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This is a continuation of the Process Intensifier - Optimization with CFD: Part 1 paper.

Residence Time Distribution

Residence time is computed using Lagrangian analysis particle tracking procedures within the resultant flow state. The tracers are assumed to be neutrally buoyant and convected along by the flow. That is, that the tracers do not influence the flow field. This class of analysis by definition applies to discrete particles and not continuous flow characteristics. Two classes of analysis are done in this fashion, which include extracting particle path information along with a variant on Poincare analysis looking at plane intersections for the determination of residence time. The plane intersections provide this residence time by recording the time, position, velocity, and a number of other variables as a particle intersects a specified plane. The standard interpretation of Poincare planes is that they are applied in mixing tanks to collapse time out of the analysis. Data extracted from plane intersections can be subsequently studied by a variety of statistical means looking at min, max, average, median, and a variety of other statistical measures.

Residence time statistics are handled from the injection point to a vertical plane at 35 inches (900 mm) down stream from the impellers. In the case of the radial impellers, the injection point is exactly below the lower impeller. In the case of the HGA the injection point is from that pipe between the criss-cross flow straighteners and the impeller shaft, which is 4 inches (100 mm) upstream of the shaft. For the LTA, the injection point is 35 inches (900 mm) up stream, either at the center of the pipe or split into two feed locations at the respective heights of the axial impellers.

1250 tracer particles were used in each CFD experiment of Table 6. LTR, HGR, and HGA had two injection ports. For these 625 tracer particles were used through each port. LTA had a singular port and so all 1250 tracer particles went through that port. The LTA - Split Injection case had two injection ports at the respective height of the impellers. Figures 19 - 20 show the results graphically.

The time scales of Figures 19-20 are logarithmic so that more detail can be given to the shorter times.

Model LTR LTR HGR HGR HGR LTA LTA LTA LTA LTA HGA HGA
Q 650 1100 650 1100 750 650 650 1100 1100 1100 650 1100
N 1750 1750 1750 1750 1500 1750 1750 1750 0 1750 1750 1750
Info         Non-Newtonian   Split Injection     Split Injection    
 
Min 0.48 0.57 0.39 0.35 0.41 1.76 1.87 1.13 1.09 1.08 0.77 0.46
Max 10.66 6.01 6.22 34.09 4.91 5.27 5.15 4.02 1.87 3.23 3.53 2.00
Spread 10.17 5.45 5.83 33.73 4.50 3.51 3.28 2.89 0.78 2.16 2.76 1.54
 
Mean 1.35 0.80 1.27 0.75 1.10 2.26 2.26 1.34 1.34 1.34 1.27 0.75
Median 1.57 1.30 1.21 1.02 1.15 2.15 2.29 1.16 1.19 1.31 1.36 0.77
Ave 1.89 1.46 1.54 1.16 1.37 2.27 2.46 1.19 1.20 1.42 1.41 0.81
STD- 0.78 0.84 0.53 0.04 0.62 1.92 1.95 1.04 1.14 1.13 1.03 0.60
STD+ 3.00 2.09 2.55 2.28 2.11 2.61 2.97 1.34 1.27 1.71 1.78 1.03
 
STD 1.11 0.62 1.01 1.12 0.75 0.34 0.51 0.15 0.07 0.29 0.37 0.21
VAR 1.23 0.39 1.01 1.25 0.56 0.12 0.26 0.02 0.00 0.08 0.14 0.05
SKEW 2.81 0.51 1.44 32.25 0.55 0.08 0.25 0.04 0.00 0.04 0.05 0.01
Table 6: Statistics of the residence time distributions of all systems tested. With the exception of VAR (variance) and SKEW all the other statistical numbers are in time units of seconds. The Mean is based on the volume and the volumetric flow rate that the tracers passed through. The flow rate, Q, is in GPM. The impeller speed, N, is in RPM.


650 GPM Radial Process Intensifier Axial Process Intensifier
Lightnin
  LTR LTA
Hayward Gordon
  HGR HGA
Figure 19: Residence Time Distribution Plots for 650 GPM (148 m3/hr).


1100 GPM Radial Process Intensifier Axial Process Intensifier
Lightnin
  LTR LTA
Hayward Gordon
  HGR HGA
Figure 20:Residence Time Distribution Plots for 1100 GPM (250 m3/hr)

Even though the Radial Process Intensifiers are fairly similar, the residence time distributions (RTD) are slightly different and show that they are not alike (Figures 19-20). At 650 GPM (148 m3/hr), each impeller develops at least 50% more flow than the overall throughput flow (Table 5). The RTD of the LTR is more normally distributed than the HGR, even though the spread of the tracers is wider for the LTR. The HGR has almost an even distribution of times through itself. The RTD is quite flat. In both cases about as many tracers go through the unit faster than the mean as are retained longer. This is illustrated in Figures 17-18. At 1100 GPM (250 m3/hr) both of them have more particles getting trapped in recirculation areas and are retained longer than the mean. At the higher flow rate, the HGR does a better job, even though the STD of LTR is much tighter. Almost all tracer particles are retained longer than the mean flow. This is actually quite amazing and shows that the tracer material will be longer mixed with the fluid around it before leaving the Process Intensifier in a fairly tight band. To help these two units, the injection of the second component should be at a better spot (see Part 2).

The Axial Process Intensifiers are not similar at all, which was to be expected from the previous discussions. The LTA can barely affect the RTD, whereas the HGA is doing a very good job at both flow rates. Figure 17 does show distribution of particles and the RTD plot does show that more than half of the particles do come out after the mean. Figure 18 also reflects the more uniform distribution as seen here. The difference has a lot to do with the point of injection (discussed later).

At both pipe flow rates, the majority of the tracer particles from LTA travel through the pipe faster than the mean flow. This is not good and indicates that the tracer particles are indeed by-passing the impellers. At 650 GPM (148 m3/hr), there is some retention of the tracers (about 40%) indicating that the impellers are doing something. Figure 17 shows that much of them do continue right through the middle, between the two impellers. At the higher flow rate, 1100 GPM (250 m3/hr), the LTA is totally overwhelmed. Figure 20 shows the tightest RTD of them all, and it is the worst mixing. Notice that there are a few tracer particles that do come in after the mean. These are tracer particles that were probably lucky enough to hit the shaft on the way. Otherwise essentially all of the tracer particles traveled pass the impellers without noticing them.

It is often said that a tight residence time distribution is desirable because all particles will "see" the same environment. A certain spreading of the residence time distribution is obviously necessary in a pipeline so that axial (or backmixing) is possible. Otherwise slugs of concentration gradients can be traveling through the pipeline. Furthermore, it appears that a tight RTD after the mean is ideal.

LTA 1100 GPM 1750 RPM Single LTA 1100 GPM 1750 RPM Dual
lta model.jpg (56180 bytes)
LTA 1100 GPM 0 RPM - Single
LTA 650 GPM 1750 RPM Single LTA 650 GPM 1750 RPM Dual
Figure 21: Residence Time Distribution Plots for LTA

Because the LTA did so poorly (especially at 1100 GPM (250 m3/hr), we decided to try another injection mode. By doing something similar to HGA, we injected the tracers at the respective heights of the impellers (Dual), but at the same location as the singular injection (single). This way, the flow will bring the tracers to the impellers instead of bypassing them completely. Figure 21 shows the RTD results at both flow rates

At 1100 GPM (250 m3/hr), the improvement is remarkable. Still the majority of the tracers go through the pipe faster than the mean, but about 50% of the particles are retained longer. This illustrates the importance of optimization. The little alteration did not cost any more power to achieve this better result. Even at the lower flow rate of 650 GPM (148 m3/hr), the retention of tracers is much better and more than 50% of them are passing through slower than the mean. Since the power for this device is so low, this would be an ideal pipe mixer for fairly easy components to mix. With the right impeller placement, two or three of these in series would do an excellent job and still use less overall power than any of the other units. Injection closer to the impellers, like HGA, probably would even do a better job (see Part 2).

The middle plot in Figure 21 is the LTA without spinning (N=0 RPM). Even though the RTD looks very different than the RTD of LTA at N=1750 RPM, they are essentially the same, with the exception of a few stragglers at 1750 RPM. They probably got stuck somewhere or were lucky enough to hit the shaft. Both of them have the first particle coming through in about 1.1 s and the last one (with exception of those stragglers) at about the mean, which is 1.34 s. In other words, without the dual injection ports, the LTA could just as well be turned off.

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