Critical rotating speed of rotor cup in an air suction open-end spinning machine

Abstract

Simulation of three-dimensional turbulent flow in a rotor spinning machine is carried out, and the flow structure and behavior in the rotor cup are analyzed. The governing equations are the steady three-dimensional Navier–Stokes equations and the Spalart–Allmaras turbulence model. The results show that the rotating speed has great influence on the flow behavior in the rotor cup. It is found that there is a critical speed of the rotor cup beyond which the pressure and velocity on the slip surface is not changed anymore regardless of the magnitude of the rotating speed. When the rotating speed is larger than this critical speed, the flow structure becomes unstable with the increasing of the rotating speed. The mechanism of this phenomenon is that the airflow in the rotor groove passes about 180 degrees from two sides along the rotor wall and a pressure balance is achieved. When the rotating speed is larger than the critical speed, the balance will break down. When the rotor speed is low, the flow characteristic in the air-inlet plane is mainly determined by the high-speed airflow at the outlet of the transfer channel. However, when the rotor speed is higher than the critical speed of n = 80,000 r/min, the flow behavior is mainly determined by the rotating rotor. In the meridian plane perpendicular to the air-inlet plane, the flow behavior is mainly determined by the rotor speed. The rotating speed of the rotor has little effect on the flow characteristics in the transfer channel.

Keywords

rotor spinning rotor speed numerical simulation flow instability

The rotor spinning technique is widely used in textile industries due to its remarkable economic prospect. The rotor is the most important component of rotor spinning machine and its speed has a significant effect on the quality of the yarn. Previous studies indicate that the flow behavior in the rotor changes significantly with the increase of speed. Chen and Slater¹ analyzed the motion of a particle on the slide wall in rotor spinning and found the main factors influencing the velocity and slide time. Koç and Lawrence² investigated the mechanics of twist insertion and the possible causes and mechanisms of wrapper fiber formation in rotor spinning under different operating conditions. Yang and Wang³ showed that the convergent point can be changed by adjusting the speed of the components in the rotor-spun composite-yarn spinning process. Three-dimensional numerical simulation of the airflow in the spinning unit is carried out, and the influence of the slip surface of rotor on the flow field is analyzed by Wu et al.⁴ Shi and Sun⁵ found that the drag reduction rate of the unsmooth rotor with the small groove on the wall surface was up to 1.281% compared with the smooth rotor. Lei et al.⁶ discussed the main factors affecting the wear of the high-speed rotor and put forward protection measures against the wear of the rotor. Two-dimensional simulation results by Zhang et al.⁷ revealed the distribution of the velocity in the rotor. The influences of rotor speed and geometric parameters on the airflow are analyzed by Xiao et al.⁸ and they found that a better axisymmetry of the vortex structure in the rotor meridional plane is achieved while the angular velocity is 2000 rad/s and the slip angle is 22°. Zou et al.⁹ studied the features of the airflow field in the rotor spinning unit based on the piecing process and revealed the rule of motion of fiber and yarn in the piecing process.

For the airflow in the transfer channel of the rotor spinning machine, some researches have been done. Lawrence and Chen^10,11 used a high-speed camera to capture the fiber morphology in the process of transmission and optimized the design of the transfer channel combined with the empirical formula. Kong and Platfoot^12,13 found that the variation of geometric dimensions of the transfer channel or the carding roller velocity affect the airflow pattern in the transfer channel. Then, the airflow alters the configuration of fibers flowing inside the channel. They also studied the effect of circulation zones on the fiber configuration during transferring within the channel. Lin et al.¹⁴ investigated the influence of the geometric parameters of the transfer channel and the spatial position between the rotor and the channel on the airflow characteristics in the rotor spinning machine.

Rotor speed is one of the most important parameters of the rotor spinning machine and it has an obvious influence on the quality and output of the yarn. Rotor speed has also been a focus in the study of the rotor spinning machine. With the development of new technology, the speed of the rotor increases. However, there is limitation for the speed of the rotor cup in actual production. Therefore, the future development of the rotor spinning machine is not to increase the rotor speed, but to explore an appropriate rotor speed.

To sum up, the research on the flow field in the rotor spinning machine is relatively poor and the effect of rotor speed on the flow field is still not clear. In this study, the work focuses on the influence of the rotor speed on the flow field of the rotor spinning machine and the results provide a theoretical basis for the choice of rotor speed of spinning machines.

Governing equations and numerical method

Geometric model

The model of the rotor spinning machine in this study is based on the RFRS30 air suction open-end spinning machine for a factory in Zhejiang province. The spinning unit is mainly composed of a transfer channel, rotor cup, false twister navel, and air suction passage. The maximum speed of the rotor is 110,000 r/min and the highest yarn speed is about 170 m/min.

For convenience of calculation and research, the numerical model is simplified with respect to the real model. Regardless of the airflow from the doffing tube, the air only flows from the inlet of the transfer channel to the outlet of the air suction passage. The simplified spinning unit is shown in Figure 1. The diameter of the rotor cup is 33 mm and the angle between the sliding surface and the y-axis is 22°. The origin of coordinates is located at the center of the bottom surface of the rotor cup. As can be seen from Figure 1, the rotor cup rotates around the y-axis.

Figure 1.

Three-dimensional flow model of the spinning unit: 1 – inlet of the transfer channel; 2 – transfer channel; 3 – outlet of the transfer channel; 4 – rotor cup; 5 – rotor groove; 6 – false twister navel; 7 – outlet of the air suction passage.

GAMBIT software is used to generate the mesh and the mesh of the rotor spinning unit is as shown in Figure 2. The unstructured tetrahedron mesh is applied to divide the computational domain. The grid density of the rotor cup is very large because the flow behavior in the rotor is mainly analyzed. The grid interval size of the rotor cup is 0.5 mm, while that of the transfer channel and air suction passage are 0.6 and 0.75 mm, respectively. The total number of the grid in the computational domain is 1.88 million.

Figure 2.

Grid of the rotor spinning unit: (a) rotor spinning unit; (b) different parts.

The grid independence has been verified at the condition that the velocity at the inlet of the transfer channel is 50 m/s, the pressure at the outlet of the air suction passage is −8000 Pa, and the rotating speed is 50,000 r/min. The numbers of the three meshes used are 1.28 million, 1.64 million, and 1.88 million. It is found that the variation of the static pressure at the monitoring point (0, 0.007, 0) calculated with the three meshes is less than 2%, as shown in Table 1. Thus, the density of the grid has little effect on the accuracy of the calculation results when the grid number is larger than 1.28 million. Therefore, the grid of 1.88 million can meet the accuracy requirements and the grid quality is good.

Table 1.

Check of grid independence

Grid number	Static pressure (P)
1.28 million	−2334.65 Pa
1.64 million	−2303.05 Pa
1.88 million	−2276.84 Pa

Numerical method

In the numerical simulation of the open-end rotor spinning machine, three turbulence models are commonly used: the Spalart–Allmaras model,¹⁵ the Standard k-ɛ model,^9,16 and the RNG k-ɛ model.^5,6,8,14 The selection of the turbulence model in the simulation of the rotor spinning unit is mostly based on the experience of other flow numerical methods by researchers. The accuracy of calculation of the turbulent flow field is largely affected by the turbulence model. The two-equation turbulence model has the disadvantages of a large amount of computation and the difficulty of convergence. Compared with the two-equation turbulence model, the Spalart–Allmaras model is of small computation time, good stability, and low requirements for the computed grid.^17,18 The influence of the turbulence model on the simulation results of the spinning unit has not been analyzed previously. In this study, three types of commonly used turbulence model are compared to choose the most suitable one for the numerical simulation in the open-end rotor spinning machine. The iteration curves of the static pressure at the monitoring points (0, 0.007, 0) for three turbulence models are shown in Figure 3. The ordinate is the static pressure and the abscissa is the iteration number from 1000 to 20,000. As can be seen from Figure 3, the iteration curve of the RNG k-ɛ turbulence model cannot converge and that of the Standard k-ɛ turbulence model converges slowly. The iteration curve of the Spalart–Allmaras model not only converges quickly, but also has high accuracy and stability. Finally, the Spalart–Allmaras turbulence model is selected in this study.

Figure 3.

Iteration curves of the static pressure at the monitoring points for three turbulence models.

Governing equations

The flow is governed by the three-dimensional incompressible Navier–Stokes equations coupled with the Spalart–Allmaras turbulence model. The steady incompressible Navier–Stokes equations are written as

\frac{\partial (ρ u_{i})}{\partial x_{i}} = 0

(1)

\frac{\partial (ρ u_{j} u_{i})}{\partial x_{j}} = f_{i} - \frac{\partial P^{*}}{\partial x_{i}} + \frac{\partial [μ_{e} (\frac{\partial u_{i}}{\partial x_{j}} + \frac{\partial u_{j}}{\partial x_{i}})]}{\partial x_{j}}

(2)

where ρ is fluid density, P* is translated pressure, including turbulent energy and centrifugal force, f_i are the components of volume force, μ_e is the effective viscosity coefficient, and μ_e = μ + μ_t, where μ is the molecular viscosity coefficient and μ_t is the turbulent viscosity coefficient, expressed as

μ_{t} = ρ C_{μ} \frac{k^{2}}{ɛ}, C_{μ} = 0.0845

(3)

The Spalart–Allmaras turbulence model is represented by the following equation

\frac{\partial}{\partial t} (ρ \tilde{ν}) + \frac{\partial}{\partial x_{i}} (ρ \tilde{ν} u_{i}) = G_{ν} + \frac{1}{σ \tilde{ν}} [\frac{\partial}{\partial x_{j}} {(μ + ρ \tilde{ν}) \frac{\partial \tilde{ν}}{\partial x_{j}}} + C_{2 b} ρ (\frac{\partial \tilde{ν}}{\partial x_{j}})^{2}] - Y_{ν} + S_{\tilde{ν}}

(4)

where

\tilde{ν}

is the turbulent kinematic viscosity,

G_{ν}

is the increase of the turbulent viscosity,

Y_{ν}

is the reduction of the turbulent viscosity, and

S_{\tilde{ν}}

is generally defined by the user.

The finite volume method is used to discretize the governing equations and the Semi-Implicit Method for Pressure Linked Equation (SIMPLE) algorithm is employed to iterate the system of the equations. The convergence criterion is set that the relative residual is less than 10^–3 for each variable.

The density of the air is 1.225 kg/m³ and the viscosity is 1.7894 × 10^–5Pa·s. The simulation of the flow field is done with the commercial software Fluent.

Boundary conditions

A uniform velocity profile is given at the inlet of the transfer channel. The air from the false twister navel is not considered in this study. Usually, the speed of the carding roller is from 5000 to 9000 r/min and the diameter is from 60 to 80 mm; therefore, the circular velocity of the carding roller is in the range of 15.7–37.7 m/s. The circular velocity of the carding roller is less than the velocity at the inlet of the transfer channel. So, the velocity at the inlet of the transfer channel is about 20–50 m/s. The operation condition of 50 m/s is mainly used in this study.

The pressure-outlet condition is set at the outlet of the air suction passage. The negative pressure in the air suction open-end spinning machine is formed by a centrifugal fan. The static pressure at the outlet of air suction passage is set as −8000 Pa.

The speed of the rotor cup is commonly from 75,000 to 150,000 r/min. In order to better understand the influence of rotor speed on the flow structure and behavior in the spinning unit, the rotor speed studied is from 20,000 to 200,000 r/min in the clockwise direction. No slip boundary condition is applied at the solid wall.

Results and discussion

Flow characteristics in the rotor spinning unit

The numerical simulation is carried out at the condition of the velocity at the inlet of the transfer channel is 50 m/s, the pressure at the outlet of the air suction passage is −8000 Pa, and the rotating speed is 50,000 r/min. The velocity vector in the rotor spinning unit is shown in Figure 4. From Figure 4(a), it can be seen that the section of the transfer channel is convergent and the air velocity is increased with the decrease of the section size. The air velocity is the largest at the outlet of the transfer channel. The high-velocity gradient of the airflow is favorable to the transfer and stretching of the fibers.

Figure 4.

Velocity vector in the rotor spinning unit: (a) transfer channel; (b) rotor cup; (c) whole unit.

In Figure 4(b), the airflow from the transfer channel is in collision with the cup wall and divided into two different airflows in the opposite direction. The air is rotated in the rotor cup and then flows to the gap between the cup body and the housing. Fibers slide on the wall of the rotating cup and move to the rotor groove under the action of centrifugal force. As the moving velocity at the rotor groove is the largest, the fiber is stretched and condensed on the slip surface in the rotating cup. Then it is gradually stripped down from the rotor groove by the doffing from the doffing tube.

In order to better illustrate the flow characteristic in the rotor spinning unit, several typical cross-sections of the unit are chosen. Figure 5 shows the different sections in the rotor spinning unit. Section A-A is through the center of the transfer channel and perpendicular to the x–z plane. Line a is at the central axis of Section A-A. Sections A-A and B-B are in the same plane. Line b is on the slip surface of Section B-B. The y coordinate of the bottom of Line a is the same as that of the top of Line b. The air-inlet plane includes Sections A-A and B-B.

Figure 5.

Sections in the rotor spinning unit.

Section C-C is the meridian plane of the rotor cup and perpendicular to Sections A-A and B-B. Line c is located at the center of Section C-C. Section D-D is the largest cross-section of the rotor groove. The intersection of Section B-B and Section D-D near the outlet of the transfer channel is the starting point of Line d. Line d is along the clockwise direction of Section D-D.

Effect of rotor speed on the flow characteristics in the transfer channel

Section A-A

The static pressure and velocity at the axis of the transfer channel (Line a) under different rotor speeds are plotted in Figure 6. From the inlet to the outlet of the transfer channel, as the y value reduces, the static pressure is gradually reduced from 5300 to 5500 Pa and the velocity is increased from 50 to 285 m/s. The gradients of the static pressure and velocity are increased, which is beneficial to the condensate of the fiber. The static pressure and velocity are almost unchanged with the increase of the rotor speed. It can be found by comparing the static pressure and velocity curves under different rotor speeds that the speed of the rotor has little effect on the flow characteristics in the transfer channel. Lin et al.¹⁹ found that the rotor speed has a small impact on the flow characteristics in the transfer channel, which is consistent with our above finding from simulation.

Figure 6.

Distribution of the static pressure and velocity at the axis of the transfer channel (Line a) under different rotor speeds: (a) static pressure; (b) velocity.

Effect of rotor speed on the flow behavior in the rotor cup

Section B-B

Figure 7 shows the streamlines on Section B-B of the rotor cup with the increase of the rotor speed. A small portion of the air from the transfer channel flows to the gap between the cup body and the cup cover, and the other air flows into the rotor cup. A large portion of the air is in collision with the cup wall and swirls with the rotor cup. In addition, the vortex and the low-pressure zone occur in the cup due to the high-speed rotation of the rotor cup. As shown in Figure 7(a) and (b), a small vortex appears in the rotor cup for the rotor speed n = 20,000 r/min and it moves to the center of the section when the rotor speed is increased to 50,000 r/min. A sudden change of the flow behavior in the rotor is observed when the rotor speed is increased to the critical speed of n = 80,000 r/min. The small vortex located at the side of the rotor cup disappears and a large vortex occupies the whole rotor. The core of the large vortex is located near the central axis of Section B-B, as shown in Figure 7(c)–(e). The large vortex moves away from the center of Section B-B and its size is decreased, as shown in Figure 7(f).

Figure 7.

Streamlines on the Section B-B of rotor cup under different rotor speed: (a) n = 20,000 r/min; (b) n = 50,000 r/min; (c) n = 80,000 r/min; (d) n = 100,000 r/min; (e) n = 150,000 r/min; (f) n = 200,000 r/min.

The contour of static pressure²⁰ on Section B-B of the rotor cup with the increase of the rotor speed is shown in Figure 8. The low-pressure area occurs at the center of the rotor cup by the action of centrifugal force without the effect of the high-velocity air at the outlet of the transfer channel. When the rotor speed is low, the influence of the rotor speed on the flow behavior is small and the flow characteristic in the rotor cup is mainly determined by the low-pressure region at the outlet of the transfer channel. As shown in Figure 8(a) and (b), the low-pressure zone is located near the outlet of the transfer channel. However, the flow behavior in the rotor cup is mainly determined by the rotating rotor when the rotor speed is higher than the critical speed of n = 80,000 r/min. It can be seen that the low-pressure region is situated near the center of the rotor at the condition of the high rotor speed in Figure 8(c)–(f). As discussed above, the flow behavior in the rotor cup is mainly determined by the balance between the low-pressure region caused by the high-speed rotating rotor and the low-pressure zone at the outlet of the transfer channel.

Figure 8.

Contour of static pressure on Section B-B of the rotor cup under different rotor speeds: (a) n = 20,000 r/min; (b) n = 50,000 r/min; (c) n = 80,000 r/min; (d) n = 100,000 r/min; (e) n = 150,000 r/min; (f) n = 200,000 r/min.

The yarn quality is affected seriously by the movement of fiber at the slip plane.²¹ Therefore, it is important to study the motion of air at the slip plane. Figure 9 shows the distributions of the static pressure and velocity on Line b under different rotor speeds. The position of Line b is as shown in Figure 5. The static pressure on the slip surface first decreases and then increases, while the velocity first increases and then decreases with the reduction of the y value. The increasing pressure gradient and velocity gradient are conducive to the drawn and traction of the fiber at the slip surface.

Figure 9.

Distribution of static pressure and velocity on Line b under different rotor speeds: (a) static pressure; (b) velocity.

It is observed from Figure 9 that, with the increase of rotating speed, the static pressure increases and the velocity decreases. When the rotor speed is higher than the critical speed of n = 80,000 r/min, neither the pressure nor the velocity change anymore. The mechanism of this phenomenon is that the airflow in the rotor groove passes 180 degrees from two sides along the rotor wall and a pressure balance is achieved as shown in Figure 10(c).

Figure 10.

Streamlines on Section D-D under different rotor speeds: (a) n = 20,000 r/min;(b) n = 50,000 r/min; (c) n = 80,000 r/min; (d) n = 100,000 r/min; (e) n = 150,000 r/min; (f) n = 200,000 r/min.

Section C-C

Figure 11 shows the streamlines on the meridian plane of the rotor cup (Section C-C) under different rotor speeds. Section C-C is perpendicular to Section B-B. As shown in Figure 11(a) and (b), a large vortex occupies the whole rotor cup and the core of the vortex is located near the central axis of the rotor cup. Then it is observed that the flow is stable and, thus, the force exerted on the rotor is uniform, which is conducive to the running stability and is not easy to wear. The flow structure becomes unstable when the rotating speed is larger than the critical speed of 80,000 r/min. The large vortex moves away from the central axis and a small vortex appears near the false twister navel in Figure 11(c), which is unfavorable to the yarn quality and the rotor balance from the viewpoint of flow stability. It is not conflicted with the point that the spinning capacity increases with the increase of rotor speed. With the further increase of rotor speed, many small vortices are generated near the false twister navel and rotor groove. The flow stability in the rotor cup is not improved until the rotor speed increases to n = 200,000 r/min. Therefore, from the above analysis, it is concluded that the flow is prone to be unstable in the meridian plane of the rotor cup when the rotor speed is larger than the critical speed of n = 80,000 r/min.

Figure 11.

Streamlines on the meridian plane of the rotor cup (Section C-C) under different rotor speeds: (a) n = 20,000 r/min; (b) n = 50,000 r/min; (c) n = 80,000 r/min; (d) n = 100,000 r/min; (e) n = 150,000 r/min; (f) n = 200,000 r/min.

A smaller rotor speed would produce more vortices around the rotor groove, which would lead to the deterioration of the fiber configurations and the yarn properties.^19,21 However, too large a rotor speed would cause yarn breakage easily due to the excessive centrifugal force.¹⁹ This phenomenon has not been fully understood. In the following, the mechanism of this phenomenon will be further analyzed.

As Section C-C is perpendicular to Sections A-A and B-B, the affect of the low-pressure zone at the outlet of the transfer channel on the static pressure at Section C-C is small and the flow structure is mainly determined by the rotating speed. Figure 12 shows the contour of static pressure on Section C-C with the increase of rotor speed. Under the action of centrifugal force, the low-pressure zone is located at the center of the rotor cup, as shown in Figure 12(a) and (b). With the further increase of the rotor speed, two airflows in opposite directions in the rotor groove pass 180 degrees along the rotor wall and collide with each other. The air with high energy is pushed to the center of the rotor cup and the pressure balance breaks down, as shown in Figure 11(c)–(e). The circumferential position of collision between two airflows moves along the clockwise direction with the increase of rotor speed. The distribution of static pressure on Section C-C is improved when the rotating speed is increased to 200,000 r/min, shown in Figure 12(f).

Figure 12.

Static pressure on the meridian plane of the rotor cup (Sectin C-C) under different rotor speeds: (a) n = 20,000 r/min; (b) n = 50,000 r/min; (c) n = 80,000 r/min; (d) n = 100,000 r/min; (e) n = 150,000 r/min; (f) n = 200,000 r/min.

The flow structure at the central axis of the rotor cup has a great influence on the twisting and traction of the fibers. The distributions of the static pressure and velocity along the y direction on Line c under six different rotor speeds is shown in Figure 13. Line c is located at the center of the rotor cup, as shown in Figure 5. It can be obtained from Figure 13(a) that the static pressure on Line c increases with the increase of rotor speed until the critical speed of n = 80,000 r/min. The static pressure increases slightly when the rotor speed is beyond 80,000 r/min. The value of velocity first decreases and then increases with the increase of the y value. The velocity near the bottom of the rotor cup is decreased with the increase of rotor speed until n = 80,000 r/min.

Figure 13.

Distribution of the static pressure and velocity along the y direction on Line c under different rotor speeds: (a) static pressure; (b) velocity.

Section D-D

The streamlines on Section D-D (the section of the rotor groove with the maximum diameter) of the rotor cup under different rotor speeds is showed in Figure 10. In Figure 10(a), the airflow from the transfer channel is in collision with the rotor wall and is divided into two airflows with different sizes in the opposite direction. A large portion of the air passes about 270 degrees along the counter-clockwise direction and meets the small portion of the air along the clockwise direction. Therefore, a series of vortices are generated in the rotor cup.

With the increase of the rotor speed, the small portion of the air along the clockwise direction is driven by the rotor and the collision position between the two airflows moves along the clockwise direction. As discussed about the distribution of the pressure in the rotor cup, the flow behavior in the rotor cup is mainly determined by the balance between the low-pressure region caused by the high-speed rotating rotor and the low-pressure zone at the outlet of the transfer channel. The airflow passes 180 degrees from two sides along the rotor groove and a pressure balance is achieved when the rotor speed is increased to 80,000 r/min, as shown in Figure 10(c). This is why the speed of 80,000 r/min is the critical speed. In addition, the collision location of two airflows has an important influence on the forward or backward taking off of the fiber from the rotor groove.

Figure 14 shows the distribution of the velocity on Section D-D under different rotor speeds. It can be seen from the Figure 14 that the air in the rotor groove is divided into two airflows at point o. The velocity of the air along the counter-clockwise direction of point o (labeled as 1 in Figure 14(a)) is high because it is near the outlet of the transfer channel. The velocity of the air in the clockwise direction of point o (labeled as 2 in Figure 14(a)) is low. The air with high velocity flows through 270 degrees along the circumferential direction and collides with the low-velocity air at point o'. Due to the rotation of the rotor cup, a low-velocity zone (labeled as 3 in Figure 14(a)) occurs at the center of the rotor. The narrow strip of the low-speed zone (labeled as 2 in Figure 14(a)) and the point o' move along the clockwise direction driven by the rotating cup, as shown in Figure 14(b). The increase of rotor speed suppresses the movement of the high-speed airflow and the size of the high-velocity zone (labeled as 1 in Figure 14(a)) is decreased. After the collision with low-velocity air, a portion of high-velocity air is pushed to the center of the rotor cup and the velocity here is increased, as shown in Figure 14(c)–(f). It is important to note that the high-velocity zone appears in the clockwise direction of point o (labeled as 2 in Figure 14(a)) when the rotor speed is up to 80,000 r/min. This is because the rotor drives the fluid in the clockwise direction and makes it faster.

Figure 14.

Distribution of velocity on Section D-D under different rotor speeds: (a) n = 20,000 r/min; (b) n = 50,000 r/min; (c) n = 80,000 r/min; (d) n = 100,000 r/min; (e) n = 150,000 r/min; (f) n = 200,000 r/min.

The distribution of the static pressure and velocity on Line d along the circumferential direction in the rotor under different rotor speed is plotted in Figure 15. The abscissa in Figure 15 is the angular coordinate along the clockwise direction. The location of point o is defined as 0° and the circumferential position of Line d can be recorded by the angle from 0° to 360° along the clockwise direction.

Figure 15.

Distribution of the static pressure and velocity on Line d along the circumferential direction in the rotor groove: (a) static pressure; (b) velocity.

From Figure 15(a), it can be seen that the static pressure near point o is the highest, which first drops, then rises along the clockwise direction. The high pressure near point o is caused by the collision between the high-speed air from the transfer channel and the rotor wall. The position of the lowest value on the pressure curve corresponds to the center of the narrow strip of the low-speed zone in Figure 14. The position of the lowest static pressure moves along the clockwise direction with the increase of rotating speed, which is consistent with the conclusion drawn from Figure 14. It can be obtained from the contrast of the six pressure curves in Figure 15(a) that the rotation speed of the rotor has little effect on the value of the static pressure. The air velocity near point o is low and it is increased with the increase of the rotor speed because the air obtains energy from the rotating rotor. The situation of lowest velocity in Figure 15(b) is almost consistent with the position of the lowest pressure in Figure 15(a). The low-velocity zone always appears at the angle of 270 degrees in the range of rotor speed in this study.

Conclusions

The airflow in the rotor spinning machine is simulated in this study. Steady three-dimensional Navier–Stokes equations and the Spalart–Allmaras turbulence model are used to simulate the flow in a rotor spinning unit applied in industry. Distributions of various flow parameters are calculated by the finite volume method and SIMPLE algorithm. The effect of rotor speed on the flow characteristics in the rotor spinning unit is studied. The main conclusions are as follows.

It is found that the Spalart–Allmaras turbulence model is more suitable for the numerical simulation of the flow field in the spinning unit compared with the Standard k-ɛ turbulence model and RNG k-ɛ turbulence model. The airflow is accelerated in the transfer channel and the velocity is the maximum at the outlet of the transfer channel. The rotating speed of the rotor has little effect on the flow characteristics in the transfer channel. The rotating speed has great influence on the flow behavior in the rotor cup. It is found that there is a critical speed of the rotor cup beyond which the pressure and velocity on the slip surface is not changed regardless of the magnitude of the rotating speed. When the rotating speed is larger than this critical speed, the flow structure becomes unstable with the increasing of the rotating speed. The mechanism of the critical speed phenomenon is that the airflow in the rotor groove passes 180 degrees from two sides along the rotor wall and a pressure balance is achieved. This balance will break down when the rotating speed is larger than the critical speed. When the rotor speed is low, the flow characteristic in the air-inlet plane (Section B-B) is mainly determined by the high-speed air at the outlet of the transfer channel. However, it is mainly determined by the rotating rotor when the rotor speed is higher than the critical speed. The flow behavior in the meridian plane perpendicular to the air-inlet plane mainly depends on the rotor speed. Flow instability is intensified in the meridian plane of the rotor cup (Section C-C) when the rotor speed is larger than the critical speed.

For the rotor cup in the RFRS30 air suction open-end spinning machine, the critical rotating speed is determined to be n = 80,000 r/min with simulation method in this study. The practical value of the critical speed may be variable for different types of rotor frames. For example, the value of the critical speed increases with the decrease of the slip angle and decreases with the increase of the speed of the carding roller (the slip angle is the angle between the rotor slip surface and the horizontal line). Therefore, the critical rotating speed of n = 80,000 r/min obtained is only suitable for the RFRS30 air suction open-end spinning machine. However, the mechanisms of the critical rotating speed phenomenon and the qualitative analytical result about the existing critical rotating speed should be appropriate for air suction open-end spinning machines.

The result in this study gives the theoretical basis for the choice of the rotor speed of spinning machines, and thus provides reference for the design of rotating cups.

Footnotes

Declaration of conflicting interests

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

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by Zhejiang Province Science and Technology Innovation Team Project (grant number 2013TD18) and the National Natural Science Foundation of China (grant numbers 51579224, 51536008).

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