, 钱煜平, 张扬军清华大学 车辆与运载学院, 汽车安全与节能国家重点实验室, 北京 100084
收稿日期：2022-12-25
基金项目：国家重点研发计划项目(2020YFB1901702)
作者简介：杨子木(1999—), 男, 博士研究生
通讯作者：诸葛伟林, 副研究员, E-mail: zhugewl@tsinghua.edu.cn
摘要：超临界二氧化碳(supercritical carbon dioxide, S-CO2) Brayton循环是中温高压循环, 采用该循环可回收利用燃气涡轮和内燃机等交通动力系统的高温排气能量, 从而提高动力系统效率。压缩机高效稳定运行对S-CO2 Brayton循环的循环性能起到至关重要的作用。该文从实验、一维流动分析、三维流动特性和流动控制4个方面综述了S-CO2离心压缩机流动特性的研究进展, 重点阐述了关于工质临界点附近的剧烈物性变化对压缩机内部流动带来的问题及其研究内容, 同时总结了S-CO2离心压缩机流动特性的相关研究, 并提出未来S-CO2离心压缩机流动特性的研究重点。
关键词：S-CO2离心压缩机一维流动三维流动特性流动控制临界点
A review of supercritical carbon dioxide centrifugal compressor flow characteristics
YANG Zimu, JIANG Hongsheng, ZHUGE Weilin
, QIAN Yuping, ZHANG YangjunState Key Laboratory of Automotive Safety and Energy, School of Vehicle and Mobility, Tsinghua University, Beijing 100084, China
Abstract: [Significance] The supercritical carbon dioxide (S-CO2) Brayton cycle is a power cycle at intermediate temperature and high pressure. This cycle is considered an important solution to improving the efficiency of traffic power systems such as gas turbines and internal combustion engines by recycling exhaust energy at high temperatures. The compressor is considered one of the most important components of this cycle. Its efficient and stable operation plays an important role in cycle performance. [Progress] In this paper, the research progress on S-CO2 centrifugal compressor flow characteristics was reviewed from four aspects: experiment, one-dimensional flow analysis, three-dimensional flow characteristics, and flow control. Researchers learned from the experimental studies of the S-CO2 centrifugal compressor that the special thermophysical properties of S-CO2, particularly their dramatic change near the critical point, brought great challenges to the design and stable operation of this compressor. Therefore, the problems of compressor flow caused by the drastic physical properties change near the critical point of the working medium, and the related research contents were emphatically expounded. The current research on one-dimensional flow analysis of the S-CO2 centrifugal compressor is mainly conducted by the one-dimensional mean streamline method considering the special thermophysical properties of S-CO2 fluid. The preliminary aerodynamic design of the S-CO2 centrifugal compressor was conducted using one-dimensional flow analysis. This method is limited by its prediction accuracy under off-design conditions. In addition, the flow details inside the compressor could not be obtained by this method. To reveal the flow mechanism of the S-CO2 centrifugal compressor, its three-dimensional flow characteristics must be deeply understood, and its internal flow field information must be obtained. The research on the three-dimensional flow characteristics of the S-CO2 centrifugal compressor was mostly conducted by the computational fluid dynamics (CFD) numerical simulation method, which can be used to obtain the flow field of the centrifugal compressor and present the relevant flow phenomenon. Because of the drastic variations in the thermophysical properties of S-CO2 fluid near the critical point, special consideration was taken in the process of the CFD simulation of the flow inside the centrifugal compressor. By applying CFD to S-CO2 centrifugal compressor three-dimensional flow characteristics, researchers found that this special thermal physical property also brought special flow phenomena inside the flow domain of the S-CO2 centrifugal compressor. The research on S-CO2 centrifugal compressor three-dimensional flow characteristics mainly focused on its steady flow and needs to further reveal deeply and comprehensively the flow mechanism of the S-CO2 centrifugal compressor under various unsteady working conditions. The flow control of the S-CO2 centrifugal compressor was mainly by the passive flow control method using the relevant control method of the air compressor for reference, and its effect was remarkable. As for the active flow control method, few studies have heeded its effect on the S-CO2 centrifugal compressor. [Conclusions and Prospects] In this paper, the flow characteristics of the S-CO2 centrifugal compressor are summarized, and their research prospects are proposed. These flow characteristics are considerably different from those of centrifugal compressors with conventional fluids, mainly because of the special physical properties of S-CO2 fluid. In the future, more advanced research methods are expected to be used, such as visual flow experiments, one-dimensional flow analysis incorporating machine learning algorithms, and active flow control, to conduct more in-depth and comprehensive studies of S-CO2 compressor flow characteristics.
Key words: supercritical carbon dioxide centrifugal compressorone-dimensional flowthree-dimensional flow characteristicsflow controlcritical point
提高交通动力系统效率是实现交通运载工具节能减排的必然选择。对于燃气涡轮和内燃机等排气温度较高的交通动力系统，排气能量损失会导致动力系统效率下降。通过底循环对排气能量进行回收利用，是提高动力系统效率的重要途径。有机Rankine循环是利用排气能量的一种方式，国内外对此研究较多，但有机Rankine循环采用的有机工质工作温度低且价格昂贵，限制了该循环在交通动力系统的广泛应用。超临界二氧化碳(supercritical carbon dioxide，S-CO2)Brayton循环是以S-CO2为工质的中温高压循环系统，相比于有机Rankine循环，其具有工质高温稳定性好、工质价廉易得等优势，被视为理想的底循环方案[1]。采用S-CO2 Brayton循环对高排温交通动力系统的排气能量加以利用，可大幅度提高如燃气轮机[2-6]、内燃机[7-10]、固体氧化物燃料电池[11-14]等动力系统的效率。
S-CO2 Brayton循环由Feher[15]和Angelino[16]于1968年提出，该循环的S-CO2工质临界温度较低、高温稳定性好，而且在超临界状态下S-CO2工质具有密度较大、黏度较低的优点。受换热器和叶轮机械制造等技术限制，S-CO2 Brayton循环在20世纪70年代后发展缓慢。21世纪后，由于换热器和叶轮机械制造技术的进步，S-CO2 Brayton循环进入快速发展时期[17]。作为高效清洁的能量转换系统，除交通运载领域之外，S-CO2 Brayton循环在诸多领域亦有较好的应用前景。例如，在固定式热力发电领域，S-CO2 Brayton循环被视为理想的下一代核能[18-20]和太阳能光热[21-23]发电侧循环方案，其还可作为地热发电、生物质燃烧发电、化石燃料燃烧发电等场合的发电侧循环方案[1]。
S-CO2 Brayton循环热效率较高的主要原因是：S-CO2工质的类液态高密度和类气态低黏度特点使压缩机功耗大幅度减少[18]。理想气体压缩机耗功约占涡轮输出功的40%，与之相比，S-CO2压缩机耗功仅约占涡轮输出功的15%[19]。因此，S-CO2压缩机是S-CO2 Brayton循环的核心部件，压缩机高效稳定运行对循环性能至关重要。
在S-CO2 Brayton循环中，目前压缩机构型绝大多数采用离心式。Jeong等[24]的研究表明，当S-CO2离心压缩机的入口状态位于CO2临界点(7.38 MPa, 30.98 ℃)附近时，S-CO2离心压缩机可获得最佳的气动性能，从而提升S-CO2 Brayton循环的系统性能。然而，在CO2临界点附近，真实气体效应问题较为严重，主要表现为CO2的密度、比焓等热力学性质随温度和压力的轻微变化而发生剧烈的非线性变化。文[25-26]的研究表明，S-CO2的特殊物理性质会对其流动和传热规律产生较大影响。因此真实气体效应会极大影响S-CO2离心压缩机内部的流动特性。
综上所述，研究S-CO2离心压缩机内部的流动特性，有助于增强对超临界流体流动规律的认识，完善叶轮机械流动理论，从而指导S-CO2离心压缩机设计，实现S-CO2离心压缩机高效稳定运行，提升S-CO2 Brayton循环系统的性能。
1 性能实验为获取S-CO2离心压缩机的气动性能及其对S-CO2 Brayton循环的影响，国内外诸多研究机构如美国Sandia国家实验室(Sandia National Laboratory，SNL)、美国西南研究院(Southwest Research Institute，SwRI)、德国杜伊斯堡大学(University of Duisburg-Essen，UDE)、韩国原子能研究院(Korea Atomic Energy Research Institute，KAERI)、韩国高新技术研究院(Korea Advanced Institute of Science and Technology，KAIST)、日本东京工业大学(Tokyo Institute of Technology，TIT)、中国科学与工程热物理研究所(Institute of Engineering Thermophysics，IET)等均搭建了S-CO2离心压缩机实验台架，并进行了实验研究。表 1为部分S-CO2离心压缩机设计参数，总结了当前公开的部分实验数据。由表 1可知，压缩机均采用离心式构型，主要原因是离心式压缩机可获得较高的压比和气动效率。部分S-CO2离心压缩机入口状态如图 1所示，这些S-CO2离心压缩机的入口状态基本都位于临界点附近，这是因为临界点附近的压缩机入口状态可使S-CO2 Brayton循环获得更高性能。
表 1 部分S-CO2离心压缩机设计参数
| 单位 | 构型 | |||||
| 美国SNL[27] | 离心式 | 3.53 | 75 000 | 7.69，32.2 | ||
| 美国SwRI[28] | 离心式 | 55.00 | 27 400 | 8.52，37.0 | ||
| 德国UDE[29] | 离心式 | 0.65 | 50 000 | 7.83，33.0 | ||
| 韩国KAERI[2] | 离心式 | 12.55 | 36 000 | 7.94，34.0 | ||
| 韩国KAIST[30] | 离心式 | 3.00 | 40 000 | 7.60，31.4 | ||
| 日本TIT[31] | 离心式 | 1.20 | 102 000 | 8.23，35.0 | ||
| 中国IET[32] | 离心式 | 16.50 | 40 000 | 8.00，35.0 |
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| 图 1 部分S-CO2离心压缩机入口状态 |
| 图选项 |
在实际运行过程中，压缩机入口的温度和压力难以保证一直处于定值。在美国SNL的S-CO2离心压缩机实验[27]中，入口温度在31.2~33.9 ℃波动，入口压力在7.70~8.14 MPa波动。由于该范围较接近CO2的临界点，因此S-CO2工质的物性变化较剧烈，如S-CO2工质的密度在344.26~686.35 kg/m3波动。在德国UDE的实验中，Hacks等[29]对S-CO2离心压缩机内部流动进行了计算流体力学(computational fluid dynamics，CFD)仿真，仿真结果和实验结果基本一致。韩国KAIST的实验[30]研究表明，当S-CO2离心压缩机流量系数减小时，气动效率急剧下降。在日本TIT的实验[31]中，当入口条件位于近临界类液相时，离心压缩机性能达到最高，这说明S-CO2工质的密度增大，而密度增大会导致压缩机体积流量减小。Cho等[33]发现，在韩国KAIST的实验中，S-CO2离心压缩机在低流量系数下会发生喘振等不稳定流动现象，这是导致其气动效率下降的重要因素。Hacks等[34]通过对德国UDE实验中的S-CO2离心压缩机进行仿真，探明了S-CO2离心压缩机叶轮尾缘附近存在流动分离现象。
由S-CO2离心压缩机的实验研究现状可知，S-CO2工质的特殊物性，尤其是其在临界点附近的剧烈物性变化，为压缩机的设计和稳定运行带来巨大挑战。而S-CO2离心压缩机的气动设计、流动机理和流动控制大多是针对入口近临界点的特殊物性展开的。
2 一维流动一维平均流线法通常应用于S-CO2离心压缩机的初步流动分析，在确定压缩机的基本结构参数后可快速预测压缩机性能。一维平均流线法具有计算速度较快、宏观性能参数计算准确的优势，在S-CO2离心压缩机的初步设计与分析阶段可发挥重要作用，还可在S-CO2 Brayton循环动态特性分析中作为压缩机性能快速预测的方法。
利用一维平均流线法对S-CO2离心压缩机进行分析时，通常忽略流动参数在其他方向的变化，只考虑流动参数在流向的变化，根据Bernoulli方程和一维Euler方程并结合经验参数，对流向的流动损失特性进行参数化建模，获得平均流线上各计算节点的相关流动参数，从而实现对压缩机性能的预测。
2.1 S-CO2压缩机流动损失模型离心压缩机的流动损失可分为叶轮内部损失和叶轮外部损失2类，离心压缩机流动损失类型及相关文献如表 2所示。对压缩机内部的流动损失进行参数化建模是利用一维平均流线法进行流动分析的重要环节。
表 2 离心压缩机流动损失类型及相关文献
| 叶轮内部损失 | 叶轮外部损失 | |||
| 类型 | 相关文献 | 类型 | 相关文献 | |
| 入口攻角损失 | [35-38] | 轮盘摩擦损失 | [35, 43] | |
| 叶片载荷损失 | [37, 39] | 外部回流损失 | [40-41] | |
| 表面摩擦损失 | [37, 39-41] | 外部泄漏损失 | [38] | |
| 叶顶间隙损失 | [37, 41] | 叶片扩压器损失 | [38, 44] | |
| 尾流混迹损失 | [37, 42] | 无叶扩压器损失 | [38, 44] | |
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对于S-CO2离心压缩机，****们的研究多是在空气离心压缩机或离心水泵的基础上，考虑S-CO2工质的特殊物性，根据Span等[45]提出的CO2真实气体状态方程和CO2的输运性质方程[46-47]，调用NIST Refprop数据库获取CO2物性，发展出S-CO2离心压缩机流动损失模型。美国SNL[27]利用构建的损失模型对S-CO2离心压缩机进行了性能预测，结果表明：这种损失模型能较好地预测非设计工况的压缩机性能。
S-CO2离心压缩机的损失模型按照预测指标可分为总压损失模型和能量损失模型。文[48-50]在空气离心压缩机流动损失模型的基础上，考虑近临界点的CO2真实气体物性，建立了基于总压损失的S-CO2离心压缩机损失模型，并利用该模型预测了压缩机的流量和能头系数。不同于总压损失模型，文[51-52]建立了基于能量损失的S-CO2离心压缩机损失模型，利用该模型对SNL实验中的压缩机性能进行预测，预测结果在设计流量工况点与实验吻合，但在大流量工况下压比预测值偏高，等熵效率预测值偏低。文[53-54]对比了基于能量和基于总压的损失模型，发现2种模型的性能预测结果存在显著差异。文[55-57]使用不同类型的模型对不同的损失进行预测，提出总压基和能量基混合的S-CO2离心压缩机损失模型，模型预测结果表明：在小流量工况下，不同模型组合对叶轮外部损失的预测结果差异较大。
上述能量基和总压基损失模型均属于一区模型，即将叶片通道看作一个区域，假设叶片出口的S-CO2工质流动均匀。另一种流动损失模型属于两区模型，根据叶片出口的“射流-尾迹”现象，假设叶片出口为主流区和二次流区，并进行建模。崔新贵等[58]利用两区模型预测了S-CO2离心压缩机性能，预测的性能曲线较为平直，但非设计工况下的预测精度有待提升。El等[59]同样利用两区模型对S-CO2离心压缩机性能进行预测，通过对比预测结果与CFD仿真结果，发现二者吻合。Liu等[60]对比了一区模型和两区模型的预测性能，结果表明：两区模型的部分经验参数不适用于S-CO2离心压缩机，一区模型更适用于预测S-CO2离心压缩机性能。
2.2 考虑真实气体效应的S-CO2压缩机性能预测与常规离心压缩机相比，利用一维平均流线法预测气动性能时，S-CO2离心压缩机需要考虑S-CO2工质的真实气体效应。Meroni等[61]利用一维平均流线法分别预测了S-CO2工质和R-134a有机工质的压缩机性能，验证结果表明：在考虑真实气体效应情况下，该方法能较好地预测压缩机性能。Behafarid等[62]在预测S-CO2离心压缩机性能时考虑了S-CO2工质的可压缩性，并将预测结果和理想气体模型预测结果进行了对比。Chen等[63]通过在归一化模型中利用S-CO2真实气体效应下的声速修正流量、转速和比焓升，达到不同入口条件下折算S-CO2离心压缩机性能的目的。Anderson等[64]则利用真实气体效应下的S-CO2密度修正了压缩机流量，同样可归一化折算压缩机性能。滕庚等[65]利用流量系数对S-CO2离心压缩机流动损失模型进行修正，修正后的模型能较好地预测S-CO2离心压缩机变工况性能。Huang等[66]将S-CO2真实气体效应引入叶轮内部损失模型，通过修正损失模型系数准确预测了S-CO2离心压缩机性能。Clementoni[67]对比了多种基于真实气体效应的S-CO2离心压缩机性能预测方法在不同工况下的预测精度并指出，这些方法在非设计工况下的准确性均有待验证。Uysal等[68]在S-CO2离心压缩机的流动控制中提出了利用理想流体作为替代工质的方法，验证结果表明：该方法可用于在相似入口条件下生成S-CO2离心压缩机性能曲线。
利用一维平均流线法快速预测S-CO2离心压缩机性能的重要意义在于：一维平均流线法在优化S-CO2 Brayton循环的系统特性时可快速获得压缩机性能曲线，并将二者匹配。因此，****们在研究S-CO2离心压缩机性能时，往往将S-CO2 Brayton循环的系统特性纳入考虑范围。Zhang等[69]利用一维平均流线法分析了S-CO2 Brayton循环的再压缩分数等参数对压缩机性能的影响，并指出压缩机在近临界点工作时可减少压缩机功耗和提高系统效率，其主要原因是工质密度较大。Yao等[70]提出循环概念和叶轮机械部件相结合的S-CO2 Brayton循环一维设计方法，并指出较大的循环流量有利于提升压缩机效率，而压缩机入口温度设计需要平衡循环系统特性和可靠性。Wang等[71]提出系统和部件耦合的S-CO2 Brayton循环及压缩机、涡轮设计方法，该方法可提高压缩机效率。Li等[72]在设计S-CO2 Brayton循环时考虑了压缩机冷凝裕度，结果表明：循环效率和压缩机抗冷凝性能相互冲突。
随着人工智能技术快速发展，机器学习算法逐渐应用于叶轮机械气动热力学领域，****们利用机器学习算法改进了S-CO2离心压缩机性能预测及气动设计方法。Xia等[73]在利用一维平均流线法进行S-CO2离心压缩机气动设计时，引入了粒子群算法和多目标遗传算法，通过对压缩机叶轮的关键结构参数进行优化，提高了压缩机效率。Tang等[74]在S-CO2离心压缩机气动设计中引入了模拟退火算法，提高了压缩机在小流量工况下的压比和等熵效率，并扩大了压缩机稳定工作范围，但是在大流量工况下压缩机压比有所下降。Du等[75]在S-CO2离心压缩机气动设计中引入遗传算法，提高了非设计工况下的压缩机性能。
综上所述，相关研究主要考虑S-CO2工质的特殊物性，并将其应用于S-CO2离心压缩机的初步气动设计。然而，一维平均流线法在非设计工况下的预测精度较低，未考虑非定常流动现象对S-CO2离心压缩机流动损失的影响，压缩机气动性能预测方法在非定常工况下的预测精度有待验证。
3 三维流动特性一维平均流线法可快速预测S-CO2离心压缩机的宏观性能，但无法获取压缩机内部流动细节，以及造成流动损失的分离流、漩涡等流动现象。若要揭示S-CO2离心压缩机流动机理，需要深入了解压缩机的三维流动特性，获取压缩机内部的流场信息。S-CO2离心压缩机三维流动特性的相关研究大多通过CFD数值仿真展开，因为该方法可获取压缩机内部的流场信息，并呈现相关的流动现象。
3.1 仿真过程中的S-CO2特殊物性获取方法由于S-CO2的物性在临界点附近会剧烈变化，所以CFD仿真计算过程需要考虑工质的物性。****们通过构建物性插值表等方法在CFD仿真过程中获取S-CO2的特殊物性，从而使压缩机流动的CFD仿真更加接近真实流动过程。
Moraga等[76]提出构建物性插值表，并在CFD计算时通过调用物性插值表获取工质物性，实现了对S-CO2这种物性非线性变化的流动工质进行数值仿真的目标。对S-CO2工质而言，物性插值表是基于Span等[45]提出的CO2真实气体状态方程和CO2的输运性质方程[46-47]，通过调用NIST Refprop工质物性数据库构建。文[77-80]通过调用物性插值表对S-CO2离心压缩机进行CFD仿真，仿真结果与实验结果吻合，证明利用CFD仿真研究S-CO2离心压缩机流动机理具有可行性。图 2为文[77]中在温度-密度平面上构建的S-CO2物性插值表。其中，图 2a为温度-密度平面的表格区，绿色实线为工质的饱和线，饱和线以下的区域为两相区；图 2b为在计算时进行插值过程应用的示意图。
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| 图 2 S-CO2物性插值表示意图[77] |
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受临界点附近S-CO2特殊物性剧烈变化影响，S-CO2离心压缩机的CFD仿真计算往往难以同时保证收敛性和准确性，****们针对这一问题开展了相关研究。Kim等[81]对比了不同入口温度下S-CO2离心压缩机的CFD仿真结果，结果表明当入口状态接近临界点时，CFD仿真预测的压缩机性能误差较大。Ameli等[82]提出了一种在保证物性插值表分辨率的前提下提高计算收敛性的方法，保证物性插值表分辨率的原因是S-CO2离心压缩机的CFD仿真计算收敛性对物性插值表精度高度敏感。文[57, 83]测试了S-CO2物性插值表精度对压缩机CFD仿真结果的影响，并提出了一种关于脊线拟对称采样的S-CO2物性插值表生成方法，该方法提高了数值计算的准确性，并能在较小影响精度的情况下减少计算时间。此外，文[84]还开发了考虑S-CO2特殊物性的S-CO2离心压缩机通流模型，该模型可评估饱和线以下区域的冷凝现象，相比于CFD仿真，大幅度缩短计算时间。Karaefe等[85]提出了基于样条曲线的物性插值表方法，并对基于该方法的S-CO2离心压缩机密度基求解器进行了优化。Hacks等[29]利用商业CFD求解器ANSYS CFX对S-CO2离心压缩机进行数值仿真时，采用Rhie-Chow插值对压力-速度进行耦合(精度设为二阶)，提高了计算准确性和收敛性。Lee等[86]在CFD仿真中考虑S-CO2特殊物性，基于真实气体等熵指数改进了流动从滞止到静态的识别方法。
3.2 S-CO2特殊物性对压缩机三维流动现象的影响S-CO2特殊物性会对其在压缩机中的流动规律产生重大影响，****们针对S-CO2特殊物性，利用3.1节所述的CFD数值仿真方法，研究了S-CO2离心压缩机区别于常规离心压缩机的三维流动现象。
压缩机性能变化可体现S-CO2特殊物性对离心压缩机流动现象的影响。Baltadjiev等[87]研究表明, S-CO2的真实气体效应使压缩机在大流量工况下的阻塞裕度减小了9%，从入口到出口的单位面积修正质量流量偏移在原基础上增加了5%。Lettieri等[88]研究表明，S-CO2的真实气体效应对压缩机在小流量下的失速裕度改善较大。王婉月[89]通过对比S-CO2工质和CO2理想气体在压缩机中的流动特性发现，真实气体效应可大幅度降低压缩机功耗。Cai等[90]同样对比了S-CO2工质和CO2理想气体在压缩机中的流动特性，结果表明：S-CO2的真实气体效应可减少叶顶间隙损失和二次流损失。Ameli等[91]指出，S-CO2离心压缩机内部的熵产、Mach数(Ma)、压力和温度等流动参数的分布对S-CO2工质在临界点附近的剧烈物性变化高度敏感。Hacks等[34]发现，S-CO2的真实气体效应会造成更大的压缩机风阻损失。文[92]还通过测试证实：S-CO2的真实气体效应会导致压缩机性能剧烈变化，最终导致S-CO2 Brayton循环运行稳定性下降。文[93]研究了S-CO2的真实气体效应对压缩机内部流动损失的影响，结果表明：真实气体效应会导致S-CO2离心压缩机流动损失，该损失主要发生于扩压器的叶片后缘和尾迹区。
Lettieri等[94]指出，由于离心压缩属于速度式压缩，S-CO2工质在压缩机叶片前缘附近的局部加速会导致其温度和压力降低至临界点以下，从而发生相变冷凝，即S-CO2工质处于液态。文[95]通过Laval喷管模拟压缩机入口状态，对冷凝现象进行了可视化实验。Rinaldi等[96]在CFD仿真中也观察到冷凝现象，该现象主要发生在S-CO2离心压缩机叶片前缘的吸力侧。冷凝现象是S-CO2离心压缩机特有的流动现象，由其微超临界的入口状态导致。Toni等[97]通过实验证实，冷凝现象会影响S-CO2离心压缩机运行。因而许多****针对S-CO2离心压缩机的冷凝现象开展了相关研究。Kim等[98]在CFD仿真中利用具有亚稳态特性的两相流体体积(volume of fluid，VOF)模型对冷凝现象进行了研究并发现，低压区出现在主叶片和分流叶片前缘，而低温区仅出现在主叶片前缘。Brinckman等[99]利用非平衡相变模型预测了冷凝现象中弥散相液滴中生长核的凝结过程，结果表明冷凝现象可能会增加S-CO2离心压缩机的传热损失，从而导致压缩机性能下降。王枭等[100]分析了冷凝现象的形成原因和变化规律。Bao等[101]研究了蜗壳周向不均匀性对冷凝现象的影响。Persico等[102]分析了冷凝现象对S-CO2离心压缩机气动性能的影响机制，通过CFD仿真获得的压缩机叶片前缘冷凝现象如图 3所示，图中青色表示可能出现的冷凝区域。Hosangadi等[103]分析了冷凝现象的动态特性及其对压缩机稳定性的影响，结果表明S-CO2离心压缩机存在“冷凝喘振”特殊不稳定现象。
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| 图 3 S-CO2离心压缩机叶片前缘的冷凝现象[102] |
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为增强对S-CO2离心压缩机内部流动特性的认识，****们研究了相关工况参数对流动的影响机理。刘智远[104]的研究表明S-CO2离心压缩机入口参数会对叶片前缘Ma分布产生较大影响，从而影响压缩机气动性能。Pham等[105]研究了入口温度对压缩机叶片前缘出现的液态区域的影响，结果表明入口温度越低，叶片前缘出现的液态区越大，而靠近临界点的入口温度会导致叶片前缘出现较大的两相区。Liese等[106]的研究表明，S-CO2离心压缩机入口压力增大会导致压缩机喘振裕度减小。Bao等[107]分析了不同入口温度对S-CO2离心压缩机内部漩涡结构和流动的周向不均匀性的影响机理。Saxena等[108]选取了8.50 MPa、35.0 ℃，10.50 MPa、50.0 ℃，7.00 MPa、20.0 ℃这3个入口状态，分别模拟正常天气、炎热天气和寒冷天气3种情况，分析了入口状态对压缩机叶片前缘阻塞的影响，结果表明在寒冷天气情况下压缩机叶片更易发生前缘阻塞，但压缩机压比更大。文[109-110]通过CFD仿真方法，研究了亚临界入口状态对S-CO2离心压缩机叶片前缘冷凝的影响。文[111]对比了亚临界入口和近临界入口这两种状态对冷凝现象的影响，结果表明在近临界入口状态下，冷凝现象对压缩机效率影响较大。Liu等[112]对亚临界、近临界和超临界入口状态的S-CO2离心压缩机流动进行对比，研究了入口状态对叶轮入口附近速比的作用机制。Kumar等[113]指出，不同流量对S-CO2离心压缩机内部密度突变区域的影响较大。
除温度、压力和流量等工况参数外，S-CO2离心压缩机的结构参数也会对其内部的流动形态产生重要影响。Raman等[114]研究了叶顶间隙对S-CO2离心压缩机流动损失的影响，同时对比了无叶扩压器和叶片扩压器对压缩机中流动堵塞的影响。文[115-116]研究了叶顶间隙泄漏流对S-CO2离心压缩机分离涡的作用机理。Du等[117]研究了不同叶片扩压器形状对扩压器中速度分布的影响，相比于圆形和翼型扩压器，楔形扩压器中速度更大、流场更均匀。Saravi等[118]研究了楔形扩压器叶片数量变化及相应的喉部面积变化对流动特性的影响。Romei等[119]研究了入口导叶角度对S-CO2离心压缩机入口预旋涡的作用机制。
上述关于S-CO2离心压缩机三维流动特性的研究均针对定常流动特性展开，而针对S-CO2离心压缩机非定常流动特性的研究尚处于起步阶段。Guo等[120]对比了S-CO2离心压缩机定常和非定常的CFD仿真，结果表明：非定常仿真结果更接近设计指标，但研究未考虑非定常仿真中时间步长的独立性。Wang等[121]的研究表明，S-CO2离心压缩机内部流动具有很强的非定常特性，但未揭示非定常流动特性产生的原因。Ma等[122]研究了S-CO2离心压缩机叶轮和叶片扩压器的相对位置变化引起的非定常流动特性，这种非定常现象使周期内压缩机的等熵效率变化超过20%，但该研究未阐明S-CO2特殊物性和这种非定常现象的关系。Bao等[123]研究了蜗壳周向不均匀性引起的S-CO2离心压缩机冷凝区域的非定常演化，但该研究未考虑S-CO2离心压缩机近临界入口状态变化引起的物性剧烈变化对这种演化的影响，S-CO2离心压缩机非定常流动特性如图 4所示。图 4中，灰色表示叶片，红色表示未冷凝区域，蓝色表示发生冷凝的区域，A1、A2、A3分别为不同的流向截面，LE为叶片前缘，SS为叶片吸力面，每个图例的左下方表示在一个旋转周期内相应的时间点，如0.35 T表示在从一个旋转周期的起点经过了0.35个周期的时间点，每个图例都在发生冷凝的区域附近标出了相应的叶高位置。由图 4可知，一个周期内不同的时间点，发生冷凝的区域不同，如在0.35 T时冷凝主要发生于0.9叶高处，而0.37 T时冷凝主要发生于0.84叶高处。
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| 图 4 S-CO2离心压缩机非定常流动特性示意图[123] |
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综上所述，当前研究大多关注定常流动特性，且研究较为全面。对于S-CO2离心压缩机非定常流动特性，相关研究主要针对由转动部件和静止部件相对位置变化引起的非定常流动特性，并未考虑由近临界入口状态变化导致工质剧烈物性变化引起的非定常流动特性，因此还需要更为深入全面地揭示S-CO2离心压缩机在各种非定常工况下的流动机理。
4 流动控制流动控制方法可分为主动流动控制和被动流动控制2种。主动流动控制是指通过监测流动状态，在流场中直接施加适当的且与流动内在模式相互耦合的扰动模式，从而控制流动；被动流动控制是指通过调整设计结构使流动形态改变，进而对流场产生影响，从而控制流动[124]。****们依据对S-CO2离心压缩机流动特性的认识，研究了其流动控制方法，当前针对S-CO2离心压缩机的流动控制方法以被动流动控制为主。
4.1 设计层面的流动控制通过叶片载荷与型线设计控制叶片通道内部流动是叶轮机械中最常见的被动流动控制方法。Hacks等[34]通过设计“变厚度，大后倾角”的特殊叶型，控制了S-CO2离心压缩机叶片通道下游和叶片吸力侧的流动分离。Xia等[73]通过改变叶片包角，实现对S-CO2离心压缩机尾缘加速区域的控制，提高了压缩机性能。Shi等[125]通过采用改变叶轮和叶片扩压器间隙的流动损失控制方法，有效控制了尾迹掺混损失，提高了压缩机压比。Pei等[126]通过改变S-CO2离心压缩机叶片前缘型线的长短轴比，实现对叶片前缘冷凝的控制，提高了压缩机的等熵效率和压比，叶片前缘型线对S-CO2离心压缩机冷凝区域的流动控制作用如图 5所示，图 5a—5d分别代表叶片前缘型线轴比为1、3、6、9时的叶片前缘附近干燥度分布。Li等[127]通过设计入口气流角，实现对压缩机冷凝现象的控制。Cho等[128]采用增加叶片后弯角的流动控制方法，提升了S-CO2离心压缩机的等熵效率。Oh等[129]的研究表明，采用增加叶片后弯角的流动控制方法还能控制S-CO2离心压缩机喘振，扩大压缩机稳定工作范围。蒋雪峰等[130]同样采用增加叶片后弯角的流动控制方法，减小了叶片尾缘附近的流动分离，在增大S-CO2离心压缩机喘振裕度的同时提高了压缩机压比。王枭等[131]综合考虑了叶片包角、叶片后弯角、叶片入口角和轮毂半径等参数，提出了利用叶片几何参数控制S-CO2离心压缩机冷凝的方法。王军里[132]详细研究了叶片包角和叶片后弯角对压缩机流动的控制作用，研究表明不同的叶片包角和叶片后弯角会改变叶片载荷，进而影响流动形态；减小叶片包角或增大叶片后弯角有利于提高压缩机压比。
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| 图 5 叶片前缘型线对S-CO2离心压缩机冷凝区域的流动控制作用示意图[126] |
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4.2 损失抑制层面的流动控制叶顶间隙损失、扩压器损失和泄漏损失是S-CO2离心压缩机流动损失的重要组成部分，控制这3种流动损失是提升压缩机气动性能的重要途径。Zhao等[133]通过控制叶顶间隙涡抑制了S-CO2离心压缩机叶片前缘低温低压区域，进而减少叶顶间隙损失，压缩机气动性能有所提升，但其稳定工作范围减小。Lettieri等[88]的研究表明, 与叶片扩压器相比，无叶扩压器的流动损失更小，更有利于S-CO2离心压缩机稳定运行。Shi等[134]通过改变叶片扩压器型线，使扩压器与其他压缩机流道参数精准匹配，减少了扩压器损失，提高了S-CO2离心压缩机在低转速工况下的压比。美国SNL[27]和德国UDE[29, 34]的实验研究表明，S-CO2离心压缩机的外部泄漏损失对其气动性能影响较大。Yuan等[135]通过设计的最佳迷宫密封齿数和间隙控制泄漏通道中的漩涡，减小了泄漏流量。Kim等[136]利用孔口直径效应、腔长效应和齿数效应实现对S-CO2压缩机迷宫密封泄漏流的控制。曹润等[137]研究了密封结构和泄漏流对S-CO2离心压缩机气动性能的影响，研究表明大流量工况下盘腔泄漏流会改善压缩机冷凝情况，从而可通过盘腔泄漏流和密封结构实现对压缩机冷凝的流动控制。
4.3 其他流动控制方法部分****利用自循环机匣、入口导叶和分流叶片等结构，实现对S-CO2离心压缩机的流动控制。Pelton等[138]研究了自循环机匣对叶尖附近漩涡的流动控制作用，研究表明自循环机匣是拓宽S-CO2离心压缩机稳定工作范围的重要方法，自循环机匣对S-CO2离心压缩机叶尖附近漩涡的流动控制作用如图 6所示。图 6对比了有自循环机匣和无自循环机匣的S-CO2离心压缩机子午面的流线和相对Ma分布；左上角方框中，无自循环机匣的S-CO2离心压缩机在流动中出现了漩涡。刘智远[104]利用自循环机匣实现对S-CO2离心压缩机近失速点泄漏流强度的控制，通过抑制泄漏流与相邻叶片的干涉，改善了叶尖堵塞状况，拓宽了压缩机失速裕度和堵塞裕度。尚鹏旭[139]通过自循环机匣实现对二次流和主流的掺混损失的控制，提升了S-CO2离心压缩机气动性能和稳定工作范围。Cich等[140]通过可变入口导叶控制S-CO2离心压缩机入口流动，使S-CO2离心压缩机在不同入口温度下仍能保持较高效率。陈俊君[141]通过改变分流叶片长度，控制了压缩机叶片通道尾缘附近的流动分离。
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| 图 6 自循环机匣对S-CO2离心压缩机叶尖附近漩涡的流动控制作用[138] |
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对于S-CO2离心压缩机，工质的特殊物性要纳入流动控制研究考虑范围。Schuster等[142]研究了考虑工质真实气体效应的S-CO2离心压缩机设计方法，该方法表明真实气体效应一定程度上会影响S-CO2离心压缩机流动控制。Budinis等[143]提出考虑真实气体效应的S-CO2离心压缩机防喘振系统调节控制方法，该方法可提高压缩机工作稳定性。
综上所述，当前的流动控制方法以被动控制为主，借鉴了空气压缩机的相关控制方法，例如改变叶片包角等参数、采用自循环机匣等结构，流动控制效果显著。这些流动控制方法大多针对定常流动，而在非定常工况下的效果有待验证。针对离心压缩机的主动流动控制方法，如可变叶片扩压器控制、可变入口导叶控制、调节电机转速控制、入口喷射控制等方法对S-CO2离心压缩机的流动控制效果还有待研究。
5 结论本文针对S-CO2离心压缩机的流动特性，从性能实验、一维流动分析、三维流动特性和流动控制4个方面进行综述，相关现状总结及发展趋势概括如下：
1) 目前关于S-CO2离心压缩机的性能实验研究较少，尚处于起步阶段。当前性能实验中，压缩机入口状态大多处于临界点附近，此处工质物性的剧烈变化会导致压缩机出现一些非常规流动特性，这为S-CO2离心压缩机的一维流动分析、三维流动特性和流动控制研究指明了方向。后续研究中，S-CO2离心压缩机流动可视化、S-CO2压缩机变工况动态等实验可引入更先进的测量手段，从而加深对S-CO2离心压缩机流动特性的理解。
2) 目前S-CO2离心压缩机的一维流动分析主要采用一维平均流线法。通过参数化建模S-CO2离心压缩机内部的流动损失，预测S-CO2离心压缩机气动性能；预测过程考虑了S-CO2 Brayton循环的系统特性，并引入机器学习算法。在一维流动分析的后续研究中，可通过推广机器学习算法，降低模型经验参数依赖性，从而发展考虑S-CO2离心压缩机非定常流动特性的参数化模型。
3) 目前S-CO2离心压缩机三维流动特性和流动控制研究主要利用CFD数值仿真进行。受近临界入口状态的影响，相比于常规工质离心压缩机，S-CO2离心压缩机的流动机理差异较大，其流动控制方法也有较大差异。S-CO2离心压缩机三维流动特性和流动控制的后续研究，可进一步考虑由各种因素引起的S-CO2离心压缩机非定常流动特性，并分析主动流动控制方法对压缩机的流动控制效果。
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