Journal of Textile Research ›› 2025, Vol. 46 ›› Issue (03): 196-206.doi: 10.13475/j.fzxb.20231202101

• Machinery & Equipment • Previous Articles     Next Articles

Optimization design of nozzle orifice structure based on response surface method

SHEN Min1, YANG Qi2, HU Feng2, WANG Zhen2, YANG Xuezheng3, LÜ Yongfa3, YU Lianqing1,2()   

  1. 1. Three-dimensional Textile Hubei Engineering Research Center, Wuhan Textile University, Wuhan, Hubei 430200, China
    2. School of Mechanical and Automation, Wuhan Textile University, Wuhan, Hubei 430200, China
    3. Shandong Rifa Textile Machinery Co., Ltd., Liaocheng, Shandong 252001, China
  • Received:2023-12-14 Revised:2024-05-10 Online:2025-03-15 Published:2025-04-16
  • Contact: YU Lianqing E-mail:2006110@wtu.edu.cn

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Abstract:

Objective The air consumption of the auxiliary nozzle accounts for approximately 75% of the air-jet loom. In order to address the issues of low jet velocity and high air consumption in the single circular-hole auxiliary nozzle, a novel-shaped orifice auxiliary nozzle was designed. The study investigated the influence of the outlet shape parameters of the auxiliary nozzle on the synthesized airflow within the novel-shaped reed groove. This paper reports on numerical simulations based on the Reynolds-Averaged Navier-Stokes (RANS) equations and a turbulent model for vortex viscosity, focusing on the three-dimensional synthesized flow field composed of the main nozzle jet and the auxiliary nozzle jet.

Method Firstly, three-dimensional synthesized flow field models for auxiliary nozzles A1, A2, A3, B1,B2 and B3 were established using Solidworks software. The synthetic flow field models were then grid-divided using specialized meshing software ICEM, and boundary condition parameters were set using computational fluid dynamics (CFD) software Fluent. Numerical simulations of the synthesized airflow were conducted based on the RANS equations, and the accuracy of the numerical results was validated through experiments. Secondly, building upon the analysis of experimental results, the range of outlet parameters for the auxiliary nozzles was defined, including the long axis, short axis, and rotation angle. Experimental combinations were generated using the Box-Behnken method, and calculations were performed using Fluent. Experimental results were presented as response surfaces, and regression equations were derived, with the accuracy of the regression equation verified through variance analysis. By analyzing the interactions between various factors, the impact of each factor on air consumption and speed was determined. In conclusion, a comparison of air consumption and average velocity among the experimental groups facilitated the identification of the optimal comprehensive performance model.

Results The numerical simulation results exhibit a decay trend in the airflow velocity curve that aligns with the experimental test results. The velocity of the primary jet rapidly decreases upon entry into the novel-shaped reed groove. When the auxiliary nozzle jet enters the reed groove, the synthesized airflow gets accelerated briefly, temporarily slowing down the overall decay of the synthesized airflow. The prioritization of the converging type of auxiliary nozzle is observed in the order of A1 > A2 > A3 and B3>B2>B1. The F-value of the response surface model for air consumption of the auxiliary nozzle under 0.3 MPa is 249.89, with a P-value smaller than 0.000 1, indicating the rationality of the selected model parameters. The results that R2=0.997 3, Adjusted R-squared (Radj2)=0.993 3, CV=1.14%<10%, and Adeq precision =56.082 8>4, indicating that the fitted regression equation conforms to the experimental principle and can be used for the analysis and prediction of air consumption. The F-value of the response surface model for velocity of the auxiliary nozzle under 0.4 MPa is 66.55, with a P-value smaller than 0.000 1, indicating the rationality of the selected model parameters. The results that R2=0.990 1, Radj2=0.975 2, CV=1.58%<10%, and Adeq precision =33.092 6>4, suggest that the fitted regression equation conforms to the experimental principle and can be used for the analysis and prediction of velocity. Through interaction analysis, it is observed that air consumption and velocity are positively correlated with the long and short axes, while the influence of the rotation angle on air consumption is relatively minimal, but the interaction between the rotation angle and the short axis has a significant effect on the velocity. Finally, compared with the average of the experimental group, the air consumption of the optimized model is reduced by 7.35%, and the average speed is increased by 2.25%.

Conclusion 1) The gas supply pressure of the elliptical hole auxiliary jet inlet is increased from 0.3 MPa to 0.4 MPa, and the air consumption of the elliptical hole auxiliary nozzle will be significantly increased. However, the distribution pattern of the response surface of the interaction of factors affecting air consumption is basically consistent. 2) The short axis of the elliptical hole has the most significant effect on the air consumption, followed by the long axis, while the change of rotation angle has no effect on the air consumption, and the interaction between the long axis and the short axis has the most significant effect on the air consumption. 3) The degree of influence on the peak value of the resultant air velocity is as follows: short axis > long axis > rotation angle, and the interaction of long axis-short axis and short axis-rotation angle on the velocity is significant; changing the rotation direction of the long axis of the elliptic hole has a significant effect on the resultant flow velocity. 4) A nonlinear relationship exists between the gas consumption of the auxiliary injection with elliptical holes and the peak velocity of the synthetic gas axis, and the gas consumption decreases when the speed increases.

Key words: air jet loom, auxiliary nozzle, spray hole, response surface methodology, air consumption

CLC Number: 

  • TS103.3

Fig.1

Structural parameters of auxiliary nozzls. (a) Model profile; (b) Elliptic orifice sections; (c) Physical drawings"

Fig.2

3-D model of multiple auxiliary nozzles combined with profiled reed. (a) Structural parameters of profiled reed; (b) Auxiliary nozzle installation positions"

Fig.3

Grid division of main and auxiliary nozzles in 3-D flow field"

Fig.4

Principle of flow velocity measurement of jet from main and auxiliary nozzles into special reed passage"

Fig.5

Average velocity measurement device for synthetic airflow in profiled reed channel"

Fig.6

Numerical simulation and experimental verification of synthetic flow field of three auxiliary nozzles. (a)Change in rotation angle of elliptical hole; (b) Change in short axis length of elliptical holes"

Fig.7

Velocity cloud maps at different distances parallel to exit section of auxiliary nozzle"

Tab.1

Factors and levels of Box-Behnken test design"

水平 A
长轴长度/mm		 B
短轴长度/mm		 C
旋转角度/rad
-1 2.0 1.0 0
0 2.2 1.2 0.393
1 2.4 1.4 0.785

Tab.2

Response surface test design and results"

试验
序号		 响应变量 响应值
长轴长
度/mm		 短轴长
度/mm		 旋转
角度/
rad		 H1:0.3MPa
耗气量/
(kg·h-1)		 H2:0.4MPa
耗气量/
(kg·h-1)
1 2.0 1.0 0.393 10.41 13.29
2 2.2 1.0 0 11.32 14.53
3 2.2 1.0 0.785 11.52 14.60
4 2.4 1.0 0.393 12.47 15.77
5 2.0 1.2 0.785 12.56 15.74
6 2.0 1.2 0 12.61 15.99
7 2.2 1.2 0.393 13.46 17.49
8 2.2 1.2 0.393 13.47 17.49
9 2.2 1.2 0.393 13.48 17.46
10 2.2 1.2 0.393 13.72 17.42
11 2.4 1.2 0.785 14.52 18.81
12 2.4 1.2 0 14.61 18.43
13 2.0 1.4 0.393 14.83 18.87
14 2.2 1.4 0 16.14 20.55
15 2.2 1.4 0.785 16.17 20.78
16 2.4 1.4 0.393 17.54 22.35

Tab.3

Variance analysis of gas comsuption regression equation under 0.3 MPa"

来源 平方和 自由度 均方和 F值 P值 显著性
模型 54.82 9 6.09 249.89 <0.000 1 **
A 9.53 1 9.53 390.81 <0.000 1 **
B 44.94 1 44.94 1 843.39 <0.000 1 **
C 0.001 0 1 0.001 0 0.041 5 0.845 2
AB 0.105 6 1 0.105 6 4.330 0 0.082 6
AC 0.000 4 1 0.000 4 0.016 0 0.903 5
BC 0.007 2 1 0.007 2 0.296 3 0.605 8
A2 0.004 6 1 0.004 6 0.186 9 0.680 6
B2 0.242 6 1 0.242 6 9.950 0 0.019 7 *
C2 0.000 3 1 0.000 3 0.012 6 0.914 3
残差 0.146 3 6 0.024 4
失拟项 0.099 2 3 0.033 1 2.11 0.278 1 不显著

Fig.8

Interactive response surface diagram of factors influencing air consumption under 0.3 MPa. (a) Long axis length and short axis length; (b) Long axis length and rotation angle; (c)Short axis length and rotation angle"

Fig.9

Interactive response plan of factors influencing air consumption under 0.3 MPa. (a) Long axis length and short axis length; (b) Long axis length and rotation angle; (c)Short axis length and rotation angle"

Fig.10

Interactive response surface diagram of factors influencing air consumption under 0.4 MPa. (a) Long axis length and short axis length; (b) Long axis length and rotation angle; (c)Short axis length and rotation angle"

Tab.4

Response surface test design and results at 0.4 MPa"

实验
序号		 响应变量 响应结果
A长轴
长度/mm		 B
短轴
长度/mm		 C
旋转角度/
rad		 V
速度/(m·s-1)
1 2.0 1.0 0.393 63.15
2 2.2 1.0 0 65.66
3 2.2 1.0 0.785 59.01
4 2.4 1.0 0.393 68.86
5 2.0 1.2 0.785 64.50
6 2.0 1.2 0 63.80
7 2.2 1.2 0.393 71.55
8 2.2 1.2 0.393 71.55
9 2.2 1.2 0.393 69.48
10 2.2 1.2 0.393 73.26
11 2.4 1.2 0.785 73.35
12 2.4 1.2 0 74.20
13 2.0 1.4 0.393 74.06
14 2.2 1.4 0 73.31
15 2.2 1.4 0.785 80.31
16 2.4 1.4 0.393 88.29

Tab.5

Analysis of variance of regression equation"

来源 平方和 自由度 均方和 F值 P值 显著性
模型 749 9 83.22 66.55 <0.000 1 **
A 192 1 192 153.54 <0.000 1 **
B 439.15 1 439.15 351.17 <0.000 1 **
C 0.005 1 0.005 0.004 0.951 6
AB 18.15 1 18.15 14.51 0.008 9 **
AC 0.600 3 1 0.600 3 0.48 0.514 3
BC 46.59 1 46.59 37.25 0.000 9 **
A2 2.31 1 2.31 1.85 0.222 9
B2 7.51 1 7.51 6 0.049 8 *
C2 42.44 1 42.44 33.94 0.001 1 **
残差 7.5 6 1.25
失拟项 0.326 6 3 0.108 9 0.045 5 0.984 8 不显著

Fig.11

Interactive response surface diagram of velocity influencing factors under 0.4 MPa. (a) Long axis length and short axis length; (b) Long axis length and rotation angle; (c)Short axis length and rotation angle"

Fig.12

Interactive response plan of velocity factors under 0.4 MPa. (a) Long axis length and short axis length; (b) Long axis length and rotation angle; (c)Short axis length and rotation angle"

Fig.13

Relationship between peak velocity and air consumption"

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