Design and Numerical Simulation of Low-Fiber Hollow Spindle in Air-Jet Vortex Spinning

ZHANG Xiao-bin (张肖斌), XUE Wen-liang (薛文良), CHENG Long-di (程隆棣)

Key Laboratory of Textile Science & Technology, Ministry of Education, Donghua University, Shanghai 201620, China

Design and Numerical Simulation of Low-Fiber Hollow Spindle in Air-Jet Vortex Spinning

ZHANG Xiao-bin (张肖斌)*, XUE Wen-liang (薛文良), CHENG Long-di (程隆棣)

KeyLaboratoryofTextileScience&Technology,MinistryofEducation,DonghuaUniversity,Shanghai201620,China

Based on the mechanical system of free-end fibers and the analysis of pulling free-end fibers out of the spun yarn during spinning, a low-fiber hollow spindle is designed and the air distribution of fluent field is simulated numerically. The negative pressure effect is much bigger at the top of low-fiber hollow spindle than that in Murata No.861, which is more conducive for single fiber to get into the channel of hollow spindle. The tangential velocity in 0-3 mm at the top of hollow spindle increases and the fluctuation of radial velocity is much stronger, which enhance the wrapping effect. In the addition, the distribution of axial velocity remains the same.

air-jetvortexspinning;numericalsimulation;free-endfiber;mechanicalsystem;low-fiberhollowspindle

Introduction

Compressed air is sprayed into the flow field and formed high-speed rotating airflow through the plurality tangential nozzles, then fibers after drafting are sucked into the channel of the hollow spindle. The front part of fibers form the core structure of yarn, and the back part of fibers bend toward the wall of hollow spindle. Back part of fibers wrap the core structure by the high-speed rotating airflow and the spinning process is accomplished. Thid is the principle of air-jet vortex spinning[1-2]. Taking a view of the investigations of air-jet vortex spinning, Zouetal.[3]simulated the air distribution numerically by computer software, and analyzed the cause of yarn snicks and weak places. References[4-7] investigated the dynamic behavior of the fiber in the air-jet vortex spinning and analyzed the effects of some nozzle structure parameters, but the motion modality of fibers was inaccurate. Khazaeietal.[8]discussed the geometrical parameters of vortex tube which helped to research the characteristics of vortex in air-jet vortex spinning. But the phenomenon of yarn snicks and weak places caused by pulling free-end fibers out of yarn during spinning is very common[9]. Based on the mechanical system of free-end fibers and the analysis of pulling free-end fiber out of the spun yarn during spinning, this paper is to put forward some conceptions of designing a kind of low-fiber hollow spindles. The function of the low-fiber hollow spindle is to decrease the noil percentage during air-jet vortex spinning, and increase the evenness and strength of yarn.

1 Numerical Simulation of Flow Field

Computational fluid dynamics (CFD) technology provides a new idea to analyze the characteristics of flow field in the air-jet vortex spinning process[10-11]. Based on the nozzle and hollow spindle structures of Murata No.861, the flow field model of air-jet vortex spinning is established in three-dimensional (3D) CFD technology, and the numerical calculations are performed by computer software Fluent6.2. The motion of fibers can be described through the analyses of pressure and velocity distributions in flow field.

1.1 Establishment of the types of flow field structure model and grid division

Figure 1 illustrates the model structure of flow field. The designs of CFD model and the grid division are accomplished by 3D graphic design software Gambit. Grid division is used Tet/Hybrid mesh type, which is constituted by tetrahedral mesh elements mainly and some hexahedral grid elements in the proper positions. The interval length between two mesh points is 0.15 mm.

Fig.1 Size of the model structure/mm

1.2 Model assumptions and calculation equation

(1) The working process of numerical calculations is adiabatic condition, and the fluid is high-speed unsteady ideal gas which is compressible.

(2) Figure 2 shows the types of the inlet and the outlet. The inlet pressure is 0.55 MPa, the average velocity of the inlet (u0) is 290 m/s, and the property of the airflow is turbulent. So the method of numerical simulation is model RNG of standardk-εturbulence, and the near-wall treatment is standard wall function.

Fig.2 Boundary conditions of model

(3) Compressible unsteady airflow can be described by theN-Sequation:

(1)

whereΩis the control body, ∂Ωis the boundary face of control area,Wis the solution variable,Fis the inviscid flux,Gis the viscous flux,Ais the area of control face,tis time,vis the velocity of the airflow, andHis the source item.

(4) The pressure-velocity coupling of the solution control is SIMPLE. Calculation accuracy of the numerical simulation is 0.001.

1.3 Boundary conditions

(1) Wall condition

The option of wall motion is stationary wall, and the shear condition is no slip.

(2) Inlet condition

The working pressure is selected 0 Pa, and the working temperature is 294 K. The type of four inlets is pressure-inlet, and the pressure is 0.55 MPa. Other elements can be calculated through the following equations.

(2)

(3)

(4)

l=0.1 L,

(5)

(6)

where,P0is the gauge total pressure;Psis the supersonic/initial gauge pressure;Mis Mach number;γis the ratio of the specific heats (γ=1.4);uais the sonic velocity (ua=340 m/s);kis turbulence kinetic energy;Reis the Reynolds of the inlet;lis the scale of turbulence length;Lis the correlation length;C0=0.009; andεis the turbulent dissipation rate. According to Eqs. (2)-(6), the values of other elements are:Ps=342 935.5 Pa;k=184.7 m2/s2; andε=824 920.7 m2/s3.

(3) Outlet condition

The type of four inlets is selected pressure-inlet, and the value of the outlet pressure is 101 325 Pa.

1.4 Analysis of numerical simulation results

According to the simulation results, this chapter analyzes the pressure and velocity distributions at field sectionY=0 shown in Figs.3-5, and contrasts the pressure and velocity variation trends atZ=1.00, 1.85, 3.00, 5.00, 7.10, and 10.00 mm of the field section shown in Figs.6-9.

Fig.3 Pressure distribution at Y=0

Fig.4 Tangential velocity distribution at Y=0

Fig.5 Axial velocity distribution at Y=0

Fig.6 Variation trend of pressure

Fig.7 Variation trend of radial velocity

Fig.8 Variation trend of tangential velocity

Fig.9 Axial velocity variation trend at different sections

The movement and stress condition of fiber in the flow field are affected by the distribution of airflow[12]. Figures 3 and 6 indicate that the negative pressure region is clear enough at the top of hollow spindle. The negative pressure region is conducive for fibers after drafting process to get into the channel of hollow spindle. According to the pressure distribution near the wall of hollow spindle, it’s conducive for fibers to bend toward the wall of hollow spindle. Tangential velocity is the reason leading free-end fibers to rotate and twist. Figures 4 and 8, 5 and 9 indicate that the farther from the wall of nozzle, the smaller of tangential and axial velocities, and this characteristic conforms to the rotating flow theory[13]. Radial and axial velocities of the airflow make free-end fibers to affix to the wall of hollow spindle during the rotating movement. Figure 7 shows that the fluctuation of radial velocity is apparent at the top of hollow spindle which disperses the fiber assembly, and increases the irregularity effect during wrapping. Figure 9 shows that the least axial velocity is near the wall and increases in a linear style along radial direction. Figures 6-9 show that the distributions of the pressure and velocity atZ=10.00 mm are different from other places due to the change of the hollow spindle structure.

2 Mechanical System of Free-End Fiber

Based on fiber formation principle of yarn in air-jet vortex spinning (Fig.10)[2], this paper divides the fiber trajectory into three parts which are core fiber structure, averted and wrapped structure, and wrapped orderly structure. The lengths of each arel1,l2, andl3. Furthermore, this paper also considers the section of yarn is a uniform cylinder, and the transverse stressqacted on core fiber is uniform during spinning. Therefore, the least forceFPof pulling free-end fiber out of yarn is:

FP=μqS=2πrfl1qμ,

(7)

whereμis the coefficient of friction between fibers,Sis the contact area, andrfis radius of fiber.

Fig.10 Fiber formation principle of yarn in air-jet vortex spinning

During spinning, the stress acted on core fiber increases gradually along with the development of fibers wrapping themselves. Therefore, free-end fibers are pulled out of the spun yarn most likely when fibers are plastered to the wall of hollow spindle and begin to move. This paper assumes angular velocity of free-end fiberωfis a constant. When the spinning speed isVy, the velocity of free-end fiber along its axisVWis synthetized by the spinning velocity and the angular velocity of free-end fiber. SoVWcan be described as:

(8)

The velocity of airflow can be decomposed to three directions: tangential, radial, and axial. Supposing the stress acted by the decomposed airflow is uniform, the stress acted on free-end fiber can also be decomposed to three components: the tangential stressFT, the axial stressFAalong the axis of hollow spindle, and the radial stressFR. Figure 11 illustrates the directions of these components. The stress can be decribed by the formula of airflow around a circular cylinder approximately[14].

Fig.11 Force acted on free-end fiber

Based on the research of infinitesimal method, the tangential stress of the free-end fiber can be described as:

(9)

Due to the relative motion between fiber and airflow, tangential stress is:

(10)

(11)

During spinning, the velocity of the free-end fiber along its axis isVW. Therefore, the axial stress of fiber can be described as:

(12)

(13)

where,KAis the coefficient of axial airflow resistance;VAais the axial velocity of the airflow;SAfis the axial frontal area of fiber;θis the angle value between the axial line of the fiber infinitesimal section dland tangential velocity of the airflow.

The radial stress of fiber can be described as:

(14)

(15)

where,KRis the coefficient of radial airflow resistance;VRais the radial velocity of the airflow;SRfis the radial frontal area of fiber;δis the angle between the axial line and the generatrix line of hollow spindle.

According to the second law of Newton, the mechanical analysis of free-end fiber during the rotating process can be described as:

dFL=afdmf,

(16)

(17)

where,ρfis the density of the fiber;mfis the mass of the infinitesimal section dl; dFLis the centrifugal force of the infinitesimal section dlduring rotating process;afis the centripetal acceleration of infinitesimal section dl.

Based on the mechanical analysis of free-end fiber during spinning, the critical conditon of pulling free-end fiber out of yarn can be described as follows without considering the friction between fiber and the wall of hollow spindle,

(18)

3 Design and Numerical Simulation of Low-Fiber Hollow Spindle

Some of the free-end fibers can be pulled out of yarn by compressed airflow during spinning. Based on Formula (18), it’s easy to get the critical conditon of pulling the fibers out of the spun yarn when the frictionfbetween the fiber and the hollow spindle is considered. The critical conditon can be described as:

(19)

Compared Formula (18) with Formula (19), the number of the fibers pulled out of the spun yarn can be decreased by increasing the friction between fiber and the wall of hollow spindle, which is also the point of designing low-fiber hollow spindle. Based on the contact style between fiber and the wall of hollow spindle during spinning, the fibers can be divided into two parts, which are the fibers pulled out of yarn and the fibers wrapped into spun yarn. The essential distinction between these two parts is the motor trend of fibers during spinning, and the values of the friction coefficient can be defined asμ1andμ2. Figure 12 shows the difference betweeceμ1andμ2, andVfindicates the movement of fiber.

Fig.12 Movements of the fiber It’s conducive to decrease the noil percentage by increasing

the value ofμ1, and it’s unconducive to wind free-end fibers into yarn by increasing the value ofμ2. Therefore, this paper establishes the projection of the low-fiber hollow spindle. Figure 13 illustrates the structure of low-fiber hollow spindle. The key points of the design can be described as follows.

Fig.13 Design chart of the low-fiber hollow spindle

(1) Use laser to process the grooves in order to increase the coefficient of friction between the hollow spindle’s wall and fiber.

(2) The direction of the grooves on the outside wall of hollow spindle is horizontal, and the inside is vertical. It is to achieve the resultμ1>μ2.

(3) Increase the top radius of hollow spindle fromr0tor1. It is to remain the same of the contact area between single fiber and the wall of hollow spindle.

The coefficient of friction of the hollow spindle’s wall is increased by processing grooves. The width of the grooves isa, the depth isb, and the spacing isc. Table 1 shows these parameters of the grooves.

Table 1 Groove parameters of low-fiber hollow spindle

Parameterr0r1abcValue/mm1.42.00.150.10.25

Due to the limitation of the groove parameters, the low-fiber hollow spindle model used for numerical simulation should be enlarged for four times. The process of simulating calculation is the same to the model in Murata No.861. Figures 14-20 illustrate the numerical simulation results of the low-fiber hollow spindle. In order to contrast the results of this two models, it’s better to define model of low-fiber(ML) for numerical simulation structure of the low-fiber hollow spindle.

Fig.14 Pressure distribution of ML at Y=0

Fig.15 Tangential velocity distribution of ML at Y=0

Fig.16 Axial velocity distribution of ML at Y=0

Fig.17 Variation trend of ML’s pressure

Fig.18 Variation trend of ML’s radial velocity

Fig.19 Variation trend of ML’s tangential velocity

Fig.20 Axial velocity variation trends of ML at different sections

In contrast with Figs. 3 and 14, 6 and 17, the negative pressure region at the top of low-fiber hollow spindle is much bigger, and the minimum value of pressure at the top region is much smaller than the value in Murata No. 861. It can be seen that low-fiber hollow spindle is more conducive to draw fibers into the alleyway. From the Figs. 4 and 15, 8 and 19, tangential velocity is much bigger in the range fromZ=1.85 mm toZ=5 mm. As a result, it will increase the wrapping effect of fiber assembly which can also increase transverse stress acted on core fiber. Compared Figs. 7 with 18, the fluctuation of radial velocity at the top of hollow spindle is much stronger, so the effect of inflation acted on the fiber assembly will be enhanced obviously, and the number of the free-end fibers winded around the core fiber will also be increased. There are almost no distinctions about the distribution of the axial velocities between these two models from Figs.5 and 16, 9 and 20.

4 Conclusions

Based on the numerical simulation of air-jet vortex spinning in Murata No.861, this paper analyzes the mechanical condition of pulling free-end fibers out of the spun yarn during spinning, and designs the low-fiber hollow spindle. The different numerical simulation results are shown as follows.

(1) Noil percentage in the spinning process can be decreased by increasing the friction between fiber and the wall of hollow spindle, which is conducive to improve the evenness of yarn.

(2) Axial and tangential velocities of the airflow in these two models are in conformity with the rotating flow theory. The effect of inflation acted on the fiber assembly by radial velocity helps the free-end fibers to wrap the core fibers.

(3) The negative pressure region at the top of low-fiber hollow spindle is much bigger which is more conducive to draw fibers into the alleyway. The fluctuation of radial velocity at the top of low-fiber hollow spindle is much stronger which enhances the effect of the inflation acted on the fiber assembly and increases the number of free-end fibers winded around the core fibers. The distribution of axial velocity remains the same.

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Foundation items: Program for Changjiang Scholars and Innovative Research Team in University, China (No. IRT1220); Shanghai Natural Science Foundation, China (No. 13ZR1400900); Keygrant Project of Chinese Ministry of Education (No. 113027A)

TS104.1 Document code: A

1672-5220(2015)01-0119-06

Received date: 2013- 09- 26

*Correspondence should be addressed to ZHANG Xiao-bin, E-mail: zhangxiaobin1989@126.com