三角转子膨胀机串联运行特性研究

doi:10.11949/0438-1157.20241387

摘要/Abstract

摘要：

容积式膨胀机在有机朗肯循环及压缩空气储能等系统中扮演着重要角色。尤其在面临高膨胀比的场合时，多级膨胀运行成为不可或缺的选择。本文依据三角转子膨胀机的三个工作腔的运行原理，构建了相应的模型，并针对两级串联三角转子膨胀机的运行特征及其影响因素展开了深入分析。研究结果显示，通过合理匹配膨胀机的容积与转速比例，可以实现66%的功率密度增长和47%的输出功率提升。与单级膨胀机相比，在设计的膨胀比条件下或实际膨胀比较高时，多级串联膨胀机的功率密度至少提高了15%，即多级串联膨胀机可适合大膨胀比或膨胀比波动较大的工况中。

关键词: 容积式膨胀机, 三角转子膨胀机, 多级膨胀, 数学模型

Abstract:

The volumetric expanders play crucial roles in applications such as the organic Rankine cycle, compressed air energy storage, and other related systems. When facing high expansion ratios, multistage expansion becomes necessary. This paper establishes an analysis model for the Wankel expander, taking into account the operation of three working chambers, and simulates expanders connected in series. The simulation results indicate that by appropriately selecting the volume and rotational speed ratio of the expander, one can achieve a maximum power density increase of 66% and an output power increase of 47%. Across a broader range of pressure ratios, the mass flow rate of two-stage series expanders remains relatively stable. When compared to a single expander, operating at a designed or higher expansion ratio results in a power density increase of at least 15%, suggesting that series-connected expanders are well-suited for scenarios with large and fluctuating expansion ratios.

Key words: volumetric expanders, wankel expanders, multistage expansion, mathematical model

中图分类号:

TK 91

黄灏, 王文, 李沛昀. 三角转子膨胀机串联运行特性研究[J]. 化工学报, 2025, 76(S1): 435-443.

Hao HUANG, Wen WANG, Peiyun LI. Research on properties of wankel expanders under series connection[J]. CIESC Journal, 2025, 76(S1): 435-443.

图/表 20

图1 进气行程长0.5π时工作腔状态随主轴转角变化

Fig.1 Variation of the working chamber stroke with the angle of the eccentric shaft during the intake stroke of 0.5π

图2 膨胀机泄漏路径示意图

Fig.2 Schematic diagram of the leakage in an expander

图3 两级三角膨胀机串联系统结构图

Fig.3 Structural diagram of a series connected Wankel expander

图4 单级膨胀机在一个时间步长内的计算流程

Fig.4 Calculation process of an expander at each time step

图5 两级串联膨胀机的仿真计算流程

Fig.5 Calculation process of a two-stage series Wankel expander system

表1 文献中给出的三角转子膨胀机数据［14-17］

Table 1 The parameters of the Wankel expander given in Refs. ［14-17］

参数	数值
转子半径R/mm	60.25
形状因子K	5
腔体高度B/mm	84
偏心度e/mm	12.05
进气行程角φ_in/(°)	110
有效工作容积V_disp/mm³	316*105
容积效率η_v	0.4
排气压力P_out/bar	0.75
工质类型	水蒸气

表2 不同进出参数与转速下文献实验结果［14］与计算结果对比

Table 2 Comparison of experimental and computational data in Ref.［14］ under different rotational speeds

转速/ (r/min)	进口压力/ bar	输出功率(实验)^[14]/kW	输出功率(计算)^[14]/kW	输出功率(本文)/kW
1000	5.7	2.7	3.0	2.85
1000	6.4	3.8	3.5	3.55
1000	7.4	4.8	4.1	4.55
2000	5.4	5.4	5.2	5.46
2000	5.8	6.7	5.7	6.30
2000	6.6	8.4	6.8	7.96
3000	5.2	7.2	6.7	7.54
3000	5.9	9.2	7.9	9.73
3000	6.6	10.0	9.1	11.90

图6 腔体容积-压力循环曲线

Fig.6 Volume-pressure cyclic curve in a expander chamber

图7 腔体压力随时间的变化曲线

Fig.7 Pressure variation in a expander chamber

表3 两级串联膨胀机参数

Table 3 Parameters of two-stage series expanders

参数	膨胀机1	膨胀机2
转子半径R/mm	50	80
形状因子K	6	6
腔体高度B/mm	25	25
转速ω/(r/min)	1200	1200
进气截面积A_in/mm²	80	80
排气截面积A_out/mm²	80	160
泄漏间隙δ/mm	0.25	0.25
进气入口压力P_in/MPa	70	—
进气入口温度T_in/K	300	—
排气背压P_b/kPa	—	20000
缓冲容积V/cm³	20	—
进气行程角φ_in/(°)	135	135
理论体积膨胀比ε	2	2
对流强度系数h/(W/ (m²·K))	1200	1800

图8 两级串联膨胀机腔体压力变化曲线

Fig.8 Pressure variation in the chambers of two expanders

图9 两级串联膨胀机腔体温度变化曲线

Fig.9 Temperature profiles in the chambers of two expanders

表4 序号1~7对应的膨胀机参数

Table 4 Expanders parameters in discussion

序号	下级膨胀机转子半径/ mm	下级膨胀机腔体高度/mm	下级膨胀机转子半径/mm	下级膨胀机腔体高度/mm	上级转速/ (r/min)	下级转速/ (r/min)
1	50	25	40	40	1200	1200
2	50	25	70	25	1200	1200
3	50	25	80	40	1200	600
4	50	25	80	25	1200	1200
5	50	25	80	30	1200	1200
6	50	25	80	40	1200	1200
7	50	25	80	60	1200	1200

表5 不同参数条件下两级膨胀机的运行性能

Table 5 Performance of two-stage expanders

序号	上下级体积流量比	上级实际膨胀比	下级实际膨胀比	等熵效率/ %	总输出功率/ kW	功率密度/ (kJ/kg)
1	1∶1.02	1.59	1.37	12.41	77.20	158.03
2	1∶1.96	1.32	1.50	16.22	100.32	235.71
3	1∶2.04	1.28	1.42	15.15	78.79	191.93
4	1∶2.56	1.48	1.95	17.20	114.04	262.82
5	1∶3.07	1.51	1.42	16.64	123.41	259.76
6	1∶4.11	1.79	1.30	14.47	126.39	237.39
7	1∶6.11	2.19	1.14	8.37	108.12	171.13

图10 不同参数条件下两级串联膨胀机的输出功率

Fig.10 Output power of two expanders with different parameters

表6 不同进出口压力下两级串联膨胀机的工作情况

Table 6 Results of a two-stage series expanders system under different inlet and outlet pressures

进口压力/kPa	出口压力/kPa	上级实际膨胀比	下级实际膨胀比	总输出功率/kW	质量流量/(kg/s)	功率密度/(kJ/kg)
70000	40000	1.19	1.07	39.96	0.3871	103.23
70000	20000	1.35	1.49	114.04	0.4339	262.82
70000	15000	1.39	1.71	134.32	0.4438	302.66
70000	10000	1.43	2.02	155.98	0.4514	345.54
70000	5000	1.44	2.28	180.77	0.4526	399.40

图11 两级串联膨胀机的能量转换效率与等熵效率随出口压力变化曲线

Fig.11 Energy conversion efficiency and isentropic efficiency of a two-stage series expanders system with different outlet pressure

表7 单级膨胀机参数

Table 7 Parameters of a single-stage expander

参数	数值
转子半径R/ mm	25
形状因子K	6
腔体高度B/mm	60
偏心度e / mm	10
进气行程角φ_in/(°)	90
转速ω/(r/min)	1200
进气截面积A_in / mm²	80
排气截面积A_out / mm²	80
泄漏间隙δ/ mm	0.25
理论体积膨胀比ε	4

图12 在不同出口压力条件下两级串联和单级膨胀机质量流量的对比

Fig.12 Comparison of mass flow rate between two-stage series expanders and single-stage expander with different outlet pressure

图13 在不同出口压力条件下，两级串联和单级膨胀机功率密度的对比

Fig.13 Comparison of power density between two-stage series expanders and single-stage expander with different outlet pressure

参考文献 22

1	Di Battista D, Mauriello M, Cipollone R. Waste heat recovery of an ORC-based power unit in a turbocharged diesel engine propelling a light duty vehicle[J]. Applied Energy, 2015, 152: 109-120.
2	Tian Y F, Xing Z W, He Z L, et al. Modeling and performance analysis of twin-screw steam expander under fluctuating operating conditions in steam pipeline pressure energy recovery applications[J]. Energy, 2017, 141: 692-701.
3	Li G, Zheng X F. Thermal energy storage system integration forms for a sustainable future[J]. Renewable and Sustainable Energy Reviews, 2016, 62: 736-757.
4	Qiu G Q, Liu H, Riffat S. Expanders for micro-CHP systems with organic Rankine cycle[J]. Applied Thermal Engineering, 2011, 31(16): 3301-3307.
5	Pantano F, Capata R. Expander selection for an on board ORC energy recovery system[J]. Energy, 2017, 141: 1084-1096.
6	Qyyum M A, Naquash A, Sial N R, et al. CO₂ precooled dual phase expander refrigeration cycles for offshore and small-scale LNG production: Energy, exergy, and economic evaluation[J]. Energy, 2023, 262: 125378.
7	Sanaye S, Mohammadi Nasab A. Modeling and optimizing a CHP system for natural gas pressure reduction plant[J]. Energy, 2012, 40(1): 358-369.
8	Handa K, Oshima S, Rembutsu T. Precooling temperature relaxation technology in hydrogen refueling for fuel-cell vehicles[J]. International Journal of Hydrogen Energy, 2021, 46(67): 33511-33522.
9	Elgowainy A, Reddi K, Lee D Y, et al. Techno-economic and thermodynamic analysis of pre-cooling systems at gaseous hydrogen refueling stations[J]. International Journal of Hydrogen Energy, 2017, 42(49): 29067-29079.
10	Yoshida J, Matsuo E, Takata Y, et al. Thermodynamic analysis of high pressure hydrogen gas refueling system with turbo-expanders[J]. Mechanical Engineering Journal, 2019, 6(3): 18-388-18-00388.
11	张兴. 井口高压天然气发电用三角转子气动机设计与仿真[D]. 成都: 西南石油大学, 2018.
	Zhang X. Design and simulation of triangular rotor pneumatic motor for wellhead high-pressure natural gas power generation[D]. Chengdu: Southwest Petroleum University, 2018.
12	Badr O, Naik S, O'Callaghan P W, et al. Rotary Wankel engines as expansion devices in steam Rankine-cycle engines[J]. Applied Energy, 1991, 39(1): 59-76.
13	Francesconi M, Caposciutti G, Antonelli M. An experimental and numerical analysis of the performances of a Wankel steam expander[J]. Energy, 2018, 164: 615-626.
14	Antonelli M, Baccioli A, Francesconi M, et al. Experimental and numerical analysis of the valve timing effects on the performances of a small volumetric rotary expansion device[J]. Energy Procedia, 2014, 45: 1077-1086.
15	Antonelli M, Baccioli A, Francesconi M, et al. Numerical and experimental analysis of the intake and exhaust valves of a rotary expansion device for micro generation[J]. Energy Procedia, 2015, 81: 461-471.
16	Antonelli M, Francesconi M, Baccioli A, et al. Experimental results of a wankel-type expander fuelled by compressed air and saturated steam[J]. Energy Procedia, 2017, 105: 2929-2934.
17	Francesconi M, Analysis and design of devices for medium temperature solar thermal energy conversion[D]. Pisa: University of Pisa. 2017: 168-230.
18	Sadiq G A, Tozer G, Al-Dadah R, et al. CFD simulations of compressed air two stage rotary Wankel expander–Parametric analysis[J]. Energy Conversion and Management, 2017, 142: 42-52.
19	王云, 刘小勇, 周勇. 三角转子气动发动机设计及性能分析[J]. 机械科学与技术, 2009, 28(7): 950-954, 959.
	Wang Y, Liu X Y, Zhou Y. Design and performance analysis of a triangle rotary piston air-powered engine[J]. Mechanical Science and Technology for Aerospace Engineering, 2009, 28(7): 950-954, 959.
20	潘剑锋, 肖曼, 范宝伟, 等. 配气相位对三角转子气动发动机性能的影响[J]. 江苏大学学报(自然科学版), 2016, 37(2): 141-146.
	Pan J F, Xiao M, Fan B W, et al. Effect of valve timing on Wankel rotor air-powered engine[J]. Journal of Jiangsu University (Natural Science Edition), 2016, 37(2): 141-146.
21	李沛昀, 孟金龙, 王文, 等. 三角转子膨胀机在有机朗肯循环中应用分析[J]. 太阳能学报, 2023, 44(2): 1-8.
	Li P Y, Meng J L, Wang W, et al. Application analysis of wankel expander for organic Rankine cycle[J]. Acta Energiae Solaris Sinica, 2023, 44(2): 1-8.
22	李沛昀, 李杨, 王文彬, 等. 三角转子膨胀机在跨临界CO₂制冷循环中的应用分析[J]. 化工学报, 2021, 72(S1): 161-169.
	Li P Y, Li Y, Wang W B, et al. Application analysis of triangular rotor expander in transcritical CO₂ refrigeration cycle[J]. CIESC Journal, 2021, 72(S1): 161-169.

[1]	李卫, 陈浩, 柯钢, 黄孝胜, 李成娇, 郭航, 叶芳. 高原环境适应性试验室模拟平台新风系统仿真[J]. 化工学报, 2025, 76(S1): 360-369.
[2]	邵明成, 潘玉贵, 王增丽, 赵强. CO₂/CH₄混合物理论跨临界增压过程的热力性能研究[J]. 化工学报, 2024, 75(10): 3742-3751.
[3]	董宜放, 于樱迎, 胡学功, 裴刚. 电场对竖直微槽润湿及毛细流动特性影响[J]. 化工学报, 2022, 73(7): 2952-2961.
[4]	方远鑫, 肖武, 姜晓滨, 李祥村, 贺高红, 吴雪梅. 膜分离耦合CO₂电催化加氢制甲酸工艺的设计及模拟[J]. 化工学报, 2021, 72(9): 4740-4749.
[5]	于仙毅, 巫江虹, 高云辉. 基于主成分分析与支持向量机的热泵系统制冷剂泄漏识别研究[J]. 化工学报, 2020, 71(7): 3151-3164.
[6]	郑传杰, 盛昌栋. 高温烟气中吸附剂捕集K的模型及其反应动力学研究[J]. 化工学报, 2019, 70(6): 2259-2268.
[7]	张壮, 邓春, 孙海兰, 冯霄. 除盐水系统建模与物料衡算分析[J]. 化工学报, 2019, 70(2): 646-652.
[8]	尤东江, 魏建云, 李雪菁, 娄景媛. 基于框架设计的液流电池流场优化模拟研究[J]. 化工学报, 2019, 70(11): 4437-4448.
[9]	周新志, 邵伦, 李荣昆, 赵成萍, 董晨龙. 基于小波去噪和改进型PSO-SVM的微波加热温度预测模型研究[J]. 化工学报, 2018, 69(S2): 291-299.
[10]	张培昆, 王立. 空分短期停车时间阈值对氧气生产调度的影响[J]. 化工学报, 2017, 68(6): 2423-2433.
[11]	董泽, 陈利平, 陈网桦, 马莹莹. 密闭容器内失控反应超压的数学建模及其在压力泄放中的应用[J]. 化工学报, 2017, 68(11): 4453-4460.
[12]	马彪, 李彦军, 郭家敏, 张国磊, 宋福元, 李健, 曾帅, 张晓宇. 不同充汽方式下供汽系统动态特性仿真[J]. 化工学报, 2016, 67(S1): 326-333.
[13]	曾帅, 史智俊, 王鹏, 张国磊, 孙宝芝, 阙晨宇, 马彪, 李健. 舰用蒸汽动力系统主汽压力控制方法仿真[J]. 化工学报, 2016, 67(S1): 334-340.
[14]	陈骏, 周伟国, 王海, 李苏. 基于等效电法的钢铁企业蒸汽系统多目标运行优化策略[J]. 化工学报, 2016, 67(9): 3804-3811.
[15]	柴俪洪, 肖长发, 权全, 刘海亮, 陈明星, 赵斌. 同质增强型PMIA中空纤维膜污染及其MBR工艺处理城市生活污水[J]. 化工学报, 2016, 67(9): 3954-3964.