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Article(id=1204388206151185205, tenantId=1146029695717560320, journalId=1189621681917173762, issueId=1204391519030587609, articleNumber=null, orderNo=null, doi=10.19620/j.cnki.1000-3703.20221016, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=null, receivedDateStr=null, revisedDate=1668614400000, revisedDateStr=2022-11-17, acceptedDate=null, acceptedDateStr=null, onlineDate=1765078124797, onlineDateStr=2025-12-07, pubDate=1703347200000, pubDateStr=2023-12-24, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1765078124797, onlineIssueDateStr=2025-12-07, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1765078124797, creator=13701087609, updateTime=1765078124797, updator=13701087609, issue=Issue{id=1204391519030587609, tenantId=1146029695717560320, journalId=1189621681917173762, year='2023', volume='', issue='12', pageStart='1', pageEnd='59', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1765078914649, creator=13701087609, updateTime=1765079351864, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1204393352914514422, tenantId=1146029695717560320, journalId=1189621681917173762, issueId=1204391519030587609, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1204393352914514423, tenantId=1146029695717560320, journalId=1189621681917173762, issueId=1204391519030587609, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=40, endPage=46, ext={EN=ArticleExt(id=1204388206356706111, articleId=1204388206151185205, tenantId=1146029695717560320, journalId=1189621681917173762, language=EN, title=Fluid Simulation and Motion Analysis of Free Piston Expander-Linear Generator, columnId=null, journalTitle=Automobile Technology, columnName=null, runingTitle=null, highlight=null, articleAbstract=

In order to improve the integration of free piston expander-linear generator, the motion of air in cylinder and the motion characteristics of piston were analyzed by using computational fluid dynamics method and dynamic grid technique, and the influence of cylinder structural parameters on the motion characteristics of piston was analyzed by orthogonal test. The results show that the air pressure and velocity change obviously when the air flows through the inlet and outlet. Cylinder orifice aperture has the greatest influence on piston velocity and displacement. Intake time, piston mass and cylinder diameter also have different influences on piston displacement and velocity.

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为提高自由活塞膨胀机-直线发电机装置的集成度，使用计算流体力学方法，运用动网格技术，分析了气缸内气体的运动情况和活塞的运动特性，并利用正交试验分析了气缸结构参数对活塞运动特性的影响程度。结果表明：气体流经进、排气通口处，气体压力和流速的变化较为明显；气缸通口孔径对活塞速度、位移的影响最大；进气时间、活塞质量、气缸直径对活塞的位移、速度也存在不同程度的影响。

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Keyword(id=1204452635538599994, tenantId=1146029695717560320, journalId=1189621681917173762, articleId=1204388206151185205, language=CN, orderNo=2, keyword=气缸), Keyword(id=1204452635681206338, tenantId=1146029695717560320, journalId=1189621681917173762, articleId=1204388206151185205, language=CN, orderNo=3, keyword=流体仿真), Keyword(id=1204452635807035470, tenantId=1146029695717560320, journalId=1189621681917173762, articleId=1204388206151185205, language=CN, orderNo=4, keyword=运动特性)], refs=[Reference(id=1204452640311718246, tenantId=1146029695717560320, journalId=1189621681917173762, articleId=1204388206151185205, doi=null, pmid=null, pmcid=null, year=2021, volume=7, issue=null, pageStart=1349, pageEnd=1359, url=null, language=null, rfNumber=[1], rfOrder=0, authorNames=PENG B Y, TONG L, GUO C D, journalName=Energy Reports, refType=null, unstructuredReference=PENG B Y, TONG L, GUO C D, et al. 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Research on Stability of Free Piston Expander and Linear Generator[J]. 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language=CN, label=图10, caption=不同进气时间下活塞的位移、速度曲线, figureFileSmall=L0Ay+LbOnJwfsqZq4mpQcA==, figureFileBig=OjeD/2k1z6GgoyCwCeFy0A==, tableContent=null), ArticleFig(id=1204452638894043407, tenantId=1146029695717560320, journalId=1189621681917173762, articleId=1204388206151185205, language=EN, label=null, caption=null, figureFileSmall=null, figureFileBig=null, tableContent=
项目 规格 项目 规格
缸径/mm 63 使用流体 空气
行程/mm 100 耐压试验压力/MPa 1.5
通口孔径/mm 4 最高使用压力/MPa 1.0
动作方式 单杆双作用 最低使用压力/MPa 0.05
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气缸规格

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项目 规格 项目 规格
缸径/mm 63 使用流体 空气
行程/mm 100 耐压试验压力/MPa 1.5
通口孔径/mm 4 最高使用压力/MPa 1.0
动作方式 单杆双作用 最低使用压力/MPa 0.05
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水平 因素A
（活塞质量）/kg		 因素B
（通口孔径）/mm		 因素C
（缸径）/mm
1 0.27 4 63
2 0.57 5 67
3 0.87 6 71
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三因素及相应的水平值

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水平 因素A
（活塞质量）/kg		 因素B
（通口孔径）/mm		 因素C
（缸径）/mm
1 0.27 4 63
2 0.57 5 67
3 0.87 6 71
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序号 因素A 因素B 因素C 位移/mm 峰值速度/m ∙s-1
1 A1 B1 C1 51.383 4.667
2 A1 B2 C2 63.936 6.232
3 A1 B3 C3 74.795 7.762
4 A2 B1 C2 48.119 3.353
5 A2 B2 C3 61.992 4.624
6 A2 B3 C1 96.950 6.759
7 A3 B1 C3 44.543 2.688
8 A3 B2 C1 77.803 4.288
9 A3 B3 C2 90.955 5.469
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正交试验方案及试验结果

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序号 因素A 因素B 因素C 位移/mm 峰值速度/m ∙s-1
1 A1 B1 C1 51.383 4.667
2 A1 B2 C2 63.936 6.232
3 A1 B3 C3 74.795 7.762
4 A2 B1 C2 48.119 3.353
5 A2 B2 C3 61.992 4.624
6 A2 B3 C1 96.950 6.759
7 A3 B1 C3 44.543 2.688
8 A3 B2 C1 77.803 4.288
9 A3 B3 C2 90.955 5.469
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参数 对于位移s的影响/mm 对于峰值速度vpeak的影响/m ∙s-1
k1 63.371 48.015 75.378 6.220 3.569 5.238
k2 69.020 67.910 67.670 4.912 5.048 5.018
k3 71.100 87.567 60.443 4.148 6.663 5.025
R 7.729 39.552 14.935 2.072 3.094 0.220
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极差分析结果

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参数 对于位移s的影响/mm 对于峰值速度vpeak的影响/m ∙s-1
k1 63.371 48.015 75.378 6.220 3.569 5.238
k2 69.020 67.910 67.670 4.912 5.048 5.018
k3 71.100 87.567 60.443 4.148 6.663 5.025
R 7.729 39.552 14.935 2.072 3.094 0.220
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自由活塞膨胀机-直线发电机流体仿真与运动分析*
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张凯 , 彭宝营 , 王鹏家 , 童亮
汽车技术 | 2023,(12): 40-46
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汽车技术 | 2023, (12): 40-46
自由活塞膨胀机-直线发电机流体仿真与运动分析*
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张凯, 彭宝营, 王鹏家, 童亮
作者信息
  • 北京信息科技大学，北京 100192
Fluid Simulation and Motion Analysis of Free Piston Expander-Linear Generator
Kai Zhang, Baoying Peng, Pengjia Wang, Liang Tong
Affiliations
  • Beijing Information Science & Technology University, Beijing 100192
出版时间: 2023-12-24 doi: 10.19620/j.cnki.1000-3703.20221016
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摘要
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为提高自由活塞膨胀机-直线发电机装置的集成度，使用计算流体力学方法，运用动网格技术，分析了气缸内气体的运动情况和活塞的运动特性，并利用正交试验分析了气缸结构参数对活塞运动特性的影响程度。结果表明：气体流经进、排气通口处，气体压力和流速的变化较为明显；气缸通口孔径对活塞速度、位移的影响最大；进气时间、活塞质量、气缸直径对活塞的位移、速度也存在不同程度的影响。

自由活塞膨胀机-直线发电机  /  气缸  /  流体仿真  /  运动特性

In order to improve the integration of free piston expander-linear generator, the motion of air in cylinder and the motion characteristics of piston were analyzed by using computational fluid dynamics method and dynamic grid technique, and the influence of cylinder structural parameters on the motion characteristics of piston was analyzed by orthogonal test. The results show that the air pressure and velocity change obviously when the air flows through the inlet and outlet. Cylinder orifice aperture has the greatest influence on piston velocity and displacement. Intake time, piston mass and cylinder diameter also have different influences on piston displacement and velocity.

Free piston expander-linear generator  /  Cylinder  /  Fluid simulation  /  Kinetic characteristic
张凯, 彭宝营, 王鹏家, 童亮. 自由活塞膨胀机-直线发电机流体仿真与运动分析*. 汽车技术, 2023 , (12) : 40 -46 . DOI: 10.19620/j.cnki.1000-3703.20221016
Kai Zhang, Baoying Peng, Pengjia Wang, Liang Tong. Fluid Simulation and Motion Analysis of Free Piston Expander-Linear Generator[J]. Automobile Technology, 2023 , (12) : 40 -46 . DOI: 10.19620/j.cnki.1000-3703.20221016
正文
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1 前言
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自由活塞膨胀机-直线发电机（Free Piston Expander-Linear Generator，FPE-LG）作为一种新型汽车余热回收装置，通过对汽车尾气进行回收利用，减少污染物排放量，提高能源利用效率。优化装置气缸部分尺寸，是提高装置集成度，使其顺利应用于汽车领域的一个重要方面，气缸内活塞的运动特性也受到诸多学者的关注。Peng等人研究了FPE-LG耦合驱动电机时活塞的运动特性[1]。赵腾龙等人基于FPE-LG试验台架研究了外接负载电阻对活塞运动特性的影响[2]。张红光等人研究了不同外部工况（驱动压力、工作频率、外接负载等）对活塞运动特性的影响[3-5]。Hou等人也研究了外部负载电阻对活塞运动特性的影响[6]。Mhadi A. Ismael等人开发自由活塞线性发电机试验台，研究了不同进气压力和阀门开启时间下的活塞运动[7]。此外，张红光等人通过仿真软件搭建了系统仿真模型，基于该模型研究了活塞初始位移、活塞-动子连杆质量以及工作频率等对活塞运动特性的影响[8]。Xu等人研究了不同气门正时对系统运动特性的影响，并通过仿真模型分析了活塞的运动特性，以及高频高压工况下系统的性能[9-11]。Li等人利用计算流体力学方法分析了不同工作频率对活塞位移的影响，以及进、排气过程中气体的流动情况[12]。李顿等人以振动特性和输出电压变化作为评价指标，研究了不同工况对FPE-LG系统平稳性的影响[13]。可以看出，对于活塞运动特性的研究主要集中在改变外部工况和外接负载方面，然而为了提高装置的集成度，气缸自身结构对活塞运动特性的影响同样需要考虑。本文使用Fluent软件，采用动网格技术对气缸进行仿真，得到气缸内气体压力和流速的分布情况，探究活塞质量、进排气通口直径、气缸直径以及进气时间对活塞运动特性的影响。
2 FPE-LG装置
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如图1a所示，FPE-LG试验台由左右两侧气缸、直线发电机、电磁阀以及各种传感器等组成。图1b所示为试验过程原理，空气压缩机产生压缩气体，储气罐起稳压作用，经压力调节阀调至适当压力后，气体进入气缸内膨胀做功，通过电磁阀控制进排气通道的开闭，实现活塞连杆的往复运动，带动直线发电机动子往复运动切割磁感线发电，从而实现将气体能量转化为电能。
3 仿真过程
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3.1 仿真模型的建立
试验装置中气缸型号为SMC MDBB 63-100nz，规格如表1所示。使用SolidWorks对气缸进行三维建模，并对模型进行合理简化，去除活塞杆，活塞初始位置为上止点，如图2所示。
3.2 网格划分
在Mash中进行网格划分：将活塞运动的区域设置为六面体网格，并选择生成映射网格（Mapped Mesh），此时网格包含的单元数量更少，计算速度更快；其余区域默认生成四面体网格。网格尺寸为0.005 m，网格节点数量为16 573个，网格单元数量为39 773个，网格划分结果如图3所示。
3.3 仿真条件设置
开启能量方程，选择Realizable k-epsilon粘性模型，壁面函数选择可缩放壁面函数（Scalable Wall Funcations），计算设置为瞬态计算。流体选择理想气体，初始进气压力设为0.3 MPa。在动网格中对6个自由度进行设置，活塞运动方向选择沿X方向平移。活塞质量为0.27 kg，忽略气缸与活塞间的摩擦。
4 仿真结果及分析
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4.1 仿真结果
4.1.1 不同阶段气体压力、速度云图
气体在气缸内共经历3个阶段，即进气阶段、膨胀阶段和排气阶段。进气阶段，通口1、通口4开启，通口2、通口3关闭，气体进入左侧气腔，活塞在气体的推动下从左向右移动。一段时间后，关闭通口1，气体在气缸内膨胀，继续推动活塞向右运动，此阶段为膨胀阶段。当活塞到达右侧极限位置时，通口2、通口3开启，通口1、通口4关闭，活塞从右向左运动，左侧气腔内的气体排出气缸，此阶段为排气阶段。
图4所示为仿真过程中气缸内气体在通口截面处不同阶段的压力云图，可以看出，进气阶段随着气体流入左侧进气腔，活塞从左向右移动，进气腔压力逐渐增大。由于活塞向右移动，活塞右侧腔体体积减小，气体受到挤压后并不能及时由排气门排出，导致右侧腔内气体压力也逐渐增大。膨胀阶段，气体停止流入气缸，气缸内的气体继续膨胀，推动活塞继续向右运动。随着活塞左侧腔体体积逐渐增大，压力逐渐降低。活塞左、右两侧压力差使得活塞进行减速运动，直到速度减为0。排气阶段，左侧腔体内气体受到挤压未能及时排出气缸，排气阶段结束时左侧腔体内的压力增大，未排出气体进入下一循环继续利用。
图5所示为仿真过程中气缸内活塞左、右两侧气体的流速，可以看出，在进气阶段和膨胀阶段，进气侧腔体内，气体由进气通孔流入气缸，受气缸约束形成涡流，排气侧腔体内气体较少，气体沿气缸轴线均匀流出气缸。处于排气阶段时，由于活塞左、右两侧腔体内均已有气体，气体间相互作用，所以气体流线规律不再明显，形成紊流现象。
4.1.2 仿真结果验证
为验证仿真结果的合理性，对比进气压力为0.3 MPa时，试验与仿真所得的活塞位移曲线，如图6所示。活塞稳定运行时，进气阶段活塞由左侧极限位置开始运动，进气一定时间后，关闭进气通道，活塞继续向右运动，直至活塞速度为0。此时，活塞左侧腔体进入排气阶段，活塞从右向左运动。由于忽略了活塞与气缸之间的摩擦，以及直线电机运行时所产生的电磁力，仿真结果与试验结果相比，活塞往复运动的周期和行程存在一定偏差，但是，活塞稳定运动后，其运动规律较为一致，均进行类正弦运动，因此，可用来进行定性分析。
4.2 活塞质量对运动特性的影响
图7所示为进、排气通口孔径为4 mm，气缸直径为63 mm，进气时间为10 ms时，活塞质量分别为0.27 kg、0.57 kg、0.87 kg和1.00 kg条件下活塞的位移、速度曲线。由图7a可以看出，气体刚进入进气腔时，活塞位移变化很小，这是由于气体未能及时充满进气腔。当气体充满进气腔后，进、排气腔产生压力差，推动活塞从初始位置向右运动，活塞速度逐渐增大。进气腔体积逐渐增大，腔内压力逐渐减小，排气腔体积逐渐减小，腔内压力逐渐增大，当活塞左、右两侧气体压力相同时，活塞加速度为0，此时速度达到最大。随后，活塞右侧气体压力较活塞左侧大，活塞进行减速运动，直到速度减为0。活塞的位移随活塞质量的增加呈现先增加后趋于平缓的趋势，当活塞质量增加到0.87 kg时，继续增加活塞质量对活塞位移的影响较小。由图7b可知，活塞的峰值速度随活塞质量的增加而减小，当活塞质量增加到0.87 kg时，继续增加活塞质量，活塞峰值速度减小的幅度变小。
4.3 进、排气通口孔径对活塞运动特性的影响
图8所示为活塞质量为0.27 kg，气缸直径为63 mm，进气时间为10 ms时，进、排气通口孔径分别为4 mm、5 mm、6 mm和7 mm条件下的活塞位移、速度曲线。由图8a可以看出，随着通口孔径的增加，活塞位移逐渐增大并趋于稳定；由图8b可以看出，活塞的峰值速度随着通口孔径的增加先增大后微弱减小。随着通口孔径的增加，10 ms内进入气缸内的气体增多，关闭进气通道的瞬间，活塞的速度更大。气体膨胀阶段，随着排气通口孔径的增加，气体由排气腔排出更快，活塞速度减至0所需的时间更短，通口孔径为6 mm时，活塞速度最先下降为0。通口孔径为7 mm时，活塞位移最大，达91 mm，通口孔径为6 mm时，活塞峰值速度最大，达8.7 m/s，且活塞速度降为0约需19 ms。
4.4 气缸直径对活塞运动特性的影响
图9所示为进、排气通口孔径为4 mm，活塞质量为0.27 kg，进气时间为10 ms时，气缸直径分别为63 mm、67 mm、71 mm、75 mm和79 mm条件下活塞的位移、速度曲线。可以看出，随着气缸直径的增加，活塞位移、速度均逐渐减小。这是因为进气时间一定，进入气缸内的气体量相同，气缸直径越大，导致进入气缸内的气体压力越小，对活塞的驱动能力越弱。所以，在进气压力、进气时间一定时，选用较小的缸径可获得较高的活塞运动速度。
4.5 进气时间对活塞运动特性的影响
图10所示为通口孔径为4 mm，气缸直径为79 mm，活塞质量为0.27 kg时，进气时间分别为10 ms、12 ms、15 ms、18 ms条件下活塞的位移、速度随时间变化曲线。当进气时间由10 ms延长至15 ms，活塞的位移增大比较明显；当进气时间进一步延长到18 ms时，活塞位移增大的幅度较小。由图10b可以看出，随着进气时间的延长，活塞的峰值速度变化并不明显。
4.6 正交试验结果分析
由以上分析可以看出，活塞质量、通口孔径和气缸直径对活塞的运动特性有着不同程度的影响。使用正交试验的方法，通过极差R分析，得到以上3种因素对于活塞运动特性的影响程度。如表2所示，因素A、B、C分别对应活塞质量、通口孔径和缸径，并各选取3个水平进行正交试验。正交试验方案设计和试验结果如表3所示，根据试验结果进行极差分析，其中ki为水平i条件下，对应因素的试验结果之和的平均值，R为某因素下ki的最大值与最小值之差，其值越大表明该因素对试验结果的影响程度越大，如表4所示：通口孔径对于活塞位移的影响程度最大，其次为气缸直径，活塞质量对活塞位移的影响最小；通口孔径对活塞峰值速度的影响程度最大，其次为活塞质量，缸径对活塞峰值速度的影响最小。
5 结束语
收起
为了提高自由活塞膨胀机-直线发电机的集成度，使得在气缸结构更加紧凑的情况下，活塞获得更高的速度，本文分析了气缸内气体的流动状态，研究了气缸结构以及进气时间对于活塞运动特性的影响，结论如下：
a. 气体流经进、排气通口处，气体压力、速度较大；气缸内气体压力有所降低、气体流速比较稳定。
b. 随活塞质量的增加，活塞位移先增加后趋于稳定；活塞速度先减小，后趋于稳定。随气缸直径的增加，活塞位移、速度均减小。
c. 随通口孔径、进气时间的增加，活塞位移、速度均先增加后趋于稳定。
d. 为了在行程较小时获得较大的活塞速度，可在气缸理论行程范围内首先考虑适当增大气门通口孔径、其次降低活塞质量，最后减小气缸直径。
基金
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  • * 北京市自然科学基金项目(3192014)
  • 北京市科技计划项目(Z191100002019004)
  • 北京市教委科技计划一般项目(KM202011232012)
文献
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2023年第卷第12期
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doi: 10.19620/j.cnki.1000-3703.20221016
  • 首发时间：2025-12-07
  • 出版时间：2023-12-24
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  • 修回日期：2022-11-17
基金
* 北京市自然科学基金项目(3192014)
北京市科技计划项目(Z191100002019004)
北京市教委科技计划一般项目(KM202011232012)
作者信息
    北京信息科技大学，北京 100192
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