• Journal of the Society of Naval Architects of Korea
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• v.60 no.3
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• pp.193-201
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• 2023

A developed code based on the unified conservation laws of incompressible/compressible fluids is applied to analyze similarity in pressure oscillations caused by pulsating air pockets in sloshing tanks. It is shown that the nondimensional time histories of pressure show good agreements under Froude and geometric similarities, provided that there are no pulsating entrapped air pockets. However, the nondimesional period of pressure oscillation due to the pulsating air pocket becomes longer as the size of the sloshing tank increases. The discrepancy in the nondimensional period is attributed to the compressibility bias of the entrapped air. To get rid of the compressibility bias, the ullage pressure in a sloshing tank is adjusted based on the Bagnold's impact number. The variation in the period of pressure oscillation according to the ullage pressure is explained based on the spring-mass system. It is shown that the nondimensional period of pressure oscillation is virtually constant when the ullage pressure is adjusted based on the Bagnold's impact number, regardless of tank size. It is found that the Bagold's impact number should be the same, if the time history of pressure is important while an entrapped air pocket pulsates.

• Journal of the Society of Naval Architects of Korea
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• v.58 no.5
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• pp.271-280
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• 2021

The code developed using a pressure-based method for unified conservation laws of incompressible/compressible fluids is expanded to handle moving or deforming body boundaries using the hybrid Cartesian/immersed boundary method. An instantaneous pressure field is calculated from a pressure Poisson equation for the whole fluid domain, including the compressible gas region. The polytropic gas is assumed for the compressible fluid so that the energy equation is decoupled. Immersed boundary nodes are identified based on edges crossing body boundaries. The velocity vector is reconstructed at the immersed boundary node using an interpolation along the assigned local normal line. The developed code is validated by comparing the time histories of pressure and wave elevation for sloshing in a rectangular and a membrane-type tank. The validated code is applied to simulate air cushion effects in a rectangular tank under sway motion. Time variations of pressure fields are analyzed in detail as the air pocket pulsates. It is shown that the contraction and expansion of the air pocket dominate the pressure loads on the wall of the tank. The present results are in good agreement with other experimental and computational results for the amplitude and the decay of the pressure oscillations measured at the pressure gauges.