直通式迷宫密封内部二维流场的数值模拟
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摘要
迷宫密封是工业上广泛采用的一种密封形式，长期以来，人们一直不断地
对它进行研究，获得了许多有益的成果，这些成果在生产实践中被充分利用，
收到了良好的经济效益。但是，随着科学技术的飞速发展，科学研究的各个领
域都面临着新一轮的挑战。就密封而言，传统的依赖于总体试验的研究方法，
在充分发挥了其在工业生产中的重要作用之后，也逐渐地暴露出自身尚存在有
待完善之处，其中之一便是对迷宫空腔及间隙内部流场和压力场的定量认识不
足。本文即是在前人已有理论成果的基础上，针对上述不足展开研究，以期在
迷宫密封的研究领域中有所渐进。
本文研究工作的技术路线是：
第一，建立直通式迷宫密封二维几何模型；
第二、提出基本假设，确立物理模型；
第三、通过数值计算，绘制出不同几何条件下直通式迷宫密封内部二维流
场的可视化图形；
第四、通过实验考察数值模拟结果是否正确；
第五、根据理论计算结果和实验结果的对比分析得出结论。
针对几何因素对直通式迷宫密封效果的影响，本文参考了相关文献资料，
确定所要研究的几何参数为：齿间距(s)、间隙高度(h)、齿高(H)和齿宽
(b)。并根据现有工业用直通式迷宫密封的结构，加以适当调整，从无量纲的
角度确定了各几何参数的研究范围是：
s／h=10～80，H／s=0.25～1.0，6／h=0.1～20.0。
本文吸收了前人在迷宫密封领域中许多重要的研究成果。在此基础上，通
过数值模拟和实验验证两种手段，对直通式迷宫密封内部二维流场进行了初步
探讨。综合近两年的论文研究工作，最后总结出以下几点浅显的认识：
一、利用MATLAB数学语言编程计算，就几何因素对直通式迷宫密封的影
响效果进行数值模拟，直观地显示出迷宫内部流场及压力场的分布情况，从而
直通式迷宫密封内部二维流场的数值模拟
确定出较为合理的几何结构。由此可见，数值模拟方法在研究迷宫内部流场和
压力场的定量研究过程中，同以总体试验为主的传统方法相比，具有一定的优
越性。
二、由数值模拟结果得出的较为合理的直通式迷宫密封几何结构参数范围
是:s/h二40或60，H/s=O.5，b/h>1O(b不宜过大)。
三、利用粒子成像(PartiCle Image Veloeimetry简称PIV)技术作为基
本实验手段，拍摄了与数值模拟条件相比，具有物理相似特征的各种情况下的
流场照片。通过实验结果与数值计算结果的对比分析，可以看出，本文对直通
式迷宫密封内部二维流场进行的数值模拟是基本正确的。因此，采用数值计算
方法得到的直通式迷宫密封几何结构参数范围，对于实际结构设计也具有一定
的参考价值。
总之，本文对直通式迷宫间隙和空腔内部流场及压力场进行了定量计算，
计算结果得到了实验结果的验证。本文比较完整地分析了直通式迷宫密封内部
流体的流动形式，为迷宫计算提供了较为完善的数学模型，并为迷宫设计提供
了依据。
Labyrinth seal is one of seal types, widely using in industry.For a long time people constantly research this method and obtain many beneficial fruits.All this fruits are made full use of in manufacture and bring favorable economic benefit.With the fast development of technology, however, every research field of science is up against new challenge.As far as labyrinth seal, though it brought into play in industry, the method connecting with overall seal test reveals limitations.One of them is lake of actual quantitative knowledge of the flow through cavum and clearance of labyrinth.On the basis of the fruits from the grand old men, aiming at the above limitations, this paper makes some research and expects to make a little progress.
The object of this research is the effect of geometrical factors on straight type labyrinth seal.The main thought is as the following:
Firstly, set up geometrical matrix of straight type labyrinth seal.Then, changing structure sizes (boundary conditions, original conditions etc.) and carrying through respectively numerical valuable calculations, protract flow field and pressure field pictures.Through contrasting and analysis of several critical parameters (the position of volution, the intension of volution, and pressure drop etc.) ensure reasonable geometricaI structures.Finally, compare these resuIts with experimental ones to find out similarities and differences and draw a cone I us ion.
In according to the existing industrial structures and making adjustment, choose the geometr ical parameters: space between teeth (s), clearance highness (h), tooth highness (H), tooth width (b).The range
of the parameters are s/h=10~80, H/s=0.25-1.0, b/h=0.1-20.0.
This paper, to some degree, discusses and researches primarily the numerical simulation experiment about the flow field and pressure field of straight type.Integrating what learned, make the following conclusions:
The first is to use MATLAB to make program and to simulate the effect of geometrical factors on straight type, which can reveal the flow field and pressure field, to ensure reasonable geometrical structure.This shows, compared with the traditional collective testing method is better.
The second is that the reasonable structure of straight type are s/h=40 & 60, H/s=0.5, b/h>10.
The third is that obtain flow field pictures under the conditions of numerical simulation through PIV ( Particle Image Velocimetry ).The contrasting shows that the above structure is correct.
In a word, this paper calculates rationally the flow field and pressure field in the cavum and clearance of straight type labyrinth, analyses the flow form, offers mathematical matrix and basis for the design of labyrinth.
对它进行研究，获得了许多有益的成果，这些成果在生产实践中被充分利用，
收到了良好的经济效益。但是，随着科学技术的飞速发展，科学研究的各个领
域都面临着新一轮的挑战。就密封而言，传统的依赖于总体试验的研究方法，
在充分发挥了其在工业生产中的重要作用之后，也逐渐地暴露出自身尚存在有
待完善之处，其中之一便是对迷宫空腔及间隙内部流场和压力场的定量认识不
足。本文即是在前人已有理论成果的基础上，针对上述不足展开研究，以期在
迷宫密封的研究领域中有所渐进。
本文研究工作的技术路线是：
第一，建立直通式迷宫密封二维几何模型；
第二、提出基本假设，确立物理模型；
第三、通过数值计算，绘制出不同几何条件下直通式迷宫密封内部二维流
场的可视化图形；
第四、通过实验考察数值模拟结果是否正确；
第五、根据理论计算结果和实验结果的对比分析得出结论。
针对几何因素对直通式迷宫密封效果的影响，本文参考了相关文献资料，
确定所要研究的几何参数为：齿间距(s)、间隙高度(h)、齿高(H)和齿宽
(b)。并根据现有工业用直通式迷宫密封的结构，加以适当调整，从无量纲的
角度确定了各几何参数的研究范围是：
s／h=10～80，H／s=0.25～1.0，6／h=0.1～20.0。
本文吸收了前人在迷宫密封领域中许多重要的研究成果。在此基础上，通
过数值模拟和实验验证两种手段，对直通式迷宫密封内部二维流场进行了初步
探讨。综合近两年的论文研究工作，最后总结出以下几点浅显的认识：
一、利用MATLAB数学语言编程计算，就几何因素对直通式迷宫密封的影
响效果进行数值模拟，直观地显示出迷宫内部流场及压力场的分布情况，从而
直通式迷宫密封内部二维流场的数值模拟
确定出较为合理的几何结构。由此可见，数值模拟方法在研究迷宫内部流场和
压力场的定量研究过程中，同以总体试验为主的传统方法相比，具有一定的优
越性。
二、由数值模拟结果得出的较为合理的直通式迷宫密封几何结构参数范围
是:s/h二40或60，H/s=O.5，b/h>1O(b不宜过大)。
三、利用粒子成像(PartiCle Image Veloeimetry简称PIV)技术作为基
本实验手段，拍摄了与数值模拟条件相比，具有物理相似特征的各种情况下的
流场照片。通过实验结果与数值计算结果的对比分析，可以看出，本文对直通
式迷宫密封内部二维流场进行的数值模拟是基本正确的。因此，采用数值计算
方法得到的直通式迷宫密封几何结构参数范围，对于实际结构设计也具有一定
的参考价值。
总之，本文对直通式迷宫间隙和空腔内部流场及压力场进行了定量计算，
计算结果得到了实验结果的验证。本文比较完整地分析了直通式迷宫密封内部
流体的流动形式，为迷宫计算提供了较为完善的数学模型，并为迷宫设计提供
了依据。
Labyrinth seal is one of seal types, widely using in industry.For a long time people constantly research this method and obtain many beneficial fruits.All this fruits are made full use of in manufacture and bring favorable economic benefit.With the fast development of technology, however, every research field of science is up against new challenge.As far as labyrinth seal, though it brought into play in industry, the method connecting with overall seal test reveals limitations.One of them is lake of actual quantitative knowledge of the flow through cavum and clearance of labyrinth.On the basis of the fruits from the grand old men, aiming at the above limitations, this paper makes some research and expects to make a little progress.
The object of this research is the effect of geometrical factors on straight type labyrinth seal.The main thought is as the following:
Firstly, set up geometrical matrix of straight type labyrinth seal.Then, changing structure sizes (boundary conditions, original conditions etc.) and carrying through respectively numerical valuable calculations, protract flow field and pressure field pictures.Through contrasting and analysis of several critical parameters (the position of volution, the intension of volution, and pressure drop etc.) ensure reasonable geometricaI structures.Finally, compare these resuIts with experimental ones to find out similarities and differences and draw a cone I us ion.
In according to the existing industrial structures and making adjustment, choose the geometr ical parameters: space between teeth (s), clearance highness (h), tooth highness (H), tooth width (b).The range
of the parameters are s/h=10~80, H/s=0.25-1.0, b/h=0.1-20.0.
This paper, to some degree, discusses and researches primarily the numerical simulation experiment about the flow field and pressure field of straight type.Integrating what learned, make the following conclusions:
The first is to use MATLAB to make program and to simulate the effect of geometrical factors on straight type, which can reveal the flow field and pressure field, to ensure reasonable geometrical structure.This shows, compared with the traditional collective testing method is better.
The second is that the reasonable structure of straight type are s/h=40 & 60, H/s=0.5, b/h>10.
The third is that obtain flow field pictures under the conditions of numerical simulation through PIV ( Particle Image Velocimetry ).The contrasting shows that the above structure is correct.
In a word, this paper calculates rationally the flow field and pressure field in the cavum and clearance of straight type labyrinth, analyses the flow form, offers mathematical matrix and basis for the design of labyrinth.
引文
[1] Sneck, H.J.Labyrinth seal liberature survey.J.L.T.October/1974
[2] 徐灏．密封．北京：冶金工业出版社，1999
[3] 刘后桂．密封技术．长沙：湖南科学技术出版社，1981
[4] 顾永泉．流体动密封．北京：石油大学出版社，1990
[5] 顾永泉．流体动密封．北京：石油大学出版社，1992
[6] 高光藩，张牢牢．迷宫密封性能影响因素分析．风机技术，1997(6)
[7] 小茂鸟和生．直通形考方．日本机械学会 论文集，1959：13(123) ：627～633
[8] 王建中，黄守龙．直通式迷宫密封的静态工作特性．武汉工业大学学报，1994
[9] 黄守龙．直通式迷宫密封的实验和数值研究：[学位论文]．华东工学院，1991
[10] HaTW, Morrison GL, Childs DW.Friction-factor characterics for narrow channel swith honey comb surfaces.ASMEJ of Tribology, 1992, 114(4) :714~721
[11] 黄守龙等．直通式迷宫静态工作特性的实验研究．弹道学报，1994，(3) ：43-47
[12] Adolf Egli, Philadelphgia, Pa..The leakage of steam through labyrinth seals
[13] K．塔鲁达纳夫斯基．非接触密封．机械工业出版社
[14] Professor W.J.Kearton, D.Eng.M.I.Mech, E.and T.h.Keh, B.sc., M.Eng..Leakage of air through labyrinth gland of stagared type
[15] Professor W.J.Kearton.The flow of air through radial labyrinth gland
[16] C.A.Meyer.The leakage through straight slant labyrinths and honeycomb seals.Journal of Engineering for power, 1975
[17] 金忠青，N-S方程的数值解和紊流模型．河海大学出版社．1989，6
[18] G.Comini, A(K-ε ) model of turbulence flow, Computer and fluids.Vol 5., 1985
[19] C.E.Thomas, K.Mokgan.A Finite Element Analysis of Flow over A backward Facing Step.Computer and Fluids.Vol.9 pp261-278, 1981
[20] 陈雄，赖国璋．Navier-Stokes方程的时间分裂有限元法.
[21] M.Nallasamy.Turbulence Models and Their Applications to the Prediction of Internal Flows, A Review.Computer and Fluids.Vol.15
[22] 赵庆贺．搭错式径向迷宫密封的计算．大连理工大学硕士学位论文，1992，1
[23] Scharrer, J.K.Rotor Dynamic Coefficients for Stepped Labyrinth Gas Seals.ASME Journal of Triblology, 1989: 111:101-1072
[24] Zabriskic, W.etal.Labyrinth Seal Leakage Analysis.ASME Journal of Basic Engineering, 1989: 81:332-340
[25] Kearton, W.J.The Flow of Air through Radial Labyrinth Glands.Proc.I.Mech.B..1995: 169:539-5504
[26] 李均卿等译．非接触密封．机械工业出版社，1986.
[27] Kearton, W.J.etal.Leakage of Air through Labyrinth Glands of Staggered Type.Proc.I.Mech.E., 1952: 166:180-195
[28] Hodkinson, B.Estimation of the Leakage through Labyrinth Gland.A.M.I.Mech.E., 1989: 141:283-288
[29] 小茂鸟和生．直通形关门考方．日本机械学会论 文集，1957：23(133) ：617～623
[30] 小茂鸟和生．空气漏出．日本机械学会论文集， 第1报：1955：21(105) ：377～382：第2报：1955：21(108) ：608～613：第3 报：1956：22(121) ：674～680：第4报：1957：23(129) ：330～336
[31] 高光藩．径向错齿式迷宫密封空腔形状的试验研究．流体工程，1993(4)
[32] Meyer, C.A.The Leakage Throught Straight and Slant labyrinths and Honeycomb Seals.ASME Journal of Engineering for Power.1995: 1495-502
[33] Brownell, J.B.etal.Nonintrusive Investigations into Life-Size Labyrinth Seal Flow Fields.ASME Journal of Engineering for Gas Turbines and Power.1989: 111:333-342
[34] 高光藩．介质流向对径向错齿式迷宫密封性能的影响．流体工程，1993(5)
[35] Kazunari Komotorietal.Leakage Characteristics of Labyrinth Seals.5th International Conference on Fluid Sealing, Warwick.1971: E4-45-E4-61
[36] Vermes, G.A Fluid Mechanics Approach to the Labyrinth Seal Leakage Problem.ASME Journal of Engineering for Power.1961: 83:161-169
[37] ZABRISKIE, W..labyrinth Seal Leakage Analysis.Trans.ASME.Sep./1959
[38] Vermes, G.A.Fluid Mechanics Approach to the Labyrinth Seal Leakage Problem.Trans.ASME.No.2, 1961
[39] Hodkinson, B.Estimation of the Leakage Through a Labyrinth Gland.Pro.Int.Mech.Eng.5/1989
[40] Giulio D' Emilia.Validation of Flow Cofficients Measurement by Laser Velocimeter in Straight-Through Labyrinth Seal Models with Full Size Test Rig Result.84-GT-280
[41] Stoff, H.Incompressible Flow in Labyrinth Seal.J.Flu.Mech.October/1990
[42] Rhode, D.L.Prediction of Incompressible Flow in Labyrinth Seals.Trans.ASME.1996
[43] Labyrinth Seal Analysis.Volume 1.Development of a Navier-Stokes Analysis for Labyrinth Seals.Final, rept.Jun.80-Mar.85
[44] Labyrinth Seal Analysis.Volume 2.User' s Manual for the Navier-Stokes Analysis for Labyrinth Seals.Final, rept.Jun.80-Mar.85
[45] Labyrinth Seal Analysis.Volume 3.Analytical and Experimental Development of a Design Model for Labyrinth Seals.Final, rept.Jun.85
[46] 周光垌等．流体力学(上)．北京：高等教育出版社，2001
[47] 蔡仁良，顾伯勤，宋鹏云．过程装备密封技术．北京：化学工业出版社，2002.5
[2] 徐灏．密封．北京：冶金工业出版社，1999
[3] 刘后桂．密封技术．长沙：湖南科学技术出版社，1981
[4] 顾永泉．流体动密封．北京：石油大学出版社，1990
[5] 顾永泉．流体动密封．北京：石油大学出版社，1992
[6] 高光藩，张牢牢．迷宫密封性能影响因素分析．风机技术，1997(6)
[7] 小茂鸟和生．直通形考方．日本机械学会 论文集，1959：13(123) ：627～633
[8] 王建中，黄守龙．直通式迷宫密封的静态工作特性．武汉工业大学学报，1994
[9] 黄守龙．直通式迷宫密封的实验和数值研究：[学位论文]．华东工学院，1991
[10] HaTW, Morrison GL, Childs DW.Friction-factor characterics for narrow channel swith honey comb surfaces.ASMEJ of Tribology, 1992, 114(4) :714~721
[11] 黄守龙等．直通式迷宫静态工作特性的实验研究．弹道学报，1994，(3) ：43-47
[12] Adolf Egli, Philadelphgia, Pa..The leakage of steam through labyrinth seals
[13] K．塔鲁达纳夫斯基．非接触密封．机械工业出版社
[14] Professor W.J.Kearton, D.Eng.M.I.Mech, E.and T.h.Keh, B.sc., M.Eng..Leakage of air through labyrinth gland of stagared type
[15] Professor W.J.Kearton.The flow of air through radial labyrinth gland
[16] C.A.Meyer.The leakage through straight slant labyrinths and honeycomb seals.Journal of Engineering for power, 1975
[17] 金忠青，N-S方程的数值解和紊流模型．河海大学出版社．1989，6
[18] G.Comini, A(K-ε ) model of turbulence flow, Computer and fluids.Vol 5., 1985
[19] C.E.Thomas, K.Mokgan.A Finite Element Analysis of Flow over A backward Facing Step.Computer and Fluids.Vol.9 pp261-278, 1981
[20] 陈雄，赖国璋．Navier-Stokes方程的时间分裂有限元法.
[21] M.Nallasamy.Turbulence Models and Their Applications to the Prediction of Internal Flows, A Review.Computer and Fluids.Vol.15
[22] 赵庆贺．搭错式径向迷宫密封的计算．大连理工大学硕士学位论文，1992，1
[23] Scharrer, J.K.Rotor Dynamic Coefficients for Stepped Labyrinth Gas Seals.ASME Journal of Triblology, 1989: 111:101-1072
[24] Zabriskic, W.etal.Labyrinth Seal Leakage Analysis.ASME Journal of Basic Engineering, 1989: 81:332-340
[25] Kearton, W.J.The Flow of Air through Radial Labyrinth Glands.Proc.I.Mech.B..1995: 169:539-5504
[26] 李均卿等译．非接触密封．机械工业出版社，1986.
[27] Kearton, W.J.etal.Leakage of Air through Labyrinth Glands of Staggered Type.Proc.I.Mech.E., 1952: 166:180-195
[28] Hodkinson, B.Estimation of the Leakage through Labyrinth Gland.A.M.I.Mech.E., 1989: 141:283-288
[29] 小茂鸟和生．直通形关门考方．日本机械学会论 文集，1957：23(133) ：617～623
[30] 小茂鸟和生．空气漏出．日本机械学会论文集， 第1报：1955：21(105) ：377～382：第2报：1955：21(108) ：608～613：第3 报：1956：22(121) ：674～680：第4报：1957：23(129) ：330～336
[31] 高光藩．径向错齿式迷宫密封空腔形状的试验研究．流体工程，1993(4)
[32] Meyer, C.A.The Leakage Throught Straight and Slant labyrinths and Honeycomb Seals.ASME Journal of Engineering for Power.1995: 1495-502
[33] Brownell, J.B.etal.Nonintrusive Investigations into Life-Size Labyrinth Seal Flow Fields.ASME Journal of Engineering for Gas Turbines and Power.1989: 111:333-342
[34] 高光藩．介质流向对径向错齿式迷宫密封性能的影响．流体工程，1993(5)
[35] Kazunari Komotorietal.Leakage Characteristics of Labyrinth Seals.5th International Conference on Fluid Sealing, Warwick.1971: E4-45-E4-61
[36] Vermes, G.A Fluid Mechanics Approach to the Labyrinth Seal Leakage Problem.ASME Journal of Engineering for Power.1961: 83:161-169
[37] ZABRISKIE, W..labyrinth Seal Leakage Analysis.Trans.ASME.Sep./1959
[38] Vermes, G.A.Fluid Mechanics Approach to the Labyrinth Seal Leakage Problem.Trans.ASME.No.2, 1961
[39] Hodkinson, B.Estimation of the Leakage Through a Labyrinth Gland.Pro.Int.Mech.Eng.5/1989
[40] Giulio D' Emilia.Validation of Flow Cofficients Measurement by Laser Velocimeter in Straight-Through Labyrinth Seal Models with Full Size Test Rig Result.84-GT-280
[41] Stoff, H.Incompressible Flow in Labyrinth Seal.J.Flu.Mech.October/1990
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