Initial Flow Rates for Ventilation Duct System Flow Analyses

The governing equations in duct system flow analyses are nonlinear, and iterative solution methods must be used. A suitable initial flow rate guess may be needed to start the calculations so that a converged solution can be finally achieved. A method to obtain a reasonably accurate initial flow rate guess is presented. In it the duct system is analyzed first in a strongly simplified setting assuming a linear (imaginary laminar) duct flow problem. The continuity equations at the junctions are satisfied. This first initial flow rate guess is then scaled to arrive at a more realistic final initial guess. The scaling is achieved by multiplication by a so-called balancing factor which is based on the application of mechanical energy balance for the whole duct system. The junction continuity equations are still satisfied for this final initial guess. A MATLAB program was generated to perform the calculations. Two demonstration example cases are presented to show the effect of the accuracy of the initial guess on the number of necessary iteration steps in connection with a PQ-duct system flow solution formulation.