There are a few numerical methods for calculating flow distribution in a duct system. The oldest method, called the equivalent nozzles method, was developed in Germany at the end of the 19th century by Bless [Lobaev, 1959]. The intent of this method is to replace the resistance of the ductwork with the equivalent resistance of a nozzle. The method is based on the quadratic law of resistance.
Kamenev (1938) developed the unit flow method. This method assumes flow through the terminal section is equal to one unit of flow. This method, as well as the equivalent nozzle method, is used in cases of quadratic law friction, which applies only when duct velocity is greater than 70 m/s (13,700 fpm). This velocity is impractical for HVAC ducts.
Butakov (1949) ref165 developed the duct characteristics method. Butakov [Butakov, 1949]used the old friction coefficient formula developed by Bless and substituted it into the Darcy-Weisbach equation. An important shortcoming of this method is that the use of Bless's formula results in pressure losses that differ by 20 percent from those found with the more accurate Colebrook (1938) ref168 or Altshul-Tsal [ASHRAE, 2001] equations.
Lobaev (1959) developed the equivalent resistance method that can be used for duct sizing and system simulation. This is the one of the best analytical methods for duct optimization.
Tsal and Shor (1967) used the steepest descent method for duct simulation and implemented it in a computer program. The descent step is normalized at each iteration as a function of maximum gradient-vector. The computer program calculates the flow distribution in branches; corrects to the fan operating point in the case of a change of flow; and calculates the required brake horsepower. Major applications include industrial exhaust systems that convey dust and where dampers are prohibited.
Tsal and Chechik (1968) developed the algorithm for the dynamic programming method for flow distribution . This method is more difficult to implement than the steepest descent method, but, unlike some other methods, it has no convergence problems.
The Newton-Raphson method was first used for network simulation by Stoecker, et al. (1974) ref205 for simulating central chilled-water systems and Gregory et al. (1975) ref181 for duct systems; the method was later translated into a computer code called TVENT1P. The main purpose of this program is the dynamic modeling of a duct system for tornado conditions using an electrical system analog for the airflow system in order to simulate the system's dynamics. TVENT1P uses only fixed resistance coefficients. After each iteration, the program must be interrupted; then, C-coefficients based on output flows must be recalculated and used as input data for the next iteration. Revised C-coefficients have to be calculated manually for all junctions, transitions, and elbows when the C-coefficients are a function of flow, velocity, or Reynolds number.
The well-known Equal Friction and Static Regain methods cannot simulate airflow.