文章快速检索 高级检索

Numerical simulation and parameter optimization of seal property of bidirectional rotating cylinder gas film
MA Gang , YANG Weiru
School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Received: 2015-10-20; Accepted: 2015-12-04; Published online: 2016-01-27
Foundation item: National Natural Science Foundation of China (51075018)
Corresponding author. Tel.:010-82317745, E-mail:mgbuaa@163.com
Abstract: Based on cognizing of advantages of cylinder gas film seal system, this paper proposes a new bidirectional rotating cylinder gas film seal system with inverted T interface structure and double-groove interface structure. It establishes mathematical model and numerical analysis model of the bidirectional rotating cylinder gas film with inverted T interface structure and double-groove interface structure based on finite element method. It develops calculation program about pressure distribution, steady and dynamic property of the gas film, and multidimensional parameter optimization of groove structure on the basis of finite element method on the VC platform. It realizes calculation and analysis of pressure distribution, property of the seal system and structural parameter optimization design. It builds physical models and finite element models of the inverted T cylinder gas film with different average thickness in Gambit. And then, this paper carries out numerical simulation of the gas film under different rotational speed through FLUENT. The simulation results of commercial software are consistent with numerical results of the self-developed program, verifying the correctness of the developed program. It calculates and compares steady and dynamic properties of two kinds of interface structures, and seal performance of inverted T type is better than double-groove type under the same design conditions, which provides reference for selection model of seal system. The calculation program of genetic algorithm-particle swarm optimization (GAPSO) has guiding significance for the design of groove parameters.
Key words: bidirectional rotating     cylinder gas film seal     numerical simulation     FLUENT simulation     GAPSO

1 理论分析 1.1 密封气膜数理模型

 图 1 坐标系中的简化密封模型及几何关系 Fig. 1 Simplified seal model and geometric relations in coordinate system
 图 2 倒斜T字型和双层斜槽型界面展开图 Fig. 2 Interface expansion plan of inverted T type and double-groove type

 (1)

1.2 柱面气膜稳态压力微分方程

 (2)

 (3)

 (4)

2 有限元方法数值计算 2.1 伽辽金法建立变分方程

 (5)
2.2 变分方程的离散求解

1) 解域离散

 图 3 倒斜T字型网格划分与节点编号 Fig. 3 Mesh generation and node number of inverted T type

2) 方程离散求解

2.3 气膜的密封特性

1) 气膜的稳态密封特性[12]

 (6)

 (7)

 (8)

 (9)

 (10)

 (11)

 (12)

 (13)

2) 气膜的动态密封特性

 (14)
 (15)

3 仿真计算及算例验证 3.1 仿真分析方法

 图 4 Gambit建立模型 Fig. 4 Model in Gambit

3.2 仿真结果

 参数 数值 转子半径Rj/mm 50 密封环轴向宽度L/mm 20 平均膜厚c/μm 10 槽数 10 偏心率 0.5 1槽宽比pb1 0.1 1槽长比pl1 0.2 2槽长比pl2 0.3 1槽深比pd1 2.0 2槽深比pd2 2.0 2槽宽比pb2 0.5 上游压力Ph/ MPa 0.3 下游压力Pl/MPa 0.1 角速度ω/(r·min-1) 20000 绝对温度T / ℃ 20 密封气体 空气

 图 5 总压云图 Fig. 5 Total pressure contours
3.3 对比验证

 图 6 气膜反力程序结果与仿真结果对比 Fig. 6 Program results of gas film counter-force compared with simulation results

 转速/(r·min-1) 膜厚/μm 点 节点压力/MPa 误差/% 程序 仿真 15000 10 1 0.41 0.43 4.88 15000 10 2 0.33 0.34 3.03 15000 6 1 0.60 0.63 5.00 15000 6 2 0.36 0.35 2.78 25000 10 1 0.49 0.51 4.08 25000 10 2 0.35 0.36 2.87 25000 6 1 0.73 0.76 4.11 25000 6 2 0.42 0.43 2.38

4 2种界面结构气膜密封性能比较

 参数 数值 转子半径Rj/mm 50 密封环轴向宽度L/mm 20 平均厚膜c/μm 10 槽数 10 偏心率 0.4 1槽宽比pb1 0.2 1槽长比pl1 0.3 2槽长比pl2 0.4 1槽深比pd1 2.0 2槽深比pd2 2.0 2槽宽比pb2 0.5 上游压力Ph/ MPa 0.601325 下游压力Pl/ MPa 0.101325 角速度ω/(r·min-1) 20000 绝对温度T / ℃ 20

4.1 稳态特性的比较

1) 气膜稳态特性随转速的变化

 图 7 不同转速下稳态特性的比较 Fig. 7 Comparison of steady state characteristics under different rotational speeds

2) 气膜稳态特性随平均膜厚的变化

 图 8 不同平均膜厚下稳态特性的比较 Fig. 8 Comparison of steady state characteristics under different average film thickness

4.2 动态特性的比较

1) 气膜动态刚度系数随转速的变化

 图 9 不同转速下气膜动态刚度系数比较 Fig. 9 Comparison of dynamic stiffness coefficients of gas film under different rotational speeds

2) 气膜动态阻尼系数随转速的变化

 图 10 不同转速下气膜动态阻尼系数比较 Fig. 10 Comparison of dynamic damping coefficients of gas film under different rotational speeds
5 GAPSO算法多维参数优化 5.1 粒子群优化算法与遗传算法结合

Xi=[pb1,pl1,pl2,pd1,pb2]iT

max F(X)

s.t. Xmin<X<Xmax

2种目标函数F(X)：① 气膜反力；② 气膜反力与泄漏量的比值。

GAPSO算法流程图如图 11所示(详细过程见文献[16-17])。

 图 11 GAPSO算法流程图 Fig. 11 Flowchart of GAPSO algorithm
5.2 界面结构参数有无优化的对比

 图 12 气膜反力优化对比 Fig. 12 Comparison of gas film counter-force optimization

 参数 初始值 优化结果 1槽宽比pb1 0.2 0.176706 1槽长比pl1 0.3 0.449489 2槽长比pl2 0.4 0.448237 1槽深比pd1 2.0 3.066440 2槽宽比pb2 0.5 0.930887 目标函数/N 124.121 150.857

 图 13 气膜反力与泄漏量的比值优化对比 Fig. 13 Comparison of ratio optimization of gas film counter-force and leakage

 参数 初始值 优化结果 1槽宽比pb1 0.2 0.151854 1槽长比pl1 0.3 0.419608 2槽长比pl2 0.4 0.263190 1槽深比pd1 2.0 1.150060 2槽宽比pb2 0.5 0.500367 目标函数 645031.54 979997.00

6 结 论

1) 建立了双向旋转倒斜T字型与双层斜槽型柱面气膜密封系统密封气膜的数理模型和基于有限元方法的密封气膜数值分析模型。

2) 在VC平台上开发了基于有限元计算的密封气膜压力分布、密封系统稳态特性与动态特性的计算分析程序。动态特性数值计算的实现突破了目前商业软件在进行动态特性分析的局限。

3) 在Gambit中建立了不同平均膜厚下倒斜T字型柱面气膜的物理模型和有限元分析模型，通过FLUENT进行了密封气膜特性数值仿真，商用软件仿真结果与自主开发程序数值计算结果对比一致性好，验证了开发程序的正确性。

4) 计算分析了转速与平均膜厚对密封特性的影响，对比了相同参数下2种界面结构的密封特性。从稳态特性和动态特性看，倒斜T字型的性能均优于双层斜槽型。

5) 计算对比了2种界面结构有无多维优化的密封特性。通过GAPSO算法进行多维优化可以有效提高密封特性。

 [1] 马纲, 栗秀花, 沈心敏, 等. 柱面气膜密封界面结构与性能分析[J]. 航空动力学报, 2011, 26 (11) : 10 –16. MA G, LI X H, SHEN X M, et al. Analysis of performance and interface structure of cylinder gas film seal[J]. Journal of Aerospace Power, 2011, 26 (11) : 10 –16. (in Chinese) [2] KOWALSKI C A, BASU P. Reverse rotation capability of spiral-groove gas face seals[J]. Tribology Transactions, 1995, 38 (3) : 549 –556. DOI:10.1080/10402009508983441 [3] YANG P, ZHU K Q, WANG X L. On the non-linear stability of self-acting gas journal bearings[J]. Tribology International, 2009, 42 (1) : 71 –76. DOI:10.1016/j.triboint.2008.05.007 [4] NOSOWICZ J, ZEUS D. A bi-directional gas face seal experience under test conditions and in practical use[J]. Lubrication Engineering, 1993, 49 (3) : 217 –221. [5] GOLD SWAIN I M.Mechanical face seals:EP,US 5375855 A[P].1994-12-27. [6] 赵亚萍. 双向干气密封的研制情况及技术分析[J]. 流体机械, 1996, 24 (4) : 46 –47. ZHAO Y P. Development situation of two way dry gas seal and technical analysis[J]. Journal of Fluid Mechanics, 1996, 24 (4) : 46 –47. (in Chinese) [7] 郝木明. 机械密封技术及应用[M]. 北京: 中国石化出版社, 2010 : 80 . HAO M M. Mechanical seal technology and its application[M]. Beijing: China Petrochemical Press, 2010 : 80 . (in Chinese) [8] SALEHI M, HESHMAT H. Performance of a complaint foil seals in a small gas turbine engine simulator employing a hybrid foil/ball bearing support system[J]. Tribology Transactions, 2001, 44 (3) : 458 –464. DOI:10.1080/10402000108982481 [9] SAYMA A I, BREARD C, VAHDATI M, et al. Aerolasticity analysis of air-riding seals for aero-engine applications[J]. Journal of Tribology-Transactions of the ASME, 2002, 124 (3) : 607 –616. DOI:10.1115/1.1467086 [10] SHAPIRO W.Numerical,analytical,experimental study of fluid dynamic forces in seals:NASA/CR 2004-213199/VOL2[R].Latham,NY:Mechanical Technology,Inc.,2004. http://cn.bing.com/academic/profile?id=1637191042&encoded=0&v=paper_preview&mkt=zh-cn [11] WALOWIT J,SHAPIRO W.Numerical,analytical,experimental study of fluid dynamic forces in seals:NASA/CR2004-213199/VOL3[R].Latham,NY:Mechanical Technology,Inc.,2004. http://cn.bing.com/academic/profile?id=844769531&encoded=0&v=paper_preview&mkt=zh-cn [12] 马纲, 席平, 沈心敏, 等. 柔性支承浮环柱面气膜密封准动态特性分析[J]. 航空动力学报, 2010, 25 (5) : 1190 –1196. MA G, XI P, SHEN X M, et al. Analysis of quasi-dynamic characteristics of compliant floating ring gas cylinder seal[J]. Journal of Aerospace Power, 2010, 25 (5) : 1190 –1196. (in Chinese) [13] LIU Y C, SHEN X M, XU W F. Numerical analysis of dynamic coefficients for gas film face seals[J]. Journal of Tribology-Transaction of the ASME, 2002, 124 (4) : 743 –754. DOI:10.1115/1.1472459 [14] GREEN I, BARNSBY R M. A simultaneous numerical solution for the lubrication and dynamic stability of noncontacting gas face seals[J]. Journal of Tribology-Transactions of the ASME, 2001, 123 (2) : 388 –394. DOI:10.1115/1.1308020 [15] 马纲, 孙晓军, 罗先海, 等. 端柱面组合密封气膜稳态特性仿真数值分析[J]. 北京航空航天大学学报, 2014, 40 (4) : 439 –443. MA G, SUN X J, LUO X H, et al. Simulation numerical analysis of steady-state properties of gas face and cylinder film seal[J]. Journal of Beijing University of Aeronautics and Astronautics, 2014, 40 (4) : 439 –443. (in Chinese) [16] 陈贵敏, 贾建援, 韩琪. 粒子群优化算法的惯性权值递减策略研究研究[M]. 西安: 西安交通大学出版社, 2002 : 70 . CHEN G M, JIA J Y, HAN Q. Research on the strategy of decreasing inertia weight in particle swarm optimization algorithm[M]. Xi'an: Xi'an Jiaotong University Press, 2002 : 70 . (in Chinese) [17] 曹春红, 张永坚, 李文辉. 杂交粒子群算法在工程几何约束求解中的应用[J]. 仪器仪表学报, 2004, 25 (4) : 397 –400. CAO C H, ZHANG Y J, LI W H. Applications of hybrid particle swarm optimization in engineering geometric constraint solving[J]. Chinese Journal of Scientific Instrument, 2004, 25 (4) : 397 –400. (in Chinese)

#### 文章信息

MA Gang, YANG Weiru

Numerical simulation and parameter optimization of seal property of bidirectional rotating cylinder gas film

Journal of Beijing University of Aeronautics and Astronsutics, 2016, 42(11): 2279-2288
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0682