This example is from a Research Study Project for AWWARF (American Water Works Association Research Foundation, Project #260; "Water Quality Modelling of Distribution System Storage Facilities").

This is a simulation of half of a cylindrical tank inspired by the blackhawk tank near Oakland, CA. The tank is modeled in filling mode with the inlet moved from its existing location near the outside wall to a position halfway to the center of the tank. We are curious to see how much this change in the inlet location changes flow behaviors within the tank. Three cases at different temperatures are shown for comparison purposes.

Isothermal Inlet (750x410 GIF 67K).

This image shows the tank under isothermal conditions. The temperature of the water coming in the inlet is the same as the temperature of the fluid in the tank. The walls are insulating. The inlet fluid is colored red, the tank was initially full of "blue" fluid. The image shows the extent of mixing of the inlet fluid throughout the tank after ~2.5 hours.

Warm Inlet (750x410 GIF 61K).

This image shows the tank under warm conditions. The temperature of the water coming in the inlet is the ~3 deg C warmer than the initial temperature of the fluid in the tank. The walls are insulating. The inlet fluid is colored red, the tank was initially full of "blue" fluid. The image shows the extent of mixing of the inlet fluid throughout the tank after ~2.5 hours. The mixing efficiency for this case is the best for this inlet location, and nearly as good as all of the cases run with the inlet near the outer wall of the tank.

Cold Inlet (750x410 GIF 87K).

This tank has fluid 1.00 Deg. C cooler flowing in the inlet. As in the previous case, the inlet fluid (now the cooler fluid) is colored red, and the display shows the mixing after 2.5 hours. The inlet fluid sinks to the bottom of the tank and spreads out along the floor. In this case the mixing within the tank is initially more efficient than the isothermal case. At later times, the mixing efficientcy is the same as the isothermal case, but 50% slower than the positively buoyant case.

The mixing rates for these three cases are shown below. The scale for the axis are the same in each case. The black line is the mean concentration of the tracer within the tank. The red line shows the history of the minimum tracer concentration in the tank (as a percentage of the mean concentration). When this reaches 1.0, the tracer concentration within the tank would be uniformly distributed throughout. The green line shows the history of the standard deviation of the tracer within the tank (also as a percentage of the mean concentration). As this approaches zero, the mixing throughout the tank becomes complete.

For reference, it requires approximately 24.2 hours to fill this tank to the mean depth of these simulated cases.

Isothermal Inlet (750x410 GIF 13K).

This image shows the tank under isothermal conditions. The temperature of the water coming in the inlet is the same as the temperature of the fluid in the tank. To reach a standard deviation of 10% of the mean, this case needed to simulate nearly 9.0 hours of tank filling. On the other hand this is only ~36% of the time to fill the tank to the mean depth of this simulation

Warm Inlet (750x410 GIF 12K).

This image shows the tank under warm conditions. The temperature of the water coming in the inlet is ~3 deg C warmer than the initial temperature of the fluid in the tank. This cases mixes the most quickly according to all the candidate mixing diagnostics. This case simulates ~7 hours to obtain a standard deviation for the tracer of 10% of the mean concentration, or ~28% of the time to fill the tank to the mean depth of this case.

Cold Inlet (750x410 GIF 13K).

This tank has fluid 1.00 Deg. C cooler flowing in the inlet. This case initially mixes almost as quickly as the warm case. But the mixing efficiency slows and at later times has a mixing efficiency more like the isothermal case.