Similarity Analysis of Scale Ratio Effects on Pulsating Air Pockets Based on Bagnold’s Impact Number

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.