*2.5. Model Validation and Discussion*

The temperature and flow field in the airship is a result of the interplay among multiple factors including solar radiation, earth reflection, infrared radiation, external forced convection and internal natural convection, which is similar to the thermal environment of a parked car. Therefore, the experimental results of Li et al. [49] were selected for model validation. In their study, the transient thermal behaviors of an airship under different solar radiation were revealed. An airship model with a spherical tank type was built in a closed laboratory. The body was covered with 0.1 mm polyimide film, and shaped by thin metal sheets. Solar irradiation was supplied by a TRM-PD solar simulator and measured by a XLP12-1S-H2 heat flow meter. Eighteen T-type thermocouples were arranged in 18 different locations to obtain the hull and inner gas temperatures. Eight points are located on plane 1 including from point 1 to point 6 and point 8. For plane 2, there are also eight points, from point 9 to point 14 and point 16. Point 18 and point 19 are distributed on plane 3. Plane 1 and plane 2 are symmetrical about plane 3 with 150 mm axial distance. In Figure 2, a full-size computational domain was modeled with the same physical dimensions as the experimental airship. The computational domain was discretized using the structured mesh with five refined inflation layers applied close to the solid surfaces. The grid independence was achieved at 0.2 million mesh elements, as shown in Table 1. To evaluate the CFD approach to model convection-radiation coupled heat transfer in the airship, the hull and inner gas temperatures were compared with experimental data in terms of the accuracy and computational cost. Six turbulence models and four radiation models were included. In each configuration, one turbulence model was combined with or without a radiation model. Finally, thirty CFD cases were obtained totally.

**Figure 2.** The airship computational domain according to [49].


**Table 1.** The grid independence test of the temperature profile at point 18.

The hull material is polyimide film with thermal conductivity λ = 0.32w/(m·K). The total solar absorptivity of the external surface is 0.45 with a 0.81 absorptivity in the infrared spectrum. The coupled solver with pseudo-transient relaxation was applied for the solution of the momentum, energy, and turbulence equations. The total calculation adopted 600 s according to the experimental sampling time.

The results of 30 designed test trips with different combinations of radiation and turbulence models are obtained. Except for the air temperature measured at point 17 and 18, the rest are measured at the airship surface. Since the solar simulator is installed above the airship and keeps both axes parallel, the temperature distributions on plane 1 and 2 are basically the same. The temperature of six locations including point 1, point 3, point 6, point 17 and point 18 are shown in Figure 3. The measured data at each point is selected as the benchmark. The temperature of the measuring point closer to the light source is higher. Among them, the temperature at point 6 is the highest, reaching more than 90 ◦C, from where the temperature drops along with the body surface. Due to the shelter of the airship, point 1 is not directly exposed to the sunlight, resulting in a similar temperature as that of the surroundings with 16.7 ◦C.

**Figure 3.** Comparisons of the experimental and numerical temperature T(*K*) in the closed airship. Simulation data floats up and down based on experimental data from [49].

To evaluate the performance of model combinations, a method called the total temperature error is proposed to assess the accuracy of numerical simulations. The total temperature error is calculated according to Equation (11). In addition, the computational cost is obtained according to the CPU calculation time when using a computer with an AMD Ryzen 7 1700X, 3.40 GHz CPU, 32 GB of RAM and 8 compute nodes.

$$T\_{Error}(\%) = \sum\_{i=1}^{18} \frac{|T\_{isimulated} - T\_{imasural}|}{T\_{imasural}} \times 100\% \tag{11}$$

where *Tisimulated* is the simulated temperature of the *ith* point, *Timeasured* is the measured temperature of the *ith* point. In the experiment, 18 points were measured totally.

In Figure 4, comparing the temperature errors with and without radiation, the predicted air and solid surface temperature profiles agree better with the experimental results when the effects of thermal radiation are accounted for in the numerical investigation. On the contrary, the total error when ignoring the surface radiation may be twice that when including the surface radiation. When the turbulence model is fixed and combined with different radiation models, it is found that the S2S and DO models perform best, while the DTRM model has the lowest accuracy. Among all turbulence models, the standard k-ω and SST k-ω models have very close accuracies to predict the temperature profiles. The SST k-ω model has a clear advantage in predicting accuracy compared to the LES model; it works the best for the high Rayleigh number buoyancy-driven flow [50]. Figure 4 reveals an M-shape trend of the calculation time according to the order of the combined model. The radiation model has a more significant impact on computation time than the turbulence model. The S2S and P1 radiation models require much less computation time than the DO model, although some small disparities exist but still are comparable. The DTRM is not compatible with parallel processing, so it will consume

more time to model radiative heat transfer. The above model validation and comparison suggest that the SST k-ω and S2S model are the best choices to predict the in-vehicle thermal environment under solar radiation. Some existing studies [51] also show that the SST k-ω model performs slightly better than the RNG k-ε model when simulating convection-radiation coupled heat transfer.

**Figure 4.** The total temperature error and computation time of 30 cases.

To validate the theoretical correlation between the ER and surface temperature, some experimental results in the previous literature were used. Table 2 displays the measured emission rates of five pollutants from the car mat under three varied temperatures and total volatile organic compounds (TVOC) from PBS-C at five different temperatures. The detailed experimental description can be found in references [52,53].


**Table 2.** The emission rate (ER) of pollutants from in-vehicle materials under varied temperature conditions.

The unit of ER for the volatile organic compounds (VOCs) and total volatile organic compounds (TVOC) is <sup>μ</sup>g·m−2·h−<sup>1</sup> and mg·m−2·h<sup>−</sup>1, respectively.

The linear curve fittings are illustrated in Figure 5. All *R*<sup>2</sup> are greater than 0.95, indicating a satisfactory correlation between the VOCs emission rate and temperature proposed in Equation (9). In the follow-up study, the little impact of existing in-air VOCs on the emission rate is ignored during the emission period [54]. Moreover, the materials maintain their original appearance and properties without any bake out treatment, which indicates abundant VOCs to be volatilized in a quasi-steady state. Besides, the effect of relative humidity on the emission factor is ignored because of the constant relative humidity in that environment [35].

**Figure 5.** (**a**) The relationship between five VOCs emissions and temperature according to the experimental data [52]; (**b**) The relationship between TVOC emission and temperature according to the experimental data [53].
