Article(id=1320037475867803799, tenantId=1146029695717560320, journalId=1316781260334530699, issueId=1320037457517728337, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1005-0329.2026.01.006, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1753372800000, receivedDateStr=2025-07-25, revisedDate=1763308800000, revisedDateStr=2025-11-17, acceptedDate=null, acceptedDateStr=null, onlineDate=1792651059357, onlineDateStr=2026-10-22, pubDate=1769702400000, pubDateStr=2026-01-30, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1792651059357, onlineIssueDateStr=2026-10-22, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1792651059357, creator=13701087609, updateTime=1792651059357, updator=13701087609, issue=Issue{id=1320037457517728337, tenantId=1146029695717560320, journalId=1316781260334530699, year='2026', volume='54', issue='1', pageStart='1', pageEnd='118', issueExtLink='null', onlineDate='null', pubDate='1769702400000', pubDateStr='2026-01-30', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1792651054982, creator='13701087609', updateTime=1792656198886, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext={EN=IssueExt(id=1320059032665183153, tenantId=1146029695717560320, journalId=1316781260334530699, issueId=1320037457517728337, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1320059032669377458, tenantId=1146029695717560320, journalId=1316781260334530699, issueId=1320037457517728337, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null, downloadFileDto=null}, startPage=40, endPage=48, ext={EN=ArticleExt(id=1320037476043964568, articleId=1320037475867803799, tenantId=1146029695717560320, journalId=1316781260334530699, language=EN, title=Study on the transient characteristics of mechanical seals considering methane dissolution, columnId=null, journalTitle=Fluid Machinery, columnName=null, runingTitle=null, highlight=null, articleAbstract=

To address the issue of axial floating and angular deflection of the seal ring caused by changes in methane solubility and gas volume fraction in the oil phase within multiphase pumps,as well as slug flow impact,leading to seal ring wear failure,a transient dynamic model for oil-gas two‑phase flow lubricated sealing considering methane dissolution is established.The model is solved using the finite difference method and the Euler method.The transient response characteristics of the seal before and after considering methane dissolution are compared,and the effects of axial pulsation and angular impact on the seal under different gas volume fractions when considering methane dissolution are investigated.The results show that when methane dissolution is considered,the fluctuations in film thickness and leakage rate are smaller,and the opening force tends to be consistent;during stage Ⅱ of axial vibration,when the gas volume fraction is 0.8,the displacement of the stationary ring is reduced by 3.25 times compared to when the gas volume fraction is 0;the stationary ring is less affected by angular impact,with the maximum change in central film thickness not exceeding 0.1 μm;when the gas volume fraction ranges from 0 to 0.8,the response of sealing performance to axial pulsation follows the same pattern;when the gas volume fraction is 0,the impact of angular shock on sealing performance is relatively small.This study provides theoretical guidance for the application of oil-gas two‑phase sealing in multiphase pumps.

, authors=Qingyang WANG1, Zengli WANG2, Weifeng WU1, Ping ZHANG1, Yude SUN1, authorsList=Qingyang WANG, Zengli WANG, Weifeng WU, Ping ZHANG, Yude SUN, authorCompany=null, correspAuthors=Weifeng WU, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1320037479562985648, articleId=1320037475867803799, tenantId=1146029695717560320, journalId=1316781260334530699, language=CN, title=考虑甲烷溶解的机械密封瞬态特性研究, columnId=1317484287230853622, journalTitle=流体机械, columnName=设计计算, runingTitle=null, highlight=null, articleAbstract=

针对多相泵中甲烷在油相中溶解度和含气率的变化,以及段塞流的冲击,导致密封环轴向浮动与角向偏摆,进而造成密封环磨损失效的问题,建立考虑甲烷溶解的油气两相流润滑密封瞬态动力学模型,并基于有限差分法和欧拉法求解,对比考虑甲烷溶解前后密封的瞬态响应规律,探讨考虑甲烷溶解时,不同含气率下轴向脉动和角向冲击对密封的影响。结果表明,考虑甲烷溶解时的膜厚及泄漏量波动幅度较小,开启力趋于一致;在轴向振动Ⅱ阶段,含气率为0.8时,静环位移比含气率为0时减小了3.25倍;静环受角向冲击的影响较小,中心膜厚最大变化量不超过0.1 μm;含气率为0~0.8时,密封性能对轴向脉动的响应规律相同;含气率为0时,角向冲击对密封性能的影响相对较小。研究可为油气两相密封在多相泵中的应用提供理论指导。

, authors=王青阳1, 王增丽2, 吴伟烽1, 张平1, 孙玉德1, authorsList=王青阳, 王增丽, 吴伟烽, 张平, 孙玉德, authorCompany=null, correspAuthors=吴伟烽, authorNote=

王青阳(1998),男,博士研究生,主要从事流体动力润滑研究,E-mail:。

, correspAuthorsNote=
吴伟烽(1980),男,教授,博士生导师,从事制冷低温与压缩机技术研究,通信地址,710049陕西省西安市咸宁西路28号西安交通大学能源与动力工程学院,E-mail:。
, copyrightStatement=作者向本刊所投稿件一经本刊录用,则该论文的复制权、发行权、信息网络传播权、翻译权、汇编权等权利视为自动转让给本刊。本刊为国内各主要数据库收录期刊,本刊所发表的稿件将同时通过互联网进行网络出版或提供信息服务。, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=thPFVYMkV3EQwAvjL0ak+w==, magXml=k2mN1MZuQH9ob6eZA1RlFQ==, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=ueIgRHiCM2qec1lm45vSAg==, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=fK1w9HecgJCgQFqlgdGWXQ==, mapNumber=null, fund=null)}, authors=[Author(id=1320037480024359096, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1320037475867803799, orderNo=0, firstName=null, middleName=null, lastName=null, nameCn=null, orcid=null, stid=null, country=null, authorPic=null, dead=0, email=wangqy0808@stu.xjtu.edu.cn, emailSecond=null, emailThird=null, correspondingAuthor=0, authorType=1, ext={EN=AuthorExt(id=1320037480099856570, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1320037475867803799, authorId=1320037480024359096, language=EN, stringName=Qingyang WANG, firstName=Qingyang, middleName=null, lastName=WANG, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=1, address=1School of Energy and Power Engineering,Xi′an Jiaotong University,Xi′an 710049,China, bio=null, bioImg=null, bioContent=null, aboutCorrespAuthor=null), CN=AuthorExt(id=1320037480179548347, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1320037475867803799, authorId=1320037480024359096, language=CN, stringName=王青阳, firstName=null, middleName=null, lastName=null, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=1, address=1西安交通大学 能源与动力工程学院,西安 710049, bio={"content":"

王青阳(1998),男,博士研究生,主要从事流体动力润滑研究,E-mail:。

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王青阳(1998),男,博士研究生,主要从事流体动力润滑研究,E-mail:。

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(a)膜厚  (b)开启力  (c)泄漏量

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Computational parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
参数数值参数数值
轴向阻尼系数DZ/(N⋅s⋅m-1)120 000螺旋角α/(°)20
轴向刚度系数KZ/(N⋅m-1)1 500槽深hg/μm15
弹簧比压psp/MPa0.02槽数Ng12
静环质量ms/kg0.5油相动力黏度μoil/(Pa⋅s)0.03
静环转动惯量IX,IY/(kg⋅m2)1.85×10-4甲烷动力黏度μgas/(Pa⋅s)1.106 7×10-7
动、静环初始角偏差γr,γs/mrad0.03空化压力pc/MPa0
初始位移相位ϕp0密封介质温度T0/K313.15
内半径ri、外半径ro/mm33,37油相密度ρoil/(kg⋅m-3)800
槽根半径rg/mm35.7甲烷密度ρgas/(kg⋅m-3)0.624 75
平衡半径rb/mm34.6外径压力po、内径压力pi/MPa0.4,0.1
膜厚h0/μm10转速n/(r⋅min-1)6 000
), ArticleFig(id=1320037485573423345, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1320037475867803799, language=CN, label=表1, caption=

计算参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数数值参数数值
轴向阻尼系数DZ/(N⋅s⋅m-1)120 000螺旋角α/(°)20
轴向刚度系数KZ/(N⋅m-1)1 500槽深hg/μm15
弹簧比压psp/MPa0.02槽数Ng12
静环质量ms/kg0.5油相动力黏度μoil/(Pa⋅s)0.03
静环转动惯量IX,IY/(kg⋅m2)1.85×10-4甲烷动力黏度μgas/(Pa⋅s)1.106 7×10-7
动、静环初始角偏差γr,γs/mrad0.03空化压力pc/MPa0
初始位移相位ϕp0密封介质温度T0/K313.15
内半径ri、外半径ro/mm33,37油相密度ρoil/(kg⋅m-3)800
槽根半径rg/mm35.7甲烷密度ρgas/(kg⋅m-3)0.624 75
平衡半径rb/mm34.6外径压力po、内径压力pi/MPa0.4,0.1
膜厚h0/μm10转速n/(r⋅min-1)6 000
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考虑甲烷溶解的机械密封瞬态特性研究
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王青阳 1 , 王增丽 2 , 吴伟烽 1 , 张平 1 , 孙玉德 1
流体机械 | 设计计算 2026,54(1): 40-48
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流体机械 |设计计算 2026 , 54 (1) : 40 -48
考虑甲烷溶解的机械密封瞬态特性研究
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王青阳1 , 王增丽2, 吴伟烽1 , 张平1, 孙玉德1
作者信息
  • 1西安交通大学 能源与动力工程学院,西安 710049
  • 2中国石油大学(华东) 石大山能新能源学院,山东 青岛 266580
通讯作者:
吴伟烽(1980),男,教授,博士生导师,从事制冷低温与压缩机技术研究,通信地址,710049陕西省西安市咸宁西路28号西安交通大学能源与动力工程学院,E-mail:。
作者简介:

王青阳(1998),男,博士研究生,主要从事流体动力润滑研究,E-mail:。

Study on the transient characteristics of mechanical seals considering methane dissolution
Qingyang WANG1 , Zengli WANG2, Weifeng WU1 , Ping ZHANG1, Yude SUN1
Affiliations
  • 1School of Energy and Power Engineering,Xi′an Jiaotong University,Xi′an 710049,China
  • 2College of New Energy,China University of Petroleum(East China),Qingdao 266580,China
出版时间: 2026-01-30 doi: 10.3969/j.issn.1005-0329.2026.01.006
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针对多相泵中甲烷在油相中溶解度和含气率的变化,以及段塞流的冲击,导致密封环轴向浮动与角向偏摆,进而造成密封环磨损失效的问题,建立考虑甲烷溶解的油气两相流润滑密封瞬态动力学模型,并基于有限差分法和欧拉法求解,对比考虑甲烷溶解前后密封的瞬态响应规律,探讨考虑甲烷溶解时,不同含气率下轴向脉动和角向冲击对密封的影响。结果表明,考虑甲烷溶解时的膜厚及泄漏量波动幅度较小,开启力趋于一致;在轴向振动Ⅱ阶段,含气率为0.8时,静环位移比含气率为0时减小了3.25倍;静环受角向冲击的影响较小,中心膜厚最大变化量不超过0.1 μm;含气率为0~0.8时,密封性能对轴向脉动的响应规律相同;含气率为0时,角向冲击对密封性能的影响相对较小。研究可为油气两相密封在多相泵中的应用提供理论指导。

多相泵  /  油气两相密封  /  甲烷溶解  /  含气率  /  瞬态响应

To address the issue of axial floating and angular deflection of the seal ring caused by changes in methane solubility and gas volume fraction in the oil phase within multiphase pumps,as well as slug flow impact,leading to seal ring wear failure,a transient dynamic model for oil-gas two‑phase flow lubricated sealing considering methane dissolution is established.The model is solved using the finite difference method and the Euler method.The transient response characteristics of the seal before and after considering methane dissolution are compared,and the effects of axial pulsation and angular impact on the seal under different gas volume fractions when considering methane dissolution are investigated.The results show that when methane dissolution is considered,the fluctuations in film thickness and leakage rate are smaller,and the opening force tends to be consistent;during stage Ⅱ of axial vibration,when the gas volume fraction is 0.8,the displacement of the stationary ring is reduced by 3.25 times compared to when the gas volume fraction is 0;the stationary ring is less affected by angular impact,with the maximum change in central film thickness not exceeding 0.1 μm;when the gas volume fraction ranges from 0 to 0.8,the response of sealing performance to axial pulsation follows the same pattern;when the gas volume fraction is 0,the impact of angular shock on sealing performance is relatively small.This study provides theoretical guidance for the application of oil-gas two‑phase sealing in multiphase pumps.

multiphase pump  /  oil-gas two‑phase sealing  /  methane dissolution  /  gas volume fraction  /  transient response
王青阳, 王增丽, 吴伟烽, 张平, 孙玉德. 考虑甲烷溶解的机械密封瞬态特性研究. 流体机械, 2026 , 54 (1) : 40 -48 . DOI: 10.3969/j.issn.1005-0329.2026.01.006
Qingyang WANG, Zengli WANG, Weifeng WU, Ping ZHANG, Yude SUN. Study on the transient characteristics of mechanical seals considering methane dissolution[J]. Fluid Machinery, 2026 , 54 (1) : 40 -48 . DOI: 10.3969/j.issn.1005-0329.2026.01.006
在边际油气资源开采过程中,多相混输工艺以其低投资成本、远距离输送、高油井产出效率等特点受到广泛应用[1]。多相泵是多相混合输送过程的核心设备之一[2-3],而泄漏是影响其效率的重要因素之一。油气两相机械密封因其稳定性高、泄漏率低、使用寿命长,被广泛应用于多相泵设备[4-5]。
多相泵输送介质为组分比例未知的油气两相流体,介质组分的复杂性和波动性是机械密封需解决的难题之一。考虑到在输送油气介质时,含气率波动范围较大,油气两相会同时进入密封端面生成油气混合润滑膜,且甲烷气体易溶解于油相。当密封端面的压力发生变化,甲烷气体会溶解析出,影响密封性能,因此有必要建立油气两相动力润滑密封模型。在多相泵的输送过程中,气液混合物在密封腔内的压力和流量会出现周期性或随机性剧烈波动,高速运动的气液界面在段塞流中对密封环施加瞬时冲击力,引发其轴向浮动及角向偏摆动态响应。此外,当流态从分层流转变为混合流或气泡流时,由于气泡形成、崩溃或合并,流体内会产生局部压力波动,这种波动可能导致密封环或其他密封结构受到冲击[6]。此时若密封环的运动得不到及时补偿,密封端面间的混相润滑膜会受到较大扰动,导致密封环磨损加剧,泄漏增大,甚至失效。因此,研究考虑甲烷溶解时,不同含气率下轴向脉动与角向冲击对油气两相密封瞬态性能和稳定性的影响具有重要意义。
随着工况向高振动、高压力、高速度发展,密封稳定性已成为研究的关键问题[7]。DENNY[8]首先测量了轴向振动引起的机械密封端面间隙的膜厚变化,指出膜厚随轴转速的变化呈周期性变化。LIU等[9]等对波浪倾斜坝机械密封在轴向速度和位移扰动下的瞬态响应进行了分析,结果表明,波幅是影响水动力效应和浮环跟踪性能的重要参数,且当薄膜中发生气蚀时,浮环的倾斜将增加水动力。HU等[10]研究了O型环阻尼对机械密封瞬态响应的影响,并分析了瞬态和稳态性能之间的差异。VARNEY等[11]讨论了机械密封在重接触和轻接触冲击下膜厚度变化的响应规律。LI等[12]建立了三自由度密封动力学模型,对密封系统在不同冲击和位移下的瞬态响应特性进行了研究,结果表明,无论冲击类型如何,密封件都可以保持流体动力润滑状态,以避免明显的表面接触。徐鲁帅等[13,14]针对螺旋槽液膜密封,研究了瞬时变化工况及启动阶段密封性能的变化规律,结果表明在启动阶段转速的增加会使得液膜承载力及厚度增大。郑国运等[15]开展了螺旋槽机械密封三维湍流流场数值计算与端面结构优化设计,得到了最优螺旋角、槽堰比、槽坝比等结构参数的最优值。李勇凡等[16]等建立了三自由度密封动力学模型,研究了密封系统在不同冲击和位移下的瞬态特性,结果表明轴向激励对补偿环角向响应无影响,随偏差值的增大,静环固定角偏差及动环初始角偏差对补偿环轴向响应的影响越发凸显。WANG等[17]建立了机械密封的非牛顿动力学模型,给出了幂律流体对密封瞬态性能的影响。ZHANG等[18]研究了压力波动对密封性能和空化特性的影响,结果表明旋转机械密封对压力波动具有良好的适应性,但位移扰动和转速突变的影响尚未研究。尚雪梅等[19]针对工作在高温环境下的螺旋槽机械密封变形的量化及其影响问题,开展了热变形方面的研究,得到了机械密封动环和静环的变形量。
综上所述,当前对于油气两相机械密封瞬态动力学特性的研究较少,且并未考虑甲烷溶解。本文将瞬态雷诺方程、甲烷溶解度方程与运动学方程相结合,建立考虑甲烷溶解的油气两相流动力润滑的三自由度运动学密封模型。基于有限差分法与欧拉法求解,对比考虑甲烷溶解前后密封对轴向扰动的响应,研究不同含气量下轴向脉动及角向扰动对密封瞬态特性的影响,为油气两相密封在多相泵中的应用提供理论指导。
油气两相密封结构如图1所示,密封环和补偿机构是密封的基本组件。开设动压槽的动环固定在轴上并随轴旋转,静环(轴向浮动环)灵活安装在弹簧座上,并由弹簧和O型圈预紧。在流体动压效应下,2个密封环之间形成微米级的油气混合润滑膜,起到减磨抑漏的作用。在油气混输过程中,段塞流冲击、轴系振动或密封环的制造、装配误差等,易引起动环的轴向跳动及角向偏摆γr,而静环也可能由于补偿机构不完善而存在角偏差γs。
图2为动环端面槽型结构,其主要由槽区、坝区、台区组成。在极坐标下,螺旋槽边界函数定义为r=rieθtanα,ri和ro分别为动环的内、外半径,rg为螺旋槽槽根半径,hg为槽深,α为螺旋角,ω为动环角速度,定义周向槽台比γ=θg/θw,θg和θw分别为槽宽和坝宽,pi和po分别为密封环内径、外径处的压力。油气混合介质流入螺旋槽产生动压效应,在端面间隙形成一层极薄的油气混相膜,槽区膜厚h=ho+hg,坝区膜厚h=ho。
流体膜厚度远小于其他方向的长度,因此忽略膜厚方向压力梯度。此外,为简化计算,提出如下假设:忽略体积力和惯性力;密封端面油气两相流体视为单相拟牛顿流体;流动为层流且等温连续。基于上述假设,具有Jakobson-Floberg-Olsson(JFO)边界条件的瞬态Reynolds方程式如下[13]:
  1r∂∂θh3∂p0∂θ+∂∂rrh3∂p0∂r=6μωr∂hΦ∂θ+12μr∂hΦ∂t
Φ=ρ/ρL
式中,h为密封端面间混相膜瞬时膜厚,μm;p0为密封端面间混相膜瞬时压力,MPa;μ为混相介质黏度,Pa⋅s;Φ为混相膜密度比;ρ为混相膜任一点密度,kg/m3;ρL为混相介质密度,kg/m3。
密封端面压力的变化会引起甲烷在油相中的溶解与析出,为准确预测甲烷溶解与析出对油气两相密封性能的影响,引入甲烷溶解度方程[20]:
c=Vgas/Voil=22 400Kp0xTρoil/MTft0+α0KpMTft0+KpxTρ0ft0Vgm
lnK=481.741/T0-18.387 4
α0=0.000 276 3t0-0.063 33
式中,c为体积溶解度,cm3/cm3;Vgas和Voil分别为溶解平衡时甲烷和油相的体积,cm3;xT=0.853 4和MT=215.36均为油相物性参数;K为平衡常数;α0为二次作用系数;f(t0)为温度系数[21];t0为流体温度,℃;Vgm为介质表观摩尔体积;T0为流体绝对温度,K。
混相的黏度主要由各组分的黏度和质量分数决定,根据式(3),可得出甲烷的质量分数方程[22]:
fgas=ρgasVgasρgasVgas+ρoilVoil=ρgascρgasc+ρoil
式中,fgas为甲烷质量分数。
假设油相中的气体体积分数为β,将密封端面油气两相流体视为单相拟牛顿流体[22],则混合物黏度计算方程如下[23]:
μ=1-βfgasμgas+1-fgasμoil+βμgas
式中,μgas和μoil分别为甲烷与油相的黏度,Pa⋅s。
密封动力学模型图3所示。其中X,Y,Z是固定的空间坐标系;xr,yr,zr是固结在动环上的参考坐标系;xs,ys,zs是固结在静环上的参考坐标系。
当密封介质流动稳定时,考虑动、静环轴向跳动,以及角向偏摆的动态膜厚表达式如下[17]:
hr,θ=h0+hgr,θ+rγsX-γrXsinθ-γsY-γrYcosθ
式中,h0为密封环之间的中心膜厚,μm;γsX,γsY分别为静环X,Y向角偏差,mrad;γrX,γrY分别为动环X,Y向角偏差,mrad。
动环轴向脉动方程和周期性角向偏摆方程分别如下[17]:
hp=Apsin(ωpt+ϕp)
γrX=γrcosωptγrY=γrsinωpt
式中,hp为轴向位移,μm;Ap为脉动幅值,μm;ωp为脉动角速度;ϕp为初始位移相位。
静环轴向及角向动力学方程如下[17]:
msh¨0+DZh˙0+KZh0=F-FcIXγ¨sX+Dγγ˙sX+KγγsX=MXIYγ¨sY+Dγγ˙sY+KγγsY=MY
式中,ms为静环质量,kg;Dz和Dγ分别为轴向和角向的阻尼,N⋅s/m;KZ和Kγ分别为轴向和角向的刚度,N/m;F为液膜开启力,N;Fc为闭合力,N;IX和IY分别为静环对X,Y轴的转动惯量,kg⋅m2;MX和MY分别为静环对X,Y轴的倾覆力矩,计算公式如下[17]:
MX=∬Ωp0rsinθdΩMY=∬Ω-p0rcosθdΩ
Dγ和Kγ可由下式计算[17]:
Dγ=12DZrs2Kγ=12KZrs2
式中,rs是O型圈的径向位置,mm。
采用有限差分法求解密封端面压力。由于运动学方程中倾覆力矩的求解需扩展成全周期计算,因此模型需以全周期计算域计算,控制体差分网格如图4所示。
基于控制体网格,采用中心差分法离散移项后的瞬态方程如下所示。
p0i,j=1/Ei,jAi,jp0i-1,j+Bi,jp0i+1,j+Ci,jp0i,j-1+Di,jp0i,j+1-Fi,jΦ(i,j)+Gi,jΦi-1,j-Hi,j
Φi,j=1/Fi,jAi,jp0i-1,j+Bi,jp0i+1,j+Ci,jp0i,j-1+Di,jp0i,j+1-Ei,jp0i,j+Gi,jΦi-1,j-Hi,j
Ai,j=hi+1/2,j3Δr/(rΔθ)Bi,j=hi-1/2,j3Δr/(rΔθ)Ci,j=(rh3)i,j+1/2Δθ/(Δr)Di,j=(rh3)i,j-1/2Δθ/(Δr)Ei,j=Ai,j+Bi,j+Ci,j+Di,jFi,j=6μωrΔrhi,jGi,j=6μωrΔrhi-1,jHi,j=12μrΔrΔθ[(hΦ)k-(hΦ)k-1]/Δt
求解时边界条件如下:
(1)内外径边界条件。
r=rip0=pir=rop0=po
(2)JFO空化边界条件。
p0>pc,Φ=1         液膜区域p0=pc,0<Φ<1  空化区域
通过求解式(1)得到混膜压力分布之后,求解式(11)得到静环的轴向及角向加速度,再根据欧拉方法,由下式计算得到下一时间步的位置及速度[16],如此循环迭代,直至计算结束。
h˙0t+Δt=h˙0t+h¨0t+ΔtΔtγ˙sXt+Δt=γ˙sXt+γ¨sXt+ΔtΔtγ˙sYt+Δt=γ˙sYt+γ¨sYt+ΔtΔt
h0t+Δt=h0t+h˙0tΔt+h¨0t+ΔtΔt2γsXt+Δt=γsXt+γ˙sXtΔt+γ¨sXt+ΔtΔt2γsYt+Δt=γsYt+γ˙sYtΔt+γ¨sYt+ΔtΔt2
求解过程中迭代精度如式(21)所示。为保证单步长求解的稳定性及程序计算速度,设定时间步长Δt=1×10-6。选择较小Δt能抑制压力场迭代中的数值振荡与发散,尤其在空化、黏度梯度等强非线性耦合时更显著;同时,步长过小会导致时间步数的增加,降低计算速度。因此,综合考虑稳定性与计算成本,选择此步长。
ε=∑i=1imax∑j=1jmaxpi,jnew-pi,jold/pi,jnew<10-6
开启力可由式(22)求解:
F=∫02π∫rirop0drdθ
闭合力可由式(23)求解:
Fc=pspπro2-ri2+piπrb2-ri2+poπro2-rb2
式中,psp为弹簧比压,MPa;rb为平衡半径,mm。
泄漏量计算公式为:
Q=-∫02πrih312μ∂p0∂rdθ
当泄漏量为正值时,密封流体向外径泵送,此时将泄漏量称为泵送量,为负值时,向内径泄漏。
网格无关性验证如图5所示。当网格数量为3 600~14 400时,各性能参数变化范围不超过0.2%,可认为计算结果在此网格范围内达到稳定。同时为保证程序计算速度,单周期计算域网格数量为3 600,全周期网格数量为槽数Ng×3 600。
为验证密封瞬态动力学计算结果的准确性,分别采用文献[13]与[9]中的密封参数进行计算,并与文献中的试验结果进行对比,如图6所示。由图可知,本文计算结果与文献数据变化趋势一致,误差在合理范围内。说明文中所建立动力学模型的准确性,可用于开展后续瞬态动力学性能研究。
油气两相密封瞬态计算参数如表1所示,在后文计算中,除研究某一参数的影响,其余参数将保持不变。
图7示出密封系统受到2 μm轴向扰动时,考虑甲烷溶解前后的瞬态响应结果。由图(a)可知,当密封系统受到扰动后,考虑甲烷溶解效应时,密封瞬态膜厚的波动幅度较小,同时平衡膜厚较小。由图7(b)可知,考虑甲烷溶解效应时,甲烷溶解效应对流体动压存在削弱作用,使得密封系统未受扰动时的开启力较小,受扰动后瞬态开启力波动幅值亦较小。由图7(c)可知,泄漏量的变化规律同膜厚相同,考虑甲烷溶解效应时,瞬态泄漏量的波动幅度及平衡值较小。由上分析可知,甲烷溶解效应对密封性能有重要影响,因此后文分析均为考虑甲烷溶解时的计算结果,不再与未考虑甲烷溶解时作对比。。
当转轴发生轴向脉动时,对密封系统的稳定性有重大影响。脉动形式如式(9)所示,其中ωp取200π。图8示出不同含气率下,由轴向脉动引起的动静环位移响应。由图可知,动环轴向窜动与转轴窜动形式一致。动环轴向窜动引起膜厚的变化,为保持膜厚的稳定性,静环对窜动具有追随性。追随性可分为3个变化阶段:一是振动I阶段(3~8 ms);二是周期性变化阶段(8~23 ms),三是振动II阶段(23~25 ms)。当含气率较大时,静环位移幅度较小,恢复稳定越快。
图9示出不同含气率下,密封性能对轴向脉动的瞬态响应。不同含气率下,中心膜厚的变化规律一致,含气率增大导致介质黏度降低,使中心膜厚的初始值及平衡值有所不同。3个阶段内不同含气率下的开启力响应规律一致。含气率较大时,泵送量较大,这是含气率升高、介质黏度下降导致的。
不同含气率下,静环对动环角向冲击的位移响应如图10所示。动环角向冲击形式如式(10)所示,其中ωp取200π。由图可知,同一含气率下,当动环产生突然的角向冲击时,静环在突变阶段发生角向振动偏摆;含气率较大时,振动幅度及振动时间较小。由于静环在稳定时存在微小角偏差,故静环受动环角向冲击时,平衡位置与动环角向冲击值之间存在偏差Δγ。
以开启力和泄漏量的变化量为因变量,展示不同含气率下密封性能对角向冲击的瞬态响应规律,结果如图11所示。
图11(a)示出不同含气率下,膜厚对动环角向冲击的瞬态响应。由图可知,动环角向冲击对中心膜厚的影响较小,最大膜厚改变量不超过0.09 μm。在初始阶段,中心膜厚振荡变化,随后振动幅度逐渐减小,直至趋于平稳。中心膜厚振动幅度及振动时间随着含气率的增大而减小。
图11(b)示出不同含气率下,开启力和泄漏量对动环角向冲击的瞬态响应。由图可知,角向冲击对开启力和泄漏量的影响均较小,开启力和泄漏量的最大变化分别不超过2.7 N,0.3 mL/min。由于角向冲击过程中闭合力未改变,故不同含气率下稳定阶段的开启力变化量近乎相同。泄漏量变化规律同中心膜厚基本相同,差异在于泄漏量的振动幅度随着含气率的增大而增大。
(1)考虑甲烷溶解效应时,膜厚及泄漏量波动幅度较小,且平衡时数值较小,但波动周期相同。考虑甲烷溶解效应前后的开启力,稳定时数值均为420.6 N。
(2)受冲击后,较高含气率下的膜厚变化较小。在15,25 ms时,膜厚的角向变化量一致,发生周期性波动。
(3)含气率为0~0.8时,密封性能对轴向脉动的响应规律相同。角向冲击对密封性能的影响相对较小,且气体含量为0时,影响最小。
本文假设流体为单相拟牛顿不可压缩流体,在未来的研究中,可对油气两相混膜中,气体可压缩性引发的动力学行为进行系统研究,并与黏度变化带来的影响进行详细的对比分析,以揭示两者的竞争机制及主导作用条件。

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2026年第54卷第1期
94
36
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doi: 10.3969/j.issn.1005-0329.2026.01.006
  • 接收时间:2025-07-25
  • 首发时间:2026-10-22
  • 出版时间:2026-01-30
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  • 收稿日期:2025-07-25
  • 修回日期:2025-11-17
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    1西安交通大学 能源与动力工程学院,西安 710049
    2中国石油大学(华东) 石大山能新能源学院,山东 青岛 266580

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吴伟烽(1980),男,教授,博士生导师,从事制冷低温与压缩机技术研究,通信地址,710049陕西省西安市咸宁西路28号西安交通大学能源与动力工程学院,E-mail:。
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2种不同金属材料的力学参数
科
Family
属数
Number of
genus
种数
Number of
species
占总种数比例
Percentage of
total species (%)
属
Genus
种数
Number of
species
占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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