Multi-dimensional NURBS model for predicting maximum free surface oscillation in swaying rectangular storage tanks

Abstract

In this paper, a multi-dimensional non-uniform rational B-spline (NURBS) model is presented aiming at predicting the maximum free surface oscillation (MFSO) in the swaying rectangular storage tanks. The accuracy and clear mathematical meaning of the NURBS formulation make it attractive for the purpose. In this regard, a numerical model is developed to simulate the liquid sloshing phenomenon in a rectangular tank by means of coupling the Reynolds averaged Navier–Stokes (RANS) solver and the volume of fluid (VOF) technique. The RANS equations are discretized and solved using the staggered grid finite difference SMAC method. In order to validate the model, a rectangular tank with specified width and water depth is exposed to a presumed horizontal periodic sway motion and the results of the numerical analysis are compared to a well-established example. In the next step, the numerical model is used to simulate the sloshing phenomenon in the rectangular storage tanks with different widths and water depths under different harmonic excitations. Finally, a multi-dimensional NURBS hyper-surface is employed to fit a multivariate function to the sloshing results based on the numerical data. As a result, a new mathematical relationship is suggested by this article to estimate the MFSO in the swaying rectangular storage tanks, so that practitioners may benefit more when they try to apply the presented methodology to their real-world problems.