Flow versus head loss data collection in the turbulent range

Experimental Methods

Previous experimentation with the flow controller has focused on flows in the laminar range. This data was fitted to a theoretical model with reasonable predictive power, but there is no good data set for where the flow becomes turbulent. To determine the outflow to height relationship in the turbulent transition range, two methods were used. The first two data sets were collected by attaching the flow controller to a ring stand and taping the 2m long outflow tubing onto a column with a fixed height. The head loss was then changed by raising or lowering the flow controller on the ring stand, which was marked in 1cm increments. The flow rate was found by measuring the flow into the cylinder for 30 second increments.

The equation for Reynold's number was used to find the expected flow rate at the turbulent transition with Re = 2100. The Hagen-Poiseuille equation was then used to find the expected delta h needed to put outflow from the flow controller at that flow rate. To collect data on the outflow to head loss relationship in the turbulent transition range, this delta h was used as the "transition height". This is the head loss theoretically needed to create a turbulent outflow.

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This delta h was used as a ballpark value for where the expected turbulent transition would take place. Beginning with a delta h smaller than the theoretical transition value, outflow data was collected at 2 cm intervals of increasing delta h. This data was meant to encompass flows from the laminar and turbulent range, including the transition range. Delta h values were varied using centimeter increment markings on the ring stand and outflow is measured by placing a graduated cylinder at the tube outlet for 30 second intervals. Theoretically, these delta h values were to include the transition range from laminar to turbulent flow. However, the flow rate never reached that of turbulent flow.

Experimentally we found that the head loss of 12 cm is not nearly large enough to create turbulent flow, so we switched to using the transition flow rate of 430 mL/min instead. The physical experimental set up was also improved upon twice during the semester. First a series of holes was machined down the side of the column. The holes are 1cm apart from center to center, and there are 40 holes. They are also the same diameter as the out flow tubing. The flow controller was placed at a fixed height with the water level even with one of the holes in the column. To adjust the head loss, the tubing was simply moved to a new hole like it is in the actual AguaClara plant rapid mix. A pressure sensor was also added at the bottom of the column. The pressure sensor was connected to Process Controller, which allowed us to gather larger data sets and calculate more precise flow rates. At this time we also realized that the flow controllers used in Honduras do not have barbed connectors for the outflow tubing, while ours in the lab did. Re-calculating the Hagen- Poiseuille expected transition flow rate without the barbed connector yielded a value of 387 mL/min, which was used as the target middle flow rate from here onward. These connectors were removed and two more data sets were collected with this set up.

When the column filled with water it was tipped into the sink to empty it. The final improvement to this set up was adding a plastic valve to the bottom of the column. The pressure sensor and the valve came off a T inserted into a connector near the column base. The valve connected to a tube that we rested in a roasting pan on the floor. When the flow controller outflow tubing was inserted into a new hole on the column, the valve would be opened to let water drain through the column while the new flow rate equilibrated. The valve could then be shut to allow water to fill the column, while Process Controller took pressure measurements every 5 seconds. This was used to collect one final data set focusing on the turbulent transition range.

All of the Process Controller data was analyzed in a MathCAD sheet. The readings from the pressure sensor were used to find dP over the data collection at a given head loss. Process Controller took data readings every 5 seconds, which was used to find a dt. This dP/dt was used in combination with the geometry of the column (inner diameter = 2cm) to convert the change in pressure to a change in column water volume, to determine the average flow rate over that time.

Experimental Results

Several sets of data were collected to determine the relationship between outflow and head loss in the flow controller. The goal was to look at Q-h in the turbulent transition range, but initial data was collected in the laminar range due to incorrect estimation of parameters. Data from plant performance in Honduras has indicated that the flow controller dosing was not varying linearly with head loss. Data from testing the flow controller in Summer 2007 showed a linear relationship, but the first two data sets gathered this fall with the same experimental set up showed more variation

The data is not linear, and it also is showing a lower outflow per head loss than theoretically expected. Small decreases of the tubing diameter (decreased by 0.053in) help fit the data to theory, which may be acceptable because of the flow controller exit geometry as discussed later in this section.

From the first two data sets collected in the expected turbulent range, we have hypothesized that a few components of the flow controller should be characterized differently. The inner diameter of the outflow tubing is most likely slightly smaller than manufacturers claim. It is sold as 3/16in (0.188in), while our data best fit the theoretical model when a diameter of 0.134in was used. This smaller inner diameter would result in higher friction in the tubing, increasing head loss. We also realized that the barbed connector used to attach the outflow tubing to the flow controller was creating a constriction in the flow, thereby increasing head loss. The AguaClara engineers in Honduras complained that the flow controller was not dosing as expected from research in the lab, and it turned out that the flow controllers in use in Honduras did not have barbed connectors in place, while those in the lab had the connectors. The barbed connector was removed from flow controllers in the lab for all testing from then onward, and all modeling was done under the assumption that tubing diameter was slightly variable.

The Process Controller column with pressure sensor set up was used to take three sets of data with more precise values than the earlier semester data. The machined holes in the column allowed us to control head loss with high levels of precision, while the pressure sensor gave accurate data that was converted into flow rate information. This set was used to gather data that actually fell around the turbulent transition range, which our earlier methods had missed.

The turbulent jump appears to occur at a flow rate of about 350mL/min, here without a barbed connector, and it can be characterized as a zone where head loss increases independently of flow rate. It is interesting to note that the data appears linear both before and after the jump, with different slopes. Below the transition the data can be made to fit the theoretical model well, while above the jump the data is generally below the theoretical curve. In the transition region it is difficult to categorize. It may be viable to use this type of flow controller for both high and low flow rates, as long as the turbulent transition region is avoided. This is constrained by the maximum inlet flow rate through the float valve, which still needs to be determined. At steady state the flow controller would not be able to ever dose more than this inflow rate, so any plant requiring more chemical dosing would need to modify this system.