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19 Oct 2012
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Numerical Simulation of Solar Radiation and Conjugate Heat Transfer through Cabin Seat Textile

Published Online: 29 Sep 2020
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Journal Details
License
Format
Journal
First Published
19 Oct 2012
Publication timeframe
4 times per year
Languages
English
Abstract

The solar radiation and the conjugate heat transfer through the cabin seat fabric were investigated numerically with a focus on a comparative analysis of various fabric solar reflectance or reflectivity (SR) and inlet cooling air velocity. For this purpose, 3D compressible Reynolds-averaged Navier–Stokes equations with the low Reynolds number turbulence model were utilized to simulate the airflow in the cabin. The discrete ordinate radiation model was adopted to describe the solar radiation. The conjugate heat transfer between the airflow and the fabric seats was included. The airflow temperature, radiative heat flux, and radiative heat transfer through the fabrics in a fixed cross section were studied. The results demonstrate that the increase in fabric SR leads to the increase in energy reflected to the atmosphere, which will bring about a lower temperature on the seat fabric. The decrease in emissivity and the energy absorbed results in the lower heat transfer and heat radiation and leads to the improvement of the cabin thermal environment. The high-temperature gradient near the seat causes the forced air circulation and is beneficial for the improvement of the thermal comfort. However, the cooling effect is not so obvious near the cabin seats when the inflow speed is increased.

Keywords

Introduction

With the rapid development of technology, the higher demands of thermal comfort in the airplane cabin bring about higher demands of the environmental control system. A comfortable cabin environment would be achieved with reasonable importation of cabin seat conditions, such as temperature, heat transfer, and solar radiation [1, 2]. The seat textile plays an important role in heat transfer and solar reflectance or reflectivity (SR). Therefore, the heat emissivity and solar radiation reflectance of seat fabric need to be selected carefully [3].

Several previous publications provide useful background and introduction to the present work, a representative sample of which is reviewed below. Kothari and Bhattacharjee [4] and Bhattacharjee and Kothari [5] developed a mathematical model to predict the conductive and radiative heat transfer through fabrics and validated this model with the thermal resistance values obtained from the experiment. Hu et al. [6] studied the heat transfer in the aircraft cabin in various inlet conditions and found that different inlet angles and velocities significantly affected the air temperature and flow field. Maier [7] analyzed the thermal comfort of the ceiling-based cabin displacement ventilation. He argued that more homogeneous cabin airflow was found in the mixture of cabin displacement ventilation and ceiling-based cabin displacement ventilation method. Günther et al. [8] investigated the airflow in an aircraft cabin using a combination of numerical simulation and experimentation by particle image velocimetry (PIV) and indicated that higher-order low Reynolds number turbulence models were suited best to predict the complex 3D-cabin airflow with separation. Zhu et al. [9] studied the air flow and conjugate heat transfer through the fabric numerically and insisted that the heat loss from the human body (the heat transfer coefficient) was the highest when the fabric had pores and the air flow penetrated through the fabric.

As can be seen from the review above, the mechanism of solar radiation and conjugate heat transfer through seat fabric need to be explored deeply. The main objective of this study is to investigate the thermal environment of the double passageway plane by computational fluid dynamics. It focuses on solar radiation heat flux and mixture airflow in the cabin.

Numerical method
Physical model and fabric properties

The physic model is a half-section passenger cabin, as shown in Figure 1. It is 2.15 m in length and 1.775 m in width. The cabin seat cushion is constructed by a foam and a fabric layers. The total thickness of the textile fabric and foaming/padding on the seats is 7 mm. The cotton fabric layer is exposed to solar radiation both on the vertical and horizontal seat surfaces. The radiative heat flux of solar rays from outside reaches to the fabric surface, then it will transfer to the foam layer because of conduction. To study the influence of SR, three types of fabric such as oyster white plain weave fabric, light grey warp knitted fabric, and dark black velvet fabric with different SRs are considered. The corresponding roughness varies from smooth (KES surface roughness of 1.285) to medium (1.825) and rough (2.572). These fabrics are composed of 95% cotton and 5% polyester with a thickness of 0.83 mm [10]. The whole flexible composite has a constant thermal conductivity of 0.12 W/(m·K) and specific heat of 1,220 J/(kg·K).

Figure 1

The geometry model.

Figure 2

Computational mesh.

Mathematical models and numerical procedure

There are several basic assumptions for the actual working condition of the solar radiation and heat transfer in the airliner cabin that are extremely complex. The working medium is the compressible perfect gas. Airflow in the air cabin is turbulent and the airflow within the fabric occurs in the laminar regime with low velocity. The cabin walls are treated as black bodies with nonradiaton.

In the Cartesian coordinate system, the three-dimensional compressible Reynolds-averaged Navier–Stokes equations [6, 10] with a Realizable k-ɛ model in tensor forms were used to solve the problems of the steady-state and the compressible turbulent [11].

When the solar rays pass through the cabin glass porthole and reach the cabin seat, the radiative heat transfer occurs between the airflow and the plane seat. The conjugate heat transfer between the solid medium and the airflow can be defined as [12, 13]: ϑTt=K(xi)2T\vartheta {{\partial T} \over {\partial t}} = K{\left({{\partial \over {\partial {x_i}}}} \right)^2}T where J and K are the thermal capacitance and the thermal conductivity of the solid pure aluminum. They should be 2.43 × 106 kg/(ms2K) and 237.42 W/(mK) under room temperature.

The radiative transfer equations are used to calculate the radiation heat flux inside the plane. The particles that are absorbing, emitting, and scattering are considered by the discrete ordinate (DO) radiation model [14, 15]. The radiative transfer equations with DO radiation model are expressed as: (Is^)=κn2σT4π+Ip(κ+κp+γ+γp)I(r,s^)+γ4πΩ=04πI(r,s^)Φ(r,s^,s^)dΩ\nabla (I\hat s) = \kappa {{{{\rm{n}}^2}\sigma {T^4}} \over \pi} + {I_p} - (\kappa + {\kappa _p} + \gamma + {\gamma _p})I(r,\hat s) + {\gamma \over {4\pi}}\int_{\Omega = 0}^{4\pi} {I(r,\hat s')\Phi (r,\hat s',\hat s)d\Omega} where Ip=i=1nεpiApiσTpi4πNi,κp=i=1nεpiApiNi,γp=i=1n(1αpi)(1εpi)ApiNi,Api=πdi24{I_{\rm{p}}} = \sum\limits_{i = 1}^n {{\varepsilon _{pi}}{A_{pi}}{{\sigma T_{pi}^4} \over \pi }{N_i},} \,\,\,{\kappa _{\rm{p}}} = \sum\limits_{i = 1}^n {{\varepsilon _{pi}}{A_{pi}}{N_i},} \,\,\,\,\,{\gamma _p} = \sum\limits_{i = 1}^n {(1 - {\alpha _{pi}})(1 - {\varepsilon _{pi}}){A_{pi}}{N_i},} \,\,\,{A_{pi}} = {{\pi d_i^2} \over 4} where In is the equivalent emission of the particles and κp and γp are the equivalent absorption coefficient and the scattering coefficient, respectively. Ni is the number density of the i particulate species, εpi, Tpi, di, Api, and αpi are its emissivity, temperature, diameter, projected area, and scattering factor, respectively. In this paper, the radiation absorption coefficient is set to 0.0001. While the emissivity and the reflectance of the walls are set to 1.0 and 0, respectively, as they are regarded as black bodies, the emissivity and reflectance of conjugate heat transfer seats are varied with the fabric type.

The equations are discretized in space by a second-order, cell-centered, and finite-volume method (FVM). The commercial code CFD++ is utilized to output the computational results [16]. To accelerate convergence, a multigrid method such as the local-time stepping is employed.

Mesh generation and boundary conditions

The commercial mesh generation software ICEM-CFD 17.0 was used to produce the three-dimensional tetrahedral mesh. The mesh independence test was carried out with three different mesh scales [17]. The numbers of nodes are 1.0 M for coarse mesh, 1.5 M for moderate, and 2.0 M for the refined mesh. We selected the refined mesh because of its accuracy to evolve the following calculations [18].

The radiative wall with an isothermal constant temperature of 297 K under non-slip condition is used on the solid walls except glass porthole. The yoz plane is treated as a symmetrical plane. The front face and the rear face are set to be in outflow conditions. The inlet is freestream air with a temperature of 293 K and a speed of 0.5 m/s or 1.0 m/s. The base pressure is set to 7.9 × 104 Pa, which relates to the pressure at airplane cruising altitude.

The inflow cooling air flows perpendicular to the direction of gravity and the buoyancy effects are considered. The gravitational acceleration vector is −9.81 m/s2, and the bulk density is set to 0.9388 kg/m3. The solar rays pass into the cabin through the glass porthole with an inclined angle of 45°. The seat textile is treated as an interface between the solid and fluid, which is set to be the conjugate heat transfer fluid/solid wall.

Results and discussion
Validation of numerical methods

The radiative heat transfer between two parallel plates is simulated to validate the numerical method. The plates are separated at a distance (L = 1 m) by an emitting, absorbing, and non-scattering medium. The temperatures of the plates are 98.6°C and 37.7°C, respectively. The plate and the wall have emissivities of 0.05 and 0.85, respectively, as shown in Figure 3.

Figure 3

Schematic of the radiative heat transfer between two plates.

The calculated radiative heat flux of the upper and bottom walls has been calculated and is compared with the experimental data [19] and Hassan’s result [20], as in Figure 4. It is depicted that the precision loss is very small both in the upper and bottom surfaces. That is to say, the numerical method can describe the radiative heat transfer accurately in the following investigations.

Figure 4

Method validation with experimental and public results.

The influence of fabric and inlet conditions

To study the cabin–fabric environment under different conditions, five kinds of simulations were carried out. The influence of SR and air conditioner flow speed is studied. SR is the ability of a material to reflect solar energy from its surface into the atmosphere. Emissivity is a material’s ability to release the absorbed energy. The SR value is a number from 0 to 1.0, while the emissivity varies from 1.0 to 0. The color and roughness of the fabric lead to the different SR values [21]. The seat fabric was simulated by three kinds of padding textiles with different reflectance. The calculated peak value of temperature (Tmax) and radiative heat flux (Qrmax) are listed in Table 1, at the same time. According to the parallel contrast between cases 1, 2, and 3, it is visible that the peak value of temperature decreased from 312.05 K to 309.04 K and 305.35 K while the SR increased from 0.10 to 0.28 and 0.52. The radiation heat flux decreased from 197.54W/m2 to 177.48 W/m2 and 137.03 W/m2, at the same time. A comparison study of cases 1, 4, and 5 shows that the maximum value of temperature decreased by about 0.6% and 1.0%, while the inlet velocity increased from 0.5 to 1.0 and 2.0. However, the radiation heat flux remaining essentially unchanged.

Various calculation conditions and numerical results

Fabric layerSRInlet air velocity (m·s−1)Tmax (K)Qrmax (W/m2)
Case 1Dark black, velvet fabric0.100.5312.05197.54
Case 2Light gray, warp knitted fabric0.280.5309.04177.48
Case 3Oyster white, plain woven fabric0.520.5305.35137.03
Case 4Dark black, velvet fabric0.101.0310.14198.21
Case 5Dark black, velvet fabric0.102.0308.72197.97

For a numerical comparison analysis, a fixed cut plane of the cabin section is selected with x = 1.38 m, as shown in Figure 5.

Figure 5

The cutting plane of x = 1.38 m and contour line of z = 0.25 m.

The flow parameters on the contour line (x = 1.5 m and z = 0.03 m) are illustrated in different cases of SR, as can be seen in Figure 6. Figure 6a shows that the temperature decreases with the increase in fabric SR. The reason is that the higher the SR is, the more the solar energy is reflected in the atmosphere; this results in fewer absorbing energy that leads to a lower temperature on the cabin seat surface.

Figure 6

Flow parameter distributions with different solar reflectance. (a) Temperature distributions, (b) Radiation heat flux distributions, (c) Stanton number distributions, and (d) Mach number distributions.

Figure 6b shows the radiation heat flux on seat reduces fiercely when the SR increases to 0.28 and 0.52. Figure 6c shows the heat transfer of the seat fabric being cut down as well as the increase in SR. The reason is that the emissivity of the fabric falls when SR is increased. As a result, heat transfer and heat radiation will be reduced. Figure 6d shows the velocity of air near the seat will increase due to the forced air circulation of high-temperature gradient.

To investigate the thermal comfort of different air conditioner speed, three types of inlet velocity are used. Figure 7a shows that the temperature decreased a lot near the inflow and outflow areas. But the cooling effect is not obvious near the cabin seats. Figure 7b shows that the air circulation speed increases rapidly near the inlet region, but kept constant near the cabin seats. This phenomenon can explain the temperature verity in Figure 7a. Different from the above phenomena, Figure 7c shows that the radiation heat flux in the cabin remained essentially unchanged. The reason is that the air condition system can improve the thermal environment by inputting cooling air, but cannot change the radiation ability of the fabric seats. Figure 7d depicts that the heat transfer on the fabric is decreased slightly, because the temperature gradient is relatively small in this area, as mentioned above.

Figure 7

Flow parameter distributions with different inlet speed. (a) Temperature distributions, (b) Mach number distributions, (c) Radiation heat flux distributions, and (d) Stanton number distributions.

Flowfeild characteristics analysis

To study the flow mechanism, the typical flow contours of the cabin are analyzed. Figure 8 shows the temperature, radiation heat flux, and Mach number contours. Figure 8a is a description of solar radiation intensity on the aircraft cabin seat surfaces and the vertical plane of x = 1.38 m. The solar light gets into the cabin room through the glass in the window with high radiation energy. In the process of light-ray propagation, a part of light radiating to the seat is absorbed by the fabric, and another part is reflected in the air. Figure 8b shows that the biggest temperature gradient appears on the intersection part of the cabin seat surface because of solar radiation. The lowest temperature region is near the entrance because of the cooling air inlet. Figure 8c portrays the radiation heat flux in the air cabin. It is thus clear that the maximum radiation value appears on the seat near the window, for which is the highest temperature zone in Figure 8b. Figure 8d depicts that the velocity distribution was not uniform in the cabin space. The air flow’s speed inflow along the ceiling wall is higher than the other part because of the boundary layer attachment effect of fluid air. The flow speed near the seat appears slightly lower than other parts owing to the interruption of a solid seat. After comprehensive consideration of Figure 8b and 8d, we can see that the protruding part of the seating chair discounts the cooling effect on the seat fabric.

Figure 8

Flow contours of case 3. (a) Solar radiation intensity in the cabin, (b) Temperature in the cabin, (c) Radiation heat flux contours, and (d) Mach number contours.

Conclusions

Aiming to obtain the cabin–fabric environment under different fabrics and flow conditions, a FVM is proposed in this article. Five kinds of different SR and velocity simulation were carried out. We have come to the conclusion as follows:

The increase in the textile SR leads to more and more solar energy reflected in the atmosphere. Therefore, the temperature on seat fabric reduces rapidly and the cabin thermal environment is improved.

The decrease in the textile emissivity brings about a decrease in energy absorption. Then, the heat transfer and heat radiation will go down. This will improve cabin thermal comfort.

The high-temperature gradient near the seat causes forced air circulation. It is a benefit for improving the thermal comfort on the seat surface. When the inflow airspeed is increased, the temperature will decrease slightly. However, the cooling effect is not so obvious near the cabin seats when the inflow speed is increased.

Figure 1

The geometry model.
The geometry model.

Figure 2

Computational mesh.
Computational mesh.

Figure 3

Schematic of the radiative heat transfer between two plates.
Schematic of the radiative heat transfer between two plates.

Figure 4

Method validation with experimental and public results.
Method validation with experimental and public results.

Figure 5

The cutting plane of x = 1.38 m and contour line of z = 0.25 m.
The cutting plane of x = 1.38 m and contour line of z = 0.25 m.

Figure 6

Flow parameter distributions with different solar reflectance. (a) Temperature distributions, (b) Radiation heat flux distributions, (c) Stanton number distributions, and (d) Mach number distributions.
Flow parameter distributions with different solar reflectance. (a) Temperature distributions, (b) Radiation heat flux distributions, (c) Stanton number distributions, and (d) Mach number distributions.

Figure 7

Flow parameter distributions with different inlet speed. (a) Temperature distributions, (b) Mach number distributions, (c) Radiation heat flux distributions, and (d) Stanton number distributions.
Flow parameter distributions with different inlet speed. (a) Temperature distributions, (b) Mach number distributions, (c) Radiation heat flux distributions, and (d) Stanton number distributions.

Figure 8

Flow contours of case 3. (a) Solar radiation intensity in the cabin, (b) Temperature in the cabin, (c) Radiation heat flux contours, and (d) Mach number contours.
Flow contours of case 3. (a) Solar radiation intensity in the cabin, (b) Temperature in the cabin, (c) Radiation heat flux contours, and (d) Mach number contours.

Various calculation conditions and numerical results

Fabric layerSRInlet air velocity (m·s−1)Tmax (K)Qrmax (W/m2)
Case 1Dark black, velvet fabric0.100.5312.05197.54
Case 2Light gray, warp knitted fabric0.280.5309.04177.48
Case 3Oyster white, plain woven fabric0.520.5305.35137.03
Case 4Dark black, velvet fabric0.101.0310.14198.21
Case 5Dark black, velvet fabric0.102.0308.72197.97

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