Cooling and Dilution


Simulation Overview

  • 0.5 m tall x 0.5. m dia. dish bottom baffled, insulated tank

  • 0.25 m pitch blade impeller,

  • Impeller centered in the tank and 0.16 m off-bottom

  • 60 RPM impeller rotation rate

  • Water at STP (300 K)

  • Inlet1:

    • Species Concentration = 1 M beginning @ 5 s

    • Temperature = 320 K

    • Speed = 1 m/s

    • Diameter = 0.05 m

  • Inlet2

    • Species Concentration = 0

    • Temperature = 300 K

    • Speed = 1 m/s

    • Diameter = 0.05 m

  • Outlet

    • Constant pressure (101 kPa)

    • Diameter = 0.05 m

  • Predict thermal blending in the tank, look for temperature differences

  • Predict the minimum residence time of the scalar field, look for bypassing.

Modeling Approach

A tank with three openings (two inlets and one outlet) with a pitch blade impeller. A temperature and scalar field were defined with the above-defined boundary conditions/initial conditions. The tank wall was perfectly insulated.

  • System resolution: 120 lattice points (dx=0.042 m)

  • DataOutputInterval and SliceOutputInterval: 0.001 s and 0.05 s

Data Collection

In addition to the standard visualization output (temperature, species concentration, speed, etc.), the solver reports the time-evolution of the mean system temperature in the thermodynamics.dat file. Likewise, the species concentration at the outlet is reported in the inletOutlet_N.dat file that corresponds to the outlet. Additional data describing the species mean concertation, standard deviation, and exposure data are also available from the speciesData_N.dat file.

Data Analysis/Results

A snapshot of the speed field, temperature field, and species concentration field after 30 seconds of agitation are presented in Figures 18-20. Links to movies are presented in the captions. In these figures, the effects of bypassing are apparent. Fluid entering the system via Inlet 1, which enters at 320 K and carries a scalar concentration 1 M, streaks across the tank and pools on the opposite side between two baffles. Below this pool, the action of the impeller helps to homogenize the fluid before it reaches the outlet. The net effect of this flow configuration is a partition inside the tank: the region above the impeller, fluid motion and heat/mass transport is dominated by the jets. This behavior leads to large temperature gradients and species concentration gradients near the top of the tank. Below the impeller, the fluid temperature and species concentration are both homogenized by the action of the impeller. As such, although the species leaving the system is well-stirred, it not homogenously distributed across the tank.


Instantons speed field


Instantaneous Temperature Field. Movie at -


Instantaneous Concentration Field Movie at:

The minimum residence time can be examined by looking at the time-evolution of the species concentration at the outlet. In Figure 20 we compare the scalar concentration at the outlet versus time. Of particular importance here is the time at which the species concentration starts to register at the outlet with physically meaningful quantities. We choose to define a “physically meaningful quantity” as a concentration that can be represented by single precision floating point number (seven decimal points). Using this metric, chemistry begins existing the system starting at time 6.89 s. Recall that the species injection via Inlet 1 started after 5 seconds of operation. This result indicates that chemistry entering the tank spends at least 1.89 seconds inside the tank before exiting through the outlet. An analysis involving scalar transport particles (injected via inlet beginning at 5 seconds) predicted a minimum time-of-flight of 1.85 .. In addition to corroborating the minimum residence time, this result also suggests that the effects of numerical diffusion on scalar transport are negligible in this system.


Time-evolution of species concentration at outlet