An investigation of some parameter effects on the internal flow characteristics in the main nozzle

Abstract

The air-jet loom is widely used in the textile industry and the main nozzle is one of its key components. In this paper, the influence of some parameters, including the input air pressure and the structure of nozzle core and its internal diameter, on the internal flow field of the main nozzle is analyzed. Then the optimized structure of the main nozzle is proposed from the perspective of fluid dynamics. In the present simulations, the realizable $k - ɛ$ model is applied to model the internal flow field of the main nozzle. The results show that the velocity in the annular throat reaches supersonic. Moreover, the pressure at the end of the nozzle core is the lowest in the main nozzle. It is also shown that the input air pressure has little effect on the axis velocity in Zone B, but on the other hand, has a great influence on the near-wall velocity field and the axis velocity in Zone C. In addition, an optimized structure of the nozzle core is proposed in this paper. It is found that with the proposed structure, the velocity boundary layer near the wall of Zone B in the accelerating tube can be well improved, and rapid diffusion of airflow in this area can be avoided. These help increase the moving speed of the weft yarn. Last but not least, we also show that decreasing of the internal diameter of the nozzle core improves the axis velocity of the weft accelerating tube. However, it brings a stronger turbulence at the same time.

Keywords

main nozzle nozzle core air-jet loom numerical simulation characteristic analysis

The air-jet loom is one of the most promising shuttless looms, which is widely used in the textile industry for its high weft insertion rate, lower consumption, high production efficiency and low noise. Its major advantage is the weft insertion system. In the weft insertion process, the weft yarn is drawn out from the weft accumulator, and sucked and accelerated by the main nozzle. It is then carried by the high-speed jet flow ejected by the relay nozzles to cross the profiled channel to the other end. In this process, the main nozzle, which supplies the initial momentum for the weft yarn, is the most critical component of the air-jet loom. The internal flow field of the main nozzle directly affects the flying speed and stability of the weft yarn. It thus affects the quality of the fabric and the efficiency of the weaving machine.

Some efforts have already been made to study the flow field of the main nozzle and the weft insertion channel. Adanur and Mohamed¹ analyzed the airflow velocity in the simplified weft insertion system by experiments in 1991. The experiments show that the velocity of the airflow in the profiled channel relates to the distance and time. In 1996, Adanur and Bakhtiyarov² developed a semi-open and corrugated weft insertion slot to measure the velocity of the airflow, and calculated the airflow friction coefficient as well as the yarn traction according to their experimental results. More recently, Turel et al.³ and Adanur and Turel⁴ set up an emulator of the weft insertion system to analyze the effect of the loom operation speed, the supplied air pressure and the distance on the flow characteristics in the weft insertion channel. Substantial measurements of the weft insertion channel were made in this work. In addition, Ishida and Okajima,⁵ Shintani et al.⁶ and Shintani and Okajima⁷ simulated a weft insertion channel with notched and un-notched cylindrical tubes. The static pressure and the velocity distribution in the wall of the main nozzle were measured by experiment. However, usage of a contact measuring instrument in the narrow nozzle entails great artificial error. Moreover, Fukai⁸ discussed the flow characteristics in the accelerating tube. A hot wire anemometer was used to measure the flow velocity in the accelerating tube according to different flow rates. He testified that it was feasible to complete weft insertion with one nozzle and a partially open pipe, without the relay nozzles. Furthermore, Oh et al.⁹ analyzed the impact of the length of shunt layer, the diameter of nozzle and the location of spray hole on the internal flow field of the profiled channel. They summarized the attenuation law of the maximum axis speed. Nonetheless, only two-dimensional (2D) simulations were performed in their work, in which the intrinsic three-dimensional (3D) features of this problem cannot be investigated. Song and Shen¹⁰ introduced a synthetic flow field model to simulate the flow field of the air-jet loom. A computational fluid dynamics (CFD) method was used to simulate the synthetic flow field. Belforte et al.¹¹ conducted a 2D simulation of the main nozzle with a different physical model in order to get a better prediction of the nozzle behavior. With the most accurate physical model they determined, they evaluate the drag force on the weft yarn of various geometry configurations by CFD. However, a 2D geometrical model may not yet reflect the real flow conditions accurately. Although many investigations of the characteristics of the nozzle have been made, there is still room for improvement. It can be seen that most available works are based on the simplified nozzle model and the systematic theory of the relationship between the nozzle structure and the internal airflow. The complex 3D flow field in a more realistic nozzle model remains to be investigated. Thanks to the great development of the computational industry and the CFD algorithms, a detailed 3D simulation of the flow field in a more realistic nozzle model will be performed in this work to fill this gap. The effect of parameters, including the input air pressure, the structure of the nozzle core and the internal diameter, on the internal flow field of the main nozzle will be analyzed through 3D simulations with the turbulence model. In addition, an optimized structure of the main nozzle is proposed from the point of view of fluid dynamics. Through extensive numerical investigations, this work aims to provide guidance to improve the performance of the main nozzle in practical applications.

Theoretical analysis of the main nozzle

The geometric structure of the main nozzle is shown in Figure 1. It can be seen that high-pressure air enters the main nozzle from inlet 2. It then passes through the accelerating region (composed of the first chamber 3) rectifier tanks 5, the second chamber 6, cone sleeve 7 and throat area 8. The air flows into the first chamber, which is annular along the axial and circumferential directions, which generates a high-speed eddy. The rectifier tanks 5 consists of grooves that are distributed circumferentially in the nozzle core. The flow direction of the high-speed vortex, which is coming from the first chamber, will be adjusted to axial after flowing through these tanks. The airflow accelerates to subsonic axial flow in the gap between the second chamber 6 and cone sleeve 7. It reaches sonic or supersonic in the annular slit throat area 8, where the high-pressure and high-speed airflow mixes with the airflow from the weft insertion channel to form a double tube coaxial jet. The cross-section of the weft accelerating tube is uniform. The velocity boundary layer between the high-speed airflow and the wall of the accelerating tube reduces the actual diameter of the pipe flow, and also increases the axial airflow velocity of the weft acceleration zone.
Figure 1.
The structure of the main nozzle.

To clearly illustrate the problem, the airflow area of the main nozzle is divided into three parts in this work (Figure 1). Zone A is the area from the yarn entrance to the end of the nozzle core, which includes the airflow inlet. Zone B is the area along the X-axis direction, with length of 20 mm forward from the end of the nozzle core. The vortexes disappear completely at the end of this zone. In addition, Zone C starts immediately after Zone B, and ends at the exit of the weft accelerating tube.

Numerical method

Mathematical model

In this work, the following assumptions are made to simplify the problem.
The airflow in the nozzle is assumed to be compressible ideal gas: (a) the physical parameters of the gas are constants both in time and space; (b) gravitational effects are excluded.

The energy equation is ignored because the heat exchange effect is not considered.

Only the statistical average amount of turbulence is considered.

The governing equations in the Euler coordinates are as follows.

Continuity equation:
$\frac{\partial (ρ u_{x})}{\partial x} + \frac{\partial (ρ u_{y})}{\partial y} + \frac{\partial (ρ u_{z})}{\partial z} = 0$
(1)

The Navier–Stokes (N-S) equations:
$ρ (\frac{\partial u_{x}}{\partial t} + u_{x} \frac{\partial u_{x}}{\partial x} + u_{y} \frac{\partial u_{x}}{\partial y} + u_{z} \frac{\partial u_{x}}{\partial z}) = - \frac{\partial p}{\partial x} + μ (\frac{\partial 2 u_{x}}{\partial x 2} + \frac{\partial 2 u_{x}}{\partial y 2} + \frac{\partial 2 u_{x}}{\partial z 2}) + ρ g_{x}$
(2)

$ρ (\frac{\partial u_{y}}{\partial t} + u_{x} \frac{\partial u_{y}}{\partial x} + u_{y} \frac{\partial u_{y}}{\partial y} + u_{z} \frac{\partial u_{y}}{\partial z}) = - \frac{\partial p}{\partial y} + μ (\frac{\partial 2 u_{y}}{\partial x 2} + \frac{\partial 2 u_{y}}{\partial y 2} + \frac{\partial 2 u_{y}}{\partial z 2}) + ρ g_{y}$
(3)

$ρ (\frac{\partial u_{z}}{\partial t} + u_{x} \frac{\partial u_{z}}{\partial x} + u_{y} \frac{\partial u_{z}}{\partial y} + u_{z} \frac{\partial u_{z}}{\partial z}) = - \frac{\partial p}{\partial x} + μ (\frac{\partial 2 u_{z}}{\partial x 2} + \frac{\partial 2 u_{z}}{\partial y 2} + \frac{\partial 2 u_{z}}{\partial z 2}) + ρ g_{z}$
(4)

According to the transonic flow characteristics in the main nozzle, the realizable $k - ɛ$ model is adopted. The transport equations for the model are as follows.

The turbulence kinetic energy equation:
$\frac{\partial}{\partial t} (ρ k) + \frac{\partial}{\partial x_{j}} (ρ {ku}_{j}) = \frac{\partial}{\partial x_{j}} [(μ + \frac{μ_{t}}{σ_{k}}) \frac{\partial k}{\partial x_{j}}] + G_{k} + G_{b} - ρ ɛ - Y_{M} + S_{k}$
(5)

The rate of dissipation equation:
$\frac{\partial}{\partial t} (ρ ɛ) + \frac{\partial}{\partial x_{j}} (ρ ɛ u_{j}) = \frac{\partial}{\partial x_{j}} [(μ + \frac{μ_{t}}{σ_{ɛ}}) \frac{\partial k}{\partial x_{j}}] + ρ C_{1} S ɛ - ρ C_{2} \frac{ɛ 2}{k + \sqrt{ν ɛ}} + C_{1 ɛ} \frac{ɛ}{k} C_{3 ɛ} G_{b} + S_{ɛ}$
(6)
where $C_{1} = max [0.43, \frac{η}{η + 5}]$ , $η = S \frac{k}{ɛ}$ , $S = \sqrt{2 S_{ij} S_{ij}}$ and $μ_{t} = ρ C_{μ} \frac{k 2}{ɛ}$ .

The parameter $C_{μ}$ in the realizable $k - ɛ$ model is no longer constant and can be computed from the following formula:
$C_{μ} = \frac{1}{A_{0} + A_{s} \frac{kU }{ɛ}}$
(7)
where $U \equiv \sqrt{S_{ij} S_{ij} + {\tilde{Ω}}_{ij} {\tilde{Ω}}_{ij}}$

The model constants are $c_{μ} = 0.09, c_{1} = 1.44, c_{2} = 1.92, σ_{k} = 1.0, σ_{ɛ} = 1.3$ _.

Boundary conditions and mesh generation

Because the flow is compressible in this case, both yarn entrance 1 and airflow inlet 2 are set as pressure inlets. The exit of the accelerating tube is the pressure outlet. The operation pressure is 101,325 Pa. This means the total pressure and the static pressure are relative pressure. No-slip and adiabatic wall boundary conditions are applied on the solid walls and enhanced wall treatment is adopted in the near-wall. The fluid is set as ideal gas as assumed previously. The convergent results are obtained after approximately 20,000 iterations.

For the mesh generation, hexahedral meshes are used for the cavity of nozzle core, weft accelerating tube and outside of the weft accelerating tube; the nozzle body cavity in the middle is meshed into unstructured tetrahedral meshes. The meshes of those small but critical parts, such as the throat and rectifier tanks, are gradually refined in space to improve the mesh quality and convergence speed. In the computational domain, there are over 3 million tetrahedral mesh elements, over 350,000 hexahedral mesh elements, over 190,000 triangular mesh elements, over 40,000 quadrilateral mesh elements and more than 1000 pyramid mesh elements. A $φ 30 \times 100$ zone was connected to the accelerating tube exit for external flow calculation. The meshes of the main nozzle with six teeth rectifier tanks are shown in Figure 2.
Figure 2.
Meshes of the main nozzle with six teeth rectifier tanks.

Results and analysis

Effect of the input pressure

Under the input pressure from 0.2 to 0.5 MPa, the velocity field in Zone B in the weft accelerating tube is as shown in Figures 3(a)–(d).
Figure 3.
The airflow distribution in Zone B in the weft accelerating tube by computational fluid dynamics.

Notice that there are six rectifier tanks in this main nozzle. Figure 3 show that the velocity of the airflow in the annular slit throat reaches supersonic (around 450 m/s). The high-speed airflow is mixed with the flow from the weft insertion channel at the end of the nozzle core, where the local pressure is close to vacuum. It can also be seen that the velocity boundary layer forms near the wall of Zone B in the accelerating tube. It thickens towards the axis of the accelerating tube, which leads to the decrease of the effective flow area and the increase of average flow velocity. However, when the velocity boundary layer expands enough, it will cause a congestion phenomenon and the yarn will be blocked in the weft accelerating channel.

The velocity boundary layer of Zone B is thin when the input pressure is low. Under the pressure of 0.5 MPa, the velocity boundary layer of Zone B is quite thick, and the congestion is quite serious.

The turbulence intensity distribution of the main nozzle under different input pressures is as shown in Figure 4. The largest turbulence intensity occurs in Zone B and the outlet of the weft accelerating tube. The larger the input pressure, the greater the turbulence intensity in these two regions.
Figure 4.
The turbulence intensity distribution of the main nozzle under different input pressure by computational fluid dynamics.

Figures 5 and 6 show the axis velocity and the Mach number of the main nozzle with six rectifier tanks under the input pressure from 0.2 to 0.5 MPa, respectively. From these figures, the converging nozzle flow can be observed in Zone A. The axis velocity of airflow increases nonlinearly with distance and the input pressure. The increasing rate slows down when it reaches a certain value. In addition, the flow in Zone B is usually referred to as sudden expansion tube flow. In this region, the accelerated flow from the throat suddenly expands to the accelerating tube, and causes vortexes near the end of the nozzle core. The vortexes disappear completely at the end of the zone. The axis velocity is unstable and changes dramatically in this area. This turbulence congestion phenomenon is determined by the structure of the region, and has nothing to do with the input pressure. In Zone C, the axis velocity of airflow increases steadily and the yarn is kept accelerated. The airflow and yarn movement is much more stable in this area. The length of the zone determines the interaction distance between the airflow and yarn. A longer length of this zone leads to more stable airflow and yarn velocity. Nevertheless, if Zone C is too long, it is likely to cause turbulence congestion in Zone B and failure of the weft insertion. Furthermore, it can be seen that the axis velocity and Mach number of the airflow decrease rapidly after the airflow enters the ambient circumstance. In summary, the above analysis shows that the value of the input pressure mainly affects the airflow velocity in Zone C, while has little effect on that in Zone B. Moreover, the greater the input velocity, the faster the axis flow velocity in Zone C. Under 0.5 MPa, the axis velocity of the outlet of the weft accelerating tube reaches its maximum value, which is about 270 m/s (0.83 Ma).
Figure 5.
Axis velocity distribution of the main nozzle under different pressures by computational fluid dynamics.

Figure 6.
Mach number distribution of the main nozzle under different pressures by computational fluid dynamics.

Figure 7 shows the static pressure distribution along the main nozzle under different pressures. The negative pressure at the end of Zone A is good for sucking the weft. The static pressure jumps to its maximum in Zone B of the weft accelerating tube. It then decreases gradually when the dynamic pressure and velocity increase. The higher the input pressure, the higher the maximum static pressure. The static pressure outside the weft accelerating tube is zero.
Figure 7.
Static pressure distribution of the main nozzle under different pressures by computational fluid dynamics.

The previous results show that the flow reaches supersonic in the annular throat. Moreover, a low-pressure area is formed at the end of the nozzle core. The input air pressure has little effect on the axis velocity of Zone B in the weft accelerating tube, while it plays an important role in near-wall surface velocity and the axis flow velocity of Zone C. Greater input pressure will lead to a thicker velocity boundary layer, more severe airflow congestion and greater turbulence intensity in Zone B. The greater the input velocity, the faster the axis flow velocity of Zone C. Under 0.5 MPa, the axis velocity of the outlet of the weft accelerating tube reaches its maximum value, about 270 m/s (0.83 Ma).

Effect of different nozzle core end structures

The velocity boundary layer of Zone B will lead to an airflow congestion problem, and thereby affects the speed of the flying weft yarn in the weft accelerating tube. The structure of the nozzle core end is modified in order to accelerate the mixing of the high-speed airflow from the throat and the low-speed airflow from the weft insertion tube. This modification is also expected to decrease the turbulence. The common nozzle core end is shown in Figure 8(a), and the modified nozzle core end with an oval shape cross-section is presented in Figure 8(b). Notice that the inclination of the oval shape is 45°.
Figure 8.
The structures of different nozzle core ends.

Figure 9 shows the airflow distribution in the main nozzle of different nozzle core end types. In Figure 9(a), high-speed and low-speed airflow at the end of the nozzle core area mixed inadequately. The velocity boundary layer in Zone B causes a more severe turbulent vortex, which is not desirable for weft flying. In Figure 9(b), the outlet area of the nozzle core is increased. Therefore, the mixing is expected to be enhanced due to the larger contact area. In addition, the velocity boundary layer in Zone B is improved. It also helps to avoid rapid air diffusion in this region and decreases the turbulent vortex intensity. In summary, the proposed structure of the nozzle core end is designed to increase the weft flying speed finally.
Figure 9.
Airflow distribution in the main nozzle with different nozzle core end types by computational fluid dynamics.

The distribution of the axis velocity in the main nozzle with different nozzle core end types is shown in Figure 10. It can be seen clearly that the axis flow velocity with the modified structure is better than that of the common structure.
Figure 10.
Axis velocity distribution in the main nozzle with different nozzle core end types by computational fluid dynamics.

Effect of the internal diameter of the nozzle core

Figures 11 and 12 show the airflow distribution and axis velocity profiles in the main nozzle with different internal core diameters, respectively. The internal nozzle core diameter in Figures 11 and 12 is 2.0 and 2.4 mm, respectively. The input pressure is the same. It can be seen that the axis flow velocity of the nozzle core with internal diameter 2.0 mm is higher than that of 2.4 mm. However, the velocity boundary layer in Zone B with 2.4 mm internal diameter is thicker. This indicates that a smaller nozzle core helps to improve the axis velocity, but brings greater turbulent vortexes. Concurrently, it also leads to more energy loss in the weft accelerating tube. Therefore, the internal diameter of the nozzle core should be carefully chosen to balance between a desired high axis velocity and energy deficiency.
Figure 11.
Velocity field in the main nozzle with different nozzle core inner diameters by computational fluid dynamics.

Figure 12.
Axis flow velocity distribution in the main nozzle with different nozzle core internal diameters by computational fluid dynamics.

Comparison with the result of experiments

The main nozzle of the same structure is used in our experiments. The input pressure is 0.2 MPa, the modified nozzle core end is adopted and the internal nozzle core diameter is 2.0 mm. As the internal diameter of the main nozzle is very tiny, it is impossible to measure the velocity in the main nozzle. The mean axis velocity along the external centerline of the main nozzle is measured. The hot wire anemometers are placed at each interval of 10 cm. The comparison curve between the calculated and measured values of axis velocity is shown in Figure 13.
Figure 13.
Comparison between calculated and measured values of axis velocity along the external center line.

The start point on the left-hand side refers to the exit position of the main nozzle. Due to the experimental error caused by artificial error and the precision of the measurement equipment, there are some differences between the experiment and CFD. However, the trend of the curves obtained by CFD and the experiment are the same. The mean axis velocity at the exit of the main nozzle is the highest. It remains until the distance is near the 270 mm point. Then the velocity decreased sharply in the following 30 mm. In order to keep the yarn flying evenly and quickly, the auxiliary jet flow should be supplied during the distance of airflow velocity sharp decreasing.

Conclusions

In this work, numerical simulations were performed to analyze the internal flow in the main nozzle of an air-jet room with six rectifier tanks. The effect of several variables on the performance of the main nozzle was investigated through detailed 3D simulations. The investigated variables include the input air pressure and the structure and the internal diameter of the nozzle core. The conclusions deduced from the present numerical results are summarized as follows.
It is feasible to use the realizable $k - ɛ$ model to study the internal flow characteristics in the main nozzle.

The velocity reaches supersonic in the annular slit throat. A low-pressure area, which is close to vacuum in Zone B, can be observed at the end of the nozzle core.

The input air pressure has little influence on the axis velocity of Zone B in the weft accelerating tube, while it has great influence on the near-wall velocity profile and the axis flow velocity in Zone C. It is also found that greater input pressure will lead to a thicker velocity boundary layer, more severe airflow congestion and greater turbulence intensity in Zone B. Higher input pressure also leads to larger axis flow velocity and higher static pressure.

An optimized nozzle core structure has been proposed in this work. It has a larger outlet area. It is designed to enhance the mixing between high-speed and low-speed airflow. In addition, it is also proved to avoid rapid air diffusion in Zone B and decrease the turbulent vortex. Thus, the modified structure of the nozzle core enables a stable and efficient incensement of the weft flying.

Last but not least, the present results show that the smaller internal nozzle core diameter helps to increase the axis velocity, but entails a stronger turbulence and more energy loss in the weft accelerating tube at the same time. Therefore, the internal diameter of the nozzle core should be carefully chosen in order to increase the axis velocity while preventing unnecessary energy loss.

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 the National Natural Science Foundation of China (Grant No. 51576180, 51206149), the Zhejiang Provincial Natural Science Foundation (Grant No. LZ14E050004) and the Project of 521 Talents Cultivation in Zhejiang Sci-Tech University.

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