ISSN 2079-3537      

 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                             
Scientific Visualization
Issue Year: 2013
Quarter: 4
Volume: 5
Number: 4
Pages: 118 - 135
Article Name: MATHEMATICAL MODELING AND VISUALIZATION OF THE SLOSHING IN THE ICE-BREAKERíS TANK AFTER IMPACT INTERACTION WITH ICE BARRIER
Authors: T. Elizarova (Russian Federation), D. Saburin (Russian Federation)
Address: T. Elizarova
telizar@mail.ru
Keldysh Institute for Applied Mathematics RAS, Moscow, Russian Federation
 
D. Saburin
asoulofan@gmail.com
Lomonosov Moscow State University, Moscow, Russian Federation
Abstract: The problem of the sloshing in the modern ice-breakerís tankers used for transporting the liquefied gas in arctic conditions after impact interaction with ice barrier is considered.
Mathematical modeling is produced using regularized shallow water equations. The calculations is made for 10-percent tanker fill with bottom shape taken into account in case of vessel velocity directed along the plane of symmetry of the tank and with angle to it. The received non-stationary motions of the free surface and stream lines were visualized for pressure distribution on the tank wall.
The regularized shallow water equations algorithm is used for the modeling. The explicit finite-difference scheme with approximation of the spatial derivatives by central differences is used for the numerical solution. The stability of the numerical algorithm is provided by components with factor τ, which value is linked with the spatial grid step. The time step was chosen in accordance of Courant condition. The preliminary numerical algorithmís factors adjustment was made during the numerical modeling of this problem in one-dimensional approximation, where the solution was calculated only in the plane of symmetry of the tank ignoring the bottom shape.
As the result of this modeling, the visualizations of received non-stationary motions of the free surface and stream lines and experimental estimations of maximum pressure values on the tank wall were obtained. The adequacy of this method was proved by full consistency of this calculations to the previous calculations based on more complete model of the process using three-dimensional nonstationary Navier-Stokes equations accomplished by surface motion.
Thus, the results of the new approach for describing sloshing in modern ice-breakerís tankers after impact interaction with ice barrier are presented in this article. The shallow water approximation is used as a mathematical model here; the numerical solution is based on the regularized form of the initial equations. The complexity of such a numerical algorithm is not great and it allows to solve the problem under consideration using ordinary personal computer. Algorithm allows to calculate the sloshing during large times in a variety of variants of vessel movement, including the sloshing on waves. The result presentation in the form of short movies gives an ability to clearly and quickly analyze the pressure distribution on the tank wall.
Language: Russian