A Summary Of Experimental Findings On Solution Methods For Mine Ventilation Networks

The primary purpose of the research summarized in this paper was to experimentally investigate the performance of numerous mine ventilation network iterative solution procedures under controlled conditions to determine which procedures were most favorable in terms of number of iterations and total computational speed. The solution methods investigated included: (1) the Newton-Raphson method, (2) the Hardy Cross method, (3) the linear theory method, and (4) the second-order approximation method. The first three of these methods have been widely used while the fourth was formulated by the authors to investigate its potential for ventilation network computation. In addition to the four solution procedures, three methods for selecting the branches in the meshes and three methods for ordering the meshes for computational purposes were also studied during the investigation. As a result of these various options, a total of 36 combinations of solution methods, mesh selection procedures, and mesh ordering schemes were studied. To investigate the performance characteristics of these combinations, an identical set of 180 randomly chosen ventilation networks was used in sets of 30 networks at six different levels of complexity. Here, the level of complexity is defined as a function of the size (number of branches) and the density (number of nodes compared with the number of branches) of the network. To eliminate variations in the solution times due to differences arising from the fans, a single fan with a fixed characteristic was utilized in all the experiments. This paper will deal only with the results for the four iterative methods used to achieve solutions to the mine ventilation networks. The minimum-resistance spanning tree method for mesh selection and random mesh ordering was used throughout the analysis. The conclusions will be based upon a detailed accounting of the efficiency of each method using the total time to achieve a solution to each problem and averaged over the total problem set. However, the number of iterations and the time to complete each iteration will be studied in order to better understand the solution procedures.