초록
Velocity gradient, G, a measure of the average velocity gradient in the fluid has been applied for complete mixing of chemicals in mechanical mixing devices. G values were calculated by the power input transferred to fluid in turbulent and transient range. Chemical reactions occur so fast that total mass transfer time required for even distribution of the chemicals determine the overall reaction time. The total mass transfer time is composed of the time for complete mixing through the reactor and for diffusion of the chemicals into the eddy. Complete mixing time was calculated by CFD (computer fluid dynamics) and evaluated by tracer tests in 2 liter jars at different rotating speeds. Turbulent range, Reynolds number above 10,000 in regular 2 liter jars occurred at revolution speed above 100 rpm (revolution per minute), while laminar range occurred at revolution speed below 10 rpm. A typical range of rotating speed used in jar tests for water and wastewater treatment was between 10 and 300 rpm, which covered both transient and turbulent range. G values supplied from a commercial jar test apparatus showed big difference from those calculated with power number specially in turbulent range. Diffusion time through eddy decreased 1.5 power-law of rotating speed. Complete mixing time determined by pumping number decreased increases in rotating speed. Total mass transfer time, finally, decreases as rotating speed increases, and it becomes 1 sec at rotating speed of 1,000 rpm. Complete mixing times evaluated from tracer tests showed higher than those calculated by power number at higher rotating speed. Complete mixing times, however, calculated by CFD showed similar to those of experimentally evaluated ones.
