h2. Velocity Gradients Experiment
h3. Introduction
Following the team's previous experimental research with velocity gradients, this experiment is aimed at differentiating the effects of velocity gradients from capture velocities on tube settler performance. In the team's previous experiments (detailed in [Exploring the Coupled Effects of Capture Velocity and Velocity Gradient on Settler Performance|PSS Spring 2010 Coupling Analysis Experiment]), it was hypothesized that keeping the length to diameter ratio of tube settlers constant would minimize the effects of capture velocity on performance. However, the results indicated that even with a constant length to diameter ratio of 20, high capture velocity significantly contributed to performance deterioration at high flow rates.
After further consideration of the results of previous experiments, the team decided to vary the length to diameter ratio of the tubes in order to keep capture velocity constant. A range of tube diameters (1", 1/2", 3/8", 1/4") were chosen based on available material, and a capture velocity of 10 m/day (the value used in AguaClara plants) was chosen as the constant value for the current set of experiments. From these starting points, the team calculated the required length of tube to achieve a range of specified upflow velocities, Vup's, and corresponding average velocities in the tubes,'s. The Vup's chosen were 1 mm/s, 2 mm/s, and 5 mm/s with corresponding Vα's of 1.04 mm/s, 2.31 mm/s, and 5.77 mm/s. While AguaClara uses an upflow velocity of 1 mm/s, it was predicted that failure would be more likely to occur at higher upflow velocities. The failure criterion used is termed ПV, which is a ratio of the settling velocity to the velocity experienced due to the velocity gradient of the average floc size captured for a 10 m/day capture velocity. If ПV is greater than 1, failure predicted to occur. Values near 1 suggest situations where failure might occur.
The procedure undertaken to calculate the necessary dimensions and flow rates for the experiments is explained below.
1. The team chose a range of tube diameter (1" ½" 3/8" ¼") based on available materials and to ensure a good range of spacings.
2. The team chose to fix capture velocity at 10 m/day based on the value used for AguaClara plants
3. The team used the following relationship for Vα to find the necessary length for each tube diameter required to achieve average velocities of 1.04 mm/s, 2.31 mm/s, and 5.77 mm/s.
{latex}
\large
$$
{{V_\alpha \sin \alpha } \over {V_C }} = {{L\sin \alpha + d\cos \alpha } \over d}
$$
{latex}
4. From the Vα's, the team determined the associated velocity gradients by the equation:
{latex}
\large
$$
{{\partial v_z } \over {\partial r}} = {{ - 2v_{ratio} Q} \over {\pi R^4 \sin \alpha }}r
$$
{latex}
5. The necessary flow rates were calculated from the capture velocities, diameters, and lengths determined above by the following relationship:
6. ПV ratios were determined for each tube evaluated by the following equation:
Table 1 below shows the resulting required lengths, flow rates, and ПV's for the tubes tested.
The table shows that for an upflow of 1 mm/s, failure is not likely to occur except for the smallest diameter tubing. For higher upflow velocities, failure is predicted to occur for more tubes. The team plans to use the 1 mm/s upflow velocity run as a control case to show success and compare performance from the 2 mm/s and 5 mm/s to evaluate failure.
h3. Experimental Methods
In order to run the experiments, the team plans to begin with the longest tubes, which correspond to an upflow of 5 mm/s. This choice was made to minimize the material costs involved in running the experiments.
The conclusions from the previous experiments Exploring the Coupled Effects of Capture Velocity and Velocity Gradient on Settler Performance Problem indicated that there was a problem with particles settling out in the turbidimeter at low flow rates. Experiments performed to evaluate this situation determined that the minimum flow rate necessary to prevent settling was 50 mL/min. Table 1 above indicates that for smaller tubes the flow rates necessary to achieve the desired conditions are less than 50 mL/min. In order to address this issue, the team has decided to use bundles of tubes joined by a manifold and a reservoir system. Equal flow distribution is ensured in the tubes by placing small orifices in the manifold to provide high headloss. The flow from the tube bundles is pumped into the reservoir continuously until a certain water height is reached. This period of time is called the "loading state." At that point, a pump begins pulling water out of the reservoir to the turbidimeter at a flow rate higher than 50 mL/min. This period of time is called the "withdrawal state." The pump shuts off when a minimum water height in the reservoir is reached, allowing the reservoir to refill to the maximum specified height before repeating the cycle.
Aside from the newly added reservoir and bundles, the system is the same as in the previous experiments detailed in Exploring the Coupled Effects of Capture Velocity and Velocity Gradient on Settler Performance Problem.
In terms of data collection, the team plans to collect usable data for at least three residence times of the tube settlers, connecting tubes, reservoir and turbidimeter system. With the reservoir system, usable data can only be collected in the withdrawal state. Data collected during the "loading state" is unusable and must be discarded.
h3. Results
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