NONLINEAR DYNAMICS OF DUAL-SOURCE THERMAL PLUME INTERACTION AND MULTI-LAYER STRATIFICATION BREAKDOWN IN MECHANICALLY DISPLACEMENT-VENTILATED SPACES

Abstract

In mechanically displacement-ventilated rooms, thermal stratification depends not only on the total heat load but also on the spatial distribution and relative strength of individual heat sources. Two separated convective sources may remain independent or merge, causing multiple interface movements and temporary breakdown of the multilayer structure. This study develops and numerically evaluates a reduced-order dynamic model of two interacting thermal plumes under variable heat loads. The model combines integral plume relations, a source-separation- and strength-dependent merging height, two moving effective interfaces, and layer energy balances. The equations are integrated using the BDF method in Python with NumPy, SciPy, and Matplotlib. Independent, step-change, and cyclic loading regimes are examined. For independent sources, the final interface elevations are 1.767 and 1.873 m. After redistribution of source powers from 2 to 7 kW and from 2 to 1 kW, respectively, plume merging occurs below the upper interface and the final elevations decrease to 1.583 and 1.705 m. Cyclic loading produces phase lag and a bounded hysteresis response. The results show that buoyancy-flux ratio and source spacing must be retained as state variables, whereas total heat load alone cannot uniquely describe the ventilation regime. The model provides a transparent screening framework for analysing transient stratification and supporting control of displacement ventilation systems.