Theory and Simulation of the Onsets of Convection Induced by Liquid Diffusion in Liquid and Incipient Instability Caused by Liquid Now in Particle Bed

The theory of transient instability of gas in aqueous liquid proposed by Tan and Thorpe (1999) was extended to study the onset of convection induced by liquid diffision in liquid. 2D time-dependent simulations were conducted using a CFD package - FLUENT to verify the analysis of transient instability. The onset of buoyancy convection induced by liquid mass difhsion was simulated for water diffused into 1-butanol, ethyl acetate and 2-butanone at different temperatures. The formation and the development of the convection plumes were successfully simulated. The transient liquid diffusion simulation was verified using Fick's Law. The average simulated transient Rayleigh number was found to be 13 15, which was close to 1404, i.e. the average value of critical Rayleigh number of 1 100 and 1708 for boundary conditions with fiee-solid and solid-solid surfaces. The simulated onset time, the critical difhsion depth and the size of the plumes were found to agree well with values predicted by theory.By recognizing that the mass transfer effect is very much smaller compared to the effect of momentum difhsion in causing the incipient instability in particle bed, the transient critical Rayleigh number proposed by Tan (2004) was re-defined based on momentum difhsion. The time-dependent simulations for incipient instability caused by liquid flow in particle bed were performed for different particle sizes, flow rates and initial bed heights. The CFD simulations were verified by the variation of particle bed height with superficial velocity. The onset time of incipient instability could be determined by the series contours of volume fraction, velocity vectors and maximum velocity. The simulated critical Rayleigh numbers based on the momentum diffusion were found to be inconsistent. A modified critical Rayleigh number was proposed by incorporating a factor of z,lH to the critical Rayleigh number. The simulated modified critical Rayleigh number was found to be almost constant, Ra,' = 16.8, which was very close to the theoretical value of 17.7 for buoyancy instability for porous media.

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