The study of effective factors on Hardy Cross method convergence in mine ventilation networks analysis

Analysis of ventilation networks is one of the most important steps in mine ventilation. Hardy Cross method is one of the oldest and the most common methods of ventilation network analysis. This method is an iterative solution procedure and the equations are repeated until the error becomes negligible. The convergence rate of this method in the first stage depends on the preliminary theoretical values ​​of the branch air quantities and the correct choice of meshes. In addition, there are other factors which may affect the convergence rate. This paper focuses on the investigation and proof of those factors. First, if the summation of the branch air quantity and its relevant mesh errors are negative, the current directory must not be changed. Secondly, mentioned branch air quantity is considered with its algebraic sign in the denominator of the Hardy Cross equation in the next iteration. Then a hypothetical network is analyzed and the Newton- Raphson method was used to validate the results. Results from proven approach are in accordance with Newton- Raphson method results.