LID COOLED CAVITY

Natural convection of water in the box cooled from the top. The top isothermal wall is kept at -10C. Side walls made of Plexiglas permit heat transfer to the cavity from an external bath kept at  temperature 20C.  Propagation of the ice front from the top wall visible. The cold liquid (red colour of the liquid crystal tracers) separates from the ice surface and flows down to the bottom along the box axis. Next it warms up (change colour from red, through green to blue), and returns along side walls back to the top. [48-50,60].

 
Image analysis allows quantitative evaluation of the colours. It gives full 2D temperature field (Particle Image Thermometry). The cross-correlation of two images taken at some time interval allows to evaluate full 2D velocity field (Particle Image Velocimetry). Latest improvement of PIV evaluation - application of Optical Flow based on the use of Dynamic Programming [56,61].

DIFFERENTIALLY HEATED CAVITY

This flow configuration resembles a popular "bench mark" case, natural convection in a cubical cavity with differentially heated end walls [52,53,55,57,59,60,62,64,66,71,72,74] . However, the behaviour of natural convection of water in the vicinity of the freezing point creates interesting and also difficult for numerical modelling flow structures. The competing effects of positive and negative buoyancy force result in a flow with two distinct circulations. First one, "normal" clockwise circulation, where the water density decreases with temperature (upper-left cavity region) and an "abnormal" one with the opposite density variation and counter-clockwise rotation (lower-right region). The convective heat transfer from the hot wall is limited by the abnormal circulation, separating it form the freezing front. Hence, the phase front which is only initially flat, with time becomes strongly deformed, with a characteristic "belly" at its lower part. This type of the flow structure appears very sensitive to thermal boundary conditions at the side walls. Despite improvements of the numerical model (side walls are included in the computational domain), the computational results differ in detail from their experimental counterparts.

  Ice front observed at centre plane (z=0.5) of the cube at 3000s, T_h=10^oC, T_c=-10^oC. TLC tracers (top left), evaluated velocity (bottom left) and temperature (top right) fields. Numerical result (bottom right), the full temperature field solution (with the side walls), external temperature of air 25^oC.

An eventual source of observed discrepancies could be supercooling of water, which delays creation of the first ice layer and deforms the flow pattern at the top of the cavity. It is well known that pure water may supercool as far as ­40^oC, before freezing occurs.  Movie below shows sequences of the flow images taken during 3000s of the freezing experiment.

Initially the whole cavity and fluid is at hot wall temperature. The experiment starts by abruptly dropping the cold wall temperature to -10^oC. At the first moment a red plume of water at temperature well below freezing point moves along the cold wall to the top of the cavity (red colour of TLC indicates cold liquid). It may cover as much as 30% of the upper wall before sudden solidification occurs (usually after 30-100s). An ice layer developed at the top quickly melts due to the hot clockwise circulation, but initial disturbance of the flow and temperature fields may affect the front propagation for a longer period.
 
 

3-D numerical simulations illustrate well the complex flow structure appearing in the differentially heated cavity.
Look at the AVS supported visulization (ICM), showing particle tracks generated from the 3-D solutions for natural convection and freezing of water. Two complex spiralling motions are present due to the water density annomaly.

Some more numerical simulations of the freezing problem can be found at Tomasz Michalek personal web page.

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Onset of convection in differentially heated cavity