Determining Blend Time

Correlations have been developed in a form involving Θ, rotational speed (N), impeller-to-tank diameter ratio (D/T), liquid-level-to-tank diameter ratio (Z/T), and number of similar impellers

(n_i): ΘN(D/T)i(Z/T) ^-jn_i^k = A (1)

If the units for time and length are consistent, A is a constant for an impeller type. Of more practical value is a rearrangement that gives actual blend time for specific types of impellers.

For a four-blade 45° pitched-blade turbine, blend time for 99% uniformity can be expressed as:

Θ_99% = (6.34/N)(D/T)^-2.3(Z/T)^0.5 n_i^-0.7 (2)

For a four-blade straight-blade turbine, which creates radial flow, the expression becomes:

Θ_99% = (4.80/N)(D/T)^-2.3(Z/T)^0.5 n_i^-0.6 (3)

For hydrofoil impellers, typical three-blade, narrow-blade or marine propellers, the expression is:

Θ_99% = (16.4/N)(D/T)^-1.7(Z/T)^0.5 n_i^-0.8 (4)

Achieving 99% uniformity may not suffice for some applications. However, because uniformity by blending follows an exponential relationship, it's possible to adjust for other degrees of uniformity (Table 1).

While Eqs. 2–4 show that a hydrofoil impeller needs more time for blending (because of its larger constant) than pitched-blade and straight-blade turbines, it offers benefits in power and torque reductions because of its lower turbulent-flow power number (Np):

N_p = 1.37 for 4-blade 45° pitched-blade turbine;
N_p = 3.96 for 4-blade straight-blade turbine; and
N_p = 0.31 for 3-blade hydrofoil impeller.

Example Calculation
Suppose a blending application involves adding a small quantity of an active agent to about 3,000 gal. of a water-like liquid in a 96 in.-dia. tank. Liquid level would be about 96 in. A single 30-in.-dia. pitched-blade turbine turning at 68 rpm (1.13 s^-1) provides mixing. Substituting these conditions into Eq. 2 yields an 81-sec. blend time. So in less than one-and-a-half minutes, the 3,000 gal. of liquid can be blended to 99% uniformity.

Figure 1: Feed rate --  Rate of addition can significantly impact the amount of time needed to attain desired uniformity.

It's also possible to find turbulent impeller power (P) in hp. via:

P = (N_p sp.gr. N³D⁵)/1.524 × 10¹³ (5)

where sp. gr. is fluid specific gravity, N is in rpm and D is in in. In this case, P is about 0.69 hp., so a 1-hp. motor would suffice.