THE CALCULATION OF OPTIMAL DIAMETERS OF HYDRAULIC NETWORK USING THE CONVECTION-DIFFUSION METHOD OF CONSTRAINED MINIMIZATION

The paper presents the calculation of optimal pipeline diameters based on the solving the constrained optimization task using the derivates. The hydraulic network consisting of several interconnected pipeline sections is designed to supply optimally the fluid or gas to various customers. In the general case, the optimization should be performed according to several criteria. For example, when transporting dangerous media through the pipeline, it is necessary to consider not only the hydraulic network cost but the dangerous factor as well.

Multi-criteria optimization can be reduced to the solution of the issue of constrained minimization of some criterion, which depends on the diameter of the pipeline sections. The authors consider the pipeline total volume to be such criterion. But the direct optimization by the segments diameters of a pipeline with the complex topology in the form of a closed hydraulic network requires the multiple iterative hydraulic calculations. The application of specialized programs and algorithms designed to get final output parameters slightly allows carrying out the optimization using the above zero order techniques. However, it seems preferable to use the deterministic methods of the first order to obtain more accurate results for solving the optimization task according to several criteria.

In this paper, for optimization, the authors used the concept of conditional minimization of a criterion, which is calculated by the decomposition method. The pipeline system is divided into separate sections, the hydraulic calculation of which is not hard to carry out. The delivery head in the nodes and the sections diameters are the independent variables and the material balance equations in the nodes are the constraining conditions. At the known values of pressure and diameters, it is easy to calculate the flow rates in the sections. The simplified hydraulic calculation allows to solving the optimization issue by using the derivatives. The multidimensional constrained optimization issue can be solved using the developed deterministic method when the convection-diffusion transfer of particles is simulated using the differential equations. The results of numerical experiments prove the applicability of the proposed approach.