Optimization and Regulation of Mach Disk Structure in High-pressure CO2 Jet for Cutting Cooling

doi:10.3969/j.issn.1004-132X.2026.10.018

Abstract

Abstract:

The structural characteristics of the Mach disk in high-pressure CO₂ jets were systematically analyzed through CFD and experimental investigations， and the relational expression between the Mach disk structure and the mass flow rate， nozzle diameter， and pressure was established. A numerical model incorporating the CO₂ condensed phase was developed using the SST k-ω turbulence model and the Eulerian two-phase flow approach， and its reliability was experimentally validated. The results indicated that the average simulation errors for the Mach disk position and diameter were 5.34% and 4.92%， respectively. For the widely used empirical formula of the Mach disk structure， the proportional coefficient $C L$ was approximately 0.52 （lower than the conventional gas value of 0.6454）， while the Mach disk diameter coefficient α was about 1.164. Furthermore， it was found that the mass flow rate had a more significant influence on the Mach disk structure than pressure， and effective control of the Mach disk structure could be achieved by adjusting the combination of nozzle diameter and pressure.

Key words: high-pressure CO? jet, Mach disk, computational fluid dynamics（CFD）, empirical formula of Mach disk, cutting cooling

摘要：

通过计算流体动力学和实验研究系统分析了高压CO₂冷却射流的马赫盘结构特性并构建了马赫盘结构与质量流量、喷嘴直径和压力的关系式。基于SST k-ω湍流模型和欧拉两相流方法，建立含CO₂凝结相的数值模型，并通过实验验证了模型的可靠性。研究结果表明：马赫盘位置和直径的仿真平均误差分别为5.34%和4.92%；针对常用马赫盘结构经验公式，比例系数 $C L$ 约为0.52（低于常规气体0.6454），马赫盘直径系数α约为1.164；此外，质量流量对马赫盘结构的影响较压力更为显著，通过调节喷嘴直径和压力组合可实现马赫盘结构的优化控制。

关键词: 高压CO₂射流, 马赫盘, 计算流体动力学, 马赫盘经验公式, 切削冷却

CLC Number:

O358

ZHU Libin, CHEN Guanyu, CHENG Peng, ZHAO Xu. Optimization and Regulation of Mach Disk Structure in High-pressure CO₂ Jet for Cutting Cooling[J]. China Mechanical Engineering, 2026, 37(10): 2556-2565.

朱利斌, 陈冠宇, 程鹏, 赵旭. 面向切削冷却的高压CO₂射流马赫盘结构优化调控[J]. 中国机械工程, 2026, 37(10): 2556-2565.

Figures/Tables 12

Fig.1 Jet computing domain and grid

Tab.1 Boundary condition settings

边界条件	类型	具体参数	备注
入口（ab）	压力入口	5.10~7.38 MPa	出入口温度条件根据实际温度设定
出口（ghij）	压力出口	0.101 325 MPa	出入口温度条件根据实际温度设定
壁面（defg）	固体	铝合金	无滑移的绝热边界

Fig.2 Principle and equipment of the experimental setup

Fig.3 Shrink high-pressure nozzle and its internal structure

Tab.2 Parameters of the front end of high-pressure CO2 jet

组别	序号	质量流量 $m ˙$ /（g·s^-1）	压力p/MPa	喷嘴直径d_n/mm
a	1	1.00	5.10	0.26
	2	1.00	6.00	0.24
	3	1.00	7.38	0.21
b	4	1.35	5.10	0.30
	5	1.35	6.80	0.26
	6	1.35	7.25	0.24
c	7	1.15	6.00	0.26
	8	1.55	6.00	0.30
	9	1.83	6.00	0.33
	10	2.85	6.00	0.40

Tab.2 Parameters of the front end of high-pressure CO2 jet

组别	序号	质量流量 $m ˙$ /（g·s^-1）	压力p/MPa	喷嘴直径d_n/mm
a	1	1.00	5.10	0.26
	2	1.00	6.00	0.24
	3	1.00	7.38	0.21
b	4	1.35	5.10	0.30
	5	1.35	6.80	0.26
	6	1.35	7.25	0.24
c	7	1.15	6.00	0.26
	8	1.55	6.00	0.30
	9	1.83	6.00	0.33
	10	2.85	6.00	0.40

Fig.4 Jet structure with ultra-high and under-expansion degree

Fig.5 Simulation results of the jet field

Fig.6 Velocity distribution along the jet axis

Fig.7 Simulation velocity cloud diagrams of jet fields

Fig.8 Time-varying diagram of the high-pressure CO2 jet structure

Fig.9 Microscopic diagram of high-pressure CO2 jet field

Fig.10 Experimental and simulation data of Mach disk position and diameter

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Optimization and Regulation of Mach Disk Structure in High-pressure CO₂ Jet for Cutting Cooling

面向切削冷却的高压CO₂射流马赫盘结构优化调控

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