Predicting Forces and Torques¶
1 m tall x 1 m diameter flat bottomed baffled tank
0.5 m pitch blade impeller
Impeller centered in the tank and 0.33 m off-bottom
60 RPM impeller rotation rate
Water at STP
Predict time evolution and steady-state impeller power number
Predict tank blend time, for tracers injected at surface 15 seconds after simulation start
Predict thrust and unbalanced hydrostatic forces on the impeller
The instantaneous power number is automatically printed to the ParaView output at a time-frequency specified by DataOutputInterval. We use the Auto Blend Time component to predict the tank blend time. Under this command, we choose to inject 50000 particles in domain after a 15.0 second initialization period. We inject the particles at the center of the tank, 5 cm below the top surface We specify 1 bin in the x- and z-directions, and 10 bins in the y-direction, which is sufficient to resolve axial variations in the concentration.
System resolution: 100 lattice points (dx=0.024 m)
Particle diameter/specific gravity: 0/0 (to make scalar particles)
DataOutputInterval 0.001 s
SliceOutputInterval 0.01 s
The post-processor automatically reports time-evolution of the power number, impeller forces, impeller moments, and impeller pumping number. We can use this data to extract the time-varying and time-averaged, steady-state power number. When the Auto Blend Time component is added to the model, an AutoBlendTime tab is also produced. This tab (and the attending data file) describe the time time-evolution of the mixing coefficient of variation, along with the normalized concentration inside each bin (10 in this case).
Time-evolution of mixing COV, as taken directly from the autoBlendtime.dat file, is presented in Figure 11. Particles are injected at t=15 seconds. Prior to this time, the mixing COV is 0 as there are no scalars in the system. Between t=15 s and approximately t=50 s, particles are aggregated about the injection location near the top of the tank. From t=50 s to approximately t=90 s, particles are homogenized across the tank volume. For times greater than 90 s, the system is homogenized. The stagnation period between t=15 s and t=50 s could be reduced by allowing the fluid to fully equilibrate before injecting the particles. The time-average, steady-state COV is approximately 0.96. Increasing the particle injection count from 50,000 to 100,000 increases the precision of the time-average, steady-state COV to a value greater than 0.99.
The time-evolution of the Power Number, as taken directly from the ParaView output, is presented in Figure 12. In the immediate 10 seconds after the start of the simulation, the Power Number is large as the impeller is pushing an initially quiescent fluid. After approximately 20 seconds, the Power Numbers converges to a steady state value of approximately 1.4. The fluctuations in Power Number with time are physical and related to eddy shedding into the trailing vortex.
The time-evolution of the forces on the impeller, as taken directly from the ParaView output, is presented below. The force in the y-direction is associated with the thrust and pumping action of the impeller. The forces in the x- and z-directions are associated with the unbalanced forces due to time-varying fluid motion.