Simplified Thermal Model of Spaces Cooled with Combined Positive Displacement Ventilation and Chilled Ceiling System

Abstract

An improved plume-multilayer model was developed and validated to represent thermal transport in enclosures conditioned by radiant cooling and displacement ventilation systems. A novel approach was developed to estimate wall plumes for non-isothermal surfaces using the similarity solution derived for power law representation of temperature difference between the room air and the wall. The nonuniform wall plume flow rates predicted by the model agreed well with flow rates in an enclosure produced by computational fluid dynamics (CFD) simulations. Wall plumes associated with a nonuniformly heated wall with varying temperature difference between the wall and the air were found to be substantially higher than the plume predicted by isothermal wall correlation. The wall plume model is integrated with a multilayer space thermal model to predict the stratification height in the space, the vertical distribution of wall and air temperatures as a function of the chilled ceiling temperature and space air supply conditions. The plume-multilayer model results were compared with results of three-dimensional CFD simulations using commercially available software. Three test cases were considered for the simulations at cooling loads of 40 W/m2 (12.7 Btu/h·ft2), 67 W/m2 (21.2 Btu/h·ft2), and 100 W/m2 (31.7 Btu/h·ft2) and supply airflow rates per unit area of 22.5 (1.2 ft3/min·ft2), 30 (1.6 ft3/min·ft2), and 37.5 m3/h·m2 (2.1 ft3/min·ft2), respectively. The vertical wall and average air temperatures for each layer agreed well with the results of the plume-multilayer model, showing maximum errors in values of average air temperature of 0.13°C (0.23°F), 0.37°C (0.66°F), and 0.3°C (0.54°F) for the low, medium, and high load cases, respectively. The simplified model accurately predicted the stratification height at a maximum error of ±0.05 m (0.16 ft) in the three test cases. The stratification height is overestimated by 35% if wall plumes are neglected in the plume-multilayer model.