Development of a method for calculating high-dimension heat networks

Abstract

A transition from the mass balance equations based on Kirchhoff’s first and second laws to modeling on the basis of a discretized continuity equation is made for describing a hydraulic network. A technique for calculating high-dimension hydraulic and heat networks based on the numerical finite-difference control volume method is developed. Unlike the existing approaches, the proposed technique does not involve the need to determine hydraulic loops and boils down to solving the problem of obtaining a unified field of pressures for the entire calculation region. This advantage of the proposed method opens the possibility of applying it for solving high-dimension problems containing more than a million of hydraulic links. The proposed numerical method features stable operation for hydraulic networks the neighboring links of which may have pressure drop coefficients differing from each other by more than 10 orders of magnitude. In contrast, the global gradient algorithm implemented in the standard software system EPANET is of little use for such applications. The convergence rate of the proposed technique is close to that of the Todini gradient algorithm and is almost independent of the problem dimension.