高速高温箔片端面密封热气弹耦合性能分析

doi:10.11949/0438-1157.20251293

摘要/Abstract

摘要：

基于气体动力润滑、弹性力学、传热学等相关理论，耦合变密度变粘度非等温雷诺方程、膜厚控制方程和三维能量方程，建立了箔片端面气膜密封热气弹多场耦合理论模型，在高速高温条件下，分析了膜温、膜压、变形、流速分布规律及工况和结构参数对密封性能的影响规律。结果表明：气体热效应增强了气膜的动压效应，使膜压和膜厚增大；高温区主要集中在楔形间隙的末端和水平区的外径处，且外径处的膜温显著高于其他位置；在本文参数研究范围内且保证箔片密封变形协调能力前提下，以提高开启力和气膜刚度、降低泄漏率和温升为优化目标，动压区和密封区箔片柔度系数在0.02~0.04、节距比在0.4~0.6、箔片数在6~8、箔坝比在1~2范围取值为宜。

关键词: 高速高温, 箔片端面密封, 流体力学, 传热, 热气弹耦合, 数值分析, 结构优化

Abstract:

Based on the theories of gas lubrication, elasticity, and heat transfer, a thermo–gas–elastic multi-field coupling theoretical model of foil end-face gas film seals was established by coupling the variable-density and variable-viscosity non-isothermal Reynolds equation, the film thickness control equation, and the three-dimensional energy equation. Under high-speed and high-temperature conditions, the distributions of film temperature, film pressure, deformation, and velocity, as well as the effects of operating and structural parameters on sealing performance, were analyzed. The results indicate that the thermal effect of the gas enhances the hydrodynamic effect of the film, increasing both film pressure and thickness. High-temperature regions are mainly concentrated at the end of the wedge-shaped clearance and at the outer diameter of the horizontal region, with the film temperature at the outer diameter being significantly higher than at other locations. Within the parameter range considered in this study and ensuring the coordinated deformation of the foil seal, the optimization objectives are to increase opening force and gas film stiffness, while reducing leakage rate and temperature rise. Accordingly, the flexibility coefficients of foils in the hydrodynamic and sealing zones should be in the range of 0.02~0.04, the pitch ratio in 0.4~0.6, the number of foils in 6~8, and the foil-to-dam ratio in 1~2.

Key words: high-speed and high-temperature, foil face seal, fluid mechanics, heat transfer, thermo-aeroelastic coupling, numerical analysis, structural optimization

中图分类号:

TH117.2

陈源, 郑施源, 李运堂, 熊典峰, 王冰清, 彭旭东. 高速高温箔片端面密封热气弹耦合性能分析[J]. 化工学报, DOI: 10.11949/0438-1157.20251293.

Yuan CHEN, Shiyuan ZHENG, Yuntang LI, Dianfeng XIONG, bingqing WANG, Xudong PENG. Thermo–gas–elastic coupling performance analysis of high-speed, high-temperature foil face seals[J]. CIESC Journal, DOI: 10.11949/0438-1157.20251293.

图/表 17

图1 CFFGS结构示意图

Fig. 1 Structural schematic of CFFGS

图2 温度边界条件示意图

Fig. 2 Schematic diagram of the temperature boundary conditions

图3 间隙区气体混合模型

Fig. 3 Gas mixing model in the clearance region

图4 箔片密封环侧传热模型

Fig. 4 Heat transfer model on the foil seal ring side

图5 热阻模型

Fig. 5 Thermal resistance model

表1 热阻参数及表达式

Table 1 Thermal resistance parameters and expressions

热阻参数	公式
平箔片热阻 R_t	t_t/(k_tA_t)
波箔片热阻 R_bp	t_bp /(k_bpA_bp)
空气间隙热阻 R_tb	h_bp /(k_airA_tb)
环基座热阻 R_b	t_b/(k_bA_b)
环境气体对流热阻 R_e	1/(h_eA_e)

表2 CFFGS结构、工况和热特性参数

Table 2 Structural configuration， operating conditions， and thermal characteristics of the CFFGS

参数名称	参数值
密封端面内半径 r_i/mm	45.5
密封端面外半径 r_o/mm	85.3
楔形高度 h_d/μm	10
平箔片厚度 t_t/mm	0.1524
波箔片厚度 t_bp/mm	0.1016
波箔高度 h_bp/mm	0.4
环基座厚度 h_r/mm	5
箔片弹性模量 E/GPa	213
动压区箔片柔度系数 α_out	0.08
密封区箔片柔度系数 α_in	0.04
箔片数 Z_g	8
节距比 b	0.4
箔坝比 γ	2
环境压力 p_a/MPa	0.1
内径处压力 p_in/MPa	0.1
外径处压力 p_out/MPa	0.3
转速 n/(r/min)	18000
空气粘度 μ₀/(Pa·s)	1.81×10^-5
空气密度 ρ₀/(kg/m³)	1.205
环境温度 T₀/K	500
空气定压比热容 c_p/(J/kg·K)	1005
空气导热系数 k_air/(W/K·m)	0.026
平箔片导热系数 k_t/(W/K·m)	16.9
波箔片导热系数 k_bp/(W/K·m)	16.9
环基座导热系数 k_b/(W/K·m)	10

图6 热气弹耦合程序流程图

Fig. 6 Flowchart of the thermo–gas–elastic coupling program

图7 程序正确性验证

Fig. 7 Verification of program correctness

图8 不同平衡膜厚下CFFGS轴向中分面处膜温分布云图

Fig. 8 Film temperature distribution at the axial mid-plane of CFFGS under different equilibrium film thicknesses

图9 气弹耦合和热气弹耦合模型下平衡膜厚对CFFGS膜压云图的影响规律

Fig. 9 Influence of equilibrium film thickness on pressure distribution contours of CFFGS under gas–elastic coupling and thermo–gas–elastic coupling models

图10 气弹耦合和热气弹耦合模型下平衡膜厚对CFFGS变形云图的影响规律

Fig. 10 Influence of equilibrium film thickness on deformation contours of CFFGS under gas–elastic coupling and thermo–gas–elastic coupling models

图11 气弹耦合和热气弹耦合模型下膜厚和膜压沿周向和径向的变化曲线

Fig. 11 Variation curves of film thickness and pressure along the circumferential and radial directions under gas–elastic coupling and thermo–gas–elastic coupling models

图12 转速n对CFFGS膜温峰值和均值以及密封性能参数的影响规律

Fig. 12 Influence of rotational speed n on the peak and mean film temperature as well as sealing performance parameters of the CFFGS

图13 介质压力po对CFFGS膜温峰值和均值以及密封性能参数的影响规律

Fig. 13 Influence of medium pressure p₀ on the peak and mean film temperature as well as sealing performance parameters of the CFFGS

图14 动压区柔度系数αout和密封区柔度系数αin对CFFGS膜温峰值和均值以及密封性能参数的影响规律

Fig. 14 Influence of flexibility coefficients αout in the hydrodynamic region and αin in the sealing region on the peak and mean film temperature as well as sealing performance parameters of the CFFGS

图15 节距比b、箔片数N和箔坝比γ对CFFGS膜温峰值和均值以及密封性能参数的影响规律

Fig. 15 Influence of pitch ratio b, number of foils N, and dam-to-foil ratio γ on the peak and mean film temperature as well as sealing performance parameters of the CFFGS

参考文献 31

[1]	Zirkelback N. Parametric study of spiral groove gas face seals[J]. Tribology Transactions, 2000, 43(2): 337-343.
[2]	Liu Y C, Shen X M, Xu W F, et al. Performance comparison and parametric study on spiral groove gas film face seals[J]. Science in China Series G: Physics, Mechanics and Astronomy, 2004, 47(1): 29-36.
[3]	Saxena M N. Dry gas seals and support systems: benefits and options[J]. Hydrocarbon Processing, 2003, 82(11): 37-42.
[4]	Kolomoets A, Dotsenko V. Experimental investigation «Dry» gas-dynamic seals used for gas-compressor unit[J]. Procedia Engineering, 2012, 39: 379-386.
[5]	江锦波, 彭旭东, 白少先, 等. 仿生集束螺旋槽干式气体密封特性的数值分析[J]. 机械工程学报, 2015, 51(15): 20-26.
	Jiang J B, Peng X D, Bai S X, et al. Numerical analysis of characteristics of a bionic cluster spiral groove dry gas seal[J]. Journal of Mechanical Engineering, 2015, 51(15): 20-26.
[6]	王衍, 胡琼, 肖业祥, 等. 超高速干气密封扰流效应及抑扰机制[J]. 航空学报, 2019, 40(10): 116-125.
	Wang Y, Hu Q, Xiao Y X, et al. Turbulence effect and suppression mechanism of dry gas seal at ultra-high speeds[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(10): 116-125.
[7]	Chen Y, Wang Q G, Peng X D, et al. Flow field and sealing performance analysis of compliant foil face gas seal[J]. Advances in Mechanical Engineering, 2022, 14(6): 16878132221108488.
[8]	Munson J, Grant D, Agrawal G. Foil face seal development[C]//37th Joint Propulsion Conference and Exhibit. 08 July 2001 - 11 July 2001, Salt Lake City, UT. Reston, Virginia: AIAA, 2001: 3483.
[9]	Munson J, Grant D, Agrawal G. Foil film riding face seal proof-of-concept testing[C]//38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit. 07 July 2002 - 10 July 2002, Indianapolis, Indiana. Reston, Virginia: AIAA, 2002: 3791.
[10]	Heshmat H, Walton J. Innovative high-temperature compliant surface foil face seal development[C]//44th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit. 21 July 2008 - 23 July 2008, Hartford, CT. Reston, Virginia: AIAA, 2008: 4505.
[11]	Heshmat H, Ren Z H, Hunsberger A, et al. The emergence of compliant foil bearing and seal technologies in support of 21st century compressors and turbine engines[C]//ASME 2010 International Mechanical Engineering Congress and Exposition, November 12–18, 2010, Vancouver, British Columbia, Canada. 2012: 95-103.
[12]	Chen Y, Chen K, Peng X D, et al. Transient elasto-aerodynamically coupling behavior and performance analysis of bump-type compliant foil face gas seal at ultra-high speeds[J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2023, 45(7): 369.
[13]	Chen Y, Chen K, Peng X D, et al. Research on the operation mechanism and performance of bump-type compliant foil face gas seal[J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2022, 44(8): 325.
[14]	王庆港, 陈源, 彭旭东, 等. 三自由度微扰下箔片端面气膜密封动态特性分析[J]. 中国机械工程, 2022, 33(15): 1828-1840.
	Wang Q G, Chen Y, Peng X D, et al. Analysis on dynamic characteristics of compliant foil face gas seals with three degrees of freedom perturbation[J]. China Mechanical Engineering, 2022, 33(15): 1828-1840.
[15]	Chen Y, Li Y S, Li Y T, et al. Leakage control design and performance analysis on upstream pumping compliant foil face gas seal[J]. Industrial Lubrication and Tribology, 2025, 77(4): 516-525.
[16]	潘永健, 陈源, 李运堂, 等. 超临界二氧化碳柔性坝箔片端面气膜密封运行机理及性能分析[J]. 摩擦学学报(中英文), 2025, 45(11): 1640-1652.
	Pan Y J, Chen Y, Li Y T, et al. Operating mechanism and performance analysis of flexible dam compliant foil face gas seal in supercritical carbon dioxide[J]. Tribology, 2025, 45(11): 1640-1652.
[17]	Salehi M, Swanson E, Heshmat H. Thermal features of compliant foil bearings: theory and experiments[J]. Journal of Tribology, 2001, 123(3): 566-571.
[18]	Feng K, Kaneko S. Thermohydrodynamic study of multiwound foil bearing using lobatto point quadrature[J]. Journal of Tribology, 2009, 131(2): 021702.
[19]	Feng K, Kaneko S. A thermohydrodynamic sparse mesh model of bump-type foil bearings[J]. Journal of Engineering for Gas Turbines and Power, 2013, 135(2): 022501.
[20]	Lee D, Kim D. Three-dimensional thermohydrodynamic analyses of Rayleigh step air foil thrust bearing with radially arranged bump foils[J]. Tribology Transactions, 2011, 54(3): 432-448.
[21]	Lehn A, Mahner M, Schweizer B. A thermo-elasto-hydrodynamic model for air foil thrust bearings including self-induced convective cooling of the rotor disk and thermal runaway[J]. Tribology International, 2018, 119: 281-298.
[22]	Zhang J Y, Qiao X Y, Chen W D, et al. Numerical investigation of Thermo-aerodynamic characteristics of gas foil thrust bearing[J]. Thermal Science and Engineering Progress, 2022, 31: 101296.
[23]	Liu X M, Li C L, Du J J, et al. The fluid-structure-thermal performance analysis of gas foil thrust bearing by using computational fluid dynamics[J]. Lubricants, 2022, 10(11): 294.
[24]	刘晖. 实际气体温度绝热指数和容积绝热指数的计算[J]. 石油化工高等学校学报, 2000, 13(4): 42-45.
	Liu H. Calculation of the isentropic temperature change exponent and isentropic volume change exponent of real gases[J]. Journal of Petrochemical Universities, 2000, 13(4): 42-45.
[25]	García-Camprubí M, Izquierdo S, Fueyo N. Challenges in the electrochemical modelling of solid oxide fuel and electrolyser cells[J]. Renewable and Sustainable Energy Reviews, 2014, 33: 701-718.
[26]	White F M. Viscous Fluid Flow[M]. New York: McGraw-Hill, 1974: 27-32.
[27]	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.
[28]	Jiang J B, Zhao W J, Peng X D, et al. A novel design for discrete surface texture on gas face seals based on a superposed groove model[J]. Tribology International, 2020, 147: 106269.
[29]	Iordanoff I. Maximum load capacity profiles for gas thrust bearings working under high compressibility number conditions[J]. Journal of Tribology, 1998, 120(3): 571-576.
[30]	闫佳佳, 刘占生, 王铮, 等. 基于Newton-Raphson迭代的动压气体止推箔片轴承特性研究[J]. 汽轮机技术, 2017, 59(2): 116-120, 124.
	Yan J J, Liu Z S, Wang Z, et al. Performance analysis of hydrodynamic gas foil thrust bearing based on Newton-raphson iterative method[J]. Turbine Technology, 2017, 59(2): 116-120, 124.
[31]	Liu X M, Li C L, Du J J, et al. Thermal characteristics study of the bump foil thrust gas bearing[J]. Applied Sciences, 2021, 11(9): 4311.