Materials
The test samples in Fig. 2 are selected from the breathable and abrasion-resistant zones of the warp-knitted Jacquard upper material. These samples can be utilized to obtain the Jacquard artisan diagrams related to their respective zones through the WKCAD system, developed by the Engineering Research Centre of the Ministry of Education, Jiangnan University, which provides a comprehensive interpretation of the Jacquard principle. As depicted in Table 1, process parameters for the jacquard organization part of the sample include jacquard offset signals denoted by H (indicating no shift) and T (indicating offset). By employing the technique of jacquard guide needle’s offset13,14,15,16, it becomes feasible to produce samples with thick and reticulated fabric structures. Using a yarn laying pattern of 1-1-1-0/1-1-1-2//, green represents thin tissue where there is no shift in guide needle position and no change in yarn arrangement; red represents thick tissue where, when on an even level within knitted fabric, corresponding guide needles are shifted to left before and after knitting needles resulting in a modified yarn laying pattern of 1-1-1-0/2-2-2-3//. On odd-numbered levels within fabric structure, relevant parts of yarn guide needles move leftward both ahead and behind knitting needles leading to a revised yarn laying pattern also as 1-1-1-0 /2–2 -2-3 //. Furthermore, the yarn laying pattern changes again into 2-2-2-1/2-2-2-3 //, causing partial loss contact between white Italian lattice elements forming mesh17.
The experimental samples are primarily composed of 120D/72F polyester DTY for the surface and bottom layers, 120D/192F polyester DTY for the jacquard weave, and polyester monofilament for the spacer layer.
Water vapor transmission test
To investigate the influence of microstructure on moisture permeability, four sample groups were prepared and named NM-1, NM-2, TQ-1, and TQ-2, respectively. As depicted in Fig. 2, the NM-1 group samples consist of a dense layer followed by a flat layer. The dense layer serves as the initial contact surface for water vapor. Conversely, the NM-2 group exhibits an inverse arrangement with the fabric’s flat layer being in direct contact with water vapor first. Subsequently, we have the TQ-1 and TQ-2 groups comprising both a breathable layer and a flat layer. In the former case, it is ensured that the breathable layer encounters water vapor initially while in contrast to this scenario lies the latter.18,19,20,23,28
Water vapor flow direction.
The experiment was conducted in accordance with GB / T12704-91 standards. Initially, the hygroscopic agent was placed in a preheated oven at 160 °C for three hours of drying treatment, as depicted in Fig. 3(a). Thirty minutes prior to completion, the test box shown in Fig. 3 (b) was opened beforehand and set to a temperature of 38 °C, relative humidity of 90%, and wind speed of 0.3 m/s to simulate the dynamic shoe cavity environment of sneakers.
After drying the desiccant, it is enclosed within a moisture-permeable cup to finalize the sample assembly, as depicted in Fig. 4(a) and Fig. 4(b). Subsequently, the composition is subjected to an experimental environment in a humidifier for 1 h and swiftly covered with the corresponding cup cover. Then, the composition is placed in a silica gel dryer at approximately 20 °C for 30 min, as illustrated in Fig. 3(c), to obtain the initial set of samples. The aforementioned test steps are repeated to acquire a second set of masses. By subtracting these two sets of data and applying Formula 1, the water vapor flux of the sample can be determined.
$$\:WVT=\frac{24\cdot\:\varDelta\:m}{S\cdot\:t}\:\:\:\:\:$$
(1)
\(\:WVT\): Moisture permeability, expressed as grams per square meter per day (g/m²/d). \(\:\varDelta\:m\): The discrepancy in weight measurements for the same test combination, g. \(\:S\): Sample test area, m2. \(\:t\): test duration, h.
CFD modeling
In this study, the powerful and user-friendly three-dimensional modeling software SOLIDWORKS was employed to generate the shoe material geometry, followed by utilizing ANSYS software for simulating fabric moisture permeability21,22.
Fabric modeling
As depicted in Fig. 3 (a), the warp-knitted Jacquard upper material comprises a surface layer, a bottom layer, and a spacer layer that connects the surface and bottom layers. Due to its distinct structure, the coil exhibits intricate interrelationships within the fabric. To enhance computational efficiency and ensure convergence of simulation results, simplification of the sample model is necessary; thus, we have made the following assumptions24,25.
The yarn in the sample model is considered to be a smooth and uniform solid with a circular cross-section, and the roughness of the gap between the yarn surface and the internal voids of the fiber bundle can be neglected.
- Each coil of the actual fabric will undergo varying degrees and directions of stretching by the extension line, resulting in diverse deformations. To enhance modeling efficiency, we assume that the sample is obtained from the same array of coils and extension lines.
- The surface layer of the warp-knitted jacquard shoe upper material is woven using multiple guide bars, each providing different knitting information. In order to alleviate computational burden, a simplified coil model will be employed for the same knitting needle, and representative structures will be created by combining multiple yarns.
- In practical production, the majority of shoe upper materials utilize polyester, which exhibits poor hygroscopicity as a raw material. Consequently, the absorption of water vapor by this raw material is disregarded when establishing the calculation model.
In the Solidworks modeling software, the coordinate system is initially established. Based on the loop height and loop width of the physical coil, a spline curve is utilized to depict a geometric figure that outlines the coil space curve. The resulting space curve is then placed separately in the sketch, and by employing scanning function, a smooth coil entity with circular cross-section is obtained. Subsequently, adjustments are made to both the coil and extension line according to the actual transverse and longitudinal density of the sample. Through permutation and combination techniques, single-layer fabric model parts are generated. It should be noted that both the diameter of the coil and ductile yarn measure 0.125 mm.
For instance, Fig. 5 (d) (e) illustrates detailed physical diagrams of both surface layer wear-resistant zone in samples as well as their corresponding model parts. Similarly, Fig. 5 (f) (g) showcases mesh detail diagrams for breathable zones along with their respective model parts. Additionally, Fig. 5 (h) (i) presents bottom detail diagrams for upper material alongside their corresponding model parts.
By assembling these aforementioned single-layer fabric models into assemblies as depicted in Fig. 5(b), we obtain a complete model of the Jacquard insole sheet fabric consistent with the actual object in Fig. 5(a), which can be further observed from the side view shown in Fig. 5(c).
The corresponding sample models were finally obtained, and they were respectively named NM-1-N, NM-2-N, TQ-1-N, and TQ-2-N.
Sample and its model establishment. (a) Take the sample of the wear-resistant area of the shoe upper material as an example, including the fabric surface layer, the spacer layer, and the fabric bottom layer. (b) Wear-resistant zone model of the upper material. (c) The side view shows the spacer layer of the wear-resistant zone model. (d) Thick tissue of the upper material surface. (e) Thick tissue model of the surface layer. (f) Mesh tissue of the upper material surface. (g) Mesh tissue model. (h) Thick tissue of the bottom layer of the upper material. (i) Thick tissue model of the bottom layer.
Grid processing
The ANSYS mesh module is utilized for fluid domain meshing in the CFD model, where the quality of the mesh significantly influences simulation results. In computational fluid dynamics, commonly employed discretization methods include finite difference, finite volume, and finite element methods. The finite volume method divides the calculation area into discrete finite volume elements and solves numerical calculations based on mass and momentum conservation equations. This method is particularly suitable for fluid mechanics applications. Grid division techniques encompass structured and unstructured grid divisions. Compared to structured grids, unstructured grids offer greater flexibility and allow for arbitrary distribution of grid nodes. They can effectively handle meshing challenges associated with irregular shapes and complex structures found in yarn models. Given the small size, intricate structure, and significant variation in yarn curvature within fabric models, this study employs an unstructured tetrahedral mesh to discretize the computational domain using the finite volume method (Fig. 6). A local section of the fabric model serves as the calculation object while establishing a complete calculation domain through Boolean operations outside of it. To ensure more accurate calculations, fluid viscosity cannot be neglected. Additionally, when individuals move wearing shoes, a relatively weak airflow layer forms on their surface; thus setting a boundary layer on the yarn’s surface becomes crucial as it affects water vapor transport (Fig. 6). Three layers are set with a growth rate of 1 to enhance calculation accuracy further by densifying the fluid domain mesh around the yarn26,27. The average side length of the grid is 2.7×10-4 m, and the maximum side length is 5.4×10-4 m.
Solver parameter
When the flow rate is very low, the fluid flows in distinct layers without mixing, resulting in laminar flow. As the flow rate increases significantly, the streamlines become indistinct and adjacent layers start to mix. This leads to the formation of small swirling vortices within the flow field, causing a perpendicular sub-velocity component to the original direction of flow. This phenomenon is referred to as turbulence. In our experimental setup, where gas flows at low speeds within the test chamber, we have selected a laminar flow model on the panel for modeling purposes. The transport rate of water vapor can be simulated using a component transport model that incorporates multiple fluids with similar phase and motion states. For setting material parameters, we have chosen a hybrid model wherein air and water vapor are considered as components with their respective ideal parameter values.
Continuous equations:
$$\frac{\partial{\rho}}{\partial{t}}+\nabla\cdot (\rho V) = 0$$
(2)
Momentum equation：
$$\frac{\partial \ {(\rho u)}}{\partial{t}}+\nabla \cdot (\rho u V) = -\frac{\partial{\rho}}{\partial{x}}+ \rho f_{x} $$
(3)
$$\frac{\partial \ {(\rho v)}}{\partial{t}}+\nabla \cdot (\rho v V) = -\frac{\partial{\rho}}{\partial{y}}+ \rho f_{y} $$
(4)
$$\frac{\partial \ {(\rho w)}}{\partial{t}}+\nabla \cdot (\rho w V) = -\frac{\partial{\rho}}{\partial{z}}+ \rho f_{z} $$
(5)
Energy equation:
$$\frac{\partial}{\partial{t}} [\rho \ (e + \frac{V^2}{2}) \ ]+\nabla \cdot [\rho \ (e + \frac{V^2}{2}) \ V ] = {\rho}{\dot{q}} – \frac{\partial \ (up)}{\partial x} – \frac{\partial \ (vp)}{\partial y} – \frac{\partial \ (wp)}{\partial z} + \rho f \cdot V $$
(6)
According to the experimental conditions, the initial temperature of the model in Fluent is set at 38 °C with a relative humidity of 90%. Based on these values, the mass fraction of water vapor is calculated to be 0.0375. During the boundary condition setup, it is necessary to repeatedly input parameters for water vapor mass fraction. The inlet boundary velocity is set at 0.3 m/s, while the outlet boundary is defined as pressure outlet. Additionally, the wall temperature is maintained at 38 °C before initiating the solution.
Extraction of fluid domain and meshing. (a) To shorten the calculation time and improve the calculation efficiency, several local structural models are obtained by cutting the fabric model. (b) According to the actual experimental conditions, the local structural geometric model is wrapped with a cuboid, and then the fabric is extracted by the Boolean operation to obtain the fluid calculation domain. (c) The computational domain is meshed by the mesh generation module of Ansys. The yarn surface is an important calculation point, and the mesh is more delicate. Due to the viscous characteristics of the fluid, it is necessary to establish a boundary layer for the fabric surface.