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Article(id=1271501752902820263, tenantId=1146029695717560320, journalId=1210938733613449225, issueId=1271501633826530070, articleNumber=PA20260121_i7eDNiQF, orderNo=null, doi=10.19666/j.rlfd.202504065, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1744992000000, receivedDateStr=2025-04-19, revisedDate=1747670400000, revisedDateStr=2025-05-20, acceptedDate=1748188800000, acceptedDateStr=2025-05-26, onlineDate=1781079241252, onlineDateStr=2026-06-10, pubDate=1769270400000, pubDateStr=2026-01-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1781079241252, onlineIssueDateStr=2026-06-10, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1781079241252, creator=admin, updateTime=1781079241252, updator=admin, issue=Issue{id=1271501633826530070, tenantId=1146029695717560320, journalId=1210938733613449225, year='2026', volume='55', issue='1', pageStart='1', pageEnd='186', issueExtLink='null', onlineDate='null', pubDate='1769270400000', pubDateStr='2026-01-25', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1781079212860, creator='ztmeta', updateTime=1786698917413, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext={EN=IssueExt(id=1295072383149301815, tenantId=1146029695717560320, journalId=1210938733613449225, issueId=1271501633826530070, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1295072383149301816, tenantId=1146029695717560320, journalId=1210938733613449225, issueId=1271501633826530070, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null, downloadFileDto=null}, startPage=134, endPage=141, ext={EN=ArticleExt(id=1271501754026893738, articleId=1271501752902820263, tenantId=1146029695717560320, journalId=1210938733613449225, language=EN, title=Reconstruction of flame physical fields via active and passive combined method under double regularization constraints, columnId=1211002405299294959, journalTitle=Thermal Power Generation, columnName=Thermal energy science research, runingTitle=null, highlight=null, articleAbstract=

The signals of flame spontaneous emission (passive method) and absorption spectrum (active method) are two commonly used optical measurement methods for reconstructing the combustion physical field. Developing an active and passive combined method by combining the respective advantages of the two methods will provide a new means for combustion detection. By introducing a laser absorption optical path into the passive measurement system to simultaneously obtain the spontaneous emission and absorption spectral signals of the flame, the combustion temperature field and the initial component concentration field reconstructed by the passive method are introduced into the active method reconstruction. The active and passive combined method is developed by combining the double regularization constraints of smoothness and the prior concentration physical field. Simulation reconstructions are carried out for typical single-peak and double-peak axisymmetric flame sections. When the measurement error is 1.00%, the average errors of the single-peak and double-peak flame combustion temperature field reconstructions are 0.92% and 1.32% respectively, and the average errors of water vapor volume fraction are 3.05% and 3.31% respectively. The results show that under the double regularization constraints, the reconstruction accuracy of water vapor concentration by the active and passive combined method is significantly improved compared with the passive method, and the number of required laser optical paths is greatly reduced compared with that of the active method, achieving accurate measurement of the combustion temperature field and component concentration field using a simple measurement system.

, authors=Ningjing ZHU, Zhe WANG, Leiheng DU, Liangying YU, Zhifeng HUANG, authorsList=Ningjing ZHU, Zhe WANG, Leiheng DU, Liangying YU, Zhifeng HUANG, authorCompany=null, correspAuthors=Zhifeng HUANG, 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=1271501753963979177, articleId=1271501752902820263, tenantId=1146029695717560320, journalId=1210938733613449225, language=CN, title=双重正则化约束下主被动结合方法重建火焰物理场, columnId=1211002405437706993, journalTitle=热力发电, columnName=热能科学研究, runingTitle=null, highlight=null, articleAbstract=

利用火焰自发辐射（被动法）与吸收光谱（主动法）信号重建燃烧物理场是常用的2种光学测量方法，结合2种方法各自优势发展主被动结合方法将为燃烧检测提供新手段。通过在被动法测量系统中引入1条激光吸收光路同时获得火焰自发辐射和吸收光谱信号，将被动法重建的燃烧温度场和组分初始浓度场引入主动法重建中，结合平滑性与先验浓度物理场双重正则化约束发展主被动结合方法。针对典型单峰与双峰轴对称火焰截面开展模拟重建，当测量误差为1.00%时，单峰与双峰火焰燃烧温度场重建平均误差分别为0.92%和1.32%，水蒸气体积分数平均误差分别3.05%和3.31%。结果表明，双重正则化约束下主被动结合方法水蒸气体积分数重建精度相较于被动法明显提升，相比于主动法所需布置激光光路数大幅减少，实现了利用简单测量系统的燃烧温度场和组分浓度场准确测量。

, authors=朱宁静, 王哲, 杜雷恒, 余亮英, 黄志锋, authorsList=朱宁静, 王哲, 杜雷恒, 余亮英, 黄志锋, authorCompany=null, correspAuthors=黄志锋, authorNote=

朱宁静（1998），男，硕士研究生，主要研究方向为燃烧诊断检测，。

, correspAuthorsNote=
黄志锋（1982），男，博士，教授，主要研究方向为燃烧检测、辐射传递计算，。
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朱宁静（1998），男，硕士研究生，主要研究方向为燃烧诊断检测，。

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朱宁静（1998），男，硕士研究生，主要研究方向为燃烧诊断检测，。

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Applied Optics, 2013, 52(20): 4827-4842., articleTitle=Measurement of nonuniform temperature and concentration distributions by combining line-of-sight tunable diode laser absorption spectroscopy with regularization methods, refAbstract=null)], funds=[Fund(id=1295064716615905799, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1271501752902820263, awardId=52476086, language=EN, fundingSource=National Natural Science Foundation of China(52476086), fundOrder=null, country=null), Fund(id=1295064716670431752, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1271501752902820263, awardId=52476086, language=CN, fundingSource=国家自然科学基金项目(52476086), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1295064707556209101, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1271501752902820263, xref=null, ext=[AuthorCompanyExt(id=1295064707568792014, tenantId=1146029695717560320, journalId=1210938733613449225, 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volume fraction reconstructed by the active and passive combined method, figureFileSmall=ZlIgIQxomHDQFRNsDMnTJg==, figureFileBig=OHe8IJ5leHHk731MRWfd/w==, tableContent=null), ArticleFig(id=1295064715990954496, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1271501752902820263, language=CN, label=图8, caption=主被动结合法重建水蒸气体积分数分布, figureFileSmall=ZlIgIQxomHDQFRNsDMnTJg==, figureFileBig=OHe8IJ5leHHk731MRWfd/w==, tableContent=null), ArticleFig(id=1295064716079034881, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1271501752902820263, language=EN, label=Fig.9, caption=Reconstruction deviations of H2O volume fraction of different methods, figureFileSmall=lI/3qIE1eyGheBXrIF4wtw==, figureFileBig=tghBpbwXHu9fUWG5DpyWZA==, tableContent=null), ArticleFig(id=1295064716150338050, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1271501752902820263, language=CN, label=图9, caption=不同方法水蒸气体积分数分布重建偏差, figureFileSmall=lI/3qIE1eyGheBXrIF4wtw==, figureFileBig=tghBpbwXHu9fUWG5DpyWZA==, tableContent=null), ArticleFig(id=1295064716238418435, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1271501752902820263, language=EN, label=Tab.1, caption=

Selected water vapor absorption transition parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
谱线序号波数/cm–1296 K时的线强S/（cm–2·MPa–1）低态能级/cm–1
17 407.788.21×10-2882.89
27 417.821.05×10-11 079.08
37 419.172.17×10-1842.36
47 424.691.14×10-21 477.30
57 427.958.67×10-31 340.86
67 429.724.44×10-2982.91
77 432.312.29×10-21 050.16
87 441.168.59×10-31 581.37
97 444.361.09×10-21 786.00
107 447.482.17×10--21 360.24
117 450.935.26×10-31 690.66
127 454.441.79×10-31 962.51
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选定水蒸气吸收跃迁参数

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谱线序号波数/cm–1296 K时的线强S/（cm–2·MPa–1）低态能级/cm–1
17 407.788.21×10-2882.89
27 417.821.05×10-11 079.08
37 419.172.17×10-1842.36
47 424.691.14×10-21 477.30
57 427.958.67×10-31 340.86
67 429.724.44×10-2982.91
77 432.312.29×10-21 050.16
87 441.168.59×10-31 581.37
97 444.361.09×10-21 786.00
107 447.482.17×10--21 360.24
117 450.935.26×10-31 690.66
127 454.441.79×10-31 962.51
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Average reconstruction deviations of H2O volume fraction of different methods

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激光光路数火焰类型扫描跃迁数量重建偏差/%
1（主被动结合法）单峰火焰123.05
双峰火焰123.31
0（被动法）单峰火焰6.18
双峰火焰7.10
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不同方法水蒸气体积分数分布重建平均偏差

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激光光路数火焰类型扫描跃迁数量重建偏差/%
1（主被动结合法）单峰火焰123.05
双峰火焰123.31
0（被动法）单峰火焰6.18
双峰火焰7.10
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双重正则化约束下主被动结合方法重建火焰物理场
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朱宁静 , 王哲 , 杜雷恒 , 余亮英 , 黄志锋
热力发电 | 热能科学研究 2026,55(1): 134-141
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热力发电 |热能科学研究 2026 , 55 (1) : 134 -141
双重正则化约束下主被动结合方法重建火焰物理场
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朱宁静 , 王哲, 杜雷恒, 余亮英, 黄志锋
作者信息
  • 武汉大学动力与机械学院，湖北 武汉 430072
通讯作者:
黄志锋（1982），男，博士，教授，主要研究方向为燃烧检测、辐射传递计算，。
作者简介:

朱宁静（1998），男，硕士研究生，主要研究方向为燃烧诊断检测，。

Reconstruction of flame physical fields via active and passive combined method under double regularization constraints
Ningjing ZHU , Zhe WANG, Leiheng DU, Liangying YU, Zhifeng HUANG
Affiliations
  • School of Power and Mechanical Engineering, Wuhan University, Wuhan 430072, China
出版时间: 2026-01-25 doi: 10.19666/j.rlfd.202504065
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摘要
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利用火焰自发辐射（被动法）与吸收光谱（主动法）信号重建燃烧物理场是常用的2种光学测量方法，结合2种方法各自优势发展主被动结合方法将为燃烧检测提供新手段。通过在被动法测量系统中引入1条激光吸收光路同时获得火焰自发辐射和吸收光谱信号，将被动法重建的燃烧温度场和组分初始浓度场引入主动法重建中，结合平滑性与先验浓度物理场双重正则化约束发展主被动结合方法。针对典型单峰与双峰轴对称火焰截面开展模拟重建，当测量误差为1.00%时，单峰与双峰火焰燃烧温度场重建平均误差分别为0.92%和1.32%，水蒸气体积分数平均误差分别3.05%和3.31%。结果表明，双重正则化约束下主被动结合方法水蒸气体积分数重建精度相较于被动法明显提升，相比于主动法所需布置激光光路数大幅减少，实现了利用简单测量系统的燃烧温度场和组分浓度场准确测量。

燃烧检测  /  主被动结合方法  /  火焰物理场重建  /  双重正则化约束

The signals of flame spontaneous emission (passive method) and absorption spectrum (active method) are two commonly used optical measurement methods for reconstructing the combustion physical field. Developing an active and passive combined method by combining the respective advantages of the two methods will provide a new means for combustion detection. By introducing a laser absorption optical path into the passive measurement system to simultaneously obtain the spontaneous emission and absorption spectral signals of the flame, the combustion temperature field and the initial component concentration field reconstructed by the passive method are introduced into the active method reconstruction. The active and passive combined method is developed by combining the double regularization constraints of smoothness and the prior concentration physical field. Simulation reconstructions are carried out for typical single-peak and double-peak axisymmetric flame sections. When the measurement error is 1.00%, the average errors of the single-peak and double-peak flame combustion temperature field reconstructions are 0.92% and 1.32% respectively, and the average errors of water vapor volume fraction are 3.05% and 3.31% respectively. The results show that under the double regularization constraints, the reconstruction accuracy of water vapor concentration by the active and passive combined method is significantly improved compared with the passive method, and the number of required laser optical paths is greatly reduced compared with that of the active method, achieving accurate measurement of the combustion temperature field and component concentration field using a simple measurement system.

combustion detection  /  active and passive combined method  /  reconstruction of flame physical field  /  double regularization constraints
朱宁静, 王哲, 杜雷恒, 余亮英, 黄志锋. 双重正则化约束下主被动结合方法重建火焰物理场. 热力发电, 2026 , 55 (1) : 134 -141 . DOI: 10.19666/j.rlfd.202504065
Ningjing ZHU, Zhe WANG, Leiheng DU, Liangying YU, Zhifeng HUANG. Reconstruction of flame physical fields via active and passive combined method under double regularization constraints[J]. Thermal Power Generation, 2026 , 55 (1) : 134 -141 . DOI: 10.19666/j.rlfd.202504065
正文
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燃烧温度和气体浓度分布是反映燃烧速率和燃烧产物的关键指标，对于开发新型燃烧技术、了解燃烧状态和优化燃烧至关重要[1-3]。光学测量方法以其非侵入、响应快、高维测量灵活等优点被广泛应用[4]。根据所使用的信号不同，光学测量方法可分为被动法和主动法。被动法依靠火焰的自发辐射作为检测信号，而主动法利用外部光源穿过火焰介质被吸收后光强作为检测信号。
被动法不需要外部光源，通过单个成像探测器即可方便地采集火焰不同方向的发射信息[1，5]，这使得检测设备非常简单，具有工业应用前景[1-3]。Liu等人[6]利用双色辐射图像测量烟黑火焰三维温度和烟尘体积分数。谢正超等[7]利用多光谱成像技术重建了火焰温度和烟尘体积分数。Cheng等人[8]在燃烧产物主要为气体介质的情况下，应用谱带积分比值方法（integrated spectral band ratio，ISBR）进行三维温度和气体浓度测量。在被动法测量工作中，通过对比分析发现，介质浓度场测量精度明显低于温度场测量精度。在利用双色图像的重建工作中[9]，信噪比为54 dB时，燃烧温度的最大误差小于1.5%，而碳烟体积分数的最大误差接近11%。在使用多光谱图像时，当信噪比为54 dB时，火焰温度平均误差为0.24%，碳烟浓度平均误差为3.17%[10]。类似地，在基于气体自发辐射的燃烧检测中，气体浓度的反演精度同样显著低于温度反演精度[7-8]。
在主动法燃烧检测中，利用激光吸收信号的可调谐二极管激光吸收光谱方法（tunable diode laser absorption spectroscopy，TDLAS）广泛用于组分浓度测量[11]。在非均匀火焰中，多激光路径的TDLAS方法通常与计算机层析成像（absorption tomography，AT）算法相结合，重建温度和物质浓度的二维或三维分布[12-13]。实际应用中为了收集足够的吸收信息，AT方法需要布置大量激光吸收路径，测量系统非常复杂，给实际工业应用带来了挑战。
针对被动法和主动法各自在介质浓度测量精度低和测量系统复杂方面的不足，本文提出一种被动法（ISBR方法）和主动法（AT方法）相结合的测量方法，以实现利用简单测量系统的燃烧温度场和介质浓度场准确测量。文中将首先介绍所发展主被动结合方法的基本理论和重建过程。接着以轴对称火焰为对象，开展模拟实验研究，验证所发展方法的重建精度。
1　火焰重建理论
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1.1　火焰辐射理论
1.1.1　气体自发辐射
在无颗粒火焰中气体组分的散射作用极小，可以忽略不计，因此燃烧区域的辐射传递方程为：
dIηds=κηIb,η−κηIη
式中：Iη和Ib，η分别为波数η下的光谱辐射强度和黑体光谱辐射强度；Κη为燃烧场气体光谱吸收系数；s为辐射光束在火焰气体介质中传递的几何距离。
对于实验室小尺寸火焰，自吸收可以忽略不计。由此化简并积分后可得到冷黑边界下窄波段[η1，η2]内气体发射辐射Iband为：
Iband=∫η1η2Iηdη=Δs∫η1η2κηIb,ηdη
在一个较窄波段内，高温气体光谱辐射强度近似不变，代入气体吸收系数计算公式可得[11]：
Iband=Δs∫η1η2κηIb,ηdη=Δs⋅Ib(T,η1+η22)⋅∫η1η2κηdη=Δs⋅Ib(T,η1+η22)⋅N(T,p)⋅∑ηi∈[η1,η2]Si(T)
式中：Ib为黑体辐射强度；Si（T）为第i条谱线的线强函数；N（T，p）为气体分子数密度；T为气体温度；p为压力。开放火焰压力为当地大气压。
1.1.2　气体吸收光谱
激光在无颗粒火焰中入射光强与出射光强间关系可以使用Beer-Lambert定律描述，波数η下激光透射率τη为：
τη=(II0)=exp(−κηLs)=exp[−S(T)ϕ(η)XipLs]
式中：Ls为激光在吸收介质内穿过的路径；Xi为气体浓度，其与N（T，p）可按如下公式换算。
N(T,p)=NLTrefTXippref
式中：NL为4.12×10–5 mol/cm3；Tref为参考温度，取296 K；pref为参考压力，取1.0个标准大气压。
定义吸光度αη为：
αη=−ln(II0)=XipS(T)ϕ(η)Ls
对吸光度αη在频域内积分，并对线型函数Φ（η）在频域做归一化处理，即可获得积分吸光度A。
A=∫−∞+∞αηdη=∫−∞+∞S(T)ϕ(η)Xi pLsdη=S(T)Xi pLs
1.2　主被动结合方法
双重正则化约束的主被动结合方法计算流程如图1所示。首先由被动法（ISBR方法）重建出火焰温度场与初始组分浓度场，并将该初始组分浓度场作为与平滑约束类似的先验物理场约束，在上述双重约束下利用主动法（AT方法）吸收信号重建获得更为精确的火焰组分浓度场。
1.2.1　轴对称火焰重建模型
对轴对称火焰，其网格划分和主被动方法测量原理如图2所示。对于主被动结合方法，实际测量中两者布置并作用于同一火焰测量对象。
对于编号为r自发辐射束，根据1.1.1节理论，其强度为：
Iband(r)=∑n=1NΔl(r,n)∫η1η2Ib,η(n)κη(n)dη
式中：Ib，η（n）和Κη（n）分别为n号圆环内气体黑体光谱辐射强度及光谱吸收系数；Δl（r，n）为r号自发辐射束在n号网格中穿过路径长度；N为重建区域总网格数。
火焰黑体光谱辐射和吸收系数决定了火焰辐射能量大小，可以用辐射源项Hband（n）表示为：
Hband(n)=∫η1η2Ib,η(n)κη(n)dη=Ib(T,η1+η22)N(T,p)∑ηi∈ η1,η2Si T(n)
测量中探测N个圆环网格中R条辐射束在X=[η1，η2]和Y=[η3，η4] 2个谱带内的辐射强度，可得如下方程组：
{Iη1,η2R=ΔLR×NHη1,η2NIη3,η4R=ΔLR×NHη3,η4N
求解上述方程组获得X与Y谱带辐射源项后，利用两者比值与圆环内气体温度T间对应关系[8]，求解得到圆环内温度。
RX/Y(n)=HX(n)HY(n)≈Ib[T(n),η1+η22]⋅∑ηi∈XSi[T(n)]Ib[T(n),η3+η42]⋅∑ηi∈YSi[T(n)]
结合主动法（AT方法）信号，编号为ml激光路径在N个网格积分吸光度可以表示为：
A˜=A/p=∑n=1NX(n)S[T(n)]Δl(ml,n)
由于圆环网格内温度T（n）已经由被动法重建获得，故仅有网格内组分浓度X（n）未知，所需吸收光谱信息大大减小。本文中考虑仅在火焰中心区域布置一条激光吸收光路，即激光光路总数Ml=1时重建气体浓度场。利用该路激光扫描T个跃迁下的目标组分吸收峰，即可得到如下方程组。
A˜Ml×T=L(Ml×T)×N×XN
式中：A˜为检测得到的激光吸光度矩阵；L为包含几何路径和线强函数的系数矩阵；X为待求的组分浓度场矩阵。
由于该问题的病态特性，需要施加正则化约束求解得到合理的浓度场结果。
1.2.2　双重约束正则化方法
对于式（12）所描述的浓度场求解问题，通过引入平滑与先验浓度场约束，此时浓度场逆向求解过程可描述为如下最小化问题：
min{‖LX−A˜‖2+λ1‖SX‖2+λ2‖X−X0‖2}
式中：λ1和λ2分别为平滑约束与先验浓度场约束正则化参数，表示2种约束在求解中占据的权重；X0为由被动法求解得到气体初始浓度场矩阵；S为平滑矩阵，实现相邻网格间物理参量平滑变化以满足真实物理量场分布特点，其表达式为：
S=(1−11−1............1−11−1)
使用双重约束下的主被动结合方法确定火焰水蒸气浓度场分布，首先要确定正则化参数λ1和λ2。通过随机模拟实验发现，对于同一测量对象，相同实验装置采集的不同随机信号，重建过程中最佳先验浓度场约束正则化参数通常集中在较窄范围内。本文中先由模拟实验确定先验浓度场约束正则化参数，再由L型曲线[14]确定平滑约束正则化参数。
2　火焰物理场重建
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2.1　模拟实验条件
模拟实验研究中首先利用准确的火焰温度场与水蒸气浓度场正向计算得到火焰中水蒸气发射与吸收辐射，将准确的水蒸气发射与吸收辐射信号添加高斯误差。
fmeasured=fexact+(μ+σξ)fexact
式中：fexact为计算得到的准确信号；μ为偏差均值，一般将其设置为0；ξ为符合高斯分布的随机数；σ为误差均方根；fmeasured为添加误差之后的信号，用该信号作为模拟实验时测量信号。
由该模拟测量信号利用双重正则化约束下的主被动结合方法重建火焰温度场与水蒸气浓度场，并将重建物理场与设定的准确物理场进行比较，计算其相对误差，并以此评估双重约束下的主被动结合方法计算精度。
实验中以轴对称火焰燃烧产物物理场作为研究对象[15]，选取2个典型模拟轴对称火焰圆形截面（单峰火焰与双峰火焰）。根据轴对称火焰特点，其截面为圆形，物理场参数仅在半径方向发生改变且对称轴经过截面圆心，火焰具体温度与水蒸气体积分数分布分别如图3和图4所示。
被动法（ISBR方法）中选取6 415~6 515 cm–1和6 915~7 015 cm–1 2个谱带作为测量谱带X和Y，主动法（AT方法）中选择表1所示的12条水蒸气吸收跃迁谱线作为模拟实验中使用的目标测试吸收跃迁[16]。
2.2　燃烧温度场重建
根据1.2节主被动结合方法介绍，该方法中燃烧温度场是通过被动法重建得到。对图3中2个典型火焰燃烧物理场截面开展温度场重建，选取信号误差水平σ=1%，测量区域划分圆环网格总数N=20。为了让重建结果更有可信度，所有重建在相同条件下重复进行500次，500次重建结果与准确物理场如图5所示。由图5可以看出，该方法对于单峰和双峰火焰都有较好的重建结果。其中单峰火焰分布特征更加简单，重建精度要高于双峰火焰。火焰中心区域温度场重建误差相对较大，这主要是由于穿过中心区域的探测器视线数偏少，收集到中心区域网格发射信息偏少；同时，中心区域火焰发射需经周围介质衰减作用而到达探测器。这些因素导致中心区域温度重建偏差较大，尤其在双峰火焰重建结果中表现更加明显。
为了进一步研究重建温度的误差分布，图6给出了500次重建结果的误差统计。结果表明，单峰火焰温度重建误差主要集中在0.5%~1.0%，双峰火焰温度重建误差主要集中在0.5%~1.5%。单峰火焰与双峰火焰500次重建结果平均相对误差分别为0.92%与1.32%，温度场具有很高的重建精度。
2.3　水蒸气浓度场重建
2.3.1　被动法重建水蒸气初始浓度场
根据重建得到的各网格辐射源项以及温度结果，通过式（9）可获得单独利用被动法重建得到的水蒸气初始体积分数如图7。从图7中可以看出，较多的重建结果偏离准确值较远，单峰和双峰火焰500次重建结果的平均相对误差分别为6.18%、7.10%。可见单纯利用被动方法对燃烧产物水蒸气体积分数分布的重建精度明显低于温度场重建精度，这是由自发辐射信号自身特点决定的，与文献[8]中结论一致。
2.3.2　主被动结合方法重建水蒸气浓度场
在主被动结合方法中，针对20网格的单峰和双峰火焰模型，在火焰截面轴心处布置一条激光光路扫描12条跃迁谱线获得光谱吸收信号，通过将被动法重建得到的燃烧温度场与水蒸气初始体积分数引入主动法（AT方法）中，结合双重正则化约束重建整个截面的水蒸气体积分数分布。设置光谱吸收信号误差σ=1%，所有模拟实验均在相同条件下重复500次。
主被动结合方法重建得到的水蒸气体积分数分布如图8所示。由图8可以看出，绝大部分重建结果与准确值偏差较小，仅有少量重建结果偏差较大。单峰和双峰火焰重建结果平均误差分别为3.05%和3.31%，可见双先验约束下主被动结合方法可以得到较为精确的水蒸气体积分数分布。
为了更直观反映主被动结合方法对气体浓度场重建精度的提高，图9给出了被动法重建初始气体体积分数分布和主被动结合方法重建气体体积分数分布500次重建结果的误差分布。从图9可以看出，不论是单峰火焰或是双峰火焰，双正则化约束下主被动结合法都能有效提高气体体积分数分布重建精度，绝大部分重建结果误差均低于单纯使用被动法重建的初始水蒸气体积分数误差，少数异常重建结果在实际应用中可以结合气体体积分数变化范围筛除。
表2给出了主被动结合方法与单纯使用被动法重建水蒸气体积分数的平均偏差。可以看出，相对于被动法，主被动结合方法在仅增加布置1条激光光路条件下，对水蒸气体积分数分布重建精度具有明显改善，测量误差减小至原误差50%左右。总体而言，主被动结合方法相较于被动法气体体积分数分布重建精度明显提高，相较于主动法测量系统大大简化，为工业应用中燃烧温度场和介质体积分数分布准确测量提供了条件。
3　结论
收起
结合被动法测量装置简单和主动法组分浓度场测量精度高的优势，本文提出了主被动结合的燃烧温度场和组分浓度场重建方法，建立了双重正则化约束的目标函数，针对单峰和双峰分布轴对称燃烧火焰开展了模拟重建研究，得出以下主要结论。
1）测量误差为1.00%时，单峰火焰温度场重建平均误差为0.92%，双峰火焰为1.32%，具有很高的重建精度。
2）对于单峰和双峰火焰，被动法重建得到的水蒸气初始体积分数分布平均误差均大于6%，精度明显低于火焰温度场精度。
3）对于单峰和双峰火焰，主被动结合方法水蒸气体积分数重建平均误差分别为3.05%和3.31%，相较于被动法重建的初始浓度场精度明显提升。
4）主被动结合方法测量装置复杂程度远低于纯主动法，为工业应用场景下燃烧温度场和介质浓度场测量提供了有效途径。
基金
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  • 国家自然科学基金项目(52476086)
文献
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参考文献 引证文献
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2026年第55卷第1期
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文章信息
doi: 10.19666/j.rlfd.202504065
  • 接收时间：2025-04-19
  • 首发时间：2026-06-10
  • 出版时间：2026-01-25
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  • 收稿日期：2025-04-19
  • 修回日期：2025-05-20
  • 录用日期：2025-05-26
基金
National Natural Science Foundation of China(52476086)
国家自然科学基金项目(52476086)
作者信息
    武汉大学动力与机械学院，湖北 武汉 430072

通讯作者:

黄志锋（1982），男，博士，教授，主要研究方向为燃烧检测、辐射传递计算，。
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