Research progress on thermodynamic performance of supercritical CO2 dry gas seal

doi:10.16085/j.issn.1000-6613.2023-1990

Abstract

Abstract:

The deployment of dry gas seal technology in supercritical carbon dioxide Brayton cycle turbine machinery, endowed with its exceptional sealing efficacy and stability, confers a safeguard for the secure operation of rotating machinery, while notably enhancing the shaft end sealing effect. In light of the distinctive physical properties of the sealing medium and the necessities of high-parameters operational milieu, intricate fluid lubrication theory is invoked in the investigation of thermodynamic performance of S-CO₂ dry gas seal. Owing to above discussion, this paper centered on the action mechanism and influence law of multifarious fluid effects and phase transition characteristics on the performance of S-CO₂ dry gas seal and flow heat transfer characteristics, elucidated in meticulous detail the analytical models and solution algorithms commonly employed in theoretical research, and thoroughly reviewed the theoretical and experimental investigations on the thermodynamic performance of S-CO₂ dry gas seal domestically and internationally. Subsequently, combining the demands of the field and existing advanced technologies, future developmental research trajectories were further proposed, with the aim of furnishing a theoretical reference for further inquiry into the correlative research and advancing the more application of dry gas seal technology in the future energy sector.

Key words: supercritical carbon dioxide, dry gas seal, phase change, fluid lubrication theory, thermodynamic performance

摘要：

干气密封技术在超临界二氧化碳（supercritical carbon dioxide，S-CO₂）布雷顿循环涡轮机械中的应用，以其卓越的密封性能和稳定性，为旋转机械的安全运行提供了保障，并显著改善了轴端密封效果。鉴于密封介质的特殊物性以及高参数化工作环境的要求，在S-CO₂干气密封热动力学性能研究过程中涉及复杂的流体润滑理论。本文重点阐述了多重流体效应以及相变特性对S-CO₂干气密封性能和流动传热特性的作用机理和影响规律，详细列出了理论研究中常采取的分析模型和求解算法，并综合评述了国内外在理论和试验方面对S-CO₂干气密封热动力学性能的研究。在此基础上，结合领域需求和现有先进技术，进一步提出了今后的发展方向，以期为深入开展相关研究提供理论参考，促进干气密封技术在未来能源领域中的广泛应用。

关键词: 超临界二氧化碳, 干气密封, 相变, 流体润滑理论, 热动力学性能

CLC Number:

TB42

JIANG Andi, DING Xuexing, WANG Shipeng, DING Junhua, LI Ning. Research progress on thermodynamic performance of supercritical CO₂ dry gas seal[J]. Chemical Industry and Engineering Progress, 2024, 43(5): 2354-2369.

江安迪, 丁雪兴, 王世鹏, 丁俊华, 力宁. 超临界CO₂干气密封热动力学性能研究进展[J]. 化工进展, 2024, 43(5): 2354-2369.

Figures/Tables 20

研究单位	涡轮机械方案	设计功率等级 /kW	设计转速 /r·min^-1	进气压力 /MPa	进口温度 /K
美国桑迪亚国家实验室^[19]	TA（12级离心压缩机，4级轴流透平）	100	75000	9.8	320
美国西南研究院/GE公司^[20-22]	TA（12级离心压缩机，4级轴流透平）	10000	27000	25.1	350
	TA（2级主压缩/4级再压缩离心压缩机，6级轴流透平/4级高压+3级低压双分流轴流透平）	50000	9500	25.1	973
	TA（2级主压缩/4级再压缩离心压缩机，6级轴流透平/4级高压+3级低压双分流轴流透平）	450000	3600
中国西安热工研究院^[23]	TA（4级离心压缩机，4级轴流透平）	5000	9000	20.0	873
韩国能源技术研究所^[24]	TA（2级主压缩/4级再压缩离心压缩机，6级轴流透平）	10	70000	7.91	773

方程	独立变量	压缩因子表达式	具体适用范围
R-K方程（Redlich-Kwong equation）^[35]	p、T	$Z 3 - Z 2 - b R 2 p 2 R g T 2 - a R p R g 2 T 2.5 + b R p R g T Z - a R b R p 2 R g 3 T 3.5 = 0$	适用于中低压（0.1~10MPa）和中高温（rt~T_c）条件下的气体状态描述，特别是液气界面附近的状态
二项截断型维里方程（second term Virial equation）^[36]	p、T	$Z (p, T) = p V m R g T ≈ 1 + B v p R g T$	适用于中等压力和温度（<P_c和T_c）下的气体状态描述，尤其在接近临界点和较低压力时，具有较高的精度
三项截断型维里方程（third term Virial equation）^[36]	p、T	$Z (p, T) = p V m R g T ≈ 1 + B v p R g T + C v - B v 2 p R g T 2$	适用范围与二项截断型维里方程相同，但由于增加了第三维里系数提高了描述的准精确度
Span-Wagner方程（Span-Wagner equation）^[37-38]	ρ、T	$Z (δ, τ) = p (δ, τ) ρ R T = 1 + δ ϕ δ r$	具有更高精度且适用范围广泛，特别适用于超临界流体和高压气体等复杂热力学系统
S-R-K方程（Soave-Redlich-Kwong equation）^[39]	p、T	$Z 3 - Z 2 - b S R 2 p 2 R g T 2 - a S R p R g 2 T 2 + b S R p R g T Z - a S R b S R p 2 R g 3 T 3 = 0$	适用于描述临界压力附近的气体状态，尤其是高温（>473K）情况
P-R方程 (Peng-Robinson equation)^[40]	p、T	$Z 3 + b p p R g T - 1 Z 2 - 3 b p 2 p 2 R g 2 T 2 - a p p R g 2 T 2 + 2 b p p R g T Z - b p p 2 R g 2 T 2 a p + 8 b p 2 p R g T + 4 b p = 0$	适用于多组分混合物的气体行为描述，在宽范围的温度（173~773K）和压力（0~100MPa）下表现良好，包括处理超临界流体

方程	独立变量	压缩因子表达式	具体适用范围
R-K方程（Redlich-Kwong equation）^[35]	p、T	$Z 3 - Z 2 - b R 2 p 2 R g T 2 - a R p R g 2 T 2.5 + b R p R g T Z - a R b R p 2 R g 3 T 3.5 = 0$	适用于中低压（0.1~10MPa）和中高温（rt~T_c）条件下的气体状态描述，特别是液气界面附近的状态
二项截断型维里方程（second term Virial equation）^[36]	p、T	$Z (p, T) = p V m R g T ≈ 1 + B v p R g T$	适用于中等压力和温度（<P_c和T_c）下的气体状态描述，尤其在接近临界点和较低压力时，具有较高的精度
三项截断型维里方程（third term Virial equation）^[36]	p、T	$Z (p, T) = p V m R g T ≈ 1 + B v p R g T + C v - B v 2 p R g T 2$	适用范围与二项截断型维里方程相同，但由于增加了第三维里系数提高了描述的准精确度
Span-Wagner方程（Span-Wagner equation）^[37-38]	ρ、T	$Z (δ, τ) = p (δ, τ) ρ R T = 1 + δ ϕ δ r$	具有更高精度且适用范围广泛，特别适用于超临界流体和高压气体等复杂热力学系统
S-R-K方程（Soave-Redlich-Kwong equation）^[39]	p、T	$Z 3 - Z 2 - b S R 2 p 2 R g T 2 - a S R p R g 2 T 2 + b S R p R g T Z - a S R b S R p 2 R g 3 T 3 = 0$	适用于描述临界压力附近的气体状态，尤其是高温（>473K）情况
P-R方程 (Peng-Robinson equation)^[40]	p、T	$Z 3 + b p p R g T - 1 Z 2 - 3 b p 2 p 2 R g 2 T 2 - a p p R g 2 T 2 + 2 b p p R g T Z - b p p 2 R g 2 T 2 a p + 8 b p 2 p R g T + 4 b p = 0$	适用于多组分混合物的气体行为描述，在宽范围的温度（173~773K）和压力（0~100MPa）下表现良好，包括处理超临界流体

湍流理论	理论基础	湍流应力处理方法	适用领域
Constantinescu湍流理论^[53-54]	Prandtl混合长度理论	以平均速度梯度进行表示	以速度流动为主的动压轴承计算
Ng-Pan-Elord湍流理论^[55-56]	Reichardt经验“壁面定律”	以平均速度梯度和涡黏系数表示	非平面流问题求解及不可压缩湍流润滑轴承
Hirs湍流理论^[57]	“Bulk flow”整体流理论	以雷诺数的幂次关系表示	雷诺数较小的湍流润滑和低运动黏度的流体润滑

黏度方程	独立变量	具体表达式	适用性
Lucas黏度方程^[36]	p、T	$μ (T, p) = {1 + a 1 p r 1.3088 / [a 2 p r a 5 + (1 + a 3 p r a 4) - 1]} μ 0$	适用于常规条件下气体混合物的黏度预测，但描述超临界流体黏度时精度较低
F-W-V黏度方程^[61]	ρ、T	$μ (ρ, T) = μ 0 (T) + Δ μ (ρ, T) + μ c (ρ, T)$	对靠近CO₂临界状态和高压下的黏度描述表现出较高的精度

黏度方程	独立变量	具体表达式	适用性
Lucas黏度方程^[36]	p、T	$μ (T, p) = {1 + a 1 p r 1.3088 / [a 2 p r a 5 + (1 + a 3 p r a 4) - 1]} μ 0$	适用于常规条件下气体混合物的黏度预测，但描述超临界流体黏度时精度较低
F-W-V黏度方程^[61]	ρ、T	$μ (ρ, T) = μ 0 (T) + Δ μ (ρ, T) + μ c (ρ, T)$	对靠近CO₂临界状态和高压下的黏度描述表现出较高的精度

传热模型	原理	涉及方程	计算复杂度	适用性
等温模型	假定密封环与流体热交换充分	流体流动方程、能量守恒方程	忽略了固体部分的一些热传递，在边界上施加恒定温度或零热通量条件即可，计算相对简单，复杂度低	适用于膜厚较薄且密封间隙内流体流速较慢的情况
绝热模型	假设固体边界热对流是绝缘的，即无热量通过固体边界	流体流动方程、能量守恒方程	忽略了固体部分的一些热传递，在边界上施加恒定温度或零热通量条件即可，计算相对简单，复杂度低	适用于气膜较厚及流速较高的情况
共轭传热模型	考虑密封环的导热以及密封环与密封腔流体之间的对流换热	流体流动方程、能量守恒方程、热传导方程	需同时求解流体和固体的热传递方程，并应用适当的耦合边界条件，计算复杂度高	适用范围广，接近于实际传热过程

计算方法	基本思想	特点
PH线性法（P-H linear method）^[64]	定义PH函数关联独立变量，再引入泛函数，并对研究点的微分线性化代替，获得近似线性方程	构造形式简洁，求解工作量大大降低
等步长有限差分法（equal step fin difference method，E-FDM）^[65]	用节值或节点差商代替微分方程中的变量或导数，并转换为差分代数方程	差分表达式简单、收敛速度快
变步长有限差分法（variable step fin difference method，V-FDM）^[66]	考虑非均匀网格的差分格式，根据问题的具体需求，步长可灵活调整	灵活性、实用性好：根据计算精度，选择适合的网格密度和差分格式，提高了计算效率
有限体积法（finite volume method，FVM）^[65,67]	在划分控制体积的基础上，利用网格节点对应控制，再对多个控制体积分，得到离散方程	（1）构造形式多样化；（2）离散求解复杂域和灵活网格划分
有限元法（finite element method，FEM）^[65,68]	找到求解域中所划分单元内连续函数对应的形函数，组装成线性表达式，求解相应的刚度矩阵	（1）具有出色的有效性和可操作性，能够精确地逼近复杂形状表面；（2）计算阶次得到提高
等几何分析法（isogeometric analysis，IGA）^[69]	使用插值函数作为形函数，通过网格节点构建待解物理场的分布	无须求解域的离散过程，且表达压力所需的自由度少，求解效率高
多重网格法（multigrid method，MG）^[70]	利用粗网格消除细网格上的低频误差，更快收敛	兼顾运算效率的同时，提高运算精度、简化计算过程

计算流体动力学

（computational fluid dynamics，CFD）^[77]

使用有限元软件来计算和分析流体流动问题

可提供详细的流体流动和传热特性分析，但对计算资源要求较大

适用于广泛的流体流动和热传递问题

分子动力学

（molecular dynamics，MD）^[78]

基于物理原理模拟流体分子或原子的性质和行为

微观尺度下计算精确，但依赖于所用力场的精确性

适用于微观尺度的流体特性分析

数据驱动模型

（data driven model，DDM）^[79]

应用机器学习算法和人工智能技术分析数据，预测流体行为

处理并集成大量复杂数据，预测迅速，但需大量高质训练数据

适用于复杂系统分析和优化设计

测试类型	试验方法	测量技术
泄漏量测试	流量计测量：保证腔内压力恒定，进气补充量为泄漏量	（1）扫描电镜：观察密封副接触表面的微观结构，检测磨损和损伤；（2）声发射技术：监测干气密封状态，捕获并分析声波信号，评估密封性能和可能出现的故障；（3）实时监测和数据采集：使用实时监测系统和数据采集设备，记录干气密封性能参数
温度和压力测试	温度测量：普遍使用温度传感器，如热电偶或热电阻传感器；压力测量：可采用压力或压差传感器对密封环境压力测量，也可通过进出口压力和膜压峰值，间接测量气膜开启力
气膜厚度测试	气膜厚度测量实质是位移和振幅的测量，常见测量方法为电涡流法
摩擦扭矩和磨损测试	摩擦扭矩测量：使用测力传感器并利用数据采集系统记录；磨损测试：观察和分析密封副端面的微观结构和磨损情况，评估磨损程度和机制

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Research progress on thermodynamic performance of supercritical CO₂ dry gas seal

超临界CO₂干气密封热动力学性能研究进展

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