Cooling beyond the boundary value in supercritical fluids under vibration

Abstract

Supercritical fluids when subjected to simultaneous quench and vibration have been known to cause various intriguing flow phenomena and instabilities depending on the relative direction of temperature gradient and vibration. Here we describe a surprising and interesting phenomenon wherein temperature in the fluid falls below the imposed boundary value when the walls are quenched and the direction of vibration is normal to the temperature gradient. We define these regions in the fluid as sink zones, because they act like sink for heat within the fluid domain. The formation of these zones is first explained using a one-dimensional (1D) analysis with acceleration in constant direction. Subsequently, the effect of various boundary conditions and the relative direction of the temperature gradient to acceleration are analyzed, highlighting the necessary conditions for the formation of sink zones. It is found that the effect of high compressibility and the action of self-weight (due to high acceleration) causes the temperature to change in the bulk besides the usual action of piston effect. This subsequently affects the overall temperature profile thereby leading to the formation of sink zones. Though the examined 1D cases differ from the current two-dimensional (2D) cases, owing to the direction of acceleration being normal as compared to parallel in case of former, the explanations pertaining to 1D cases are judiciously utilized to elucidate the formation of sink zones in 2D supercritical fluids subjected to thermal quench and vibrational acceleration. The appearance of sink zones is found to be dependent on several factors such as proximity to the critical point and acceleration. A surface three-dimensional plot illustrating the effect of these parameters on onset time of sink zones is presented to further substantiate these arguments.

Vibration-induced thermal instabilities in supercritical fluids in the absence of gravity

“…In this section, we present the mathematical model applied to solve the full set of governing equations (see also details in [24,25]). Let us consider a Newtonian fluid characterized by its thermo-physical properties, namely density , isothermal compressibility, and thermal expansion coefficient at constant pressure, .…”

“…Thetis, which has already been described and validated for a number of benchmark cases for incompressible fluids [26,27] and compressible fluids [24,[28][29][30]. The fluxes in the equations are discretized using second order centred difference scheme.…”

On the long-time transient formation of sink zones in near-critical fluids. A theoretical perspective

“…2005 a , b ) and simultaneous thermal quench and vibration (Amiroudine & Beysens 2008; Zappoli, Beysens & Garrabos 2016; Sharma, Erriguible & Amiroudine 2017 a , b ). A striking phenomenon, wherein the temperature of the SCF in the bulk drops below the imposed boundary temperature upon simultaneous thermal quench and vibration in zero-gravity conditions, was previously investigated numerically (Sharma, Erriguible & Amiroudine 2017 a ). This subcooling phenomenon was also observed in experiments performed under microgravity in low Earth orbit by using SF 6 at liquid-like density (Beysens, Fröhlich & Garrabos 2011).…”

“…This subsequently affects the overall temperature profile thereby leading to the formation of sink zones. The explanation for the one-dimensional case can be judiciously extended to explain the sink-zone appearance in the two-dimensional numerical simulations of Sharma, Erriguible & Amiroudine (2017 a , b ). Furthermore, the appearance of sink zones is found to depend on several factors such as proximity to the critical point and acceleration.…”

“…The temperature in their case was found to rise above the wall temperature near the corners. Very recently, Sharma, Erriguible & Amiroudine (2017 a , b ) analysed numerically the behaviour of a SCF under the combined effect of thermal perturbation and mechanical vibration. They considered a square cell (size h = 7 mm) with solid walls filled with supercritical H 2 .…”