RESEARCH UNSTEADY A PRESSURE HEAD PIPE FLOW BASED ON MATHEMATICAL MODELS

2017;
: 48-52
1
Lviv Polytechnic National University, Department of hydraulics and plumbing
2
Lviv Polytechnic National University, Department of hydraulics and plumbing
3
Lviv Polytechnic National University, Department of hydraulics and plumbing

The article deals with mathematical modeling of non-stationary processes non-periodic pressure of the fluid in cylindrical tubes. Based on the Navier-Stokes equations for compressible fluid withdrawn simplified equation for the case of long pipes. It is shown that modeling of single processes, these equations contain only one dimensionless parameter. Identifies conditions which may further simplify these equations to a form that does not contain a dimensionless parameter. Total non-periodic accelerated research process is based on the review model problem for which elected a process in tube for instant pressure changes. Specified the conditions under which you can go to traffic patterns and incompressible fluid movements with high attenuation. The criterion of the transition from laminar to turbulent motion mode that allows you to determine the scope of application of these models movement.To date, no theory calculation since buckling laminar flow regime and transition to a turbulent unsteady flows and therefore no limits applicability of the above models laminar motion, making it necessary to use physical simulation results obtained from experimental data.

1. Adamkowski A. Experimental examination of unsteady friction models for transient pipe flow simulation / Adam Adamkowski, Mariusz Lewandowski // Trans. ASME. J. Fluids Eng. – 2006. – 128. – No. 6. – С. 1351–1363. 2. Reinhold I. Velocity profile influence on electromagnetic flowmeter accuracy / I. Reinhold // Proc. FLOMEKO. – 1978. – Netherland. – P. 181–185. 3. Letelier S. M. F. Unified approach
to the solution of problems of unsteady flow in long pipes/ S.M. F. Letelier, H. J. Leutheusser // J. Appl. Mech. – 1983. – Vol. 50, N 1. – P. 8–12. 4. Байбаков Б. С. Сопротивление трения при ускоренном
течении в трубе / Б. С. Байбаков, О. Ф. Орешкин, А. М. Прудовский // Изв. АН СССР. Механ. жидк. и газа. – 1981. – No. 5. – С. 137–139. 5. Логов И. Л. К вопросу о сопротивлении трения при ускоренном течении в трубе / И. Л. Логов // Изв. АН СССР, Механ. жидк. и газа. – 1983. – № 6. – С. 169–174. 6. Jayasinghe D. A. P. Pulsatile Waterhammer Subject to Laminar Friction / D. A. P. Jayasinghe, H. J. Leutheusser // J. Fluids Eng. – 1972. – No. 94(2). – С. 467–472. 7. Чарный И. А. Неустановившееся движение реальной жидкости в трубах / И. А. Чарный. – М.: Недра, 1975. – 296 с. 8. Попов Д. Н. Нестационарные гидромеханические процессы / Д. Н. Попов. – М.: Машиностроение, 1982. – 239 с. 9. Masliyah J. H. Laminar Transient flow in pipes / J. H. Masliyah, С. А. Shооk // Can. J. Chem. Eng. – 1975. – Vol. 53. – No. 10. – P. 469–475. 10. Leutheusser H. J. Problems of accelerated fluid motion / H. J. Leutheusser// Proc. XVII Cong. IAHR, Baden-Baden, Germany. – 1977. – Vol. 6. – P. 247–252. 11. Бондаренко Ю. А. Математические модели и численные методы для решения задач нестационарной газовой динамики / Ю. А. Бондаренко. Обзор зарубежной литературы / Ю. А. Бондаренко, В. В. Башуров, Ю. В. Янилкин. – М. 2003. – (Препринт / РФЯЦ ВНИИЭФ; – No. 88-2003). 12. Jachno O. M. Równania niestacjonarnego przepływu laminarnego cieczy ściśliwej w rurze cylindrycznej / O. M. Jachno, R. M. Hnatiw, I. R. Hnatiw // Nauka i studia. – 2017. – No. 2 (163). – ISSN 1561–6894. – C. 97–102.