Thermal environment characteristics of large space building with stratified air conditioning based on Block-Gebhart model during the cooling season

. The thermal environment of large space building with stratified air distribution is characterized by its obvious gradient of vertical temperature, and the stratified air conditioning load (SACL) is closely related to the thermal environment. The Block-Gebhart (B-G) model in summer is established for an actual large space building which has two stratified air distribution (STRAD) systems. One system is the air supply nozzles (ASN) arranged at middle sidewall, the other is the half-cylinder diffusers (HCD) arranged at low sidewall. In order to quickly calculate the air temperature of unoccupied zone (ATUZ), two regression equations for the air temperature gradient under the conditions of two STRAD systems were proposed. Considering six factors, the B-G model was used to calculate 648 cases and the two equations were obtained by multiple regression analysis. Through the field measurement in summer, in three cases of ASN system, the mean absolute error (MAE) between predicted and experimental values of ATUZ was 1(cid:2)(cid:3)(cid:4), and the mean absolute percentage error (MAPE) was 4.5%; in three cases of HCD system, the MAE was 1(cid:2)(cid:5)(cid:4) and the MAPE was 3.0%. The results of this study establish the foundation for the calculation of SACL.


Introduction
Large space buildings often use stratified air conditioning to reduce energy consumption [1][2][3]. Previous studies have shown that the thermal environment of large space buildings with stratified air distribution is characterized by its obvious gradient of vertical temperature [4][5][6]. And the stratified air conditioning load (SACL) is susceptible to the thermal environment [7][8][9].
Mathematical models are often used to predict the indoor thermal environment. Among them, the earlier ones include the zonal model [10] and the nodal model [11]. The principles of the both two models are to divide the object space into several regions or nodes in the vertical direction. Togari [12] proposed the Block model based on the zonal model to study the indoor thermal environment. At present, the Block model has developed into the Block-Gebhart (B-G) model [13,14], in which the air temperature and the inner wall temperature are calculated synchronously by combining the Block model with the Gebhart radiation model. Wang [15] predicted the vertical air temperature distribution in three hybrid ventilation scenarios based on the B-G model. The results of field measurements showed that the average deviations of air temperature were 0ႏ (in summer), ႏ (in summer), 0ႏ (in winter).
Through the above study, it was found feasible and accurate to use the B-G model to predict the thermal 2 B-G model

Block model
The B-G model divides the space into several regions in vertical direction. The indoor air temperatures can be calculated by establishing the mass and energy balance equations for each region. The schematic diagram of Block model is shown as Fig. 1 where i is the index of Block; m is the number of wall divisions in Block i; Cp is the specific heat capacity of the air, J/(kgႏ; Min(i,k) is the mass flow rate from wall surface airflow k to Block i (kg/s); TM (i,k) is the temperature of wall surface airflow k in Block i (ႏ) Mout(i,k) is the mass flow rate from Block i to wall surface airflow k (kg/s); T(i) is the air temperature in Block i, For a specific Block, the constituent elements such as air supply, air return, air exhaust and air entrainment are added or deducted according to the real condition.

Gebhart model
Gebhart model [17] is a theoretical model that can calculate the radiant heat transfer between inner wall surfaces. The energy balance equation of each inner wall surfaces is established to achieve the temperature distribution of the inner wall surfaces as shown in Eq. (2).
where hk is the convective heat transfer coefficient of surface k (W/(m 2 āႏ);Tj, Tk are the inner wall temperature of surface j and k ႏ; Tm is the area-weighted average temperature of the inner wall surface (ႏ); İk is the emittance of surface k; ı is is Stephen-Boltzmann constant, 5.67×10 -8 [W/(m 2 ·K 4 )]; j is the index of wall surface in the horizontal direction; Gjk is the Gebhart absorption factor from surface j to surface k; Kk is the envelope heat transfer coefficient of wall k [W/(m 2 āႏ]; te,k is the sol-air temperature of wall k ႏ; qin,k is the radiant heat emitted by all internal heat sources to the wall k (W/m 2 ).

B-G model
For the Block model, we can calculate the indoor air temperatures by the known inner wall temperatures. In the same way, for the Gebhart model, we can also calculate the wall temperatures by the known air temperatures. Therefore, the B-G model is to combine the Block model with Gebhart model to synchronously calculate the air and wall temperatures. There is a coupling relationship between the air and wall temperatures, so the iterative method is adopted. The details of B-G model can be found in the previous study [14].

Research object
The research object of this paper is a large space computerized numerical control (CNC) machine zone. It has two stratified air distribution (STRAD) systems

Experimental scheme
The arrangement of vertical temperature measuring points is shown as Fig. 3. The air temperatures in the space above 3 m were measured by the PT1000 temperature sensors (an accuracy of ±0.2 ႏ) fixed on the vertical measuring lines. The air temperatures below 3 m were measured by testo 174T (an accuracy of ±0.5 ႏ) at line A, C, E, I, K.   Table 1, in which A1~A3 are the cases of ASN system, B1~B3 are the cases of HCD system, and the parameters in the table are the experimentally measured values.
where t is the vertical air temperature gradient (ႏP), Tuo, To are the air temperature of unoccupied zone and occupied zone (ႏ), ǻK is the height difference between the unoccupied zone and occupied zone (m). Six influencing factors and the value ranges are shown in Table 2 [18]. A total of 648 calculation conditions are designed, and there are 324 calculation conditions for ASN system and HCD system respectively. In all the calculation cases, only the values of six influencing factors are changed. The outdoor parameters are selected in Shanghai [18]. The design temperature of the occupied zone is 26°C. It assumes that the air is exhausted at the top of the unoccupied zone. The exhaust ratio ȕe= Mex / Ms. The length of building L (m) 13.8-138.0 The width of building W (m) 9.0-90.0

Multiple regression analysis
The indoor vertical air temperatures of 648 cases were calculated based on the B-G model, and two regression equations for the air temperature gradient under the conditions of two STRAD systems were proposed by the multiple regression method. The temperature gradient has a high correlation with q1 q2 ȕe and H, but has a low correlation with L and W. In the multiple regression, L and W are eliminated, and the first-order polynomial regression equations for temperature gradient are obtained. The equations are shown as Eq. (4)  (5) where nex is the air exhaust per hour in unoccupied zone (h -1 ). nex=Mex/V2, V2 is the volume of unoccupied zone (m 3 ). Since the exhaust ratio ȕe is difficult to obtain in the design stage, nex is used to describe the air exhaust. Fig. 4 shows the relative error of Tuo between the results obtained from B-G model and Eq.(4), (5). It can be seen that the relative error is basically within ±10%. The applicable ranges of two regression equations are: q1<150W/ m 3 q2<80W/ m 3 nex<4 h -1 H<55m.

Experimental validation
According to the experimental scheme in Section 3.2, the ATUZ Tuo under six experimental conditions were obtained. The regression equations proposed in this paper can also be used to calculate the ATUZ Tuo. The calculated values of the ATUZ Tuo were compared with the experimental values as shown in Table 3. It could be seen that in the three cases of ASN system, the MAE between the experimental and calculated values was 1.4 °C, and the MAPE was 4.5%. In the three cases of HCD system, the MAE was 1.0 °C and the MAPE was 3.0%. It indicates that the two regression equations proposed in this paper can be used to predict the vertical air temperature gradient and the ATUZ Tuo of the actual large space buildings.

Conclusion
In this paper, a thermal environment experiment was carried out in a large space CNC machine zone. Two B-G models were established for two STRAD systems. Considering six factors, 648 cases were calculated based on B-G model. Then two equations for t were proposed by multiple regression analysis, and the ATUZ T uo can also be calculated. Finally, the regression equations proposed in this paper were experimentally verified according to the six experimental cases. The results showed that in the three cases of ASN system, the MAE was 1.4 °C, and the MAPE was 4.5%. In the three cases of HCD system, the MAE was 1.0 °C, and the MAPE was 3.0%.