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Article(id=1319293650085991085, tenantId=1146029695717560320, journalId=1316781260334530699, issueId=1319293461287780384, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1005-0329.2025.10.012, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1737302400000, receivedDateStr=2025-01-20, revisedDate=1752681600000, revisedDateStr=2025-07-17, acceptedDate=null, acceptedDateStr=null, onlineDate=1792473717471, onlineDateStr=2026-10-20, pubDate=1761840000000, pubDateStr=2025-10-31, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1792473717471, onlineIssueDateStr=2026-10-20, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1792473717471, creator=13701087609, updateTime=1792473717471, updator=13701087609, issue=Issue{id=1319293461287780384, tenantId=1146029695717560320, journalId=1316781260334530699, year='2025', volume='53', issue='10', pageStart='1', pageEnd='118', issueExtLink='null', onlineDate='null', pubDate='1761840000000', pubDateStr='2025-10-31', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1792473672458, creator='13701087609', updateTime=1792473672458, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=102, endPage=110, ext={EN=ArticleExt(id=1319293650270540462, articleId=1319293650085991085, tenantId=1146029695717560320, journalId=1316781260334530699, language=EN, title=Optimization study on atomization performance of external‑mix air‑atomizing nozzle based on surrogate model, columnId=null, journalTitle=Fluid Machinery, columnName=null, runingTitle=null, highlight=null, articleAbstract=

To investigate the influence of operating parameters on the atomization performance of external‑mix air‑atomizing nozzles and determine the optimal operating parameters for achieving the best atomization effect，a combined method of finite element model construction and optimization calculation was adopted for relevant research.Using gas inlet pressure，liquid inlet pressure，and liquid kinematic viscosity as optimization variables，and atomization cone angle and outlet flow coefficient as optimization objectives，an orthogonal experiment was designed and conducted.Based on the orthogonal experimental data，a response surface surrogate model was established，and this surrogate model was optimized using genetic algorithm，followed by simulation verification and comparative analysis of results.The results show that gas inlet pressure，liquid inlet pressure，and liquid kinematic viscosity all have significant effects on nozzle atomization performance；when the gas inlet pressure is 0.057 2 MPa，liquid inlet pressure is 0.111 2 MPa，and liquid kinematic viscosity is 0.057 3 Pa·s，the nozzle atomization performance reaches its optimum.Compared with the original model，the atomization cone angle increases by 34.62%，and the outlet flow coefficient improves by 49.36%.The research can provide references for the setting of operating parameters for nozzles.

, authors=Zegang SUN, Zhonghao ZHENG, Yu LIU, Zhuomin WANG, authorsList=Zegang SUN, Zhonghao ZHENG, Yu LIU, Zhuomin WANG, authorCompany=null, correspAuthors=Zhonghao ZHENG, 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=1319293654192214731, articleId=1319293650085991085, tenantId=1146029695717560320, journalId=1316781260334530699, language=CN, title=基于代理模型外混式空气雾化喷嘴雾化性能优化研究, columnId=1317484300472271469, journalTitle=流体机械, columnName=应用技术, runingTitle=null, highlight=null, articleAbstract=

为探究工况参数对外混式空气雾化喷嘴雾化性能的影响规律，并确定喷嘴达到最佳雾化效果时的最优工况参数，采用有限元模型构建与优化计算相结合的方法开展相关研究。以气体入口压力、液体入口压力及液体运动黏度为优化变量，以雾化锥角和出口流量系数为优化目标，设计并进行正交试验。基于正交试验数据建立响应面代理模型，通过遗传算法对该代理模型进行优化计算，随后开展仿真验证与结果对比分析。结果表明：气体入口压力、液体入口压力及液体运动黏度均对喷嘴雾化性能具有显著影响；当气体入口压力为0.057 2 MPa、液体入口压力为0.111 2 MPa、液体运动黏度为0.057 3 Pa·s时，喷嘴雾化性能达到最优。与原模型相比，雾化锥角增大34.62%，出口流量系数提升49.36%。研究可为喷嘴的工况参数设置提供参考。

, authors=孙泽刚, 郑中豪, 刘煜, 王卓敏, authorsList=孙泽刚, 郑中豪, 刘煜, 王卓敏, authorCompany=null, correspAuthors=郑中豪, authorNote=

孙泽刚（1975），男，博士，副教授，研究方向为液压元件优化和设计，E-mail：。

, correspAuthorsNote=
郑中豪（1997），男，硕士研究生，研究方向为计算流体力学研究和应用，通信地址：643000四川省自贡市自流井区汇兴路519号四川轻化工大学机械工程学院重点实验室，E-mail：。
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孙泽刚（1975），男，博士，副教授，研究方向为液压元件优化和设计，E-mail：。

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孙泽刚（1975），男，博士，副教授，研究方向为液压元件优化和设计，E-mail：。

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figureFileBig=83k2LLqyeVbjHozBXcBUZQ==, tableContent=null), ArticleFig(id=1319293659565118208, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293650085991085, language=CN, label=图11, caption=雾化锥角拟合曲线

（a）气体入口压力 （b）液体入口压力 （c）液体运动黏度

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（a）气体入口压力 （b）液体入口压力 （c）液体运动黏度

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（a）原模型 （b）优化模型

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Orthogonal test factor level table

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项目A/MPaB/MPaC/（Pa·s）
水平10.0200.090.038
水平20.0350.100.048
水平30.0500.110.058
水平40.0650.120.068
水平50.0800.130.078
), ArticleFig(id=1319293660148126472, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293650085991085, language=CN, label=表1, caption=

正交试验因子水平

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项目A/MPaB/MPaC/（Pa·s）
水平10.0200.090.038
水平20.0350.100.048
水平30.0500.110.058
水平40.0650.120.068
水平50.0800.130.078
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Orthogonal test results

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项目A/MPaB/MPaC/（Pa·s）出口流量系数雾化锥角/（°）
10.0200.110.0580.38110
20.0200.100.0480.32514
30.0350.110.0380.3115
40.0500.900.0480.20030
50.0650.110.0480.32227
60.0500.130.0380.29618
70.0500.110.0680.21524
80.0650.120.0580.24744
90.0800.120.0380.25023
100.0350.120.0480.34816
110.0500.120.0780.22523
120.0650.900.0780.19126
130.0800.100.0680.15525
140.0800.110.0780.16119
150.0350.130.0580.33117
160.0800.130.0480.23140
170.0200.120.0680.28312
180.0200.130.0780.38714
190.0200.900.0380.4097
200.0650.130.0680.24420
210.0800.900.0580.14226
220.0350.100.0780.22427
230.0500.100.0580.18920
240.0650.100.0380.24420
250.0350.100.0680.21621
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正交试验结果

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项目A/MPaB/MPaC/（Pa·s）出口流量系数雾化锥角/（°）
10.0200.110.0580.38110
20.0200.100.0480.32514
30.0350.110.0380.3115
40.0500.900.0480.20030
50.0650.110.0480.32227
60.0500.130.0380.29618
70.0500.110.0680.21524
80.0650.120.0580.24744
90.0800.120.0380.25023
100.0350.120.0480.34816
110.0500.120.0780.22523
120.0650.900.0780.19126
130.0800.100.0680.15525
140.0800.110.0780.16119
150.0350.130.0580.33117
160.0800.130.0480.23140
170.0200.120.0680.28312
180.0200.130.0780.38714
190.0200.900.0380.4097
200.0650.130.0680.24420
210.0800.900.0580.14226
220.0350.100.0780.22427
230.0500.100.0580.18920
240.0650.100.0380.24420
250.0350.100.0680.21621
), ArticleFig(id=1319293660445922059, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293650085991085, language=EN, label=Tab.3, caption=

Analysis of variance for atomization cone angle

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项目A方差/PaB方差/PaC方差/（Pa·s）
F7.785.767.23
K111.422.014.6
K217.220.025.4
K323.017.023.4
K427.423.620.4
K526.621.821.8
), ArticleFig(id=1319293660529808140, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293650085991085, language=CN, label=表3, caption=

雾化锥角方差分析结果

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项目A方差/PaB方差/PaC方差/（Pa·s）
F7.785.767.23
K111.422.014.6
K217.220.025.4
K323.017.023.4
K427.423.620.4
K526.621.821.8
), ArticleFig(id=1319293660605305613, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293650085991085, language=EN, label=Tab.4, caption=

Analysis of variance for outlet flow coefficient

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项目A方差/PaB方差/PaC方差/（Pa·s）
F24.014.716.1
K10.3570.2320.302
K20.2860.2440.285
K30.2250.2780.258
K40.2500.2710.223
K50.1880.2980.238
), ArticleFig(id=1319293660697580302, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293650085991085, language=CN, label=表4, caption=

出口流量系数方差分析

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项目A方差/PaB方差/PaC方差/（Pa·s）
F24.014.716.1
K10.3570.2320.302
K20.2860.2440.285
K30.2250.2780.258
K40.2500.2710.223
K50.1880.2980.238
), ArticleFig(id=1319293662434022159, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293650085991085, language=EN, label=Tab.5, caption=

Surrogate model accuracy verification

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项目xyz原始值预测值误差绝对值
数值564-41.97-42.130.16
), ArticleFig(id=1319293662576628497, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293650085991085, language=CN, label=表5, caption=

代理模型精度验证

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项目xyz原始值预测值误差绝对值
数值564-41.97-42.130.16
), ArticleFig(id=1319293662652125970, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293650085991085, language=EN, label=Tab.6, caption=

Comparison between algorithm optimization results and original results

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项目气体入口压力/MPa液体入口压力/MPa液体运动黏度/（Pa·s）雾化锥角/（°）出口流量系数
原始值0.050 00.100 00.048 0260.235
优化值0.057 20.111 20.057 3350.351
提升百分比/%———34.6249.36
), ArticleFig(id=1319293662731817747, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1319293650085991085, language=CN, label=表6, caption=

算法优化结果与原模型结果对比

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项目气体入口压力/MPa液体入口压力/MPa液体运动黏度/（Pa·s）雾化锥角/（°）出口流量系数
原始值0.050 00.100 00.048 0260.235
优化值0.057 20.111 20.057 3350.351
提升百分比/%———34.6249.36
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基于代理模型外混式空气雾化喷嘴雾化性能优化研究
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孙泽刚 , 郑中豪 , 刘煜 , 王卓敏
流体机械 | 应用技术 2025,53(10): 102-110
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流体机械 |应用技术 2025 , 53 (10) : 102 -110
基于代理模型外混式空气雾化喷嘴雾化性能优化研究
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孙泽刚（1975），男，博士，副教授，研究方向为液压元件优化和设计，E-mail：。

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孙泽刚 , 郑中豪 , 刘煜, 王卓敏
作者信息
  • 四川轻化工大学 机械工程学院，四川 自贡 643000
通讯作者:
郑中豪（1997），男，硕士研究生，研究方向为计算流体力学研究和应用，通信地址：643000四川省自贡市自流井区汇兴路519号四川轻化工大学机械工程学院重点实验室，E-mail：。
作者简介:

孙泽刚（1975），男，博士，副教授，研究方向为液压元件优化和设计，E-mail：。

Optimization study on atomization performance of external‑mix air‑atomizing nozzle based on surrogate model
Zegang SUN , Zhonghao ZHENG , Yu LIU, Zhuomin WANG
Affiliations
  • School of Mechanical Engineering，Sichuan University of Science & Engineering，Zigong 643000，China
出版时间: 2025-10-31 doi: 10.3969/j.issn.1005-0329.2025.10.012
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摘要
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为探究工况参数对外混式空气雾化喷嘴雾化性能的影响规律，并确定喷嘴达到最佳雾化效果时的最优工况参数，采用有限元模型构建与优化计算相结合的方法开展相关研究。以气体入口压力、液体入口压力及液体运动黏度为优化变量，以雾化锥角和出口流量系数为优化目标，设计并进行正交试验。基于正交试验数据建立响应面代理模型，通过遗传算法对该代理模型进行优化计算，随后开展仿真验证与结果对比分析。结果表明：气体入口压力、液体入口压力及液体运动黏度均对喷嘴雾化性能具有显著影响；当气体入口压力为0.057 2 MPa、液体入口压力为0.111 2 MPa、液体运动黏度为0.057 3 Pa·s时，喷嘴雾化性能达到最优。与原模型相比，雾化锥角增大34.62%，出口流量系数提升49.36%。研究可为喷嘴的工况参数设置提供参考。

外混式空气雾化喷嘴  /  气体入口压力  /  液体入口压力  /  液体运动黏度

To investigate the influence of operating parameters on the atomization performance of external‑mix air‑atomizing nozzles and determine the optimal operating parameters for achieving the best atomization effect，a combined method of finite element model construction and optimization calculation was adopted for relevant research.Using gas inlet pressure，liquid inlet pressure，and liquid kinematic viscosity as optimization variables，and atomization cone angle and outlet flow coefficient as optimization objectives，an orthogonal experiment was designed and conducted.Based on the orthogonal experimental data，a response surface surrogate model was established，and this surrogate model was optimized using genetic algorithm，followed by simulation verification and comparative analysis of results.The results show that gas inlet pressure，liquid inlet pressure，and liquid kinematic viscosity all have significant effects on nozzle atomization performance；when the gas inlet pressure is 0.057 2 MPa，liquid inlet pressure is 0.111 2 MPa，and liquid kinematic viscosity is 0.057 3 Pa·s，the nozzle atomization performance reaches its optimum.Compared with the original model，the atomization cone angle increases by 34.62%，and the outlet flow coefficient improves by 49.36%.The research can provide references for the setting of operating parameters for nozzles.

external‑mix air‑atomizing nozzle  /  gas inlet pressure  /  liquid inlet pressure  /  liquid kinematic viscosity
孙泽刚, 郑中豪, 刘煜, 王卓敏. 基于代理模型外混式空气雾化喷嘴雾化性能优化研究. 流体机械, 2025 , 53 (10) : 102 -110 . DOI: 10.3969/j.issn.1005-0329.2025.10.012
Zegang SUN, Zhonghao ZHENG, Yu LIU, Zhuomin WANG. Optimization study on atomization performance of external‑mix air‑atomizing nozzle based on surrogate model[J]. Fluid Machinery, 2025 , 53 (10) : 102 -110 . DOI: 10.3969/j.issn.1005-0329.2025.10.012
正文
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0　引言
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外混式空气雾化喷嘴具有雾化效率高、雾滴粒径均匀的特点，已广泛应用于各类工业场景，其雾化性能对生产效率与产品质量具有显著影响。该喷嘴的主要原理是利用高压液体与高压气体在流动过程中以一定角度相互撞击，使液滴破裂，从而产生细微雾滴［1］。合理调试喷嘴的工况参数，是提升其雾化性能的关键环节。
近年来，众多学者主要通过数值模拟与试验相结合的方法，围绕喷嘴雾化性能展开系统研究。陈有锦等［2］采用数值模拟方法，探究了不同流量与气体压力对喷嘴雾化效果的影响规律。蒋仲安等［3］自主搭建了喷嘴雾化试验平台，分析了流量与压力对雾化效果的作用机制，明确了雾滴粒径变化规律及最优气液压力-流量配比。刘联胜等［4］构建试验系统，重点研究气液质量流量比与工作压力对喷嘴除油效果及能耗的影响，最终确定了最佳气液质量流量比与工作压力参数。李卫军等［5］通过数值模拟方法，分析水流量对喷嘴内流场空气速度的影响，得出水流量增加会导致空气速度增大、雾滴粒径随之变大的结论。彭枢廷等［6］针对燃油喷嘴开展数值模拟研究，建立了喷嘴出口流量系数预测模型，并验证了模型的准确性，为喷嘴流量设计与校核提供了可靠方案。陈方备等［7］通过试验探究了入口压力、温度及流量对喷嘴雾化粒径的影响，发现入口压力对雾化效果的影响最为显著，而温度对雾化粒径的影响不明显。罗俊伟等［8］分析了介质流量与黏度对喷嘴雾化质量的作用，采用2种模拟方法耦合仿真喷嘴内部流场，得出雷诺数增大时，液膜厚度变薄、流量系数降低且雾化角增大的规律。谢远等［9］结合仿真与试验方法研究了环境压力对雾化效果的影响，指出雾化锥角随环境压力的增加呈缓慢增大趋势。吴雄［10］基于数值模拟方法，对U型管道喷嘴进行仿真分析，重点探讨压力参数对雾滴场分布的影响机制。于浩洋等［11］采用多种模拟方法对离心喷嘴展开研究，分析不同黏度液体对雾化性能的影响，发现喷嘴出口速度与液膜厚度均随液体黏度的增加而增大。
上述学者在喷嘴雾化性能优化领域已取得诸多研究成果，但关于多工况参数综合影响喷嘴雾化效果及多目标优化的研究较少。本文基于Fluent软件的VOF模块，对喷嘴内流场进行系统仿真分析，重点探究气体入口压力、液体入口压力及液体运动黏度这3个关键参数及其交互作用对喷嘴雾化特性的影响规律。通过设计正交试验获取基础数据，并基于该数据集构建以雾化锥角和出口流量系数为目标的响应面代理模型，采用遗传算法对代理模型进行多目标优化计算，最终确定最优工况参数组合。同时，通过对比优化前后的仿真结果，验证优化方案的有效性，为工程实践中喷嘴雾化性能的工况参数设置提供参考。
1　外混式空气雾化喷嘴的建模与仿真
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外混式空气雾化喷嘴的三维结构如图1所示。该喷嘴具有气体和液体双流道结构。
采用Fluent软件提取喷嘴内部流体域，同时在喷嘴出口处构建外计算域，用于模拟液体喷射过程。喷嘴计算域如图2所示。通过Mesh模块完成网格划分，网格总数为150万，且均采用六面体结构化网格。为确保仿真结果的可靠性，通过分析网格数量变化对雾化锥角的影响，开展网格无关性验证，验证结果如图3所示。
当网格数量减少时，雾化锥角的计算误差为5.28%；当网格数量增加时，雾化锥角的计算误差仅为0.77%。网格数量增加对雾化锥角计算结果的影响程度显著小于网格减少的影响，但网格数量增加会导致计算时间呈指数级增长。综合考虑计算精度与效率，最终确定150万左右的网格数量为最优方案。
文中基于Fluent软件中VOF方法［12］模拟喷嘴内流场。设置喷嘴气液入口类型为压力入口，出口为压力出口，出口压力为标准大气压。设定出口回流系数为0，以保证出口只有气体回流。为实现不同通道流入不同流体，将气体通道的气体体积分数设置为1，液体通道的气体体积分数设置为0。空气和油液之间的表面张力系数设定为0.04 N/m。设置初始迭代步数3 000步，迭代步长为10-5，并监测出口流量系数，当其差值小于2%时判定计算结果收敛。
以实际工况为例，对喷嘴内流场的流动特性展开系统分析。喷嘴出口速度云图如图4所示。可以看出，喷嘴出口中心区域速度最大，且沿径向向边缘逐渐递减。喷嘴出口回流区压力云图如图5所示。可以看出，喷嘴出口处压力最小。由于出口位置压力减小且流体速度显著增大，使得喷嘴出口压力低于外界环境压力，形成负压效应，进而导致外界空气倒灌入喷嘴口，最终在喷嘴口中心位置形成回流区。
喷嘴出口液体周向分布云图如图6所示。可以看出，受出口中心回流区的影响，液体以圆锥形态实现雾化喷射。
为验证文中仿真模型的准确性，对文献［13］中的标准模型进行等效仿真分析，仿真模型验证及结果对比见图7。可以看出，文中仿真结果与文献［13］中数据的误差均处于合理范围内（误差值均小于15%），表明所建仿真模型具备良好的准确性。为进一步保障研究结果的可靠性，基于该验证后的仿真模型进行重复仿真试验，结果显示多次仿真数据的误差甚微，证实仿真结果具有优异的可靠性与重复性。
2　多目标优化
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2.1　优化目标的确定
文中通过文献调研梳理大量喷嘴相关工况参数，结合单因素仿真试验分析，初步确定喷嘴的气体入口压力（A）、液体入口压力（B）及液体运动黏度（C）为影响雾化性能的关键因素。气体入口压力、液体入口压力及液体运动黏度影响曲线如图8~10所示。可以看出，当单独改变气体入口压力、液体入口压力或液体运动黏度时，喷嘴的雾化锥角与出口流量系数均呈现显著变化，进一步证实了上述3个参数对雾化性能的重要影响。
2.2　正交试验设计
采用正交试验方法［14-15］，以选取气体入口压力（A）、液体入口压力（B）及液体运动黏度（C）作为正交试验的核心影响因素，并结合喷嘴实际工况，合理设定各因素的水平梯度。具体参数水平设计如表1所示。
2.3　响应面代理模型
响应面法适用于多参数统计分析，且具备任意试验点的预测能力，其核心优势在于试验周期短、所需试验次数少［16］。基于该方法建立的回归方程如下［17-18］：
y=a0+∑i=1nbijxi+∑i<i1≤ncijxixi1+∑i=1ndijxi2
式中，y为评价指标；xi为第i个设计变量；a0，bij，cij，dij为代理模型多项式的系数。
3　结果分析及讨论
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正交试验共设计25组工况，试验结果如表2所示。
以气体入口压力、液体入口压力及液体运动黏度为自变量，以出口流量系数Q和雾化锥角θ为评价指标。选取上述指标的核心依据如下：雾化锥角是表征喷嘴雾化性能的关键参数，其数值大小直接决定喷雾覆盖范围与气液混合均匀性［19-20］；出口流量系数则是量化喷嘴流量特性的重要指标，具体定义为单位时间内流经喷嘴出口的流体质量或体积［21-22］。
3.1　方差分析
方差分析是检验两个及以上因素对试验结果影响显著性的常用统计方法。采用函数F对各因素间交互作用的影响显著性进行方差分析［23-24］：
Fαn1,n2=F
式中，α为置信区间；n1为各因素或各因素之间交互作用的自由度；n2为误差自由度之和。
由F分布表查得F0.05(2,15)=3.68。某因素F计算值大于F0.05(2,15)时，表示该因素对结果影响显著，显著程度由F值大小来决定。
雾化锥角方差分析结果如表3所示。FA，FB，FC均大于F0.05，表明气体入口压力、液体入口压力和液体运动黏度对雾化锥角的影响显著。由K4A>K5A>K3A>K2A>K1A，K4B>K1B>K5B>K2B>K3B，K2C>K3C>K5C>K4C>K1C可知，雾化锥角随气体入口压力增大而增大，随液体入口压力增大呈现先减小、后增大的变化趋势，随液体运动黏度增大呈现先增大、后减小的变化趋势。
出口流量系数方差分析如表4所示。FA，FB，FC均大于F0.05，表明气体入口压力、液体入口压力和液体运动黏度对出口流量系数的影响显著。由K1A>K2A>K4A>K3A>K5A，K5B>K3B>K4B>K2B>K1B，K1C>K2C>K3C>K5C>K4C可知，出口流量系数随气体入口压力增大呈现减小的趋势（除K4A），随液体入口压力增大呈现增大的趋势（除K4B），随液体运动黏度增大呈现减小的趋势（除K4C）。
3.2　回归分析
为进一步揭示气体入口压力、液体入口压力及液体运动黏度对喷嘴雾化锥角和出口流量系数的影响规律，基于表3、表4中的试验因素与评价指标数据进行拟合分析。针对雾化锥角、出口流量系数与上述3个关键参数间的相关性曲线，均采用三次多项式拟合方法构建回归关系。
雾化锥角与各关键参数的拟合曲线如图11所示。可以看出，随气体入口压力的增大，雾化锥角呈先升后降的变化趋势，当气体入口压力约为0.07 MPa时，雾化锥角达到该区间内的最大值；随液体入口压力的增大，雾化锥角呈现先减小、后增大、再减小的波动趋势，其中液体入口压力约为0.102 MPa时，雾化锥角达到区间最小值，而当压力增至约0.126 MPa时，雾化锥角达到区间最大值；随液体运动黏度的增大，雾化锥角呈先增大、后减小、再增大的变化特征，当液体运动黏度约为0.05 Pa·s时，雾化锥角达到区间最大值。
出口流量系数与各关键参数的拟合曲线如图12所示。可以看出，随气体入口压力的增大，出口流量系数呈持续减小趋势，当气体入口压力约为0.02 MPa时，出口流量系数达到该区间内的最大值；随液体入口压力的增大，出口流量系数呈持续增大趋势；随液体运动黏度的增大，出口流量系数呈先减小、后增大的特征，其中液体运动黏度约为0.038 Pa·s时，出口流量系数达到区间最大值，而当黏度增至约0.072 Pa·s时，出口流量系数达到区间最小值。
3.3　响应面代理模型的建立
采用DOE（design of experiment）软件并根据正交试验表，分别建立雾化锥角和出口流量系数的响应面代理模型，其表达式如下：
yθ=0.05+14.9x1-8.5x2+8.4x3-18.1x1x2+17.6x1x3-6.3x2x3+8.3x12+3.1x22+2.2x32+17.3x1x2x3+27.6x12x2-27.7x12x3-9.0x1x22-9.2x1x32-4.7x22x3+3.8x2x32-9.9x13+1.1x23
yQ=0.03+0.57x1-0.31x2+0.27x3-0.82x1x2+0.81x1x3-0.27x2x3+0.43x12+0.13x22+0.14x32+0.8x1x2x3+1.2x12x2-1.24x12x3-0.45x1x22-0.42x1x32-0.12x22x3+0.13x2x32-0.44x13+0.04x23
式中，yθ为雾化锥角，（°）；yQ为出口流量系数；x1为气体入口压力，MPa；x2为液体入口压力，MPa；x3为液体运动黏度，Pa·s。
雾化锥角yθ方程、出口流量系数yQ方程的回归系数分别为R2=0.93，R2=0.94，表明方程的拟合精度较高，适用于优化计算。为进一步验证代理模型的精度，根据文献［25］提出的方法进行验证。选取任意点（x，y，z）分别代入原模型［25］与代理模型，并对结果进行对比，如表5所示。结果表明，得到的代理模型在精度上已经非常接近原始函数，能够达到工程应用的要求。
以雾化锥角和出口流量系数都达到最大值作为最佳雾化效果的评价标准，其约束条件如下：
maxyθ=fx1,x2,x3maxyQ=fx1,x2,x30.02≤x1≤0.08,0.09≤x2≤0.13,0.38≤x3≤0.78
采用理想点法［26-27］进行多目标规划。鉴于雾化锥角与出口流量系数对喷嘴雾化质量的影响同等重要，故赋予两者相同权重（均为0.5）。对雾化锥角和出口流量系数进行归一化处理后，得到表达式如下：
Y=0.5(yθ-0.413 8)2+0.5(yQ-0.009 5)2
式中，Y为多目标函数值。
3.4　优化计算及结果分析
通过MATLAB软件构建代理模型，采用遗传算法［28-30］进行优化计算，设定相应控制参数并遵循优化流程执行，迭代曲线如图13所示。
遗传算法的控制参数设置：迭代次数500次，种群数量100，交叉概率0.6，变异概率0.05。优化前后的参数与性能指标对比分析结果见表6。
优化后雾化锥角较原模型增大34.62%，出口流量系数较原模型增加49.36%。原模型与优化模型雾化锥角的仿真结果对比如图14所示。原模型的雾化锥角为26°，优化模型的雾化锥角为35°。
4　结论
收起
（1）气体入口压力对喷嘴雾化性能影响最显著，气体入口压力增大能显著提升出口流量系数和雾化锥角。出口流量系数和雾化锥角均随液体入口压力和液体运动黏度的增加而逐渐增大。
（2）基于外混式空气雾化喷嘴优化前后仿真结果对比分析可知，当气体入口压力为0.057 2 MPa、液体入口压力为0.111 2 MPa、液体运动黏度为0.057 3 Pa·s时，喷嘴雾化性能达到最优，此时雾化锥角比原模型增大34.62%，出口流量系数比原模型增加49.36%。

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2025年第53卷第10期
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doi: 10.3969/j.issn.1005-0329.2025.10.012
  • 接收时间：2025-01-20
  • 首发时间：2026-10-20
  • 出版时间：2025-10-31
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  • 收稿日期：2025-01-20
  • 修回日期：2025-07-17
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    四川轻化工大学 机械工程学院，四川 自贡 643000

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郑中豪（1997），男，硕士研究生，研究方向为计算流体力学研究和应用，通信地址：643000四川省自贡市自流井区汇兴路519号四川轻化工大学机械工程学院重点实验室，E-mail：。
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