Abstract
The solution multiplicity of natural ventilation in buildings is very important to personnel safety and ventilation design. In this paper, a four-zone model of buoyancy ventilation in typical underground building is proposed. The underground structure is divided to four zones, a differential equation is established in each zone, and therefore, there are four differential equations in the underground structure. By solving and analyzing the equilibrium points and characteristic roots of the differential equations, we analyze the stability of three scenarios and obtain the criterions to determine the stability and existence of solutions for two scenarios. According to these criterions, the multiple steady states of buoyancy ventilation in any four-zone underground buildings for different stack height ratios and the strength ratios of the heat sources can be obtained. These criteria can be used to design buoyancy ventilation or natural exhaust ventilation systems in underground buildings. Compared with the two-zone model in (Liu et al. 2020), the results of the proposed four-zone model are more consistent with CFD results in (Liu et al. 2018). In addition, the results of proposed four-zone model are more specific and more detailed in the unstable equilibrium point interval. We find that the unstable equilibrium point interval is divided into two different subintervals corresponding to the saddle point of index 2 and the saddle focal equilibrium point of index 2, respectively. Finally, the phase portraits and vector field diagrams for the two scenarios are given.
Highlights
Nonlinear characteristics exist in systems with various research directions, such as neural network [1,2,3], chaotic circuit [4,5,6,7,8,9,10,11,12], and information security [13,14,15]
Many papers have been published on the problem of multiple solutions to building natural ventilation [17,18,19,20,21,22,23]. ese studies can be divided into three categories according to the number of building zones and vents. e first kind research is about the solution multiplicity of single-zone and doubleopening buildings under the combined effect of wind pressure and thermal pressure [19, 24,25,26,27]
Heiselberg et al [24] studied the multiple steady-state properties of single-zone and double-opening buildings under the action of wind pressure and buoyancy through a salt water experiment and CFD simulation; Lishman and Woods [25] reported solution multiplicity in both inclined tunnels and two-story aboveground buildings, and the study focused on the confrontation of wind pressure and buoyancy in a single-story building; Yuan and Glicksman [19, 26] researched the effects of different initial conditions on the generation of multiple steady states in single-zone buildings under the combined action of wind pressure and buoyancy; Pulat and Ersan [27] found that different turbulence parameters may produce multiple solutions through CFD simulation. e second kind research is about the solution multiplicity of single-zone and multiple opening buildings [28, 29]
Summary
Nonlinear characteristics exist in systems with various research directions, such as neural network [1,2,3], chaotic circuit [4,5,6,7,8,9,10,11,12], and information security [13,14,15]. Yang et al [30, 31] analyzed in detail multiple steady states in a two-zone building by theoretical analyses and CFD simulations; Li et al [32] studied the buoyancy ventilation in a two-story building with two heat sources and three openings by establishing a mathematical model of nonlinear ordinary differential equation; Yang et al [33] analyzed the smoke exhaust spread of the three entrance tunnel in the fire scenarios and obtained six possible equilibrium states. In 2020, Liu et al [35] made nonlinear dynamic analysis of solution multiplicity of buoyancy ventilation in a typical underground structure. Ey gave a description of mathematical model of second-order nonlinear differential equation to underground structure with two zones and two tunnel connecting to the outdoor environment. The nomenclature of every variables and constants are shown in abbreviation section
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