Hydrofoil impellers are typically associated with turbulentflow mixing. Simple calculations, computational fluid dynamics, mixing software, and laboratory testing reveal that they are also effective in laminarflow applications.
The selection of an agitator impeller for mixing fluids in tanks is a widely researched field, with many resources available to study fluid flow. Conventional wisdom holds that mediumviscosity fluids in transitional flow are best mixed with a pitchedblade turbine (Figure 1a) and lowviscosity fluids in turbulent flow are mixed best with a hydrofoil impeller (Figure 1b). (Highviscosity fluids in a laminar regime are best mixed with a closeclearance impeller such as a helical ribbon, which is not discussed in this article.)
Pitchedblade turbines typically have four blades at an angle of 45 deg. and have been used since at least the 1940s for generalpurpose mixing of low and mediumviscosity fluids, as well as for simple blending and solids suspension. They can create a vortex at the liquid surface to incorporate dry solids or gases. Their simple shape makes them economical to manufacture.
Hydrofoil impellers have been used since the 1970s in many mixing applications. They usually have three blades, a low angle of attack (15–25 deg. at the blade tip, to avoid boundary layer separation), and a camber in the blade that causes the chord angle to increase from tip to hub (Figure 2). They have been used to blend lowviscosity liquids in shearsensitive applications and to suspend solids. The aerodynamic shape makes the blades more effective at producing flow for a given power and speed than pitchedblades and requires less torque for the same mixing conditions.
Although hydrofoil impellers are usually used in turbulent flow and pitchedblade turbine impellers in transitional flow, both have use in some laminarflow applications. This article compares the performance of pitchedblade turbines and hydrofoils in four ways: manual calculations, computational fluid dynamics (CFD), mixing software, and realworld laboratory testing of a fluid that is very difficult to mix — a highsolids biomass slurry. The analyses demonstrate the utility of hydrofoils in laminarflow applications and show that they perform better in laminarflow than pitchedblade turbines. Advantages of hydrofoils include higher pumping for a given power and shaft speed, as well as a more axial flow pattern and better control of shearthinning fluids.
Impeller performance
Impeller performance characteristics are generally determined empirically by correlating measured data as a function of dimensionless numbers. The four main dimensionless numbers used to study mixing are based on seven key variables: the power delivered (P); the fluid’s density (ρ); the shaft speed (N); the impeller diameter (D); the impeller pumping rate (Q); the fluid’s viscosity (µ); and the tank diameter (T). These variables form the dimensionless numbers:
 power number, N_{P} = P/ρN^{3}D^{5}
 pumping number, N_{Q} = Q/ND^{3}
 Reynolds number, N_{Re} = D^{2}Nρ/µ
 the ratio of impeller diameter to tank diameter, D/T.
Figure 3 presents generic curves for these dimensionless numbers. Flow is fully laminar at Reynolds numbers less than 10, though anything below 40 can be considered laminar flow for most practical purposes. Note that D/T has an effect on both power number and pumping number in turbulent flow, but no effect in laminar flow. Also note that power number is constant in turbulent flow (Reynolds number above 10,000), and becomes inversely proportional to Reynolds number in laminar flow. The dimensionless laminar power number constant, K_{L}, is defined as:
Similarly, the pumping number is constant in turbulent flow. It drops as the flow goes through the transition regime, and then becomes constant in laminar flow.
Compare pumping rates by manual calculation
An effective way to study the mixing performance of different impellers is to calculate the power drawn by each impeller under the same conditions. The power number (N_{P}) and the laminar power number constant (K_{L}) act as a foundation to calculate the power. The literature gives values for K_{L} of 27.4 for a typical hydrofoil and 43.2 for a pitchedblade turbine (1). The pumping number (N_{Q}) is used to calculate impeller pumping; the published value of N_{Q} is 0.214 for hydrofoils and 0.2954 for pitchedblade turbines operating in laminar flow (2). With these data, the relative pumping for both impellers operating at the same power input can now be calculated.
In this example, the tank has a diameter of 2 m, and the fluid has a density of 1,000 kg/m^{3} and a viscosity of 100 kg/msec (100,000 cP). The diameter of the pitchedblade turbine (D_{PBT}) is 0.8 m and the shaft speed is 0.5 sec^{–1}.
To compare the mixing effectiveness of a pitchedblade and a hydrofoil impeller, first calculate the power draw and pumping provided by the 0.8mdia. pitchedblade turbine. Then perform iterative calculations to determine the diameter of a hydrofoil impeller that would draw the same power.
For the pitchedblade turbine impeller:
Reynolds number:
Power number:
Power draw:
Impeller pumping:
The 0.8mdia. pitchedblade turbine impeller drawing 533 W provides a pumping rate of Q_{PBT} = 0.0756 m^{3}/sec.
Now determine the diameter of a hydrofoil impeller that would draw the same power at the same shaft speed. Assume a diameter, calculate Reynolds number, then power number, then power; repeat with different diameters until the power for the hydrofoil matches...
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