Viscous effects on liquid sloshing under external excitations

Abstract The viscous effects on liquid sloshing under external excitations were investigated in this study. A 3D two-phase flow numerical model was adopted to simulate sloshing of highly viscous fluids by properly resolving boundary layer near tank walls. The numerical model was validated against available analytical solutions and previous numerical results. In addition, the laboratory experiment of the sloshing of glycerin was conducted in this study, providing additional data for numerical model verification. The effects of liquid adherence to side walls due to high viscosity was discussed. The verified numerical model was then employed to study the sloshing of fluids with different kinematic viscosities ranging from 10−6 m2/s to 10−2 m2/s. The free surface profiles during the sloshing wave impact on the wall were analyzed, in connection with the pressure response characteristics. Special attentions were made on the extended rising time during the impact process for fluids with large viscosity. The fast Fourier transform technique was used to study the frequency responses of the sloshing. The critical value of viscosity, at which the response type shifts from natural frequency response to external excitation response, was identified. Finally, the comparisons between water and glycerin under six degree-of-freedom excitations were presented and discussed.

[1]  J. Frandsen.  Sloshing motions in excited tanks , 2004 .

[2]  J RomeroV,et al.  A numerical model for 2-D sloshing of pseudo-viscous liquids in horizontally accelerated rectangular containers. , 1970 .

[3]  Peng Wu,et al.  The analysis of second-order sloshing resonance in a 3-D tank , 2014 .

[4]  J. Navickas,et al.  Modeling Criteria for Scaled LNG Sloshing Experiments , 1985 .

[5]  De-yu Wang,et al.  The effect of liquid viscosity on sloshing characteristics , 2015 .

[6]  Pengzhi Lin,et al.  A numerical study of three-dimensional liquid sloshing in tanks , 2008, J. Comput. Phys..

[7]  G. X. Wu,et al.  The effect of viscosity on the transient free-surface waves in a two-dimensional tank , 2001 .

[8]  Stefan aus der Wiesche.  Sloshing dynamics of a viscous liquid in a spinning horizontal cylindrical tank , 2008 .

[9]  K. Bathe,et al.  Transient solution of 3D free surface flows using large time steps , 2015 .

[10]  Yu Tang,et al.  Effect of viscosity on dynamic response of a liquid storage tank , 1993 .

[11]  R. Z. Uras,et al.  Sloshing analysis of viscous liquid storage tanks , 1995 .

[12]  De-yu Wang,et al.  Effects of boundary layer and liquid viscosity and compressible air on sloshing characteristics , 2015 .

[13]  Mario Alberto Storti,et al.  Numerical modelling of 3D sloshing experiments in rectangular tanks , 2018, Applied Mathematical Modelling.

[14]  Jae In Park,et al.  Simulation of Sloshing in Fuel Tanks and Parametric Study on Noise Reduction by Decreasing Impact Pressure , 2005 .

[15]  M. Souli,et al.  Numerical Simulation of Liquid Sloshing in Tanks , 2017 .

[16]  G. H. Keulegan,et al.  Energy dissipation in standing waves in rectangular basins , 1959, Journal of Fluid Mechanics.

[17]  Jean-Marc Rousset,et al.  Experimental Study of Viscous Cargo Behaviour and Investigation on Global Loads Exerted on Ship Tanks , 2017 .

[18]  W. C. Parkinson,et al.  Damping of surface waves in an incompressible liquid , 1957, Journal of Fluid Mechanics.

[19]  D. Peregrine.  Water-wave impact on walls , 2003 .

[20]  S. Turnock,et al.  Multiphase CFD modelling of a lateral sloshing tank , 2009 .

[21]  W. Nyborg,et al.  Parametrically Excited Surface Waves , 1965 .

[22]  Odd M. Faltinsen,et al.  A numerical nonlinear method of sloshing in tanks with two-dimensional flow , 1978 .

[23]  A. Borthwick,et al.  Fully non-linear simulation of second-order resonance in a three-dimensional tank using the PSME method , 2012 .

[24]  Torgeir Moan,et al.  A probabilistic assessment of design sloshing pressure time histories in LNG tanks , 2008 .

[25]  R. Eatock Taylor,et al.  Numerical simulation of sloshing waves in a 3D tank , 1998 .

[26]  Pengzhi Lin,et al.  A numerical study of breaking waves in the surf zone , 1998, Journal of Fluid Mechanics.

[27]  W. G. Price,et al.  Numerical simulation of liquid sloshing phenomena in partially filled containers , 2009 .

[28]  J. Abedi,et al.  Comparison of finite element and pendulum models for simulation of sloshing , 2003 .

[29]  Odd M. Faltinsen,et al.  Multidimensional modal analysis of nonlinear sloshing in a rectangular tank with finite water depth , 2000, Journal of Fluid Mechanics.

[30]  Chih-Hua Wu,et al.  Hydrodynamic forces induced by transient sloshing in a 3D rectangular tank due to oblique horizontal excitation , 2013, Comput. Math. Appl..

[31]  Decheng Wan,et al.  MPS-FEM coupled method for sloshing flows in an elastic tank , 2017 .

[32]  David F. Hill,et al.  Transient and steady-state amplitudes of forced waves in rectangular basins , 2003 .

[33]  Pengzhi Lin,et al.  Wave–current interaction with a vertical square cylinder , 2003 .

[34]  Moo-Hyun Kim,et al.  A parametric sensitivity study on LNG tank sloshing loads by numerical simulations , 2007 .

[35]  Pengzhi Lin,et al.  A Numerical Model for Breaking Waves: The Volume of Fluid Method. , 1997 .

[36]  A. Chorin.  Numerical solution of the Navier-Stokes equations , 1968 .