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 2D simulation 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 at the center of the tank. Therefore, the geometry is cylindrically symmetric, and can be modeled accurately in 2 dimensions. We are curious to see how much this change in the inlet location changes flow behaviors within the tank. Two cases at different temperatures are shown for comparison purposes.

Comparison of Isothermal Inlet and Warm Inlet @ 2.0 hours (750x410 GIF 67K).

This image shows the tracer concentration for two tanks after 2.0 hours. On the left, the temperature of the water coming in the inlet is the same as the temperature of the fluid in the tank. On the right, the inlet water is 10 degrees C warmer. The walls are insulating. The inlet fluid is colored red, the tank was initially full of blue fluid.

Comparison of Isothermal Inlet and Warm Inlet @ 5.0 hours (750x410 GIF 67K).

This image shows the tracer concentration for the same two tanks after 5.0 hours. On the left, the temperature of the water coming in the inlet is the same as the temperature of the fluid in the tank. On the right, the inlet water is 10 degrees C warmer. A similar effect occurs for inlet temperatures that are warm but not as warm as this warm case on the right. Even with the inlet warmer by 10 degrees C, the effect in tracer concentration is rather small.

Comparison of Isothermal Inlet and Warm Inlet @ 9.0 hours (750x410 GIF 67K).

This image shows the tracer concentration for the same two tanks after 9.0 hours. The effect seen at earlier times is still present. But notice that in all cases, the difference in tracer concentration between the isothermal case and the warm case could be hard to detect. For example, in this case the difference gets as dramatic as 0.34 vs 0.36.

The mixing rates for theses 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 ~4.0 hours of tank filling. This is equivalent to ~15% of the time to fill the tank to the mean depth of this simulation. This is the most efficient mixing performance of all cylindrical CFD studies done in this project.

Warm Inlet (by 2.7 deg C) (750x410 GIF 13K).

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 does not have a fully stratified flow, but is in the transition between stratified and non-stratified flow. This case requires ~5 hours to obtain a standard deviation for the tracer of 10% of the mean concentration, or ~20% of the time to fill the tank to the mean depth of this case.

Warm Inlet (by 10 deg C) (750x410 GIF 12K).

This image shows the tank under warmer conditions. The temperature of the water coming in the inlet is ~10 deg C warmer than the initial temperature of the fluid in the tank. This cases has a stratified flow field. The upper half of the tank contains the circulation cell, and the lower half of the tank is static. Still, the tracer does diffuse to this region as shown in this plot of the mixing statistics. This case mixes approximately as efficiently as the case with "transitional" flow, or ~20% of the time to fill the tank to the mean depth of this case.