1 Introduction

The air pressure in aircraft cabin is lower than standard atmospheric pressure at cruising period. The planes are designed to maintain an air pressure that is at least equivalent to the air pressure at 2,500 m above sea level (around 75 kPa) [1]. In recent years, the comfort in aircraft cabin is more and more important. To evaluate the comfort level, it is necessary to know the thermal environment conditions and the passengers’ reaction. The most common method used is to evaluate thermal sensation by questionnaire. The ASHRAE/ISO 7-point thermal sensation scale is based on Fanger’s PMV model. The PMV model was originally designed for standard atmospheric pressure environment. Whether this model could be used under low-pressure environment is not clear. Li et al. [2] investigated convection and evaporation heat dissipation under low-pressure environment and found that convection heat dissipation would decrease and evaporation heat dissipation would increase in low-pressure environment. In PMV model, other heat dissipation factors are also included such as radiation and heat release through breathing. In this study, an experiment was conducted in a chamber where low-pressure environment could be simulated to evaluate thermal sensation. Theoretically, the heat dissipation was calculated using real experiment conditions. With these two results, the preliminary model which could predict thermal sensation was proposed.

2 Methods

The experiment was conducted in low-pressure environment chamber in Qingdao Technological University. Six conditions were designed: 22 and 27 °C (1.0/0.9/0.8 atm). Thirty subjects were recruited including 20 males and 10 females (university students). They were divided into 6 groups and participated in all environment conditions. Latin-square method was used to decide the order. Subjects wore uniform clothes (around 1.11clo), and the metabolic rate of 1.0 was met when sat still. Each experiment lasted 90 min, and the procedure is shown in Table 37.1. The 7-point thermal sensation scale was used.

Table 37.1 Experiment procedure
Full size table

The heat dissipation was divided into four parts: convection heat loss through the skin, evaporation heat loss through the skin, radiation heat loss, and heat loss through breathing. With these four parts, the heat storage of the human body could be calculated. The PMV model gives the relationship between heat storage and vote results. In this study, unary linear regression was applied between thermal sensation vote and heat storage rate. In this way, the model to predict human thermal sensation under low-pressure environment could be proposed.

3 Results

3.1 Experiment Results

Figure 37.1 shows the results of thermal sensation vote under different air pressure and temperature. The trend in both temperatures was the same. As air pressure decreased, TSV value also decreased. Significant difference was found between 1.0 atm and other two low-pressure environments. Between 0.8 and 0.9 atm, no significant difference was found. But under 27 °C, the difference in TSV values between 0.9 and 0.8 atm was larger than 22 °C.

Fig. 37.1
figure 1

Thermal sensation vote under different temperature and air pressure

Full size image

3.2 Numerical Calculation

The heat dissipation was divided into four parts: convection heat loss through the skin, evaporation heat loss through the skin, radiation heat loss, and heat loss through breathing. The values of real experiment condition parameters used in calculating are shown in Table 37.2.

Table 37.2 Parameters used in the calculation
Full size table

According to the study of Li et al. [2], the equation to calculate convection heat dissipation through skin is as follows:

$$ C_{p} =\, \frac{{f_{\text{cl}} h_{c,\,p} \left( {t_{\text{sk}} - t_{a} } \right)}}{{f_{\text{cl}} h_{c,\,p} I_{\text{cl}} + 1}} \,=\, \frac{{f_{\text{cl}} h_{c,\,0} \left( {\frac{{P_{p} }}{{P_{0} }}} \right)^{2n} \left( {t_{\text{sk}} - t_{a} } \right)}}{{f_{\text{cl}} h_{c,\,0} \left( {\frac{{P_{p} }}{{P_{0} }}} \right)^{2n} \left( {I_{\text{cl}} - t_{a} } \right)}} $$
(37.1)

In this equation, n = 0.33. The heat dissipation was calculated from 22 to 27 °C, which is shown in Fig. 37.2. The figure on the left indicated that convection heat dissipation decreased rapidly as temperature rose, and when pressure decreased, heat dissipation also decreased, but the scale was rather smaller. The right figure showed the heat dissipation with different pressure under 22 and 27 °C. At higher temperature, the decreasing speed of heat dissipation was slower than low temperature.

Fig. 37.2
figure 2

Convection heat dissipation under different pressure and temperature

Full size image

The radiation heat dissipation would not be affected by air pressure change, and the following Eq. (37.2) was used.

$$ R = 3.96 \times 10^{ - 8} f_{\text{cl}} \times [(t_{\text{cl}} + 273)^{4} - (\bar{t}_{r} + 273)^{4} ] $$
(37.2)

The clothes’ surface temperature t cl would change with air temperature. In this study, it was assumed that the human skin temperature would not change with air temperature, and the change in convection heat dissipation under different pressure levels could be neglected. So t cl could be calculated with Eq. (37.3).

$$ t_{\text{cl}} = t_{\text{sk}} - I_{\text{cl}} (R + C) $$
(37.3)

Figure 37.3 shows the results of t cl and radiation heat dissipation R. It was clear that the clothes’ surface temperature t cl increased when air temperature rose. And due to the rise in t cl, the radiation heat dissipation decreased when air temperature rose.

Fig. 37.3
figure 3

Clothes’ surface temperature and radiation heat dissipation

Full size image

Evaporation heat dissipation through skin was calculated according to Eq. (37.4). The results showed that the change in evaporation heat dissipation was just opposite to that of convection heat dissipation. As temperature rose or pressure decreased, the heat loss increased. At higher temperature, the change in heat loss was more obvious with pressure change (Fig. 37.4).

Fig. 37.4
figure 4

Evaporation heat dissipation under different pressure and temperature

Full size image
$$ E_{{{\text{sk}},\,p,\,n}} = \frac{{\omega f_{\text{cl}} \times 39.27(t_{\text{cl}} - t_{a} )^{0.25} \left( {\left( {\frac{{P_{0} }}{{P_{p} }}} \right)P_{\text{sk}} - P_{a,0} } \right)}}{{f_{\text{cl}} \times 39.27(t_{\text{cl}} - t_{a} )^{0.25} \frac{{I_{\text{cl}} }}{{16.5 \times i_{\text{cl}} }} + \left( {\frac{{P_{0} }}{{P_{p} }}} \right)^{2n} }} $$
(37.4)

Heat dissipation through breathing was divided into two parts: sensible heat dissipation C res and latent heat dissipation E res, and the equations were as follows [3].

$$ C_{\text{res}} = 0.0014\,{\text{M}}(34 - t_{\text{a}} ) $$
(37.5)
$$ E_{\text{res}} = 0.0173\,{\text{M}}(5.867 - P_{a,\,0} (P_{p} /P_{0} )) $$
(37.6)

The results were shown in Fig. 37.5. As temperature rose, the heat dissipation decreased, and under low-pressure environment, the heat loss would increase. It was also clear that the heat loss through breathing was much smaller than through convection and evaporation.

Fig. 37.5
figure 5

Heat dissipation through breathing under different pressure and temperature

Full size image

The total heat dissipation is shown in Fig. 37.6. At 22 °C, heat loss was significantly higher than at 27 °C. Under low-pressure environment, total heat loss increased. But the increasing level was quite different under different temperature. According to the results, under hotter environment, more heat would be lost when pressure decreased. Then the heat storage could be calculated using Eq. (37.7).

Fig. 37.6
figure 6

Total heat dissipation under different pressure and temperature

Full size image
$$ {\text{HS}} = M - W - C_{p} - R - E_{{{\text{sk}},\,p}} - C_{{{\text{res}},\,p}} - E_{{{\text{res}},\,p}} $$
(37.7)

The thermal sensation vote and heat storage are shown in Table 37.3. Unary linear regression was done between TSV and HS. The new parameter to predict thermal sensation under low-pressure environment is defined as PMVp, and the regression result was as Eq. (37.8) shows.

$$ {\text{PMV}}_{0.8} = 0.074{\text{HS}} + 0.715,\,R^{2} = 0.999 $$
(37.8)
Table 37.3 Thermal sensation vote and heat storage
Full size table

4 Discussion

Both the TSV values and the calculation results confirm that under low-pressure environment, heat dissipation will increase compared with standard atmospheric environment. So, it is necessary to revise the existing PMV model which could not predict thermal sensation under low-pressure environment well. This study is a preliminary investigation and many results need to improve. For example, there were actually two important assumptions in calculating. One was that the metabolic rate would not change under different pressure level, and the other was skin surface temperature maintained stable under all conditions. The aim of the two assumptions was to make the calculation simple. Whether these two assumptions are reliable needs further validation. The data used to establish the new model are still not enough. In Fanger’s PMV model, the coefficient before the heat storage is a function related with metabolic rate. But in the new model, the coefficient is a constant. So the data under different metabolic rate should be included.

5 Conclusion

The main results could be concluded as follows:

  1. 1.

    Thermal sensation vote value decreases under low-pressure environment compared with standard atmospheric environment.

  2. 2.

    As pressure goes down, convection heat dissipation decreases and evaporation heat dissipation increases.

  3. 3.

    Total heat dissipation increases when pressure decreases, and when temperature is higher, the decrease is more significant.