Establishment and solution of governing equation for plana-grooved liquid seals based on three-control-volume theory

Purpose This paper aims to study the dynamic characteristics of the straight-through labyrinth seals, which is applied on an oil sealing belt of hydrostatic support system (HSS) oil pocket, the establishment and solution process of seal governing equation is deduced. Design/methodology/approach The three-control-volume model theory is an efficient approach that is applied well. This paper starts with three relative governing equations for the flow characteristics of straight-through labyrinth seals in the plane direction. Referring to the establishment process of governing equations for circumferentially-grooved liquid seals, the governing equation based on space rectangular coordinate system is established, which are transformed into dimensionless equations through a nondimensionalized process and solved by a perturbation method. It contains a zeroth-order equation, through which a steady fluid distribution is determined, and a first-order equation, through which the seal’s dynamic coefficients can be acquired. Findings The governing equation for plane-grooved straight-through labyrinth seals can be established and solved by the three-control-volume theory. Practical implications This study have important guiding significance for further theoretical research and structural design of the straight-through labyrinth seals on the oil sealing belt of HSS oil pocket. Originality/value In this paper, a straight-through labyrinth seal is installed in an oil sealing belt. The three-control-volume governing equations is established in space rectangular coordinate system, and the shear force of the fluid Y-direction is different from the previous model.