h2. Velocity GradientsGradient Experiment
h3. Introduction
Following the team's Stepping from previous experimental research with velocity gradients, this experiment isseeks to aimeduncouple attheir differentiatingeffects theon effectstube ofsettler velocityperformance gradientsdeterioration from capturethose velocitiesof onthe tubecapture settlervelocity. performance. In the team's previouslast 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 keepingmaintaining a theconstant length to diameter ratio ofin tube settlers constant would minimize the effects of the capture velocity on performance. However, the
The results indicatedshowed that even withat a constant length to diameter ratio of 20, high capture velocityvelocities contributed significantly contributedto poor tosettler performance deterioration at high flow rates.
After further consideration This can best be explained by the fact that at high capture velocities, our settlers fail to eliminate a large portion of the results of previous experiments floc particles generated in our floc blanket system from the effluent stream. The flocs exist in this system in a wide range of densities and settling velocities, in a distribution that is currently unknown.
After considering these results, the team decided to varyallow the length to diameter ratio ofto the tubeschange in order to keep the capture velocity constant among tubes of different diameters. A range of tube diameters (1", 1/2", 3/8", 1/4") werewas chosen based both onupon available material, and the fact that these diameters represent a reasonably applicable range for AguaClara spacing values. A capture velocity of 100.12 m/day (mm/s was chosen for these experiments because it corresponds to the value currently used in AguaClaraAguaCalara 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, V ~up~ 's, and corresponding average velocities in the tubes,V ~α~ 's. The V ~up~ 's chosen were 1 mm/s, 2 mm/s, and 5 mm/s with corresponding V ~α~ 's of 1.04 mm/s, 2.31 mm/s.
Starting from this capture velocity, the team chose to test three different up-flow velocities: 1, 2 and 5 mm/s. The first value is that currently used by AguaClara, and the range represents a considerable spectrum of flow rates, and thus velocity gradients, experienced in the tube settlers. The velocity of the influent water increases as it enters the settlers due to hydraulic contraction, and this is a velocity of interest to the team since it also represents the average flow rate through the settler, taking into account also its angle of inclination. These values for this experiment are: 1.04, 2.31, 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 П ~V~ , which is a ratio of the settling velocity, and can be calculated from the following relationship: {latex}
\large
$$
{{V_\alpha }} = {{ V_{up} } \over {\sin \alpha }}
$$
{latex}
Failure is defined as П V, the ratio of the average floc's settling velocity (a function of both the capture velocity and the flocs's density, and thus also a function of the flocculation process), to the velocity experienced due to the velocity gradientby the particle at its diameter exposed to the effluent stream. Particles on the bottom wall of the settler that experience a higher velocity at their exposed edge than the velocity at which they settle out of the average floc size captured for a 10 m/day capture velocity. If П ~V~tube will experience a torque upwards that causes them to exit with the effluent. Thus when П V is less than 1, failure predicted one under specific circumstances, roll-up is expected to occur. Values near 1 suggest situations where failure might A value of unity suggests an equilibrium point where roll-up may or may not occur.
The procedure undertaken to calculate the necessaryrequired dimensions and flow rates lengths for the experimentstubes is explained below.as follows:
1. TheChoose 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 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 V ~α~ '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}
where
v ~ratio~ = 2 for tubes and 1.5 for plates
α = 60 degrees
R = radius of the tube
5. The necessary flow rates were calculated from the capture velocities, diameters, and lengths determined above by the following relationship:
{latex}
\large
$$
Q = {{L\cos \alpha + d\sin \alpha } \over d}(\pi r^2 )n_{tube} V_C
$$
{latex}
where
L = length of the tube
d = diameter of the tube
α = 60 degrees
r = radius of the tube
n ~tube~ = number of tubes
6. П ~V~ ratios were determined for each tube evaluated by the following equation:
{latex}
\large
$$
\Pi _V = {{{{g\sin (\alpha )d_0 ^2 \rho _{floc.0} (C_{Alum,} C_{Clay} ) - \rho _{H20} } \over {18\varphi \nu \rho _{H20} }}({{d_{floc} (V_C )} \over {d_0 }})^{d_{fractal} ^{ - 1} } } \over {{{2V_{UP} } \over {\sin \alpha }}(1 - ({{{d \over 2} - d_{floc} (V_C )} \over {{d \over 2}}}))^2 }}
$$
{latex}
where
d ~0~ = diameter of clay particle
d ~floc~ (V ~C~ ) - diameter of floc captured based on capture velocity
d ~fractal~ number generally between 2-3 for flocs that describes the volume of dirt in the floc compared to the volume of water. A value of 3 indicates that the floc has no water within it.
ρ ~floc.0~ (C ~Alum~,C ~Clay~) - density of floc based on concentration of alum and clay, respectively
ρ ~H20~ \- density of water
ν - kinematic viscosity of water
Φ - shape factor
A comprehensive [materials list|^materials list.png] details the resulting required lengths, flow rates, and П ~V~ 's for the tubes tested. A documented [MathCAD|^spring 2010 new mathcad file, 510.xmcd] file has been developed and tailored to this specific experiment. It allows the user to conveniently enter capture and upflow velocities, in order to calculate the pi ratio and other critical parameters.
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 Conclusions from the previous experiments ([Exploring the Coupled Effects of Capture Velocity and Velocity Gradient on Settler Performance|PSS Spring 2010 Coupling Analysis Experiment]) indicatedshowed that there was a problem with particles settling out in the turbidimeter at low flow rates. The Experimentsteam performed an toexperiment evaluatein thiswhich situationit determinedfound that the minimum to prevent this settling, a flow rate necessaryof toat preventleast settling was 50 mL/min needs to be driven through the turbidimeter. Table 1 aboveof the conclusions indicates that for the smaller tubestube, the flow rates necessarywere toconsiderably achieve the desired conditions are less lower than 50this mL/minvalue. In order toTo address this issue, the team has decided to use bundles of tubestube 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 1 cm highof headloss. The flow fromrate through the tube bundles is pumped into the reservoir continuously until a certain water heightlevel is reached. This period of time is called the "loading state." At that point, a pump begins to pullingpull water out offrom 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 offdown when a minimum water height in the reservoir is reachedresearched, 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 The reservoir's sample is continuously stirred and mixed; this should provide an average turbidity reading the turbidimeter. A full analysis of residence times is still in progress.
Aside from the reservoir and bundled tubes, the system is the same as in the previous teams' experiments. For data collection, the team plans to collect usable data for at least three residence times ofin the system, containing: tube settlers, connecting tubes, reservoir, and turbidimeterturbididimeter. system. With the reservoir system, usable data can only be collected in the withdrawal state. Data collected during the "loading state" is unusable and mustshould be discarded.
h3. Results
The experiments have not been performed, but the [materials list|^materials list.png] indicates in the introduction elaborates on the expected results. The following figure shows the ratioinverse of the experiencedpi velocity to the settling velocity of the average diameter floc particle that would be captured at a capture velocity of 0.116 mm/s, ratio plotted against the diameter of the tube settler (this is the inverse of the aforementioned pi ratio). For diameters at which thisthe ratioinverse is greater abovethan unityone, roll-up is expected to occur.
!roll-up curve2.png|width=460px,align=center,height=400! |
