T-Method Computerized Duct Simulation

The objective of duct simulation is to model airflows by obtaining pressure balancing [Tsal, et al.1990]. The system simulation solution is obtained when the total pressure loss for each system path is equal to the fan total pressure. The following requirements must be satisfied:

• Kirchoff's first law. For each node, the mass flow in and out must be equal.
• Pressure balancing. The total pressure loss in each pathmust be equal to the fan total pressure. In other words, for any node the total pressure losses for all paths must be the same.
• Fan and system characteristics. Available fan pressure and flow depend on the fan characteristic curve. Fan flow and pressure must match the system flow rate and resistance.

The T-Method computerized duct simulation determines the flow within each section of a duct system for known duct sizes and fan characteristics. The T-Method duct simulation is based on the same tee-staging idea as Dynamic Programming [Bellman 1957 ref159; Tsal and Chechik, 1968]. The T-Method incorporates the following major procedures:

• System condensing. The branched tree system is condensed into a single imaginary duct section with identical hydraulic characteristics and the same life-cycle cost as the entire system.
• Selection of an operating point. The actual system flow and pressure are determined by locating the intersection of the fan and system curves.
• System expansion. The condensed imaginary duct section is expanded into the original flow distribution system with appropriate airflow rates. The expansion procedure distributes the fan airflow throughout the system's sections. Unlike the condensing procedure, the expansion procedure starts at the root section where the fan is located and continues in the direction of the outlets.

To simulate a combined supply-return system, the distribution of the pressure losses between subsystems must be found. The T-Method can find the distribution by first condensing each subsystem separately and then expanding both condensed sub-roots, which are interpreted as two sections (supply and return) connected in series. [Farajian, et al, 1992]