A linear model of the effects of residence time distribution on mixing pattern in a ventilated airspace

Abstract

The ability of a simple linear response model is evaluated to explain the mixing efficiencies in an incomplete mixing ventilated airspace. Data interpretation and mean residence time calculation for a specified output concentration profile can also be evaluated. The residence time distribution (RTD) functions take the form of the two-parameter gamma distribution and account for different mixing types such as complete mixing, piston flow (no mixing), incomplete mixing, and various combinations of the above types. In these combinations, the different mixing types simulated by different RTDs conceptually represent airflow regions in series. The mixing efficiency was introduced to characterize the extent or degree of mixing in a ventilation system in that mixing efficiency equals zero for piston flow (no mixing), unity for complete mixing, and a value in between these two extremes for incomplete mixing. An environmental chamber experiment was conducted to generate several output profiles to evaluate the applicability of the model. Carbon dioxide was employed as the tracer gas. Our results show that an overall root-mean-squared error value of 8.64±5.25 ppm is low, indicating that the combination mixing patterns are generally found to be minimally biased and give better fitting than other simpler mixing patterns. Despite their neglect of molecular diffusion and possible temporal/spatial nonlinearities, these linear response models appear reasonably robust, making them at least as useful to building microenvironment designers in reconsidering the possibilities and consequences of various forms of incomplete mixing related to indoor air quality problems.