Page 233 - Modelling in Transport Phenomena A Conceptual Approach

7.6. DESIGN OF A SPRAY TOWER 213

Once the air mass flow rate, *a, is calculated from Eq. (7.6-2), the diameter
of the tower is calculated as

(7.6-3)

7.6.2 Determination of Tower Height

Tower height, H, is determined from
H=vtt (7.6-4)

The terminal velocity of the falling particle, ut, is determined by using the formulas
given in Section 4.3. The required cooling time, t, is determined from the unsteady-
state energy balance around the melt particle.

7.6.2.1 Terminal velocity

The Turton-Clark correlation is an explicit relationship between the Archimedes
and the Reynolds numbers as given by Eq. (4.3-12), i.e.,

Ar
Rep = - [1+ 0.0579 Ar0*412] -1.214 (7.6-5)
18
The Archimedes number, Ar, can be calculated directly when the particle diam-
eter and the physical properties of the fluid are known. The use of Eq. (7.6-5)
then determines the Reynolds number. In this case, however, the definition of
the Reynolds number involves the relative velocity, v,, rather than the terminal
velocity of the melt particle, i.e.,

(7.6-6)

Since the air and the melt particle flow in countercurrent direction to each other,
the relative velocity, wT, is
21, = Vt + Va (7.6-7)

7.6.2.2 Cooling time

The total cooling time consists of two parts: the cooling period during which
the melt temperature decreases from the temperature at the inlet to T, and, the
solidification period during which the temperature of the melt remains at T,.

i) Cooling period: Considering the melt particle as a system, the terms appearing