Unsteady Flows in Deformable Pipes: The Energy Conservation Law
- 12 Downloads
We derive a quasi-one-dimensional energy equation that corresponds to the flow of a compressible viscous fluid in a deformable pipeline. To describe the flow of such a fluid in a pipeline, we couple this equation with the previously derived continuity and momentum equations as well as with the equations of state for the internal energies of the fluid, the pipe deformations, pressure, and the cross-sectional area of the pipe. The derivation of the equations is based on averaging over the pipeline cross section. The equations obtained are designed for numerical simulations of long-distance transportation of a compressible fluid.
Unable to display preview. Download preview PDF.
- 1.A Collection of Problems on Mathematics for Technical Universities, Part. 2: Special Sections of Mathematical Analysis, Ed. by A. V. Efimov and B. P. Demidovich, 2nd ed. (Nauka, Moscow, 1986) [in Russian].Google Scholar
- 4.L. I. Sedov, Mechanics of Continuous Media (Nauka, Moscow, 1973; World Sci., River Edge, NJ, 1997), Vol. 1.Google Scholar
- 5.V. L. Streeter, E. B. Wylie, and K. W. Bedford, Fluid Mechanics (WCB/McGraw-Hill, Boston, 1998).Google Scholar
- 6.S. I. Sumskoi, A. S. Sofin, and M. V. Lisanov, “Developing the model of non-stationary processes of motion and discharge of single- and two-phase medium at emergency releases from pipelines,” J. Phys.: Conf. Ser. 751, 012025 (2016).Google Scholar
- 8.S. I. Sumskoi, A. M. Sverchkov, M. V. Lisanov, and A. F. Egorov, “Modelling of non-equilibrium flow in the branched pipeline systems,” J. Phys.: Conf. Ser. 751, 012022 (2016).Google Scholar
- 9.S. I. Sumskoi, A. M. Sverchkov, M. V. Lisanov, and A. F. Egorov, “Simulation of systems for shock wave/compression waves damping in technological plants,” J. Phys.: Conf. Ser. 751, 012023 (2016).Google Scholar
- 10.S. I. Sumskoi, A. M. Sverchkov, M. V. Lisanov, and A. F. Egorov, “Simulation of compression waves/shock waves propagation in the branched pipeline systems with multi-valve operations,” J. Phys.: Conf. Ser. 751, 012024 (2016).Google Scholar