A Lumped-Parameter Model Describing the Behavior of Carbon Dioxide Concentrations in a Slot-Ventilated Airspace (I)

Modeling and Mathematical Analysis

Abstract

Mathematical analysis of a model for describing the dynamic behavior of carbon dioxide concentration at any location within a slot-ventilated airspace is presented from the standpoint of a lumped-parameter approximation. The system equation can be represented by a first-order time-invariant vector-matrix differential equation. The key point of the model structure is the system state matrix [A] contains the essential dynamic characters of the system. The inverse transport matrix [Q]^-1 is the product of the inverse local airflow matrix and the transition probability matrix. This product can be used to evaluate the local transport phenomena of carbon dioxide concentration. From the physical and mathematical properties of the model, the overall mixing factor of the ventilation system can be estimated. An analysis of the stability properties of the system equation is presented.