# Simulation Analysis and Experimental Study of the Cooker Hoods of High-Rise Residential Buildings
## 2 Simulation of Centralized Flue System in High-Rise Residential Buildings  
### Simulation Theory of Centralized Flue System  
When simulating the centralized flue system of a high-rise residential building, it is necessary to undertake a pre-theoretical analysis for the structure of centralized flue in high-rise residential building, and then the simulation system is built under the guidance of theoretical analysis to ensure the reliability of simulation of centralized flue environment. The centralized flue system is shown Figure 1; it consists of centralized flue, branch exhaust flues, exhaust cowl, and cooker hoods. The exhaust cowl is located at the top of the centralized flue, which promotes effluent removal through natural ventilation.  
Figure 1: Schematic of centralized flue system with cooker hoods in high-rise residential building.  
In this work, the calculation model of the centralized flue system is constructed based on the energy equations and the flow continuity equation of fluid mechanics. For m-storey residential buildings, the energy equation of oil fumes flow from the \(i\)th floor to the centralized flue can be expressed as  
\[p_{ai}+\frac{\rho_{y}v_{ai}^{2}}{2}+\Delta p_{ei}=p_{i}+\frac{\rho_{y}v_{i}^{2}} {2}+\xi_{1}\frac{\rho_{y}}{2}(\frac{q_{i}}{A_{y}})^{2} \tag{1}\]  
in which \(p_{ai}\) is the pressure of indoor air, \(p_{i}\) is the pressure of centralized flue, \(\rho_{y}\) is the density of oil fumes, \(v_{ai}\) is the flow velocity of oil fumes in cooker hood inlet, \(v_{i}\) is the average flow velocity of oil fumes in centralized flue, \(\Delta p_{ei}\) is the full pressure of cooker hood, \(q_{i}\) is the flow rate of cooker hood, \(\xi_{1}\) is the resistance coefficient of check valve (including local resistance coefficient of oil fumes from exhaust pipe of cooker hood into the centralized flue), and \(A_{y}\) is the cross-sectional area of exhaust pipe of cooker hood.  
The energy equation of oil fumes flow from the \(i\)th floor to the exhaust cowl outlet can be expressed as  
\[p_{i}+\frac{\rho_{y}v_{i}^{2}}{2}+iH_{0}\rho_{y}g=p_{a0}+\frac{\rho_{y}v_{a}^{ 2}}{2}+NH_{0}\rho_{y}g+\sum\
olimits_{j=i}^{N}\lambda\frac{H_{0}}{d_{e}} \frac{\rho_{y}v_{j}^{2}}{2}+\sum\
olimits_{j=i}^{n}\xi_{h2}\frac{\rho_{y}v_{ j}^{2}}{2}+\xi_{j}\frac{\rho_{y}v_{a}^{2}}{2} \tag{2}\]  
in which \(H_{0}\) is the height of single floor, \(d_{e}\) is the equivalent diameter of centralized flue, \(g\) is the gravity acceleration, \(p_{a0}\) is the air pressure of the exhaust cowl outlet, \(v_{a}\) is the flow velocity of oil fumes in the exhaust cowl outlet, \(N\) is the total floors of high-rise residential buildings, \(n\) is the total operation number of cooker hood in high-rise residential building, \(\lambda\) is the frictional resistance coefficient when oil fumes flow through the centralized flue, \(\xi_{h2}\) is the local resistance coefficient after mixing oil fumes in the centralized flue with oil fumes from the exhaust pipe of cooker hood, and \(\xi_{f}\) is the resistance coefficient of exhaust cowl in high-rise residential building.  
The continuity equation of oil fumes in the centralized flue system of high-rise residential building can be expressed as  
\[v_{i}A=\sum\
olimits_{i=1}^{m}q_{i} \tag{3}\]  
Equations (1)-(3), the flow rate, total pressure, fumes pressure, and flow velocity of cooker hoods installed on different floors can be calculated; they can provide important references for designers of cooker hoods and provide a theoretical basis for the simulation of centralized flue systems in high-rise residential buildings.