Numerical simulation of the flow of viscous incompressible fluid through cylindrical cavities


  • Ya. P. Trotsenko Taras Shevchenko National University of Kyiv



The flow of viscous incompressible fluid in a cylindrical duct with two serial diaphragms is studied by the numerical solution of the unsteady Navier–Stokes equations. The discretization procedure is based on the finite volume method using the TVD scheme for the discretization of the convective terms and second order accurate in both space and time difference schemes. The resulting system of non-linear algebraic equations is solved by the PISO algorithm. It is shown that the fluid flow in the region between the diaphragms is nonstationary and is characterized by the presence of an unstable shear layer under certain parameters. A series of ring vortices is formed in the shear layer that causes quasi-periodic self-sustained oscillations of the velocity and pressure fields in the orifice of the second diaphragm. There can be four self-sustained oscillation modes depending on the length of the cavity formed by the diaphragms. With the increase in the distance between the diaphragms, the frequency of oscillations decreases within the same self-oscillation mode and rises sharply with the switch to the next mode.

Key words: direct numerical simulation, cylindrical cavity, duct with diaphragms, vortical structures, self-sustained oscillations.

Pages of the article in the issue: 218-221

Language of the article: Ukrainian


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How to Cite

Trotsenko, Y. P. (2019). Numerical simulation of the flow of viscous incompressible fluid through cylindrical cavities. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics, (1), 218–221.



Differential equations, mathematical physics and mechanics