S.D. Vynnychuk, V.Ya. Kondrashchenko
Èlektron. model. 2017, 39(2):59-74
The problem of minimizing the weight of the hydraulic distribution system with following constraints: the system graph is the directed rooted tree, element diameters of the branches that are downstream the compressible fluid, may not exceed the diameter of the cells adjacent to its branch being upstream. When calculating the pressure losses on the elements, the use of the models of its determination is not limited.
The variant of algorithm of choosing discrete values of the diameters meeting k-admissibility requirements, when the size of diameter of the branch elements cannot exceed the minimum admissible value no more than by k positions. The best of these options diameters was called k-optimal and the algorithm of its search—k-optimal algorithm A. It is shown that the computational complexity of the algorithm A is estimated at T = O(V(k + 1)E1 + VL), where V —the number of nodes in the graph, E1 — a subset of the branches, which endpoint nodes are internal nodes of the graph, L — the number of diameter standard sizes. Moreover, for the graph, which all the internal components are combined by three branches (binary tree), the number of exhaustion options for 1-optimal algorithm A does not exceed 2E/2.
distribution network of compressible and incompressible fluid, weight minimization.
l. Shevelev, F.A. and Shevelev, A.F. (1984), Tablitsy dlya gidravlicheskogo rascheta vodoprovodnykh trub. Spravochnoye izdaniye, 6-e izd., dop. i pererab [Tables for the hydraulic calculation of water pipes. Reference edition, 6-th ed., ext. and rev.], Stroyizdat, Moscow, Russia
2. “Encyclopedia of mechanical engineering XXL”, available at: http://mash-xxl.info/article/435717/ (accessed October 6, 2016).
3. “Reference chemist 21. Chemistry and chemical technology”, available at: http://chem21.info (accessed October 6, 2016).
4. Available at: http://www.intechgmbh.ru/pipelines_calc_and_select.php#quest_optimal_pipeline_dia.
5. Kormen, T., Leyzerson, Ch., Riverst, R. and Shtayn, K. (2011), Algoritniy: postrayeniye i analiz, 2-e izd. [Algorithms: construction and analysis, 2nd ed.], Izdatelskiy dom “Viliyams”, Moscow, Russia.
6. Nekrasov, B.B. (1967), Gidraviika i eye primeneniye na letatelnykh apparatakh [Hydraulics and its application in aircraft], Mashinostroyeniye, Moscow, Russia.
7. Abramovich, G.N. (1969), Prikladnaya gazovaya dinamika, 3-v izd., pererab [Applied gas dynamics, 3-rd ed., revised], Nauka, Moscow, Russia.
8. Kondrashchenko, V.Ya., Vvnnychuk, S.D. and Fedorov, M.Yu. (1990), Modelirovaniye gazovykh i zhidkostnykh raspredelitelnykh system [Simulation gas and fluid distribution systems], Naukova dumka, Kiev, Ukraine.
9. Vynnychuk, S.D. and Samoylov, V.D. (2015), “Determination of the currents in the switching structures of the electrical energy networks with tree graph’s structure”, Elektronnoe modelirovanie, Vol. 37, no. 5, pp. 89-104.