A general method of optimization of the flow distribution in a complex ventilation network

Abstract

One of the most complicated stages in the creation of mathematical techniques for automation of coal mines is the development of methods, algorithms, and programs for making computerized calculations concerning ventilation. In planning the ventilation of new and reconstructed pits, it is necessary to choose optimum parameters and types of main and local ventilator fans, to regulate the network with the aid of additional regulating devices, and to determine the aerodynamic parameters of all branches of the network. The most general mathematical formulation of the problem of optimum current distribution appears as follows: we are to find the aerodynamic resistance of the additional regulating devices, the air flow rates in all branches of the network, and the depressions and outputs of the sources of draft which minimize an objective function, namely the energy expended on ventilation of the network. We must satisfy certain physical and technological constraints which are described. Our investigations have shown that an algorithm for decomposition of the network laws must be adaptive and self-adjusting in the course of the process in order to improve the convergence of the calculation. This is achieved by periodic changes in the mathematical model of the network, i.s., the system ofmore » fundamental nodes and the system of independent cycles. The rate of convergence of the iterative processes of flow and depression optimization is most markedly influenced by the ratio of the sum of the resistances of the branches of the tree and antitree with allowance for the constraints on the flows and depressions.« less