Cooling tower

What happens

A cell of 3 × 3 m with 1.2 m of fill cools the water of a plant’s condenser. The water falls through the fill and the fan draws the air up through it; in each of twelve layers the air approaches the state of the water’s surface: its moisture relaxes towards the saturation moisture at the water’s temperature with the transfer units h_d·a·V/q_a (q_a and q_w are the mass flows of air and water), its temperature towards the water’s with Lewis’s factor of 0.92 in addition. Most of the heat goes into evaporating a little of the water; what the air gains in enthalpy, the water loses. Air that leaves a layer supersaturated condenses the excess as fog. The basin under the fill mixes the cooled water with fresh make-up water and sends it back to the condenser.

With 600 kW on 15 kg/s and air at 25 °C and 50 % (wet bulb 17.9 °C), the basin settles at 24.2 °C: the water is cooled through a range of 9.4 K to an approach of 6.5 K above the wet bulb, and 0.22 kg/s evaporates – 0.15 % of the flow for each kelvin of range. Twice the heat raises the basin to 27.1 °C. Drier air cools further: at 15 % the fill’s outlet falls from 25.5 to 23.0 °C, while half the air raises it to 29.3 °C. On a cold, humid day of 5 °C and 80 % the air leaves at 22.4 °C, saturated and carrying 1.07 g of fog per kilogram – the plume; the basin settles at 16.1 °C.

Model: twelve layers in counterflow, solved by shooting from the bottom; Buck’s saturation pressure; a constant Lewis factor; the transfer coefficient 1.8·q_w^0.4·q_a^0.6; the basin of 4 t one well-mixed mass; the fan’s power as the cube of its speed; RK4 at 1 s.

Try this

Let the basin settle, then double the heat load or slow the fan and watch the approach. Make the air dry, then cold and humid: the plume appears.