_lo.dat
ftt_vbz130_38_lo.dat
mu_vbz130_38_lo.dat
fuu_vbz130_38_lo.dat
$x=57.15$ mm mt_vbz0_57_lo.dat
ftt_vbz0_57_lo.dat

Temperature profiles across the cavity at mid-height of the 5cm top and bottom rubber walls, at various spanwise $z$ positions:

Temperature profiles across the cavity on the external surface of the front and back perspex walls, at various $y/H$ positions:

Front wall temperature Back wall temperature
$y/H=0.05$ mt_pb_y05_lo.dat
$y/H=0.061$ mt_pf_y06_lo.dat
$y/H=0.10$ mt_pb_y10_lo.dat
$y/H=0.30$ mt_pb_y30_lo.dat
$y/H=0.311$ mt_pf_y31_lo.dat
$y/H=0.50$ mt_pb_y50_lo.dat
$y/H=0.511$ mt_pf_y51_lo.dat
$y/H=0.70$ mt_pb_y70_lo.dat
$y/H=0.711$ mt_pf_y71_lo.dat
$y/H=0.90$ mt_pb_y90_lo.dat
$y/H=0.938$ mt_pf_y95_lo.dat
$y/H=0.95$ mt_pb_y95_lo.dat

Time series of vertical velocity data at selected positions:

Position Velocity time series
$y/H=0.95$, $z=0$, $x=38.1$ mm l_vel_1.dat
$y/H=0.9$, $z=0$, $x=60.2$ mm l_vel_2.dat

#### Higher Rayleigh Number: $Ra = 1.43 \times 10^6$

Profiles across the centre of the cavity ($z=0$) at various heights $y/H$:

Profiles across the cavity at $z=130$ and $230$ mm at various heights $y/H$:

Profiles at $z=130$ mm Profiles at $z=230$ mm
Vertical Velocity Temperature Temperature
Mean $V$
Rms $v'$
Mean $T$
Rms $t'$
Mean $T$
Rms $t'$
$y/H=0.05$ mv_z130_05_hi.dat
fvv_z130_05_hi.dat
mt_z130_05_hi.dat
ftt_z130_05_hi.dat
mt_z230_05_hi.dat
ftt_z230_05_hi.dat
$y/H=0.50$ mv_z130_50_hi.dat
fvv_z130_50_hi.dat
mt_z130_50_hi.dat
ftt_z130_50_hi.dat
mt_z230_50_hi.dat
ftt_z230_50_hi.dat
$y/H=0.95$ mv_z130_95_hi.dat
fvv_z130_95_hi.dat
mt_z130_95_hi.dat
ftt_z130_95_hi.dat
mt_z230_95_hi.dat
ftt_z230_95_hi.dat

Near-wall profiles normal to the front perspex wall, at $y/H=0.511$ at various $x$ positions across the cavity:

Temperature
Mean $T$
Rms $t'$
$x=19.05$ mm mt_y511_19_hi.dat
ftt_y511_19_hi.dat
$x=38.1$ mm mt_y511_38_hi.dat
ftt_y511_38_hi.dat
$x=57.15$ mm mt_y511_57_hi.dat
ftt_y511_57_hi.dat

Near-wall profiles normal to the top wall, at $z=0$ and $130$ mm for various $x$ positions across the cavity:

Profiles at $z=0$ mm Profiles at $z=130$ mm
Temperature Horizontal Velocity Temperature Horizontal Velocity
Mean $T$
Rms $t'$
Mean $U$
Rms $u'$
Mean $T$
Rms $t'$
Mean $U$
Rms $u'$
$x=19.05$ mm mt_vtz0_19_hi.dat
ftt_vtz0_19_hi.dat
$x=38.1$ mm mt_vtz0_38_hi.dat
ftt_vtz0_38_hi.dat
mu_vtz0_38_hi.dat
fuu_vtz0_38_hi.dat
mt_vtz130_38_hi.dat
ftt_vtz130_38_hi.dat
mu_vtz130_38_hi.dat
fuu_vtz130_38_hi.dat
$x=57.15$ mm mt_vtz0_57_hi.dat
ftt_vtz0_57_hi.dat

Near-wall profiles normal to the bottom wall, at $z=0$ and $130$ mm for various $x$ positions across the cavity:

Profiles at $z=0$ mm Profiles at $z=130$ mm
Temperature Horizontal Velocity Temperature Horizontal Velocity
Mean $T$
Rms $t'$
Mean $U$
Rms $u'$
Mean $T$
Rms $t'$
Mean $U$
Rms $u'$
$x=19.05$ mm mt_vbz0_19_hi.dat
ftt_vbz0_19_hi.dat
$x=38.1$ mm mt_vbz0_38_hi.dat
ftt_vbz0_38_hi.dat
mu_vbz0_38_hi.dat
fuu_vbz0_38_hi.dat
mt_vbz130_38_hi.dat
ftt_vbz130_38_hi.dat
mu_vbz130_38_hi.dat
fuu_vbz130_38_hi.dat
$x=57.15$ mm mt_vbz0_57_hi.dat
ftt_vbz0_57_hi.dat

Temperature profiles across the cavity at mid-height of the 5cm top and bottom rubber walls, at various spanwise $z$ positions:

Temperature profiles across the cavity on the external surface of the front and back perspex walls, at various $y/H$ positions:

Front wall temperature Back wall temperature
$y/H=0.05$ mt_pb_y05_hi.dat
$y/H=0.061$ mt_pf_y06_hi.dat
$y/H=0.10$ mt_pb_y10_hi.dat
$y/H=0.30$ mt_pb_y30_hi.dat
$y/H=0.311$ mt_pf_y31_hi.dat
$y/H=0.50$ mt_pb_y50_hi.dat
$y/H=0.511$ mt_pf_y51_hi.dat
$y/H=0.70$ mt_pb_y70_hi.dat
$y/H=0.711$ mt_pf_y71_hi.dat
$y/H=0.90$ mt_pb_y90_hi.dat
$y/H=0.938$ mt_pf_y95_hi.dat
$y/H=0.95$ mt_pb_y95_hi.dat

Time series of vertical velocity data:

Position Velocity time series
$y/H=0.5$, $z=0$, $x=66.2$ mm h_vel_1.dat

The flow formed one of the testcases studied in the 5th ERCOFTAC/IAHR Workshop on Refined Flow Modelling, held at Chatou, Paris in 1996.

1. Bokhari, I.H. (1996), Turbulent Natural Convection in a Tall Cavity. Ph.D. Thesis, UMIST.
2. Betts, P.L., Bokhari, I.H. (2000), Experiments on turbulent natural convection in an enclosed tall cavity. Int. J. Heat and Fluid Flow, Vol. 21, pp. 675-683.
3. Dafa'Alla, A.A., Betts, P.L. (1996). Experimental study of turbulent natural convection in a tall air cavity. Exptl. Heat Transfer, Vol. 9, pp. 165-194.

Indexed data:

case079 (dbcase, confined_flow)
case079
titleTurbulent natural convection in an enclosed tall cavity
authorBetts, Bokhari
year1996
typeEXP
flow_tag2d, scalar, buoyant