Ihor Raynovskyy

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https://researchid.co/iraynovskyy

RESEARCH, TEACHING, or OTHER INTERESTS

Applied Mathematics

6

Scopus Publications

Scopus Publications


  • Damped steady-state resonant sloshing in a container of circular cross-section for arbitrary periodic nonparametric forcing
    , I. A. Raynovskyy, A. N. Timokha, and
    Taras Shevchenko National University of Kyiv
    Nonlinear modal Narimanov-Moiseev—type equations are investigated to study resonant sloshing in a vertical cylindrical tank. The tank moves periodically in the space with the forcing frequency close to the lowest natural sloshing frequency. We show that the considered sloshing problem can to within the higher-order asymptotic terms be reduced to the case of orbital tank motions in the horizontal plane. Analytical solutions of the secular system which couples the dominant amplitudes of the steady-state sloshing are analytically solved. Effect of viscous damping is accounted. The results are compared with experimental measurements conducted by diverse authors for longitudinal and circular orbital tank excitations. A parametric analysis of the amplitude curves is done to clarify how the steady-state wave regimes and their stability change versus the forcing frequency and the semi-axes ratio of the elliptic orbit. The main result consists of confirming the experimental disappearance of the counter-directed swirling wave mode (relative to the elliptic orbit direction) when passaging to the circular orbit.

  • Steady-state resonant sloshing in upright cylindrical tank due to elliptical forcing
    I. A. Raynovskyy
    Taras Shevchenko National University of Kyiv
    The nonlinear Narimanov-Moiseev multimodal equations are used to study the swirling-type resonant sloshing in a circular base container occurring due to an orbital (rotary) tank motion in the horizontal plane with the forcing frequency close to the lowest natural sloshing frequency. These equations are equipped with linear damping terms associated with the logarithmic decrements of the natural sloshing modes. The surface tension is neglected. An asymptotic steady-state solution is constructed and the response amplitude curves are analyzed to prove their hard-spring type behavior for the finite liquid depth (the mean liquid depth-to-the-radius ratio h>1). For the orbital forcing only swirling occurs. This behavior type is supported by the existing experimental data. Phase lags, which are piecewise functions along the continuous amplitude response curves in the undamped case, become of the non-constant character when the damping matters. The wave elevations at the vertical wall are satisfactory predicted except for a frequency range where the model test observations reported wave breaking and/or mean rotational flows.

  • Damped steady-state resonant sloshing in a circular base container
    I A Raynovskyy and A N Timokha
    IOP Publishing
    To describe the damped resonant sloshing in a circular base container, the nonlinear modal equations by Faltinsen et al (2016 J. Fluid Mech. 804 608–45) are equipped with linear damping terms associated with the logarithmic decrements of the natural sloshing modes. The damping coefficients express a cumulative effect of diverse dissipative phenomena. The surface tension is neglected, the container performs a prescribed periodic sway/surge/pitch/roll motion, the forcing frequency is close to the lowest natural sloshing frequency, and the mean liquid depth—to the tank radius ratio h ≳ 1.2. An asymptotic steady-state solution of the modal equations is derived; its stability is analysed by the linear Lyapunov method. The dominant amplitudes and the phase-lags of the two primary excited natural sloshing modes are governed by four (secular) nonlinear algebraic equations whose structure is the same as if the container were to perform an elliptic orbital horizontal translatory motion. The steady-state response curves are studied versus the semi-axes ratio of the horizontal elliptic orbit; a line segment (horizontal longitudinal) and a circle (rotary forcing) are two limiting cases. For the longitudinal forcing, planar (standing) and swirling steady-state waves are possible, otherwise, only swirling occurs. A focus is on the phase-lags, which are piecewise functions along the continuous amplitude response curves in the undamped case, but they become of the non-constant character when the damping matters. A comparison is done with measurements of the phase-lag by Royon-Lebeaud et al (2007 J. Fluid Mech. 577 467–94) (longitudinal forcing) to show that, if the damping rates are associated with the boundary layer at the wetted tank surface and the bulk viscosity, a satisfactory agreement is established with lower wave amplitudes but the cumulative damping effect must be larger to fit the experiments with increasing amplitudes. For elliptic forcing, stable swirling can be co- or counter-directed with the forcing direction. However, damping makes the counter-directed swirling impossible as the elliptic forcing orbit tends to a circle.

  • Resonant steady-state sloshing in upright tanks: Effect of three-dimensional excitations and viscosity
    Alexander N. Timokha and Ihor A. Raynovskyy
    American Society of Mechanical Engineers
    Bearing in mind recent experimental and theoretical results showing that viscous damping can qualitatively affect resonant sloshing in clean tanks, the Narimanov-Moiseev multimodal sloshing theory for an upright circular container is revised to analytically analyze steady-state surface waves when the container performs a small-amplitude sway/roll/pitch/surge prescribed periodic motion with the forcing frequency close to the lowest natural sloshing frequency. The revised theory is applicable for the radius-scaled mean liquid depths h > 1 providing the secondary resonance phenomenon does not occur at the primary resonance zone. A focus is on how the damping influences the phase lag as well as on the amplitude response curves versus the forcing type, which can in the lowest-order approximation be treated as if the container translatory moves along an elliptic orbit in the horizontal plane. The analytical results are compared with existing experiments for longitudinal and circular orbital tank excitations. Whereas a good agreement is found for longitudinal excitations, a discrepancy is detected for the circular orbital forcing. The discrepancy may, most probably, be explained by the wave breaking and mean angular mass-transport (Ludwig Prandtl, 1949) phenomena. Occurrence of the Prandtl phenomenon makes inapplicable the existing analytical inviscid sloshing theories, even if they are modified to account for damping.

  • Steady-State Resonant Sloshing in an Upright Cylindrical Container Performing a Circular Orbital Motion
    Ihor Raynovskyy and Alexander Timokha
    Hindawi Limited
    The nonlinear Narimanov-Moiseev multimodal equations are used to study the swirling-type resonant sloshing in a circular base container occurring due to an orbital (rotary) tank motion in the horizontal plane with the forcing frequency close to the lowest natural sloshing frequency. An asymptotic steady-state solution is constructed and the response amplitude curves are analyzed to prove their hard-spring type behavior for the finite liquid depth (the mean liquid depth-to-the-radius ratio h>1). This behavior type is supported by the existing experimental data. The wave elevations at the vertical wall are satisfactorily predicted except for a frequency range where the model test observations reported wave breaking and/or mean rotational flows.