Thermo-Hydrodynamic Analysis of Low-Temperature Supercritical Helium Spiral-Grooved Face Seals: Large Ambient Temperature Gradient

Abstract

Hhighly efficient and reliable sealing technology is essential to improve the efficiency of precooled aeroengines. To explore the effects of large ambient temperature gradients on the sealing performance, the thermo-hydrodynamic characteristics of a supercritical helium spiral-grooved face seal were studied numerically, under low-temperature conditions. Considering the real gas effect of helium, the thermal deformations of the seal were analyzed numerically, under different temperature gradients. Additionally, the distributions of the pressure, temperature, and film thickness of the gas film were calculated, and the sealing performances of the seal under a wide range of working conditions were evaluated simultaneously. Results showed that a turning point occurred at the sealing pressure of 1.6 MPa in both the dynamic pressure effect and temperature rise of the gas film under the ambient-temperature gradient, leading to the transformation of the sealing gap, from convergent to divergent. The temperature gradient contributed to decreasing the thermal deformation and improving the sealing performance of the face seal. As the temperature gradient increased, although a mutational phenomenon existed near the sealing temperature of 250 K with both the dynamic pressure effect and the temperature rise, the variation of the opening force was within 120 N and the leakage was more than halved, indicating the broad application prospects of gas face seals in precooled aeroengine systems.

1. Introduction

The rapid development and application of precooling technology to supersonic aeroengines demand high requirements of the sealing technology [1,2]. Gas face seals are potential candidates in such engines, due to their suitability in harsh working conditions, low leakage and high reliability [3,4,5,6]. In the supercritical helium precooled loop of a synergetic air-breathing rocket engine, seals are used to separate the low-temperature refrigerant and high-temperature lubricating oil, resulting in operating conditions of large ambient temperature gradients, and challenging their seal reliability [7,8,9]. However, research has illustrated that the ambient temperature gradient of seal rings leads to a larger thermal deformation for both the seal rings and the gas film under high-temperature conditions, thereby damaging the sealing performance [10]. Meanwhile, the thermal deformation and sealing performance of supercritical helium face seals under low-temperature conditions have yet to be explored, in particularly the large ambient temperature gradient conditions.

Generally, the temperature gradient generated by the friction, heat convection, and dissipation in seal rings significantly affects the thermal deflections of face seals [11,12,13,14]. Considering the thermal effect, Thomas et al. [15,16] established an analytical model to investigate the thermo-hydrodynamic behaviors of a face seal under high-pressure conditions, and they found that an obvious temperature gradient existed, and a converging gap was formed correspondingly to this. More extensive research into the thermo-hydrodynamic characteristics of gas face seals was then carried out [17,18,19,20]. Focusing on the shape and parameters of microgrooves, Blasiak et al. [21], Ding et al. [22], and Du et al. [23], respectively, analyzed the sealing behaviors of gas face seals with different dynamic pressure grooves, such as spiral grooves and inclined-ellipse dimples. Results showed that the temperature gradient of gas film between the inlet and outlet of the seals ranged from 10 K to 50 K, resulting in a divergent deformation. In addition to the dynamic pressure grooves, the operating condition is another important factor affecting the thermo-hydrodynamic characteristics of gas face seals [24,25,26]. Under high temperatures and high rotational speed conditions, Zhu et al. [27] numerically analyzed the thermal hydrodynamic behaviors of a supercritical CO₂ T-grooved face seal, and found that the maximal temperature difference of the gas film could reach 140 K; a convergent sealing gap was formed simultaneously when the sealing temperature was 600 K and the linear rotational velocity exceeded 400 mm/s.

Furthermore, with an ambient temperature gradient exerted on the gas face seal, Xie et al. [10] explored the thermal distortion and sealing performance of a N₂ face seal compared with the condition without an ambient temperature gradient. It was found that the extra temperature gradient contributed to generating a sharp divergent deformation of the face seal, decreasing its load capacity, and increasing its leakage.

The research on thermo-hydrodynamic behaviors of face seals under low-temperature conditions has mainly focused on liquid oxygen and liquid nitrogen, which is seriously inadequate for the supercritical helium face seal [28,29,30]. Helium is an inert refrigerant, and widely selected in precooled circulation systems, owing to its advantages of high specific heat, low cyclic-pressure ratio, and safety [1,31,32]. However, the thermophysical properties of helium in its supercritical state change significantly with respect to temperature and pressure, especially its viscosity [33,34]. Taking the real gas effect into account, Zhu et al. [35] numerically explored the thermo-hydrodynamic characteristics of a T-grooved face seal operating with supercritical helium under low-temperature and high-pressure conditions. Results showed that the temperature of the gas film varied significantly from the inlet radius to the outlet radius of the seal, leading to a divergent deformation, a 17% increase in the leakage, and a 15% decrease in the opening force, with a decrease in sealing temperature from 300 K to 150 K. However, the thermal deformation and sealing performance of supercritical face seals are still unconsidered when seals operate under an ambient temperature gradient.

In this manuscript, the effects of large ambient temperature gradients on the thermo-hydrodynamic behaviors of a supercritical helium spiral-grooved face seal are analyzed numerically under low-temperature conditions. Considering the real gas effect of helium in its supercritical state, a thermo-elasto-hydrodynamic lubrication model is established, and the thermal deformation characteristics of the face seal are discussed under different temperature gradient conditions. Additionally, the distributions of pressure, temperature, and film thickness of the gas film are assessed under a wide range of working conditions to explain the effects of temperature gradient further. Finally, the sealing performances of the face seal under different operating conditions are evaluated, including the sealing pressure, sealing temperature, rotational speed, and basic film thickness. The results obtained in this manuscript provide a theoretical basis for the rational design of gas face seals in supercritical helium precooled systems.

2. Theoretical Model

2.1. Geometrical Model

The geometrical model of a spiral-grooved face seal and the three-phase diagram of helium are illustrated in Figure 1. The critical temperature and pressure of helium are 5.2 K and 0.228 MPa, respectively, making it easy to reach the supercritical state. The thermo-hydrodynamic behaviors of the helium face seal are analyzed in its supercritical state in this manuscript. Face seals work by the flow restriction and gas compression generated by the high-speed shear between the non-contacting seal rings. Once the stator and rotor rotate relative to each other, a micron gas film is formed by the sufficient opening force, realizing the sealing effect and also generating a certain leakage of the sealing medium along the direction of the pressure gradient. In order to enhance the dynamic pressure effect of the gas film, various grooves were generally designed on the seal rings; spiral grooves are the typical grooves in practical applications [36,37,38]. According to the principles of gas face seals, the deformation of seal rings affects the sealing performance significantly because the clearance gap between non-contacting rings are usually 3–5 μm and the distortion is recommended to be controlled within 1 μm/mm [39,40]. Therefore, the theoretical prediction of the thermo-hydrodynamic behaviors of the micron gas film are essential to the design of gas face seals under low-temperature and large ambient temperature gradients. The relevant geometrical parameters of the spiral-grooved face seal are listed in

Table 1. Relevant geometrical parameters of the spiral-grooved face seal.

Parameters	Units	Values
Outlet radius/ri	mm	44
Inlet radius/ro	mm	50
Spiral radius/rg	mm	48
Spiral angle/β	-	16
Groove depth/hd	μm	5
Groove numbers/N	-	12
Thickness of seal rings/h1, h2	mm	15
Thickness of gas film/h	μm	-

.

2.2. Governing Equations

The thermo-elasto-hydrodynamic lubrication model was established by taking the thermal distortion, the inertial effect, the choked-flow effect, and the real gas effect of helium, into account. During the modeling, the thermal boundary conditions referred to the Refs. [41,42]. The heat flux was set between the gas film and the friction interfaces of the seal rings, and the convective and adiabatic boundaries were imposed between the seal rings and their surroundings, which can be seen in Figure 1.

The thermo-hydrodynamic characteristics of the supercritical helium spiral-grooved gas face seal were obtained by solving the governing equations jointly in the lubrication model, on the bases of the geometrical model and boundary conditions of the face seal. The governing equations mainly included the Reynolds equation, energy equation, heat conduction equation, and interface equation, which are described in detail as follows [43].

The steady-state Reynolds equation was used to describe the motion of the sealing medium, which is expressed in the polar coordinates as:

$$\frac{\partial }{r\partial \theta }\left(\frac{h^3\rho }{\eta }\frac{\partial p}{r\partial \theta }\right)+\frac{\partial }{r\partial r}\left(\frac{r{h}^3\rho }{\eta }\frac{\partial p}{\partial r}\right)=6\omega \frac{\partial (\rho h)}{\partial \theta },$$

(1)

where p is the pressure of the gas film, r and θ are the radial and circumferential coordinates, respectively, and η and r are the viscosity and density of helium, respectively.

The energy equation of the gas film was derived by analyzing the variation of the internal energy of the gas film, including the flow work, friction work, energy loss induced by the interfacial heat conduction, and heat extrusion, which is described in the polar coordinates as:

$$\begin{array}{l}\left(\frac{h^3}{12\eta }\frac{\partial p}{r\partial \theta }-\frac{wrh}{2}\right)\frac{\partial T}{r\partial \theta }+(\frac{h^3}{12\eta }\frac{\partial p}{\partial r})\frac{\partial T}{\partial r}\\ =-\frac{\eta w^2{r}^2}{h\rho c_v}+\frac{h^3}{12\eta \rho c_v}\left[{\left(\frac{\partial p}{r\partial \theta }\right)}^2+{\left(\frac{\partial p}{\partial r}\right)}^2\right]-\frac{k_{\mathit{gs}1}}{\rho c_v}(T_{s1}-T)-\frac{k_{gs2}}{\rho c_v}(T_{s2}-T)\end{array}$$

(2)

where c_v is the specific heat capacity of helium gas, T_s1 and T_s2 are the temperature values of seal rings at their friction interfaces, and k_ga1 and k_gs2 are the convection heat transfer coefficients at the friction interfaces.

The Laplace equation was adopted to describe the heat convection of solid rings, and the heat convection equation for the stationary seal ring in the polar coordinates is shown as:

$$\frac{{\partial }^2{T}_s}{r^2\partial {\theta }^2}+\frac{\partial }{r\partial r}\left(r\frac{\partial T_S}{\partial r}\right)+\frac{{\partial }^2{T}_s}{\partial z^2}=0,$$

(3)

Owing to the existence of the interfacial velocity, the heat convection equation for the rotating seal ring in the polar coordinates is shown as:

$$\frac{k_{c2}}{{\rho }_{s2}{c}_{s2}}\left[\frac{{\partial }^2{T}_s}{r^2\partial {\theta }^2}+\frac{1}{r}\frac{\partial }{\partial r}\left(r\frac{\partial T_s}{\partial r}\right)+\frac{{\partial }^2{T}_s}{\partial z^2}\right]=w\frac{\partial T_s}{\partial t},$$

(4)

where k_c is the coefficient of heat conduction of seal rings, r_s is the density of seal rings, and c_s is specific heat capacity of seal rings.

Additionally, a forced convection heat transfer exists between the gas film and the interfaces, owing to the high-speed flow of the sealing medium on the interfaces of the seal rings, which satisfies the following equations.

$$-k_{c1}{\left(\frac{\partial T_s}{\partial n}\right)}_s=k_{s1}(T_{s1}-T),$$

(5)

$$-k_{c2}{\left(\frac{\partial T_s}{\partial n}\right)}_s=k_{s2}(T_{s2}-T),$$

(6)

where k_s is the coefficient of the convection heat transfer at the friction surfaces.

Considering the compressibility of the sealing medium, the pressure involved in the governing equations satisfies the following relationship:

$$p=\epsilon c_p\rho i_d{E}_m,$$

(7)

and the temperature of the gas film expresses as:

$$T=\frac{i_d{E}_m}{c_v},$$

(8)

where ε is the compressibility coefficient of the gas, c_p is the constant coefficient of pressure, i_d is the freedom degree of gas molecules motion, E_m is the energy of gas molecular per freedom.

The leakage and opening force are the main parameters used to measure the sealing performance, and they can be defined as follows, respectively.

$$Q=\frac{h^{3}r\rho }{12\eta }{\displaystyle {\int }_0^{2r}\frac{\partial p}{\partial r}}d\theta$$

(9)

$$F={\displaystyle {\int }_0^{2\pi }{\displaystyle {\int }_{r_i}^{r_0}prdrd\theta }}$$

(10)

2.3. Theoretical Calculations

The materials of the stationary and rotating seal rings are stainless steel and graphite, respectively, and their performance parameters are listed in

Table 2. Material performance parameters of seal rings [35].

Item	Graphite	Stainless Steel
Material density/kg·m−3	1800	7930
Young’s modulus/GPa	300	400
Poisson’s ratio	0.17	0.17
Specific heat capacity/J·kg−1·K−1	710	500
Thermal conductivity/W·m−1·K−1	129	16.2
Linear thermal expansion coefficient/10−6 K	2.75	5.5

. The thermo-hydrodynamic parameters set out in the theoretical calculations are shown in

Table 3. Themo-hydrodynamic parameters used in the theoretical calculations [35].

Item	Symbol	Specification
Convection heat transfer coefficient of solid rings at ambient condition/W·m−2·K−1	k1, k2	8.0
Thermal conductivity of helium/W·m−1·K−1	kc	0.024
Degrees of freedom of motion of gas molecules	id	3
Sealing temperature/K	T0	100~350
Sealing pressure/MPa	p0	0.1~5.0
Basic film thickness/μm	h0	1.0~5.0
Rotational speed/rpm	n	3000~50,000

. Additionally, the thermophysical properties of helium could refer to Ref. [35], in which the compressibility coefficient, the heat capacity, and the viscosity of helium were discussed under different operating conditions, based on the data base of NIST REFPROP. The viscosity of helium changes markedly, while the compressibility coefficient and the heat capacity change little for the temperature range between 100 K and 400 K, and the pressure range between 0.1 MPa and 5 MPa. In addition, the density is also an important factor influencing the thermo-hydrodynamic characteristics of the face seal. According to Figure 2, the density of helium varies distinctly under different operating conditions. For different temperatures, the density increases almost by a factor of 7 with an increase of pressure from 0.6 MPa to 5.0 MPa, while its density decreases to 70% in values with an increase of temperature from 100 K to 400 K for all pressure conditions.

In calculations, except for the thermal boundary conditions, the pressure adopted the forced boundary conditions, and the temperature adopted the dynamic boundary conditions [10]. Meanwhile, the reliability of the thermo-hydrodynamic analysis had also been validated in Ref. [10], in which the numerical results of the temperature distribution were compared with the experimental date of Ding’s work, and they were in good agreement.

3. Results and Discussion

3.1. Thermal Deformation Characteristics

The effect of a large ambient temperature gradient on the thermal deformation of the seal was analyzed by considering the thermophysical properties of helium under low-temperature conditions. The cross-sectional temperature distribution of the face seal and the deformation of the gas film are presented in Figure 3 and Figure 4, respectively, and were calculated under the sealing pressure of 5 MPa and the sealing temperature of 100 K and 350 K, respectively. Owing to the fixed outlet-ambient-temperature of 350 K, the seal worked under a large ambient-temperature gradient condition or an isothermal condition.

According to Figure 3, it was obvious that the gas film in the groove area had the lowest temperature and the temperature decreased along the gas flow, except for the groove area. A temperature difference existed between the inlet and outlet of the seal, which were 28.6 K and 27.9 K for the temperature gradient condition and the isothermal condition, respectively. Correspondingly, the temperature of the seal rings was distributed similarly to the gas film, but the temperature difference of the stationary seal ring was larger than the rotating seal ring, owing to their different coefficients of heat conduction, which were 4.95 K and 0.27 K for the condition of the large temperature gradient, and 6.05 K and 0.23 K for the isothermal condition. Additionally, a significant temperature rise for the entire gas film occurred, which was 221.6 K and 144.5 K, respectively, for the two temperature-gradient conditions. Therefore, the ambient temperature gradient resulted in a larger temperature difference of the gas film between the inlet and outlet of the seal and also a larger temperature rise of the entire gas film.

On the basis of the temperature distributions, the gas film appeared a divergent deformation under both conditions with a temperature gradient and without a temperature gradient, which are presented in Figure 4. The film thickness at the outlet of the seal was larger than the inlet, which increased by 0.94 μm and 1.04 μm for the temperature gradient condition and isothermal condition. Therefore, although the ambient-temperature gradient tended to obtain larger a temperature difference and temperature rise of the gas film, it contributed to decreasing the extent of the thermal deformation of the gas film.

3.2. Thermo-Hydrodynamic Characteristics

Under different sealing pressures, the effect of a large ambient-temperature gradient on thermo-hydrodynamic characteristics was investigated. The distributions of pressure, temperature, and film thickness were calculated between the sealing pressure 0.1 MPa and 4.6 MPa under a large ambient-temperature gradient condition, and the results are presented in Figure 5. In the calculations, the basic film thickness was 3.0 μm, the rotational speed was 50,000 rpm, and the inlet and outlet ambient-temperature values were 200 K and 350 K, respectively. According to Figure 5a, a local high pressure occurred at the tip of the spiral grooves, illustrating that spiral grooves had a distinct dynamic pressure effect. The dynamic pressure effect was not enhanced continuously with the increase of the sealing pressure, which increased gradually with the increase of sealing pressure to 1.6 MPa, and then started to decrease as the sealing pressure increased continuously. As a result, in Figure 6 the pressure increase on the base of the sealing pressure increased from 0.13 MPa to 1.29 MPa, and then decreased to 0.42 MPa. The turning point of the hydrodynamic pressure effect was owing to the stronger inertial effect and choked-flow effect, with the increase of the sealing pressure.

According to Figure 5b, the temperature distribution of the gas film did not change much with respect to the sealing pressure, and the variation of the maximum temperature at the inlet of the seal was controlled within 14.5 K under different sealing pressure conditions. The temperature rise of the entire gas film was obvious, ranging between 194.7 K and 207.1 K for different sealing pressure conditions. As shown in Figure 6, the variation of temperature rise was similar to the variation of the pressure increase, which increased firstly from 204.5 K to 207.1 K as the sealing pressure increased from 0.1 MPa to 1.6 MPa, and then decreased to 194.7 K when the sealing pressure increased continuously to 4.6 MPa. The temperature rise of the gas film was generated by the high-speed shearing, while it was heavily influenced by the gas expansion. An obvious temperature drop at the outlet of the seal occurred due to the gas expansion, and it became more and more obvious as the sealing pressure increased.

Under the collective contributions of the pressure and temperature distributions, the deformation of the gas film displayed a transformation from convergent to divergent at the sealing pressure of 1.6 MPa, which is presented in Figure 5c. Here, the film thickness deformation was defined as positive when the film thickness at the inlet of the seal was less than that at the outlet, forming a divergent clearance; otherwise it was negative, forming a convergent clearance. As shown in Figure 6, when the sealing pressure increased from 0.1 MPa to 1.1 MPa, the film thickness at the inlet of the seal was larger than that at the outlet of the seal, and the deformation of the gas film decreased from 0.35 μm to 0.10 μm. When the sealing pressure increased continuously from 1.6 MPa to 4.6 MPa, the film thickness at the inlet of the seal was lower than that at the outlet of the seal, and the deformation of the gas film increased from 0.04 μm to 0.91 μm.

These results above were obviously different from those which did not consider the ambient temperature gradient, in Ref. [35], in which the supercritical helium gas face seal with T-grooves showed a divergent clearance, with the sealing pressure growing from 1.0 MPa to 5.0 MPa. Therefore, although the temperature rise of the gas film was large, the existence of the ambient-temperature gradient contributed to achieving a better dynamic pressure effect and lower thermal deformation of the supercritical helium face seal, near the sealing pressure of 1.6 MPa.

Furthermore, the distributions of the pressure, temperature, and film thickness of the sealing medium were calculated numerically under different ambient-temperature gradients. In the calculations, the sealing temperature ranged from 100 K to 350 K, forming different temperature gradients on the base of a fixed temperature 350 K, at the outlet of the seal. Additionally, the basic film thickness was 3.0 μm, the rotational speed was 50,000 rpm, and the sealing pressure values at the inlet and outlet of the seal were 5.0 MPa and 0.1 MPa, respectively.

According to Figure 7, the dynamic pressure effect of the spiral grooves was still obvious with the decrease of the temperature gradient, but there was a mutation around the sealing temperature of 250 K. From Figure 8, the pressure increase of the gas film decreased initially when the sealing temperature increased from 100 K to 240 K, after which the dynamic pressure effect was suddenly enhanced, as the sealing pressure reached 250 K, and later the effect was weakened again with the continuous increase of the sealing temperature. Meanwhile, the temperature of the entire gas film also increased significantly under different temperature-gradient conditions. Similarly with the dynamic pressure effect, a sudden increase of the temperature rise was also found at the sealing temperature of 250 K. The increase of pressure and temperature did not change much, and showed a declining trend as a whole. Therefore, the temperature gradient contributed to obtaining a larger dynamic pressure effect and temperature rise of the sealing medium.

Under the collective contributions of the pressure and temperature distributions, the supercritical helium spiral-grooved face seal showed a divergent deformation, according to the film thickness distributions in Figure 7c. According to Figure 8, the degree of the distortions increased with the decrease of the temperature gradient, which further indicated that the ambient-temperature gradient contributed to weakening the film thickness deformation.

3.3. Sealing Performance

Under the ambient-temperature gradient condition, the sealing performance of the supercritical helium spiral-grooved face seal under a wide range of working conditions was evaluated, including the sealing pressure, sealing temperature, rotational speed, and basic film thickness.

The relationship between the sealing performance and the sealing pressure is presented in Figure 9. According to Figure 9a, the pressure at the inlet of the seal was lower than the inlet ambient pressure, showing a pressure loss. However, the pressure loss was not significant when the sealing pressure was lower than 1.1 MPa. As the sealing pressure continued to increase, the pressure loss increased. Additionally, the pressure at the outlet of the seal was larger than the outlet ambient pressure, illustrating a choked-flow effect. As the sealing pressure increased, the pressure rise increased from 0.01 MPa to 0.27 MPa, which was much larger than the outlet ambient pressure of 0.1 MPa.

Under the influence of the inertial effect, choked-flow effect, and dynamic pressure effect, the opening force and leakage of the sealing-medium helium with respect to the sealing pressure were calculated. According to Figure 9b, both the opening force and leakage showed an upward trend with the increase of the sealing pressure from 0.1 MPa to 4.6 MPa. While the opening force increased at a high rate initially, before slowing down, the leakage displayed an opposite trend, the result of the changes in variations of dynamic pressure effect, temperature rise, and thermal deformation of the gas film. As the sealing pressure increased to 4.6 MPa, the opening force increased to 6968 N, multiplying by a factor of 29 compared with the sealing pressure of 0.1 MPa. Meanwhile, the leakage was 1.28 g·min⁻¹ at the sealing pressure of 4.6 MPa, which was much larger than 0.00167 g·min⁻¹ at 0.1 MPa. Compared with the results without considering a temperature gradient in Ref. [35], although the opening force and leakage showed similar trends to the sealing pressure, the value of the leakage was almost half of that in the reference on the base of little difference in the opening force values. Therefore, the ambient-temperature gradient tended to improve the sealing performance.

The relationship between the sealing performance and the sealing temperature is presented in Figure 10. Owing to the fixed ambient temperature of 350 K at the outlet of the seal, the temperature gradient along the radius direction decreased with the increase of the sealing temperature at the inlet of the seal. According to Figure 10a, at the sealing temperature of 100 K, the pressure loss induced by the inertial force and the pressure increase induced by the choked-flow effect were both remarkable. As the sealing temperature increased from 100 K to 350 K, the pressure loss at the seal inlet decreased gradually from 8.2% to 3.0%, and the choked-flow effect was weakened at the same time, with a decrease in pressure rise from 0.44 MPa to 0.23 MPa.

Additionally, the opening force of the sealing medium displayed a complicated variation as the sealing temperature increased from 100 K to 350 K. As seen in Figure 10b, although the general trend of the opening force was downward, a mutational increase occurred at 250 K, which was consistent with the variations of the temperature rise and dynamic pressure effect of the gas film. The variation in the opening force in values was relatively small, and was within 120 N. Meanwhile, the leakage of the sealing medium displayed an upward trend with the increase of the sealing temperature, which was consistent with the extent of the thermal deformation. The leakage value at the sealing temperature of 350 K was more than twice as much as that at 100 K, illustrating that the ambient-temperature gradient improved the sealing performance again.

The relationship between the sealing performance and the rotational speed is presented in Figure 11. From Figure 11a, both the pressure loss at the inlet of the seal and the pressure increase at the outlet of the seal were affected significantly by the rotational speed, while the amount of variation was relatively small. On the basis of these effects, the opening force of the sealing medium showed an upward trend with the increase in the rotational speed, while the leakage increased initially before decreasing, reaching a maximum value of 1.444 g·min⁻¹ at the rotational speed of 20,000 rpm. However, such a trend in the leakage was opposite to that in Ref. [35], in which the leakage decreased initially before increasing. Without the influence of the ambient-temperature gradient, the temperature increase increased and thermal deformation was enhanced with the increase of the rotational speed, leading to the decrease in the opening force and the increase in the leakage. The values of the leakage were lower, and changed little under the ambient temperature-gradient condition, owing to its contributions in decreasing thermal deformation. Therefore, the ambient temperature gradient contributed to improving the sealing performance.

Finally, the relationship between the sealing performance and the basic film thickness is presented in Figure 12. As demonstrated in Figure 12a, the pressure at both the inlet and outlet of the seal changed significantly as the basic film thickness increased from 2 μm to 10 μm. The pressure loss at the inlet of the seal decreased from 4.9 MPa to 2.96 MPa, and the pressure rise at the outlet of the seal increased from 0.3 MPa to 0.87 MPa. Meanwhile, with the increase of the clearance gap, the opening force of the sealing medium decreased by more than 50%, and the leakage value increased sevenfold. Therefore, the increased clearance played a dominant role in controlling the sealing performance.

4. Conclusions

The effect of large ambient-temperature gradients on the thermo-hydrodynamic characteristics of the supercritical helium face seal was analyzed theoretically. Meanwhile, the relationship between the ambient-temperature gradient and sealing performance under different working conditions was discussed. The main results are shown as follows:

(1)

Large ambient-temperature gradients significantly affected the thermo-hydrodynamic characteristics of the supercritical helium face seal. Although the ambient temperature gradient tended to increase the temperature rise of the gas film, it contributed to decreasing the extent of the film-thickness deformation of the gas film.

(2)

The large ambient temperature gradient contributed to improving the sealing performance of the supercritical helium face seal. The ambient-temperature gradient increased, resulting in a larger opening force and lower leakage of the face seal, illustrating the broad application prospects of gas face seals in precooled aeroengine systems.