Coal - The Use of the Digital Computer for Mine Ventilation Problems

An earlier paper1 introduced a rapid solution for mine ventilation network problems, employing the digital computer. In this paper, refinements and additions to the computer program which expand its scope of application and a solution to a ventilation network having a coal-mine configuration are presented. The revised program-written in FORTRAN for the IBM 7074 computer in Penn State's Computation Center-is applicable to any mine ventilation network employing natural splitting and having its fan located externally. It accomplishes the following: 1) Distributes an assumed total quantity of air flow among all airways of the network, performing iterations until an acceptable level of error is attained and the flow in each airway is known. 2) Computes the pressure drop (head loss) in all airways and the overall network and mine head losses. 3) Determines the operating point for the mine and a given fan, adjusting all air flows and head losses to the actual values. The basis of analysis used is the Hardy Cross method of successive approximation for solution of any fluid network, explained in detail in the earlier article. In brief, corrections to assumed air flows are computed for all the loops of a network; following distribution to the airways of each loop, the process is repeated until acceptable accuracy is attained. When a hand or desk-calculator solution is used, there is advantage to close approximation of the actual flows in the original assumption of air-flow distribution in the network. Since publication of the previous paper, in which assumption of initial quantities was also necessary in the computer solution, the program has been modified to make the first distribution itself, assigning the total quantity to one specified path in a split and then proceeding to correct the flows. The number of iterations required for a high-accuracy solution is little affected, at least in networks of few loops, 10 to 15 being sufficient to reduce the error to 1 pct or less. The principal limitation of the original program was that it contained no provision for handling a fan. Further, it did not determine the overall head loss in the network and was not designed for multiple parallel openings, such as occur in coal mines. The revised program was written to overcome these disadvantages and also to print out the adjusted flows for all airways, corrected for the system operating point. At the present time, the program can handle only an external fan. The procedure employed in solving a ventilation network is now as follows: 1) Input data consisting of airway characteristics and loop designation along with assumed direction of flow, for each branch of the network and any trunk airways, are fed into the computer. 2) Employing the resistance relationship, where R is resistance, K is friction factor, P is perimeter, L is length, A is area, and n is number of airways (where multiple intakes and returns are employed); values are computed for all airways. 3) An arbitrary, continuous route of flow through the circuit—from beginning to end—is selected and the path identified by airway numbers and read in. 4) Based on a total assumed quantity of flow Q (usually 100,000 cfm.) the computer employs the procedure described in the previous article in distributing quantities of flow among all the airways until a satisfactory level of accuracy has been attained (in the current program, the machine is turned off when the cumulative corrective error in cfm, is reduced to five times the number of airways). 5) Airway head losses H are calculated by the relation H = R Q2 and cumulated along the original designated flow route to find the overall head loss for the network. Trunk airways are then included to obtain the mine head.