Study On The Hydrodynamic Characteristics Of Moonpool Resonance Based On Linear Potential Flow Theory

The main content of this paper is to predict the resonant frequency of the moonpool.Here two methods are adopted.One is to use the WAMIT program with boundary element method to calculate the elevation inside the moonpool,and find the singularities through the curve frequency-elevation,which represent the resonant frequencies of the moonpool.The other method is eigenfunction matching method,which is a kind of semi-analytical method and based on the linear potential flow theory.The resonant frequencies from this method can be obtained by solving the velocity potential of each subdomain,finding the frequencies of the singular point through the curve of frequency-elevation;they can also be obtained directly by solving the characteristic equation of the matrix of coefficients,but the exact wave elevation is unknown in this way.For WAMIT program,this article mainly introduces two different ways of modeling,namely the method of directly writing the grid point value and calling the WAMIT subroutine,respectively.It should be noted that the interference caused by irregular frequencies sometimes occurs during calculation,which leads to peaks of wave elevation at non-resonant frequencies.At this time,the model needs to ’have a lid’ to remove the influence of irregular frequencies.As for calling the WAMIT subroutine method,when the WAMIT built-in program does not have the required model,a callable model subroutine can be added referring to the built-in program.This method is very convenient for multiple calculations that require changing parameters.For the use of the eigenfunction matching method,the resonant frequencies of a three-dimensional recessed moonpool in infinite water depth are solved,and it compares with the resonant frequencies of two-dimensional one.The results of longitudinal resonant frequencies agree well,but the three-dimensional model can be solve the transverse sloshing resonant frequencies.Meanwhile,an explicit expression that can calculate the longitudinal frequencies is derived in this article,which facilitates the calculation to a certain extent.Besides,this paper also extends the infinite water depth model to the case of finite water depth,taking the effect of water depth,ship length,and ship width on resonance frequency into consideration.Water depth,ship length,and boat width have little effect on pistons and high-order sloshing modes,but first-order sloshing decreases as the ratio of ship width to moon pool width increases,and increases as the water depth increases.In addition,this paper studies the diffraction problem of asymmetric and symmetric two-dimensional moonpools in a two-layer fluid with finite depth.The parametric studies are analyzed as well.It is observed that,compared with the solutions in surface wave mode,the wave exciting forces in internal wave mode are much smaller,and show more peaks and valleys in low-frequency region.As the wave frequency increases,the bandwidth of sloshing mode resonances decreases.Extensive parametric studies have been performed to examine the effects of moonpool geometry and density stratification on the resonant wave motion and exciting forces.It is found that,for twin bodies with deep draft in surface wave mode,the decreasing density ratio has little effects on the sloshing mode resonance frequencies but can somehow suppress the horizontal wave exciting forces and surface wave elevations around piston mode resonance region.In addition,the presence of lower-layer fluid can lead to the reduction of piston mode resonance frequency.