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Article(id=1256186029682377534, tenantId=1146029695717560320, journalId=1255847867265597444, issueId=1256186027853624275, articleNumber=null, orderNo=null, doi=10.11858/gywlxb.20251227, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1760457600000, receivedDateStr=2025-10-15, revisedDate=1764000000000, revisedDateStr=2025-11-25, acceptedDate=null, acceptedDateStr=null, onlineDate=1777427688284, onlineDateStr=2026-04-29, pubDate=1775318400000, pubDateStr=2026-04-05, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1777427688284, onlineIssueDateStr=2026-04-29, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1777427688284, creator=13701087609, updateTime=1777427688284, updator=13701087609, issue=Issue{id=1256186027853624275, tenantId=1146029695717560320, journalId=1255847867265597444, year='2026', volume='40', issue='4', pageStart='040101-1', pageEnd='045301-13', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1777427687845, creator=13701087609, updateTime=1777427791253, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1256186461888627074, tenantId=1146029695717560320, journalId=1255847867265597444, issueId=1256186027853624275, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1256186461888627075, tenantId=1146029695717560320, journalId=1255847867265597444, issueId=1256186027853624275, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=040103-1, endPage=040103-14, ext={EN=ArticleExt(id=1256186030328300353, articleId=1256186029682377534, tenantId=1146029695717560320, journalId=1255847867265597444, language=EN, title=Energy Conversion Prediction Model of Expansion Tube under Near-Field Blast Loading, columnId=1256186029531345878, journalTitle=Chinese Journal of High Pressure Physics, columnName=Young Scientists’ Forum, runingTitle=null, highlight=null, articleAbstract=

The explosion near-field is the core zone of munition-induced damage, involving the coupled load effect of intense shock waves and detonation products. Currently, the mechanical response and energy conversion mechanisms of expansion tube structures (ETS) under such extreme loading conditions remain unclear. In this study, ETS is adopted as a representative energy-absorbing structure to investigate its energy conversion behavior under the coupled action of near-field shock waves and detonation products. Based on the experimental verification, numerical simulation methods were employed to analyze the characteristics of near-field blast loading and the dynamic response of ETS. Furthermore, a theoretical prediction formula for near-field blast loading was established, and a theoretical model for predicting energy conversion efficiency was developed based on the strong-shock assumption. The results show that the energy conversion efficiency decreases significantly with increasing scaled distance. The energy conversion efficiency drops to below 10% when the scaled distance exceeds 0.80 m/kg1/3. Moreover, the energy conversion efficiency exhibits a strong positive correlation with the specific impulse of the reflected wave, indicating that specific impulse is a key factor determining energy transfer. This work elucidates the intrinsic mechanism of energy conversion in ETS under near-field coupled loading. The proposed theoretical model provides a robust foundation for the design and performance evaluation of near-field protective structures.

, correspAuthors=Yuliang LIN, authorNote=null, correspAuthorsNote=null, copyrightStatement=Copyright © 2026 Chinese Journal of High Pressure Physics. All rights reserved., 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, authorCompany=null, fund=null, authors=null, authorsList=Zizhen QI, Minghao LI, Yuyan ZHANG, Minzu LIANG, Yuwu ZHANG, Yuliang LIN), CN=ArticleExt(id=1256186055389266092, articleId=1256186029682377534, tenantId=1146029695717560320, journalId=1255847867265597444, language=CN, title=近场爆炸加载下扩胀管能量转化预测模型研究, columnId=1256186029946581977, journalTitle=高压物理学报, columnName=优秀青年专辑, runingTitle=null, highlight=null, articleAbstract=

爆炸近场是弹药爆炸毁伤的核心区域，涉及强冲击波与爆轰产物的耦合载荷作用。目前，扩胀管结构（expansion tube structure, ETS）在此类极端载荷下的力学响应及能量转化机制尚不明确。为此，将ETS作为典型吸能结构，研究其在近场强冲击波与爆轰产物耦合作用下的能量转化机制。在试验验证的基础上，通过数值模拟方法研究近场爆炸载荷特性及ETS的动态响应特性，建立了近场爆炸载荷的理论预测公式，并在强冲击假设的基础上构建了能量转化效率的理论预测模型。结果表明：能量转化效率随着比例距离的增加而显著下降，当比例距离超过0.80 m/kg1/3时，能量转化效率低于10%；能量转化效率与反射波比冲量呈显著正相关，说明比冲量是决定能量传递的关键因素。研究结果揭示了ETS在近场爆炸载荷作用下能量转化的内在机制，所建立的理论模型为近场防护结构设计与性能评估提供了有力的理论支撑。

, correspAuthors=林玉亮, authorNote=null, correspAuthorsNote=
林玉亮（1978－），男，博士，教授，博士生导师，主要从事爆炸与冲击动力学研究. E-mail：
, copyrightStatement=版权所有©《高压物理学报》编辑部 2026, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=97/sIy8EVUMykjkDMsXEsw==, magXml=6u/bNpUWbgV0JrH4QJsAoA==, pdfUrl=null, pdf=3W1CnAEFX4ZWNA4EU58kYw==, pdfFileSize=8517319, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=DPbsHPTTOwxkxKItVGG+5g==, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=10masFQMMXlP+RKisD0r4A==, mapNumber=null, authorCompany=null, fund=null, authors=

祁子真（1995－），男，博士，讲师，主要从事爆炸与冲击动力学研究. E-mail：

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祁子真（1995－），男，博士，讲师，主要从事爆炸与冲击动力学研究. E-mail：

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祁子真（1995－），男，博士，讲师，主要从事爆炸与冲击动力学研究. E-mail：

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figureFileBig=Dg2wFfQrFJK9f6F6jlhNjg==, tableContent=null), ArticleFig(id=1256186070790750522, tenantId=1146029695717560320, journalId=1255847867265597444, articleId=1256186029682377534, language=EN, label=Fig.14, caption=Energy conversion efficiency at different scaled distances and the corresponding peak reflected overpressure (pr) and specific impulse (Ir), figureFileSmall=OUMBjAokgC9tBFN0FdBqOw==, figureFileBig=dr/norKI64JYkfA13OmNJA==, tableContent=null), ArticleFig(id=1256186070966911291, tenantId=1146029695717560320, journalId=1255847867265597444, articleId=1256186029682377534, language=CN, label=图14, caption=不同比例距离处的能量转化效率及其对应的反射超压峰值（pr）和比冲量（Ir）, figureFileSmall=OUMBjAokgC9tBFN0FdBqOw==, figureFileBig=dr/norKI64JYkfA13OmNJA==, tableContent=null), ArticleFig(id=1256186071067574588, tenantId=1146029695717560320, journalId=1255847867265597444, articleId=1256186029682377534, language=EN, label=Tab.1, caption=

Geometric parameters of each component in ETS

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Thin-wall tubeCone piston
MaterialLT/mmr0/mmh/mmMaterialrdie/mmlD/mmlC/mmα/(°)mC/g
1060/H12 aluminum48.013.01.0304 steel13.52.05.05.7116.8
Supporting rodSlider
MaterialDR/mmlR/mmmR/gMaterialDS/mmlS/mmlE/mmmS/g
304 steel10.027.014.98304 steel40.037.05.0149.8
), ArticleFig(id=1256186071210180925, tenantId=1146029695717560320, journalId=1255847867265597444, articleId=1256186029682377534, language=CN, label=表1, caption=

ETS各部件的几何尺寸

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Thin-wall tubeCone piston
MaterialLT/mmr0/mmh/mmMaterialrdie/mmlD/mmlC/mmα/(°)mC/g
1060/H12 aluminum48.013.01.0304 steel13.52.05.05.7116.8
Supporting rodSlider
MaterialDR/mmlR/mmmR/gMaterialDS/mmlS/mmlE/mmmS/g
304 steel10.027.014.98304 steel40.037.05.0149.8
), ArticleFig(id=1256186071306649918, tenantId=1146029695717560320, journalId=1255847867265597444, articleId=1256186029682377534, language=EN, label=Tab.2, caption=

Summary of test plan and measurement results[16]

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W/kgCaseR/mZ/(m·kg−1/3)L/mmW/kgCaseR/mZ/(m·kg−1/3)L/mm
2.00W2-E10.600.4813.355.00W5-E10.630.3733.88
W2-E20.630.5017.40W5-E20.720.4227.54
W2-E30.720.5713.05W5-E30.770.4530.89
W2-E40.770.6121.75W5-E40.870.5122.80
W2-E50.800.637.68W5-E51.050.6121.91
W2-E61.050.835.52W5-E61.080.6315.64
W2-E71.080.863.12W5-E71.140.6711.44
W2-E81.311.042.24W5-E81.310.776.69
W2-E91.311.042.56W5-E91.310.777.48
W2-E101.401.112.08W5-E101.350.794.66
W2-E111.421.131.44W5-E111.400.825.98
W2-E121.461.160.64W5-E121.460.859.68
4.01W4-E10.630.4029.573.01W3-E10.600.4225.14
W4-E20.720.4515.93W3-E20.630.4425.72
W4-E30.770.4919.18W3-E30.720.509.02
W4-E40.800.5012.72W3-E40.770.536.34
W4-E50.870.5511.97W3-E50.800.558.52
W4-E61.050.666.69W3-E60.870.6011.32
W4-E71.080.6810.21W3-E71.050.732.52
W4-E81.140.727.92W3-E81.080.754.56
W4-E91.310.834.22W3-E91.140.792.60
W4-E101.310.835.72
W4-E111.350.853.52
W4-E121.400.883.08
W4-E131.420.894.22
W4-E141.460.926.69
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试验工况及结果统计[16]

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W/kgCaseR/mZ/(m·kg−1/3)L/mmW/kgCaseR/mZ/(m·kg−1/3)L/mm
2.00W2-E10.600.4813.355.00W5-E10.630.3733.88
W2-E20.630.5017.40W5-E20.720.4227.54
W2-E30.720.5713.05W5-E30.770.4530.89
W2-E40.770.6121.75W5-E40.870.5122.80
W2-E50.800.637.68W5-E51.050.6121.91
W2-E61.050.835.52W5-E61.080.6315.64
W2-E71.080.863.12W5-E71.140.6711.44
W2-E81.311.042.24W5-E81.310.776.69
W2-E91.311.042.56W5-E91.310.777.48
W2-E101.401.112.08W5-E101.350.794.66
W2-E111.421.131.44W5-E111.400.825.98
W2-E121.461.160.64W5-E121.460.859.68
4.01W4-E10.630.4029.573.01W3-E10.600.4225.14
W4-E20.720.4515.93W3-E20.630.4425.72
W4-E30.770.4919.18W3-E30.720.509.02
W4-E40.800.5012.72W3-E40.770.536.34
W4-E50.870.5511.97W3-E50.800.558.52
W4-E61.050.666.69W3-E60.870.6011.32
W4-E71.080.6810.21W3-E71.050.732.52
W4-E81.140.727.92W3-E81.080.754.56
W4-E91.310.834.22W3-E91.140.792.60
W4-E101.310.835.72
W4-E111.350.853.52
W4-E121.400.883.08
W4-E131.420.894.22
W4-E141.460.926.69
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Simulation results of reflected peak overpressure and specific impulse of the near-field blast loading

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Z/(m·kg−1/3)W/kgpr2/MPaIr2/(Pa·s)Z/(m·kg−1/3)W/kgpr2/MPaIr2/(Pa·s)
0.30261.663770.760.301075.996044.95
0.3557.723152.270.3563.565663.29
0.4048.932636.030.4057.114531.02
0.4536.942240.100.4541.894476.01
0.5027.892107.740.5034.634442.93
0.6020.281682.530.6018.393088.02
0.7014.661281.500.7014.232436.08
0.808.191070.140.8013.462107.83
0.30361.134094.750.303071.068429.43
0.3553.593309.890.3555.226430.83
0.4045.442389.840.4044.785125.89
0.4539.122184.190.4535.744656.37
0.5034.392109.400.5027.213985.79
0.6018.211732.510.6019.633735.01
0.7012.011276.290.7013.153043.11
0.808.56950.220.809.542498.36
0.30572.085006.160.305077.949821.96
0.3544.643729.770.3564.937193.28
0.4037.132908.950.4055.935515.95
0.4532.902989.500.4538.425887.95
0.5024.992201.570.5031.444784.21
0.6017.871958.200.6019.373877.84
0.7014.341537.500.7012.562869.21
0.8010.361066.830.809.712526.05
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近场爆炸载荷下反射峰值超压和比冲量的数值模拟结果

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Z/(m·kg−1/3)W/kgpr2/MPaIr2/(Pa·s)Z/(m·kg−1/3)W/kgpr2/MPaIr2/(Pa·s)
0.30261.663770.760.301075.996044.95
0.3557.723152.270.3563.565663.29
0.4048.932636.030.4057.114531.02
0.4536.942240.100.4541.894476.01
0.5027.892107.740.5034.634442.93
0.6020.281682.530.6018.393088.02
0.7014.661281.500.7014.232436.08
0.808.191070.140.8013.462107.83
0.30361.134094.750.303071.068429.43
0.3553.593309.890.3555.226430.83
0.4045.442389.840.4044.785125.89
0.4539.122184.190.4535.744656.37
0.5034.392109.400.5027.213985.79
0.6018.211732.510.6019.633735.01
0.7012.011276.290.7013.153043.11
0.808.56950.220.809.542498.36
0.30572.085006.160.305077.949821.96
0.3544.643729.770.3564.937193.28
0.4037.132908.950.4055.935515.95
0.4532.902989.500.4538.425887.95
0.5024.992201.570.5031.444784.21
0.6017.871958.200.6019.373877.84
0.7014.341537.500.7012.562869.21
0.8010.361066.830.809.712526.05
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Energy absorption of ETS at different distances under a 10 kg TNT equivalent charge

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R/mZ/(m·kg−1/3)Ee
Simulation/JTheory/JError/%
0.8620.40119.12140.5718.01
1.0770.50114.81101.29−11.77
1.2930.6055.1859.427.68
1.5080.7034.1139.5916.07
1.7240.8025.2826.063.09
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10 kg 炸药当量下不同比例距离处ETS的能量吸收

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R/mZ/(m·kg−1/3)Ee
Simulation/JTheory/JError/%
0.8620.40119.12140.5718.01
1.0770.50114.81101.29−11.77
1.2930.6055.1859.427.68
1.5080.7034.1139.5916.07
1.7240.8025.2826.063.09
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近场爆炸加载下扩胀管能量转化预测模型研究
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祁子真 , 李明浩 , 张钰研 , 梁民族 , 张玉武 , 林玉亮 *
高压物理学报 | 优秀青年专辑 2026,40(4): 040103-1-040103-14
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高压物理学报 | 优秀青年专辑 2026, 40(4): 040103-1-040103-14
近场爆炸加载下扩胀管能量转化预测模型研究
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祁子真 , 李明浩, 张钰研, 梁民族, 张玉武, 林玉亮*
作者信息
  • 国防科技大学理学院, 湖南 长沙　410073

    • 祁子真（1995－），男，博士，讲师，主要从事爆炸与冲击动力学研究. E-mail：

通讯作者:

林玉亮（1978－），男，博士，教授，博士生导师，主要从事爆炸与冲击动力学研究. E-mail：
Energy Conversion Prediction Model of Expansion Tube under Near-Field Blast Loading
Zizhen QI , Minghao LI, Yuyan ZHANG, Minzu LIANG, Yuwu ZHANG, Yuliang LIN*
Affiliations
  • College of Science, National University of Defense Technology, Changsha 410073, Hunan, China
出版时间: 2026-04-05 doi: 10.11858/gywlxb.20251227
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摘要
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爆炸近场是弹药爆炸毁伤的核心区域，涉及强冲击波与爆轰产物的耦合载荷作用。目前，扩胀管结构（expansion tube structure, ETS）在此类极端载荷下的力学响应及能量转化机制尚不明确。为此，将ETS作为典型吸能结构，研究其在近场强冲击波与爆轰产物耦合作用下的能量转化机制。在试验验证的基础上，通过数值模拟方法研究近场爆炸载荷特性及ETS的动态响应特性，建立了近场爆炸载荷的理论预测公式，并在强冲击假设的基础上构建了能量转化效率的理论预测模型。结果表明：能量转化效率随着比例距离的增加而显著下降，当比例距离超过0.80 m/kg1/3时，能量转化效率低于10%；能量转化效率与反射波比冲量呈显著正相关，说明比冲量是决定能量传递的关键因素。研究结果揭示了ETS在近场爆炸载荷作用下能量转化的内在机制，所建立的理论模型为近场防护结构设计与性能评估提供了有力的理论支撑。

近场爆炸  /  爆轰产物  /  能量转化  /  超压  /  比冲量

The explosion near-field is the core zone of munition-induced damage, involving the coupled load effect of intense shock waves and detonation products. Currently, the mechanical response and energy conversion mechanisms of expansion tube structures (ETS) under such extreme loading conditions remain unclear. In this study, ETS is adopted as a representative energy-absorbing structure to investigate its energy conversion behavior under the coupled action of near-field shock waves and detonation products. Based on the experimental verification, numerical simulation methods were employed to analyze the characteristics of near-field blast loading and the dynamic response of ETS. Furthermore, a theoretical prediction formula for near-field blast loading was established, and a theoretical model for predicting energy conversion efficiency was developed based on the strong-shock assumption. The results show that the energy conversion efficiency decreases significantly with increasing scaled distance. The energy conversion efficiency drops to below 10% when the scaled distance exceeds 0.80 m/kg1/3. Moreover, the energy conversion efficiency exhibits a strong positive correlation with the specific impulse of the reflected wave, indicating that specific impulse is a key factor determining energy transfer. This work elucidates the intrinsic mechanism of energy conversion in ETS under near-field coupled loading. The proposed theoretical model provides a robust foundation for the design and performance evaluation of near-field protective structures.

near-field blast  /  detonation products  /  energy conversion  /  overpressure  /  specific impulse
祁子真, 李明浩, 张钰研, 梁民族, 张玉武, 林玉亮. 近场爆炸加载下扩胀管能量转化预测模型研究. 高压物理学报, 2026 , 40 (4) : 040103-1 -040103-14 . DOI: 10.11858/gywlxb.20251227
Zizhen QI, Minghao LI, Yuyan ZHANG, Minzu LIANG, Yuwu ZHANG, Yuliang LIN. Energy Conversion Prediction Model of Expansion Tube under Near-Field Blast Loading[J]. Chinese Journal of High Pressure Physics, 2026 , 40 (4) : 040103-1 -040103-14 . DOI: 10.11858/gywlxb.20251227
正文
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在精确打击武器系统持续迭代升级的推动下，现代弹药的毁伤模式正经历由“面杀伤”向“点摧毁”转变。随着命中精度的提升，结构防护设计的关注重点逐渐聚焦于爆炸近场[1]（比例距离Z≤0.8 m/kg1/3的区域，其中，Z=R/W1/3，R为爆距，W为TNT当量）这一关键区域。在该区域内，爆炸冲击波与爆轰产物强烈耦合，载荷具有高幅值、短历时的典型特征，极易导致防护目标发生严重损伤甚至失效。为了抵御此类高强冲击载荷，常采用扩胀管、铝蜂窝、波纹板等典型吸能结构（见图1[2–3]）吸收冲击能量，对目标进行防护。然而，当爆炸载荷作用于吸能结构时，其能量并非全部被结构吸收，部分能量将以反射波、热能、声能等形式耗散[4]。该能量转化过程受到爆炸载荷特性与结构动态响应特性的共同制约，因此，即便某类结构具备优良的能量吸收能力（如高比吸能），其实际防护效能仍可能不足。由此可见，深入揭示近场爆炸载荷与吸能结构之间的能量转化机理，对于提升防护结构设计的科学性与有效性具有重要意义。
在近场爆炸载荷作用下，爆炸冲击载荷与吸能结构存在复杂的相互作用[5–11]。为深入研究相关因素对吸能结构在近场爆炸载荷作用下能量转化机制的影响，本研究选用力学响应稳定、无回弹变形且压缩力可调控的扩胀管结构（expansion tube structure，ETS）[12–13]作为研究对象。ETS主要由滑块、支撑杆、锥套和薄壁管组成，如图2所示，其中：p(t)为冲击波压力时程，rdie为锥套定径带半径，lC为锥套扩径带长度，lD为锥套定径带长度，α为锥套半锥角，h为薄壁管壁厚，LT为薄壁管长度，r1为薄壁管的中径半径，r0为薄壁管内半径。在爆炸载荷作用下，锥套受力向右推进并嵌入薄壁管，促使薄壁管发生径向扩胀，实现能量耗散。目前，针对ETS在准静态、动态和爆炸加载下的能量吸收特性已有大量试验、数值模拟及理论研究。例如：Choi等[13]研究了不同冲击速度（均低于10 m/s）下ETS的能量吸收性能，发现由于管材的应变率效应，动态冲击下的能量吸收高于准静态加载条件下的能量吸收；Liu等[14]研究了锥套半锥角对ETS力学响应的影响，结果表明，锥套的最大冲击加速度随半锥角的增大呈波动变化，这是径力、ETS能量吸收能力等多种因素共同作用的结果；Shakeri等[15]研究了摩擦对ETS能量吸收特性的影响；Qi等[11]通过爆炸试验研究了ETS在冲击波作用下的动态嵌入行为，发现由于爆炸冲击载荷具有近似三角形的压力-时间曲线，其有效冲量与ETS的扩径应力阈值呈负相关关系，因此，扩径应力较高的ETS反而表现出较低的能量吸收能力。综上所述，尽管ETS在不同载荷条件下的响应机制已有一定的研究基础，但是在近场爆炸区域冲击波与爆轰产物的耦合作用下，ETS的动态响应可能显著区别于常规加载条件，因此，近场爆炸载荷作用下ETS的能量转化行为及其影响机理仍需进一步系统研究。
本研究聚焦于ETS在爆炸冲击波与爆轰产物耦合作用下的能量转化机理及影响因素。首先，通过数值模拟研究近场爆炸载荷特性以及ETS在该耦合载荷作用下的力学响应和吸能特性，结合爆炸试验对数值模拟结果进行验证；在此基础上，建立近场爆炸冲击载荷的计算公式，进一步构建近场冲击载荷与ETS之间能量转化效率的理论预测模型，分析载荷峰值超压和比冲量对冲击波能量转化效率的影响规律，为近场防护结构的设计与评估提供理论支撑。
1　数值模拟研究及验证
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采用LS-DYNA和ABAQUS有限元软件建立包含炸药和空气域的完整模型，以模拟近场爆炸范围内冲击波与爆轰产物的耦合作用。考虑到ETS的迎爆面强度较高，且在短历时爆炸载荷作用期间的位移较小，因此，将ETS迎爆面设置为刚性壁面，采用流固耦合方法计算指定爆距处刚性壁面的爆炸冲击载荷，并提取其压力时程曲线，然后将获得的压力时程作为边界载荷施加于ETS的有限元（finite element，FE）模型上，以高效、准确地模拟ETS在近场爆炸下的动态响应。
1.1　近场爆炸冲击载荷及其作用下的ETS响应模拟
本数值模拟研究主要包括2个部分：近场爆炸冲击载荷数值模拟以及在该载荷作用下ETS力学响应的模拟分析，如图3[16]所示。在近场爆炸冲击载荷模拟中，基于LS-DYNA有限元软件建立了包含空气域、刚性壁面和TNT球形装药的二维轴对称自由场计算模型，如图3(a)所示。其中，β为刚性壁面中心点的法线与爆心之间连线的夹角，在正入射条件下，β=0°。模型边界条件设置为轴对称边界和非反射边界，刚性壁面则设定为固支边界。设TNT装药质量为2～50 kg，空气域模型边长为1.6～2.7 m，单元尺寸为1.60～4.80 mm。TNT炸药和空气均采用多物质任意拉格朗日-欧拉（arbitrary Lagrangian-Eulerian，ALE）算法的ALE 2D单元进行建模；刚性壁面通过*MAT_RIGID关键字描述，流固耦合则采用*CONSTRAINED_LAGRANGE_IN_SOLID关键字描述。TNT炸药模型选用*MAT_HIGH-EXPLOSIVE-BURN，其状态方程采用Jones-Wilkins-Lee（JWL）方程；空气则采用*MAT-NULL材料模型和*EOS_LINER_POLYNOMIAL状态方程[16]描述。
采用ABAQUS有限元软件建立的ETS有限元模型如图3(c)所示，模型中各部件的材料选取和几何尺寸如表1所示，其中：DR为支撑杆直径，lR为支撑杆轴向长度，DS为滑块迎爆面直径，lE为滑块迎爆面厚度，lS为滑块轴向长度，mR、mC和mS分别为支撑杆、锥套和滑块的质量。薄壁管的网格采用C3D8R单元，沿轴向划分为100个单元，沿厚度方向划分4层单元，以准确预测管壁的弯曲变形和场应变的空间分布。薄壁管右端通过刚性基板在y方向实现固定约束，基板采用R3D4单元建模。滑块、支撑杆和锥套均采用C3D4单元。锥套与薄壁管之间采用面面接触，并引入各向同性库仑摩擦模型，摩擦系数f取0.09[17]。将近场爆炸载荷模拟中提取的压力时程作为输入载荷施加于ETS的迎爆面，如图3(b)和图3(c)所示。
有限元模型中薄壁管材质为1060/H12铝合金，其应变硬化和应变率效应采用Johnson-Cook本构模型描述，表达式为
$ {\sigma }_{\text{d}}=(A+B\varepsilon _{\text{e}}^{n})(1+c\ln {\dot{\varepsilon }}^{*}) $
式中：等号右边第1项和第2项分别表示材料的应变硬化效应和应变率效应对应力的影响；$ {\sigma }_{\mathrm{d}} $为等效流动应力；$ {\varepsilon }_{\text{e}} $为等效塑性应变；$ {\dot{\varepsilon }}^{*}=\dot{\varepsilon }/{\dot{\varepsilon }}_{0} $为无量纲塑性应变率，其中，$ {\dot{\varepsilon }}_{0} $为准静态拉伸试验的应变率，$ {\dot{\varepsilon }}_{0} $=6.67×10−4 s−1；A为准静态加载下材料的屈服强度；B为材料应变硬化系数；c为应变率敏感系数。本研究中，1060/H12铝合金的Johnson-Cook本构模型参数[16]为：A=127.43 MPa，B=99.67 MPa，n=1.029，c=0.03993。锥套、滑块和支撑杆材料均为304钢，采用弹塑性本构模型表示。
1.2　数值模拟结果验证与分析
1.2.1　近场爆炸载荷数值模拟结果验证与分析
数值模型的准确性通过与规范UFC 3-340-02[18]对比进行验证。ETS的模拟工况及结果验证主要参考Qi等[16]的近场爆炸试验结果，图4为试验布局示意图。炸药为球形TNT，装药质量分别为2.00、3.01、4.01和5.00 kg，炸药距离地面1.5 m。ETS通过万向节安装在固定钢架上，其迎爆面正对爆心。为了研究不同比例距离处爆炸冲击波与爆轰产物耦合载荷作用下ETS的响应，将ETS按照螺旋式布置在不同的比例距离处，具体工况见表2，其中，L为爆炸后ETS的嵌入位移。
图5展示了近场爆炸冲击载荷的入射与反射峰值超压随比例距离Z的关系，对比了模拟结果（点）与规范UFC 3-340-02的计算值（线），其中，浅红色阴影区域表示以UFC 3-340-02的计算结果为中心的±20%误差带。结果表明：有限元模型的预测结果与UFC 3-340-02计算结果整体上吻合良好，尤其在Z≥0.60 m/kg1/3范围内；在Z<0.60 m/kg1/3范围内，模拟得到的反射峰值超压与规范结果的相对偏差逐渐增大，可能源于规范UFC 3-340-02在近场爆炸载荷计算中未考虑爆轰产物的贡献[19]，而数值模型则完整耦合了冲击波与爆轰产物的联合作用。进一步分析表明，无论是入射峰值超压，还是反射峰值超压，数值模拟结果基本落在规范UFC 3-340-02预测值的±20%误差区间内。考虑到近场爆炸载荷具有高度非线性、强瞬态性和多物理场耦合特征，该量级的偏差在工程应用中通常被视为合理且可接受的，从侧面验证了所建模型在载荷表征方面的可靠性。
图6展示了数值模拟获得的不同炸药当量、不同比例距离下的反射压力-时间曲线。可以看出，当Z<0.80 m/kg1/3时，反射压力时程曲线呈现出明显的多峰特征。结合冲击波与爆轰产物向外传播的作用时序分析[16]可知，首个压力峰值主要由冲击波阵面引起，而后续的峰值则源于爆轰产物持续作用于结构表面所致；当Z≥0.80 m/kg1/3时，反射压力曲线趋于平滑，表明爆轰产物的贡献显著减弱，载荷特性逐渐由单一冲击波主导。
1.2.2　ETS响应数值模拟结果对比验证
图7展示了爆炸冲击波与爆轰产物耦合作用下ETS（面密度$ {\overline{\rho }}_{\rm s} $=68.53 kg/m2，等效强度$ {\overline{\sigma }}_{\rm s} $=1.49 MPa）的嵌入过程[16]。在加载初始阶段（tA时刻之前），由于近场爆炸载荷具有极高的峰值超压和陡峭的压力上升沿，滑块受到强烈冲击而急剧加速，其速度在极短时间内达到最大值。此阶段以惯性主导，结构尚未与薄壁管发生显著相互作用，能量主要转化为滑块、支撑杆和锥套的动能。之后（tA～tD），锥套开始接触并嵌入薄壁管内壁，薄壁管因径向扩胀而产生显著的塑性变形，由此产生的扩径阻力迅速上升。此时，滑块的加速度由正转负，薄壁管的扩径阻力趋于稳定，并最终以近似恒定的减速度继续运动直至停止。该阶段是能量耗散的核心过程：爆炸输入的能量通过锥套-薄壁管界面的摩擦与材料塑性流动被转化为热能和塑性功。数值模拟结果表明，薄壁管的环向应力和等效塑性应变在此阶段集中分布于锥套与薄壁管接触区域，呈现出典型的局部化变形特征。
图8展示了ETS在不同比例距离下嵌入位移（L）的数值模拟与试验结果。结果表明，随着比例距离的增加，ETS的嵌入位移呈指数衰减趋势，主要归因于爆炸载荷的峰值超压和比冲量随距离增大而迅速衰减。值得注意的是，数值模拟预测的嵌入位移变化趋势与试验测量结果高度一致，且两者在量级上基本吻合。尽管近场爆炸试验受装药一致性、环境干扰及测量精度等因素影响，存在一定的数据离散性，但数值模拟结果能够准确复现载荷衰减对结构响应的关键影响规律。因此，本研究建立的有限元模型能够有效表征爆炸冲击波与爆轰产物耦合作用下ETS的动态响应和能量吸收特性，具备用于后续参数分析和理论建模的可靠性。
2　爆炸近场冲击载荷与ETS间能量转化理论预测模型
收起
以下将基于近场爆炸数值模拟结果，建立近场爆炸冲击载荷等效计算模型，并推导其加载下ETS的嵌入控制方程，构建爆炸冲击载荷能量转化效率理论预测模型，分析峰值超压、比冲量等关键因素对爆炸近场冲击载荷能量转化的影响规律和机制。
2.1　近场爆炸冲击载荷等效计算模型
在爆炸近场范围内，冲击载荷呈现出典型的双波峰特性，且整个载荷的持续时间较短；此外，分析表明，近场爆炸载荷与吸能结构之间的能量转化主要由载荷比冲量主导。因此，为便于理论建模与分析，将近场爆炸载荷的反射压力pref按照等比冲量的原则简化为具有一定幅值和持续时间的双峰三角形压力脉冲[1]，如图9所示，其表达式为
$ {p}_{\text{ref}}(t)=\begin{cases} 0&\;\;\text{0}\leqslant \;t\text{ \lt }{\tau }_{0}\\{p}_{\text{r}1}\left(1-\dfrac{t-{\tau }_{0}}{{\tau }_{1}-{\tau }_{0}}\right)&\;{\tau }_{0}\leqslant t\text{ \lt }{\tau }_{1}\\{p}_{\text{r}2}\left(1-\dfrac{t-{\tau }_{1}}{{\tau }_{2}-{\tau }_{1}}\right)&\;{\tau }_{1}\leqslant t\text{ \lt }{\tau }_{2}\\0&\;\quad \;\;\;\; t\geqslant {\tau }_{2}\end{cases} $
式中：pr1和pr2分别为冲击波反射峰值超压和爆轰产物反射峰值超压；$ {\tau }_{0} $和$ {\tau }_{1} $分别为冲击波和爆轰产物到达结构表面的时刻，其差值$ {\tau }_{1}-{\tau }_{0} $反映了两者作用的时序关系；$ {\tau }_{2} $为载荷作用结束时间。
数值模型预测的爆轰产物峰值超压pr2和耦合载荷比冲量Ir的结果列于表3，采用负幂函数对其拟合，得到耦合载荷反射波峰值超压和比冲量的经验公式
$ {p}_{\text{r}2}=18.06-\frac{39.64}{Z}+\frac{32.40}{{Z}^{2}}-\frac{4.71}{{Z}^{3}} $
$ {I}_{\text{r}}={W}^{1/3}\left(-1.75+\frac{3.23}{Z}-\frac{1.21}{{Z}^{2}}+\frac{0.20}{{Z}^{3}}\right) $
$ {i}_{\text{r}}=\frac{{I}_{\text{r}}}{{W}^{1/3}} $
式中：pr2的单位为MPa；Ir的单位为kPa·s；ir为比例比冲量，单位为kPa·s/kg1/3。式(3)和式(4)的拟合相关性R2>0.99，其决定系数（coefficient of determination，COD）分别为0.950和0.917，表明拟合度均较高。此外，pr1、$ {\tau }_{0} $以及$ {\tau }_{1} $采用以下公式[1]计算
$ {p}_{\rm r1}=-11.68+\frac{11.83}{Z}+\frac{4.05}{{Z}^{2}}-\frac{0.42}{{Z}^{3}} $
$ {\tau }_{0}={W}^{1/3}(44.6{Z}^{3}+394.0{Z}^{2}+109.8Z+4.7) $
$ {\tau }_{1}={W}^{1/3}(576.9{Z}^{3}-683.1{Z}^{2}+791.0Z-104.2) $
式中：pr1的单位为MPa，$ {\tau }_{0} $和$ {\tau }_{1} $的单位均为μs。通过式(3)～式(8)计算得到近场爆炸载荷的各个参数后，根据
$ {I}_{\text{r}}=\frac{1}{2}\left[\left(2{p}_{\text{r}1}-\frac{{\tau }_{1}-{\tau }_{0}}{{\tau }_{2}-{\tau }_{1}}{p}_{\text{r}2}\right)({\tau }_{1}-{\tau }_{0})+{p}_{\text{r}2}({\tau }_{2}-{\tau }_{1})\right] $
可获得耦合载荷的结束时间$ {\tau }_{2} $。
为验证式(3)和式(4)计算的pr2和Ir的准确性，将其预测结果与规范UFC 3-340-02进行对比，如图10所示，其中：红色实线代表耦合载荷反射波峰值超压和比冲量的经验公式预测结果，黑色虚线为规范UFC 3-340-02提供的爆炸试验实测值。对比分析显示，式(3)和式(4)的拟合结果与UFC 3-340-02的结果的整体变化趋势一致。具体而言，图10(a)显示，式(3)预测的载荷峰值超压整体上均略低于UFC 3-340-02的结果，这是耦合载荷的多峰值现象所致。图10(b)表明，式(4)预测的耦合载荷比冲量在大部分比例距离范围内与UFC 3-340-02的结果吻合良好，但在Z<0.45 m/kg1/3的极近场区域内存在一定偏差。该偏差可能源于当前数值模型对爆轰产物喷射方向性及局部能量分布随机性的简化处理，而UFC 3-340-02的结果则基于大量试验数据统计拟合，其结果在工程应用中更偏向于保守和可靠[1]。综上所述，本研究提出的式(3)和式(4)能够有效预测耦合载荷反射波峰值超压和比冲量。
2.2　近场爆炸载荷加载下ETS嵌入控制方程及能量转化预测模型
爆炸载荷下ETS的扩径力-位移曲线可分为上升阶段、平台阶段和屈曲密实阶段，如图11所示。从图11可以看出：在上升阶段，扩径力随锥套位移的增加而线性增大；当锥套嵌入位移达到临界位移LP后，ETS进入稳定扩径变形阶段，此时，扩径力稳定在某一水平，该阶段称为平台阶段；当锥套位移达到最大允许位移Lmax后，薄壁管发生屈曲变形，扩径力急剧增加，此阶段称为屈曲密实阶段。因此，ETS的扩径力F与嵌入位移L的关系可以描述为
$ F=\begin{cases} {F}_{\text{s}}\dfrac{L(t)}{{L}_{\text{P}}} &\; \quad \quad L(t)\leqslant {L}_{\text{P}}\\{F}_{\text{s}} & \;{L}_{\text{P}} \lt L(t) \lt {L}_{\max }\end{cases} $
式中：Fs为平台阶段的扩径力。统计分析发现，LP=1.7lC。Fs的计算公式[20]如下
$ {F}_{\text{s}}=2\text{π} {r}_{1}h{\sigma }_{\text{L}} $
$ {\sigma }_{\text{L}}=\frac{\beta (1+\varphi )}{\varphi }\left(1+c\ln \frac{2{v}_{\max }\tan \alpha }{\sqrt{3}{r}_{0}{\dot{\varepsilon }}_{0}}\right)\left[\left(1-\frac{r_{1}^{\varphi }}{r_{2}^{\varphi }}\right)A+{\left(\frac{2}{\sqrt{3}{r}_{1}}\right)}^{n}Br_{1}^{\varphi }\varphi \int\nolimits_{{r}_{1}}^{{r}_{2}}\frac{{(r-{{r}_{1}})}^{n}}{{r}^{\varphi +1}}\text{d}r\right] $
$ {r}_{2}={r}_{\text{die}}+\frac{h}{2}+\frac{1}{2}\sqrt{{h}^{2}{(1-\cos \alpha )}^{2}+2h{r}_{1}(1-\cos \alpha )} $
式中：vmax为ETS的最大嵌入速度，$ {\sigma }_{\text{L}} $为嵌入过程中管壁的等效流动应力，β=1.15，$ \varphi =f\cot \alpha $。进一步，ETS的等效扩径应力$ {\sigma }_{\text{s}} $、等效强度$ {\overline{\sigma }}_{\text{s}} $及面密度$ {\overline{\rho }}_{\text{s}} $定义如下
$ {\sigma }_{\text{s}}=\frac{F({L})}{{S}_{ \text{S}}} $
$ {\overline{\sigma }}_{\text{s}}=\frac{{F}_{\text{s}}}{{S}_{ \text{S}}} $
$ {\overline{\rho }}_{\text{s}}=\frac{{m}_{\text{SSC}}}{{S}_{ \text{S}}} $
式中：SS为滑块迎爆面的面积，$ {m}_{\text{SSC}} $为滑块、支撑杆、锥套三者（统称为SSC）的质量之和。
在爆炸载荷作用滑块迎爆面的初始时刻（t = 0），SSC的位移和速度分别为L(0) = 0和L′(0) = 0。研究结果表明，爆炸冲击载荷正压区的持续时间较短，且爆炸加载结束时SSC的嵌入位移较小，因此，SSC嵌入对反射波稀疏的影响较为有限。假设在爆炸冲击波作用期间，爆炸冲击载荷在ETS迎爆面上的反射为固壁反射，则爆炸载荷作用下SSC的嵌入加速度$ {L}{''}(t) $为
$ \begin{cases} {\overline{\rho }}_{\text{s}}{L}{''}(t)={p}_{\text{r}2}-{\sigma }_{\text{s}} &\; t\leqslant {\tau }_{2}\\{\overline{\rho }}_{\text{s}}{L}{''}(t)=-{\sigma }_{\text{s}} &\; t \gt {\tau }_{2}\end{cases} $
根据式(17)，可得到ETS在耦合载荷作用下的响应历程示意图，如图12所示。图12采用分离式多Y轴布局，分别展示不同物理量的变化趋势，从而克服了因量纲差异带来的表示难题。具体而言，黑色曲线代表近场耦合载荷的压力时程，红色曲线对应ETS的等效应力时程，蓝色曲线表示ETS的嵌入位移时程，而绿色曲线则展示ETS的速度历程。在爆炸载荷作用阶段（t < tcr，其中tcr为临界时刻），耦合载荷压力大于ETS的等效扩径应力，导致SSC的速度持续增加；在临界时刻$ {t}_{\text{cr}} $，耦合载荷压力等于ETS等效扩径应力，此时SSC的速度达到最大值$ {v}_{\max } $；随后，SSC速度开始下降，直至t=$ {\tau }_{2} $，在此时刻之后，耦合载荷结束加载，SSC速度呈线性下降直至零；最终，在$ {t}_{\text{final}} $时刻，SSC停止运动，对应的最终嵌入位移为Lfinal。通过上述计算可获得ETS的扩径力-嵌入位移曲线，积分可得爆炸耦合载荷与ETS之间的能量转化。定义Ee为ETS吸收爆炸载荷的能量，则
$ {E}_{\text{e}}=\int\nolimits_{0}^{{L}_{\text{final}}}F(L)\text{d}L $
根据Taylor[21]提出的空气中爆炸产生强激波的相似解，可推导出热空气膨胀过程中用于克服大气压力做功的能量E2，其表达式如下
$ {E}_{2}=\frac{4\text{π} {E}_{0}}{{\gamma }_{2}b\left({\gamma }_{2}\right)}\left[0.217{\left(\frac{{\gamma }_{2}+1}{\text{2}{\gamma }_{2}}{y}_{1}\right)}^{\tfrac{1-{\gamma }_{2}}{{\gamma }_{2}}}-\frac{\text{2}{\gamma }_{2}}{{\gamma }_{2}+1} \frac{1}{3{y}_{1}}\right] $
式中：E0为爆炸能量，E0=QvW，其中，Qv为炸药爆热（对于TNT, Qv=4.56×106 J/kg）；$ {\gamma }_{2} $为比热比；$ {y}_{1} $为压力比。
$ {y}_{1}=\frac{{p}_{1}}{{p}_{0}}=\frac{\text{2}{R}^{-3}{E}_{0}}{\left({\gamma }_{2}+1\right){p}_{0}b\left({\gamma }_{2}\right)} $
式中：p1为冲击波入射超压；p0为初始压力，对于空气，p0=0.1 MPa，$ {\gamma }_{2} $=1.4，$ b({\gamma }_{2}) $= 5.317。
设Ew为近场爆炸范围内作用在滑块迎爆面上的强爆炸冲击载荷能量，其表达式为
$ {E}_{\text{w}}=\frac{{S}_{ \text{S}}}{4\text{π} {R}^{2}}{E}_{2} $
进一步，爆炸冲击波与ETS之间的能量转化效率η可以定义为
$ {\eta }=\frac{{E}_{\text{e}}}{{E}_{\text{w}}}\times 100\text{%} $
能量转化效率η用于表征爆炸冲击载荷对ETS的做功效率，其值越大，爆炸冲击波能量中被ETS所吸收的比例越高。
2.3　能量转化预测模型验证及分析
通过以上推导，可预测近场耦合载荷作用下ETS吸收的能量Ee。图13展示了理论预测的W=10 kg、Z=0.60 m/kg1/3处ETS的响应过程及能量吸收的理论预测和数值模拟结果。对比发现，理论预测的耦合载荷反射压曲线和ETS的嵌入过程均与数值模拟结果较为一致，且理论预测的能量吸收与数值模拟结果的相对偏差为7.68%。为进一步验证模型的普适性，表4汇总了W=10 kg时不同比例距离处ETS能量吸收的数值模拟预测值、理论预测值及两者的相对偏差。结果表明，所有工况下预测误差均控制在±20%以内，最大相对偏差为18.01%，最小相对偏差为−11.77%。考虑到近场爆炸载荷具有强非线性、高瞬态性和多物理场耦合特征，此误差水平是可接受的[1]。综上所述，本研究提出的近场耦合载荷等效简化是合理的，将经验公式计算得到的等效波形曲线代入基于刚性固壁假设建立的ETS嵌入控制方程中，能够有效预测近场耦合载荷与ETS之间的能量转化。
图14(a)展示了在不同炸药当量下，爆炸冲击载荷与ETS（$ {\overline{\rho }}_{\text{s}} $=68.53 kg/m2、$ {\overline{\sigma }}_{\text{s}} $=1.49 MPa）之间能量转化效率随比例距离变化的趋势。总体而言，随着比例距离的增加，能量转化效率显著下降。这是由于，当比例距离增加时，爆炸冲击载荷的超压和比冲量显著减小，导致反射系数降低[17]，从而减弱了反射波的强度。通过对比图14(a)与图14(b)，可以发现，爆炸冲击载荷的能量转化效率与反射压及比冲量的变化趋势高度一致，表明比冲量是主导能量传递过程的关键物理量。具体而言：Z在0.30～0.40 m/kg1/3范围内时，比冲量随Z的增大而急剧下降，相应地，能量转化效率也快速降低，反映出强耦合载荷下能量输入的剧烈衰减；Z在0.40～0.60 m/kg1/3范围内时，不同炸药当量下的能量转化效率呈现出差异化波动，如2、3 kg工况中下降平缓，而10、50 kg工况中出现局部回升。结合图14(b)可见，该区间内各工况的比冲量变化趋势本身存在差异，例如：大当量炸药的比冲量出现了显著局部回升。这种比冲量演化路径差异直接传导至结构响应，表现为能量转化效率的非单调变化。当Z>0.60 m/kg1/3时，比冲量趋于平缓衰减，能量转化效率亦随之缓慢下降，尤其当Z>0.80 m/kg1/3时，能量转化效率基本低于10%。上述现象说明，能量转化效率并非单纯由峰值超压决定，而是由载荷的时间积分效应（比冲量）主导。这是因为ETS的能量吸收依赖于滑块在载荷作用时间内的持续运动，而比冲量反映了载荷对结构的累积冲量输入能力。因此，在近场爆炸防护设计中，应将比冲量作为评估吸能结构性能的核心参数，而非仅关注瞬时压力峰值。
3　结　论
收起
研究了近场爆炸条件下冲击波与爆轰产物耦合作用下冲击载荷与ETS之间的能量转化机理，结合试验验证与数值模拟，建立了载荷等效模型和能量转化效率预测模型，主要结论如下：
(1) 随着比例距离的增加，近场爆炸载荷与ETS之间的能量转化效率显著降低，当比例距离超过0.80 m/kg1/3时，能量转化效率普遍低于10%；
(2) 能量转化效率与反射波的比冲量呈显著正相关，说明在近场爆炸中决定能量向结构传递效率的关键因素是载荷的冲量特性，而不仅仅是峰值压力；
(3) 基于强冲击假设构建了能量转化效率理论模型，该模型能够合理反映载荷参数与结构响应之间的关系，为近场防护结构的快速性能预估提供了理论工具。
由于本研究所采用的 ETS 模型基于特定几何构型和材料参数，且将迎爆滑块简化为刚体，未考虑其可能的塑性变形，因此，结构整体刚度和构型多样性对吸能性能的影响尚未系统探讨。此外，当前分析仅针对爆炸载荷正入射工况，未涉及非正入射条件下的载荷演化规律与能量转化特性。未来工作将重点围绕结构整体刚度对能量吸收的影响，发展适用于非正入射爆炸载荷表征方法。
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doi: 10.11858/gywlxb.20251227
  • 接收时间：2025-10-15
  • 首发时间：2026-04-29
  • 出版时间：2026-04-05
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  • 收稿日期：2025-10-15
  • 修回日期：2025-11-25
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    国防科技大学理学院, 湖南 长沙　410073

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林玉亮（1978－），男，博士，教授，博士生导师，主要从事爆炸与冲击动力学研究. E-mail：
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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
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光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
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