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Article(id=1319293122023108788, tenantId=1146029695717560320, journalId=1316781260334530699, issueId=1319293088569344063, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1005-0329.2025.04.011, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1731254400000, receivedDateStr=2024-11-11, revisedDate=1739376000000, revisedDateStr=2025-02-13, acceptedDate=null, acceptedDateStr=null, onlineDate=1792473591570, onlineDateStr=2026-10-20, pubDate=1745942400000, pubDateStr=2025-04-30, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1792473591570, onlineIssueDateStr=2026-10-20, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1792473591570, creator=13701087609, updateTime=1792473591570, updator=13701087609, issue=Issue{id=1319293088569344063, tenantId=1146029695717560320, journalId=1316781260334530699, year='2025', volume='53', issue='4', pageStart='1', pageEnd='118', issueExtLink='null', onlineDate='null', pubDate='1745942400000', pubDateStr='2025-04-30', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1792473583595, creator='13701087609', updateTime=1792473583595, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=75, endPage=82, ext={EN=ArticleExt(id=1319293122199269557, articleId=1319293122023108788, tenantId=1146029695717560320, journalId=1316781260334530699, language=EN, title=Study on low temperature turbine pneumatic design and performance of impeller with notch, columnId=null, journalTitle=Fluid Machinery, columnName=null, runingTitle=null, highlight=null, articleAbstract=

In view of a low temperature turbine expansion machine with excessive axial load and the insufficient performance study of the gap，firstly，the pneumatic design designed the pneumatic structure of the main structure of the gap，and then simulate the numerical simulation based on the simulation results.The results show that the presence of the impeller gap will change the flow field distribution within the roof gap，the impeller and the depth ratio of the gap，the impeller efficiency and power are reduced，and the axial force decreases.When the gap depth ratio of the gap is 0.3，the equal entropy efficiency decreases by 2.9% compared with 2.4% and the power，and the axial force is reduced by 38.1%.Meet the performance index.This study provides theoretical reference for the application of impeller with gap in low temperature turbine expander.

, authors=Baiqiang LI, Anna DIAO, Yuebo ZENG, Fan YANG, Weiwei YUAN, authorsList=Baiqiang LI, Anna DIAO, Yuebo ZENG, Fan YANG, Weiwei YUAN, authorCompany=null, correspAuthors=Anna DIAO, 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=1319293125743456462, articleId=1319293122023108788, tenantId=1146029695717560320, journalId=1316781260334530699, language=CN, title=带豁口叶轮的低温透平气动设计及性能研究, columnId=1317484287230853622, journalTitle=流体机械, columnName=设计计算, runingTitle=null, highlight=null, articleAbstract=

针对某低温透平膨胀机叶轮轴向载荷过大和带豁口叶轮相关性能研究不足的现状，对原半开式叶轮进行豁口结构进行气动设计，得到4种不同豁口深度的叶轮，并对所设计的各带豁口结构叶轮数学模型进行全流道三维数值模拟，分析不同豁口深度对低温透平膨胀机叶轮的膨胀特性、外泄漏特性，以及叶轮轴向力特性的影响。结果表明，叶轮豁口的存在会改变叶顶间隙、叶轮及泄漏通道内部的流场分布；随着叶轮豁口深度比的增加，叶轮效率、功率有所降低，轴向力呈现先增加、后降低的趋势，其中，在带豁口叶轮豁口深度比为0.3时，相较原半开式叶轮等熵效率降低2.9%，功率降低2.4%，轴向力降低38.1%，在满足性能指标的情况下，使得叶轮轴向载荷有效降低。研究为低温透平膨胀机中带豁口结构叶轮的设计分析提供参考。

, authors=李百强, 刁安娜, 曾跃波, 杨凡, 袁玮玮, authorsList=李百强, 刁安娜, 曾跃波, 杨凡, 袁玮玮, authorCompany=null, correspAuthors=刁安娜, authorNote=

李百强（2000），男，硕士研究生，主要从事透平膨胀机结构设计与CFD流场仿真等工作，E-mail：。

, correspAuthorsNote=
刁安娜（1981），女，博士研究生，研究员，主要研究方向为能源装备开发及应用研究，通信地址：200090上海市闵行区莘庄工业区华宁路3111号中国船舶集团有限公司第七一一研究所，E-mail：。
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李百强（2000），男，硕士研究生，主要从事透平膨胀机结构设计与CFD流场仿真等工作，E-mail：。

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李百强（2000），男，硕士研究生，主要从事透平膨胀机结构设计与CFD流场仿真等工作，E-mail：。

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tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293122023108788, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=17, rfOrder=24, authorNames=null, journalName=null, refType=null, unstructuredReference=ZHANG K L，LI S Y，DUAN Y，et al. Uncertainty quantification of parameters in SST turbulence model for inlet simulation［J］.Acta Aeronautica et Astronautica Sinica，2023，44（Sup.2）：89-99., articleTitle=null, refAbstract=null)], funds=null, companyList=[AuthorCompany(id=1319293125978337487, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293122023108788, xref=null, ext=[AuthorCompanyExt(id=1319293125986726096, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293122023108788, companyId=1319293125978337487, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=Shanghai Marine Diesel Engine Research Institute，Shanghai 200090，China), AuthorCompanyExt(id=1319293125995114705, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293122023108788, companyId=1319293125978337487, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=中国船舶集团有限公司 第七一一研究所，上海 200090)])], figs=[ArticleFig(id=1319293129354752241, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293122023108788, language=EN, label=Fig.1, caption=Schematic diagram of radial surface and scallop depth of turbine expander, figureFileSmall=0dHOkU2PTLfwuE+Z1mGjEw==, figureFileBig=VZpZsnqCeVXpS0Tdgrs4EQ==, tableContent=null), ArticleFig(id=1319293129430249714, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293122023108788, language=CN, label=图1, caption=透平膨胀机流道子午面及豁口深度示意, figureFileSmall=0dHOkU2PTLfwuE+Z1mGjEw==, figureFileBig=VZpZsnqCeVXpS0Tdgrs4EQ==, tableContent=null), ArticleFig(id=1319293129606410483, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293122023108788, language=EN, label=Fig.2, caption=Regional model of turbine expander basin calculation, figureFileSmall=XRqW3HlhHCjBSRkWlnphNg==, figureFileBig=sjCmus+rse2pUmwgqVQRKw==, tableContent=null), ArticleFig(id=1319293129681907956, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293122023108788, language=CN, label=图2, caption=透平膨胀机流域计算区域模型, figureFileSmall=XRqW3HlhHCjBSRkWlnphNg==, figureFileBig=sjCmus+rse2pUmwgqVQRKw==, tableContent=null), ArticleFig(id=1319293129740628213, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293122023108788, language=EN, label=Fig.3, caption=Verification of mesh independence, figureFileSmall=PduWtmtRNn1XykqH3opORA==, figureFileBig=W1HRbNjCHudIhMA/TcA6Sw==, tableContent=null), ArticleFig(id=1319293129807737078, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293122023108788, language=CN, label=图3, caption=网格无关性验证, figureFileSmall=PduWtmtRNn1XykqH3opORA==, figureFileBig=W1HRbNjCHudIhMA/TcA6Sw==, tableContent=null), ArticleFig(id=1319293129870651639, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293122023108788, language=EN, label=Fig.4, caption=Reliability Verification, figureFileSmall=jTVLELwkEAOgRhkO8ZR9xg==, figureFileBig=i7xqsos+CIXmZdZrsDAivg==, tableContent=null), ArticleFig(id=1319293129929371896, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293122023108788, language=CN, label=图4, caption=可靠性验证, figureFileSmall=jTVLELwkEAOgRhkO8ZR9xg==, figureFileBig=i7xqsos+CIXmZdZrsDAivg==, tableContent=null), ArticleFig(id=1319293129988092153, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293122023108788, language=EN, label=Fig.5, caption=Pressure field，temperature field and distribution diagram of turbine expander without notch, figureFileSmall=cbvh1kKsMQ7SH7pcehIJsg==, figureFileBig=xJYzZ5Jh/TJbeTodka/9HA==, tableContent=null), ArticleFig(id=1319293130055201018, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293122023108788, language=CN, label=图5, caption=无豁口时透平膨胀机压力、温度及熵分布

（a）压力分布　　（b）温度分布　　（c）熵分布

, figureFileSmall=cbvh1kKsMQ7SH7pcehIJsg==, figureFileBig=xJYzZ5Jh/TJbeTodka/9HA==, tableContent=null), ArticleFig(id=1319293130130698491, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293122023108788, language=EN, label=Fig.6, caption=Distribution diagram of the turbine expander pressure and temperature under the notch depth ratio of 0.2, figureFileSmall=chIs4IHYeQZIlZ2AvtSsZg==, figureFileBig=t6zHLozH3NHJMhHFkTGgiA==, tableContent=null), ArticleFig(id=1319293130202001660, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293122023108788, language=CN, label=图6, caption=豁口深度比0.2下透平膨胀机压力、温度及熵分布

（a）压力分布　　（b）温度分布　　（c）熵分布

, figureFileSmall=chIs4IHYeQZIlZ2AvtSsZg==, figureFileBig=t6zHLozH3NHJMhHFkTGgiA==, tableContent=null), ArticleFig(id=1319293130273304829, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293122023108788, language=EN, label=Fig.7, caption=Distribution diagram of the turbine expander pressure and temperature under the notch depth ratio of 0.4, figureFileSmall=Zd3eWt2UzE2fS1MjdbBvmA==, figureFileBig=4vXqRDEHoj7io+18nJtcvA==, tableContent=null), ArticleFig(id=1319293130357190910, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293122023108788, language=CN, label=图7, caption=豁口深度比0.4下透平膨胀机压力、温度及熵分布

（a）压力分布　　（b）温度分布　　（c）熵分布

, figureFileSmall=Zd3eWt2UzE2fS1MjdbBvmA==, figureFileBig=4vXqRDEHoj7io+18nJtcvA==, tableContent=null), ArticleFig(id=1319293130436882687, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293122023108788, language=EN, label=Fig.8, caption=Effect of impeller notch depth on turbine efficiency, figureFileSmall=4LQ/ntXbbxNrTNyq8BZ1mg==, figureFileBig=bbn5Fti5YF/cVRVuiOsAAQ==, tableContent=null), ArticleFig(id=1319293130520768768, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293122023108788, language=CN, label=图8, caption=叶轮豁口深度对透平效率的影响, figureFileSmall=4LQ/ntXbbxNrTNyq8BZ1mg==, figureFileBig=bbn5Fti5YF/cVRVuiOsAAQ==, tableContent=null), ArticleFig(id=1319293130596266241, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293122023108788, language=EN, label=Fig.9, caption=Flow field velocity streamline diagram of turbo expander at different notch depth ratios, figureFileSmall=qk41MadccxBckz61fdsIcw==, figureFileBig=GcK6DeRehYbzgFuCBZLNuQ==, tableContent=null), ArticleFig(id=1319293130671763714, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293122023108788, language=CN, label=图9, caption=不同豁口深度比下透平膨胀机流场速度流线

（a）无豁口　　（b）豁口深度比0.3　　（c）豁口深度比0.4

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（a）无豁口　　（b）豁口深度比0.2　　（c）豁口深度比0.4

, figureFileSmall=XnCmUyPnYrVPMU7ja+kP5Q==, figureFileBig=kTTZ5SIQnub+MtLpZ4lipQ==, tableContent=null), ArticleFig(id=1319293131124748553, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293122023108788, language=EN, label=Tab.1, caption=

Design parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
工质质量流量/(kg⋅s-1）进口总压/MPa进口总温/K出口静压/MPa
氮气1.140.94134.150.12
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设计参数

, figureFileSmall=null, figureFileBig=null, tableContent=
工质质量流量/(kg⋅s-1）进口总压/MPa进口总温/K出口静压/MPa
氮气1.140.94134.150.12
), ArticleFig(id=1319293131271549195, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293122023108788, language=EN, label=Tab. 2, caption=

Partial geometric parameters of turbine expander

, figureFileSmall=null, figureFileBig=null, tableContent=
参数数值
喷嘴叶片数ZN/个17
叶轮叶片数ZN/个18
喷嘴叶高/mm2.82
叶轮进口直径/mm157.50
叶轮出口内径、外径/mm29.20，76.20
叶轮叶顶间隙/mm0.50
叶轮转速/（r⋅min-1）27 500
), ArticleFig(id=1319293133213511948, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293122023108788, language=CN, label=表2, caption=

透平膨胀机部分几何参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数数值
喷嘴叶片数ZN/个17
叶轮叶片数ZN/个18
喷嘴叶高/mm2.82
叶轮进口直径/mm157.50
叶轮出口内径、外径/mm29.20，76.20
叶轮叶顶间隙/mm0.50
叶轮转速/（r⋅min-1）27 500
), ArticleFig(id=1319293133309980941, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293122023108788, language=EN, label=Tab.3, caption=

Impeller axial force under different notch depth ratios

, figureFileSmall=null, figureFileBig=null, tableContent=
轴向力无豁口0.10.20.30.4
F15 445.203 725.253 103.482 578.722 144.05
F2-4 484.44-2 660.99-2 271.19-1 953.40-1 727.67
F3-80.36-80.31-80.29-80.38-80.46
合力880.40983.95752.00544.94335.92
), ArticleFig(id=1319293133637136654, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293122023108788, language=CN, label=表3, caption=

不同豁口深度比下的叶轮轴向力

, figureFileSmall=null, figureFileBig=null, tableContent=
轴向力无豁口0.10.20.30.4
F15 445.203 725.253 103.482 578.722 144.05
F2-4 484.44-2 660.99-2 271.19-1 953.40-1 727.67
F3-80.36-80.31-80.29-80.38-80.46
合力880.40983.95752.00544.94335.92
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带豁口叶轮的低温透平气动设计及性能研究
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李百强 , 刁安娜 , 曾跃波 , 杨凡 , 袁玮玮
流体机械 | 设计计算 2025,53(4): 75-82
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流体机械 |设计计算 2025 , 53 (4) : 75 -82
带豁口叶轮的低温透平气动设计及性能研究
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李百强（2000），男，硕士研究生，主要从事透平膨胀机结构设计与CFD流场仿真等工作，E-mail：。

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李百强（2000），男，硕士研究生，主要从事透平膨胀机结构设计与CFD流场仿真等工作，E-mail：。

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李百强 , 刁安娜 , 曾跃波, 杨凡, 袁玮玮
作者信息
  • 中国船舶集团有限公司 第七一一研究所，上海 200090
通讯作者:
刁安娜（1981），女，博士研究生，研究员，主要研究方向为能源装备开发及应用研究，通信地址：200090上海市闵行区莘庄工业区华宁路3111号中国船舶集团有限公司第七一一研究所，E-mail：。
作者简介:

李百强（2000），男，硕士研究生，主要从事透平膨胀机结构设计与CFD流场仿真等工作，E-mail：。

Study on low temperature turbine pneumatic design and performance of impeller with notch
Baiqiang LI , Anna DIAO , Yuebo ZENG, Fan YANG, Weiwei YUAN
Affiliations
  • Shanghai Marine Diesel Engine Research Institute，Shanghai 200090，China
出版时间: 2025-04-30 doi: 10.3969/j.issn.1005-0329.2025.04.011
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摘要
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针对某低温透平膨胀机叶轮轴向载荷过大和带豁口叶轮相关性能研究不足的现状，对原半开式叶轮进行豁口结构进行气动设计，得到4种不同豁口深度的叶轮，并对所设计的各带豁口结构叶轮数学模型进行全流道三维数值模拟，分析不同豁口深度对低温透平膨胀机叶轮的膨胀特性、外泄漏特性，以及叶轮轴向力特性的影响。结果表明，叶轮豁口的存在会改变叶顶间隙、叶轮及泄漏通道内部的流场分布；随着叶轮豁口深度比的增加，叶轮效率、功率有所降低，轴向力呈现先增加、后降低的趋势，其中，在带豁口叶轮豁口深度比为0.3时，相较原半开式叶轮等熵效率降低2.9%，功率降低2.4%，轴向力降低38.1%，在满足性能指标的情况下，使得叶轮轴向载荷有效降低。研究为低温透平膨胀机中带豁口结构叶轮的设计分析提供参考。

透平膨胀机  /  叶轮  /  气动设计

In view of a low temperature turbine expansion machine with excessive axial load and the insufficient performance study of the gap，firstly，the pneumatic design designed the pneumatic structure of the main structure of the gap，and then simulate the numerical simulation based on the simulation results.The results show that the presence of the impeller gap will change the flow field distribution within the roof gap，the impeller and the depth ratio of the gap，the impeller efficiency and power are reduced，and the axial force decreases.When the gap depth ratio of the gap is 0.3，the equal entropy efficiency decreases by 2.9% compared with 2.4% and the power，and the axial force is reduced by 38.1%.Meet the performance index.This study provides theoretical reference for the application of impeller with gap in low temperature turbine expander.

turbine expander  /  impeller  /  pneumatic design
李百强, 刁安娜, 曾跃波, 杨凡, 袁玮玮. 带豁口叶轮的低温透平气动设计及性能研究. 流体机械, 2025 , 53 (4) : 75 -82 . DOI: 10.3969/j.issn.1005-0329.2025.04.011
Baiqiang LI, Anna DIAO, Yuebo ZENG, Fan YANG, Weiwei YUAN. Study on low temperature turbine pneumatic design and performance of impeller with notch[J]. Fluid Machinery, 2025 , 53 (4) : 75 -82 . DOI: 10.3969/j.issn.1005-0329.2025.04.011
正文
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0　引言
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透平膨胀机可为各类应用领域提供所需的制冷量，其中包括工质本身的降温需求和利用工质降温提供低温条件两种应用场景［1］。目前，透平膨胀机的应用范围已从空气分离、天然气液化等传统低温制冷领域，扩展到余压利用及废热回收等能源再生领域［2］。作为低温系统的核心装置，透平膨胀机的性能表现直接关系着系统整体的可靠运行及经济效能，其中，通流部件喷嘴及叶轮则作为能量转换的核心部件，决定了膨胀机性能的优劣。因此，合理的喷嘴及叶轮设计不仅可以有效提高透平膨胀机的效率［3-6］，还能提高膨胀机的稳定性、安全性及经济性。
作为透平膨胀机的关键组件，叶轮的结构性能稳定性直接关系到该设备运行的安全性与可靠性［7］。近年来，国内外学者就透平膨胀机叶轮设计、数值模拟及试验研究等方面，进行了深入的研究与分析。张雁兴等［8］利用CFD软件研究了叶片角对径向透平性能的影响，发现叶轮进口叶片角与气体来流方向差异过大时，会导致等熵效率降低。HUO等［9］利用流体力学仿真研究了低温透平中叶轮平衡孔对轴向力的影响，并分析了平衡孔对透平效率的作用，发现径向位置对轴向力的影响较小。LIU等［10］通过计算分析了ORC余热回收系统中透平叶轮的叶片参数和叶顶间隙，发现当叶顶间隙从0 mm增长至1.2 mm时，效率下降了8.9%。KE等［11］针对低温透平膨胀机在偏离设计参数工况下的运行特性展开研究，基于迭代优化与参数匹配方法实现了工质流量的精准调控，研究证实，采用Hepak实际气体模型开展数值仿真可显著提升计算精度，从而确保性能预测的可靠性。YANG等［12］研究了透平膨胀机内湿空气的凝结过程，通过数值模拟和试验研究，深入探讨了成核过程和液滴分布的相关规律。LI等［13］对透平膨胀机内部流场进行了网格划分和数值模拟，对其压力和速度分布进行了分析。张志航等［14］研究了叶顶间隙对氮低温透平效率的影响，发现叶顶间隙值低于流道出口高度的1.5%，且每增加0.5%间隙量，等熵效率约下降1.5%；非均匀间隙下，径向密封效率损失大于轴向密封。张泽等［15］研究了氦透平膨胀机在降温过程和低温条件下的热力学特性，测试值和仿真结果之间的最大差值为0.45%。
由上述可知，目前相关学者对低温透平膨胀机叶轮叶片角、叶顶间隙等参数对透平性能的影响均进行了深入研究，而对低温透平相关开式叶轮的研究较少，其主要原因是开式叶轮相比半开式及闭式叶轮效率有所降低，但随着低温透平应用领域的拓展及实际应用场景的需求，开式叶轮的应用场景在不断拓展，因此，开展低温透平叶轮豁口对其具体特性影响的研究有所必要。本文基于某氮气低温透平膨胀机，采用CFX软件进行全流场三维数值模拟仿真，对叶轮豁口结构对低温透平性能的影响进行深入分析。
1　通流核心部件设计
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喷嘴和叶轮是通流部件的关键，气体焓降主要在它们内部完成。气体通过喷嘴获得倾斜角后进入叶轮，叶轮旋转使气体膨胀并做功，降低温度。然而，气体在通流部件中的流动复杂，存在流动损失，直接设计气动较为困难。通常采用一元稳定流动理论简化设计，并忽略一些次要损失，通过一维热力计算设计透平膨胀机。喷嘴和叶轮的性能决定了透平的性能，是设计的关键部分。氮低温透平膨胀机的热力设计参数见表1。设计要求等熵效率超过73%，功率超过47 kW。
通过一维流动设计计算，根据喷嘴、叶轮速度等经验参数的选取，经过迭代计算得到低温透平膨胀机的几何参数，其部分几何参数见表2。
根据迭代计算得到的一维几何参数进行通流部件三维结构设计与模型建立，透平膨胀机的叶轮、喷嘴及迷宫密封等部件均通过SOLIDWORKS软件进行绘制。利用所绘得的三维实体模型，可以得到CFD计算所需的计算区域模型，其主要分为喷嘴、叶轮及泄漏通道等3个部分。为便于研究，根据不同叶轮豁口深度分别得到了对应的计算区域模型。其中，透平膨胀机的子午面及叶轮豁口、部分计算区域模型分别如图1、图2所示。
在获取透平膨胀机的通流结构模型之后，需要对其开展更为细致的分析研究，文中针对叶轮轮背不同豁口深度对透平膨胀机性能影响进行研究。豁口深度比的定义式如下：
δ=HR0-R1
式中，H为豁口深度，mm；R0为叶轮入口半径，mm；R1为叶轮出口内径，mm。
由式（1）可知，叶轮的几何尺寸确定后，其豁口深度比与豁口深度呈线性关系。
文中以叶轮豁口深度为变量，分析其对透平性能的影响，忽略其他变量。通过数值模拟和结果对比，研究了包括无豁口在内的5个不同豁口深度比的计算区域模型。
2　数值模拟
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2.1　网格划分
在对通流部件的流场进行数值模拟仿真之前，需要对计算域进行离散处理。计算区域模型利用商业软件Ansys中的MESH模块进行网格划分，其中，Physics Preference（物理偏好）选择CFD，Solver Preference（求解器偏好）选择CFX，确保在进行网格划分时满足使用CFX软件进行数值模拟的需求。同时，在喷嘴、叶轮及泄漏通道的壁面区域均采用网格精细化处理。最终得到网格的质量（正交性、网格伸展比率与网格尺寸）均满足Ansys CFX软件的计算要求。
2.2　湍流模型
透平膨胀机内氮气工质流量大，流速高，非定常且包含多尺度的涡旋结构，属于湍流流动。目前，在旋转机械等工程方面，往往采用雷诺平均N-S方程求解，该方法计算量较少，需要借助湍流模型使方程组封闭。常见的湍流模型为标准k-ε模型、BSL k-ω模型和SST k-ω模型［16］。CFX软件在求解计算中使用的湍流模型为SST k-ω模型。该模型的具体形式为：
∂ρk∂t+∂ρuik∂xj=P1-β*ρωk+∂∂xjμ+σkμt∂k∂xj
∂ρω∂t+∂ρuiω∂xj=γνtP1-βρω2+∂∂xjμ+σωμt∂ω∂xj+2(1-F1)ρσω2ω∂k∂xj∂ω∂xj
该湍流模型主要是对湍动能k和比耗散率ω两个湍流量建立输运方程，式（2）等号右边依次为生成项、耗散项、扩散项，式（3）等号右边依次为生成项、耗散项、扩散项和交叉扩散项［17］。对BSL k-ω模型进行一系列改进得到了SST k-ω湍流模型，其在边界层及其外部的自由剪切流采用标准k-ε模型求解，并且考虑了湍流中剪切应力的输运，因此，该模型既能保证计算的准确性，又可以对近壁现象与自由流动现象进行准确预测。
2.3　边界条件设置
边界条件是流动工质（即氮气）在边界上的确定性条件，比如温度、压力、流量等。数值计算收敛残差设置为10-6，边界条件：（1）进口气体为总温134.15 K和总压0.94 MPa；（2）出口气体为静压，叶轮出口设置为0.12 MPa，迷宫密封泄漏通道出口设置为0.20 MPa；（3）设置叶轮转速27 500 r/min。同时，对边界面和工质进行设置，动静转子交界面上各项参数的信息传递采用General Grid Interface（GGI）连接，动静交界面设置为“Stage（Mixing-Plane）”。在透平流道中模拟计算所用工质为氮气，由NIST查询的热物理性质数据导入到CFX软件中，完成物性设置。
2.4　网格无关性验证
构建了6个叶轮豁口深度不同的计算区域模型，并通过选取无豁口模型进行网格无关性验证，确保计算精度。网格无关性验证见图3。结果显示，当网格总数达到1 861万时，等熵效率值的波动小于0.1%，表明网格模型在该数量下已达到无关性。
2.5　可靠性验证
为了验证本研究所建数值模型的可靠性，采用无豁口叶轮进行样机试验。图4示出不同膨胀比下，质量流量和等熵效率的模拟与试验结果对比。可以看出，仿真值与实测值趋于一致，误差较小。质量流量和等熵效率的最大相对误差分别不超过3.1%和2.5%，证实了数值模型的可靠性。
3　结果分析
收起
3.1　膨胀特性分析
分别对豁口深度比为0，0.2，0.4的透平流场进行分析讨论。不同豁口深度的透平膨胀机压力、温度及熵分布如图5~7所示。
由图5（a）、6（a）、7（a）可看出，氮气在通流部件内膨胀导致压力下降，流场压力呈放射状分布。最低压力位于叶轮出口的轮毂区域而非叶顶处，因为叶顶间隙导致潜流损失，部分气体未膨胀，使得叶顶压力高于轮毂。对比压力分布图可看出，随着豁口深度的增加，叶轮叶顶处压降区域减小，豁口深度比为0.4时压降区域消失，豁口底部轮毂交界处压力明显下降，表明叶轮豁口显著改变压力分布。
分析图5（b）、6（b）、7（b），喷嘴区域气流温度呈中心对称，叶轮区域叶片出口压力面温度高于吸力面，豁口底部与轮毂交界处温度变化大。由图5（c）、6（c）、7（c）可以看出，喷嘴区域熵增主要出现在主体和出口，叶轮区域熵增则横向扩展，叶片处从根部向顶部扩散。对比不同叶轮豁口深度的熵分布，发现豁口内部无熵增，气体在豁口外部熵增集中。这说明叶轮豁口显著改变透平叶轮的熵分布，影响叶轮流场和效率。
叶轮豁口深度对透平效率的定量影响关系如图8所示。
随着叶轮豁口深度增加，透平等熵效率逐渐降低。与无豁口模型相比，叶轮豁口深度比为0.1时，效率下降1.9%。但效率下降趋势随豁口深度比增加而减缓，深度比为0.4时，效率降低3.42%。
3.2　泄漏特性分析
影响透平膨胀机性能的因素除了流道损失，泄漏损失也是其中之一。泄漏损失包含内泄漏和外泄漏。内泄漏主要指叶轮内部的泄漏，如叶顶间隙泄漏，不影响气体流量，但减少做功气体量。外泄漏涉及低温气体通过壁面导热和叶轮背侧向壳体内的泄漏。文中假设叶顶间隙固定且忽略漏热，重点分析叶轮豁口深度变化对透平膨胀机内泄漏损失的影响。为降低气体泄漏，透平膨胀机叶轮背侧设计了迷宫密封通道。
不同豁口深度比下透平膨胀机截面的流场速度流线如图9所示。可以看出，在喷嘴出口与叶轮进口之间的图中标识区域（图9（c）黑框）气流发生逆向流动并形成涡旋结构，导致喷嘴与叶轮之间工质产生回流损失。有豁口时，泄漏通道内的流动比无豁口时复杂。叶轮豁口内形成半封闭区域，流体顺着压力梯度从喷嘴出口泄漏至豁口区域。
从图可见，叶轮豁口深度增加，豁口区域对流场分布影响增大，底部出现涡流，加剧外泄漏。对于低温透平膨胀机而言，叶轮豁口的存在会较大程度地影响低温气体在泄漏通道内的流场分布，导致透平膨胀机流量及功率降低。
图10示出不同豁口深度比对透平膨胀机的叶轮背侧向壳体的泄漏量及功率的影响。
从图10可以发现，无豁口时泄漏量仅为0.247 g/s；当叶轮豁口深度比为0.1时，泄漏量增至0.963 g/s，随着叶轮豁口深度比的增大，叶轮背侧向壳体泄漏量逐步增加，在叶轮豁口深度比由0.3增大至0.4时，气体泄漏量由2.205 g/s增至3.508 g/s，表明叶轮豁口深度比的增大将导致透平膨胀机外泄漏量大幅度增加，这将使得透平膨胀机流量有所降低。透平膨胀机功率和效率的变化趋势相似，主要受流量减少和等熵效率下降影响。无豁口时功率为52.57 kW，豁口深度比为0.1时为51.31 kW，豁口深度比为0.3时为50.56 kW，相对原始叶轮降低2.4%。表明豁口会减少功率，但功率下降速度随豁口深度比增加而减慢。
3.3　叶轮轴向力特性分析
文中所用氮低温透平膨胀机的冷量大，工质流量大，进出口压降高，叶轮的轴向力大，对轴承的要求高。根据实际工程应用，轴向推力在500~700 N范围内更便于轴承的选型。
叶轮轴向力分布见图11。计算中，叶轮上的轴向力被简化为三部分：背部气体压力F1，气体流动方向变化产生的动量变化轴向推力F2，以及叶轮出口气体对端面的压力F3。轴向推力计算主要运用经验模型法、理论解析方法和CFD数值仿真技术。研究透平膨胀机叶轮气动推力的核心在于精确分析轮背与固壁间隙内的压力场分布。
利用CFD数值模拟，分析了叶轮轮背间隙中的压力分布和轴向推力。图12为不同豁口深度下轮背侧外壁面的压力分布。
由图12可以看出，无豁口时叶轮背侧气膜最大压力0.43 MPa，豁口存在时增至0.46 MPa，最小压力基本保持不变。豁口深度比增加导致叶轮背侧气膜压力变化更显著，压力梯度增大，这是因为豁口深度影响了低温气体在泄漏通道内的流场分布。
根据上述计算方法，表3列出透平膨胀机叶轮的轴向力（表中正数表示力的方向与图11所示的正方向相同）。可以看出，无豁口时叶轮的轴向力为880.4 N，豁口深度比为0.1时增至983.95 N，豁口深度比为0.3时降至544.94 N，此时转子轴向力相对原始叶轮降低了38.1%。这表明叶轮的轴向力随豁口深度的增加而先增大、后减小。
4　结论
收起
（1）叶轮豁口会影响压力和流场分布，导致效率降低。随着豁口深度比增大，叶轮叶顶处压降区域逐渐缩小。透平等熵效率在叶轮豁口深度比为0.1时下降1.9%，但效率下降趋势随豁口深度比增加而减缓。
（2）叶轮豁口会影响低温气体流场分布，豁口深度比增大导致泄漏量显著上升。无豁口时泄漏量为0.247 g/s，豁口深度比为0.4时泄漏量增至3.508 g/s。外泄漏损失会降低透平功率，功率下降趋势与等熵效率变化相似。当豁口深度比为0.3时，透平膨胀机功率为50.56 kW。
（3）随着豁口深度比增大，叶轮背侧气膜压力梯度有所增大。叶轮轴向力随豁口深度比的增加，呈现先增加、后降低的趋势，豁口深度比为0.1时，叶轮轴向力由初值880.4 N增至983.95 N，但豁口深度继续增大时，轴向力急剧降低，豁豁口深度比为0.3时降至544.94 N。
（4）在豁口深度比为0.3时，叶轮等熵效率和功率输出降至77.56%和50.56 kW，产生的轴向力为544.94 N，转子轴向力降低38.1%，此时该设计结构不仅满足热力性能参数要求，还有效降低了叶轮轴向载荷。

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2025年第53卷第4期
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doi: 10.3969/j.issn.1005-0329.2025.04.011
  • 接收时间：2024-11-11
  • 首发时间：2026-10-20
  • 出版时间：2025-04-30
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  • 收稿日期：2024-11-11
  • 修回日期：2025-02-13
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    中国船舶集团有限公司 第七一一研究所，上海 200090

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刁安娜（1981），女，博士研究生，研究员，主要研究方向为能源装备开发及应用研究，通信地址：200090上海市闵行区莘庄工业区华宁路3111号中国船舶集团有限公司第七一一研究所，E-mail：。
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