Influence of micro-gap high-speed fluid effects on compliant foil cylindrical gas film seal performance

doi:10.11949/0438-1157.20240505

Abstract

Abstract:

Using supercritical carbon dioxide as the lubrication, a theoretical model of foil cylindrical air film seal lubrication is established considering the high-speed fluid effects such as turbulence, blockage and inertia. The study investigates the variations in the seal end flow field and foil deformation under different combinations of high-speed fluid effects, revealing the operational mechanism of high-speed, high-pressure supercritical carbon dioxide compliant foil cylindrical gas film seal. Furthermore, the impact of operating conditions and structural parameters on sealing performance is analyzed, providing an optimal range for structural parameters. The results show that turbulent effects have a significant impact on the flow field and sealing performance of the supercritical carbon dioxide compliant foil cylindrical gas film seal lubrication interface, while blockage and inertia effects are relatively minor. There are interactions among various fluid effects: turbulent effects reduce the pressure at the blockage exit boundary, while inertia effects increase it. Moreover, under turbulent conditions, inertia effects have a more significant impact on the float force. Optimal sealing performance is achieved when the length-to-diameter ratio is between 2.0—2.5 and the flexibility coefficient is between 0.001—0.003.

Key words: compliant foil seal, supercritical carbon dioxide, high-speed fluid effects, sealing performance, numerical analysis

摘要：

以超临界二氧化碳为润滑介质，考虑湍流、阻塞、惯性等高速流体效应建立箔片柱面气膜密封润滑理论模型，研究不同高速流体效应组合下密封端面流场、箔片变形的变化规律，揭示了高速高压超临界二氧化碳箔片柱面气膜密封的运行机理，进一步分析工况和结构参数对密封性能的影响规律，获得了结构参数的优选范围。结果表明：湍流效应对超临界二氧化碳箔片柱面气膜密封润滑界面流场和密封性能影响较大，阻塞效应和惯性效应影响相对较小；各流体效应之间存在交互作用，湍流效应会使阻塞出口边界压力减小，惯性效应会使阻塞出口边界压力增大，湍流效应条件下惯性效应对气膜浮升力的影响作用更为显著；当长径比取2.0~2.5、柔度系数取0.001~0.003时，密封性能较优。

关键词: 箔片密封, 超临界二氧化碳, 高速流体效应, 密封性能, 数值分析

CLC Number:

TH 117.2

Aoxiang JIANG, Yuan CHEN, Yuntang LI, Jinbo JIANG, Xudong PENG, Cong ZHANG, Bingqing WANG. Influence of micro-gap high-speed fluid effects on compliant foil cylindrical gas film seal performance[J]. CIESC Journal, 2024, 75(10): 3691-3704.

江澳翔, 陈源, 李运堂, 江锦波, 彭旭东, 章聪, 王冰清. 微间隙高速流体效应对箔片柱面气膜密封性能的影响[J]. 化工学报, 2024, 75(10): 3691-3704.

Figures/Tables 15

Fig.1 Schematic diagram of CFCGS structure and lubrication principle

Fig.2 Compliant foil structure and parameter characterization

Table 1 Working condition parameters

参数	数值
环境压力p_a/MPa	0.1
进口压力p_in/MPa	8
出口压力p_out/MPa	—
转速n/(r/min)	30000
介质温度T/K	314

Table 2 Structural parameters

参数	数值
半径R/mm	25.4
密封长度L/mm	50.8
半径间隙C/μm	10
偏心率ε	0.6
波箔片厚度t_b/mm	0.8
波箔片节距s/mm	4.572
波箔片半弦长l/mm	1.778
泊松比	0.3
弹性模量/GPa	214

Table 3 High-speed fluid effects combination model

高速流体效应	Case Ⅰ	Case Ⅱ	Case Ⅲ	Case Ⅳ	Case Ⅴ	Case Ⅵ
湍流效应	忽略	考虑	忽略	考虑	忽略	考虑
阻塞效应	忽略	忽略	考虑	考虑	考虑	考虑
惯性效应	忽略	忽略	忽略	忽略	考虑	考虑

Fig.3 Flow field program validation

Fig.4 Gas film velocity distribution of high-speed fluid effects combination model

Fig.5 Gas film pressure distribution of high-speed fluid effects combination model

Fig.6 Distribution of foil deformation of high-speed fluid effects combination model

Fig.7 Influence of inlet pressure on seal performance

Fig.8 Influence of rotational speed on seal performance

Fig.9 Influence of temperature on seal performance

Fig.10 Influence of eccentricity on seal performance

Fig.11 Influence of structural parameters on floating force

Fig.12 Influence of structural parameters on mass leakage rate

References 30

1	Cho J, Choi M, Baik Y J, et al. Development of the turbomachinery for the supercritical carbon dioxide power cycle[J]. International Journal of Energy Research, 2016, 40(5): 587-599.
2	Wang K, He Y L, Zhu H H. Integration between supercritical CO₂ Brayton cycles and molten salt solar power towers: a review and a comprehensive comparison of different cycle layouts[J]. Applied Energy, 2017, 195: 819-836.
3	Thanganadar D, Fornarelli F, Camporeale S, et al. Thermo-economic analysis, optimisation and systematic integration of supercritical carbon dioxide cycle with sensible heat thermal energy storage for CSP application[J]. Energy, 2022, 238: 121755.
4	Bidkar R A, Sevincer E, Wang J F, et al. Low-leakage shaft-end seals for utility-scale supercritical CO₂ turboexpanders[J]. Journal of Engineering for Gas Turbines and Power, 2017, 139(2): 022503.
5	Wright S, Radel R, Vernon M, et al. Operation and analysis of a supercritical CO₂ Brayton cycle[R]. Albuquerque, NM, and Livermore, CA (United States): Sandia National Laboratories (SNL), 2010.
6	Salehi M, Heshmat H, Walton J, et al. The application of foil seals to a gas turbine engine[C]//35th Joint Propulsion Conference and Exhibit. Reston, Virginia: AIAA, 1999: 2821.
7	Heshmat H, Walowit J A, Pinkus O. Analysis of gas-lubricated foil journal bearings[J]. Journal of Lubrication Technology, 1983, 105(4): 647-655.
8	Salehi M, Heshmat H. On the fluid flow and thermal analysis of a compliant surface foil bearing and seal[J]. Tribology Transactions, 2000, 43(2): 318-324.
9	Salehi M, Heshmat H. Analysis of a compliant gas foil seal with turbulence effects[C]//37th Joint Propulsion Conference and Exhibit. Reston, Virginia: AIAA, 2001: 3482.
10	Xu J, Yu S R, Ding X X, et al. Performance of the compliant foil gas seal with surface micro-textured top foil[J]. Applied Sciences, 2022, 12(11): 5633.
11	王学良, 刘美红, 熊忠汾, 等. 考虑表面粗糙度的柔性箔柱面气膜密封紊流特性分析[J]. 化工学报, 2022, 73(4): 1683-1694.
	Wang X L, Liu M H, Xiong Z F, et al. Turbulence characteristics of compliant foil gas seal considering surface roughness[J]. CIESC Journal, 2022, 73(4): 1683-1694.
12	Zhang W F, Chen L Q, Yang J, et al. Static instability of the smooth annular seals with choked/unchoked flow[J]. Tribology International, 2020, 144: 106120.
13	车国铚, 杨启超, 魏志国, 等. 超临界二氧化碳透平机械用气体轴承的研究进展及关键技术[J]. 中国电机工程学报, 2022, 42(15): 5616-5630.
	Che G Z, Yang Q C, Wei Z G, et al. Research progress and key technologies of gas bearings for supercritical carbon dioxide turbomachinery[J]. Proceedings of the CSEE, 2022, 42(15): 5616-5630.
14	Constantinescu V N, Galetuse S. Operating characteristics of journal bearings in turbulent inertial flow[J]. Journal of Lubrication Technology, 1982, 104(2): 173-179.
15	温建全. 超临界二氧化碳介质箔片轴承弹流耦合研究[D]. 哈尔滨: 哈尔滨工业大学, 2017.
	Wen J Q. Theoretical study on characteristics of compliant foil bearings lubricated with supercritical carbon dioxide[D]. Harbin: Harbin Institute of Technology, 2017.
16	朱鹏程, 管玉坤, 门日秀, 等. 超临界二氧化碳系统用箔片气体动压轴承静特性研究[J]. 振动工程学报, 2024, 37(5): 875-884.
	Zhu P C, Guan Y K, Men R X, et al. Static characteristics of gas foil bearing for supercritical carbon dioxide system[J]. Journal of Vibration Engineering, 2024, 37(5): 875-884
17	许恒杰, 宋鹏云, 毛文元, 等. 层流状态下高压高转速二氧化碳干气密封的惯性效应分析[J]. 化工学报, 2018, 69(10): 4311-4323.
	Xu H J, Song P Y, Mao W Y, et al. Analysis on inertia effect of carbon dioxide dry gas seal at high speed and pressure under laminar condition[J]. CIESC Journal, 2018, 69(10): 4311-4323.
18	沈伟, 彭旭东, 江锦波, 等. 高速超临界二氧化碳干气密封实际效应影响分析[J]. 化工学报, 2019, 70(7): 2645-2659.
	Shen W, Peng X D, Jiang J B, et al. Analysis on real effect of supercritical carbon dioxide dry gas seal at high speed[J]. CIESC Journal, 2019, 70(7): 2645-2659.
19	韩煜航, 李红智, 张一帆, 等. 超临界二氧化碳干气密封实际气体效应和湍流效应分析[J]. 热力发电, 2023, 52(6): 63-72.
	Han Y H, Li H Z, Zhang Y F, et al. Analysis of real gas and turbulence effect of supercritical carbon dioxide dry gas seal[J]. Thermal Power Generation, 2023, 52(6): 63-72.
20	胡航领, 林志民, 虞翔宇, 等. 高参数超临界二氧化碳干气密封性能分析研究[J]. 化工设备与管道, 2022, 59(5): 62-68.
	Hu H L, Lin Z M, Yu X Y, et al. Simulation analysis on sealing performance of supernal parameters supercritical carbon dioxide dry gas seal[J]. Process Equipment & Piping, 2022, 59(5): 62-68.
21	章聪, 彭旭东, 江锦波, 等. 实际气体、阻塞和湍流效应对超临界CO₂干气密封性能的影响[J]. 中国电机工程学报, 2022, 42(20): 7563-7574.
	Zhang C, Peng X D, Jiang J B, et al. Influence of real gas, choked flow, and turbulence effect on performance of supercritical CO₂ dry gas seals[J]. Proceedings of the CSEE, 2022, 42(20): 7563-7574.
22	江锦波, 滕黎明, 孟祥铠, 等. 基于多变量摄动的超临界CO₂干气密封动态特性[J]. 化工学报, 2021, 72(4): 2190-2202.
	Jiang J B, Teng L M, Meng X K, et al. Dynamic characteristics of supercritical CO₂ dry gas seal based on multi variables perturbation[J]. CIESC Journal, 2021, 72(4): 2190-2202.
23	朱新龙. 高速低黏度润滑剂的滑动轴承润滑性能分析[D]. 合肥: 合肥工业大学, 2015.
	Zhu X L. Lubrication performance analysis for high speed and low viscosity lubricant journal bearing[D]. Hefei: Hefei University of Technology, 2015.
24	Constantinescu V N, Galetuse S, Kennedy F. On the comparison between lubrication theory, including turbulence and inertia forces, and some existing experimental data[J]. Journal of Lubrication Technology, 1975, 97(3): 439-448.
25	Salehi M, Heshmat H. Evaluation of large compliant gas foil seals under engine simulated conditions[C]//38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit. Reston, Virginia: AIAA, 2002: 3792.
26	Zhang G H, Xu K F, Han J Z, et al. Performance of textured foil journal bearing considering the influence of relative texture depth[J]. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2022, 236(11): 2105-2117.
27	张正. 高速低黏粗糙表面滑动轴承弹性流体动力润滑分析[D]. 合肥: 合肥工业大学, 2017.
	Zhang Z. Elastohydrodynamic lubrication analysis for high speed and low viscosity rough surface of journal bearing[D]. Hefei: Hefei University of Technology, 2017.
28	Salim M S, Saeed M, Kim M H. Performance analysis of the supercritical carbon dioxide re-compression brayton cycle[J]. Applied Sciences, 2020, 10(3): 1129.
29	严如奇, 洪先志, 包鑫, 等. 超临界二氧化碳干气密封相态分布规律与密封性能研究[J]. 化工学报, 2020, 71(8): 3681-3690.
	Yan R Q, Hong X Z, Bao X, et al. Phase-distribution regularity and sealing performance of supercritical carbon dioxide dry gas seal[J]. CIESC Journal, 2020, 71(8): 3681-3690.
30	岑少起, 杨金锋, 郭红, 等. 惯性项对动静压浮环径向轴承压力场的影响[J]. 郑州工业大学学报, 2001, 22(3): 6-8.
	Cen S Q, Yang J F, Guo H, et al. The pressure field of cylinder floating ring bearing with the influence of fluid's inertiaforce[J]. Journal of Zhengzhou University of Technology, 2001, 22(3): 6-8.

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