Modeling the airflow field of vortex spinning

Abstract

Vortex spinning technology adopts a high-speed swirling airflow to rotate the fibers with open-ends to form yarn with real twists. The airflow behavior within the nozzle has a great effect on the yarn-formation process. In this study, a three-dimensional calculation nozzle model and corresponding three-dimensional airflow region model were established to enable the numerical calculation; airflow behavior—pressure, velocity, and the turbulent airflow field, and the streamline of airflow—was investigated in the presence of fiber bundles within the vortex spinning nozzle. Hybrid hexahedral/tetrahedral control volumes were utilized to mesh the grids in the calculation region. To consider airflow diffusion and convection in the nozzle, the Realizable k-ε turbulence model with wall function was adopted to conduct the calculation. Dynamic and static pressure values were obtained by numerical analysis to predict the action of the inner surface of nozzle and the wall resistance on the high-speed swirling airflow. The numerical simulation of dynamic airflow behavior can generate great insight into the details of airflow behavior and its distribution characteristics, and is helpful for understanding the spinning mechanism and promoting optimization of the spinning process.

Keywords

Vortex spinning technology spinning mechanism high-speed swirling airflow airflow distribution airflow behavior numerical simulation

Vortex spinning exhibits an unusual spinning mechanism: it utilizes a high-speed swirling airflow to twist the fibers with large aspect ratio to form a special skin–core structure yarn with more real twists than any other spinning technology with air.^1,2 Compared with the traditional spinning technique, vortex spinning has some benefits: fast speed with a short process, good pilling resistance, reduced hairiness, and better yarn evenness.³ In spite of the widespread application of vortex spinning, an understanding of the spinning mechanism, airflow behavior, and coupling phenomena within the complicated nozzle remains a challenge. In the spinning process, the fibers generate large nonlinear deformation with tensile bending and torsion because of the effect of the airflow; in turn, the rotating airflow is disturbed by the existence of the fibers and the fiber motion, which results in the redistribution of the high-speed rotating airflow field within the nozzle.^4–6 The distribution of the airflow field is the crucial basis of the study of air forming in yarn technology. Many spinning experiments are expensive and time consuming; however, the numerical calculation approach has offered an effective tool to predict the airflow field distribution.

Computational fluid dynamics software is usually used to build two-dimensional or three-dimensional models to simulate the airflow field in the air jet spinning nozzle and vortex spinning nozzle; the characteristics of the airflow field with different nozzle parameters have been simulated,^7–13 and the influence of airflow field on the fiber motion has also been reported.^14–19 Oh et al.²⁰ simulated the airflow in the nozzle of air jet loom; the distribution of pressure and airflow velocity were obtained, and the nozzle structural parameters were optimized. Rwei et al.²¹ obtained air deformation results under different process conditions by simulating and analyzing the airflow field in the air deformation nozzle. Ortlek et al.²² divided the airflow velocity into three components: radial, tangential, and axial; the axial velocity of airflow affects the fiber transport, the tangential velocity of airflow affects the fiber separation and twisting, and the radial velocity of airflow affects the fiber binding. Gan et al.^23–25 proposed an improved 3D numerical model to calculate fluid flow, multi-component mass transport, and heat transfer to investigate mass transport and to research multiphysical processes. Zhao et al.²⁶ simulated the supercritical water turbulent flow in straight and helical tubes by the computational fluid dynamics method to examine the effects of buoyancy forces, property variations, and centrifugal forces. A 3D transient transfer model was proposed by He et al.^27,28 to forecast the distribution in the deposited layer. Huang et al.²⁹ researched mass and heat transport during the laser metal deposition process. Xu et al.³⁰ measured the heat transfer of the supercritical CO₂ flow in the helical tube. The multi-component mass transfer model has been reported in metal casting and chemical engineering.^31,32 The influence of the related parameters on distribution of the airflow was analyzed by using laser Doppler tachometer, infrared photography technology, particle image tachometer, and high-speed photography technology, and the motion of the airflow within the nozzle was also tracked.^33–39

In these studies, scholars have simplified the theoretical model in various ways to facilitate the research, such as simplified nozzle structure, enlarged the nozzle size, conducting a simple simulation, and so on. As the twisting process of vortex spinning is the separation and condensation of free-end fibers in three-dimensional space, three-dimensional simulation of the airflow field in a nozzle of real size and structure is closer to reality. In addition, although the previous simulations have offered an effective tool to evaluate airflow behavior during the spinning process, few models considered the airflow field distribution with the presence of moving fibers in this process.

The airflow field distribution affects the spinning process, yarn-forming mechanism, yarn body structure controllability, and so on. If these problems are not solved, it will restrict the upgrading and improvement of vortex spinning technology. In this study, a 3D airflow region model was built to conduct the numerical calculation, and the airflow behavior, including the pressure, the velocity, and the turbulence of the airflow field, and the streamlines of the rotating airflow, were investigated in presence of fiber bundles within the vortex spinning nozzle. Hybrid hexahedral/tetrahedral control volumes were adopted to divided grids in the computational area, and the Realizable k-ε turbulence model with wall function combined with the equations of mass, momentum, and energy conservation was adopted to conduct the calculation. This research demonstrates that the numerical simulation of dynamic airflow movement phenomena can generate significant insight into the details of airflow behavior and its distribution characteristics, and is helpful for understanding the spinning mechanism and promoting the optimization of the spinning process.

Numerical simulation

Model construction

A 3D vortex spinning nozzle model is shown in Figure 1. The vortex spinning nozzle contains four main parts: guiding body, vortex tube, cone body, and doffing tube. The role of the guiding body is agglomeration and guiding; the fiber twisting is finished in the vortex tube; the cone body supports the free-end fibers; and the doffing tube plays the role of drawing-in the fibers and output of the resultant yarn.¹³ The parameters of the main nozzle structure in this research are set as follows: the angle of spiral surface of the guiding body is 35°; the length of the guiding needle is 1.5 mm; the number, diameter, and angle to the Z-axis of jet orifices on the vortex tube are five, 0.5 mm, and 60°, respectively; the tip angle and the inlet diameter of the cone body are 10° and 1.5 mm, respectively; the number, diameter, and angle to the Z-axis of jet orifices on the doffing tube are five, 0.4 mm, and 45°, respectively. The parameters of the main nozzle structure in this research are set as follows: the number of jet orifices on the vortex tube is five, the jet orifice diameter is 0.5 mm, and the length of the guiding needle is 1.5 mm. The calculation model of the airflow region within the vortex spinning nozzle model is presented in Figure 2: the Z-axis is the direction of the yarn outlet, the X-axis is the radial direction, and the Y-axis is the tangential direction.

Governing equations

The conservation of mass equation, the momentum-transport equation, and the energy equation are formulated as equations (1) to (3).

\frac{\partial ρ}{\partial t} + div (ρ \vec{u}) = 0

(1)

\frac{\partial (ρ u)}{\partial t} + div (ρ u \vec{u}) = div (μ \cdot grad u) - \frac{\partial p}{\partial x}

(2a)

\frac{\partial (ρ u)}{\partial t} + div (ρ v \vec{u}) = div (μ \cdot grad v) - \frac{\partial p}{\partial y}

(2b)

\frac{\partial (ρ w)}{\partial t} + div (ρ w \vec{u}) = div (μ \cdot grad w) - \frac{\partial p}{\partial z}

(2c)

\frac{\partial (ρ T)}{\partial t} + div (ρ \vec{u} T) = div (\frac{k}{C_{p}} \cdot grad (T))

(3)

where ρ represents the air density; t represents the time; div () represents the divergence;

\vec{u}

represents the air velocity vector,

\vec{u} = \vec{u i} + \vec{v j} + \vec{w k}

; u, v, and w represent the components of the velocity in the x, y, and z directions; μ represents the effective viscosity, which is a sum of molecular viscosity and turbulent viscosity; p represents the air pressure; grad () represents the gradient; T represents the temperature; c_p represents the specific heat capacity; and k represents the heat conductivity.

In this paper, the Realizable k-ε model is adopted, and the transport equations are formulated as equations (4) and (5).

k-transport equation:

\frac{\partial (ρ k)}{\partial t} + div (ρ k \vec{u}) = div [(μ + \frac{μ_{t}}{σ_{k}}) \cdot grad k] - ρ ε + μ_{t} p_{G}

(4)

ε-transport equation:

\frac{\partial (ρ ε)}{\partial t} + div (ρ ε \vec{u}) = div [(μ + \frac{μ_{t}}{σ_{ε}}) \cdot grad ε] - ρ C_{2} \frac{ε^{2}}{k} + μ_{t} C_{1} \frac{ε}{k} p_{G}

(5)

where,

\begin{array}{l} μ_{t} = ρ C_{μ} \frac{k^{2}}{ε}, \\ p_{G} = 2 [{(\frac{\partial u}{\partial x})}^{2} + {(\frac{\partial v}{\partial y})}^{2} + {(\frac{\partial w}{\partial z})}^{2}] \\ + {(\frac{\partial u}{\partial y} + \frac{\partial v}{\partial x})}^{2} + {(\frac{\partial u}{\partial z} + \frac{\partial w}{\partial x})}^{2} + {(\frac{\partial v}{\partial z} + \frac{\partial w}{\partial y})}^{2} \end{array}

In the above equations, k is the turbulence kinetic energy (J); ε is the turbulence kinetic energy dissipation rate (%); C_μ is coefficient, it is no longer a constant in the Realizable k-ε model; σ_K, σ_ε, C₁, C₂ are all constant, and their values are 1.00, 1.30, 1.44, 1.92, respectively.

In this study, the dynamic pressure reduction range is around 10%. Reynolds number is the ratio of inertia force to viscous force of fluid flow; its value decides whether the type of pipe flow is laminar flow or turbulent flow, and Reynolds number is related to turbulent viscosity. The reduction of turbulent viscosity can be calculated by the turbulence dissipation rate ε. The near-wall area of the nozzle where the airflow flows through has a greater influence on the overall airflow, and the Reynolds number in this area is lower than that in the core area. The wall function method can be used for a supplementary solution. For each transport equation, the formula connecting the nozzle wall surface value and the node value in the core area are given:

v^{+} = \frac{v}{v_{τ}} = {\begin{matrix} y^{+} & (y^{+} < 11.63) \\ \frac{1}{k_{0}} \ln (E y^{+}) & (y^{+} > 11.63) \end{matrix}

(6)

y^{+} = \frac{Δ y C_{μ}^{1 / 4} k^{1 / 2}}{μ}

(7)

τ_{w} = \frac{ρ C_{μ}^{1 / 4} k^{1 / 2} v}{v^{+}}

(8)

where, v⁺ and y⁺ are the dimensionless fluid velocity and the distance from the grid center to the wall surface, respectively. y⁺ = 11.63 is the boundary point between the viscous bottom layer and the logarithmic law layer of the airflow, the range of y⁺ is 30∼100 in this paper; τ_w is the shear stress of the wall surface; v is the time-averaged velocity of the fluid at the node; v_τ is the shear velocity of the wall surface; Δy is the distance from the node to the wall surface; k₀ is the von Karman constant; E is the constant related to the wall roughness, for the smooth wall surface: k₀ = 0.4, E = 9.8. The boundary condition of turbulent kinetic energy k on the wall surface is:

\frac{\partial k}{\partial n} = 0

(9)

where n is the local coordinate perpendicular to the wall surface.

The expressions for the turbulent kinetic energy generation term G_k and the turbulence dissipation rate ε are calculated as follows:

G_{k} = τ_{w} \frac{τ_{w}}{k_{0} ρ C_{μ}^{1 / 4} k^{1 / 2} Δ y}

(10)

ε = \frac{C_{μ}^{3 / 4} k^{3 / 2}}{k_{0} Δ y}

(11)

Boundaries and initial conditions

The boundaries of the computational region are illustrated in Figure 2. On the solid walls, adiabatic, no-slip conditions are prescribed. The pressure loss range is about 15%.

Pressure inlet boundary: the nozzle inlet and five jet orifice inlets; the initial pressure of the five jet orifice inlets is set at 0.6 Mpa; the initial pressure of the nozzle inlet is set equal to the atmospheric pressure; airflow velocity, airflow trajectory, and the turbulent kinetic energy are simulated by the numerical calculation.

Pressure outlet boundary: the yarn outlet and the cone body outlet; the atmospheric pressure is prescribed for the initial outlet boundary; the initial airflow velocity is set to 0.

Mesh generation

The three-dimensional unstructured grid depicted in Figure 3 is set up for the computations performed in this research. Hybrid hexahedral/tetrahedral control volumes are used to discretize the mixing zone; these kinds of volumes are suitable for flow that has boundary layers and wall effects.^40–42 The ICEM-CFD module in ANSYS is used to mesh the airflow area into five parts. To catch the main feature of the airflow, the calculation grids have been refined near the locations with high gradients, such as the wall surfaces, the air jet orifices, and the guided needle. Based on the grid independency test,⁴³ 1,790,510 hexahedral/tetrahedral grids with a minimum grid size of 1 × 10⁻¹⁵ m³ in the locations of high gradients is adopted.

The airflow region is partitioned based on the idea of mesh partitioning.⁴⁰ 3D front and top views of the grid are shown in Figure 3(a) and (b), respectively; the grids are shown in Figure 3(c); and a partial enlarged sectional view of the mesh is shown in Figure 3(d) which has five grid regions: (1) zone 1: the region of airflow field at nozzle inlet (structured hexahedral grids); (2) zone 2: the region where the nozzle inlet is connected with the air jet orifices of the vortex tube (structured hexahedral grids); (3) zone 3: the region near the air jet orifices of the vortex tube (unstructured tetrahedral grids with local mesh refinement areas which are at air jet orifices and guided needle); (4) zone 4: the region of twisting chamber in the vortex tube (unstructured tetrahedral grids without local mesh refinement); (5) zone 5: the region of doffing tube (structured hexahedral grids).

The dynamic shape of the airflow field is explicitly described by a moving mesh;²⁹ in the simulation calculation, in order to reduce computation cost and accelerate the convergence, the grid region of the airflow field contains two kinds, motion and non-motion, as shown in Figure 3(c): zone 1 and zone 5 are defined as relative stationary regions; zone 2 and zone 4 are deformation regions of airflow field caused by the movement of zone 3; zone 3 is a user-defined region, which contains the fiber movement caused by the high-speed swirling airflow.

Numerical solver

In this paper, ANSYS FLUENT® V17.0 (2016) software with the finite volume method is adopted. Reynolds number is defined as the fluid flow’s ratio of inertia force to viscous force; its value determines the type of airflow. The Reynolds number in the twisting chamber is beyond 10⁴,^10,13 therefore the airflow within the vortex spinning nozzle is turbulent flow. The coupling between pressure and velocity is solved by SIMPLE algorithm.⁴⁴ The Realizable k-ε turbulence model and the coupled implicit solver are combined to conduct the simulation. In order to connect the airflow between the viscous sub-layer near the wall and the fully turbulent region, the wall function technique is used to calculate the solution variables. Because of the non-linearity and the coupling of the control equations, numerous iterations are carried out to obtain a converged solution. Detailed information regarding this computational algorithm is introduced elsewhere.^45–47 The time step size is set as 0.2 and the Courant number is set as 4. The monitored pressure near the nozzle outlet does not change with the iteration when the relative residuals decrease by several orders of magnitude, and the airflow balances for the entire computation domain are achieved, and the numerical simulation is considered converged.

Results and discussion

Pressure field

The total pressure field along the Z-axis in the nozzle is depicted in Figure 4(a). From Figure 4(a), the location of the maximum pressure is at the outlet of the five air jet orifices, ranging from 2.50 × 10⁵ Pa–4.93 × 10⁵ Pa, that is, between 2.5 and 4.93 atmospheres (1 atm is a standard atmospheric pressure, and 1 atm = 1.01325 × 10⁵Pa ≈ 0.1 Mpa; for simplicity, it is hereafter referred to as several “atms”). In addition, in most areas, the total pressure value of the airflow is low and the value continues to decrease along the direction of the nozzle outlet; however, in some parts of the twisting chamber the values are even negative. The existence of negative pressure contributes to the fiber bundle being attracted into the nozzle.

The function of Figure 4(b) is mainly to accurately locate and describe the position of the cross-section of the three-dimensional model. The middle cross-section of the airflow field model in the nozzle and the XY axis and the four quadrants is shown in Figure 4(b). The S-S cross-section is the entrance section of the cone body. After passing through this section, the free-end fiber affected by the swirling airflow will produce a certain angular displacement on the inner fiber along with the motion of the fiber bundle, and then will wind around the outer part of the yarn to finish twisting. Therefore, this paper takes the S-S cross-section as an example to study.

The 13 quadrant, 24 quadrant, X-axis and Y-axis dynamic and static pressure distribution values on the S-S cross-section are shown in Figure 4 (c–j). The dynamic pressure, static pressure, and total pressure studied in this paper are usually the basic concepts of fluid mechanics. The static pressure is defined as the pressure of air on the surface of an object parallel to the airflow. Generally speaking, the static pressure refers to the pressure that overcomes the resistance of the nozzle pipe; in this paper, the static pressure is the pressure of the airflow acting perpendicularly on the wall of the nozzle. The dynamic pressure is defined as the pressure generated by the airflow velocity, that is, the kinetic energy required for the airflow is converted into pressure; it is common to say that the dynamic pressure is the pressure that drives the airflow forward. The total pressure is the sum of dynamic pressure and static pressure. In order to realize the airflow twisting into the yarn, the high-speed rotating airflow not only overcomes the pipe resistance of the nozzle inner wall surface, but also drives the airflow to move forward continuously.

Figure 4(c) is a dynamic pressure distribution scatter plot of 13 quadrants. It can be seen from Figure 4(c) that the dynamic pressure value of the first quadrant ranges from 0 to 1.5 atm, and the dynamic pressure value drops to 1 atm near the wall surface; the dynamic pressure in the third quadrant ranges from 0.02 to 1 atm, and the dynamic pressure decreases to 0.6 atm near the wall. Figure 4(d) is a static pressure distribution scatter plot of 13 quadrants. From Figure 4(d), the value of the static pressure at the first quadrant ranges from –0.15 to 0.125 atm; the static pressure value of the third quadrant ranges from −0.175 and 0.075 atm. Figure 4(e) is a dynamic pressure distribution scatter plot of 24 quadrants. From Figure 4(e) that the dynamic pressure value of the second quadrant ranges from 0 to 1 atm, and the dynamic pressure value decreases to 0.4 atm near the wall surface; the dynamic pressure in the fourth quadrant ranges from 0.02 to 0.85 atm, and the dynamic pressure decreases to 0.8 atm near the wall. Figure 4(f) is a static pressure distribution scatter plot of 24 quadrants. From Figure 4(f), the static pressure value of the second quadrant ranges from −0.225 to 0.1 atm; the static pressure value of the fourth quadrant ranges from –0.125 to 0.09 atm. Figure 4(g) is a dynamic pressure distribution scatter plot of the X-axis. From Figure 4(g), the dynamic pressure value in the positive direction of X-axis ranges from 0 to 0.7 atm, and the value drops sharply near the wall surface to 0.3 atm; the dynamic pressure in the negative direction of X-axis ranges from 0.01 to 1.45 atm, and the dynamic pressure decreases to 0.9 atm near the wall surface. Figure 4(h) is a static pressure distribution scatter plot of X-axis. From Figure 4(h), the static pressure along the positive direction of X-axis ranges from –0.125 to 0.175 atm, the value along the negative direction of X-axis ranges from –0.225 to 0.2 atm. Figure 4(i) is a dynamic pressure distribution scatter plot of Y-axis. From Figure 4(i), the dynamic pressure value in the positive direction of Y-axis ranges from 0 to 0.9 atm, and the value decreases to 0.8 atm near the wall surface; the dynamic pressure in the negative direction of Y-axis ranges from 0.02 to 1.4 atm, and the dynamic pressure decreases to 0.8 atm near the wall surface. Figure 4(j) is a static pressure distribution scatter plot of the Y-axis. From Figure 4(j), the static pressure along the positive direction of Y-axis ranges from –0.175 to 0.75 atm; and the value along the negative direction of Y-axis ranges from –0.125 to 0.3 atm.

From the above numerical analysis, the maximum dynamic and static pressure values in the airflow field are distributed near the wall surface, and the dynamic pressure value is greater than the static pressure value. Therefore, the dynamic pressure near the wall surface helps to drive the airflow continuously forward, thereby facilitating the withdrawal of the tail-ends of the partial fibers from the yarn body to form the free-end fibers, and facilitating the movement of the free-end fibers.

The dynamic pressure value is an asymmetrical “U”-type distribution with different degrees of fluctuation. The value of the central part is small and the fluctuation of the value is also small. The dynamic pressure value increases near the wall surface with large fluctuation, the fluctuation of the first and second quadrants near the wall surface is the largest, and the air pressure is also significantly increasing. This is because the airflows from the nozzle inlet, the air jet orifices, and the doffing tube meet and collide in these two quadrants, then the three combined airflows at this position collide with the cone body inlet and the yarn body to increase the airflow fluctuation, thus forming turbulence.

The static pressure value is an asymmetrical “山” type distribution with varying degrees of fluctuation. The static pressure is negative and fluctuating near the chamber center. The negative pressure is the force of the nozzle wall in turn against the airflow. The negative pressure at the chamber center is beneficial to the fiber being sucked into the nozzle and is conducive to the wrapping fiber winding around the core fiber, thereby increasing the yarn strength. The static pressure value is positive and does not fluctuate near the wall surface, but the static pressure value is less than the dynamic pressure value, which helps the airflow to move forward against the resistance of the inner wall of the nozzle.

Velocity field

The velocity vector is shown in Figure 5. The airflow velocity vector is divided into axial, tangential, and radial velocity. The airflow axial velocity affects the fiber and the yarn body motion; the airflow tangential velocity affects the twisting of free-end fibers; and the airflow radial velocity affects the aggregation and separation of the fibers.^8,9 The velocity volume rendering diagram, the velocity vector diagram, the velocity cloud map of the airflow along the Z-axis and along the Z-Z section are shown in Figure 5. Figure 5(a) is a three-dimensional volumetric overall rendering of the airflow velocity field, which is used to display the airflow velocity field in the nozzle in a comprehensive and three-dimensional way. Figure 5(b–e) are enlarged views of airflow velocity field in different orientations.

The compressed air is jetted from the air jet orifices (as shown in Figure 2) which are arranged equidistantly in the circumferential direction and tangentially to the surface of inner wall in the twisting chamber; the entrainment of high-speed circumferential airflow drives the air in the annular twisting chamber to become to be a high-speed swirling airflow. Figure 5 shows the overall situation of the airflow in the nozzle: the accelerated airflow is attracted into the twisting chamber along the air jet orifices, and continuously moves forward; during the moving process, the airflow at the nozzle inlet and the airflow at the doffing tube meet and merge, causing the airflow vortex; a part of the confluent airflow collides with the guiding needle, and then the converging airflow moves and collides with the cone body’s outer surface, and the airflow continues to move along with the cone body’s outer surface and the vortex tube’s inner surface until the end of the twisting chamber outlet and the nozzle outlet. Therefore, the airflow is constantly fluctuating, and the airflow distribution is asymmetrical. Downstream of the air jet orifices, because of the movement and rupture of the airflow vortex, the airflow direction gradually deviates from the central axis and spreads around. The continuous formation of the anticlockwise air vortex upstream of the twisting chamber and the reverse rotation of the air vortex both contribute to the generation of more wrapped fibers and larger twisting angle. The movement of the vortex and the vortex ring formed in the annular twisting chamber prolong the residence time of the fiber bundle and the free-end fiber, which will make the fiber bundle much looser and will be beneficial to one end of the fiber leaving the fiber bundle and becoming the free-end fiber. This result was also reported in the research of Guo.³⁷ As the air pressure in the air compressor is as high as 5 atm, there is a huge difference in airflow pressure between the air compressor and the annular twisting chamber; moreover, the air jet orifice is a cone-shaped body with a wide inlet and a narrow outlet, which makes the airflow in the air jet orifices accelerate continuously and reach the maximum value at the air jet orifices’ outlet.

It can be seen from the simulation results in Figure 5 that the airflow has reached nearly 550 m/s at the exit of the air jet orifices, which is supersonic, shown by the red area in the simulation results; after entering the annular twisting chamber, the airflow velocity is rapidly reduced. In addition to air jet orifices and its outlet, and part area of the twisting chamber, the air velocity in other parts of the nozzle is lower, but the airflow velocity in the connection area between the guiding body and the twisting chamber is relatively large, as shown in the bright green area in Figure 5; this is due to the flared spiral passage with a decreasing space in the guiding body, and the nozzle inlet is the airflow inlet. Thereby, the airflow at the nozzle inlet is temporarily accelerated from the nozzle inlet to the twisting chamber inlet under the entrainment of the high-speed swirling airflow in the nozzle.

The airflow has a high speed in the region between the cone body’s outer wall surface and the vortex tube’s inner wall surface. This part of the airflow is the high-speed air ejected along the air jet orifices that then collides with the outer surface of cone body and collides again with inner wall surface of the twisting chamber, as shown in Figure 5 in the yellow-green area in the velocity cloud map. There are different degrees of irregular turbulent eddies in XY plane, as shown in Figure 5(d); this is because the airflow at the nozzle inlet merges into the airflow from the twisting chamber and air jet orifices, then causes the collisions of airflow of different speeds, resulting in irregular airflow turbulence.

In the annular region between the cone body’s outer surface and the vortex tube’s inner surface, the airflow moves regularly to the outlet and its velocity decreases gradually. The airflow velocities in the region of the spiral passage of the guiding body, the outlet of the vortex tube, and doffing tube are small, as shown in the dark blue area. The swirling airflow rotates irregularly in the nozzle and gradually flows spirally toward the output of the nozzle, and is finally discharged from the twisting chamber’s exit and the nozzle outlet.

In Figure 5(b–e), the tip end of the cone body extends into twisting chamber, and the airflow ejected from air jet orifices collides with it to generate a winding airflow around it; this is in the winding airflow region where the free-end fibers move with the swirling airflow to finish the twisting process. To clarify the influence of the cone body on the airflow, this section will also take the S-S section as an example to study. Figure 6 is the velocity distribution diagram of airflow on the S-S section. Figure 6(a) is a scatter plot of 13 quadrant axial velocity distribution along the Z-axis on the S-S cross-section. In Figure 6(a), the axial velocity of the first quadrant ranges from –50 to 130 m/s, and the axial velocity drops sharply to 0 m/s near the wall; the axial velocity in the third quadrant ranges from –50 to 70 m/s, and the value drops to 0 m/s near the wall. In Figure 6(b), the resultant velocity of the airflow distribution in the first quadrant ranges from 20 to 425 m/s, and the value of airflow velocity near the wall first decreases to 370m/s and then drops sharply to 0 m/s. The resultant velocity of the airflow in the third quadrant ranges from 80 to 370m/s, and the value near the wall first decreases to 315 m/s and then drops sharply to 0 m/s. Figure 6(c) is a scatter plot of 24 quadrant axial velocity distribution along the Z-axis on the S-S cross-section. In Figure 6(c), it can be seen that the axial velocity of the second quadrant ranges from –150 to 150 m/s, the value of airflow velocity near the wall first decreases to 125 m/s and then drops sharply to 0 m/s; the axial velocity in the fourth quadrant ranges from –50 to 80 m/s, and the value drops to 0 m/s near the wall. Figure 6(d) is the scatter plot of 24 quadrant resultant velocity distribution. In Figure 6(d), the resultant velocity of the airflow distribution in the second quadrant ranges from 13 to 375 m/s, and the velocity value near the wall first decreases to 250 m/s and then drops sharply to 0 m/s; the resultant velocity of the airflow distribution in the fourth quadrant ranges from 100 to 340 m/s, and the velocity value near the wall first decreases to 325 m/s and then drops sharply to 0 m/s. Figure 6(e) is a scatter plot of the tangential velocity (Y-axis direction) distribution along X-axis on the S-S cross-section. In Figure 6(e), the tangential velocity in positive direction of Y-axis ranges from –275 to 50 m/s, and the value drops to 0 m/s near the wall; the tangential velocity in negative direction of Y-axis ranges from –15 to 375 m/s, and the velocity value near the wall first decreases to 320 m/s and then drops sharply to 0 m/s. Figure 6(f) is a scatter plot of the axial velocity (Z-axis direction) distribution along X-axis on the S-S cross-section. It can be seen in Figure 6(f) that the axial velocity in positive direction of Z-axis ranges from –60 to 125 m/s, and the value drops to 0 m/s near the wall; the axial velocity in negative direction of Y-axis ranges from –130 to 150 m/s, and the velocity value near the wall drops sharply to 0 m/s. Figure 6(g) is a scatter plot of the resultant velocity distribution along X-axis on the S-S cross-section: the resultant velocity in positive direction of X-axis ranges from 40 to 290 m/s, and the velocity value near the wall first decreases to 225 m/s and then drops sharply to 0 m/s; the resultant velocity in negative direction of the X-axis ranges from 65 to 400 m/s, and the velocity value first decreases to 350 m/s and then drops sharply to 0 m/s near the wall. Figure 6(h) shows the scatter plot of the radial velocity (X-axis direction) distribution along Y-axis: the radial velocity in positive direction of Y-axis ranges from –75 to 350 m/s, and the velocity value near the wall drops sharply to 0 m/s; the radial velocity in the negative direction of the Y-axis ranges from –370 to 0 m/s, and the velocity value drops sharply to 0 m/s near the wall. Figure 6(i) is a scatter plot of the axial velocity (Z-axis direction) distribution along Y-axis on the S-S cross-section. It can be seen in Figure 6(i) that the axial velocity in positive direction of Z-axis ranges from −125 to 65 m/s, and the value drops sharply to 0 m/s near the wall; the axial velocity in the negative direction of the Z-axis ranges from –60 to 170 m/s, and the velocity value near the wall drops sharply to 0 m/s. Figure 6(j) is a scatter plot of the resultant velocity distribution along Y-axis on the S-S cross-section: the resultant velocity in the positive direction of the Y-axis ranges from 90 to 390 m/s, and the value near the wall first decreases to 320 m/s and then drops sharply to 0 m/s; the resultant velocity in the negative direction of the Y-axis ranges from 25 to 350 m/s, and the velocity value first decreases to 325 m/s and then drops sharply to 0 m/s near the wall.

From Figure 6, the distributions of radial velocity, axial velocity, and tangential velocity are not axisymmetric, and the radial velocity and tangential velocity are opposite, as shown in Figure 6(e) and (h). In the area of cone body inlet twisting zone section, the airflow velocity value is large near the wall surface; this is because once the high-speed swirling airflow collides with the cone body and yarn body, the airflow will spread out sharply in all directions; the diffused airflow then collides with the inner wall of the twisting chamber, and pushes forward along the inner wall of the twisting chamber under the action of dynamic pressure until it comes out from the vortex tube’s exit.

The airflow velocity values at the nozzle center are much smaller and there are different levels of fluctuation. On the one hand, this is because the high-speed airflow collides with the cone body and the yarn body; one part of the airflow is rapidly spreading around and collides again with the inner wall surface of the twisting chamber, which will cause circumfluence, fluctuation, and even counter flow, and the other part of the airflow quickly dissipates along the tip of the cone body to the nozzle outlet under the action of pressure difference. On the other hand, as mentioned above, this is because the airflow at the nozzle entrance meets the airflow at the air jet orifices and the airflow from the doffing tube. As can be seen from Figure 6 the axial velocity of the airflow has a certain negative value in all quadrants and coordinate axes, but the value is small and the change is also small. In theory, part of the airflow is reflected from the wall surface of the nozzle when the radial velocity is blocked and reflected by the cone body’s outer wall surface and the twisting chamber’s inner wall surface, then the reflected airflow creates a countercurrent in the radial direction, so the radial velocity will change greatly in both direction and value. From the simulation results in the above figures, it can be seen that the value of the radial velocity of the airflow and its direction do change greatly. The radial airflow velocity in the negative direction of Y-axis varies from –370 to 0 m/s, which is negative, the changes in the tangential and axial velocity values are small, and the direction is almost unchanged. It is shown that the circumfluence, fluctuation, and even countercurrent generated by the impact of the airflow on the wall surface and yarn as well as the combined action of airflow will affect the magnitude and direction of the radial velocity, but have little effect on the tangential and axial velocity directions.

The turbulent airflow field

Figure 7 shows the turbulent field, turbulent kinetic energy, and turbulent viscosity distribution in the vortex spinning nozzle. Figure 7(a) shows the airflow’s turbulence field along the Z-axis. In Figure 7(a), the turbulent kinetic energy reaches the largest value in the outlet of the air jet orifices, and then the turbulent kinetic energy gradually decreases in the annular twisting chamber.

Figure 7(b) shows the volume cloud diagram of turbulent kinetic energy in the nozzle. It can also be seen that one of the prominent features of the turbulent kinetic energy is that the value at one side near the wall surface of the air jet orifices is the largest, as shown in the bright green area in the Figure 7(b); this is because the end of the twisting chamber channel is connected to the atmosphere, a part of the twisting chamber channel is connected to the spiral guiding body channel, and the tip end of the spiral guiding channel is connected to the atmosphere, so both ends of the cut-through connected regions are connected to the atmosphere, which is called a cut-through connected region, and the airflow moves smoothly and is less turbulent. The region where the twisting chamber is not connected with the spiral guiding channel is called the uncut-through connected region, the light green area in the figure. In the uncut-through connected region, only the tail-end is connected with the atmosphere, and the head-end is the inner wall of the nozzle. The collision probability of airflow is increased because of the existence of fiber and cone body in the central area of the twisting area; coupled with the effects of airflow confluence, circumfluence, collision and counter airflow, etc., the airflow in the nozzle is disturbed, resulting in continuous turbulence.

Figure 7(c) shows the turbulent viscosity volume cloud diagram in the twisting chamber. It can be seen from Figure 7(c) that the turbulent viscosity is small in the area of the entrance and the center of the twisting chamber (except the cut-through connected region), as in the blue area; the turbulent viscosity of the cut-through connected region along the direction of the twisting chamber exit gradually increases, as in the bright green region; the turbulent viscosity is maximum at the exit of the twisting chamber. Viscosity has a great influence on airflow movement. The airflow viscosity comes from two mechanisms: one is the intermolecular cohesion, and the other is the momentum exchange caused by the molecular exchange between layers of the moving airflow. The turbulent viscosity here comes from the second mechanism.

Figure 7(d–i) show the turbulent kinetic energy and turbulent viscosity of the airflow in the nozzle along the X0 plane, the Y0 plane, and the XY axis intermediate plane of the Z-axis. It can be seen from Figure 7(d–i) that the turbulent vortex is approximately elliptical; from the center of the turbulent vortex to the circumference, the elliptic shape gradually cracks and dissipates. The color of the cloud map also gradually changes from red, yellow, and orange, to green, light green, blue, and light blue, indicating that the value of the turbulent kinetic energy is largest at the turbulent vortex center, then the turbulent kinetic energy decreases gradually with the rupture and dissipation of the turbulent vortex. From Figure 7(d–i) it can also be seen that the existence of the cone body has a certain influence on the turbulent vortex region: it can also accelerate the rupture and dissipation of the turbulent vortex; in addition to the air jet orifices area, most of the airflow’s turbulent kinetic energy is small; however, the turbulent viscosity changes greatly and becomes larger and larger.

Airflow streamline

Figure 8 shows the airflow streamlines at the nozzle inlet, the air jet orifices of vortex tube, and doffing tube. This shows the airflow’s trajectory characteristics. The airflow streamlines not only show the flow trend, but also show the airflow velocity by different colors. In Figure 8, the blue color shows that the airflow velocity is small, whereas the red color indicates that the airflow velocity is large. It can be seen from Figure 8 that the distribution of the airflow streamlines at the nozzle inlet, the air jet orifices of vortex tube, and doffing tube is not axisymmetric; the airflow streamline at the vortex tube’s jet orifices is mostly orange, red, green, and yellow; the nozzle inlet airflow streamline is mostly blue; and the airflow streamline at the doffing tube is mostly light blue, so that the airflow velocity at air jet orifices of vortex tube is larger than that at the doffing tube, and the airflow velocity at the doffing tube is larger than that at the nozzle inlet.

In Figure 8 (a and b), the accelerated nozzle inlet airflow regularly enters the twisting chamber along the spiral guiding channel in the guiding body, then a lot of irregular air bubbles are formed in the twisting chamber, and their shapes and sizes are different; these irregular air bubbles can cause airflow disorder resulting in constant turbulence; the trajectory of this part of the airflow in the twisting chamber is relatively complex. This part of the airflow finally enters the airflow region of the vortex tube’s jet orifices and moves with each other together. Because of the excessive turbulence generated in the early stage, this part of the airflow rotates asymmetrically and irregularly in the annular region between the vortex tube’s inner wall and the cone body’s outer wall; after several rotation cycles, the airflow gradually becomes a radial flow without rotation and then dissipates from the twisting chamber outlet.

The airflow streamline at the vortex tube’s air jet orifices is more regular than that at the nozzle inlet, but it also forms a weak reverse balloon near the wall, as shown in Figure 8(c and d) in the blue protruding reverse flow. Because the pressure of the airflow injected from the compressed air chamber of the air compressor is nearly 5 atm, the pressure difference between the outside and inside of the twisting chamber has a large difference. Under the action of the high pressure, the airflow is injected into the nozzle at a high speed along the tangentially arranged jet orifices on vortex tube, and the high-speed swirling airflow is formed; then the airflow streamline in the vortex tube also gradually becomes a non-rotating radial shape after several cycles of rotation and escapes from the outlet of the twisting chamber. The weak reverse airflow balloon occurs because the high-speed rotating airflow collides with the tip of cone body and a part of the airflow is reflected and collides again with the inner wall surface of the twisting chamber to cause circumfluence, fluctuation, and even reverse flow.

The airflow streamline at the doffing tube forms a weak reverse countercurrent balloon on one side of its inlet, as shown in Figure 8(e and f). This reverse airflow stream first forms a reverse countercurrent, and then it changes direction and rotates in the same direction with the high-speed swirling airflow. On the one hand, this weak reverse countercurrent helps one end of the free-end fiber to be detached from the yarn body; after the weak reverse countercurrent changes the direction of rotation and rotates with the high-speed swirling airflow, the hairiness of the vortex spinning yarn is reduced, the yarn body is smooth, and the yarn evenness is improved. On the other hand, this reverse airflow reaches the tip end of the cone body and is refracted back, then continues to move along the cone body’s outer wall surface instead of continuing to spread upward, which is also favorable for the lodging of the free-end fibers. As the inlet size of the doffing tube is only 1–1.5 mm, there are fewer airflow streamlines here, and the airflow streamlines are relatively sparse and asymmetrical with small rotation; this airflow stream then continues to flow along the annular region and dissipates from the outlet of the twisting chamber. The reverse airflow of the cone body inlet region has a certain effect on fiber transport, which was also reported in Guo’s research.⁹ The existence of reverse airflow destroys the straightness of the fiber and affects the forming yarn characteristics. The reverse airflow not only creates bending nodes, but also increases the transport time of the fibers in the nozzle, resulting in mutual collision and entanglement between fibers. From Figure 8(g and h), it can be seen that the airflow at the nozzle inlet and the vortex tube’s air jet orifices forms a series of air balloons upstream of the air jet orifices; downstream of the air jet orifices, the evolution of the air balloons is complicated, with some air balloons gradually breaking up and some air balloons not forming a closed loop.

Conclusions

The airflow behavior is investigated utilizing a 3D model of the vortex spinning nozzle. The 3D pressure field, velocity field, the turbulent behavior, and the airflow trajectory are explained and predicted by the transient airflow field distribution. This study draws the following conclusions.

The pressure field: the maximum dynamic and static pressure values are distributed near the wall surface, and the dynamic pressure value is greater; the dynamic pressure is an asymmetrical “U”-type distribution with different degrees of fluctuation, and the value in the central part is small, which helps to drive the airflow continuously forward. The static pressure is an asymmetrical “山” type distribution with varying degrees of fluctuation, and the value is negative near the twisting chamber center which is beneficial to the fiber being sucked into the nozzle and is conducive to the wrapping fiber winding around the core fiber, thereby increasing the yarn strength.

The velocity field: the airflow velocity reaches nearly 550 m/s at the exit of the air jet orifices, then is sharply reduced after being drawn into the annular twisting chamber. The distribution of radial, axial, and tangential velocities is not axisymmetric, and the radial and tangential velocity are opposite. Except for a few areas with negative values, the radial velocity is almost positive, which contributes to the formation of free-end fibers and the increase of the wrapped fibers, thus contributing to the improvement of the yarn strength. The tangential velocity helps the free-end fibers to be twisted and wrapped into the yarn. The cone body’s tip end extends into the twisting chamber, and the airflow ejected from the air jet orifices collides with it to generate a winding airflow around it. The continuous formation of an anticlockwise air vortex and the reverse rotation of the air vortex both contribute to the generation of more wrapped fibers and larger twisting angle. The movement of the vortex and the vortex ring formed in the annular twisting chamber prolong the residence time of the fibers, which will make them much looser and will be beneficial to one end of the fiber leaving the bundle to become the free-end fiber.

The turbulent airflow field: because of the effects of airflow confluence, circumfluence, collision, and counter airflow, etc., the airflow in the nozzle is disturbed, resulting in continuous turbulence. The basic mechanism of turbulence is vortex diffusion, and the turbulence viscosity has a great influence on airflow movement. In addition to the air jet orifices area, most of the airflow’s turbulent kinetic energy is small. The turbulent vortex is approximately elliptical; from the center of the turbulent vortex to the circumference, the elliptic shape gradually cracks and dissipates. The value of the turbulent kinetic energy is largest at the turbulent vortex center, and then decreases gradually with the rupture and dissipation of the turbulent vortex. The cone body, the fiber bundle, and the inner wall surface of the nozzle have a certain influence on the turbulent vortex; they can accelerate the rupture and dissipation of the turbulent vortex.

Airflow streamline: the airflow streamlines’ distribution at the nozzle inlet, the air jet orifices of vortex tube, and doffing tube is not axisymmetric; the velocity at the vortex tube’s air jet orifices is larger than that at the doffing tube, and the velocity at the doffing tube is larger than that at the nozzle inlet. After several cycles of rotation, the airflow gradually becomes a radial flow without rotation and then dissipates from the twisting chamber outlet. The reverse airflow of the cone body inlet region has a certain effect on fiber transport; it increases the transport time of the fibers in the nozzle, resulting in mutual collision and entanglement between fibers. The reverse countercurrent also helps one end of the free-end fiber to become detached from the yarn body; after the weak reverse countercurrent changing the direction of rotation and rotating with the high-speed swirling airflow, the hairiness of the vortex spinning yarn is reduced, the yarn body is smooth, and the yarn evenness is improved.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work is supported by the “National Key R&D Project of China (2019YFB1802702)” and the “National Natural Science Foundation of China (No. 52106205 and No. 51703124).”

ORCID iDs

Shanshan Shang

Chongwen Yu

Xinhou Wang

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