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Article(id=1286676603728019822, tenantId=1146029695717560320, journalId=1146119989267898375, issueId=1286676566465819629, articleNumber=null, orderNo=null, doi=10.7654/j.issn.2097-1974.20260303, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1753286400000, receivedDateStr=2025-07-24, revisedDate=1774368000000, revisedDateStr=2026-03-25, acceptedDate=null, acceptedDateStr=null, onlineDate=1784697207623, onlineDateStr=2026-07-22, pubDate=1782316800000, pubDateStr=2026-06-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1784697207623, onlineIssueDateStr=2026-07-22, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1784697207623, creator=13041195026, updateTime=1784697207623, updator=13041195026, issue=Issue{id=1286676566465819629, tenantId=1146029695717560320, journalId=1146119989267898375, year='2026', volume='', issue='3', pageStart='1', pageEnd='106', issueExtLink='null', onlineDate='null', pubDate='1782316800000', pubDateStr='2026-06-25', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1784697198739, creator='13041195026', updateTime=1784702152269, updator='13041195026', preIssue=null, nextIssue=null, articleTotal=null, ext={EN=IssueExt(id=1286697343156204129, tenantId=1146029695717560320, journalId=1146119989267898375, issueId=1286676566465819629, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1286697343156204130, tenantId=1146029695717560320, journalId=1146119989267898375, issueId=1286676566465819629, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null, downloadFileDto=null}, startPage=15, endPage=23, ext={EN=ArticleExt(id=1286676603941929327, articleId=1286676603728019822, tenantId=1146029695717560320, journalId=1146119989267898375, language=EN, title=Analysis for Performance Parameter Sensitivity of Staged Combustor Cycle Kerosene/Oxygen Rocket Engine, columnId=1154057566893105509, journalTitle=Missiles and Space Vehicles, columnName=Propulsion, runingTitle=null, highlight=null, articleAbstract=

The performance of staged combustion cycle engines is affected by various uncertain factors, where even minor disturbances may cause the engine's operating conditions to deviate from the designed parameters, compromising system stability. To investigate the influence of uncertain factors (e.g., manufacturing tolerances, turbine and pump performance) on the performance of staged combustion cycle engines, 120-ton LOX/kerosene engine is selected as the research object. A combined approach of single-factor sensitivity screening and Monte Carlo-based multi-factor coupled sensitivity analysis is employed to assess the impact of these disturbances. The results indicate that volume-related factors (e.g., gas generator and thrust chamber) have negligible effects on engine system performance. In contrast, turbine efficiency and nozzle diameter exhibit moderate influence. Under multi-factor coupling conditions, the impact of nozzle diameter on system performance parameters is relatively minor, whereas the turbine stator flow area significantly affects gas generator chamber pressure. Additionally, turbine efficiency and the pump heads of both fuel and oxidizer pumps also influence system performance parameters, albeit with distinct patterns. These findings demonstrate that the combined single-factor/multi-factor sensitivity analysis method provides valuable engineering guidance. Special attention should be paid during design and manufacturing to critical factors such as turbine stator flow area and turbopump efficiency.

, authors=Yu XIE, Wei ZHU, Chenchu ZHOU, Chenpei LI, Haifeng HU, authorsList=Yu XIE, Wei ZHU, Chenchu ZHOU, Chenpei LI, Haifeng HU, authorCompany=null, correspAuthors=null, 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=1286676605263135100, articleId=1286676603728019822, tenantId=1146029695717560320, journalId=1146119989267898375, language=CN, title=补燃循环液氧煤油发动机性能敏感性分析, columnId=1154057567014740326, journalTitle=导弹与航天运载技术（中英文）, columnName=动力系统, runingTitle=null, highlight=null, articleAbstract=

补燃循环发动机性能受多种不确定因素影响，微小的扰动也可能导致发动机实际工况偏离设计工况，影响系统稳定性。为探究加工散差、涡轮泵性能等不确定因素对补燃循环发动机性能的影响程度，以120吨级补燃循环液氧煤油发动机为研究对象，先采用一种单因素敏感性筛选，再基于蒙特卡罗的多因素敏感性耦合分析的方法进行扰动因素影响分析。结果表明：发生器、推力室等容积影响因素对发动机系统性能影响微弱，几乎可以忽略；涡轮效率、推力室喉部直径等因素对系统有一定影响；在多因素耦合的情况下，推力室喉部直径对系统性能参数影响相对较小；涡轮静子流通面积对发生器室压影响显著；涡轮效率及两泵的扬程对系统性能参数也有一定的影响，且影响规律不同。以上结果表明，这种单因素/多因素结合的敏感度分析方法具有一定工程指导意义，在设计加工过程中需要注意涡轮静子流通面积、涡轮泵效率等影响因素。

, authors=谢豫, 朱伟, 周晨初, 李晨沛, 胡海峰, authorsList=谢豫, 朱伟, 周晨初, 李晨沛, 胡海峰, authorCompany=null, correspAuthors=null, authorNote=

谢 豫（1998—），男，工程师，主要研究方向为液体火箭发动机系统数值仿真。

朱 伟（1988—），男，高级工程师，主要研究方向为液体动力数字化设计仿真技术。

周晨初（1990—），男，高级工程师，主要研究方向为液体火箭发动机系统数值仿真与数字化设计。

李晨沛（1993—），女，博士，高级工程师，主要研究方向为液体火箭发动机系统数值仿真与数字化设计。

胡海峰（1986—），男，博士，研究员，主要研究方向为液体动力数字化设计仿真技术。

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谢 豫（1998—），男，工程师，主要研究方向为液体火箭发动机系统数值仿真。

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谢 豫（1998—），男，工程师，主要研究方向为液体火箭发动机系统数值仿真。

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朱 伟（1988—），男，高级工程师，主要研究方向为液体动力数字化设计仿真技术。

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朱 伟（1988—），男，高级工程师，主要研究方向为液体动力数字化设计仿真技术。

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周晨初（1990—），男，高级工程师，主要研究方向为液体火箭发动机系统数值仿真与数字化设计。

"}, bioImg=null, bioContent=

周晨初（1990—），男，高级工程师，主要研究方向为液体火箭发动机系统数值仿真与数字化设计。

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李晨沛（1993—），女，博士，高级工程师，主要研究方向为液体火箭发动机系统数值仿真与数字化设计。

"}, bioImg=null, bioContent=

李晨沛（1993—），女，博士，高级工程师，主要研究方向为液体火箭发动机系统数值仿真与数字化设计。

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胡海峰（1986—），男，博士，研究员，主要研究方向为液体动力数字化设计仿真技术。

"}, bioImg=null, bioContent=

胡海峰（1986—），男，博士，研究员，主要研究方向为液体动力数字化设计仿真技术。

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Sensitivity analysis of civil turbofan engines[J]. 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1—燃料预压泵； 2—氧化剂预压泵； 3—发生器燃料阀； 4—液氧主阀； 5—发生器； 6—点火导管； 7—流量调节器； 8—起动箱； 9—燃料一级泵； 10—燃料二级泵； 11—燃料节流阀； 12—燃料主阀； 13—推力室； 14—氧泵； 15—主涡轮。

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Parameter error table

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参数稳态误差/%动态误差/%
推力室室压2.212.69
主涡轮转速2.055.38
燃料一级泵泵后压力0.511.82
氧主泵泵后压力2.277.88
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选取参数误差表

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参数稳态误差/%动态误差/%
推力室室压2.212.69
主涡轮转速2.055.38
燃料一级泵泵后压力0.511.82
氧主泵泵后压力2.277.88
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Sensitivity of output parameter

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输入参数输出参数
推力发生器室压发生器混合比发生器温度
-5%-3%3%5%-5%-3%3%5%-5%-3%3%5%-5%-3%3%5%
燃料一级泵扬程0.3630.2530.1850.2280.1900.0010.1260.1840.5640.0510.3200.4560.6440.0580.3650.520
氧主泵扬程0.4690.1650.1190.1750.5220.2860.2860.4481.2110.8100.7661.2511.3830.9240.8741.430
推力室喉部直径1.9751.1201.0261.6320.8480.4150.3460.4401.8860.9370.8331.1152.1541.0700.9841.273
主涡轮效率0.5920.4000.3290.5390.3830.350.2000.3220.8490.7900.4840.7960.9700.9020.5520.909
主涡轮静子喉部面积0.6390.3670.4120.6871.6820.9431.0131.6570.1700.2070.1040.0260.1950.2370.1190.211
推力室容积0.0460.0460.04600.1210.1210.12100.1090.1090.10900.1210.1210.1230
发生器容积0.0460.046000.1210.121000.1090.109000.1210.12100
发生器氧头腔容积0.0460.046000.1210.121000.1090.109000.1210.12100
), ArticleFig(id=1286676611831415218, tenantId=1146029695717560320, journalId=1146119989267898375, articleId=1286676603728019822, language=CN, label=表2, caption=

输出参数敏感度

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输入参数输出参数
推力发生器室压发生器混合比发生器温度
-5%-3%3%5%-5%-3%3%5%-5%-3%3%5%-5%-3%3%5%
燃料一级泵扬程0.3630.2530.1850.2280.1900.0010.1260.1840.5640.0510.3200.4560.6440.0580.3650.520
氧主泵扬程0.4690.1650.1190.1750.5220.2860.2860.4481.2110.8100.7661.2511.3830.9240.8741.430
推力室喉部直径1.9751.1201.0261.6320.8480.4150.3460.4401.8860.9370.8331.1152.1541.0700.9841.273
主涡轮效率0.5920.4000.3290.5390.3830.350.2000.3220.8490.7900.4840.7960.9700.9020.5520.909
主涡轮静子喉部面积0.6390.3670.4120.6871.6820.9431.0131.6570.1700.2070.1040.0260.1950.2370.1190.211
推力室容积0.0460.0460.04600.1210.1210.12100.1090.1090.10900.1210.1210.1230
发生器容积0.0460.046000.1210.121000.1090.109000.1210.12100
发生器氧头腔容积0.0460.046000.1210.121000.1090.109000.1210.12100
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补燃循环液氧煤油发动机性能敏感性分析
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谢豫 , 朱伟 , 周晨初 , 李晨沛 , 胡海峰
导弹与航天运载技术（中英文） | 动力系统 2026,(3): 15-23
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导弹与航天运载技术（中英文） |动力系统 2026 , (3) : 15 -23
补燃循环液氧煤油发动机性能敏感性分析
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李晨沛（1993—），女，博士，高级工程师，主要研究方向为液体火箭发动机系统数值仿真与数字化设计。

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胡海峰（1986—），男，博士，研究员，主要研究方向为液体动力数字化设计仿真技术。

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谢豫, 朱伟, 周晨初, 李晨沛, 胡海峰
作者信息
  • 西安航天动力研究所，液体火箭发动机技术重点实验室，西安，710100
作者简介:

谢 豫（1998—），男，工程师，主要研究方向为液体火箭发动机系统数值仿真。

朱 伟（1988—），男，高级工程师，主要研究方向为液体动力数字化设计仿真技术。

周晨初（1990—），男，高级工程师，主要研究方向为液体火箭发动机系统数值仿真与数字化设计。

李晨沛（1993—），女，博士，高级工程师，主要研究方向为液体火箭发动机系统数值仿真与数字化设计。

胡海峰（1986—），男，博士，研究员，主要研究方向为液体动力数字化设计仿真技术。

Analysis for Performance Parameter Sensitivity of Staged Combustor Cycle Kerosene/Oxygen Rocket Engine
Yu XIE, Wei ZHU, Chenchu ZHOU, Chenpei LI, Haifeng HU
Affiliations
  • Xi'an Aerospace Propulsion Institute, Science and Technology on Liquid Rocket Engine Laboratory, Xi'an, 710100
出版时间: 2026-06-25 doi: 10.7654/j.issn.2097-1974.20260303
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摘要
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补燃循环发动机性能受多种不确定因素影响，微小的扰动也可能导致发动机实际工况偏离设计工况，影响系统稳定性。为探究加工散差、涡轮泵性能等不确定因素对补燃循环发动机性能的影响程度，以120吨级补燃循环液氧煤油发动机为研究对象，先采用一种单因素敏感性筛选，再基于蒙特卡罗的多因素敏感性耦合分析的方法进行扰动因素影响分析。结果表明：发生器、推力室等容积影响因素对发动机系统性能影响微弱，几乎可以忽略；涡轮效率、推力室喉部直径等因素对系统有一定影响；在多因素耦合的情况下，推力室喉部直径对系统性能参数影响相对较小；涡轮静子流通面积对发生器室压影响显著；涡轮效率及两泵的扬程对系统性能参数也有一定的影响，且影响规律不同。以上结果表明，这种单因素/多因素结合的敏感度分析方法具有一定工程指导意义，在设计加工过程中需要注意涡轮静子流通面积、涡轮泵效率等影响因素。

补燃循环发动机  /  敏感性分析  /  蒙特卡罗方法  /  多参数分析  /  影响因素

The performance of staged combustion cycle engines is affected by various uncertain factors, where even minor disturbances may cause the engine's operating conditions to deviate from the designed parameters, compromising system stability. To investigate the influence of uncertain factors (e.g., manufacturing tolerances, turbine and pump performance) on the performance of staged combustion cycle engines, 120-ton LOX/kerosene engine is selected as the research object. A combined approach of single-factor sensitivity screening and Monte Carlo-based multi-factor coupled sensitivity analysis is employed to assess the impact of these disturbances. The results indicate that volume-related factors (e.g., gas generator and thrust chamber) have negligible effects on engine system performance. In contrast, turbine efficiency and nozzle diameter exhibit moderate influence. Under multi-factor coupling conditions, the impact of nozzle diameter on system performance parameters is relatively minor, whereas the turbine stator flow area significantly affects gas generator chamber pressure. Additionally, turbine efficiency and the pump heads of both fuel and oxidizer pumps also influence system performance parameters, albeit with distinct patterns. These findings demonstrate that the combined single-factor/multi-factor sensitivity analysis method provides valuable engineering guidance. Special attention should be paid during design and manufacturing to critical factors such as turbine stator flow area and turbopump efficiency.

afterburning cycle engine  /  sensitivity analysis  /  Monte Carlo method  /  multiparameter analysis  /  factors affecting
谢豫, 朱伟, 周晨初, 李晨沛, 胡海峰. 补燃循环液氧煤油发动机性能敏感性分析. 导弹与航天运载技术（中英文）, 2026 , (3) : 15 -23 . DOI: 10.7654/j.issn.2097-1974.20260303
Yu XIE, Wei ZHU, Chenchu ZHOU, Chenpei LI, Haifeng HU. Analysis for Performance Parameter Sensitivity of Staged Combustor Cycle Kerosene/Oxygen Rocket Engine[J]. Missiles and Space Vehicles, 2026 , (3) : 15 -23 . DOI: 10.7654/j.issn.2097-1974.20260303
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0 引 言
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发动机是运载火箭、武器导弹的核心组成部分，也是研发难度最大的部分之一，发动机的研制需要结合流动、燃烧、传热、结构、强度、材料等多专业的知识［1］。发动机的性能参数受到各种因素不确定性与随机性的影响，微小的扰动就可能会导致系统的性能发生较大偏差，造成发射任务失败的风险［2］。掌握对发动机性能影响较大的因素，在研制、生产阶段加以关注并控制，对于保证发动机稳定可靠工作来说是非常必要的。
在工程应用中，常使用敏感性来评价影响因素与相关参数对发动机性能的影响程度［3］。发动机性能参数随输入参数变化而产生的变化量大小称为发动机性能的敏感度，变化量越大，敏感度越高，说明该输入参数对发动机的性能影响越大。因此，通过敏感性分析可以筛选出对发动机性能影响较大的参数，剔除影响较小的次要因素，为产品设计人员或制造人员提供参考。
在液体火箭发动机领域，有学者采用不同的参数敏感性分析方法对不同类型、不同工质的发动机进行了敏感性分析。郑大勇等［4］采用正交试验法分析了氢氧火箭发动机的敏感性，结果表明，涡轮泵的效率特性和个别调节器件特性对于发动机性能参数影响较大。李强等［5］以过氧化氢/煤油补燃循环发动机为研究对象进行敏感性评估，得到了发动机推力、混合比等性能在不同影响因素下的敏感性。巩岩博等［6］引入了方差分析法，以液氧甲烷发动机为研究对象，得到了发动机推力、混合比等性能对同一因素的敏感性。有学者和设计人员通过对发动机进行敏感性分析来指导设计或改善发动机性能。Tong等［7］对发生器循环系统进行了敏感性分析与多目标优化，求解得到了最优系统参数。Nikischenko等［8］通过推导发动机循环参数来降低比冲量损失，改善了液氧煤油上层火箭发动机的性能。Son等［9］在分析发生器循环发动机时考虑了发动机参数的随机变化，结合实例分析和确定参数的方根和方根分析发现发动机部件的加工异常和发动机中存在的随机噪声会改变火箭发动机循环的性能。由此可见，敏感性分析对发动机设计、加工生产有一定指导作用。
本文主要以120吨级补燃循环液氧煤油发动机为研究对象，建立发动机系统仿真模型，采用单因素/多因素敏感性结合的方法对发动机主要性能在不同输入参数的影响下进行分析，既提高了分析效率，又提高了分析深度，得到了影响发动机性能外在因素的显著性大小，以及在推力室喉部直径、头腔容积、涡轮泵扬程等多参数耦合的前提下，各参数对发动机性能的影响，为发动机设计制造提供理论依据。
1 原理与方法
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敏感性分析方法可以用来确定补燃循环发动机系统输入参数对性能影响的大小。本文通过建立系统仿真模型，对输入参数的敏感度进行研究。由于输入参数繁多，首先需要进行单参数的敏感性分析，筛选出了对发动机系统性能有一定影响的参数，而后采用基于蒙特卡罗的多因素敏感性分析，以研究参数对发动机性能影响的大小。原理与方法流程如图1所示。
1.1 仿真模型确认
仿真模型确认是指将仿真模型的仿真值与试验数据进行对比，对其误差进行评估，为后续敏感性分析提供可靠的系统仿真模型。本文将仿真曲线分为稳态与动态两部分进行评估，稳态评估满足式（1）：
e=|De-Dt|Dt×100%
式中 e为稳态误差；Dt为试验数据；De为仿真数据。
动态评估采用包络面积法，以时间轴为自变量对仿真曲线与试验曲线进行积分，则有：
R=|Sp-SA|SA
式中 R为动态误差；Sp为仿真曲线积分；SA为试验曲线积分。
1.2 单因素敏感性分析
目前单因素敏感度常被定义为液体火箭发动机的性能参数相对偏差与影响因素相对偏差之间的比值［10］。若发动机的某一性能参数记为Fi，受到n个输入参数的影响，分别为x1，x2，x3，…，xn，则有数学模型［11］：
Fi=(x1，x2，x3，…，xn)(i=1，2，3，…，m)
取发动机设计状态的仿真结果为基底Fi=f(x¯1，x¯2，x¯3，…，x¯n)(i=1,2,3,…,m)，有发动机的性能参数空间F1,F2,F3,…,Fm，则当空间内某个输入参数xj(j=1,2,3,…,n)变化为xj*时，发动机性能参数空间变化为F1*,F2*,F3*,…,Fm*。记输入参数的偏差量为Δxj=xj*-xj，发动机性能参数的偏差量为ΔFi=Fi*-Fi，则单因素敏感度为S(xj)满足：
S(xj)=|ΔFi|/Fi|Δxj|/xj
从上述单因素敏感度分析可知，输出参数对某一影响因素越敏感，则输出参数的变化就越明显［12］。单因素敏感性分析较为简单，能够快速直观地反映发动机性能随某一影响因素变化的梯度。但是单因素分析方法每次只能对影响因素空间的某一点进行分析，通过对某一方向的局部梯度判断影响因素的作用效果，存在一定片面性［13-14］。
1.3 基于蒙特卡罗的多因素敏感性分析
在单因素敏感性分析的基础上对筛选出的参数进行进一步分析，首先输入参数蒙特卡罗模拟结果的频数分布，然后采用皮尔逊相关系数法进一步分析输入参数对发动机性能影响的显著性大小。
a）蒙特卡罗模拟结果频数分析。
在单因素敏感度分析中，已经分析了对系统性能影响较大的参数，并进行了筛选。在蒙特卡罗模拟中，以筛选出的输入参数为变量，假设每个输入的影响因素都是独立的，将其构成一个独立的正态分布，通过重复n次计算来得到输出参数的频数分布，每一次模拟输入参数以正态分布随机生成。
b）皮尔逊相关系数分析。
为分析输入参数对发动机性能影响的大小，传统方式一般依据正交试验设计原理进行敏感性因素的设计组合，具有均衡分散和整齐可比的特点，这样既可以满足多因素要求，又可以减少多因素组合分析所包含的水平组合数，用部分试验来代替全局试验，通过对部分试验结果的分析，了解全局试验的情况［15］。但是正交试验对每种参数的偏差选择是人为固定的，不具有随机性，因此，本文在蒙特卡罗模拟的基础上，通过计算输入参数与输出参数之间能反映其线性关系的皮尔逊相关系数进行评估，以检验输入参数与输出参数之间的依赖关系。若皮尔逊相关系数为rXY，则满足：
rXY=∑j=1N(Xj-X¯)(Yj-Y¯)∑j=1N(Xj-X¯)2∑j=1N(Yj-Y¯)2
式中 N为X和Y中的元素数；X¯，Y¯分别为X和Y的平均值。
皮尔逊相关系数为-1表示完全负相关，为+1表示完全正相关。为0表示X和Y之间的零依赖关系［16］。
2 系统模型与验证
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以补燃循环液氧煤油发动机为对象开展敏感性分析工作，在敏感性分析之前，需要搭建系统仿真模型［17］，并与试验进行对比，验证模型的准确性。
2.1 系统模型
图2为某补燃循环发动机系统示意［18］，包括氧化剂供应系统、燃料供应系统、吹除系统等。该液氧煤油发动机采用泵压式供应系统、高压补燃循环方案［19］。
2.2 系统验证
为验证仿真模型的合理性，选取了推力室压力Pc、主涡轮转速nt、燃料一级泵泵后压力Pepf1、氧主泵泵后压力Pepo4组参数的仿真值与试验数据归一化曲线进行了对比，如图3所示。随后计算仿真模型的稳态误差与动态误差大小。
a）稳态误差计算。
在发动机整个工作过程中，认为3 s时发动机已进入稳态工作段，选取3 s为稳态误差计算参考点，采用式（1）进行计算，计算结果汇总如表1所示。
b）动态误差计算。
动态误差主要考虑起动段发动机的误差大小，在该发动机的实际起动过程中，认为1~3 s为发动机的起动阶段，选取该阶段为动态误差的评估区间，采用包络法（式（2））进行计算，计算结果汇总如表1所示。
以上结果对比了推力室压力Pc、主涡轮转速nt、燃料一级泵泵后压力Pepf1、氧主泵泵后压力Pepo的稳态与动态误差。根据计算结果，稳态误差最大为2.27%，动态误差最大为7.88%，试验与仿真值拟合较好，整体趋势相似，可认为有较好的一致性。
3 敏感性分析
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单因素敏感性分析具有简单直观、易于操作的优点，但忽略了影响因素之间的相互影响，分析结果可能会失真，适用于初步分析场景［20］。多因素敏感性分析结果准确，能够提高分析深度［21］，但是分析过程较为繁琐，计算资源占用较大。因此，先采用单因素分析初步筛选出对系统影响较大的参数，剔除影响较小的参数，再结合基于蒙特卡罗的多因素分析方法探究该发动机性能的敏感度，进而提高分析结果的准确性，同时减少资源的占用［22］。
3.1 单因素敏感性分析
在进行多因素敏感性分析之前，首先将选取的参数进行单因素敏感度分析，目的在于排除对系统没有影响或影响较小的参数，提高计算效率。敏感度分析参数的选取一般为总装参数（管路长度、通径、流容组件容积等可测量参数）与设计参数（涡轮泵效率、泵扬程、燃烧组件燃烧效率等）。
输出参数对某一输入参数单因素敏感度的大小采用式（3）进行计算。结果为当输入参数发生变化时，输出参数的相对变化量与输入参数的相对变化量的比值，该比值越小则说明输入参数发生一定的偏差时，输出参数的变化越小，即输出参数对输入参数的敏感度越小，反之则说明输出参数对输入参数的敏感度越大。一般当该比值大于0.2时，认为输入参数对输出参数的影响不可忽略，小于0.1时认为输入参数对输出参数影响可忽略，介于0.1与0.2之间时需再进行讨论。
以仿真模型输入参数均未发生偏差的仿真结果为基底，选取燃料一级泵扬程ζf、氧主泵扬程ζo、推力室喉部直径dN、主涡轮效率η、主涡轮静子喉部面积At、推力室容积Vc、发生器容积Vg及发生器氧头腔容积Vgo8组参数。选取发动机推力FN、燃气发生器室压Pgg、发生器混合比Km及发生器温度Tgg为输出参数，计算输出参数的敏感度，具体如表2所示。其中影响因素偏差在-5%~5%之间。由于篇幅有限，这里选取的8个参数并未覆盖模型中所有的输入参数，在实际工程应用当中，如燃烧室燃烧效率、管路参数等可能对系统有较大影响的参数也应考虑。
根据表2的结果，计算不同输入参数对输出参数的单因素平均敏感度，结果如图4所示。
根据以上计算结果可知，在影响因素变化范围内，推力室容积Vc、发生器容积Vg及发生器氧头腔容积Vgo几乎对发动机性能没有影响，在后续进行多因素敏感性分析时，这些影响因素可以忽略。燃料一级泵扬程ζf对发动机系统性能影响较小，具体需进一步进行分析。主涡轮效率η、主涡轮静子喉部面积At、推力室喉部直径dN、氧主泵扬程ζo4个影响因素对输出参数敏感度较大，不可忽略。
3.2 基于蒙特卡罗的多因素敏感性分析
a）频数分布分析。
结合单因素敏感性分析，将筛选出的5个关键输入参数基于蒙特卡罗方法进行多因素敏感性分析。输入参数包括主涡轮效率η、主涡轮静子喉部面积At、推力室喉部流通直径dN、燃料一级泵扬程ζf、氧主泵扬程ζo。输出参数包括燃气发生器室压Pgg、发生器温度Tgg、推力FN及发生器混合比Km。
在实际的发动机产品中，加工的误差、扰动导致的燃烧效率偏差等因素，都会使发动机实际工况偏离设计工况，假设以上选取的输入参数最大偏差均为5%，每个输入参数都是相互独立的，可以构成一个正态分布，中位数在标称值处，在最大偏差处的3σ标准偏差处。将这些参数通过多次随机输入的蒙特卡罗方法来计算获得输出参数的频数分布。
随机次数对模拟结果的准确性有一定影响，模拟次数较少可能会导致结论偏离正确结果，夸大或减小某一输入参数对发动机的性能影响。理论上来说模拟次数越多结果的正确性越高，但是增加模拟次数也会增加时间与计算机资源的成本。因此，为平衡随机模拟的次数，在模拟300次时［16］，能够保证结果的准确性且不会花费过多时间与计算机资源成本。进行300次模拟的结果如图5所示。
图5中横坐标表示输出参数与该参数基底的比值，纵坐标表示落在某一比值范围内的相对频数，即相对频数=频数/模拟次数×100%。通过这种方法可获取在多输入参数的综合影响下，对输出参数的频数影响。
1）发生器混合比与温度相对频数。
发生器混合比和发生器温度频数分布接近正态分布，频数集中于0.98~1.02，但是中心较低，呈现出“双峰”，二者频数分布极为相似。其原因是在数值模拟的模型中，发生器温度通过混合比计算得到，其强依赖于发生器温度。此外，3σ=0.08，说明输入参数发生±5%的偏差下，发生器混合比与温度最大会发生±4%左右的偏差。
2）发生器室压相对频数。
发生器室压的频数在0.94~1.06区间内，即3σ=0.06，方差σ为0.02，说明发生器室压在输入参数发生±5%的偏差下，最大会可能会发生±3%左右的偏差。
3）推力相对频数。
对于推力曲线，呈现出“双峰”，且频数最大值未出现在中心点，说明推力易受到输入参数的影响，且3σ=0.08，推力在输入参数发生±5%的偏差下，最大会发生±4%左右的偏差。
b）敏感性影响大小分析。
为了进一步分析多输入参数的变化影响下，某一输入参数对某一输出参数影响的大小，计算五组输入参数与发动机性能输出参数的无量纲皮尔逊相关系数。通过对皮尔逊相关系数的分析得出输入参数对发动机性能参数的影响大小，直观来看皮尔逊相关系数越大，则该输入参数对输出参数的影响越大。皮尔逊相关系数计算结果如图6所示。
1）发生器混合比。
推力室喉部直径与主涡轮静子流通面积的皮尔逊相关系数约为-0.05，接近于0，可以认为二者的变化对混合比几乎没有影响。而燃料一级泵扬程与氧泵扬程的皮尔逊相关系数均为±0.2左右，说明二者对混合比的影响相当，且呈现相反的趋势，氧泵扬程的增加会使混合比增加，而燃料泵相反。由于燃料一级泵和氧主泵为同轴结构，主涡轮效率提升后，做功能力增加，对氧泵的影响更明显，综合来看，这是由泵特性决定的，因此主涡轮效率对混合比影响相对较大，主涡轮效率的增加会使得发生器混合比增加。
2）发生器温度。
推力室喉部直径与主涡轮静子流通面积对发生器温度几乎没有影响，其皮尔逊相关系数接近0。燃料一级泵扬程与氧泵扬程对发生器温度的影响呈现出相关且相反的趋势。这里可以将燃料一级泵扬程与氧泵扬程对发生器温度和发生器混合比的影响作一个对比，输入参数对温度和混合比的影响完全呈现出相反的状态，通过上述分析可知，发生器为富氧发生器，混合比增加一定会更偏离恰当混合比，从而导致发生器温度降低。主涡轮效率与发生器温度之间呈现负相关状态，是因为影响了混合比进而影响发生器温度。
3）发生器室压。
推力室喉部直径对室压几乎没有影响，主涡轮效率增加会使得氧泵与燃料泵扬程增加，直接影响发生器内推进剂的积累量，从而使室压增加，因此二者呈现出正相关关系。主涡轮静子流通面积直接影响涡轮的流量大小，流量的变化会影响涡轮的功率，从结果上看，主涡轮静子流通面积变大，功率会减小，燃料泵与氧泵的扬程减小，进而影响室压，呈现负相关。随着氧泵扬程的增加，流量增大，使得发生器内燃气积累量增加，室压升高。随着燃料一级泵扬程的增加，燃料泵扬程增加，但是氧泵扬程减少，最终使得发生器内燃气积累量减少，室压降低。
4）推力。
推力室喉部直径对推力影响较小，主要是随着推力室喉部直径变化，整个系统的推进剂流量会有所变化，导致推力变化，呈现出正相关关系。主涡轮效率增加使得推进剂流量增加从而增加了推力，且涡轮效率对推力的影响相对较大。主涡轮静子流通面积直接影响涡轮的流量大小，流量的变化会影响涡轮的功率，从结果上看，主涡轮静子流通面积变大，功率会减小，流量会减小导致推力降低。燃料一级泵扬程增加，使得燃料流量增加，进而燃烧室混合比更接近恰当混合比，温度升高，推力增加。氧泵扬程增加，使得氧泵流量增加，但同时温度会降低。综合来看，由于推进剂有所增加，会使得推力增加，与燃料一级泵扬程相比，氧泵扬程的影响较小。
3.3 小 结
以上分析先采用单因素方法筛选输入参数提高分析效率，再采用多因素方法提高结果精度与深度，简化了整体的分析过程，减少了分析时间与计算机资源占用，小结如下：
a）单因素分析。
单因素，分析量化了各输入参数对发动机性能的影响，结果表明，容积类参数对系统性能影响较小，后续多因素敏感性分析时可以忽略该类参数。其他5个参数对系统性能影响较大，在系统分析时应着重考虑。受篇幅限制，本文未对其他可能对系统有影响的参数进行分析，实际应用时应加以考虑。
b）多因素分析。
基于单因素分析的结果，开展了多因素分析，结果显示，发动机各性能参数在输入参数影响下，频数呈现出大方差、双峰、中心偏移等现象。在皮尔逊相关系数的分析中，输入参数对发动机性能参数均有一定影响，与单因素分析的结果一致。
4 结 论
收起
本文以补燃循环液氧煤油发动机为对象，搭建了120吨级补燃循环液氧煤油发动机系统仿真模型，通过试验验证了模型的准确性，基于模型开展了单因素与多因素敏感度分析，综合了单因素与多因素分析的优势，得到结论如下：
a）推力室容积、发生器容积等参数对于所选取的性能参数影响较小，可忽略不计。两泵扬程、涡轮效率等参数对系统影响较大，在系统设计进行性能优化时应重点考虑。
b）推力室喉部直径、主涡轮静子流通面积等结构化参数对系统性能影响较大，在加工制造时应提高这些参数的加工标准，减少加工散差，以提高发动机工作的稳定性。
本文分析的结果是基于某台次发动机试验与仿真模型实现的。在实际工程应用中，可能会由于不同仿真模型，不同台次发动机以及不同试验导致所得到敏感度显著性有一定差异，但主要影响规律不会发生变化。总体来看，单因素/多因素结合的敏感度分析方法具有一定的参考性，可用于工程指导。

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doi: 10.7654/j.issn.2097-1974.20260303
  • 接收时间：2025-07-24
  • 首发时间：2026-07-22
  • 出版时间：2026-06-25
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  • 收稿日期：2025-07-24
  • 修回日期：2026-03-25
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    西安航天动力研究所，液体火箭发动机技术重点实验室，西安，710100
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