MODELING OF FLUID FLOW IN PIPELINE AND THE DIFFERENCE SCHEME STABILITY INVESTIGATIONS
Keywords:
Navier-Stokes system, boundary conditions, pipeline’s section narrowing, low leakage, numerical method, stability, spectrum characteristics of stabilityAbstract
A mathematical model of viscous fluid flow in the pipeline with the presence of flow across the surface and the narrowing of pipeline section, which is based on a system of Navier-Stokes equations in two-dimensional rectangular region with a special type of boundary conditions has been designed. The geometric configuration of the leakage zone is taken into the account. It is believed that the fluid motion is under the influence of constant length of pressure difference. For the solving of this system, the numerical method of finite differences was developed by which the finite differences scheme is realized – the first step is implicit in longitudinal coordinate, and the second – on the transversal. The study on the stability of the spectral features method, stability conditions are established for the case of flow calculation with specified parameters and for the given type of the pipeline geometry. The criterion of numerical stability is presented taking to account the model’s parameters
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2. Pat. 5205173 United State, Int. Cl. G 01 M 003/00. Method and apparatus for detecting leaks in pipelines using cross-correlation techniques / Allen, Trevor J. – Application No. 718746; filed on 21.06.91; issued on 27.04.93.
3. Pat. 6668619 United State, Int. Cl. G 01 M 3/24. Pattern matching for real time leak detection and location in pipelines / Yang B.-W., Recane M. Application No. 10/146745; filed on 15.05.02; issued on 30.12.03.
4. Pat. 5361636 United State, Int. Cl. G 01M 003/24. Apparatus and process for measuring the magnitude of leaks / Farstad Jerry E., Cremean Stephen P. – Application No. 948597; filed on 23.09.92; issued on 08.11.94.
5. Pat. 5349568 United State, Int. Cl. G 01 S 003/80, G 01 M 003/00. Leak locating microphone, method and system for locating fluid leaks in pipes / Kupperman D. S., Spevak L. – Application No. 127742 ; filed on 27.09.93 ; issued on 20.09.94.
6. Brodetsky I., Savic М. 1993, “Leak monitoring system for gas pipelines”, Acoustics, Speech, and Signal Processing, vol. 3, pp. 17-20.
7. Brunone B., Ferrante М., 2001, “Detecting leaks in pressurised pipes by means of transients”, Journal of hydraulic research, vol. 39, no. 4, pp. 1-6.
8. Shkadov V.J., Zapryanov Z.D., 1984, Viscous liquid, University Press, Moscow.
9. Shcherbakov S.G., 1982, Problems of oil and gas pipeline transport, Nedra, Moscow.
10. Anderson D., Tannehil J. & Pletcher R., 1990, Computational fluid and heat, Mir, Moscow.
11. Schlichting G., 1974, Theory of the boundary layer, Nauka, Moscow.
12. Dyachenko V.F., 1977, The basic concepts of computational mathematics, Nauka, Moscow.
13. Georgievsky D.V., 1998, The stability of visco-plastic deformation processes objects, "URSS", Moscow.
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