Mathematical modelling of the systems providing groups of blast-furnaces with blast via a common manifold

Two types of the systems providing groups of blast-furnaces with blast through one or two common manifolds were analyzed in the article. The first system consists of four turbo-superchargers, working in parallel for one common manifold and four blast furnaces supplied with blast from that manifold. A differential equation was found for such a system, describing pressure alterations inside the manifold, due to parameters of the blast consumed by the furnaces and due to the operation of turbo-superchargers working in parallel for that manifold. The second system of blast supply has the same number of turbo-superchargers and blast-furnaces, but has two common manifolds, connected by a pipeline. A mathematical description of this work as a system of two differential equations, describing the dependence of the blast pressure upon the parameters of turbo-superchargers and the mode of blast-furnaces operation was developed. The obtained differential equations are differential equations with random coefficients. Then it was shown that by replacing these random coefficients with their average values and analyzing the set systems operation mode afterwards it will be possible to evaluate the parameters of the turbo-superchargers, that will make it possible to provide the blast furnaces with blast with preset parameters. Detailed examples were given for each type of the systems, in which the required parameters of the turbo-superchargers were found. It was shown that the second type of blast supply was more preferable, although it re-quires increased parameters of turbo-superchargers