Optimum design of the injection nozzle system of a three-drive jigger dyeing machine

Abstract

A jigger dyeing machine is used to dye fabric across the width, which enables the fabric to be passed back and forth in a perfect dyeing bath. A three-drive jigger dyeing machine contains an injection nozzle system. The flowfield inside the injection nozzle system was computed using ANSYS CFX software and was evaluated by mass flow rate, velocity, and pressure. The injection nozzle system was observed by installing two different division plates and by changing the diameter and distance of the outlet holes to improve dyeing efficiency. The division plates have slits and holes help to distribute the dye liquid evenly over all the holes. The standard deviations of the mass flow rate of the division plates with slits and holes were 0.000551 and 0.000368, respectively. The effects of distance and diameter of the outlet holes were analyzed and evaluated by mass flow rate and standard deviation. The developed injection nozzle system of the jigger machine has more uniform mass flow rate. A diameter of 5 mm for the outlet holes and a distance of 50 mm between them were selected to manufacture a prototype. The prototype of the injection nozzle system of the three-drive jigger machine was manufactured and tested. The test results were compared with the computational results from the developed three-drive jigger dyeing machine, the original three-drive jigger dyeing machine, and a classic jigger dyeing machine.

Keywords

Computational Fluid Dynamics injection nozzle jigger uniform flow

A jigger dyeing machine is a type of batch dyeing machine that avoids staining of the dye in water, and is still the most economical and versatile for the pre-treatment, bleaching, and dyeing of textile materials. The machine has main advantages in regard to speed, fabric roll thickness, volume of the dye liquid, and temperature range. Figure 1 shows a schematic view of classic and three-drive jigger dyeing machines.¹ Both the jigger machines have a main roller, guide roller, and dye bath. Dyeing fabric passes from the guide roller through the dye bath and then into a driven main roller on the other side. The direction is reversed when all the fabric has passed through the bath. The fabrics with different widths can be colored in several stages of preparation of the dye, dyeing fixation, washing, and drying.^2,3

Figure 1.

Schematic view of (a) classic jigger dyeing machine and (b) three-drive jigger dyeing machine.

The three-drive jigger dyeing machine has an injection nozzle system, as shown in Figure 1(b). The three-drive jigger dyeing machine is used for dyeing a fabric across the width, which enables the fabric to be passed back and forth perfectly by the injection nozzle. The injection nozzle system is an important part in the three-drive jigger dyeing machine. The performance and efficiency of the dyeing machine depend on the injection nozzle system. The dye liquid is sprayed under high pressure through the outlet holes when the dyeing fabric moves. The injection nozzle system has a head, body parts, and outlet holes, which are located at the head of the nozzle.

The injection nozzle system was investigated to improve dyeing efficiency by obtaining uniform flow rate at the outlet holes. The diameter of the outlet holes and the distance between them on the nozzle were analyzed to find a proper dye liquid volume and to increase the dyeing width of fabric. The flowfield of the injection nozzle system was analyzed for mass flow rate, velocity, and pressure using ANSYS CFX software. The objective of this study is to develop an injection nozzle system for a jigger machine to improve the uniformity of the mass flow rate.

Analysis

Computational tools and domain

Computational Fluid Dynamics (CFD) technologies have become a vital part of design and analysis in both research and commercial industries. CFD offers the ability to conduct very detailed and through studies of flowfields, and it is capable of solving a broad range of flow problems.⁴ Many industrial flow problems with jets and wakes include turbulent flow characteristics, which cannot be resolved accurately, even when using Direct Numerical Simulation on current computers. Even though researchers cannot analyze the flowfield accurately, CFD methods with Reynolds-averaged Navier–Stokes equations and turbulence models can be used to compute the averaged turbulent stresses. These models often limit the accuracy of CFD simulations, but the computational results might be good for engineering purposes. The ANSYS Workbench provides the geometry or modifies the geometry read through data formats from various computer-aided design software and it generates a computational grid. CFX-Pre is used for the initial problem setup and definition of the prescribed motion of the geometry. CFX-Solver solves the high-speed, highly separated flow problems, and its capabilities represent the culmination of the growing experience in developing advanced simulation software and associated physical models. CFX-Post is a three-dimensional graphical post-processor that analyzes the CFD results.⁵

The main component of the jigger dyeing machine is the injection nozzle system. The nozzle injects the dye liquid into fabric during the dyeing processes and temporarily blocks the airflow in a particular area.⁶ The dyeing efficiency depends on the shape and performance of the nozzle.⁷ The injection nozzle system has head and body parts. The outlet holes are located at the head part of the nozzle. The dye liquid is sprayed under high pressure through the outlet holes when the dyeing fabric moves. Figure 2 shows the computational domain of the injection nozzle system.^8,9 The inlet holes of the injection nozzle system are 40 mm in diameter, while the length, width, and height are 2100, 65, and 80 mm, respectively. There are 37 outlet holes on the top part of the injection nozzle system. The shapes of the outlet holes can be rectangles, circles, or ovals.¹⁰ The circle shape was used in this study. The diameter of the outlet holes was 5 mm, and the distance between the outlet holes was 45 mm.

Figure 2.

The computational domain of the injection nozzle system: (a) three-dimensional view; (b) side view.

Turbulence model Shear Stress Transport

Standard two-equation turbulence models often fail to predict the onset and the amount of flow separation under adverse pressure-gradient conditions. The k-ω-based Shear Stress Transport (SST) model was designed to make highly accurate predictions of the onset and the amount of flow separation under adverse pressure gradients by the inclusion of transport effects into the formulation of the eddy viscosity.^11,12 The choice of the turbulence model depends on considerations such as the flow physics, including massive flow separations, the established practice of a specific class of problem, the level of accuracy required, the computational resources available, and the amount of computing time available for the simulation. The k-ω-based SST model has similar governing equations to the standard k-ω model by Wilcox:¹³

\frac{\partial}{\partial t} (ρ k) + \frac{\partial}{\partial x_{i}} (ρ {ku}_{i}) = \frac{\partial}{\partial x_{i}} (Γ Γ_{k} \frac{\partial k}{\partial x_{j}}) + \tilde{G_{k}} - Y_{k} + S_{k}

(1)

\frac{\partial}{\partial t} (ρ ω) + \frac{\partial}{\partial x_{i}} (ρ ω u_{i}) = \frac{\partial}{\partial x_{i}} (Γ Γ_{ω} \frac{\partial ω}{\partial x_{j}}) + G_{ω} - Y_{ω} + D_{ω} + S_{ω}

(2)

In Equations (1) and (2),

\tilde{G_{k}}

is the generation of turbulence kinetic energy due to mean velocity gradients.

G_{ω}

represents the generation of ω, which is the dissipation per unit turbulence kinetic energy.

Γ_{k}

and

Γ_{ω}

are the effective diffusivity of k and ω, respectively. Y_k and

Y_{ω}

represent the dissipation of k and ω due to the turbulence.

D_{ω}

is the cross-diffusion term. S_k and S_ω are user-defined source terms.

Boundary and solver conditions and the grid validation for the computational domain

The wall boundary condition was applied at the nozzle body, as given in Table 1. All walls in the domain were treated as viscous surfaces with no-slip velocity conditions. The inlet pressure was specified at the inlet hole of the domain. Open conditions were applied at the outlet holes. Table 2 shows the settings for the computational analysis. The working fluid was water under atmospheric pressure conditions. The computational domain was analyzed in steady-state conditions.

Table 1.

The boundary conditions for the computational domain

Boundary condition	Location	Value
Inlet	Inlet hole	16,000 [Pa]
Opening	Outlet holes	0 [Pa]
Wall	Nozzle body	No-slip

Table 2.

The solver conditions for the computational domain

The domain settings	Value
Relative pressure, Pa	0
Temperature, ℃	25
Fluid type	Water
Turbulence model	SST

SST: Shear Stress Transport.

The computational mesh was generated by hex dominant meshing. The grid validation study was performed to ensure that the computed quantities would properly converge. Figure 3 shows the grid validation results by comparing the mass flow rate of outlet holes 1 and 19 with various grid elements. The prescribed boundary conditions were applied for the computations as given in Table 1. The numbers of grid elements were varied between 1.0 million for the computations, as the grid test indicated that the proper number of grid elements was about 2.0 million, while the maximum and minimum element sizes were 0.0001 and 0.00004 m, respectively.

Figure 3.

The grid validation results with the mass flow rate and grid elements.

Results and discussion

Computational results of the original injection nozzle system

The objective of this research was to obtain an optimum injection nozzle system design with uniform flow at the outlet holes of the injection nozzle system. The original injection nozzle system was investigated to understand the flowfield of the nozzle. The flowfield of the injection nozzle system is shown in Figure 4. The dye liquid enters the injection nozzle system through the inlet, and then hits the opposite wall of the injection nozzle system and is expelled through the outlet holes. High pressure appears at the center of the nozzle, and the pressure is gradually reduced from the center toward the edge. There are a total of 37 outlet holes in the injection nozzle system, and the center outlet hole number is 19. The mass flow rate at the outlet holes was considered as a parameter to obtain uniform flow. Figure 5 shows the mass flow rate distribution at the outlet holes of the nozzle. The outlet holes were numbered to analyze the mass flow rates at each hole. Some portion of the liquid is directly expelled from the center outlet hole (the 19th hole), which is opposite the inlet. The rest of the liquid hits the nozzle wall. The mass flow rate decreased due to the stronger turning force in the axial direction of the flow than that exiting through the outlet holes around the center outlet hole. The mass flow rate increased farther away from the center of the nozzle in the axial direction, and decreased again at the ends of the nozzle.

Figure 4.

The velocity and pressure distributions of the injection nozzle system: (a) streamline view and (b) cross-sectional vector plot at the center of the nozzle.

Figure 5.

The mass flow rate distributions at the outlet holes of the injection nozzle system.

Effect of division plate with slits or holes

The original injection nozzle system was modified by installing two different division plates. The slit division plate was installed in the nozzle body at 50 mm from the inlet hole in Case 1. The thickness of the division plate is 0.1 mm, and the plate divides the nozzle body. The slit size was 10 mm, as given in Table 3. The division plate with holes, which have the diameter of 10 mm and distance between the holes of 10 mm, was installed in the nozzle body at 50 mm from the inlet hole in Case 2. Figure 6 shows the velocity distributions for two cases. Some portion of the dye liquid after entering through the inlet hole flows through the slit toward the outlet holes, while some portion of the liquid circulates around both sides of the inlet hole.

Figure 6.

The velocity vector and pressure distributions for Case 1 and Case 2: (a) streamline view of Case 1; (b) cross-sectional view of Case 1; (c) streamline view of Case 2 and (d) cross-sectional view of Case 2.

Table 3.

The original and developed injection nozzle system (cross-sectional view)

Cases 1 and 2 show similar velocity distributions. The upper part of the injection nozzle has more vortical motion than the lower part under the plate, as shown in Figure 6. The flow is fully vortical under the plate around the inlet hole. Figure 7 shows the mass flow rate at the outlet holes for all cases. The mass flow rate at the center outlet hole was much higher in the original case than in other cases. Also, the mass flow rate at the center hole is higher than those at neighboring holes. This is probably due to the direct injection toward the opposite wall of the center hole. The standard deviations of the original case, Case 1, and Case 2 were 0.00134, 0.000551, and 0.000368, respectively. The standard deviations indicate that the mass flow rates through outlet holes are evenly distributed around the average mass flow of the holes. The standard deviation clearly shows the effectiveness of the division plates with slits or holes. The division plates with slits or holes distribute dye liquid evenly over all the holes. In Case 2, the division plate with holes has the lowest standard deviation.

Figure 7.

The mass flow rate distributions at the outlet holes of the injection nozzle system for all cases.

Effects of the distance and diameter of the outlet holes

The diameter of the outlet holes and the distance between the outlet holes were analyzed to find a proper dye liquid volume and to increase the dyeing width of the fabric. The outlet holes were located on top of the injection nozzle system. The diameter of the outlet holes was changed to 4.5, 5.0, and 5.5 mm. The total mass flow rate of the outlet holes increased as the diameter increased, as given in Table 4. The difference of the mass flow rate occurred because the total mass flow rates of the outlet holes were not high when the diameters were 5.0 and 5.5 mm. The diameter of 5.0 mm was chosen for further analysis.

Table 4.

The total mass flow rate of the outlet holes with different diameters

Diameter, mm	4.5	5.0	5.5
Total mass flow rate of the outlet hole, kg/s	2.4867	2.9550	3.2562

The outlet holes were distributed with various distances of 40, 50, and 60 mm to analyze the dyeing width of the fabric. The dyeing widths were 1600, 1800, and 2000 mm. The effects of the outlet holes distributions were investigated with the injecting area. Figure 8(a) shows the velocity vector in the nozzle and injecting area. The injecting area is the area around the outlet holes. The length of the area was the same as the length of the nozzle, and the width and height were 60 mm. The velocity contour and streamline distributions when the distance between the outlet holes was 50 mm are shown in Figure 8. The dye liquid is injected from the outlet hole and hits the fabric as a spray. Figure 9 shows the mass flow distributions at the outlet holes for all distances. The mass flow rates at the center outlet hole (hole 19) were slightly different at all distances. Table 5 shows the standard deviation of the mass flow rate for all distances. The distance of 50 mm resulted in the lowest standard deviation, while the distance of 40 mm led to the highest standard deviation. The distance of 50 mm gives the required distance distribution. The outlet holes of the nozzle with the distance of 50 mm were selected to manufacture the prototype and for testing.

Figure 8.

The velocity contour and streamline distributions of the nozzle with the injecting area: (a) the cross-sectional view and (b) the top view with a distance of 50 mm.

Figure 9.

The mass flow rate distributions at the outlet holes with different distances.

Table 5.

The standard deviations of the mass flow rate with different distances

Distance, mm	40	50	60
Standard deviation	0.0004261	0.000268	0.0003812

Comparison of the test results of the jigger machines

The three-drive jigger dyeing machine was chosen to improve its dyeing efficiency of cotton and knit fabrics, which are sensitive to tension. The machine was able to dye the fabrics with low tension. The optimum design of the injection nozzle system of the jigger machine was developed numerically. The prototype of the injection nozzle system of the developed jigger machine was manufactured and tested. The prototype has the division plate with holes and the diameter of the outlet holes and distance between the outlet holes were 5 and 50 mm, respectively. The experimental test results were compared between the developed three-drive system, the original three-drive machine, and the classic jigger dyeing machine. The comparison results among the three jigger machines are given in Table 6. The developed machine and the original three-drive jigger machine can be operated in a tension-free state and with tension under 50 kg/m². The bath ratio was 1:2 in kilograms of textile per liter of water. The half dye-liquid volume was applied by the developed injection nozzle system of the jigger dyeing machine. The total length of the developed injection nozzle system was 2100 mm. The developed injection nozzle system can dye fabric with 1800-mm width. The running speed of the fabric was 15–150 m/min. The optimum injection nozzle system was obtained through the computational analyses, and the appropriate injection volume was used. Cotton, nylon acetate, and spandex fabrics could be used for the jigger machine with no-tension and low-tension. The system of the three guiding rollers squeezes the dyed fabric and the moisture rate decreases.

Table 6.

Comparing developed results with locally used results

Performance	Developed three-drive jigger machine	Original three-drive jigger machine	Classic jigger machine
Tension, kg/m²	0–50	0–50	15–100
Bath ratio	1:2	1:4	1:4
Fabric width, mm	1800	1400	1400
Speed, m/min	15–150	15–150	15–100
Injected dye-liquid volume, l/min	1500	2000	Not developed
Applied fabric	Cotton, nylon, acetate, spandex	Cotton, nylon, silk, spandex	Nylon
Pickup ratio, %	60	80	80

The developed injection nozzle system of the three-drive jigger dyeing machine improved the dyeing quality of the machine.

Conclusions

The injection nozzle system of the three-drive jigger machine was investigated to improve dyeing efficiency by using ANSYS CFX software. The computational domain of the injection nozzle system was evaluated by mass flow rate, velocity, and pressure. The domain was observed by installing two different division plates in the body of the nozzle (slit and holes plate), and by changing the diameter of the outlet holes and the distance between them. The effects of the division plates and the distance and diameter of the outlet holes were analyzed. The division plates were installed in the nozzle at 50 mm from the inlet hole to obtain uniform flow. The thickness of the division plates was 0.1 mm, the slit size of the division plate was 10 mm, and the diameter and distance between the holes of the division plate were 10 mm. The division plate distributes dye liquid evenly over all the holes. The standard deviations of mass flow rates for the division plates with slit and holes were 0.000551 and 0.000368, respectively. The division plate with holes has the lowest standard deviation.

The diameter of the outlet holes was analyzed with values of 4.5, 5.0, and 5.5 mm. The mass flow rate had a slight difference when the diameters were 5.0 and 5.5 mm. The outlet holes were distributed with distances of 40, 50, and 60 mm. The distances of 40 and 50 mm led to the highest and lowest standard deviation values. The diameter of 5 mm and distance of 50 mm were selected to manufacture the prototype.

A prototype of the developed injection nozzle system of the three-drive jigger dyeing machine was manufactured and tested. The developed injection nozzle system of the three-drive jigger dyeing machine has uniform mass flow rate. The test results of the developed three-drive jigger machine were compared with the original three-drive and classic jigger dyeing machines. The developed three-drive jigger dyeing machine can be operated in a tension-free state. The developed injection nozzle system of the three-drive jigger dyeing machine can dye fabric with 1800-mm width. The dye-liquid volume was decreased, and the dyeing width of fabric was increased by improving the outlet holes of the injection nozzle system and installing the division plate.

Footnotes

Acknowledgement

This work was supported by the 2013 Yeungnam University Research Grant.

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