Whole field measurements to identify the critical Rayleigh number for the onset of natural convection in top open cavity

ABSTRACT

We report the results of interferometry-based experiments to identify the onset of natural convection in an air-filled top open cavity. Transition from no flow to the onset of fluid motion was identified as the sharp change in local heat transfer characteristics that occur for a small variation in Rayleigh number. Experiments revealed the presence of a thermally stratified layer at the bottom of the cavity when the Rayleigh number is below its threshold value. However, beyond the critical Rayleigh number, a clear distortion of these layers was observed. Interferometric data provided a direct evidence of the possible breakdown of flow symmetry due to the onset of natural convection. Experiments as well as selected numerical simulations indicated toward the existence of a mirror image solution wherein the flow patterns showed transition from one steady state to another (mirror image of first one) due to the inherent perturbations present in the system.

KEYWORDS:

• Top open cavity
• onset of natural convection
• critical Rayleigh number
• interferometry
• mirror image solution

Nomenclature

Cp	=	Specific heat, J/kg K
g	=	Acceleration due to gravity, m/s2
Hc	=	Characteristic height, m
Lb	=	Cavity length, m
p	=	Pressure, Pa
P	=	Dimensionless pressure
Pr	=	Prandtl number
Ra	=	Rayleigh number
T	=	Time, sec
TC	=	Test cell
$\mathrm{\Delta }T$	=	Temperature difference
U,V	=	Dimensionless fluids velocities
X, Y	=	Dimensionless Cartesian coordinate
x, y	=	Cartesian coordinate

Greek Symbols

$\alpha$	=	Thermal diffusivity, m2/s
β	=	Volumetric coefficient of thermal expansion, 1/K
$\rho$	=	Fluid density, kg/m3
$\theta$	=	Dimensionless temperature
$\tau$	=	Dimensionless time

Subscripts

B	=	Bottom
C	=	Critical
c	=	Characteristic
Loc	=	Local
H	=	Hot

Notes

¹ The fact that the cavity is open from the top, as against the conventionally employed configurations, in the present system, the velocity has the normal as well as the tangential components at the top surface.

² It is worth mentioning here that all possible measures were taken during the experimental run time to minimize the effects of system perturbations and external disturbances on the phenomenon under study. For instance, the surfaces of the cavity walls were machine finished in an attempt to minimize surface roughness, floor vibrations were avoided to the extent possible by placing the experimental set-up on vibration isolation pneumatic legs, people’s movement while performing these experiments was strictly prohibited, air conditioners were switched off while recording the experimental data, etc.