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Article(id=1236679386422899673, tenantId=1146029695717560320, journalId=1210938733613449225, issueId=1236679384321544791, articleNumber=null, orderNo=null, doi=10.19666/j.rlfd.202404080, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1713974400000, receivedDateStr=2024-04-25, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1772776942115, onlineDateStr=2026-03-06, pubDate=1735056000000, pubDateStr=2024-12-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1772776942115, onlineIssueDateStr=2026-03-06, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1772776942115, creator=13701087609, updateTime=1772776942115, updator=13701087609, issue=Issue{id=1236679384321544791, tenantId=1146029695717560320, journalId=1210938733613449225, year='2024', volume='53', issue='12', pageStart='1', pageEnd='160', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1772776941614, creator=13701087609, updateTime=1772777031740, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1236679762404504298, tenantId=1146029695717560320, journalId=1210938733613449225, issueId=1236679384321544791, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1236679762404504299, tenantId=1146029695717560320, journalId=1210938733613449225, issueId=1236679384321544791, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=68, endPage=76, ext={EN=ArticleExt(id=1236679388159341533, articleId=1236679386422899673, tenantId=1146029695717560320, journalId=1210938733613449225, language=EN, title=Effect of dimensionless force on heat transfer of supercritical hydrogen in U-shaped tube, columnId=1236679385139434073, journalTitle=Thermal Power Generation, columnName=Special topic of low-carbon power technology, runingTitle=null, highlight=null, articleAbstract=

Against the cooling problem of engine heat exchangers, the flow and heat transfer characteristics of hydrogen in vertical and U-shaped tubes at supercritical pressures are studied. The influence of pressure and mass flow rate on heat transfer of the pipeline is studied by numerical method, and the heat transfer law is obtained. The heat transfer mechanism of the elbow section is discussed in depth, and the effect of dimensionless force on heat transfer is analyzed. The results show that, the closer the pressure is to the quasi-critical or when the mass flow rate increases, the convective heat transfer coefficient will increase, resulting in heat transfer enhancement. The bend section of the U-shaped tube can enhance heat transfer effectively, reaching a peak near θ=90°. There is a buoyancy effect in the straight pipe section at the inlet, but when the pressure is higher than 2.0 MPa, the buoyancy effect can be ignored after the hydrogen flows through the elbow section due to the influence of density difference. The Dean vortex caused by the secondary flow is the main factor to enhance the heat transfer performance of the elbow section, and the influence on the inlet section is significantly weaker than that on the outlet section.

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针对发动机换热器的冷却问题，开展了超临界压力下氢气在竖直管和U形管内流动传热特性研究。采用数值方法研究了压力和质量流率对管道换热的影响，从而得到换热规律，深入讨论弯管段的换热机理，分析了无量纲力对换热的影响。结果表明：压力贴近拟临界或质量流率增大均会增加对流换热系数，产生换热强化；U形管的弯管段可有效强化换热，在θ=90°附近达到峰值；入口直管段存在浮升力作用，但当压力高于2.0 MPa时，由于密度差影响，浮升力作用在弯管段后可忽略；由二次流引起的迪恩涡是强化弯管段换热性能的主要因素，其中对入口段的影响显著弱于出口段。

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杨帆（1981），女，博士，教授，主要研究方向为超临界流体流动传热技术，。
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高月（1998），女，硕士研究生，主要研究方向为超临界流体流动传热技术，。

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高月（1998），女，硕士研究生，主要研究方向为超临界流体流动传热技术，。

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高月（1998），女，硕士研究生，主要研究方向为超临界流体流动传热技术，。

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Boundary conditions for the straight and U-shaped tubes

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项目数值
U形管直管
管道内径d/mm44
绝热段长度/mm150150
曲率半径/mm15
氢气流动方向z轴正方向z轴正方向
入口温度/K33.533.5
热流密度/(kW·m–2)1010
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直管和U形管边界条件

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项目数值
U形管直管
管道内径d/mm44
绝热段长度/mm150150
曲率半径/mm15
氢气流动方向z轴正方向z轴正方向
入口温度/K33.533.5
热流密度/(kW·m–2)1010
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无量纲力对超临界氢气在U形管内传热的影响
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高月 1 , 张丽 2 , 海笑 1 , 李洋 1 , 杨帆 1 , 李鹏飞 1 , 王长顺 1
热力发电 | 低碳电力技术研究专题 2024,53(12): 68-76
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热力发电 | 低碳电力技术研究专题 2024, 53(12): 68-76
无量纲力对超临界氢气在U形管内传热的影响
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高月1 , 张丽2, 海笑1, 李洋1, 杨帆1 , 李鹏飞1, 王长顺1
作者信息
  • 1.辽宁石油化工大学石油天然气工程学院，辽宁　抚顺　113001
  • 2.辽宁石油化工大学机械工程学院，辽宁　抚顺　113001

    • 高月（1998），女，硕士研究生，主要研究方向为超临界流体流动传热技术，。

通讯作者:

杨帆（1981），女，博士，教授，主要研究方向为超临界流体流动传热技术，。
Effect of dimensionless force on heat transfer of supercritical hydrogen in U-shaped tube
Yue GAO1 , Li ZHANG2, Xiao HAI1, Yang LI1, Fan YANG1 , Pengfei LI1, Changshun WANG1
Affiliations
  • 1.College of Petroleum Engineering, Liaoning Petrochemical University, Fushun 113001, China
  • 2.College of Mechanical Engineering, Liaoning Petrochemical University, Fushun 113001, China
出版时间: 2024-12-25 doi: 10.19666/j.rlfd.202404080
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摘要
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针对发动机换热器的冷却问题，开展了超临界压力下氢气在竖直管和U形管内流动传热特性研究。采用数值方法研究了压力和质量流率对管道换热的影响，从而得到换热规律，深入讨论弯管段的换热机理，分析了无量纲力对换热的影响。结果表明：压力贴近拟临界或质量流率增大均会增加对流换热系数，产生换热强化；U形管的弯管段可有效强化换热，在θ=90°附近达到峰值；入口直管段存在浮升力作用，但当压力高于2.0 MPa时，由于密度差影响，浮升力作用在弯管段后可忽略；由二次流引起的迪恩涡是强化弯管段换热性能的主要因素，其中对入口段的影响显著弱于出口段。

氢气  /  超临界流体  /  U形管  /  传热特性  /  迪恩涡

Against the cooling problem of engine heat exchangers, the flow and heat transfer characteristics of hydrogen in vertical and U-shaped tubes at supercritical pressures are studied. The influence of pressure and mass flow rate on heat transfer of the pipeline is studied by numerical method, and the heat transfer law is obtained. The heat transfer mechanism of the elbow section is discussed in depth, and the effect of dimensionless force on heat transfer is analyzed. The results show that, the closer the pressure is to the quasi-critical or when the mass flow rate increases, the convective heat transfer coefficient will increase, resulting in heat transfer enhancement. The bend section of the U-shaped tube can enhance heat transfer effectively, reaching a peak near θ=90°. There is a buoyancy effect in the straight pipe section at the inlet, but when the pressure is higher than 2.0 MPa, the buoyancy effect can be ignored after the hydrogen flows through the elbow section due to the influence of density difference. The Dean vortex caused by the secondary flow is the main factor to enhance the heat transfer performance of the elbow section, and the influence on the inlet section is significantly weaker than that on the outlet section.

hydrogen  /  supercritical fluid  /  U-shaped tube  /  heat transfer characteristics  /  Dean vortex
高月, 张丽, 海笑, 李洋, 杨帆, 李鹏飞, 王长顺. 无量纲力对超临界氢气在U形管内传热的影响. 热力发电, 2024 , 53 (12) : 68 -76 . DOI: 10.19666/j.rlfd.202404080
Yue GAO, Li ZHANG, Xiao HAI, Yang LI, Fan YANG, Pengfei LI, Changshun WANG. Effect of dimensionless force on heat transfer of supercritical hydrogen in U-shaped tube[J]. Thermal Power Generation, 2024 , 53 (12) : 68 -76 . DOI: 10.19666/j.rlfd.202404080
正文
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随着社会发展，我国的能源量需求不断增加，开发新能源刻不容缓[1]。作为节能减排的模范大国，我国不断开发可再生能源。而氢能因其来源广泛、可存储、可再生、可发电、零污染等优点，受到了广泛关注[2-5]。氢是一种清洁、高效的二次能源，可代替其他燃料应用于航天领域，还可以应用于工业生产中，作为冷却介质为大型发动机降温，但现阶段对此方面研究还存有许多不足，补充相关理论基础进而进行深入探索变得尤为重要。
目前，常用的冷却剂主要包括二氧化碳、碳氢燃料、甲烷等，各国学者针对这些介质的传热特性已经进行了各类实验及模拟研究[6-9]。宿诗雨等[10]分析了再生冷却通道内甲烷的冷却机理，发现在竖直管内发生传热恶化的主要原因是浮升力，在弯管段中迪恩涡的出现会强化换热，并在弯管中部位置表现最为突出；王彦红等[11]对水平放置的U形加热通道内航空煤油的传热特性进行分析发现，受非均匀加热影响，直管段出现微弱二次流，弯管段受离心力作用热流偏移显著，出现强二次流，且提高入口温度可以有效提升换热效率；Fu等人[12]对碳氢燃料在U形管内进行流动换热实验，发现导热系数随弯曲半径的增大而减小，弯管段受离心力影响导热系数远大于直管段；Shokri等人[13]探究了甲烷在直/弯管内的流动传热变化，发现曲率半径对流体比热容变化有直接影响，提高底壁温度、降低出口压力或降低质量流率均可增加底壁附近流体速度及热流密度，进而强化管道换热，并使传热恶化位置提前。
氢气目前主要充当冷却介质被应用于工业及航空领域，多位学者对其流动传热特性进行了研究。Shanmugam等人[14]分析了冷却通道内肋条参数对氢气传热的影响，发现肋板角度、肋板尺寸、肋板取向均对可促进传热，弧形肋强化换热性能最优；周彪等[15]着重分析了弯管段流体的流动换热机理，发现离心力使弯管处产生轴对称的涡流，流体向外侧偏移，流速更快，使得外侧换热得到强化，内侧换热恶化，在出口处传热恶化现象最严重；Li等人[16]探究了微肋冷却通道内氢气的流动传热特性，发现微肋在热边界层过厚时对通道冷却作用有限，只有通过促进主流流体热扩散才能使局部强化换热。
综上所述，当前对于超临界流体的传热研究更多集中在圆形或U形通道内[17-19]，对于二者局部换热能力进行对比的研究还很少见。基于此，本文对超临界压力下氢气在竖直管及U形管内的流动换热进行了对比研究，着重分析了不同压力和质量流率对管道强化换热的影响，并通过无量纲力对氢气在管道内的流动机理做出简要阐述，旨在为超临界压力下氢的流动与传热后续探索提供理论参考。
1　数值计算方法
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1.1　几何模型
模拟所使用的U形管及直管几何模型如图1所示。模型均竖直放置，重力方向为z轴负方向（g=9.81 m/s2）。氢气进出口方向如图1所示，通道截面为r=2 mm的圆形，曲率半径R=15 mm，U形管的直管段长380 mm，并设置有150 mm绝热段用以避免入口段效应对传热的影响。
1.2　控制方程
为确保氢气在管道中流动传热特性的稳定，需要对模型进行处理。通过对比各模型处理方法得知，使用RNG k-ε模型结合强化壁面处理对换热结果的计算较为精准[20]。k-ε控制方程为：
∂∂xi(ρkui)=∂∂xi(αkue∂k∂xi)+Gk+Gb−ρε
∂∂xi(ρεui)=∂∂xi(αεue∂ε∂xi)+C1εGkεk−C2εε2k−Rδ
能量守恒方程为：
∂∂xi(ρuicpT)=∂ui∂xi[μe(∂ui∂xj+∂uj∂xi)−23μe∂uk∂xkδij]+π∂∂xi(Ke∂T∂xi)
动量守恒方程为：
∂∂xj(ρuiuj)=∂∂xj[μe(∂ui∂xj+∂uj∂xi)−23μe∂uk∂xk]−∂p∂xi+ρgi
连续性方程为：
∂∂xi(ρui)=0
式中：p为压力，MPa；T为流体温度，K；cp为定压比热容，J/(kg·K)；μ为动力黏度，Pa·s；i、j代表不同方向分量；Gk为湍动能因速度梯度生成项；Gb为湍动能因浮升力生成项。
1.3　工质物性
氢气临界压力1.3 MPa，临界温度34.178 K。图2为1.5 MPa下氢气的定压比热容cp、密度ρ、热导率λ和动力黏度µ，采用线性插值方法[21]进行数值模拟计算。
1.4　边界条件
进口边界条件设置为质量流率入口，温度为33.5 K，出口边界条件设置为压力出口，加热段外部热流密度设置为恒定。其他边界条件见表1。
1.5　网格无关性验证
U形通道和直管存在相似性，因此对U形通道进行网格独立性分析[22]。采用ICEM前处理软件进行网格划分，为提高边界处流动及传热特性相关数据观测的准确性，对壁面处的网格进行局部加密处理，以无量纲距离y+<1作为网格划分依据，结果如图3所示。
通过对照4组网格选定最优网格，网格数量及壁面温度如图4所示。在相同工况下，随着网格数量的增加壁面温度变化曲线逐渐趋于重合，考虑到人工及计算时间等因素，最终选用网格数1 710 708作为本次模拟网格划分。
1.6　数值方法验证
压力与速度耦合采用SIMPLE算法，动能和动量方程以及湍流动能和湍流耗散率均采用二阶迎风格式离散。收敛残差均设置为10–8，当残差基本保持不变，且进出口流量近似相等时，可认为计算结果收敛。为验证所选用计算模型的合理性，与Fu等人[12]所作实验基础数据进行对比，结果如图5所示。由图5可以看出，模拟得到的外壁面处温度与实验结果变化趋势相同，总体呈升高趋势，仅在弯管入口处略微降低，二者最大误差为1.9％左右，偏差范围合理，证明本次模拟选用计算方法合理。
2　结果与讨论
收起
2.1　压力对传热的影响
本节讨论运行压力对换热的影响，运行参数为：热流密度10 kW/m2，质量流率100 kg/(m2·s)，入口温度33.5 K，压力1.5、2.0、2.5 MPa。
图6给出了不同压力下壁面温度Tw和换热系数h沿流动方向的变化情况。由图6可以看出：直管段壁面温度均沿流向升高，压力较高时尤为显著；压力的增加使壁面温度变化幅度减缓，对传热的影响逐渐降低，弯管段更明显，这是由于管道内运行压力距离拟临界压力越远，氢气的物性变化越平稳，浮升力对其影响越小；弯管段壁面温度骤降，传热系数迅速上升，随着压力的升高弯管段处出现温度极值点，传热系数也对应出现谷值，温度极值点逐渐向弯管出口处移动。根据传热系数增长速率可以看出，压力对竖直管的影响明显小于弯管。
由图6a)可以看出，竖直管壁温直至出口处仍有缓慢上升趋势，而U形管外壁温度迅速降低，出现温度谷值，但随流动的进行差距逐渐缩小直至出口处温度与直管壁温近似，这在图6b)中也有体现，在弯管段壁温谷值处换热系数出现峰值，换热能力提升39.48％~59.73％。此外，在1.5 MPa下直管与U形管平均壁温差距最大，因为弯管处的二次流使U形管流体间扰动能力提升，增强整体换热能力，壁面温度降低，与周星[23]通过实验所得规律相同。
图7为U形管特征截面（θ=90°）处氢气的黏度、密度、定压比热容和导热系数在不同压力下的径向变化情况。由图7可以看出，氢气黏度在径向变化并不明显，受二次流影响其在内母线附近略高，压力为1.5 MPa时径向平均黏度较小，氢气流动速度较快，雷诺数达到最大，说明1.5 MPa下二次流动能最大，随着压力的升高，平均黏度变化逐渐减小，径向密度趋势与黏度相同，均出现明显分层，内外侧母线附近存在明显密度差，进而出现较大速度梯度，外侧质量流率高，流体掺混作用剧烈，使外母线附近换热能力明显强于内母线。由图7可知，在1.5 MPa下，径向截面物性参数变化较为剧烈，管道内侧梯度变化更明显，二次流对管道传热的强化作用远高于其他工况。
2.2　质量流率对传热的影响
本节讨论质量流率对换热的影响，运行参数为：热流密度10 kW/m2，压力1.5 MPa，入口温度33.5 K，质量流率75、100、125 kg/(m2·s)。
图8给出了不同质量流率下壁面温度Tw和换热系数h沿流动方向的变化情况。由图8可以看出：竖直管及U形管入口直管段温度均随着质量流率的增大而减小，且质量流率增大，二者差距逐渐减小，这是由于质量流率变大，管内流速加快，湍流强度增加，流体间扰动作用加剧，此时弯管段对于管道内流体影响较小；相同质量流率下，直管段管道外壁温呈现上升趋势，对流换热系数变化趋势仅入口初始段与之对应，后出现迅速下降趋势，之后呈现缓慢上升状态，这是由于入口处突然出现高热流密度，管壁迅速升温，流体间出现明显温度梯度，使壁面出现分层，阻碍热量传递，壁面处温度激增；随着流动的进行，温差逐渐缩小，分层逐渐减小，恢复正常传热。
由图8b)可以看出：相较于直管，弯管段出现明显强化换热现象，流体流速增加，边界层受到剧烈切削变薄，流体与壁面间导热能力增强，壁面温度急剧降低，换热系数相应急剧上升；弯管段换热系数在90°附近出现明显峰值，换热系数达到最大，较相同位置的直管提升84.62％~97.65％，其中提升最为明显的为G=75 kg/(m2·s)工况。
图9为U形管特征截面（θ=90°）处氢气的黏度、密度、定压比热容和导热系数在不同质量流率下的径向变化情况。由图9可以发现：质量流率增加对热物性的影响由外母线指向内母线并逐渐减小，这是由于二次流的作用使氢气流速产生明显分层，外母线附近流体流速较快，强化传热；质量流率由75 kg/(m2·s)升高到100 kg/(m2·s)对热物性的影响明显高于由100 kg/(m2·s)升高到125 kg/(m2·s)时，这是由于质量流率较低，二次流使流体产生较大湍动能，湍流强度在75 kg/(m2·s)工况下高于其余工况；当质量流率增加，由密度差所引起的自然对流随着径向截面梯度减小，二次流强度降低，强化换热能力升高幅度放缓；质量流率为75 kg/(m2·s)时，外母线附近导热系数与其余工况出现明显差异，r/R在0~0.15区间内导热系数升高，此时二次流流速较慢，不能很好切削热边界层，从而使外母线附近存在较大换热系数梯度。
2.3　无量纲力分析
Ri被认为是判断管道内浮升力对流动传热影响的标准，以0.001为判断界限，低于此标准则浮升力对换热影响可忽略[24]。图10给出了浮升力Ri沿流动方向的分布情况。
由图10可以看出，当压力改变时，入口和出口直管段均受到入口效应的影响Ri出现峰值，上升直管段沿程Ri数均大于0.001，浮升力因素应被考虑。压力改变，曲线出现多次重合，Ri数在1.5 MPa下变化趋势最为平缓，2.5 MPa下变化趋势呈现断崖式降低，结合雷诺数及温度变化曲线可以看出，此时浮升力主要受由主流与壁面间密度分层引起的速度差的影响。在未达到拟临界温度时，密度随压力减小而骤降，管道内流体流速迅速升高，浮升力较小。在弯管段及后续直管段仅1.5 MPa压力下Ri数大于0.001，随着压力的增加，达到拟临界温度后，密度变化并不显著，速度梯度减小，因此在2.0 MPa和2.5 MPa压力下浮升力较小，对换热影响可忽略不计。质量流率变化是通过改变氢气流速，从而对通道换热能力产生影响，通道内由二次流引起的迪恩涡对流体扰动增强，但Ri数减小明显。由此可见，随着质量流率增加，浮升力作用减弱，离心力对换热占据主导作用。
为进一步分析弯管段迪恩涡的影响，绘制出De沿流动方向的变化情况，结果如图11所示。迪恩数计算公式如式(6)所示[25]：
De=Re⋅(r/R)1/2
图11a)中：沿流动方向De在进入弯管时迅速上升，此时迪恩涡的出现对传热强化的作用最为明显，壁温骤降，h升高幅度显著；随着流动的进行，h上升速率逐渐减小，这是由于随主流速度和温度的升高，氢气主要受自然对流的影响，Re增长速率变缓，这在高压力下更为显著，说明高压力下二次流对传热的作用更强。
图11b)中，不同质量流率下De变化趋势相同，沿流动方向De无明显变化。但与图11a)不同的是，G升高使De在100～125 kg/(m2·s)区间升高速率大于75～100 kg/(m2·s)区间，这是由于流速升高使管道内湍动能升高。
为深入分析换热机理，划分了4个特征截面：P1（l=0.380 m）、P2（l=0.407 m）、P3（l=0.416 m）、P4（l=0.433 m）。在1.5 MPa压力下，弯管段特征截面速度云图及流线分布情况如图12所示。
由图12可以看出：氢气速度在管内P1位置时呈现主流向壁面逐渐降低的阶梯分布，流线方向由外侧壁面均匀指向内侧壁面，无二次流动；随着流动的进行，高流速阶梯呈现“未封闭扇形”分布，并逐渐向外侧壁面移动，出现二次流动；在P2位置，流线分布逐渐发生变化，因二次流动产生迪恩涡并向内母线方向移动，此时换热性能达到最优，这与图6中对流换热系数变化相贴合；在P3位置，图中出现多对沿轴对称且方向相反的迪恩涡，流体间掺混剧烈，此时受惯性力作用，截面上的流动方向转变迅速，流动阻力骤增，流速分层明显，部分迪恩涡对传热起到阻碍作用，换热系数略微降低；在P4位置，主流附近迪恩涡逐渐消失，仅存的一对迪恩涡向壁面偏移，持续挤压边界层，直至流出弯管段。
3　结论
收起
1）与竖直管相比，U形管的弯管段由于二次流作用，整体换热能力得到强化；迪恩涡的数量及位置也会对换热性能产生影响，且高压力下更显著。
2）压力减小、质量流率增加均会使氢气流动速度加快，热边界层受到挤压，使U形管的换热能力提升；当质量流率G=75 kg/(m2·s)时，U形管90°位置处较直管换热能力提升约97.65％；p=1.5 MPa时，换热能力提升约59.73％。
3）1.5 MPa压力下，当氢气质量流率改变时，Ri均大于0.001，整段管道受浮升力和离心力的共同作用。但当质量流率一定，压力大于2.0 MPa时，Ri数远小于0.001，浮升力作用在流入弯管后可忽略，管道内流体主要受离心力作用。
基金
收起
  • 国家自然科学基金项目(52006094)
  • 辽宁省教育厅基本科研项目(LJKMZ20220725)
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2024年第53卷第12期
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文章信息
doi: 10.19666/j.rlfd.202404080
  • 接收时间：2024-04-25
  • 首发时间：2026-03-06
  • 出版时间：2024-12-25
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  • 收稿日期：2024-04-25
基金
National Natural Science Foundation of China(52006094)
国家自然科学基金项目(52006094)
Fundamental Research Project of Liaoning Provincial Department of Education(LJKMZ20220725)
辽宁省教育厅基本科研项目(LJKMZ20220725)
作者信息
    1.辽宁石油化工大学石油天然气工程学院，辽宁　抚顺　113001
    2.辽宁石油化工大学机械工程学院，辽宁　抚顺　113001

通讯作者:

杨帆（1981），女，博士，教授，主要研究方向为超临界流体流动传热技术，。
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2种不同金属材料的力学参数
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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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