## 1 Introduction  
An aircraft's engine is the core part of an aircraft and is also an important index for determining a country's basic industrial prowess [1]; sealing devices are an important engine component, and improvements in sealing performance can improve efficiency, save energy and reduce pollution. Therefore, advanced sealing technologies are necessary to realise future improvements in aircraft performance [2]. An aircraft's engine requires many parts to establish a tight seal; the oil seal of a bearing chamber is an important sealing system in engine. For example, the bearing chamber oil seal should feature high operational capacity and minimal air leakage to create a strong seal, reduce engine weight and improve performance. To reduce weight and space, the high- and low-pressure rotors in modern engines are usually installed concentrically. In such a case, the intermediate bearing seal between two rotors (also known as the'seal between shafts') should be capable of forming a seal between two moving interfaces. Especially in engines where the two rotors rotate in reverse, the operating environment of the seal between shafts (known as the'seal between reverse shafts') is more hostile. The sealing interface has an extremely high relative sliding speed and small available space, exceeding the operating limits of traditional contact seals. While non-contact labyrinth seals can be used for forming seals between reverse shafts, these seals are prone to leaks and contact wear because their fixed-clearance design cannot adapt to the rotors' excitation. These factors are likely to affect an engine's overall performance and have prompted advances in gas film seal technology based on the principle of hydrodynamic and hydrostatic pressure for creating seals between aircraft engine shafts. In 1983, [PERSON] of the NASA Lewis Research Center designed a dynamic and static pressure mixed gas film face seal that could slide back and forth in an axial direction [3], leading to the application of the gas film's seal between engine shafts running in reverse directions. The authors found these seals had leakage rates that were 50-60% of those of the labyrinth seal. However, the test still generated significant friction, and smoking was noted [4]. The reverse gas film face seal has a high risk of contact wear due to axial engine rotor movement. To mitigate this risk, new design schemes have been proposed. Considering this area's vulnerability to wear and rupture, seals may fail even when a rigid structure's sealing dam works. [PERSON] et al. proposed a foil gas film face seal structure with a dynamic pressure floating sealing dam; meanwhile, to improve the dynamic pressure effect, a ring groove was made on the upper-end face of the ring body [5]. Given the fan's hostile sealing environment, [PERSON] et al. proposed a method for gas film non-contact dual-face mechanical sealing suitable for use with fans [6]. Considering the poor opening performance of the existing foil gas film face seal, [PERSON] et al. invented a foil gas film face sealing structure with enhanced opening due to circumferential flow and with an airfoil foil as elastic support [7]. To improve the seal's opening and dynamic pressure effects at high speeds, [PERSON] et al. invented a gas film face sealing structure with a microporous foil surface [8]. Since the face seal cannot adapt to high axial excitation, some scholars proposed the cylinder gas film seal technology to form seals between reverse shafts. For instance, [PERSON] et al. [9] proposed a flexible cylinder sealing structure with metal rubber and calculated the effects of rotor tilt, centrifugal expansion and other factors under stable conditions on the gas film's pressure distribution using a numerical computational method. Rotor tilt and centrifugal expansion had major effects on the gas film's pressure distribution. [PERSON] et al.