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Article(id=1325528736199885071, tenantId=1146029695717560320, journalId=1205116786560364546, issueId=1325528735126151362, articleNumber=null, orderNo=null, doi=10.16236/j.cnki.nrjxb.202501007, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1708012800000, receivedDateStr=2024-02-16, revisedDate=1721750400000, revisedDateStr=2024-07-24, acceptedDate=null, acceptedDateStr=null, onlineDate=1793960277842, onlineDateStr=2026-11-06, pubDate=1737734400000, pubDateStr=2025-01-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793960277842, onlineIssueDateStr=2026-11-06, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793960277842, creator=13701087609, updateTime=1793960277842, updator=13701087609, issue=Issue{id=1325528735126151362, tenantId=1146029695717560320, journalId=1205116786560364546, year='2025', volume='43', issue='1', pageStart='1', pageEnd='95', issueExtLink='null', onlineDate='null', pubDate='1737734400000', pubDateStr='2025-01-25', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793960277585, creator='13701087609', updateTime=1793960521174, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext={EN=IssueExt(id=1325529757923951150, tenantId=1146029695717560320, journalId=1205116786560364546, issueId=1325528735126151362, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1325529757923951151, tenantId=1146029695717560320, journalId=1205116786560364546, issueId=1325528735126151362, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null, downloadFileDto=null}, startPage=55, endPage=63, ext={EN=ArticleExt(id=1325528736388628752, articleId=1325528736199885071, tenantId=1146029695717560320, journalId=1205116786560364546, language=EN, title=RDE emission prediction for in-use light-duty vehicles based on virtual simulation model, columnId=null, journalTitle=Transactions of CSICE, columnName=null, runingTitle=null, highlight=null, articleAbstract=

An engine-after-treatment virtual simulation model was built for emission prediction of in-use light-duty vehicles under real drive emission(RDE) conditions. First, a one-dimensional engine model was built and calibrated with steady-state and transient experimental engine emissions. The results show that the relative errors of cumulative mass of CO and NO emissions are 9.2% and 5.8%, respectively, under RDE conditions. Secondly, the after-treatment performance tests were conducted, and the after-treatment temperature, light-off time and aging models were verified. The results show that during the first 35s in world light vehicle test cycle(WLTC), the maximum error of temperature in the axial direction of the front catalytic converter is 52℃, and the absolute(relative) errors of post-catalytic cumulative masses of CO and NO are 0.0385g(5.90%) and 0.0011g (0.75%), respectively. Finally, the emission patterns of WLTC, RDE and standardized random test-aggressive driving style (RTS-95) working conditions were investigated under different catalytic converter aging conditions using the virtual simulation model. It is found that NO emission is more sensitive to the working conditions and the risk of exceeding the limit is higher. The NO instantaneous mass emission threshold is set to 8mg/s, and the warning window width was investigated for the RTS-95 operating condition with a catalytic converter dispersion factor of 0.6. The result shows that increasing the warning window width will reduce the misjudgment rate and the recognition probability of cold start overrun.

, authors=Qingpeng Su, Hua Zhao, Yuxin Hu, Fan Zhang, Yiqiang Pei, authorsList=Qingpeng Su, Hua Zhao, Yuxin Hu, Fan Zhang, Yiqiang Pei, authorCompany=null, correspAuthors=Fan Zhang, 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=1325528740423549223, articleId=1325528736199885071, tenantId=1146029695717560320, journalId=1205116786560364546, language=CN, title=基于虚拟仿真模型的轻型车在用RDE排放预测, columnId=null, journalTitle=内燃机学报, columnName=, runingTitle=null, highlight=null, articleAbstract=

为进一步准确预测在用乘用车实时驾驶排放，搭建了以发动机-后处理虚拟仿真为核心的在用排放预测模型．首先建立了发动机一维模型，与稳态和瞬态发动机原排测试数据进行了对比和标定．结果表明：在用实际行驶排放测试(RDE)工况下，CO和NO的原排累积质量相对误差分别为9.2%、5.8%；其次进行后处理性能试验，对后处理温度、起燃和老化模型进行标定验证，在全球轻型车测试循环工况(WLTC)前35s，三元催化转化器轴向最大温度误差为52℃，CO、NO的排放累积质量误差为0.0385g(5.90%)和0.0011g(0.75%)；最后利用RDE排放预测模型在不同催化器老化状态下，进行WLTC、RDE和95%分位的激烈驾驶参考循环(RTS-95)工况的排放规律探究．研究发现：NO排放对工况更加敏感，超限风险更高．设定NO瞬时质量排放阈值为8mg/s，以RTS-95循环在分散因子为0.6条件下的NO仿真结果为例，对催化器分散因子进行预警窗口宽度探究，结果表明：增加预警窗口宽度将会降低误判率和冷启动超限的识别概率．

, authors=苏庆鹏, 赵华, 胡雨馨, 张帆, 裴毅强, authorsList=苏庆鹏, 赵华, 胡雨馨, 张帆, 裴毅强, authorCompany=null, correspAuthors=张帆, authorNote=

苏庆鹏，博士研究生，．

, correspAuthorsNote=
张帆，博士，副教授，．
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苏庆鹏，博士研究生，．

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苏庆鹏，博士研究生，．

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Applied Energy，2019，242：1074-1089., articleTitle=Analysis of the high instantaneous NO emissions from Euro 6 diesel passenger cars under real driving conditions, refAbstract=null)], funds=[Fund(id=1325528749088981358, tenantId=1146029695717560320, journalId=1205116786560364546, articleId=1325528736199885071, awardId=cstc2020jscx-dxwtBX0024, language=CN, fundingSource=重庆市技术创新与应用发展重点资助项目(cstc2020jscx-dxwtBX0024), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1325528740700373288, tenantId=1146029695717560320, journalId=1205116786560364546, articleId=1325528736199885071, xref=null, ext=[AuthorCompanyExt(id=1325528740712956201, tenantId=1146029695717560320, journalId=1205116786560364546, articleId=1325528736199885071, companyId=1325528740700373288, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=State Key Laboratory of Engines，Tianjin University，Tianjin 300350，China), AuthorCompanyExt(id=1325528740725539114, 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figureFileBig=KA3sfuxyOPyrucuQt/IvgA==, tableContent=null), ArticleFig(id=1325528747998462305, tenantId=1146029695717560320, journalId=1205116786560364546, articleId=1325528736199885071, language=CN, label=图11, caption= RTS-95测试工况下超限警告窗口时长与超限次数关系, figureFileSmall=BquylP1LpQMNgvx0f7dDKQ==, figureFileBig=KA3sfuxyOPyrucuQt/IvgA==, tableContent=null), ArticleFig(id=1325528748078154082, tenantId=1146029695717560320, journalId=1205116786560364546, articleId=1325528736199885071, language=EN, label=Tab.1, caption=

Catalyst specifications

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参数数值
长度/mm180
直径/mm100
贵金属载量/(g·件-1)1.9
孔密度/(个·cm-2)93
壁厚/mm7.6
轴向分区长度比4.5∶5
贵金属涂敷比6.5∶1
储氧量/(mg·L-1)800
), ArticleFig(id=1325528748174623075, tenantId=1146029695717560320, journalId=1205116786560364546, articleId=1325528736199885071, language=CN, label=表1, caption=

催化器技术参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数数值
长度/mm180
直径/mm100
贵金属载量/(g·件-1)1.9
孔密度/(个·cm-2)93
壁厚/mm7.6
轴向分区长度比4.5∶5
贵金属涂敷比6.5∶1
储氧量/(mg·L-1)800
), ArticleFig(id=1325528748237537636, tenantId=1146029695717560320, journalId=1205116786560364546, articleId=1325528736199885071, language=EN, label=Tab.2, caption=

Reaction kinetic parameter

, figureFileSmall=null, figureFileBig=null, tableContent=
反应序号反应物生成物指前因子活化能/(kJ·mol-1)
R1CO＋0.5O2CO25.542×1013121.450
R2C3H6＋4.5O23CO2＋3H2O1.917×1015129.530
R3H2＋0.5O2H2O1.814×1015111.450
R4CO＋H2OCO2＋H21.800×10556.720
R5C3H6＋3H2O3CO＋6H21.230×10581.920
R62Ce2O3＋O24CeO22.9435.296
R7Ce2O3＋NO2CeO2＋0.5N27.920×10225.101
R8CO＋2CeO2Ce2O3＋CO21.824×10-131.768
R9C3H6＋12CeO26Ce2O3＋3CO＋3H2O13.57039.070
R10H2＋2CeO2Ce2O3＋H2O2.84531.768
R11CO＋NOCO2＋0.5N22.857×10952.374
R12C3H6＋9NO3CO2＋3H2O＋4.5N22.994×101180.063
R13H2＋NOH2O＋0.5N27.880×101069.370
), ArticleFig(id=1325528748308840805, tenantId=1146029695717560320, journalId=1205116786560364546, articleId=1325528736199885071, language=CN, label=表2, caption=

反应动力学参数

, figureFileSmall=null, figureFileBig=null, tableContent=
反应序号反应物生成物指前因子活化能/(kJ·mol-1)
R1CO＋0.5O2CO25.542×1013121.450
R2C3H6＋4.5O23CO2＋3H2O1.917×1015129.530
R3H2＋0.5O2H2O1.814×1015111.450
R4CO＋H2OCO2＋H21.800×10556.720
R5C3H6＋3H2O3CO＋6H21.230×10581.920
R62Ce2O3＋O24CeO22.9435.296
R7Ce2O3＋NO2CeO2＋0.5N27.920×10225.101
R8CO＋2CeO2Ce2O3＋CO21.824×10-131.768
R9C3H6＋12CeO26Ce2O3＋3CO＋3H2O13.57039.070
R10H2＋2CeO2Ce2O3＋H2O2.84531.768
R11CO＋NOCO2＋0.5N22.857×10952.374
R12C3H6＋9NO3CO2＋3H2O＋4.5N22.994×101180.063
R13H2＋NOH2O＋0.5N27.880×101069.370
), ArticleFig(id=1325528748392726886, tenantId=1146029695717560320, journalId=1205116786560364546, articleId=1325528736199885071, language=EN, label=Tab.3, caption=

Engine specifications

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参数数值
缸径/mm74
活塞行程/mm87
排量/L1.5
压缩比11.4
喷油系统/MPa35
喷油方式汽油直接喷射式
最大功率/kW130(5500r/min)
最大转矩/(N·m)270(1500～4000r/min)
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发动机技术参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数数值
缸径/mm74
活塞行程/mm87
排量/L1.5
压缩比11.4
喷油系统/MPa35
喷油方式汽油直接喷射式
最大功率/kW130(5500r/min)
最大转矩/(N·m)270(1500～4000r/min)
), ArticleFig(id=1325528748568887656, tenantId=1146029695717560320, journalId=1205116786560364546, articleId=1325528736199885071, language=EN, label=Tab.4, caption=

Vehicle specifications

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参数数值
整备质量/kg1550
驱动方式前驱
变速箱7速双离合变速器
), ArticleFig(id=1325528748648579433, tenantId=1146029695717560320, journalId=1205116786560364546, articleId=1325528736199885071, language=CN, label=表4, caption=

车辆技术参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数数值
整备质量/kg1550
驱动方式前驱
变速箱7速双离合变速器
), ArticleFig(id=1325528748715688298, tenantId=1146029695717560320, journalId=1205116786560364546, articleId=1325528736199885071, language=EN, label=Tab.5, caption=

Corresponding critical diffusion factors under different critical emission factors

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测试循环NOCO
WLTC0.680<0.1
RTS-950.200<0.1
RDE0.127<0.1
), ArticleFig(id=1325528748799574379, tenantId=1146029695717560320, journalId=1205116786560364546, articleId=1325528736199885071, language=CN, label=表5, caption=

不同物质临界排放因子下对应的临界分散因子

, figureFileSmall=null, figureFileBig=null, tableContent=
测试循环NOCO
WLTC0.680<0.1
RTS-950.200<0.1
RDE0.127<0.1
), ArticleFig(id=1325528748891849068, tenantId=1146029695717560320, journalId=1205116786560364546, articleId=1325528736199885071, language=EN, label=Tab.6, caption=

R2 of NO emission factor and instantaneous mass

, figureFileSmall=null, figureFileBig=null, tableContent=
工况95百分位90百分位80百分位
WLTC0.9860.9700.952
RDE0.9870.9960.989
RTS-950.9980.9900.890
), ArticleFig(id=1325528748979929453, tenantId=1146029695717560320, journalId=1205116786560364546, articleId=1325528736199885071, language=CN, label=表6, caption=

NO排放因子与瞬时质量排放相关系数R2

, figureFileSmall=null, figureFileBig=null, tableContent=
工况95百分位90百分位80百分位
WLTC0.9860.9700.952
RDE0.9870.9960.989
RTS-950.9980.9900.890
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基于虚拟仿真模型的轻型车在用RDE排放预测
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苏庆鹏 , 赵华 , 胡雨馨 , 张帆 , 裴毅强
内燃机学报 | 2025,43(1): 55-63
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内燃机学报 | 2025 , 43 (1) : 55 -63
基于虚拟仿真模型的轻型车在用RDE排放预测
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苏庆鹏 , 赵华, 胡雨馨, 张帆 , 裴毅强
作者信息
  • 天津大学先进内燃动力全国重点实验室，天津 300350
通讯作者:
张帆，博士，副教授，．
作者简介:

苏庆鹏，博士研究生，．

RDE emission prediction for in-use light-duty vehicles based on virtual simulation model
Qingpeng Su , Hua Zhao, Yuxin Hu, Fan Zhang , Yiqiang Pei
Affiliations
  • State Key Laboratory of Engines，Tianjin University，Tianjin 300350，China
出版时间: 2025-01-25 doi: 10.16236/j.cnki.nrjxb.202501007
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摘要
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为进一步准确预测在用乘用车实时驾驶排放，搭建了以发动机-后处理虚拟仿真为核心的在用排放预测模型．首先建立了发动机一维模型，与稳态和瞬态发动机原排测试数据进行了对比和标定．结果表明：在用实际行驶排放测试(RDE)工况下，CO和NO的原排累积质量相对误差分别为9.2%、5.8%；其次进行后处理性能试验，对后处理温度、起燃和老化模型进行标定验证，在全球轻型车测试循环工况(WLTC)前35s，三元催化转化器轴向最大温度误差为52℃，CO、NO的排放累积质量误差为0.0385g(5.90%)和0.0011g(0.75%)；最后利用RDE排放预测模型在不同催化器老化状态下，进行WLTC、RDE和95%分位的激烈驾驶参考循环(RTS-95)工况的排放规律探究．研究发现：NO排放对工况更加敏感，超限风险更高．设定NO瞬时质量排放阈值为8mg/s，以RTS-95循环在分散因子为0.6条件下的NO仿真结果为例，对催化器分散因子进行预警窗口宽度探究，结果表明：增加预警窗口宽度将会降低误判率和冷启动超限的识别概率．

虚拟仿真模型  /  催化转化器老化  /  在用实际行驶排放测试  /  排放预测

An engine-after-treatment virtual simulation model was built for emission prediction of in-use light-duty vehicles under real drive emission(RDE) conditions. First, a one-dimensional engine model was built and calibrated with steady-state and transient experimental engine emissions. The results show that the relative errors of cumulative mass of CO and NO emissions are 9.2% and 5.8%, respectively, under RDE conditions. Secondly, the after-treatment performance tests were conducted, and the after-treatment temperature, light-off time and aging models were verified. The results show that during the first 35s in world light vehicle test cycle(WLTC), the maximum error of temperature in the axial direction of the front catalytic converter is 52℃, and the absolute(relative) errors of post-catalytic cumulative masses of CO and NO are 0.0385g(5.90%) and 0.0011g (0.75%), respectively. Finally, the emission patterns of WLTC, RDE and standardized random test-aggressive driving style (RTS-95) working conditions were investigated under different catalytic converter aging conditions using the virtual simulation model. It is found that NO emission is more sensitive to the working conditions and the risk of exceeding the limit is higher. The NO instantaneous mass emission threshold is set to 8mg/s, and the warning window width was investigated for the RTS-95 operating condition with a catalytic converter dispersion factor of 0.6. The result shows that increasing the warning window width will reduce the misjudgment rate and the recognition probability of cold start overrun.

virtual simulation model  /  catalytic converter aging  /  in-use real drive emission measurement  /  emission prediction
苏庆鹏, 赵华, 胡雨馨, 张帆, 裴毅强. 基于虚拟仿真模型的轻型车在用RDE排放预测. 内燃机学报, 2025 , 43 (1) : 55 -63 . DOI: 10.16236/j.cnki.nrjxb.202501007
Qingpeng Su, Hua Zhao, Yuxin Hu, Fan Zhang, Yiqiang Pei. RDE emission prediction for in-use light-duty vehicles based on virtual simulation model[J]. Transactions of CSICE, 2025 , 43 (1) : 55 -63 . DOI: 10.16236/j.cnki.nrjxb.202501007
正文
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随着中国环境保护和大气污染防治工作的逐步深入，乘用车国Ⅵ排放法规已全面实施，国Ⅵ排放法规相较国Ⅴ法规引入了实际驾驶排放测试(RDE)要求，用以间接监控车辆实际驾驶过程的排放水平．轻型汽油车的排放测试通常是基于发动机底盘测功机进行，而RDE测试是根据实际路况进行行驶，不同地域不同时间会有不同的行驶工况．车辆在实际道路上实测排放量与试验中特定工况下排放特性差异性较大，这给发动机排放功能开发和在用排放性能监测带来了巨大挑战[1-2]．轻型车在用过程中，随着行驶里程的增加以及后处理的失效，催化器性能的老化和失效过程中的RDE在线排放预测显得格外重要，是目前在线排放检测的短板．在用RDE排放预测不仅可以监测车辆实际使用的排放情况，对排放超标的工况可采取相应的提前预警措施，还可以对发动机排放开发和后处理系统的匹配优化提供数据和模型支持．
一般而言，后处理系统需要满足发动机优化导致的原排变化，并达到同样的后处理效果．作为汽油机中应用最广泛的三元催化转化器(TWC)，其老化特性的预测是一件很困难又非常重要的事情．研究结果显示，发动机不正常燃烧、催化器与发动机距离较近及催化器内部受热不均都会导致催化剂受热老化[3-5]，且高温是导致老化的最重要的原因．这是由于高温会导致TWC涂层中的γ-氧化铝转变为α-氧化铝，氧化铝发生相变，比表面积降低，使储氧量降低[6-7]；同时，贵金属与CeO2在高温下出现烧结现象[8-9]．李有东等[6]发现，当温度从800℃升至950℃，Pt晶粒尺寸增大约两倍，CeO2晶粒尺寸也增大一倍以上．因此，以CeO2为代表的储氧量降低是后处理器老化的一个显著标志．催化剂老化会提高反应温度，进而使得排放恶化．Kang等[10]发现随着车辆行驶里程增加，TWC活性降低，反应所需温度升高；Winkler等[11]测TWC老化后的常见阿尔忒弥斯驾驶循环催后排放量，结果显示NO排放量增加一倍以上，HC排放增加两倍以上．同时，车辆排放性能评估已不局限于单一测试工况和新鲜催化器条件，而是拓展到老化催化器与真实道路驾驶工况，增大了催化器选型、排放标定等工作的难度、成本和周期．催化器仿真作为研发体系中增效降本的有效手段，随着催化器模型和化学反应机理的不断完善和发展，模型精度和鲁棒性近年显著提升，TWC模型研究也日益成熟，其中双点位储、清氧反应可提高不同温度下瞬态循环的排放模拟精度[12]；副产物相关反应的引入与标定也正在进行[13]；亦有使用长短期记忆(LSTM)神经网络建立TWC瞬态观测模型的研究[14]；催化器在不同涂敷条件下的排放特性模拟也得到充分重视[15]．要实现轻型车在用RDE排放预测模型，准确的后处理及其老化模型的建立是必不可少的．目前，还没有学者对整车完整瞬态工况以及完整生命周期内的瞬态排放的模拟预测．
基于此，笔者对某满足国Ⅵ排放法规的汽油轻型车搭建在用RDE排放预测模型．该模型基于GT-Power发动机仿真软件搭建，由原排和后处理模型构成．发动机原排使用一维燃烧模型，输入瞬态转速、转矩及过量空气系数对原排CO和NO体积分数进行预测．后处理模型与原排模型耦合后，将真实车载自动诊断系统(OBD)测定储氧量作为老化指标输入模型，对催化器在不同老化程度下的工作状态进行模拟，计算催化器转化效率和出口排放物．
1　在用RDE排放预测平台构建
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1.1　发动机模型
RDE排放预测技术的核心是搭建具有一定鲁棒性的高精度发动机和后处理模型，并具有实时解算能力．首先搭建了基于一维发动机模型，如图1所示，用于原排预测，由于RDE循环工况多变，采用给定燃烧参数的Wiebe燃烧模型无法适应，须使用预测燃烧模型对燃烧过程进行计算．预测燃烧模型具备任意工况下燃烧放热率、燃烧效率、点火滞燃期和燃烧相位的预测能力，是一系列模型的统称，其包含流动模型、燃烧模型、点火模型和循环变动率(COV)模型等[16]．流动计算方面，采用GT-Power自带的EngCylFlow模型，该模型可对缸内滚流比和湍动能、湍流尺度做出预测，为湍流燃烧模型提供输入．燃烧模型以SITurb准维燃烧模型为基础，该模型以湍流尺度λ与层流火焰传播速度SL之比τ作为时间尺度，用以控制进入反应区的混合气质量Me向燃烧产物质量Mb转化的速率，即
dMe/dt=ρuA(ST+SL)
dMb/dt=(Me−Mb)/τ
τ=λ/SL
式中：ρu为未燃气体密度；ST为湍流火焰传播速度；A为火焰面面积．
根据缸内高温、高压环境分别对层流火焰传播速率SL和湍流火焰传播速率ST分别进行了重新推导拟合，如式(4)与式(5)所示．
SL=A⋅Yreactm⋅(TuT0)r⋅(Tb−T0Tb−Tu)n
ST=SL+SL0.46Le⋅u′0.3SLReT0.25(ppref)0.2
式中：Yreactm为反应物的质量分数；Tu、Tb和T0分别为未燃、已燃和参考气体温度；m、r和n为模型参数，分别取值为1.7、1.1和2.2；u′为湍流脉动速度；Le为刘易斯数；p为压力；ReT为湍流雷诺数．COV模型在燃烧模型基础上构建，在湍流脉动速度中加入了随机正态分布随机变动因素，具备燃烧相位、持续期及平均有效压力(IMEP)的循环变动预测能力．层流火焰传播速率来源于Hann等[17]研究结果；而湍流火焰传播速率则根据公式(5)[18-19]进行了重新拟合修正．
在一维模型开发的过程中，引入CFD计算对一维流动模型中随时间变化的滚流比和湍动能开展标定．为了确定循环变动模型中的随机扰动，引入了大涡模拟，采用CFD得到的湍流脉动结果，对模型参数开展了标定．CO和NO原排放模型分别使用经典的CO单步反应(公式(6))和NO三步反应(公式(7)～(9))．
CO+OH=CO2+Hk1=6.76×107eT/1   102
O+N2=NO+Nk2=7.60×1010e−38   000/T
N+O2=NO+Ok3=6.40×106e−3   150/T
N+OH=NO+Hk4=4.10×1010
式中：k1、k2、k3和k4为各个反应的反应速率常数；T为反应温度．
1.2　后处理模型
催化器详细参数如表1所示．该模型由催化器进/出口管路一维模型、催化器换热模型和反应动力学模型构成．催化器换热模型由白载体温升试验进行标定．催化剂模型中主要涉及氧化(R1～R3)、水煤气及蒸气重整(R4～R5)、清氧储氧(R6～R10)和NO还原(R11～R13)4类反应，反应动力学参数通过合成气小样起燃试验进行标定，并通过阿雷尼乌斯公式计算化学反应速率[20]，如表2所示，稳态模型标定结果见图2，模型可以很好复现稳态TWC运行．该小样试验采用Hiden-HPR20质谱检测反应器出口处各组分浓度．
所使用一维模型假设蜂窝状催化器各通道状态均一，通道内为拟均相圆柱形反应器，气相为理想气体，反应器内压力均匀恒定，忽略气体沿径向的流动．催化器载体内发生的反应是排气组分与贵金属催化剂在载体壁面上进行的，即固体催化剂表面进行的催化反应．根据气体质量和能量守恒定律及固体质量和能量守恒定律，可建立催化转化器内气/固两相的质量守恒和能量守恒数学模型．催化器入口给定气体体积分数和温度，出口采用零梯度边界条件．
1.3　发动机模型验证
1.3.1　稳态原排的全工况验证
原排气体组分浓度对催化器工作状态有显著影响，因此，发动机稳态原排NO、CO体积分数的计算精度是在用RDE排放预测模型的基础．这里的稳态及后续的瞬态工况都是采用直采设备：Horiba MEXA-ONE-D2采集并测量催化器前发动机排气组分CO、NO等．发动机参数如表3所示．
图3为稳态工况下试验和仿真得到的排气NO、CO体积分数以及绝对误差．结果显示，发动机模型对NO峰值浓度预测准确，均在3.4×10-3～3.6×10-3之间，但在高浓度区间的工况分布更宽，主要体现在中低转速(1500～3500r/min)的中等负荷(100～150N·m)工况．在中等转速的小负荷区域，模型预测浓度相比试验值低．NO体积分数整体预测精度较高，浓度误差小于0.25×10-3的工况占比超过70%．模型误差最大的区域主要集中在低速大负荷区域，该区域气门重叠角较大，部分新鲜空气被扫出缸外．由于扫气量直接决定了燃烧时缸内实际过量空气系数，而一维计算对扫气计算有一定的误差，导致预测的过量空气系数与实际存在一定偏差，最终对NO和CO排放均产生一定影响．因此，需改进对扫气的预测精度以提高对排放的预测精度；而在中高转速的大负荷工况中，发动机存在混合气主动加浓，过量空气系数可控，模型对该加浓工况预测精度较高．
1.3.2　瞬态原排测试循环验证
在整车瞬态试验中，按照排放法规，进行了5组不同工况下的试验，对应了国Ⅵ排放法规中的WLTC试验和自定义的RDE道路试验等测试循环，后者相较于WLTC弱化了怠速阶段的占比，强化了中速、高速和超高速的占比．试验车辆技术参数见表4，使用的发动机参数见表3．
图4对比了试验和模拟的WLTC和RDE工况下NO和CO的累计质量．经过统计，WLTC工况下累积NO、CO排放质量分别低于试验值20.9%、10.2%，CO的整体计算精度高于NO，与稳态原排对应模拟结果对应．需要说明的是，此处的误差是众多工况点的累积误差，产生原因涉及到稳态万有特性下的原排误差、瞬态下燃烧相位误差(稳态下试验的燃烧相位是燃烧分析仪测试的，是已知的参数，计算按照燃烧相位与试验相同处理，而瞬态下无法测量燃烧相位，计算以试验的点火角作为输入，燃烧相位与试验存在一定的偏差)和瞬态下控制精度误差等各种不确定因素．而模拟的CO峰值普遍高于试验测量值，可能与发动机燃烧模型中对CO的预测整体偏高有关．但是累积的NO与CO体积分数在各时间段试验值与模拟值吻合程度都较高．
1.4　后处理模型验证
1.4.1　换热模型验证
首先对后处理模型的换热模型进行标定，包括传热系数、热熔和热阻的标定，即对物理模型中涉及到的数学参数进行调整．这里采用的是WLTC起燃阶段温度变化最剧烈、最难模拟的阶段进行温度的校验．图5为试验和仿真得到的WLTC前35s的催化器温度变化，4个热电偶分别测得催化器入口、前1/3、后1/3及催化器出口的温度变化．可以看到，仿真值与试验值非常接近，能准确体现前级催化器瞬态起燃的3个阶段是：(1)0～10s的怠速阶段，催化器温度缓慢上升；(2)10～18s的加速阶段，催化器前部温度快速上升(前部完全起燃)；(3)18～35s的催化器中后部起燃．
1.4.2　起燃模型验证
起燃阶段的模拟是TWC模拟的难点[21]，因而该阶段温度和浓度的准确预测决定了TWC瞬态模拟的精度．图6为CO和NO在起燃阶段的进/出口瞬时体积分数和出口累积质量排放．结果显示起燃模型对催化器出口体积分数和累积质量排放的计算精度较好，其中累积质量误差均小于13%．具体对比试验与仿真数据发现，该模型均在20s左右完全起燃，其中CO起燃较早，其次为NO．同时，该后处理模型能较准确地计算各种排放物在冷启动阶段的累积质量排放．瞬态循环下的换热模型和起燃工况验证是后处理模型的核心，为下一步全生命周期的排放监测打下了基础．
1.4.3　老化模型验证
为了进行生命周期的排放模拟，须将车辆的行驶公里数与催化器老化状态进行对应，而采用能够代表催化器储氧状态的实际分散因子Ce来表示催化器的老化性能是普遍采用的方法[22]．定义催化器分散因子为当前活性点位密度/新鲜状态活性点位密度，用以表征催化器老化程度，老化程度越高，催化器Ce越低．通过改变Ce可以模拟催化剂老化、中毒或部位的一般失活而导致的活性降低等现象，此处Ce进行归一化处理，并对老化后Ce进行标定．车辆经过16万标准道路循环(SRC)，行驶里程获得的催化器测得其相应的老化状态，对应的催化器储氧量为486mg，Ce为0.52．为简化老化模型，考虑Ce与铂族金属(PGM)同步老化，即两者Ce始终相同．
2　计算结果与分析
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2.1　在用RDE排放预测结果
通过试验开展轻型车全生命周期的排放预测是一件费时、费力的工作．这里通过对以上发动机模型和后处理模型的搭建，形成了一个可以进行轻型车在用RDE排放预测的仿真模型．图7给出了轻型车在用RDE排放预测过程，即Ce和PGM在不同分散因子下对应的催化器，在WLTC、RTS-95和RDE测试循环下对NO和CO的预测．图中排放因子定义为平均每公里的排放物质量．
总览NO和CO排放物结果，最激进、行驶里程最短的RTS-95循环在不同老化程度(不同分散因子)下的排放均最高．以NO排放结果为例，考虑到国Ⅵ标准以及前、后级催化器的作用比例，定义排放因子预警值Ra为
Ra=lim6b⋅CF/(mex/mmid)
式中：lim6b为国Ⅵb Ⅰ型试验限值；CF为国Ⅵ排放法规中Ⅱ型试验符合性因子；mex为当前测试车后级催化器出口累积质量；mmid为前级催化器出口累积质量．
计算得到NO排放因子预警值为0.11025g/ km．从RTS-95循环的总体排放结果可知，NO排放因子与驾驶工况、催化器分散因子的非线性度较高，在分散因子小于0.5时，排放因子急剧增大，在催化器失效阶段(分散因子小于或等于0.2)的排放因子达到预警值的6倍，而更柔和的WLTC、RDE循环在催化器失效阶段的排放因子均小于预警值的2倍．
图7(a)为在3种不同测试循环下的NO排放随分散因子变化曲线．结果显示：在16×104km等效耐久里程(分散因子为0.520)时，RDE和WLTC循环中NO排放表现良好，在全生命使用周期内，在催化器失效阶段均会超过预警值．WLTC、RDE循环的预警临界分散因子分别为0.200、0.127，而在RTS-95循环中高达0.680，表明在超过RDE限制的激进驾驶中，NO排放对工况的敏感程度远超CO，即在未来更严格的在用车排放法规中，需要通过更精细的催化剂匹配和发动机管理系统排放标定来降低该风险．与之相反，图7(b)中CO均未超过排放限值，即使在最激进的RTS-95循环且分散因子小于或等于0.2的情况，距离排放因子预警值(5.25g/km)仍有超过1.00g/ km的余量．WLTC与RDE循环的CO排放随老化的恶化趋势相似，RTS-95循环在分散因子大于0.5时，排放因子与RDE循环接近，但随着老化程度进一步加深，RTS-95循环的排放开始恶化，在催化器失效阶段远超RDE循环．
2.2　瞬时质量排放
确定了临界排放因子下对应的临界分散因子，提取后如表5所示．相比于CO和HC，NO临界排放因子下对应的临界分散因子较高，且在WLTC工况下达到0.680．将主要针对超限风险最大的NO排放进行分析，并将基于公里数的排放因子(g/km)转化为瞬时质量排放(mg/s)，使用计算负担更小、更简易的方式对排放进行评价和预警．
定义80/90/95百分位为完整循环下某污染物瞬时质量排放(mg/s)数值升序排列，取第80/90/95百分位数值，用以表征该循环某污染物的瞬时质量排放强度．这里分别统计上节中瞬时NO质量排放的95、90和80百分位，结果如图8所示．对比发现，95百分位瞬时排放速率与排放因子变化趋势更接近(图8(a)与图7(a))，在催化器老化早期(分散因子为0.5～1.0)便有上升．更低百分位的瞬时排放对早期老化并不敏感，即使是RTS-95循环的90、80百分位瞬时排放也未出现显著变化，而是到分散因子小于0.4时，瞬时排放速率才显著上升．由此可见，影响老化后排放因子的主要因素为瞬时排放速率的前5%．
图9标识了临界分散因子对应的临界瞬时排放速率，直线为拟合值．其中95百分位的临界瞬时排放速率(0.11025g/km)受驾驶工况影响很小，数值较接近，相应在RTS、WLTC、RDE循环中依次为6.8、7.2和8.2mg/s，而在更低的百分位统计时，则出现较大的相对差异．
以上结果表明，95百分位的瞬时排放速率与完整循环的排放因子可能存在较大相关性，为此将两个排放指标进行相关性分析．表6为图9对应的相关系数R2统计结果．综合结果发现，95百分位点的相关性更好，且RTS测试循环下R2达到0.998．一般认为，在RDE循环中大部分NO质量及颗粒物数量排放来源于高瞬时质量排放[23]，70%～95%的NO质量排放的时间占比仅为3%～20%．特定95百分位点的NO瞬时排放可近似表征车辆在全生命周期内各驾驶工况的排放因子．
2.3　NO排放预警
在实际道路车辆排放预警中，OBD根据催化器模型计算催后瞬时质量排放进行监控，在瞬时排放超过阈值后进行记录，低于阈值则不记录．可以达到对NO排放进行有效预警的目的，而且该方式比计算排放因子更便捷(累积实时行驶里程及累积质量排放)．图10为RTS-95测试工况下NO瞬时质量排放及超限警告窗口示意．根据图8已知95百分位瞬时质量排放为8.2mg/s．以RTS-95循环在分散因子为0.6条件下的NO仿真结果为例，该工况等效排放因子为0.1213g/km，NO瞬时质量排放计数阈值参考95百分位，设定为8mg/s，排放模型以1Hz计算催后NO质量流量，并在超过8mg/s时进行计数．计数器用来记录最近的设定时间段内的排放超限数量．图10同时显示了NO瞬时质量排放及计数窗口宽度分别为100s、300s的计数值．当窗口宽度为100s时，设定窗口期内超限率达到5%(5次)进行排放预警(如图10蓝线所示)，标志着超过了瞬时质量排放阈值的参考95百分位(8mg/s)；并且会分别在冷启动及高速工况进行2次报警，持续时长为101s和184s．将计数窗口增加至300s，则超限次数需达到15次才进行预警(如图10黄线所示)，并在高速段达到报警限值，持续时长为316s．需要说明的是，计数窗口宽度会对排放超限判定产生较大影响，计数窗口变窄会增加报警频次，降低单次报警持续时长，而计数窗口变宽则相反，且可能无法识别冷启动工况下的排放超限．超限警告窗口时长与超限次数的定量分析如图11所示．这里选用的数据是高速工况下，此时不同窗口长度对超限次数要求的影响较小，设置16次超限后报警可以基本适用于高速工况下不同窗口长度．但计数窗口宽度会对排放超限判定产生一定影响，尤其是冷态启动工况，计数窗口变窄会增加报警频次，降低单次报警持续时长；而计数窗口变宽则相反，且可能无法识别冷启动工况下的排放超限．
3　结论
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(1) 建立并验证给出了轻型车在用RDE排放预测模型，其中发动机模型稳态NO和CO模拟低误差工况占比超过70%，瞬态测试循环峰值结果略有差异；后处理模型温度、起燃、老化验证模拟与试验值拟合较好，并对在用RDE排放预测模型准确性较高，可用于预测实际工况．
(2) 在用RDE排放预测结果显示，对比3种气态排放物，NO排放对发动机和催化器运行工况敏感程度更高；对比3种测试循环，工况最剧烈的RTS-95循环在催化剂不同老化程度下，3种气体排放因子都最高，其中分散因子小于或等于0.1时，NO排放因子为预警值6倍．
(3) 80、90百分位NO瞬时排放速率只在分散因子小于0.4时出现上升趋势，而95百分位该速率在老化早期就出现上升，说明老化后排放因子主要受瞬时排放速率前5%影响．
(4) 95百分位NO瞬时排放速率与完整循环排放因子相关性较大，可选择95百分位NO瞬时排放近似表征在用阶段各驾驶工况的排放因子，在此基础上设置NO排放阈值进行排放预警．
基金
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  • 重庆市技术创新与应用发展重点资助项目(cstc2020jscx-dxwtBX0024)
文献
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2025年第43卷第1期
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doi: 10.16236/j.cnki.nrjxb.202501007
  • 接收时间：2024-02-16
  • 首发时间：2026-11-06
  • 出版时间：2025-01-25
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  • 收稿日期：2024-02-16
  • 修回日期：2024-07-24
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重庆市技术创新与应用发展重点资助项目(cstc2020jscx-dxwtBX0024)
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    天津大学先进内燃动力全国重点实验室，天津 300350

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张帆，博士，副教授，．
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2种不同金属材料的力学参数
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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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