Numerical Investigation of Heat Transfer in Garment Air Gap

In the present work, heat transfer through clothing involving air gap is analyzed and temperature distribution on clothing surface is predicted. A standard female body and a type of fitting apparel are chosen here. The surface of the female body is established by the CLO 3D virtual try-on programs. Then, the girth feature curves were extracted by adding distance ease to the editable feature curves of the initial 3D mannequin [11]. Basic dimensions of body and clothing are given in Table 1.

The unstructured grids are generated with fine mesh near walls by the commercial mesh generation software ICEM-CFD 17.0. For the symmetry of the human body, only half-geometry meshes are generated in this study to reduce computation load and improve precision. 3D garment and mesh are shown in Figure 2.

Figure 2

This study focused on the distance ease in the horizontal direction, and four characteristic landmarks (Figure 3(a)) were selected to measure the distance ease and airflow contours. The virtual model of a clothed mannequin was simulated by commercial software Geomagic Qualify to obtain the 3D air gap distance, namely distance ease (Figure 3(b)). The distance ease is below 5 mm at the location of the shoulder, right side bust, side waist, and side thigh. The ease allowance value is between 5 mm and 15 mm at the chest, waist, and abdomen.

Figure 3

Coupled Reynolds-averaged Navier–Stokes (RANS) equations [12] with radiative transfer equations (RTE) were used to simulate heat transfer and fluid flow in a cloth-air-skin system. Three-dimensional continuity, momentum, and energy equations with the realizable k-ɛ model [13, 14] in tensor forms were considered for modeling heat transfer and fluid flow in the air gap. The divergence of the radiative heat flux can be obtained using: (1) ∇⋅qR=κ(4πIb−G) \nabla \cdot {q_R} = \kappa \left( {4\pi {I_b} - G} \right) where I_b is the blackbody intensity, is defined as: (2) Ib=σT4/π {I_b} = \sigma {T^4}/\pi

G is the irradiation, is expressed as: (3) G=∫Ω=04πI(Ω)dΩ G = \int_{\Omega = 0}^{4\pi } {I\left( \Omega \right)d\Omega }

The solid angle Ω and radiation intensity I obtained by solving radiative transfer equations. The particles absorbing, emitting, and scattering are considered by the discrete ordinate radiation model (DORM).

The radiative transfer equations (RTE), used to calculate the radiation heat flux inside the air gap, are solved using the DORM, which is expressed as [15]: (4) ∇(Is^)=κn2σT4π+Ip−(κ+κp+γ+γp)I(r,s^)+γ4π∫Ω=04πI(r,s^′)Φ(r,s^′,s^)dΩ \nabla \left( {I\hat s} \right) = \kappa {{{n^2}\sigma {T^4}} \over \pi } + {I_p} - \left( {\kappa + {\kappa _p} + \gamma + {\gamma _p}} \right)I\left( {r,\hat s} \right) + {\gamma \over {4\pi }}\int_{\Omega={0}} ^{4\pi } {I\left( {r,\hat s'} \right)\Phi \left( {r,\hat s',\hat s} \right)} d\Omega where I_p is the equivalent emission of the particles, κ_p, γ_p is the equivalent absorption coefficient and scattering coefficient. They can be expressed as: (5) Ip=∑i=1nεpiApiσTpi4πNi,κp=∑i=1nεpiApiNi,γp=∑i=1n(1−αpi)(1−εpi)ApiNi,Api=πdi24 {I_p} = \sum\limits_{i = 1}^n {{\varepsilon _{pi}}{A_{pi}}{{\sigma T_{pi}^4} \over \pi }{N_i},{\kappa _p} = \sum\limits_{i = 1}^n {{\varepsilon _{pi}}{A_{pi}}{N_i},{\gamma _p} = \sum\limits_{i = 1}^n {\left( {1 - {\alpha _{pi}}} \right)\left( {1 - {\varepsilon _{pi}}} \right){A_{pi}}{N_i},{A_{pi}} = {{\pi d_i^2} \over 4}} } }

N is the number density of the i particulate species, ɛ_pi, T_pi, d_i, A_pi, α_pi, is its emissivity, temperature, diameter, projected area, and scattering factor. In this article, the radiation absorption coefficient is set to 0.0001 for air medium.

To get the numerical solution for the heat transfer in air gap, some variable conditions, such as initial and boundary conditions, are needed. Owing to the complexity of heat transfer in air gap, some assumptions are adopted to simplify the numerical model. The flow inside air gap can be characterized as turbulent, weakly hem, natural convection due to buoyancy and heat radiation due to temperature gradient compressible flow containing forced convection due to the airflow from the clothing. The airflow within the fabric occurs in a laminar regime with low velocity. The buoyancy effects are considered because of natural convection heat transfer. The air bulk density is set to 1.29 kg/m³. Gravity is considered to be acting in a vertically downward direction. The gravitational acceleration vector is −9.81 m/s². The mesh independence test was carried out with three different mesh scales, namely, 1.1 million for coarse mesh, 1.6 million for moderate, and 2.2 million for a refined mesh. The refined mesh was selected because of its accuracy to evolve the following calculations [16].

The freestream airflow was applied to the inlet, which is specified as a standard atmosphere with T_air = 283.15K and v_air = 0.5 m/s, the gases emissivity is set to 0.02. The outlet properties are extrapolated from inner cells. The body skin and inner fabric are considered as diffuse surfaces, with the emissivity of 0.98 and 0.95 [8, 17] ] (Table 2).

The numerical method is validated first against the available results [8, 18, 19] for a 2D horizontal impermeable cylinder, namely, human limb, with an external environment of 283K. The cylindrical clothing microclimates between the limb and the cloth surface are investigated. Figure 4(a) and (b) shows the present results for heat transfer Nusselt number and dimensionless tangential velocity variation along the skin, respectively, compared against the public works. The present method is found to be well in agreement with the available results and is satisfactory to carry out the following investigation.

Figure 4

The temperature contours under the condition of conduction, convection, and radiation are shown in Figure 5. As can be seen, the temperature distribution looks uneven all over the surface. The locations of the shoulder, upper chest, back chest, lower bust, and lower hem of cloth surface are the highest temperature regions.

Figure 5

To analyze the temperature quantitatively, temperature distributions near chest (y = 69 cm), bust (y = 58 cm), waist (y = 42 cm), and hip girth (y = 22 cm) are exhibited with the distance ease in Figure 6. As is shown, the temperature was increased with the ease allowance decrease. The temperature of the cloth was overall higher at the chest and bust girth (Figure 6(a) and (b)), and lower at the waist and hip (Figure 6(c) and (d)). This is partly because the conduction heat flux can cross through the narrow ease and reaches the cloth surface easily. However, the temperature increases nonlinearly with increasing ease distance. The most significant changes are noticeable between X = 0.05 m and 0.07 m at chest and between X = 0.09 m and 0.11 m at bust because of the high-temperature results from high-speed cooling airflow, as we will explain in Chapter 4.4. This is a new and interesting observation of the present study.

Figure 6

The total heat transfer and radiative heat flux are shown in Figure 7. Predictably, the air gap between the skin and the garment strongly influences the airflow and heat transfer in this region. The area around the neck, waist, and under the bust is the high heat flux regions (HFRs) where the lost total heat flux is above 1400 W/m² (Figure 7 (a)). This phenomenon mainly results from narrow distance ease. Interestingly, the total heat flux under the bust is also very high, for which the distance ease is wide enough. The circumference around the thigh has the maximum heat loss of more than 3200 W/m². These phenomena might result from air-forced convection, which is taken by the inflow of cooling air from the skirt's hemline. Compared with Figure 7(a), the high radiative HFR (Figure 7(b)) is very different from that of total heat flux. The radiative heat flux on the cloth surface is relatively small about 150 W/m² on the area of middle bust, waist, and abandon. If considered Figure 6 and Figure 7(b) together, we will find that the high cloth surface temperature regions in Figure 6 are similar to low radiative heat transfer regions in Figure 7(b) to some extent. This is because the radiative exchange between the body and clothing depends on the distance between them and the temperature difference. The lower radiation heat transfer across air gap occurs due to the lower temperature gradient.

Figure 7

To analyze the heat transfer distribution quantitatively, heat flux curves at different cross-sections were obtained. It is to be noted that all the heat flux curves present wavelike appearance both on the front and backside of the body (Figure 8). The smaller distance ease leads to the higher heat flux on the whole, further confirming the influence of distance ease on the heat flux. It is also important to note here that the relationship between distance and heat flux is a little complex; the heat flux curve raises to a high level when the ease curve decreases especially at the location of X = 0.00 m to 0.02 m and X = 0.10m to 0.12 m. However, the heat flux curve does not keep pace with the distance ease curve (Figure 8(b) and (d)). Therefore, the total heat flux is affected by air gap distance, and the airflow between the body and clothing should be considered at the same time.

Figure 8

To understand the physical reason behind heat flux and air gap width, another important factor of air velocity was considered. Based on airflow velocity obtained from the CFD analysis for the space of body and cloth, the stream traces are shown in Figure 9(a). As can be seen, the air velocity is relatively small between the double legs because of the wide space. The air velocity increases to a high level around the waist, bust, and chest because of narrow ease distance. The 3D velocity contours distribution between the body and clothing are shown in Figure 9(b). As shown, the high speed appears on the upper chest, bust, and waist with the Mach number of more than 0.02.

Figure 9

If considered Figures 6 and 8 together, we will find that the peak value of temperature partly results from the high-speed cooling airflow. The comparison of high-velocity region (HVR) and HFR are shown in Table 3. These distributions are helpful to understand the influence of forced convection.