Computational Fluid Dynamic Simulation of Fabric Cooling in a Stenter Machine

Abstract

Stenter machines are used to remove moisture from fabrics produced in the textile industry. Following the drying process, the cooling process, which is applied to fabrics using injector channels, is conducted in the last section of a stenter machine, preventing fabrics from expanding and the degradation of their quality. The present study mainly aimed to investigate the fabric-cooling process in a stenter machine used actively in a textile company. First, industrial data were obtained with some experiments, and computational fluid dynamics (CFD) simulations were then conducted by validating the industrial data. All CFD models were simulated using ANSYS Fluent commercial CFD software. A total of four parameters, including two geometric and two operating parameters, were considered in order to investigate their effects on the fabric-cooling performance of the stenter machine. While the geometric parameters were the porosity (β) and injector angle (α), the operating parameters were the velocity of the airflow that cools the fabrics and fabric velocity, representing the movement of the fabric. As outputs of CFD simulations, fabric surface temperature values, the distributions of fabric surface temperatures, and some streamlines were illustrated. Although low values of porosity (β₁ = 0.05) and injector angle (α₁ = 0°) provided better performance, airflow velocity could be increased one or two times for the range of these constant parameters.

1. Introduction

According to historical perspectives, textiles and clothing were the very first manufactured products in many nations during the industrialization stage [1]. From England to the USA and Japan, the textile industry sparked economic development through industrialization and global merchandising. However, the textile industry is now a major contributor to the growth of the economy in developing nations [2]. Therefore, the textile industry still has an important role in total energy consumption, with a high production capacity of 62 million tons of fabric per year worldwide [3]. The drying process of fabrics is one of the most energy-intensive steps in the textile industry [4]. Stenter machines are widely used for the drying process of fabrics in the textile industry [5]. In these machines, wet fabrics are fixed with fasteners at the edges and moved by means of moving chains. Stenter machines facilitate fabric drying by using hot air, which impinges on fabric surfaces passing through injectors. By introducing a hot airflow jet through injectors on both sides of the wet fabric, it is dried. The drying process of a stenter machine takes place in cabins, where the process is gradually completed. The fabric, which almost reaches the temperature of the last cabin of the stenter machine, is then exposed to a cooling process to ensure its temperature is close to ambient; then, it is stacked by folding. If the fabric is not cooled after the drying process, it is stacked and stored at drying temperature. When fabrics are stacked at drying temperature, the cooling is retarded, the fabric expands, and its quality deteriorates. In this case, the fabric is wasted. The fabric-cooling performance of stenter machines is therefore worth examining.

In the available literature, some researchers have examined the drying performance and energy efficiency of stenter machines numerically or experimentally. Llanos et al. [6] performed three different CFD simulations using the standard k-ε turbulence model in COMSOL software (https://www.comsol.com/, accessed on 17 January 2024) to determine the drying performance of a stenter machine. They observed non-uniform turbulence density in the flow volume and that the highest velocities were at the edge of the injectors. Wang et al. [7] measured the mesoscopic structure parameters and mechanical properties of three different fabrics. Utilizing ANSYS Fluent software (https://www.ansys.com/products/fluids/ansys-fluent, accessed on 17 January 2024), they modeled the three fabrics as porous media and improved formulas that accurately predicted the convection heat transfer and thermodynamic properties of the fabrics. To improve productivity and save energy, Wang et al. [8] used a finite element model to simulate continuous fabric drying processes and an optimization method to optimize process parameters based on the model. They revealed the characteristics of constant fabric-drying processes and optimized process parameters. CFD simulations in ANSYS Fluent were conducted by Ramic et al. [9] to predict fabric temperature and density in stenter machines. The energy consumption of the stenter machine was predicted with a 14% error of absolute errors in their study. Akan and Özkan [10,11] carried out an experimental study using fabric with 95% cotton + 5% Lycra content at three different air-drying temperatures (110–130–150 °C) and 10 m/min fabric velocity by operating a stenter machine with 10 cabins under real production conditions. They showed how different air-drying temperatures affected the heat-transfer coefficients and energy efficiency. They observed that the heat transfer coefficient increased by about 6% by increasing from 110 °C to 130 °C, and the energy efficiency decreased by 4%. With experimental data obtained from 9 different drying operations in a 10-chamber hot-oil-heated stenter and 12 different empirical and semi-empirical thin-layer models, Akan and Ünal [12] mathematically modeled the drying behavior of 67% cotton + 33% polyester knit fabrics containing Thessaloniki knit fabrics. Their models were in good agreement with experimental data for different thin-layer drying models. Baxi et al. [13], using MATLAB SIMULINK software (https://www.tutorialspoint.com/matlab/matlab_simulink.htm, accessed on 17 January 2024), developed a mathematical model for mass, moisture, and heat transfer balance for rotary dryers that can be used in different industries and demonstrated the applicability of the model in a stenter machine. Patel et al. [14] conducted a comparison study based on energy modeling for two different stenter machines and belt conveyors. Based on their energy modeling, it was shown that cotton and wool fabrics could be dried and transported with ten percent less energy consumption when using stenter machines and belt conveyors.

Airflow in stenter machines has also been numerically investigated by other researchers. Juraeva et al. [15] modeled the airflow in the injector channel of a stenter machine using ANSYS CFX software (https://www.ansys.com/products/fluids/ansys-cfx, accessed on 17 January 2024). The effects of the injector channel’s geometry (flat-inclined), the height of the injector channel (40 mm, 80 mm, and 160 mm), and the injector hole’s geometry (circle, ellipse, quadrilateral, and pentagon) on the flow were investigated. They compared the mass flow rates passing through each injector on the nozzle and revealed that a 40 mm channel height, circular hole geometry, and straight channel type gave better results. Sigirci and Erdogan [16] numerically presented the velocity distribution of airflow in a stenter machine channel and examined the effect of some geometric parameters of the injector duct and nozzle on airflow velocity distribution in the stenter machine cabin.

According to the available literature, although many studies have been conducted on the drying performance and energy efficiency of stenter machines, investigations into airflow distribution in stenter machines are limited. Most of all, it appears that there are hardly any studies on the cooling performance of stenter machines in the available literature. This study aims to reveal the effect of geometric and operating parameters such as porosity (β), injector angle (α), airflow velocity (V_a), and fabric velocity (V_f) on the fabric-cooling performance of stenter machines and airflow distribution.

2. Methodology

The stenter machine considered in the present study is actively used in a textile company in Malatya, Türkiye. In order to investigate the performance of fabric cooling in the last section of the available stenter machine, industrial data were initially obtained by conducting experiments. The numerical models created were subsequently validated by comparing them with the industrial data. In the end, CFD models were used with a variety of geometric and operational parameters to determine the values resulting in the best performance.

2.1. Geometry and Parameters

The number of cabins in a stenter machine depends on its capacity. In this study, the existing stenter machine consists of 10 cabins, with each cabin having a total of 12 injector channels—6 in the upper section and 6 in the bottom section. Each injector channel contains 24 square-shaped holes. The injector channels and their geometric details in the cabins of the stenter machine are identical to those in the cooling section. Figure 1 illustrates cooling section of the stenter machine. The fabric in the cabins is exposed to hot airflow to dehumidify it. The cooling process occurs as the fabric exits the cabin and passes between the upper and bottom injector channels. To conduct this process, airflow jet at ambient temperature is impinged on the fabric surface. The geometric details of the injector channels, one channel at bottom level and one channel at upper level, are shown in Figure 2. A centrifugal fan supplies the airflow into the injector channel. Once air passes through the injector holes, it contacts the fabric surface. The airflow exits the fluid domain and diffuses into the ambient environment.

The geometric and operating parameters considered in this study are given in

Table 1. Geometric and operating conditions.

Porosity—β	Injector Angle—α	Airflow Velocity—Va	Fabric Velocity—Vf
(-)	(°)	(m/s)	(m/s)
0.05	0	0.5	0.25
0.1	10	1	0.3
0.2	20	2	0.35
0.3	30	-	-
0.4	-	-	-

. Among these parameters, porosity is the ratio of the perforated surface area of the air injector channel to its total surface area [17]. As can be seen in Figure 2, injector angle (α) represents angle between injector surface and horizontal plane. V_a and V_f are velocity of airflow in the inlet surface of the fluid domain and fabric velocity in z-direction, respectively. Porosity plays a crucial role in influencing the distribution of airflow on the fabric surface, which, in turn, affects the volume flow rate supplied to the cooling zone. The injector angle, which determines the contact angle between the fabric and airflow, must be considered in studies of cooling performance in the stenter machine. Additionally, the airflow velocity affects heat transfer in convection, while fabric velocity directly influences the contact time, which affects the heat transfer between the fabric and airflow.

2.2. Experiments

A validation study is needed to ensure mesh sensitivity and the selection of an appropriate turbulence model. Computational fluid dynamics (CFD) studies are usually validated with experimental results. Some experimental measurements were therefore obtained in the industrial plant. The airflow velocity was measured at the cross-section of inlet surface of injector channel. The cross-section has rectangle shape, which is 0.235 m in size for each edge, and airflow velocities were measured at 25 different points, as suitable for ASHRAE Standard-111 [18]. A pitot tube (±0.01 m/s), integrated with multifunctional data logger (TESTO 435-4, Testo, Seattle, WA, USA), was used for measuring airflow velocity. Thanks to these velocity measurements, the mean velocity of airflow at the inlet section was obtained. In the validation study simulations, the mean airflow velocity value at the inlet section was identified as the boundary condition. The validation study was carried out using temperature measurements of the fabric surface. In the last section of stenter machine, fabric surface temperatures were obtained by thermal camera. The temperature measurement points on the fabric surface are illustrated in Figure 3. An average temperature value was obtained by measuring the surface temperatures of the fabric before and after each injector channel by using a thermal camera (TESTO 870-2, $\pm$2% °C) from 10 different points on a line in Figure 3. The average temperatures obtained before each injector channel were defined as inlet into injector channels boundary condition of fabric. These temperature values were used in the validation study. The air temperature flowing in the injector channel was measured using thermocouple (±0.3 °C) integrated into the TESTO 435-4 multifunctional data logger.

2.3. CFD Model

The fabric cooling process in the stenter machine is modeled using the Finite Volume Method (FVM). Solid models of the last section of the stenter machine, where the cooling process occurs, are created by simplifying the geometry in order to reduce computation costs and data storage. In this case, instead of modeling all injector channels in a single simulation (total of 12 injector channels, 6 injector channels at upper level and 6 injector channels at bottom level), each pair of injector channels (1 injector channel at upper level and 1 injector channel at bottom level) is separately modeled. All CFD simulations are conducted using commercial CFD software ANSYS Fluent 14.0.

Mesh and Simulation Details

Tetrahedral mesh type is generated in all CFD models. The maximum size of the mesh in the body is 15 mm. A face sizing of 2 mm is performed on injector hole surfaces to ensure that the analysis is sensitive. Although there are small differences in being geometric, especially such as in analysis of porosity and injector angle, approximately 500,000 tetrahedral mesh elements are created in all models. The maximum skewness value is 0.8, which is acceptable value [19], while the average skewness value is 0.20. The mesh is refined throughout the entire flow domain. Next, 18° is determined for the span angle of the mesh curvature. Coarse and medium options are selected as the relevance center and mesh smoothing characteristics. Figure 4 shows the mesh model of the injector channel.

This study utilizes Reynolds-Averaged Navier–Stokes (RANS) governing equations for mass, momentum, and energy in CFD analysis. Additionally, the Realizable k-ε turbulence model equations are employed in simulations. The velocity inlet boundary condition is defined for the two inlet surfaces of the fluid domain given in Figure 2. A total of four outlet surfaces, two in the (+) x-direction and two in the (−) x-direction, located between the injector channels and fabric, are defined as pressure outlet boundary conditions. Surfaces identified as symmetry boundary conditions can be clearly seen in Figure 2. In order to avoid computational costs and data storage issues, two surfaces in the (+) z-direction and two surfaces in the (−) z-direction are considered symmetry boundary conditions. Wall boundary condition with no slip shear is applied to all other surfaces. All CFD simulations are conducted with air treated as an ideal gas and as a Newtonian fluid.

Simulations are solved under unsteady-state conditions because the fabric movement should be carefully integrated into CFD models. The fabric velocity toward (+) z-direction is 0.3 m/s, as obtained from the stenter machine control panel. It is supposed that the fabric moves as a flat surface. The velocity value of the porous zone movement is set to 0.3 m/s in the CFD model. Since the distance of the fabric movement is 0.47 m and the fabric velocity (V_f) is 0.3 m/s in the models, simulations are carried out for 1.57 s (0.47 m/0.3 m.s⁻¹ = 1.57 s). In all simulations, time step size is 0.001 s, and the number of time steps is therefore 1570. In other two analyses examining the effect of fabric velocity (V_f = 0.25 m/s and V_f = 0.35 m/s), the number of time steps varies naturally depending on the fabric velocity. In the present study, the fabric considered as porous media is lycra fabric, and its thermophysical properties [20] are illustrated in

Table 2. Thermophysical properties of the fabric.

Fabric	Thickness	Porosity	Density	Specific Heat Capacity	Coefficient of Heat Conduction
	(mm)	(-)	(kg/m3)	(kJ/kg·K)	(W/m·K)
Full Lycra	1	0.5	266.39	1989.37	0.0555

. Based on the assumption that the fabric is isotropic in all directions, the fabric porous zone has 1.4 × 10⁷ viscous resistance provided by the manufacturer.

At initial condition of unsteady-state CFD simulations, the temperatures of both fluid domain and airflow at the inlet surface are 26.85 °C, while temperature of fabric porous zone is 130 °C. The SIMPLE algorithm is utilized to obtain the solution of pressure–velocity coupling. By using the Second Order Upwind Scheme, all scalars in each fluid domain are spatially discretized. All scaled residuals except energy are computed using double-precision calculations until 10⁻⁴ is reached. Finally, 10⁻⁶ residual criteria are aimed and obtained for energy equation.

3. Results and Discussions

3.1. Validation Study

In order to validate the CFD models in terms of sensitivity and accuracy, this study includes a validation study comparing the CFD model with industrial data. Averages at different 10 points of temperature values of the fabric surface before and after each pair of six injector channel pairs (one channel in the upper level and one channel in the bottom level) were therefore compared. Figure 5 depicts a comparison of fabric temperature values obtained from both simulations and experiments. It can be seen that the fabric cooling occurs almost at the same value after each pair of injector channels. The effect of the cabin interior temperature of the stenter machine on the cooling section may explain minor differences between industrial data and CFD simulations. Based on the conditions considered in this study, the CFD model appears well-validated.

A reference study aimed at validating the turbulence model was conducted using five different turbulence models and considering only two injector channels.

Table 3. Turbulence model study.

Analysis	Fabric Temperature (K)	Error (%)
Industrial	122.82	-
Standard k-ε	111.99	8.82
RNG k-ε	107.56	12.42
Realizable k-ε	117.97	3.95
Standard k-ω	112.58	8.34
SST k-ω	112.81	8.15

presents the results of simulations using five different turbulence models, comparing them with the industrial data. Although Realizable k-ε is a relatively new model compared to other k-ε turbulence models, early studies have shown that this turbulence model gives better results in certain validation studies [19]. Additionally, the 3.95% error between the industrial data and CFD simulation indicates that the Realizable k-ε turbulence model is more suitable in this study.

In Figure 6, obtained from CFD simulation, different positions of the fabric are shown at different times (at initial time, 0.3 s, 1 s, and 1.5 s). The fabric, which was modeled in the CFD simulations, completes its movement with a 0.001 s time step size in 1.57 s for this fabric velocity.

3.2. Porosity (β) Study

Fluid passing through holes is affected by porosity, which plays a key role in flow control. In addition to the porosity value (0.05) of the available stenter machine in the company that supports this study, four other porosity values (0.1, 0.2, 0.3, and 0.4) were used to examine the effects of porosity on the cooling performance of the stenter machine. Increasing porosity was carried out by increasing the number or the diameters of holes. In the present study, increasing the number of holes is preferred. Figure 7 shows the fabric temperature predicted through CFD software Ansys Fluent 14.0 in different simulations based on geometric parameters. As can be seen in Figure 7a, as the porosity increases from 0.05 to 0.4, the average fabric temperature at the end of the cooling process also increases. In other words, as porosity increases, cooling performance decreases. With increasing porosity, there are more injector holes, so more air passes through them at low velocity, and ultimately, most of the air exits the fluid domain without contacting the fabric. Figure 8 shows the temperature distribution on the fabric surface for different porosity values at the end of the cooling process (t = 1.57 s). In all the contours showing the temperature distributions on the fabric surfaces, there are mainly two different regions on the fabric surface at t = 1.57 s. One of these regions is the cooled region, which is primarily blue-green-yellow in color. This region represents the fabric that exited between the injector channels and cooled. In order to examine the cooling performance of the stenter machine, this region is considered. The other one, which can be neglected at the end of the cooling process, is the hot regionm which is between the injector channels at t = 1.57 s. Figure 9 depicts the velocity streamlines on the surface at the end of the upper injector channel. These streamlines provide additional insights into the effects of porosity and injector angles on airflow distribution in the fluid domain. Air jets passing through holes form vorticity. As the number of holes increases, airflow trends generate two different vortexes on both the right and the left sides. There is one order of holes in β₁ porosity, whereas there are two orders in the others. With an increase in porosity, the airflow velocity at the hole decreases. High porosity values result in airflow jets passing through holes in the inner row, colliding with each other and with geometric corners, causing turbulence to dissipate.

3.3. Injector Angle (α) Study

One of the important geometric parameters of the stenter machine is the injector angle. This geometric parameter plays a key role in determining the angle at which air contacts the fabric surface. Currently, injector channels with a 30° injector angle are used in the stenter machine in the company. Reducing this angle is expected to improve the contact between air and fabric, leading to better cooling performance compared to increasing it. Therefore, three different angles of 0°, 10°, and 20° were determined. The results predicted by CFD simulations to reveal the cooling performance for the four different injector angles are presented in Figure 7b. Following the cooling process (t = 1.57 s), Figure 10 and Figure 11 show the temperature contour of fabric surfaces and the streamlines on the surface located in the upper injector channel for different injector angles, respectively. If these figures are examined together, with an increase in the injector angles, the fabric surface temperature at the end of the cooling process increases. The cooling performance is adversely affected by the increased angle between the horizontal plane and the injector hole plane. In the case of contacting air with the fabric vertically (α = 0°), more effective cooling performance can be reached. If the injector angles are higher than 0°, the air injected through injector holes cannot directly contact the fabric. Some air may exit the fluid domain without coming into contact with the fabric.

3.4. Airflow Velocity (V_a) Study

In the operating conditions of the available stenter machine, fabric cooling was conducted with an airflow velocity of V_a,1 = 0.5 m/s. It is thought that this velocity value is insufficient for the cooling performance. To prove this, as well as to observe how increasing the airflow velocity affects cooling performance and temperature distribution on the fabric surface, airflow velocities of V_a,2 = 1 m/s and V_a,3 = 2 m/s were determined. The effects of increasing airflow velocity can be seen in Figure 7c. Since all operating parameters identified in the CFD models reflect real operating conditions, based on airflow velocity simulations, the inverter centrifugal fan, located at the end of the stenter machine, should be driven at an airflow velocity of 2 m/s to deliver cooling air. Figure 12 clearly illustrates this. Following the cooling process, the temperature distributions on the fabric are a crucially important factor. From these contours, it can be concluded that an airflow velocity of V_a,3 = 2 m/s enables more homogeneous temperature distributions on the fabric surface.

3.5. Fabric Velocity (V_f) Study

In the stenter machine, fabric velocity is crucial because it significantly influences the drying and cooling process that the fabric undergoes. Excessively high fabric velocity can result in insufficient tension on the fabric, leading to distortion or stretching of its shape and size. On the other hand, if the fabric velocity is too low, the fabric may be exposed to excessive heat and tension, which can cause shrinkage or damage to the fabric.

Therefore, maintaining control over the fabric velocity in the stenter machine is crucial to ensure proper fabric cooling. For this reason, three fabric velocity values (0.25, 0.3, 0.35 m/s) were identified. The value of V_f = 0.3 m/s was used as an operating condition in the machine available at the company. Figure 7d illustrates the cooling performance obtained for different fabric velocities. Similar results were reported by Llanos et al. [21]. It can also be said that the value V_f = 0.3 m/s gives better performance among these fabric velocities in Figure 13.

4. Conclusions

In contrast to available studies, this study focused on the fabric-cooling process more than the fabric-drying process. The fabric-cooling process, which is commonly applied in the textile industry, was simulated by the CFD method while considering geometric and operating parameters.

• Industrial data obtained by experimental measurements validate the mesh quality, the fabric model supposed as a porous medium, fabric movement, heat and airflow mechanisms in the fabric cooling process in the stenter machine, and the turbulence model. In the prediction of industrial data by the CFD, the Realizable k-ε turbulence model provides good agreement.
• If the injector channel has a low porosity, it will perform better in a low-airflow supply, whereas if the injector channel has a high porosity, it will perform better in a high-airflow supply.
• In order to minimize vortices near corners and contact fabric and air directly, a horizontal position (α = 0°) will provide the best cooling performance.
• It is obviously seen that the current airflow velocity (V_a = 0.5 m/s) is too low and should be increased.
• The best cooling process and fabric temperature distribution are achieved when the fabric velocity is 0.3 m/s under certain constant parameters.

In future work, the detailed solid model with entire channels and centrifugal fan and thermal CFD analyses could be investigated to optimize operating and geometric parameters.