I. A. Lukovsky

Natural sloshing frequencies in rigid truncated conical tanks

Purpose – The main purpose of this paper is to develop two efficient and accurate numerical analytical methods for engineering computation of natural sloshing frequencies and modes i the case of truncated circular conical tanks.Design/methodology/approach – The numerical‐analytical methods are based on a Ritz Treftz variational scheme with two distinct analytical harmonic functional bases.Findings – Comparative numerical analysis detects the limit of applicability of variational methods in terms of the semi‐apex angle and the ratio between radii of the mean free surface and the circular bottom. The limits are caused by different analytical properties of the employed functional bases. However, parallel use of two or more bases makes it possible to give an accurate approximation of the lower natural frequencies for relevant tanks. For V‐shaped tanks, dependencies of the lowest natural frequency versus the semi‐apex angle and the liquid depth are described.Practical implications – The methods provide the nat...

Weakly nonlinear sloshing in a truncated circular conical tank

Sloshing of an ideal incompressible liquid in a rigid truncated (tapered) conical tank is considered when the tank performs small-magnitude oscillatory motions with the forcing frequency close to the lowest natural sloshing frequency. The multimodal method, the non-conformal mapping technique and the Moiseev type asymptotics are employed to derive a finite-dimensional system of weakly nonlinear ordinary differential (modal) equations. This modal system is a generalization of that by Gavrilyuk et al 2005 Fluid Dyn. Res. 37 399?429. Using the derived modal equations, we classify the resonant steady-state wave regimes occurring due to horizontal harmonic tank excitations. The frequency ranges are detected where the ?planar? and/or ?swirling? steady-state sloshing are stable as well as a range in which all steady-state wave regimes are not stable and irregular (chaotic) liquid motions occur is established. The results on the frequency ranges are qualitatively supported by experiments by Matta E 2002 PhD Thesis Politecnico di Torino, Torino.

Compressible potential flows with free boundaries. Part I : Vibrocapillary equilibria

Various variational formulations describing nonstationary compressible fluid flows are considered. In particular, for high-frequency excitations a variationally based approximation frame is deduced which may explain experimentally observed phenomena.

Generalizing the Multimodal Method for the Levitating Drop Dynamics

The present paper extends the multimodal method, which is well known for liquid sloshing problems, to the free-surface problem modeling the levitating drop dynamics. The generalized Lukovsky-Miles modal equations are derived. Based on these equations an approximate modal theory is constructed to describe weakly-nonlinear axisymmetric drop motions. Whereas the drop performs almost-periodic oscillations with the frequency close to the lowest natural frequency, the theory takes a finite-dimensional form. Periodic solutions of the corresponding finite-dimensional modal system are compared with experimental and numerical results obtained by other authors. A good agreement is shown.