ANC CONTROL

EXPERIMENT 3: Addition of sloping glass column above the lime feeder and Tube-length Calculations

INTRODUCTION

In order to overcome the difficulties faced at the end of the second experiment, a new design was considered, which consists of a diagonal column attached at the top of the vertical column. The design would retain small lime particles while allowing the saturated lime water to exit. Since the velocity in the slanted tube is affected by the angle, its vertical component is lower than the upflow velocity of the primary column. The equation relating the capture velocity to the geometry of lime feeder is:

The angle of inclination and laminar flow regime allows certain sized lime particles to settle back into the column and thus prevent unnecessary lime loss. Thus the primary column would be used as a storage vessel for the suspended lime bed while the slanted tube above it would allow more lime particles to settle back to the column below, making the process more economical.  
The two constraints are the tube's length and the terminal velocity of the particle. This terminal velocity should be larger than the capture velocity. The length should be large enough to let the flow in the slanting tube to become a fully developed flow; the relevant criteria can be found in the MathCad file

Figure 1: Sloping Column Lime feeder

Calculations were made using the following assumptions for simplification:

1)It was assumed that the original lime is solid powder with a fractal dimension of lime particles to be around 3. These solid lime particles keep dissolving as we keep pushing in a raw water supply so as to make an effluent solution of saturated lime with a pH of 12.
Hence, giving a fractal dimension of 3 essentially implies that when lime particles stick together or dissolve to attain a smaller size, their density is not affected.

2) Density of lime is 2.211 g/m^3 and this remains constant throughout the process.

3) Shape Factor of lime particles = 1 i.e. the lime particles are perfectly spherical.

4) Settling velocity = 10 m/day i.e. 0.012cm/s. A flow rate of 80 mL/min (as determined by experiment 1)and a tube of inner diameter 2.4cm corresponds to an upflow velocity of 0.295cm/s.

CALCULATIONS ANALYSIS

Under the assumption that the flow rate of the lime feeder keeps at 80mL/min and 2.4cm as diameter of the tube, we can measure the relationship between the tube length and the capture velocity(Capture velocity is a function of the geometry of the tube), we also suppose that the smallest particle the tube can capture has the same terminal velocity as the capture velocity, so we have the relationship between the particle size and it's required capture velocity. Figure 2 shows the change of capture velocity and the particle size it can capture as the function of the slantign tube length.
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Figure 2: the relationship between tube length, capture velocity, and the smallest particle diameter the tube can capture.

We use a 1.5m vertical tube connect with 1.5m slanting tube in our experiment. Under our assumption of flow rate, a length of 1.5m has a capture velocity of 0.12 mm/s, and the smallest particle it can capture is 1.35μm. We could cut the slanting tube for saving space but the capture velocity the tube could provide and the smallest particle size it could capture would both decrease, this relationship could also be found on figure 2.

The lime particles used in our experiment have a nonuniform particle size, it cause some small size particel fall out at the begining of our experiment and the rest majority which have a larger density than the flocs could be kept in suspension. Also, larger lime means their settling velocities will be higher than the assumed 10m/day(0.12 mm/s). so a 1.5m could help to make a good suspension after the initial period which some of the smallest particals washed out with the effluent water.

To measure if the particle has the rollup risk, the relationship between critical velocity and terminal velocity was also calculated, as the particle's size increases, terminal velocity becomes much larger than critical velocity, due to the fact that critical velocity is linear with respect to particle diameter but terminal velocity is proportional to the square of the diameter. However, if the slanting tube's diameter decreases, there will be the risk that small particles would roll up from the tube, but it would not happen in our apparatus.

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Figure 3: Critical velocity vs Capture velocity

With the new apparatus, as shown in figure-4 below, a fourth trial will be carried out and evaluated. The modifications will be tested to see whether or not it will be successful in maintaining the pH at 12 and if so, for how long.

For this trial, distilled water will be used instead of tap water. It has been observed that after a few hours into any experimental run using lime, the lime instead of remaining in suspension as soluble particles, forms a single mass and becomes insoluble. It is hypothesized (by the previous research team) that this happens because some or all of the lime gets converted into calcium carbonate(which is insoluble)if tap water is used since the water received at Cornell is alkaline in nature. This should not be a problem in Honduras because the raw water to be treated will not be as alkaline. However, under laboratory conditions, in order to get a true estimate of the lime feeder's efficiency (in dissolving lime for a longer period and thereby lasting for a longer time) distilled water having a lower pH than tap water will prove to be more accurate. In the pictures below, the ANC Control team can be seen carrying the distilled water tank on to the platform where the experiment is to be set up.

Figure 4: Apparatus for experiment 3
With the design described on Experiment 3, three trials were done:
Trial 1: Using tap water

Trial 2: Using tap water - increasing lime amount

Trial 3: Using distilled water, changing lime brand