The flow of a liquid in a cylindrical duct with diaphragms of a rectangular profile


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



duct with diaphragms, vortex structures, self-sustained oscillations


The flow of a viscous incompressible liquid in a cylindrical duct with two serial diaphragms of a rectangular profile 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 non-stationary and is characterized by the presence of an unstable shear layer under the certain parameters. A series of ring vortices is formed in the shear layer that causes quasi-periodic self-sustained oscillations of the velocity field in the vicinity of the orifice of the second diaphragm. In comparison with the case of rounded diaphragms, an increase in the maximum jet velocity is observed, which in turn leads to an increase in the frequency of self-sustained oscillations and a decrease in the Reynolds numbers at which quasi-periodic oscillations are excited.

Pages of the article in the issue: 76 - 81

Language of the article: Ukrainian


ZIADA, S. and LAFON, P. (2014) Flow-excited acoustic resonance excitation mechanism, design guidelines and counter measures. Appl. Mech. Rev., 66 (1), p. 010802.

VOVK, I.V., GRINCHENKO, V.T. and MAKARENKOV, A.P. (2011) Akustika dyihaniya I serdechnoj deyatel’nosti. Akust. visn., 14 (1), p. 3–19.

WILSON, T.A., BEAVERS, G.S., DECOSTER, M.A., HOLGER, D.K. and REGENFUSS, M.D. (1971). Experiments on the fluid mechanics of whistling. J. Acoust. Soc. Am., 50 (1B), p. 366–372.

VOVK, I.V. & MALYUGA, V.S. (2012). Zvukovoye pole, generiruyemoye potokom v kanale so stenozami. Prykl. Hidromeh., 11 (4), p. 17–30.

TROTSENKO, YA. and VOVK, I. (2020) Numerical simulation of the 3-D flow in a cylindrical duct with two diaphragms at low Mach numbers. J. Theor. Appl. Mech. (Bulgaria), 50 (2), p. 190–201.

SWEBY, P.K. (1984). High resolution schemes using flux limiters for hyperbolic conservation laws. J. Numer. Anal., 21 (5), p.995–1011.

FERZIGER, J.H. and PERIC, M. (2002). Computational methods for fluid dynamics. Berlin: Springer.

BARRETT, R., BERRY, M., CHAN, T.F., DEMMEL, J., DONATO, J.M., DONGARRA, J., EIJKHOUT, V., POZO, R., ROMINE, C. and VAN DER VORST, H. (1994). Templates for the solution of linear systems: Building blocks for iterative methods, 2nd Ed. Philadelphia: SIAM.

MALYUGA, V.S. (2010). Chislennoye issledovaniye techeniya v kanale s dvumya posledovatel’no raspolozhennyimi stenozami. Algoritm resheniya. Prikl. Hidromeh., 12 (4), p. 45–62.

VOVK, I.V., MATSYPURA, V.T. and TROTSENKO, Ya.P. (2020) Excitation of self-sustained oscillations by a flow of liquid in a cylindrical duct with two diaphragms. J. Math. Sci., 247 (2), p. 258–275.




How to Cite

Trotsenko, Y. P. (2021). The flow of a liquid in a cylindrical duct with diaphragms of a rectangular profile. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics, (4), 76–81.



Differential equations, mathematical physics and mechanics