Stage separation of recoverable liquid launch vehicle by using moving pulsating ball analogue for propellant sloshing

In the process of stage separation of recoverable liquid launch vehicles, because of the large amount of residual fuel in the storage tanks, the influence of liquid sloshing on separation safety must be considered. Considering calculation simplicity and operation practicability, the Moving Pulsating Ball Model (MPBM) of large amplitude liquid sloshing is introduced into the calculation of launch vehicle stage separation. Combining the dynamic equation of the model with the energy relationship during “breathing movement”, the formula calculating the force of liquid on the rigid body is derived. Compared with the calculations of commercial CFD calculation software, the accuracy of MPBM model is verified. Then, all the external forces and moments are applied to the rigid body of the stages, so that the translational and rotational dynamic equations of the stages are obtained respectively. According to the relative position of the two stages, the geometric shape of the interstage section and the engine of the second stage, the minimum clearance in the separation process can be decided to guarantee that the separation process is safe.