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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.
qRes=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 (hBlade/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“), qRes,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/m3) 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 m3/hr, qRes=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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