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Article(id=1325528789853422232, tenantId=1146029695717560320, journalId=1205116786560364546, issueId=1325528735126151362, articleNumber=null, orderNo=null, doi=10.16236/j.cnki.nrjxb.202501005, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1711209600000, receivedDateStr=2024-03-24, revisedDate=1726588800000, revisedDateStr=2024-09-18, acceptedDate=null, acceptedDateStr=null, onlineDate=1793960290633, onlineDateStr=2026-11-06, pubDate=1737734400000, pubDateStr=2025-01-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793960290633, onlineIssueDateStr=2026-11-06, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793960290633, creator=13701087609, updateTime=1793960290633, 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=38, endPage=46, ext={EN=ArticleExt(id=1325528790037971609, articleId=1325528789853422232, tenantId=1146029695717560320, journalId=1205116786560364546, language=EN, title=Hydrogen jet and mixing characteristics under different critical states, columnId=null, journalTitle=Transactions of CSICE, columnName=null, runingTitle=null, highlight=null, articleAbstract=

When injecting hydrogen gas into the intake air path and in-cylinder environment of an internal combustion engine, there is a transition from supercritical to subcritical between the injection pressure and ambient pressure. High-speed schlieren imaging technology was used to study the injection characteristics under different conditions in a constant volume combustion bomb. The results show that the penetration distance, jet surface area, and jet volume of the hydrogen jet vary with time under different conditions. However, the change in the jet cone angle after 1ms is not significant, and the difference remains within 2°. When the supercritical injection enters the supercritical environment, the interaction between the jet and surrounding gases enhances turbulence intensity, which facilitates the entrainment of more surrounding gases. An empirical formula for the jet penetration distance of the hydrogen jet was proposed, which has proved to be high accuracy. These results can be utilized to optimize the mixture formation and combustion of hydrogen internal combustion engines, providing references for hydrogen injection strategies.

, authors=Xin Li, Hao Chen, Linlei Luo, Zhihao Ma, Xin Wang, authorsList=Xin Li, Hao Chen, Linlei Luo, Zhihao Ma, Xin Wang, authorCompany=null, correspAuthors=Zhihao Ma, 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=1325528793510855342, articleId=1325528789853422232, tenantId=1146029695717560320, journalId=1205116786560364546, language=CN, title=不同临界状态下氢气射流与混合特性, columnId=null, journalTitle=内燃机学报, columnName=, runingTitle=null, highlight=null, articleAbstract=

在内燃机气道和缸内环境下喷射氢气时，喷射压力和环境压力之间会出现高超临界向超临界以及超临界向亚临界的转变，采用高速纹影成像技术，在定容燃烧弹中研究了不同条件下的喷射特性．结果表明：不同条件下氢气射流的贯穿距、射流表面积以及射流体积随时间的增长趋势不同，但射流锥角在1ms后随时间变化不大，差值稳定在2°以内；在超临界喷射进入超临界环境时射流与周围气体相互作用使湍流强度增强，这有利于夹带更多的周围气体．最后提出的氢气射流贯穿距经验公式具有较高的精度，可以利用这些结果优化氢内燃机混合气的形成和燃烧，为喷氢策略提供参考．

, authors=李欣, 陈皓, 罗林雷, 马志豪, 王鑫, authorsList=李欣, 陈皓, 罗林雷, 马志豪, 王鑫, authorCompany=null, correspAuthors=马志豪, authorNote=

李欣，硕士研究生，．

, correspAuthorsNote=
马志豪，博士，教授，．
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李欣，硕士研究生，．

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李欣，硕士研究生，．

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Appl Energy，2013，105：8-16., articleTitle=Experimental and numerical investigation on the jet characteristics of spark ignition direct injection gaseous injector, refAbstract=null)], funds=[Fund(id=1325528803266806509, tenantId=1146029695717560320, journalId=1205116786560364546, articleId=1325528789853422232, awardId=51906061, language=CN, fundingSource=国家自然科学基金资助项目(51906061), fundOrder=null, country=null), Fund(id=1325528803354886894, tenantId=1146029695717560320, journalId=1205116786560364546, articleId=1325528789853422232, awardId=LMQYTSKT038, language=CN, fundingSource=龙门实验室资助项目(LMQYTSKT038), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1325528793787679407, tenantId=1146029695717560320, journalId=1205116786560364546, articleId=1325528789853422232, xref=null, ext=[AuthorCompanyExt(id=1325528793800262320, tenantId=1146029695717560320, journalId=1205116786560364546, articleId=1325528789853422232, companyId=1325528793787679407, language=EN, country=null, province=null, 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Experimental parameter

, figureFileSmall=null, figureFileBig=null, tableContent=
参数数值
喷射气体H2
环境气体N2
喷射压力pa/MPa0.4，0.8，1.2，2.0，4.0，6.0
喷射对比压力par0.31，0.62，0.93，1.54，3.08，4.63
环境压力pb/MPa0.1，0.5，1.0，1.5，2.0
环境对比压力pbr0.08，0.39，0.77，1.16，1.54
试验温度/K298
孔径/mm0.35
喷射脉宽/ms4
分辨率992×744
), ArticleFig(id=1325528802851570408, tenantId=1146029695717560320, journalId=1205116786560364546, articleId=1325528789853422232, language=CN, label=表1, caption=

试验参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数数值
喷射气体H2
环境气体N2
喷射压力pa/MPa0.4，0.8，1.2，2.0，4.0，6.0
喷射对比压力par0.31，0.62，0.93，1.54，3.08，4.63
环境压力pb/MPa0.1，0.5，1.0，1.5，2.0
环境对比压力pbr0.08，0.39，0.77，1.16，1.54
试验温度/K298
孔径/mm0.35
喷射脉宽/ms4
分辨率992×744
), ArticleFig(id=1325528802935456489, tenantId=1146029695717560320, journalId=1205116786560364546, articleId=1325528789853422232, language=EN, label=Tab.2, caption=

State parameters of hydrogen under different injection pressures

, figureFileSmall=null, figureFileBig=null, tableContent=
参数数值
p0/MPa0.40.81.22.04.06.0
ρa/(kg·m-3)0.2350.6480.9691.6083.1794.713
m/(g·s-1)0.0240.0470.0710.1180.2350.350
P/(kg·m·s-2)0.0280.0570.0850.1420.2830.422
m*/(g·s-1)0.0210.0400.0600.1010.1990.298
P*/(kg·m·s-2)0.0240.0490.0730.1210.2400.358
), ArticleFig(id=1325528803010953962, tenantId=1146029695717560320, journalId=1205116786560364546, articleId=1325528789853422232, language=CN, label=表2, caption=

不同喷射压力下氢气的状态参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数数值
p0/MPa0.40.81.22.04.06.0
ρa/(kg·m-3)0.2350.6480.9691.6083.1794.713
m/(g·s-1)0.0240.0470.0710.1180.2350.350
P/(kg·m·s-2)0.0280.0570.0850.1420.2830.422
m*/(g·s-1)0.0210.0400.0600.1010.1990.298
P*/(kg·m·s-2)0.0240.0490.0730.1210.2400.358
), ArticleFig(id=1325528803082257131, tenantId=1146029695717560320, journalId=1205116786560364546, articleId=1325528789853422232, language=EN, label=Tab.3, caption=

Hydrogen density at different ambient pressures

, figureFileSmall=null, figureFileBig=null, tableContent=
参数数值
环境压力/MPa0.10.51.01.52.0
氮气密度/(kg·m-3)1.1315.65811.32617.00122.682
), ArticleFig(id=1325528803157754604, tenantId=1146029695717560320, journalId=1205116786560364546, articleId=1325528789853422232, language=CN, label=表3, caption=

不同环境压力下氮气的密度

, figureFileSmall=null, figureFileBig=null, tableContent=
参数数值
环境压力/MPa0.10.51.01.52.0
氮气密度/(kg·m-3)1.1315.65811.32617.00122.682
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不同临界状态下氢气射流与混合特性
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李欣 , 陈皓 , 罗林雷 , 马志豪 , 王鑫
内燃机学报 | 2025,43(1): 38-46
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内燃机学报 | 2025 , 43 (1) : 38 -46
不同临界状态下氢气射流与混合特性
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李欣 , 陈皓, 罗林雷, 马志豪 , 王鑫
作者信息
  • 河南科技大学车辆与交通工程学院，洛阳 471003
通讯作者:
马志豪，博士，教授，．
作者简介:

李欣，硕士研究生，．

Hydrogen jet and mixing characteristics under different critical states
Xin Li , Hao Chen, Linlei Luo, Zhihao Ma , Xin Wang
Affiliations
  • Vehicle and Transportation Engineering College，Henan University of Science and Technology，Luoyang 471003，China
出版时间: 2025-01-25 doi: 10.16236/j.cnki.nrjxb.202501005
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摘要
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在内燃机气道和缸内环境下喷射氢气时，喷射压力和环境压力之间会出现高超临界向超临界以及超临界向亚临界的转变，采用高速纹影成像技术，在定容燃烧弹中研究了不同条件下的喷射特性．结果表明：不同条件下氢气射流的贯穿距、射流表面积以及射流体积随时间的增长趋势不同，但射流锥角在1ms后随时间变化不大，差值稳定在2°以内；在超临界喷射进入超临界环境时射流与周围气体相互作用使湍流强度增强，这有利于夹带更多的周围气体．最后提出的氢气射流贯穿距经验公式具有较高的精度，可以利用这些结果优化氢内燃机混合气的形成和燃烧，为喷氢策略提供参考．

亚/超临界  /  氢气射流  /  混合特性  /  卷吸比

When injecting hydrogen gas into the intake air path and in-cylinder environment of an internal combustion engine, there is a transition from supercritical to subcritical between the injection pressure and ambient pressure. High-speed schlieren imaging technology was used to study the injection characteristics under different conditions in a constant volume combustion bomb. The results show that the penetration distance, jet surface area, and jet volume of the hydrogen jet vary with time under different conditions. However, the change in the jet cone angle after 1ms is not significant, and the difference remains within 2°. When the supercritical injection enters the supercritical environment, the interaction between the jet and surrounding gases enhances turbulence intensity, which facilitates the entrainment of more surrounding gases. An empirical formula for the jet penetration distance of the hydrogen jet was proposed, which has proved to be high accuracy. These results can be utilized to optimize the mixture formation and combustion of hydrogen internal combustion engines, providing references for hydrogen injection strategies.

sub/supercritical  /  hydrogen jet  /  mixing characteristics  /  entrainment ratio
李欣, 陈皓, 罗林雷, 马志豪, 王鑫. 不同临界状态下氢气射流与混合特性. 内燃机学报, 2025 , 43 (1) : 38 -46 . DOI: 10.16236/j.cnki.nrjxb.202501005
Xin Li, Hao Chen, Linlei Luo, Zhihao Ma, Xin Wang. Hydrogen jet and mixing characteristics under different critical states[J]. Transactions of CSICE, 2025 , 43 (1) : 38 -46 . DOI: 10.16236/j.cnki.nrjxb.202501005
正文
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目前，社会经济的飞速发展加速了化石燃料消耗，导致CO2排放大幅度增加，全球气候变暖现象加剧，而交通运输产生的温室气体排放总量稳居第一[1]．由于低碳和可持续发展的要求，高效、清洁的可再生替代燃料受到了各国广泛关注．H2作为无碳能量载体，燃烧不会产生任何碳排放，此外H2来源广泛，能够利用化石燃料和可再生能源(生物质、风能和太阳能)等方法制取[2]，其中利用光伏系统和风电系统获取电力，再通过电解水获取的“绿氢”正成为全球氢能发展的焦点[3]，为目前全球环境问题和燃料消耗提供了解决方案．H2的能量密度(120MJ/kg)约是汽油(43.5MJ/kg)的3倍[4]，被认为是未来最重要的清洁替代燃料方案之一．
氢内燃机热效率高、排放污染较小，但混合气的均匀程度对其性能影响显著[5]，因而研究氢气射流与混合特性显得尤为重要．刘政等[6]基于纹影法研究了氩-氧氛围中不同喷射压力和环境压力对氢气射流贯穿距、射流锥角及卷吸率发展的影响，发现对于一定的喷射压力，随着环境压力的升高卷吸率增加，但环境压力升高到一定值后卷吸率反而会减小．Shahsavan等[7]模拟了氢气在不同比热比的环境气体下射流的发展过程和混合特性表明，相比于氢气与氮气或氙气，氢气在氩气中具有更快的混合速率．Deng等[8]针对氩循环氢发动机，在定容燃烧弹中对比氩气氛围下氢气和氧气的射流发展时发现，氢气直喷策略优于氧气直喷策略．邓俊等[9]研究了不同喷射压力和喷射温度对氢气射流特性和卷吸特性的影响表明，氢气对周围气体的卷吸能力会随压力比的增加呈先增后减的趋势，卷吸比随温度的升高而显著下降．
以上研究大多为氢气在不同喷射压力和环境压力情况下的射流发展及混合特性，而在内燃机环境下会出现超临界氢气向亚临界环境以及超临界氢气向超临界环境下的喷射，氢气在亚超临界的特性不同，必然对其喷射特性产生影响，从而影响一定时间内氢气与环境气体的混合，而大部分研究并未考虑亚超临界状态对喷射特性及环境气体混合的影响．Ma等[10]利用定容燃烧弹研究了液体燃料在亚/超临界环境条件下喷射过程表明，超临界环境与亚临界环境下的喷射在形态学特征上存在较大差异．张纪宝[11]开展了正庚烷超临界喷射混合特性的模拟研究，得出超临界压力下正庚烷的热力参数随温度和压力呈连续非线性变化的规律．Gao等[12]将亚/超临界条件下的航空煤油喷入静止的氮气中，观察发现超临界压力下出现激波结构且随着喷射压力的增加，马赫盘的尺寸及喷射锥角都会增加．Hou等[13]利用模拟进行了超临界和亚临界环境压力下氢射流的分子动力学研究表明，超临界条件下射流径向密度变化率很小，超临界环境压力下氢射流中分子应力是亚临界的88.9%．
当前，超临界现象研究大多集中在亚/超临界喷雾和超临界液滴蒸发与燃烧的模拟，以及部分关于超临界或超超临界锅炉的排放特性研究，超临界气体射流的相关试验鲜见报道．此外，氢气射流研究中的喷射压力范围多为超临界，环境压力范围多为亚临界．因此，笔者开展氢气亚临界喷射进入亚临界环境(简称“亚-亚”)、超临界喷射进入亚临界环境(简称“超-亚”)及超临界喷射进入超临界环境(简称“超-超”)下射流现象学研究是必要的，可以为氢气在氢内燃机上的应用提供理论指导，同时为模拟研究提供试验依据．
1　试验方案
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1.1　试验系统设计
试验采用如图1所示的定容燃烧弹系统，主要包括定容燃烧弹、高速摄像机、光学纹影系统、喷射系统和喷射控制系统．
定容燃烧弹两侧有直径为100mm的光学石英玻璃观察窗，可以承受7MPa的环境压力．光学纹影系统由两面凹面镜和两面平面镜组成‘Z’字形光路，纹影法的原理是光强差异的偏转角与折射率梯度呈正比，通过流场的折射率反映密度变化．在试验系统调试中发现，周围气体扰动引起的密度变化会对射流本体的采集产生影响，使射流边缘难以识别，因而在试验开始前花费了大量的时间去调整背景的亮度与刀口的开度，在保证射流边缘可见的前提下，适当降低对比度，减小气流扰动造成的明暗变化，最终选择刀口的切割量为60%进行试验．选用NAC Memrecam GX-8高速摄相机，均在992×744的分辨率和5000幅/s的帧率下进行拍摄．喷射系统由气瓶、管路、压力表和喷嘴组成，分别利用安装在氢气高压管路和容弹主体上的高精度压力表控制喷嘴的喷射压力和容弹内氮气的压力．喷嘴在容弹内伸出的距离设置为6mm，以保证射流不受康达效应的影响．喷射控制系统利用法国EFS公司生产的8426和8427模块控制喷射规律和喷射脉宽．通过电脑控制端可以同时触发高速摄像机与单次喷射仪．
1.2　试验工况
氢内燃机有进气道喷射和缸内直喷两种喷射方式，其喷射压力和环境压力范围广、跨度大，因而笔者选择了表1的试验工况，喷射压力pa与氢气临界压力pcr之比定义为喷射对比压力par，环境压力pb与氢气临界压力pcr之比定义为环境对比压力pbr，par和pbr大于1时表示氢气处于超临界压力状态，使用的汽油直喷喷射器孔径为0.35mm．试验时固定喷射脉宽为4ms，所有试验工况点都满足环境压力小于喷射压力的0.528倍，因而出口流速始终保持在当地声速，具有最大的理论质量流量且与环境压力无关，仅受喷射压力和喷孔流通截面积的影响，见式(2)．
假设H2是理想气体，氢气在喷嘴内的流动为绝热等熵过程，当环境压力pb与喷射压力pa之比小于0.528时，氢气流动在喷嘴内阻塞．在可压缩流体中，阻塞流条件下的临界压力比ε可以表示为
ε=p*pa=(2k+1)kk−1
式中：p*为临界条件下的环境压力；k为氢气的比热比，k＝1.41．
在临界条件下，喷嘴出口截面上气体流动速度达到当地声速，质量流量最大．此时喷嘴出口的质量流量m、动量P分别为
m=ρuA=A(kρapa)1/2(2k+1)k+12(k−1)
P=mu=A  k pa(2k+1)kk−1
式中：A为喷嘴出口截面积；u为喷嘴出口流速；ρa为喷射压力下氢气的密度；ρ为气体密度．
将氢气的密度代入式(2)和式(3)得到不同喷射状态下氢气的质量流量m和动量P．考虑喷嘴内部的压力损失，Tsujimura等[14]研究了不同喷射条件对喷嘴流量系数的影响表明，喷射脉宽大于5ms时流量系数与喷射脉宽无关，稳定在0.90附近；喷射脉宽小于5ms时由于针阀运动对流量影响较大，使得流量系数略微减小．因此，结合试验工况条件取喷嘴流量系数Cd为0.85，将m和P分别乘以Cd得到实际气体喷射下的质量流量m*和动量P*．氢气在不同状态下的喷射参数如表2所示．表3显示了在不同环境压力下氮气的密度．
1.3　图像处理
通过纹影法获得的氢气射流图像通过matlab程序进行批量处理，使用一系列图像形态学matlab函数提取射流轮廓，如图2所示．首先喷射序列中的每一张图像(图2(a))减去背景图像以突出显示射流轮廓，如图2(b)所示．随后利用滤波函数和二值化处理消除背景噪声，提高对比度，如图2(c)所示．填充射流二值化图像的空洞，如图2(d)所示．最后使用matlab开运算和闭运算重构射流图像，并利用canny算子获取射流边界轮廓，如图2(e)和图2(f)所示．
二值化处理中阈值R的选择会影响射流的边缘轮廓，进而会对试验结果产生一定的影响．图3显示在3种不同阈值下二值化后的射流轮廓．随着阈值增加会导致边缘轮廓的收缩，同时阈值过大也会导致边缘特征的丢失，为了保证试验结果的可靠性，选择二值化的阈值为0.40．
1.4　特征参数
通过对射流序列图像的后处理获得了射流贯穿距、射流锥角、射流表面积与射流体积等特征参数．
射流贯穿距定义为喷嘴到喷嘴所在的铅锤线与射流前锋面交点的距离，即喷嘴所在的像素点与喷嘴铅锤线与射流前锋面相交的像素点间的距离，通过像素比例尺换算得到射流贯穿距L，射流表面积为射流轮廓边缘所包含的所有像素点的面积S，如图4(a)所示．由于射流前锋面存在涡流的影响，射流形状变化大，射流锥角为射流外部边界的夹角，为了减小射流外围褶皱的影响，对射流主体小于L/2的部分采用了边界拟合的算法，即在纵向上每隔一定的像素点获取射流边界，在横向上的左边界与右边界点的像素点坐标，对获得的左边界点和右边界点分别使用polyfit函数拟合，这两条拟合线的夹角即为射流锥角，如图4(b)所示．射流体积定义为射流主体所占有的体积，假设射流在图片上每行像素点上是直径与宽度相等的微小圆柱体，对不同行像素点上的微小圆柱体的体积Vd叠加即为射流主体的体积V，如图4(c)所示．
为评估不同喷射状态下氢气对于周围气体的卷吸能力，用卷吸比ϕ评估氢气射流的混合特性[15]．卷吸比定义为
ϕ=(V−V0)/V0
式中：V0为氢气射流中氢气的体积，通过质量流量计算；V为射流主体的体积，通过纹影图片处理得到．
2　结果及分析
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2.1　氢气射流发展
图5为3种状态下射流发展随时间的变化．由于3种状态下喷射参数的不同，喷射时氢气的密度不同，周围气体密度也不同．超-超状态下氢气射流图像更加清晰，亚-亚与超-亚状态下，射流前锋区域较为模糊．不同状态下射流贯穿距均随时间增加，超-超状态下的射流锥角比其他两种喷射状态略微增大，射流近场区域边界较为平滑，而远场区域射流边界由于动量和能量交换以及热质传递产生褶皱．图5中亚-亚、超-亚和超-超状态下雷诺数分别为36280、173019和99813，雷诺数Re由式(5)计算而得．雷诺数越大，射流中从大涡到小涡之间的过渡越复杂，涡系结构越丰富，同时环境压力的增加会使环境密度增大，对射流的阻力也更大，褶皱更加明显，因而超-超状态下射流在0.8ms时射流前锋区域出现了非常明显的褶皱，其射流前锋的宽度更大；在0.8ms之后，超-超状态下射流前锋褶皱依旧明显．亚-亚状态下射流随射流贯穿距的增加，射流前锋轮廓更加不清晰，这主要是由于亚-亚状态下氢气密度小，且随着扩散与环境密度的差异更小，是光的折射减弱造成的．
Re=(ρauDe)/μ
De=Dρa/ρb
式中：ρa为射流流体密度；u为射流速度；μ为流体动力黏度；De为当量直径；D为喷嘴孔径；ρb为环境密度．
2.2　亚-亚与超-亚对比分析
图6所示对比压力为0.31、0.62和0.93表示氢气亚-亚状态下射流宏观特性随时间的变化，对比压力为1.54、3.08和4.63表示氢气超-亚状态下射流宏观特性随时间的变化．
图6(a)为两种状态下射流贯穿距随时间的变化趋势．由于1ms以前喷射出的氢气量较少，后续从喷嘴喷出的氢气不断地给射流提供动量，推动前端射流向前发展，射流贯穿距离随时间增加而迅速增长，超-亚状态下氢气射流贯穿距的斜率大于亚-亚状态下射流贯穿距斜率，这是由于氢气进入相同的环境，超临界氢气相较亚临界具有更大压差且密度大，氢气射流膨胀程度更大，超临界氢气射流贯穿距略微大于亚临界射流．1ms后贯穿距随射流发展趋势变缓，主要有两方面原因造成：(1)随着时间的推移，射流前端氢气发生扩散并与氮气混合，氢气浓度逐渐减小，前端氢气携带的动量几乎全部耗散，此时射流前端整体质量增加，后续射流携带的动量需要推动更多的气体，进而减弱了射流的强度和贯穿能力；(2)低密度氢气射流在穿过高密度氮气环境的过程中会与氮气分子相互碰撞，从而转移动量和能量，导致射流的速度减小和能量损失，使得射流贯穿能力减弱．超-亚状态下氢气射流的密度较亚-亚状态下的大，质量流量随之增加，出口动量增大，后续射流可以对前端射流提供更多的能量传递，从而导致射流贯穿距的增加，3ms时超-亚状态下氢气射流贯穿距较亚-亚状态平均增加31.5%．
图6(b)为射流锥角随时间的变化趋势．射流锥角的变化趋势以1ms时为界可以分为两段：1ms前的射流初期由于针阀存在节流作用，喷射的氢气量较小时，氢气作为低密度气体，气体分子间距与液体相比要大的多，分子间作用力非常微小，分子可以自由运动，极易变形，因而射流锥角变化较大；当喷嘴流量稳定后，射流形态变得稳定，1ms后射流锥角均在各自的平均值±1°内浮动．在0.2ms时尽管由于存在针阀的运动导致了质量流量不稳定，但超-亚状态下的氢气密度和质量流量仍大于亚-亚状态，而两种状态下的射流轴向贯穿距相差3mm左右．因此，两种状态下质量流量的差异表现在射流锥角上．亚-亚状态下，喷射对比压力从0.31升高到0.93，射流锥角增加3°左右；而在超-亚状态下喷射对比压力从1.54增加到4.63时，射流锥角增加了1.5°左右．超-亚状态下平均射流锥角均大于亚-亚状态下的，这是由于超-亚状态下氢气射流密度大，后续射流对前端射流能量传递的更多，射流边界层与氮气的湍流程度也更大，卷吸周围气体的量随之增加，使得径向贯穿能力增加，导致射流锥角增大．
图6(c)为射流表面积随时间的变化趋势．不同状态下氢气射流的表面积均随时间增长．超-亚状态下氢气射流表面积比亚-亚状态下氢气射流表面积大，3ms时超-亚状态下氢气射流面积较亚-亚状态平均增加33.6%，是因为超-亚状态下氢气射流贯穿距和射流锥角均大于亚-亚状态．在亚-亚状态下，不同喷射压力下射流表面积曲线的斜率相差不大，而超-亚状态下氢气射流表面积曲线的斜率差异较大，可见超-亚状态下氢气射流表面积对喷射压力的改变较敏感，而亚-亚状态下射流表面积对喷射压力的改变不太敏感．
图6(d)为射流体积随着时间的变化趋势．在不同状态下氢气的射流体积随时间而增加．在亚-亚状态下，氢气射流体积增加缓慢，而超-亚状态下氢气射流体积迅速增加．超-亚状态下，超临界氢气会被压缩为更高密度的状态，当氢气射流进入氮气环境中时，由于压差会发生膨胀过程，一些试验和数值模拟[16-17]已经证明了随着压差的增大，射流的膨胀程度更大，因而超临界氢气膨胀程度更大．同时超临界氢气的密度和黏性较大，与氮气接触的边界湍流强度更强，卷吸周围气体的量增加．因此，随着射流的发展，其射流体积迅速增加，3ms时超-亚状态下氢气射流体积较亚-亚状态平均增加200.7%．
2.3　超-亚与超-超对比分析
图7为超-亚与超-超状态下射流特征参数对比．其中：对比压力为0.08、0.39和0.77表示氢气超-亚状态下射流宏观特性随时间的变化；对比压力为1.16、1.54表示氢气超-超状态下射流宏观特性随时间的变化．
图7(a)为射流贯穿距随时间的变化趋势．射流贯穿距的发展同样呈现为两个阶段，在1ms以前射流贯穿距随时间迅速增加，随后贯穿距随时间的增长趋势变缓，此时超-超状态下氢气射流贯穿距的斜率小于超-亚状态下的氢气射流贯穿距斜率，这是因为超-超状态下，虽然喷嘴出口处氢气状态与超-亚状态相同，即后续射流对前端射流提供的动量相同，但由于容弹内环境状态不同，环境处于氢气的超临界条件，环境密度大，背压和分子间作用力加剧了氢气射流的阻力，氢气射流的动量耗散加快，后续射流更难推动前端射流向前发展．超-超状态下，超临界环境使得其贯穿能力明显小于超-亚状态下的贯穿能力．3ms时超-亚状态下氢气射流贯穿距较超-超状态平均增加47.6%．
图7(b)为射流锥角随时间的变化趋势．与图6(b)所述的亚-亚与超-亚状态下的对比相似，1ms前射流初期锥角由于针阀的运动射流锥角变化较大；1ms后射流后期锥角都在各自的平均值±1°内浮动．由于氢气射流进入超临界环境时环境密度增加导致受到的阻力增加，其轴向穿透能力减弱，更多向径向发展，超-超状态下氢气射流锥角大于超-亚状态下的锥角．超-亚状态下，环境对比压力从0.08升高到0.77，射流锥角增加5°左右；而在超-超状态下环境压力从1.16增加到1.54时，射流锥角增加了1°左右．可以发现，超-超状态下氢气射流锥角对环境变化不敏感，而超-亚状态下氢气射流锥角对环境变化较为敏感．
图7(c)为射流表面积随时间的变化趋势．超-亚与超-超状态下氢气射流的表面积均随时间增大．但超-亚状态下氢气射流表面积比超-超状态下氢气射流表面积大，是因为超-亚状态与超-超状态相比，氢气喷射时的热力学性质相同，然而环境从亚临界过渡到超临界，氢气在高密度介质中穿透能力减弱，限制了氢气射流的扩散．超-亚状态下射流贯穿距大、射流锥角小，其射流面积增加，说明射流面积受贯穿距的发展影响最大．3ms时超-亚状态下氢气射流表面积较超-超状态平均增加51.5%．
图7(d)为射流体积随着时间的变化趋势．在不同状态下氢气射流体积随时间快速增加．超-亚与超-超状态相比，超-亚状态下射流体积大于超-超状态下的射流体积，其原因类似于两种状态下氢气射流表面积的发展．3ms时超-亚状态下氢气射流体积较超-超状态平均增加130.6%．
2.4　卷吸比
图8为氢气射流在3种状态下的卷吸比．实际喷射过程中，在针阀开启初期流通截面积较小，导致射流初期实际的质量流量比计算所得的结果小，因而使得卷吸比出现了负值．但实际针阀运动的时间极短，不影响对3种状态下卷吸比的比较分析．
图8(a)显示了卷吸比随时间的变化趋势，在1ms以前，3种状态下卷吸比均随射流发展增加较快，随后缓慢增加．与贯穿距随时间的变化趋势相同，氢气刚流出喷嘴时具有较大的动量，与周围气体相互作用引起的湍流强度较大，因而氢气射流可以夹带较多的周围气体．随着射流与周围气体间的动量交换，射流与周围气体之间的速度差减小使得湍流强度减小，夹带能力减弱．喷射条件从亚临界到超临界时，氢气射流的卷吸比增大，是因为超临界氢气具有更大的密度，当喷射进入环境中时，会产生更大的膨胀和加速效果，与环境气体的接触面积较大，可以携带更多的环境气体．环境条件从亚临界到超临界时，氢气射流的卷吸比同样增加则是因为环境气体的压力升高会使其密度增加，射流中的高速气流会与高压环境气体相互作用，由于密度差异更大，在相互作用区域会产生更强的湍流和涡旋结构，将周围环境气体混合到射流中，从而增加了环境气体的携带量．在3ms时，超-超状态下氢气射流卷吸比相较亚-亚状态增加了349%，较超-亚状态增加了109%．化学计量比下氢气与空气的体积比为2.38，则理论空燃比下氢气射流的卷吸比为1.38．虽然亚-亚状态下卷吸比较低，但仍能够携带足够的空气．在缸内直喷氢内燃机中，于压缩上止点附近喷入氢气，其喷射条件能满足超-亚或超-超状态，有利于实现氢气的稀薄分层燃烧．
图8(b)为3种状态下卷吸比随贯穿距的变化趋势．卷吸比随贯穿距呈线性增长，贯穿距越大，卷吸比越大．随着喷射条件和环境条件从亚临界过渡到超临界，卷吸比随贯穿距增长的斜率更大．随着时间的增加卷吸比增长趋势变缓，但随着贯穿距的增长依然保持相同的斜率．在环境条件从亚临界到超临界时，尽管超-超状态下贯穿距减小了，但仍具有较好的卷吸能力，因而缸内直喷氢内燃机适当提高缸内压力，有利于氢气射流卷吸更多的空气．
2.5　氢气射流贯穿距经验公式
Turner[18]在1962年首次提出了欠膨胀气体射流的数学模型，该模型把气体射流的几何形状近似为球形涡头和传递动量的准稳态射流区域．后来Hill等[19]在Turner[18]的基础上，通过圆孔喷嘴天然气射流的试验，提出气体射流的贯穿距是孔径、时间、出口总动量流率和周围气体密度的函数，并建立了射流贯穿距的数学公式，如式(7)所示．
y=Γ(Mn/ρ0)0.25t0.5
式中：y为射流贯穿距；Γ为贯穿常数，由试验确定，Hill等[19]的试验中贯穿常数Γ为3.0±0.1；Mn为动量流率，即为表2中的P*；ρ0为周围气体密度；t为时间．
Chitsaz等[20]研究了孔径为0.5～1.0mm和压比(喷射压力/环境压力)在1.5～36.0下的氦气射流贯穿距，得出Γ在1.89～2.95内．通过以上研究发现贯穿常数Γ由于喷射条件、喷嘴结构和孔径的不同并不是固定值，且大部分工作都是针对天然气进行的．因此，基于现有的试验数据验证式(7)对氢气射流的适用性．
图9给出了y/(Mn/ρ0)0.25随t0.5的变化规律，可见量纲为1的贯穿距曲线均呈直线，直线的斜率即为Γ．但是将Γ代入式(7)中得到贯穿距曲线整体上比试验值偏大，笔者根据试验数据提出了氢气喷射的贯穿距经验公式为
y=Γ(Mn/ρ0)0.25t0.5+a
式中：a为修正常数，-0.004<a<-0.002．
图10显示射流贯穿距试验值与拟合值的对比．在环境温度为298K、喷嘴孔径为0.35的试验条件下提出的氢气射流贯穿距经验公式具有较好的精度，贯穿常数Γ为2.55±0.2．对氢气射流贯穿距经验式(8)中的Γ和a是否与氢气浮力有关以及对式(8)的优化将在以后的工作中深入讨论．
3　结论
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(1) 不同喷射状态下，射流贯穿距均随时间增加，但射流锥角的变化不大，射流近场区域边界较为平滑，而远场区域射流边界由于与周围气体的动量交换变得更加皱褶．
(2) 超-亚与亚-亚状态相比，3ms时超-亚状态下氢气射流贯穿距较亚-亚状态增加31.5%，射流面积增加33.6%，射流体积增加200.7%；射流锥角的差值在误差带范围内，两种状态下相差不大；氢气超临界喷射有利于增大射流贯穿距．
(3) 超-亚与超-超状态相比，3ms时超-亚状态下氢气射流贯穿距较超-超状态增加47.6%，射流面积增加51.5%，射流体积增加130.6%，但超-超状态下射流锥角较超-亚状态增大23.8%；当环境从亚临界到超临界状态时，射流在径向上的发展较为明显．
(4) 对于3种状态下卷吸比的对比，发现超-超状态下其射流卷吸周围气体的能力更强，在3ms时卷吸比较超-亚状态增加了109%，较亚-亚状态增加了349%，由此可见超临界环境有利于氢气射流混合；在试验条件下提出了关于氢气射流贯穿距经验公式，引入了修正常数使其具有较高的精度．
基金
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  • 国家自然科学基金资助项目(51906061)
  • 龙门实验室资助项目(LMQYTSKT038)
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2025年第43卷第1期
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doi: 10.16236/j.cnki.nrjxb.202501005
  • 接收时间：2024-03-24
  • 首发时间：2026-11-06
  • 出版时间：2025-01-25
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  • 收稿日期：2024-03-24
  • 修回日期：2024-09-18
基金
国家自然科学基金资助项目(51906061)
龙门实验室资助项目(LMQYTSKT038)
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    河南科技大学车辆与交通工程学院，洛阳 471003

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马志豪，博士，教授，．
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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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