The study of knitted fabric thermal insulation using thermography and finite volume method

Abstract

The article concerns the widespread issue of thermal comfort; investigations into textiles and thermal insulation problems are presented. Materials that were tested include double-layer knitted fabrics with potential application in multi-layer garments addressed to a specific group of users. The investigated materials were constructed with the following raw materials: cotton, polypropylene, polyester, polyamide, bamboo, and viscose. The textiles with a comparable geometric structure and different composition were tested for their thermal insulation. In the experimental section the temperature gradients in specific constant ambient conditions using a thermal imaging camera were obtained. In the simulation section three-dimensional models of actual textiles were designed and the temperature gradients on the basis of performed simulations were calculated. Both measurements and simulations yielded comparable results and showed that the comparatively thick knitted fabrics’ thermal insulation strongly depends on the raw materials from which they were made and less on the parameters of the yarn.

Keywords

knitted fabric simulation heat transport phenomena thermal insulation modeling thermography finite volume method

Thermal comfort is the result of many factors related to the human body, climatic conditions, environment, and clothing. Clothing is a barrier that protects the body from the negative influence of external factors, and the impact of clothing on the process of heat exchange between the human body and the environment largely depends on the structure of the material—that is, the number and configuration of the individual layers of clothing, as well as the thermal insulation properties of the material from which the garment is made. Thermal properties are basic features that should be considered for any potential clothing user. Thus, the heat exchange between the user and the environment should be balanced to ensure comfortable conditions and prevent either hypothermia or hyperthermia.

Structural modeling of textiles is a tool that promotes enhanced understanding of the impact of morphology on physical properties. In addition, it can provide information on the critical parameters of materials that make up a particular type of knitted fabric, significantly influencing the selected physical properties of the designed product. Thermal properties are basic characteristics to consider with respect to the potential use of clothing.

Over the past few years, designing textile models to better understand the impact of morphology on thermal and mechanical properties has been the subject of many studies. With increasing computing power, accurate models that better address the construction of real materials and their physical properties can be developed.

Zhang et al.¹ focused on the numerical study of heat and moisture transfer in clothing assemblies, which is described by a multi-component and multiphase air–vapor–heat flow, with a moving interface. In the article, a splitting semi-implicit finite volume method was applied for a system of nonlinear parabolic equations, and an implicit Euler scheme was used for the interface equation. Wang et al.² presented a three-dimensional transient CFD simulation of heat and mass transfer in the flame manikin test of thermal protective clothing. The grid model used in that study, which was simulated from the Donghua Flame Manikin, had real dimensions that accurately formed the shape of a typical Chinese man. The solver and physical models were defined in the FLUENT system, and the CFD simulation of a naked flame manikin test was accomplished. Temperature and velocity fields on the manikin surface and in the chamber during the four-second flash fire combustion were obtained, providing acceptable predictions of the average heat flux distribution. Hang et al.³ presented a numerical study of heat and moisture transfer in three-dimensional clothing assemblies. Based on a multi-component and multiphase flow model, the study included heat/moisture convection and conduction/diffusion, as well as phase change (in the form of condensation/evaporation and vapor absorption by fiber). Degrave et al.⁴ presented an experimental set-up based on classical 1-D flow experiments in order to obtain data on fluid flow through a photocatalytic textile, and proposed a numerical model at the optical fiber scale using COMSOL Multiphysics to perform numerical simulations in a geometrical domain consisting of a representative volume element (RVE) of the photocatalytic textile with periodic boundary conditions. A good fit was found between the permeability of the fabric given by the numerical model and that obtained from experimental measurements, and was also in agreement with the value calculated from an experimental determination of the fabric porosity using a permeability model for fibrous media. The aim of Mert’s study⁵ was to investigate the effect of a heterogeneous vertical air gap with different configuration of folds (size and frequency) on dry heat loss using a heated cylinder. Result showed that the presence of folds in the garment led to an increased heat loss from the body in comparison to a homogeneous air gap of comparable size. Additionally, the size of folds did not have an influence on the dry heat loss. The outcomes from this study are useful for modeling of realistic dry heat loss through the clothing, and contribute to the improvement of design of protective and active sport garments. Zhu et al.⁶ investigated the resistance effects of the electric double layer (EDL) on the coupled heat and liquid moisture transfer in porous textiles. A series of computations were carried out to investigate the resistance effects of the EDL on the coupled heat and liquid moisture transfer in these fabrics. The predicted changes in temperature at the upper surface of the fabrics were compared with experimental measurements, and good agreement was observed between the two, indicating that the mathematical model was satisfactory with regard to the EDL. Jun et al.⁷ conducted a numerical study of the buoyancy-driven convection of a viscoelastic fluid saturated in an open-top porous square box under a constant heat flux boundary condition. The effects of the relaxation and retardation times on the onset of the oscillatory convection, the convection heat transfer rate, and the flow pattern transition were investigated. The aim of Neves’ study⁸ was to develop methodologies and experimental procedures to determine the textile parameters required for numerical approaches to heat and mass transfer through textiles. Privileging techniques usually available in textile/clothing laboratories and experimental approaches were defined, which allowed an estimation of all required parameters, while taking into consideration the presence of water in the fibers and, hence, the effect of fibers’ hygroscopic properties.

The aim of this article is associated with the problem of thermal comfort. In this article, studies on the problems of textiles thermal insulation are shown, which are a continuation of research carried out in earlier work.⁹ The subjects of this work are double-layer knitted fabrics with potential application in multi-layer garments addressed to a specific group of users, namely, newborns. The studied materials were constructed from the following raw materials: cotton, polypropylene, polyester, polyamide, bamboo, and viscose. Knitted fabrics with a comparable geometric structure and different composition were tested for their thermal insulation. In the experimental section, the temperature gradients in specific constant ambient conditions were investigated using a thermal imaging camera. The main goal of this paper was to design an optimal model of textiles to carry out theoretical research on their thermal insulation, where results can be confirmed by tests on actual materials. In the simulation section, three-dimensional (3-D) models of the textiles, constructed in SolidWorks 2014 software, of varying yarn mapping accuracy, were designed, and the temperature gradients were calculated on the basis of performed simulations.

Materials and methods

The subject of this research was a set of 10 double-layer knitted fabrics (an example image of their surface is presented in Figure 1). Each knitted fabric was composed of two layers connected to a single polyamide thread. The layers had comparable structure (single jersey), similar thickness, and comparable yarn length in single stitch and yarn diameter.

Figure 1.

Knitted fabric image.

Each layer of the textiles was made of one or two raw materials, including cotton, bamboo, polypropylene, polyester, polyamide, and viscose. In Table 1, the characteristics of the investigated knitted fabric were presented.

Table 1.

Characteristics of investigated materials

No.	Knitted fabric	Knitted fabric thickness^a (mm)	Mass per unit area^b (g·m⁻²)	Layer thickness^a (mm)	Yarn diameter^d (mm)	Yarn linear density^c (tex)	Yarn twist^d (m⁻¹)	Yarn length in single stitch^d (mm)	Fiber diameter^d (μm)	Fiber number^d	Surface area of yarn in single stitch^d (mm²)
1	cotton cotton	1.34 ± 0.01	242 ± 16	0.70 ± 0.01 0.64 ± 0.01	0.25 ± 0.01 0.26 ± 0.01	20 20	770 707	3.19 ± 0.05 3.20 ± 0.05	15.2 ± 0.2 15.1 ± 0.3	122 ± 5 122 ± 5	18 ± 1 19 ± 1
2	cotton	1.40 ± 0.01	206 ± 14	0.73 ± 0.01	0.25 ± 0.01	20	636	3.19 ± 0.05	15.3 ± .0.2	122 ± 5	18 ± 1
	PP			0.67 ± 0.01	0.27 ± 0.01	8	0	3.01 ± 0.05	27.4 ± 0.3	109 ± 5	21 ± 2
3	cotton	1.44 ± 0.01	227 ± 15	0.75 ± 0.01	0.26 ± 0.01	20	855	3.16 ± 0.05	15.1 ± .0.2	122 ± 5	19 ± 1
	PET			0.69 ± 0.01	0.30 ± 0.01	15	0	3.12 ± 0.05	26.2 ± 0.1	96 ± 4	20 ± 1
4	cotton	1.30 ± 0.01	182 ± 12	0.68 ± 0.01	0.25 ± 0.01	20	785	3.20 ± 0.05	15.2 ± 0.2	122 ± 5	18 ± 2
	PA			0.62 ± 0.01	0.28 ± 0.01	14	0	3.14 ± 0.05	23.4 ± 0.3	102 ± 5	22 ± 1
5	bamboo	1.39 ± 0.01	236 ± 16	0.72 ± 0.01	0.22 ± 0.01	20	912	3.17 ± 0.05	24.4 ± 0.2	86 ± 4	17 ± 2
	PP			0.67 ± 0.01	0.27 ± 0.01	8	0	3.00 ± 0.05	27.3 ± 0.3	109 ± 5	21 ± 2
6	bamboo	1.36 ± 0.01	222 ± 15	0.71 ± 0.01	0.22 ± 0.01	20	912	3.16 ± 0.05	24.3 ± 0.2	86 ± 4	17 ± 1
	PET			0.65 ± 0.01	0.30 ± 0.01	15	0	3.11 ± 0.05	26.2 ± 0.2	96 ± 5	20 ± 2
7	bamboo	1.16 ± 0.01	195 ± 13	0.60 ± 0.01	0.22 ± 0.01	20	912	3.15 ± 0.05	24.3 ± 0.2	86 ± 4	17 ± 1
	PA			0.56 ± 0.01	0.28 ± 0.01	14	0	3.14 ± 0.05	23.1 ± 0.3	102 ± 5	22 ± 3
8	viscose	1.38 ± 0.01	236 ± 16	0.72 ± 0.01	0.22 ± 0.01	20	778	3.09 ± 0.05	29.4 ± 0.2	81 ± 4	15 ± 1
	PP			0.66 ± 0.01	0.27 ± 0.01	8	0	3.03 ± 0.05	27.1 ± 0.1	109 ± 5	21 ± 2
9	viscose	1.25 ± 0.01	221 ± 15	0.65 ± 0.01	0.22 ± 0.01	20	778	3.10 ± 0.05	29.3 ± 0.2	81 ± 4	15 ± 2
	PET			0.60 ± 0.01	0.30 ± 0.01	15	0	3.14 ± 0.05	26.2 ± 0.2	96 ± 5	20 ± 2
10	viscose	1.19 ± 0.01	238 ± 16	0.62 ± 0.01	0.22 ± 0.01	20	778	3.11 ± 0.05	29.4 ± 0.2	81 ± 4	15 ± 2
	viscose			0.57 ± 0.01	0.21 ± 0.01	20	778	3.12 ± 0.05	29.3 ± 0.2	81 ± 4	15 ± 2

Obtained according to EN ISO 5084:1996.

Obtained according to EN 12127:2000.

Obtained according to EN ISO 2060:1997.

Obtained according to our and own methodology, as described in Experimental study below.

The aim of this study was to estimate the thermal insulation of textiles in conditions comparable to those in a climatic chamber, using the so-called model of human skin, during the thermal resistance calculation of textiles (air temperature, T_air = 20℃, relative humidity, φ_air = 65%).

Studies of knitted thermal insulation were divided into two parts: experimental and simulation. Experimental studies were carried out on the actual material using thermal imaging. In the simulation studies, three-dimensional geometric models were created, and simulations of energy transport phenomena were performed. Both experimental and simulation investigations were performed in steady state.

Experimental study

To assess the thermal insulation, knitted fabrics were placed in a room (Great Climatic Chamber made by Weiss Technik, Germany) with a constant air temperature (T_air = 20℃ ± 0.1℃) and constant humidity (φ_air = 65% ± 1%) on a flat plate (Measurement Technology North West, USA) with a constant temperature (T_plate = 35℃ ± 0.1℃). In accordance with the construction of the newly designed clothing, the bottom layer of a double layer knitted fabric was made of chemical fibers (PP, PET, PA) or cotton and viscose while the top layer was made of cotton, bamboo, or viscose. Using a thermal imaging camera (FLIR SC5000 model, USA) and included software (Altair–Thermal Image Analysis Software), the minimum temperature of the material—that is, the temperature on the top surface (facing the environment) of the knitted fabric—was measured. With regard to the maximum temperature of the material—that is, the temperature on the bottom surface (adjacent to, and in thermal equilibrium with, the plate) of the knitted fabric—a temperature gradient in the direction perpendicular to the surface of the fabric was calculated. The temperature measurement was performed for samples with an area of approximately 25 cm², but the real sample size was larger (about 50 cm²) in order to reduce the impact of boundary conditions.

Measurements of every material were carried out after reaching a steady state (about 10 minutes). Measurement errors in the temperature resulting from the thermal imaging camera were ±1℃. The scheme of the experiment is presented in Figure 2.

Figure 2.

Scheme of thermal imaging measurement.

Simulation study

The main aim in this portion of the work was to create a three-dimensional model of the tested knitted fabrics as potential components for multi-layer garments that demonstrate thermal balance between the user and the environment. Two 3-D models of knitted fabrics were developed in SolidWorks 2014 software based on stereoscopic optical microscope images (Figure 3). In the first approach, the developed model (the so-called mono-fiber model) did not take into account individual fibers (i.e. the yarn was treated as a single-component, continuous object). For each knitted fabric a separate mono-fiber model was created, taking into account the following different physical parameters of the textiles: (1) knitted fabric thickness, (2) yarn length in single stitch, and (3) yarn diameter (equivalent diameter, since the actual yarns did not have a circular cross-section). In the second approach, to better reproduce the knitted fabric’s thermal properties, a new model was created (the so-called multi-fiber model). This model took into account the same three physical parameters of the textiles from the mono-fiber model, but it also mapped the internal structure of the yarn, including fiber shape: (4) fiber length in single stitch, (5) fiber diameter, (6) fiber number, (7) specific surface area of yarn and (8) yarn twist. The fiber length in single stitch was approximately equal to the yarn length because the twist per stitch length (approximately 3 mm) did not exceed one. In both models for each textile, knitted fabric thickness, layer thickness, yarn diameter, and yarn length in single stitch were the same (all according to Table 1), and did not include the single polyamide thread connecting the two layers due to its negligible mass compared to the mass of the knitted fabric, and its small influence on the thermal phenomena occurring in the fabric.

Figure 3.

Mono-fiber model (top) and multi-fiber model (bottom) made on the basis of stereoscopic optical microscope images.

Average values of the following physical parameters (Table 1) were experimentally measured according to relevant standards: knitted fabric thickness, layer thickness (EN ISO 5084:1996), and mass per unit area (EN 12127:2000). Yarn twist was calculated based on the knowledge of values, including the linear density of the yarn and the metric twist factor, α_m. The yarn equivalent diameter and yarn length in single stitch were estimated based on stereoscopic optical microscope images (fiber diameter was measured based on scanning electron microscope images) using Image J software, and were mapped into the design of the 3-D models. The specific surface area of the yarn was calculated on the basis of knowledge of fiber number. In both models, the circular cross-section of the yarn, as well as the circular cross-section of the fiber in the multi-fiber model, was assumed. In the case of cotton fibers the equivalent diameter was used because of its cross-section (the cross-section of the other chemical fibers was circular).

The first stage in designing the model was to create a 2-D sketch of the axis of a single stitch in the plane using Non-Uniform Rational B-Spline (NURBS) curves. The shape of the curve was determined by the average sizes of the stitch using real material (e.g. cotton): height = 1.10 mm and width = 0.91 mm (Figure 4(a)).

Figure 4.

Stages of designing the 3-D multi-fiber model of a single stitch (the diameter of the fibers was intentionally increased in relation to the real sizes (Table 1) in order to improve readability of the scheme).

The next step was to construct a sketch describing the profile of the stitch in a plane perpendicular to the previous one (Figure 4(b)). Adding the projection operation of the first sketch to the profile, a 3-D axis of the stitch was obtained (Figure 4(c)). The next step of the design was to prepare a cross-sectional sketch of yarn built of individual fibers (Figure 4(d)). The final shape of the stitch was obtained using a swept boss/base operation performed on the objects that were created in the preceding two steps (Figure 4(e)).

Equations describing the simulation of heat transfer

Flow simulation solves the Navier–Stokes equations, which are formulations using mass, momentum, and energy conservation laws for fluid flows. The equations are supplemented by fluid state equations defining the nature of the fluid, and by empirical dependencies of fluid density, viscosity, and thermal conductivity on temperature.¹⁰ The system of Navier–Stokes equations is supplemented by definitions of thermophysical properties and state equations for the fluids. Flow simulation models gas and liquid flows with density, viscosity, thermal conductivity, specific heat, and species diffusivity as functions of pressure, temperature, and species concentrations in fluid mixtures. Equilibrium volume condensation of water from steam can also be taken into account when simulating steam flows.

Knitted fabric is a complex structure of fibers and void spaces between fibers filled by fluid, such as air or liquid. Heat is transported through the textile structure through both monofilaments (solid body) and fluids (fluid media), with simultaneous exchange between these environments. Heat transfer in fluids is expressed by the following conservation equation

\frac{\partial}{\partial t} [ρ (h + \frac{u^{2}}{2})] + \frac{\partial}{\partial x i} [ρ u i (h + \frac{u^{2}}{2})] = \frac{\partial}{\partial x i} [u j (τ ij + τ_{ij}^{R}) + q i] + \frac{\partial p}{\partial t} - τ_{ij}^{R} \frac{\partial u i}{\partial x j} + ρ ɛ + S i u i + Q H

(1)

where S_i = S_i^porous+ S_i^gravity+ S_i^rotation is the mass-distributed external force per unit mass due to porous media resistance (S_i^porous), buoyancy (S_i^gravity= –ρg_i), and the coordinate system rotation (S_i^rotation). The subscripts are used to denote summation over the three coordinate directions.

The heat flux density is defined by the following equation

q i = (\frac{μ}{\Pr} + \frac{μ t}{σ c}) \frac{\partial h}{\partial x i}; i = 1, 2, 3

(2)

where

μ t = \frac{C μ ρ k^{2}}{ɛ}

(3)

The constant C_μ is determined according to SolidWorks¹⁰ as equal to C_μ = 0·09, whereas σ_c = 0.9. The equations describe both laminar and turbulent flows. Moreover, transitions from one case to another and back are possible. The parameters k and μ_t are zero for pure laminar flows. The phenomenon of anisotropic heat conductivity in solid media is described by the following correlation

\frac{\partial (ρ e)}{\partial t} = \frac{\partial}{\partial x i} (λ i \frac{\partial T}{\partial x i}) + Q H

(4)

where e = cT. It is assumed that the heat conductivity tensor is diagonal to the considered coordinate system and that the heat transport within polypropylene is direction-independent—that is, we introduce an isotropic medium, and can denote λ₁ = λ₂ = λ₃ = λ. The energy exchange between the fluid and solid media is calculated via the heat flux in the direction normal to the solid/fluid interface, taking into account the solid surface temperature and the fluid boundary layer characteristics, if necessary.

Flow simulation enables the simulation of thermal radiation based on a so-called discrete transfer model. The main principle of this can be described as follows: the radiation leaving the surface element in a certain range of solid angles can be approximated by a single ray. The radiation heat is transferred along a series of rays emanating from the radiative surfaces only. Rays are then traced as they traverse through the fluid and transparent solid bodies until they hit another radiative surface. This approach, usually called “ray tracing,” allows “exchange factors” to be calculated as fractions of the total radiation energy emitted from one of the radiative surfaces that is intercepted by other radiative surfaces (this quantity is a discrete analog of view factors). If “exchange factors” between radiative surface mesh elements are calculated at the initial stage of the solver, then it allows a matrix of coefficients to form for a system of linear equations which can be solved on each iteration. The surfaces that lose heat by radiation can emit, absorb, and reflect solar or thermal radiation. The thermal radiation determined by the surface or radiation source is expressed as a sum of material radiation (described by the surface emissivity and a prescribed area of radiation) and incoming radiative transfer. This problem is defined by the following equation⁹

Q_{T}^{out} = ɛ \cdot σ \cdot T^{4} \cdot A + (1 - ɛ) \cdot Q_{T}^{in}

(5)

The main result of the radiation heat transfer calculation is the solid’s surface or internal temperature. However, these temperatures are also affected by heat conduction in solids and solid/fluid heat transfer. To see the results of the radiation heat transfer calculation only, the user can view the leaving radiant flux over the selected radiative surfaces at surface plots. Users can also see the maximum, minimum, and average values of these parameters.

Figure 5.

3-D models of double layer knitted fabric: mono-fiber model (top) and multi-fiber model (bottom). In the multi-fiber model the diameter of the fibers was intentionally increased in relation to the real sizes (Table 1) in order to improve the readability of the scheme.

Simulations of thermal insulation

Simulations were determined with the SolidWorks Flow Simulation module using the finite volume method. The double-layer knitted fabric models were situated on the top surface of a rectangular plate that served as a heater. Both elements were positioned on the bottom of a rectangular computational domain, with a volume equal to 4.8·10⁻⁹ m³ (4.0·10⁻³× 1.0·10⁻³ × 1.2·10⁻³) m that was filled with air (Figure 6). To eliminate the effects of asymmetric boundary conditions, settings were applied to imitate an infinite layer of fabric propagating outside of the domain in all three directions. The initial conditions of the model were assumed as follows: T_plate = 35℃, T_{knitted fabric} = 20℃, T_air = 20℃, p_air = 1013.25 hPa and ϕ_air = 60 %.

Figure 6.

3-D model of double layer knitted fabric positioned on a heating plate located on the bottom of a computational domain of size (4.0x1.0x1.2)·10⁻³ m.

The computational domain was divided into approximately 60,000 cells (multi-fiber model) and approximately 25,000 cells (mono-fiber model) of three types (fluid cells, solid cells, and partial cells). Fluid cells were filled with air, while solid cells had the material characteristics of the knitted fabric, the heating plate, or both the knitted fabric and the heating plate. The partial cells contained both solid material and air. The number of cells was dependent on the number, shape, and size of the elements making up the model of the particular knitted fabric. A much larger number of cells in the multi-fiber model in comparison to the mono-fiber model resulted from the mapping the individual fibers. In the multi-fiber model the largest number of cells were partial cells (approximately 48%), while the fluid cells represented about 44% and solid cells about 8%. The mono-fiber model consisted of partial cells (approximately 45%) while the fluid cells were about 43% and solid cells about 12%. In Table 2 accurate information about cell numbers in each model in relation to the geometrical parameters of the yarns and fibers are presented. For both models (mono- and multi-fiber) several simulation were conducted for each of the ten knitted fabrics to verify the dependence between accuracy of the results and finite volume mesh density. Further increasing the number of cells did not significantly affect the accuracy of all calculated parameters (presented in Table 4).

Table 2.

Cell number in each model in relation to the geometrical parameters of the yarns and fibers

No	knitted Knitted fabric	yarn Yarn diameter in both models ([mm)]	fiber Fiber number in the multi-fiber model	fiber Fiber diameter in the multi-fiber model ([mm)]	number Number of cells
					monoMono-fiber model				multiMulti-fiber model
					partialPartial	fluidFluid	solidSolid	allAll	partialPartial	fluidFluid	solidSolid	allAll
1	cottonCotton	0.25	122	15.2	12660	12098	3376	28134	31396	28780	5233	65408
1	cottonCotton	0.26	122	15.1	12660	12098	3376	28134	31396	28780	5233	65408
2	cottonCotton	0.25	122	15.3	11962	11430	3190	26582	29595	27129	4933	61657
2	PP	0.27	109	27.4	11962	11430	3190	26582	29595	27129	4933	61657
3	cottonCotton	0.26	122	15.1	11713	11193	3124	26030	27795	25478	4632	57905
3	PET	0.30	96	26.2	11713	11193	3124	26030	27795	25478	4632	57905
4	cottonCotton	0.25	122	15.2	12036	11501	3210	26746	28626	26240	4771	59637
4	PA	0.28	102	23.4	12036	11501	3210	26746	28626	26240	4771	59637
5	bambooBamboo	0.22	86	24.4	10478	10012	2794	23284	28209	25858	4701	58769
5	PP	0.27	109	27.3	10478	10012	2794	23284	28209	25858	4701	58769
6	bambooBamboo	0.22	86	24.3	9779	9344	2608	21731	28088	25748	4681	58517
6	PET	0.30	96	26.2	9779	9344	2608	21731	28088	25748	4681	58517
7	bambooBamboo	0.22	86	24.3	10101	9653	2694	22448	28919	26509	4820	60249
7	PA	0.28	102	23.1	10101	9653	2694	22448	28919	26509	4820	60249
8	viscoseViscose	0.22	81	29.4	10209	9755	2722	22687	29196	26763	4866	60826
8	PP	0.27	109	27.1	10209	9755	2722	22687	29196	26763	4866	60826
9	viscoseViscose	0.22	81	29.3	9960	9518	2656	22134	28356	25993	4726	59075
9	PET	0.30	96	26.2	9960	9518	2656	22134	28356	25993	4726	59075
10	viscoseViscose	0.22	81	29.4	9604	9178	2561	21343	26278	24088	4380	54746
10	Viscose	0.21	81	29.3	9604	9178	2561	21343	26278	24088	4380	54746

Table 3.

Physical parameters applied in simulations

Physical parameter	Cotton	PA	PP	Bamboo	Viscose	PET
Density (kg·m⁻³)	1550	1230	940	1400	1520	1370
Specific heat (J·kg⁻¹·℃⁻¹)	1330	2050	1720	1300	1470	1380
Thermal conductivity W·m⁻¹·℃⁻¹)	0.072	0.220	0.260	0.042	0.060	0.084
Emissivity (for black body = 1)	0.78	0.69	0.97	0.87	0.80	0.70

Table 4.

Physical parameters calculated in simulations

No.	Knitted fabric	Mono-fiber model						Multi-fiber model
No.	Knitted fabric	T (℃)	ΔT (℃)	HF (W·m⁻²)	ΔHF (W·m⁻²)	LRF (W·m⁻²)	ΔLRF (W·m⁻²)	T (℃)	ΔT (℃)	HF (W·m⁻²)	ΔHF (W·m⁻²)	LRF (W·m⁻²)	ΔLRF (W·m⁻²)
1	Cotton	32.34	0.02	365	45	539	2	31.79	0.02	272	41	543.12	0.09
	Cotton	35.00	0	6698	38	584	2	35.00	0	6578	27	638.23	0.01
2	Cotton	32.67	0.02	318	85	507	2	31.99	0.02	395	77	503.43	0.6
	PP	35.00	0	6283	46	688	1	35.00	0	6438	41	812.41	0.05
3	Cotton	32.48	0.01	428	69	544.03	0.05	31.88	0.02	271	65	548	2
	PET	35.00	0	6595	19	572.73	0.03	35.00	0	6476	18	607.85	0.11
4	Cotton	32.83	0.01	291	52	594.6	0.2	32.20	0.01	381	92	544.1	0.7
	PA	35.00	0	6517	38	610.84	0.03	35.00	0	6474	23	595.52	0.03
5	Bamboo	32.35	0.02	270	54	504.74	0.13	31.85	0.02	283	52	502.2	0.6
	PP	35.00	0	6690	35	550.20	0.02	35.00	0	6507	50	561.08	0.04
6	Bamboo	32.19	0.02	220	27	539	1	31.76	0.02	307	69	542	2
	PET	35.00	0	6555	67	560.1	0.7	35.00	0	6479	64	565.66	0.04
7	Bamboo	32.70	0.01	402	50	552.19	0.03	32.07	0.02	405	53	544.3	0.5
	PA	35.00	0	6329	36	641.39	0.19	35.00	0	6293	57	587.09	0.05
8	Viscose	32.56	0.02	345	51	509	2	31.93	0.02	404	86	501	1
	PP	35.00	0	6401	28	616	2	35.00	0	6369	36	624.15	0.05
9	Viscose	32.40	0.01	282	63	569.8	0.2	31.85	0.02	285	47	538.8	0.8
	PET	35.00	0	6771	95	635.7	0.2	35.00	0	6330	63	599.51	0.03
10	Viscose	32.15	0.02	383	49	521	1	31.65	0.02	248	30	523	1
	Viscose	35.00	0	6441	50	570.8	0.6	35.00	0	6485	29	618.02	0.11

In Table 3, the physical parameters of raw materials applied in the 3-D geometric models of knitted fabrics are presented. Emissivity was obtained experimentally according to the following procedure. Before starting the investigations, the results of which are presented in the article, the following calibration of the infrared camera to select the right emissivity for each raw material (cotton, bamboo, viscose, PET, PP, PA) was performed: (1) layers were separated from each other and placed in an air conditioned chamber at a constant temperature of 20℃ and relative humidity 65%; and (2) after 24 hours (when the materials and the air were in thermal equilibrium) temperature measurements for each raw material were performed (the emissivity of raw material was chosen so that the camera indicated the real temperature of the layer: 20℃). The above two steps were repeated for temperatures of 30℃ and 40℃ (always with the relative humidity at 65%). The three other parameters—specific heat, thermal conductivity, and density—of all raw materials were taken from the literature.^11–14

Results and comments

The SolidWorks Flow Simulation module allows for modeling of the following five physical phenomena: (1) heat conduction in a solid material (i.e. fibers of the knitted structure); (2) convection heat transfer from solid surfaces; (3) radiation heat transfer from solid surfaces; (4) gravitational effects influencing air molecule transport within void spaces; and (5) laminar and turbulent fluid flow within void spaces. The software simultaneously calculates the parameters of all selected thermodynamic processes within the assumed structural computational domain. Based on the output results, the software creates 3-D color visualizations on the surfaces of the entire model or its selected parts. For the previously mentioned models of knitted fabrics, the distribution of temperature (Figure 7(b) and (c)), heat conductivity (Figure 8(a) and (b)) and heat radiation, as the most effective method of heat loss (Figure 8(c) and (d)), were determined. The software does not permit specification and illustration of energy losses by convection only, despite the fact that this phenomenon is taken into account. In Figure 7(a), sample thermal images obtained during the measurement of the temperature distribution of both the top surface of knitted fabric and on the surface of the simulated 3-D models are presented.

Figure 7.

The sample thermal image obtained by measurement of temperature distribution on the top surface of knitted fabric (a) and temperature distribution on surface 3-D models obtained from simulations: for mono-fiber model (b) and multi-fiber model (c). (In the multi-fiber model the diameter of the fibers is intentionally increased in relation to the real sizes (Table 1) in order to improve readability of the pictures). Different palettes of color and ranges of temperatures were applied as a result of different software applications (SolidWorks and Altair–Thermal Image Analysis Software).

Figure 8.

The sample of distributions of the heat flux in the knitted fabric: (a) mono-fiber model; (b) multi-fiber model), and the leaving radiant flux: (c) mono-fiber model; (d) multi-fiber model). (In multi-fiber model the diameter of the fibers is intentionally increased in relation to the real sizes (Table 1) in order to improve readability of the pictures).

As a result of the simulations, the following parameters of the knitted fabrics were also calculated (Table 4):

the minimum temperature of the material—that is, the temperature on the top surface of the knitted fabric, which faces the environment;

the maximum temperature of the material—that is, the temperature on the bottom surface of the knitted fabric, which is adjacent to and in thermal equilibrium with the plate (this was assumed to be equal 35℃ and was not calculated—calculation error equal to 0);

the average heat flux (HF, W·m⁻²) on the surface of top and bottom layer of knitted fabric;

the average leaving radiant flux (LRF, W·m⁻²) on the surface of top and bottom layer of knitted fabric.

The heat flux and leaving radiant flux results are presented in the graph in Figure 9. Both in Table 4 and Figure 9, calculation errors were present (ΔT, ΔHF, ΔLRF), resulting from the geometry of the model and the finite volume mesh density.

Figure 9.

Simulation results of heat flux and leaving radiant flux for top and bottom layers of knitted fabrics (solid symbols indicate mono-fiber model, open symbols indicate multi-fiber model). Broken curves guide the eye.

Simulations carried out on the mono-fiber model and multi-fiber model for the heat flux and the leaving radiant flux showed comparable results. Accordingly, all knitted fabrics lost a lot of energy as a result of the thermal conductivity of the bottom layer (e.g. heat flow in the range of 6283–6690 W·m⁻² for the mono-fiber model and 6293–6578 W·m⁻² for the multi-fiber model), while less energy was lost as a result of the thermal conductivity of the upper layer (e.g. heat flow in the range of 220–428 W·m⁻² for the mono-fiber model and 248–405 W·m⁻² for the multi-fiber model). Energy loss by radiation of both layers for every knitted fabric was between the above mentioned ranges. For most studied knitted fabrics, a similar trend showing the influence of raw material composition on heat conduction and radiation losses for both applied models was found. In regard to the heat flux results obtained, the biggest difference in the models between the two materials was observed in viscose/PET (6%) and bamboo/PP (3%) for the bottom layer and cotton/PET (37%) and viscose/viscose (35%) for the top layer. For the calculated leaving radiant flux outcomes, the biggest differences in the models between two materials was observed in cotton/PP for both the bottom layer (15%) and the top layer (2%). Considerable differences in these models probably result from of the inclusion of air between the individual fibers in the multi-fiber model. The amount of air is different for each knitted fabric because of differences in fiber diameter, fiber number, surface area of yarn in single stitch, and yarn twist. The size of individual fibers affects the surface area through which heat transfer takes place as a result of both conduction and radiation. Moreover, yarns are made of layers of different knitted fabrics characterized by different twist.

The outcomes obtained from measurements using a thermal imaging camera showed a correlation between knitted fabric thermal insulation and the raw materials from which they were made. The comparison of the experimental and simulation data is presented in Figure 10 and Table 5. The largest temperature gradient was observed for three textiles: viscose/viscose, cotton/cotton, and cotton/PET, while the smallest temperature gradient was observed for cotton/PA and bamboo/PA. The smaller thermal gradient of the last two knitted fabrics is probably a consequence of the presence of a polyamide, which is characterized by a much greater thermal conductivity. The simulation results showed a similar relationship between the thermal gradient and knitted fabrics composition. In the mono-fiber model, lower values were obtained (approximately 2℃) than in the experimental results for all of the materials. This difference was probably a consequence of the above-mentioned simplification of the yarn construction: the model does not take into account voids between the single fibers filled with air, which is a much better thermal insulator than the raw materials of the textiles. The application of the multi-fiber model resulted in better compliance with experimental results, and differences were within the range of measurement error of the thermal imaging camera (i.e. less than 1℃). In the near future, the multi-fiber model will be further developed to improve the effective method of designing textiles with desired thermal insulation properties.

Figure 10.

Experimental and calculated values of thermal gradient for studied knitted fabrics.

Table 5.

Experimental and simulation results for temperature gradient in studied knitted fabrics

No	Knitted fabric	Experiment		Mono-fiber model		Multi-fiber model
No	Knitted fabric	▿T (℃)	Δ▿T (℃)	▿T (℃)	Δ▿T (℃)	▿T (℃)	Δ▿T (℃)
1	Cotton Cotton	4.12	1	2.66	0.02	3.21	0.02
2	Cotton PP	3.55	1	2.33	0.02	3.01	0.02
3	Cotton PET	4.09	1	2.52	0.01	3.12	0.02
4	Cotton PA	3.21	1	2.17	0.01	2.80	0.01
5	Bamboo PP	3.64	1	2.65	0.02	3.15	0.02
6	Bamboo PET	3.86	1	2.81	0.02	3.24	0.02
7	Bamboo PA	3.63	1	2.30	0.01	2.93	0.02
8	Viscose PP	3.62	1	2.44	0.02	3.07	0.02
9	Viscose PET	3.80	1	2.60	0.01	3.15	0.02
10	Viscose Viscose	4.17	1	2.85	0.01	3.35	0.02

Conclusions

The experimental outcomes and calculation simulations performed using both the mono-fiber and multi-fiber models showed clear relation between the thermal insulation of textiles and the thermal properties of their raw materials. The model that took into account the internal structure of the yarn gave gradient temperature values comparable to those obtained by the thermal imaging camera. Moreover, as can be seen from Figure 10, the curves connecting points for both model are almost identical in shape, which may indicate that the key parameters of the models were the following properties of the raw materials—density, specific heat, thermal conductivity, and emissivity—while of less importance were parameters describing yarn structure—yarn twist, fiber number, fiber diameter, and surface area of yarn. Simulation outcomes showed that applied software can be an effective tool to complement experimentation on real materials, and can be used to predict thermal properties of newly-designed textiles.

Footnotes

Acknowledgments

We would like to thank Professor Krzysztof Kowalski (Department of Knitting Technology, Lodz University of Technology, Lodz, Poland) for preparing knitted fabrics for research.

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: These studies were supported by the National Science Centre (Poland) under the research project No. UMO-2011/03/B/ST8/06275 “Optimization of the structure of protective clothing for prematurely born infants with the use of original tools aiding the designing process”.

Nomenclature

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