Auxiliary
Scale-up of the Auxiliary Tanks
Since the auxiliary impellers are not affected by the flow from the pumper, and since they do not contribute to the net flow through the SX-circuit, the auxiliary impellers are designed independent of the pumper. Experience has shown, though, that up-pumping is better than down-pumping axial impellers because down-pumpers add to the overall head of the pumper. With Equations 9 and 10, the auxiliary tanks can also be designed. The effect of residence time on the dispersion stability is very complicated. In some cases, a longer residence time requires a higher power. In other cases it is exactly the opposite. For this reason, the trend of residence time on the operating range has been neglected. The variability is approximately ± 0.02 kW/m3. The typical operating range is between 0.036–0.13 kW/m3 regardless of Z/T. In order to get a really good top-to-bottom flow pattern the axial impellers should neither be too small nor too large. A good range is from D/T=0.3 to 0.5.
The design procedure is once again iterative. First see if one auxiliary can fulfill the requirements of Equations 9 and 10. If not, try two or three. Conceptually split the auxiliary stage into equal zones.
Example 7: A full-scale auxiliary impeller is to be designed
to go along with the pumper in Example 4: The auxiliary tank is 20% greater in volume,
but has the same footprint.
From Example 5, the flow rate is Q=0.745 m3/s (11808 GPM). The pumper
stage volume, VP=39.2 m3=39,200 L (10356 gallons). T=3.66m (144”).
The volume of the auxiliary stage is 1.2*39.2 m3=47 m3
(12412 gallons). Z=3.51m (138”). Z/T=0.96. Res=63 seconds. Operating range is
between 0.075–0.092 kW/m3. Assuming that DI/T=0.375, the unit must
run at 82 RPM.
PI/VI=0.079 kW/m3. PI=3.73 kW.
Example 8: Solve Example 7 with 2
A310s.
The lower one is at the same place as the one in Example 7. DI/T=0.375. The
spacing, S=1.75 m (69”). COV/D=1.28. COV/T=0.479. The operating range according to
Equations 9-10 is 0.060–0.069 kW/m3 per impeller. Running the impellers
at 60 RPM makes PI=1.46 kW each. The total power is 2.92 kW, which is 0.81 kW
less than Example 7. PI/VI=0.062 kW/m3.
Sometimes none of this works ideally. Lightnin has recently developed the
A510 with variable tip chord
angle (TCA) for just this purpose. Different power numbers result from the different
TCAs, allowing for some fine tuning and achieving an optimum dispersion at the least
possible power, without compromising an ideal impeller diameter ratio.
Comparison With Other
Impeller Designs
In this paper, I have demonstrated the use of dimensionless numbers for the
design and scale-up of SX-pumpers. The
R300 was used because enough data on it has already been published. It is not the
best impeller for this purpose, since its hydraulic efficiency is only in the low 20%.
The Holmes Narver straight bladed pumper obtains 25% less head than the
R300 and the only difference is
the blade height (hBlade/D=1/8) [2,6]. By increasing the orifice opening
from DO/D=0.33 to DO/D=0.46, the hydraulic efficiency of this impeller increases from
21% to about 29%. Not enough data is published to construct the head-flow and
power-flow plots.
The Davy BB is a curved bladed impeller with a disk and a lower shroud spinning
on top of a draft tube half its size. It, too, has a narrow blade height of (h
Blade/D=1/7) [6]. The Davy BB normally has six curved blades, although pictures of
it have shown up with 8 blades [10,11]. The six-bladed version can reach a
hydraulic efficiency of 26% [2-5]. Not enough data is published to construct the
head-flow and power-flow plots.
The Lightnin R323 and the R320
are curved bladed impellers with different blade radii. The hydraulic efficiencies of
these impellers is 32% and 39%, respectively [2-5]. Other curved bladed pumpers
have reportedly reached 45-67% [6]. Not enough data is published to construct the
head-flow and power-flow plots. Scale-up tests at Lightnin confirmed the technique [16].
Comparison with the Outokumpu pumper and auxiliary mixer requires detective work.
Finding the answers is not easy. Thus, some of the following comparisons may be slightly
off, due to guesswork on my part.
The Outokumpu DOP appears to be similar to a Davy BB, but with more blades. Based on
the water test data reported for the DOP in Zaldivar, the 1.68m (66”) DOP operates
at Nq=0.186, Np=1.51, and Nh=0.575 at 70 RPM [8]. The hydraulic efficiency is 34.8%.
At 40 RPM, Np=1.26, Nh=0.44 and e =32.0%. The volume of the DOP casing is about 2.78
m3, having a 5 second residence time at 2000 m3/hr. During
normal running conditions the DOPs consumed 8.5 kW in the extraction and wash stages.
That makes 3.07 kW/m3 in the DOP casing, Np=1.77, Nh=0.726 and e =35.3%. In
the stripping stage the power was 11 kW. PP/VP=3.98 kW/m3
, Np=2.43, Nh=0.726, and e =27.3%.
Some data is available for the Outokumpu DOP at Radomiro Tomic, Chile [12-14].
DP=2.0 m (78.7”), T=5.0 m (197“), q Res,DOP=3-5 seconds,
QMax=3600 m3/hr=1m3/s (15850 GPM) [14]. Volumes of
the tanks are not given, but the total mean residence time at 3500 m3/hr is
3 minutes [12]. Since the volume of both Spirok mixers is about 100 m3, the
residence time in each Spirok mixer would be 51.7 seconds, meaning that the DOP has a
larger volume [14]. In Zaldivar, the VDOP/VSPIROK=30/40=0.75
[15]. Keeping the dimensions similar also because the diameter ratios of the tanks are
the same, too, VDOP=37.5 m3 and Z=0.4 and qRes
=35 seconds. Fitting the head-flow data of [12] gives some strange results. Take the
point Q=4000 m3/hr, TS=4.2 m/s, amd H=0.4 m, would result in Nq=0.208,
Nh=0.435, Np=0.7 (so that P/V=0.17 kW/m3) and e=63.7%
which I doubt very much. Maybe the volume should be larger or the P/V is really higher
than stated in the reports. Take another point, Q=2000 m3/hr, TS=3.8 m/s,
H=0.55 m. Then Nq=0.115, Nh=0.75, Np=0.6 (P/V=0.07 kW/m3) e =
70.9% or Np=1.45 (P/V=0.17 kW/m3) e =29.3%. One last point, Q=3000 m3
/hr, TS=5.03 m/s, H=0.92 m. Then Nq=0.13, Nh=0.712, Np=0.25 (P/V=0.07 kW/m
3) e=183% (not possible) or Np=0.61 (P/V=0.17 kW/m3) e =75%.
Obviously, too much data had to be guessed and that is probably the reason for the
strange power numbers. Too bad Outokumpu makes it so hard to find the data
(4 publications spanning 4 years)!
The Outokumpu Spirok is the auxiliary impeller of the VSF Design at Zaldivar.
They have determined that 0.15 kW/m3 is required to maintain a fit dispersed mixing
state. With a volume of about 41.7 m3 for each Spirok mixing tank, P/V=0.173
kW/m3 and 0.252 kW/m3 for the extraction and wash stages, and the stripping
stage, respectively. P=7.2-10.5 kW. Assuming the same proportions as the Radomiro
Tomic Spirok, T=Z=3.76 m and D/T=0.708, D=2.66 m. Assuming similar tip speeds as at
Radomiro Tomic (TS=3.5 m/s), N=25 RPM. Np=0.75, qRes=60 seconds.
The Outokumpu Spirok at Radomiro Tomic, Chile have T=4.0 m, DSPIROK=2.83,
D/T=0.708. With a volume of about 50 m3, Z=4 m , so Z/T=1 [14]. At 3500 m
3/hr, q Res=51.7 seconds. TS=3.5 m/s, so that N=24 RPM and Np=0.75,
PIVI=0.17 kW/m3.
I found some small-scale data from Outokumpu [11]. As with the data above, the data
is incomplete. For these tests an 8-bladed DOP was compared to a Holmes and
Narver straight bladed pumper. The DOP looked very similar to a Davy BB. The tank was
T=144mm, Z=144mm and D/T=0.694, D=100mm. No information was given on flow rate or
power consumption, so all we can look at is the head number, Nh. TS is in m/s, H in mm,
and Nh is of course dimensionless. This table demonstrates the power of scaling up using
the methodology outlined in this report. The Nh values that Outokumpu reported on for
the Holmes and Narver pumper are very similar to those found in Figure 5 near
optimum efficiency. The DOP would have a much higher hydraulic efficiency even if the
power and flow were just the same. The Nh values of the DOP are very similar to
those determined at plants with a linear scale-up of 20 times or a volumetric scale-up
of 21700 times (see Radomiro Tomic above).
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