三段变径基圆渐开线涡旋型线模型与流场数值模拟

doi:10.16183/j.cnki.jsjtu.2024.359

上海交通大学学报 ›› 2026, Vol. 60 ›› Issue (8): 1345-1351.doi: 10.16183/j.cnki.jsjtu.2024.359

三段变径基圆渐开线涡旋型线模型与流场数值模拟

刘涛(), 刘瑜, 邬再新, MOHAMMED Salah Taresh Abdo

兰州理工大学机电工程学院, 兰州 730050

收稿日期:2024-09-12 修回日期:2024-10-29 接受日期:2024-11-25 出版日期:2026-08-28 发布日期:2026-09-02
作者简介:刘涛(1971—),教授,博士生导师,主要研究复杂型面设计理论、薄壁零件精密加工、信号分析与故障诊断等.E-mail:cathyliu1999@126.com.
基金资助:
国家自然科学基金(52265034)

Three-Segment Variable-Radius Involute Based Scroll Profile Model and Flow Field Numerical Simulation

LIU Tao(), LIU Yu, WU Zaixin, MOHAMMED Salah Taresh Abdo

School of Mechanical and Electrical Engineering, Lanzhou University of Technology, Lanzhou 730050, China

Received:2024-09-12 Revised:2024-10-29 Accepted:2024-11-25 Online:2026-08-28 Published:2026-09-02

摘要/Abstract

摘要：

为了满足涡旋压缩机对综合性能优良型线的需求,提出一种结合渐变截面与变截面优势的三段变径基圆渐开线(T-VRI)涡旋型线模型.首先,基于微分几何理论,建立基于曲率半径函数的T-VRI统一数学模型.然后,详细推导吸气腔和排气腔的容积计算公式,并提出容积比、面积利用系数及泄漏线长度等几何评价指标.最后,利用有限元仿真软件Pumplinx对T-VRI型线的变截面涡旋压缩机进行计算流体动力学(CFD)数值模拟.结果表明:在相同安装尺寸下,相较于传统圆渐开线等截面型线,T-VRI型线的内容积比提升18.37%,面积利用系数提升9.19%,提高了容积效率与材料利用率;相比具有相同容积比的变径基圆渐开线(VRI)渐变截面型线,泄漏线长度减少19.47%.此外,相邻高压腔及对称工作腔的压差分别降低了22.16%和11.55%,更有利于涡旋压缩机的平稳运行,该研究为高性能变截面涡旋型线的设计提供了理论支持与方法依据.

关键词: 涡旋压缩机, 三段变径基圆渐开线, 型线模型, 流场数值模拟

Abstract:

To meet the demand for profiles with excellent overall performance of scroll compressors, this paper proposes a three-segment variable-radius involute (T-VRI) scroll profile integrating the metrics of gradually varying and variable cross-sections. First, a unified mathematical model for the T-VRI profile is established based on the curvature radius function using differential geometry theory. Analytical expressions for the volumes of suction and discharge chambers are derived with key geometric evaluation metrics defined, including volume ratio, area utilization coefficient, and leakage line length. Finally, transient computational fluid dynamics (CFD) simulations of the T-VRI scroll compressor are conducted via Pumplinx software to analyze its internal flow field. The results show that under identical installation dimensions, the T-VRI profile increases the internal volume ratio and area utilization coefficient by 18.37% and 9.19%, respectively, compared with the traditional circular involute equal-section profile, thereby improving both volumetric efficiency and material utilization. Compared with the variable-radius involute (VRI) profile, the T-VRI profile reduces the leakage line length by 19.47% at the same volume ratio. Additionally, the pressure differentials between adjacent high-pressure chambers and symmetrical working chambers are decreased by 22.16% and 11.55%, respectively, which facilitates more stable operation of scroll compressors. These findings provide effective theoretical references for the design of high-performance variable cross-section scroll profiles.

Key words: scroll compressor, three-segment variable-radius involute (T-VRI), profile models, flow field numerical simulation

中图分类号:

TH455

刘涛, 刘瑜, 邬再新, MOHAMMED Salah Taresh Abdo. 三段变径基圆渐开线涡旋型线模型与流场数值模拟[J]. 上海交通大学学报, 2026, 60(8): 1345-1351.

LIU Tao, LIU Yu, WU Zaixin, MOHAMMED Salah Taresh Abdo. Three-Segment Variable-Radius Involute Based Scroll Profile Model and Flow Field Numerical Simulation[J]. Journal of Shanghai Jiao Tong University, 2026, 60(8): 1345-1351.

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型线类型	a₁/mm	a₂/mm	k	R_or/mm	ϕ₁/rad	ϕ₂/rad	ϕ₃	V_s/cm³	V_d/cm³	L/mm	ν	ε
圆渐开线	3.572	-	-	5.6	-	-	7.6π	176.89	28.85	1 048.7	6.131	0.174
VRI	3.572	-	-0.04	5.6	-	-	9π	193.39	26.65	1 279.5	7.256	0.190
T-VRI	3.572	6.372	-0.04	5.6	2	4	7π	193.39	26.65	1 030.4	7.256	0.190

三段变径基圆渐开线涡旋型线模型与流场数值模拟

Three-Segment Variable-Radius Involute Based Scroll Profile Model and Flow Field Numerical Simulation

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[1]	闫敏, 刘涛, 麻德权, 党旭. 利用代数-阿基米德双螺线构建变截面涡旋齿组合型线[J]. 上海交通大学学报, 2024, 58(8): 1282-1289.
[2]	彭斌, 刘慧鑫, 陶耀辉. 基于变径基圆渐开线涡旋压缩机的几何模型及优化研究[J]. 上海交通大学学报, 2023, 57(8): 1046-1054.
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[4]	侯才生，刘涛. 基于Frenet标架的变截面涡旋型线构建与性能研究[J]. 上海交通大学学报, 2019, 53(12): 1495-1501.