Applying the state-space method to simulate the instantaneous field of indoor gaseous contaminant concentration

Ventilation is an efficiency measure to dilute indoor pollutants and improve indoor air quality. It is important to predict contaminant concentration distribution in space and time to evaluate ventilation efficiency and optimize indoor air flow. CFD (Computational Fluid Dynamics) technique is a strong tool to simulate indoor gaseous contaminant transport under a ventilation mode. It can provide the temporal spatial distribution of indoor air pollutant concentration by numerically solving the governing equation of the concentration field both in time and space. However, because the time is discretized, the relationship between the concentration fields at the different time is not revealed. Besides, for determining the concentration field at the specified time, the concentration fields at every discrete time before the time must be also calculated. Therefore, for overcoming the above mentioned shortcomings of CFD method, state spaces method is applied to simulate the concentration in this paper. State space method is commonly applied in the control field to solve the so-called state-space equation. Different from CFD method, the time discretization is not necessary. The governing equation of the concentration field is discretized only in space to obtain a state-space equation. Then the solution of the state-space equation is derived based on the control theory. From the solution, the effect of the initial concentration field on the temporal concentration field is shown obviously. And based on the solution, the concentration field at the specified time can be calculated directly. Because piston flow is the simple 1-D flow and transport of contaminant through the flow has been studied for many years, the analytic solution of the concentration field of piston flow is used to validate the result from the proposed state-space method. The comparison shows a good agreement. Under a 2-D indoor flow, the velocity field is calculated by CFD method and is validated by the experiment in the literature. Based on the velocity field, the state-space equation is obtained and the transient concentration field is calculated by the state-space method. Then the concentration field is compared with the result by the CFD method. An acceptable error shows the validation of the state-space method. Therefore, it comes to a conclusion that the state-space method can be used to simulate the concentration field accurately and solve some disadvantage of the CFD method.