The focus of this work was to investigate non-wetting liquids in unsaturated packed beds in order to establish a better understanding of effective liquid drop size, velocity and contact areas between liquids and particles based on a microscopic analysis.
Results from this work show that binary drop break up mechanisms can be used as a basis for predicting effective drop size for liquid in unsaturated packed beds. A theory is developed to predict the average drop size, Vavg, in the bed due to the binary break up. Experiments were conducted to determine the break up mechanisms by impacting liquid drops on non-wetting particles and in non-wetting packed beds. The liquids used in these experiments were water, mercury, and glycerol and wax particles of diameter 20 mm were used in the packed beds. A significant advantage of this model is that the effect of liquid properties, drop shape, particle properties, bed size, structure and flow rate on the liquid distribution is incorporated.
A model to predict the average velocity, uavg, of a liquid drop through a non-wetting unsaturated packed bed is developed using a simple force model. It treats the liquid as a discrete phase and includes the effects of gravity, gas drag and inertial and viscous bed resistance. Experiments were conducted to measure the average velocity of liquid drops through beds of cylindrical and spherical particles. Both single drops and point source continuous flow were used. These data also were compared with Liu's (1999) macroscopic level liquid flow studies in non-wetting packed beds irrigated with point sources. Experimental materials used in these studies were similar. Water, mercury and glycerol were used as testing liquids through packed beds of wax particles. The model predictions are consistent with the experiments.
Drop flow was observed for large spherical particles and low liquid flow rate.
The average drop size, Vavg is given by:
Vavg=π/12 [(αe+αl) √(3(1-cosθ )/(Bo +12) dp]3
where Bo is the Bond number, dp is the particle diameter, αl is the landing angle αe is the critical equilibrium and θ is the static contact angle.
The contact area of a sliding drop with the solid Als is given by:
Als=π/4 ((We+Bo+12)/(C We/√Re+3(1-cosθ))d20
where We and Re are the liquid Weber number and Reynolds number at uavg, d0 is the liquid diameter, θ is the static contact angle and C is a constant equal to 4.2 for the low-viscosity liquid and 6.38 for the high-viscosity liquids.
The model is used to predict the average liquid size and velocity of liquid iron and slag in the blast furnace lower zone. For the first time, a model is presented which predicts the effective liquid drop size, average velocity and liquid-particle contact areas of liquid iron and slag separately.
A mathematical model of heat transfer in the dripping zone has been developed that estimates the steady state temperature of gas, solid, liquid iron and slag. This model considers the liquid iron and slag as separate non-wetting liquids. Liquid iron moves fast within the coke bed with low contact areas. Thus, the principal heat transfer mode to the liquid iron is from the gas.