Differentiated Control of Large Spatial Environments: Air Curtain Grid System

Abstract

Large public buildings (LPBs) are the main energy consumers in cities, and the air conditioning system contributes a large part. Supply air allocation by partition can avoid excessive regulation of the system. In spatially interconnected LPBs, thermal coupling relationships exist between different subzones. The convective heat transfer to the non-occupied zone increases the actual cooling/heating capacity of the air conditioning area. This paper applies the air curtain as an airflow barrier indoors, and the air curtain grid system (ACGS) is created by the combined operation of multiple air curtains, which aims to reduce the convective heat exchange between adjacent subzones. The computational fluid dynamics (CFD) model is established and simulated. The main conclusions are as follows: (1) For the scenarios addressed in this paper, the combination of a 60° diffuser air supply angle and 2 m/s air curtain velocity can reduce the convective load from the adjacent space by more than 50%. (2) It is recommended to install incomplete air curtains indoors, and a 50% air curtain coverage ratio can reduce 52% of the heat exchange. (3) The mathematical model of air infiltration/exfiltration under the combined operation of multiple air curtains is established and verified in ACGS. This paper provides a new approach to the air conditioning partition control of LPBs.

1. Introduction

Building energy consumption can account for 40% of the primary energy usage, most of which is used to create a comfortable environment for indoor occupants [1]. As urbanization progresses, large public buildings (LPBs) are increasing in size, such as open offices and commercial complexes. Their heating, ventilation, and air conditioning (HVAC) energy consumption should also be of concern. Enclosed spaces account for a large proportion of such buildings. The indoor load is mainly related to personnel activities. Adjusting the air conditioning supply area according to personnel distribution is a common method to reduce energy consumption [2]. However, LPBs are internally connected. Even if the occupied zone is targeted for air supply, the heat in the non-occupied zone accumulates and retransfers to the occupied zone through convective heat exchange [3]. To achieve “thermal isolation” in LPBs, it is necessary to reduce this heat transfer, which puts forward high requirements for the air distribution design. Furthermore, if this air supply subzone can be created, the demand control of air conditioning systems based on occupancy information can also be better promoted in LPBs.

Tradition mixture ventilation has been proven to be inefficient [4]. The essence of this full-space environment control method is the dilution principle so as to maintain uniform parameters in the room. Based on this, some new ventilation strategies have been developed, such as displacement ventilation (DV) [5], underfloor air distribution (UFAD) [6], and stratified air conditioning [7]. These methods are designed to ensure the comfort of the space where the occupants are located and to send the airflow directly below the working plane. This vertical stratification of indoor load can improve ventilation efficiency and effectively reduce air conditioning energy consumption [8]. However, such methods still create a uniform environment below the working plane. Due to the different thermal environment requirements of occupants [9], the ventilation methods mentioned above cannot meet personalized needs [10]. In addition, the scope of personnel activities is limited. The actual required air conditioning area only occupies a small part of the building. The air supply without considering personnel distribution leads to energy waste, accompanied by local overcooling and overheating [11]. This requires that the building is equipped with controllable air conditioning terminal devices and a corresponding system control strategy in the horizontal dimension.

In a building with clear room division, the air conditioning system can adopt the demand control ventilation (DCV) strategy according to the indoor occupancy rate [12,13]. Therefore, each room can maintain a low level of energy consumption while ensuring the supply of fresh air for occupants. The interior wall of the building creates a relatively closed air supply area, which creates conditions for independent control of different rooms. Since LPBs do not have physical barriers inside, the differentiated thermal environment is difficult to maintain.

Presently, the partition control methods of LPBs can be summarized as airflow restriction (AR) and personalized ventilation (PV). AR aims to prevent the diffusion of air conditioning jets to non-occupied areas. Wang et al. [14] proposed a fan network. The additional power of the fan can change the direction of the original air conditioning jet and improve the air supply effect of the occupied zone. Lo et al. [15] used multiple slot diffusers and central return vents to limit the conditioned air to the space below the diffuser, reducing cooling dissipation. Although AR optimizes the air conditioning jet path, the convective heat transfer between adjacent air supply zones still needs to be reduced. PV directly supplies air to the occupied area, which can meet the comfort requirements of different personnel and relax the temperature range of the non-occupied zone [16]. The air supply terminal of the PV can be arranged in the seat [17], desktop [18], and ceiling [19] according to the occupant distribution. This feature makes it possible to ignore the specific geometric characteristics of the room and also has a good application prospect in LPBs. However, in the existing LPBs, such as office buildings and commercial complexes, indoor functional partitions are changing regularly. [20] Although PV can supply airflow to the personnel area, it is difficult to transform the system due to the complexity of its pipeline and equipment installation. In summary, the existing LPB partition control does not have a suitable air supply form.

An air curtain can create a virtual partition to isolate heat exchange between two sides that does not affect the free passage of people or require additional pipeline connections. This air supply device is widely used in building entrances. Gil-Lopez et al. [21] applied air curtains to the entrance of cold storage rooms, which could reduce the cooling energy consumption by 39.6% compared to sliding doors. They verified the advantages of this method in carbon emission reduction, and this method can be extended to the renovation of old buildings. Yue et al. [22] designed an up-supply air curtain for a vehicle painting drying workshop to reduce heat dissipation. In addition, air curtains have been developed for other applications to reduce the air conditioning load, such as doors of refrigerated vehicles [23] and urban railways [24].

When this virtual barrier is applied to the interior of the building and operates stably, it can play a role in environmental separation similar to that of the interior wall. Shen et al. [10] divided the office into occupied and non-occupied areas with air curtains according to the distribution of heat sources. The simulation results show that an air curtain jet velocity of 2 m/s can maintain a relatively stable temperature difference between the two sides. This thermal isolation has also been applied in museums. Luo et al. [25] used horizontal air curtains to separate the cultural relics area from the exhibition hall, ensuring the temperature and humidity environment required for the relics. Furthermore, air curtains have shown improvements in reducing the overall exposure to contaminants and infection risk compared to traditional ventilation systems [26,27]. Cao et al. [28] studied the control effect of air curtains on indoor pollutants. By optimizing the air conditioning supply parameters, the pollutant concentration difference between the contaminated and clean zone can be controlled to a maximum of 2800 ppm. Moreover, they developed a strategy named “protected zone ventilation” (PZV). Through a plane jet diffuser, the risk of cross-infection of indoor occupants is effectively reduced [29]. This air supply method has been extended to medical places. The ward can be divided into the patient area and medical care area through an air barrier to ensure the life and health of nursing workers [30].

This paper holds that the environmental creation potential of air curtains in LPBs needs to be explored. It does not require additional air ducts for connection during air supply. This flexible reforming feature enables it to adapt to the functional partition of LPBs at different stages of use. When the adjacent partitions are in the occupied state, the air curtain can be closed, and these zones can be classified as the same space for temperature control. In the literature, previous studies focused on the isolation effect of a single air curtain on both sides of the environment. No scholar has tried to use an air curtain group to create closed subspaces in LPBs. The stability of combined operation with multiple air curtains is unknown. Moreover, the operation status of an indoor air curtain is affected by the jet of the air supply diffuser, and this correlation has not been discussed.

This paper studies the airflow construction mode for LPB partition, which is named the air curtain grid system (ACGS). For optimizing its parameters, the impacts of the diffuser supply angle, air curtain velocity, and boundary coverage ratio were numerically investigated. Through velocity/temperature distribution, air curtain efficiency, and COP, the feasibility and energy-saving potential of ACGS are verified. This provides a theoretical basis for effectively blocking heat in different air supply zones of LPBs.

2. Methodology

This section first analyzes the design points of ACGS. Then, the infiltration model of the air curtain at the building entrance mentioned in the previous study is reviewed. We try to extend this model and apply it to the evaluation of ACGS operating status, which is verified in the following sections. The details of CFD modeling and the evaluation criteria of ACGS are also presented in this section.

2.1. Establishment of ACGS

Maintaining the independence and stability of each air supply area is the foundation of ACGS. In this paper, the design principles are summarized into the following four points:

(a)

For rooms controlled by the mechanical ventilation system, the indoor pressure is determined by the difference between the supply and return air volume. Therefore, it must be guaranteed that each ACGS zone has both an air supply vent and a return vent. Otherwise, the air curtain will be damaged due to the high/low pressure difference.

(b)

Conventional ceiling diffusers should be avoided. The air supply flow adheres to the ceiling because of the Coanda effect and mixes with the air curtain jet after the adherent jet section. This “diffuser—air curtain short circuit” phenomenon reduces the regulating effect of conditioned air on the occupant zone, which will be verified in this paper.

(c)

The zone division shape of ACGS should be compatible with the air supply flow type of the diffuser. For instance, in the square ACGS zone, symmetrical diffusers should be used to maximize the restriction of the air curtain on the jet.

(d)

When the adjacent ACGS zones are occupied and the indoor temperature setting points are the same, the air curtain between the two zones should be closed to avoid energy waste. At this point, these two zones are merged.

A multi-flow ceiling-cassette-type diffuser (MCD) is selected as the implementation device of ACGS airflow mode in this paper. It consists of a central return vent and surrounding slot air supply outlets. Each outlet is equipped with a deflector to control the air supply angle. Lo et al. [15] and Ishiguro et al. [31] have demonstrated the zoning control potential of MCD in open spaces. The partitioning effect generated by the diffuser is beneficial to the creation of an independent air supply space. Moreover, MCD meets the principles mentioned above, which is compatible with ACGS. It is worth mentioning that the background ventilation of ACGS is not unique. Due to the diversity of the tuyere layout, other methods will not be discussed in this paper.

When the air curtain is applied to the building entrance, the air can be taken outdoors or indoors according to the type of building. In order to resist the bending of the air curtain jet caused by pressure, the supply air outlet should deflect 15°–20° to the warm side [32]. When ACGS is used to divide the indoor space, its operation status is related to the occupancy of different control zones. The “internal space” and “external space” corresponding to each air curtain are convertible. Therefore, the air curtain return vent in this paper is set at the vertical upward position and attracts air from adjacent ACGS zones on both sides. The supply vent is arranged vertically downward.

2.2. Mathematical Description

For the air curtain at the building entrance, indoor and outdoor pressure $P_i$ and $P_o$, respectively, are the main factors affecting its operation effect. According to the pressure difference ${\Delta P}_{oi}$ (${\Delta P}_{oi}=P_o-P_i$), previous studies have divided aerodynamics conditions into three types: optimum condition, inflow break-through, and outflow break-through. As shown in Figure 1, they are divided by the upper critical pressure difference ${\Delta P}_{uc}$ and lower critical pressure difference ${\Delta P}_{lc}$ [33]. At any time, we want the air curtain to operate under optimal conditions and for the air curtain jet to reach the floor, which requires minimum air infiltration and exfiltration.

In most conditions, we hope to quantify the air infiltration and exfiltration rates $Q$ during the operation of the air curtain through ${\Delta P}_{oi}$. At an entrance without an air curtain, the air infiltration can be calculated by the orifice equation [34], as shown in Equation (1), where $\mu$ is the flow coefficient related to the structure of the door, $F$ is the cross-sectional area of the building entrance, and $\rho$ is the air density, which is related to the actual temperature.

$$Q=sign\left({\Delta P}_{oi}\right)\mu F\sqrt{\frac{2\left|{\Delta P}_{oi}\right|}{\rho }}$$

(1)

Wang [33] considered the operation cycle during the use of the door and introduced the average flow coefficient $C_{Dave}$ (as shown in Equation (2)). $C_{D,a}$, $C_{D,b}$, $C_{D,c}$, and $C_{D,d}$ represent the flow coefficients of the door in four different operation stages in a cycle. $a$, $b$, $c$, and $d$ represent the operation duration of the respective stage. The influence of an air curtain can be expressed by a correction term $D_{D,ave}$, which is related to the air curtain operation state (Equation (3)).

$$C_{D,ave}=\frac{C_{D,a}a+C_{D,b}b+C_{D,c}c+C_{D,d}d}{a+b+c+d}$$

(2)

$$\frac{Q}{A\sqrt{2/\rho }}=sign\left({\Delta P}_{oi}\right)C_{D,ave}\sqrt{\left|{\Delta P}_{oi}\right|}+D_{D,ave}$$

(3)

The above formula can be sorted into an expression about air exchange quantity $Q$ (Equation (4)), which is irrelevant to the environmental parameter ${\Delta P}_{oi}$. It can be simplified into a more general form, Equation (5). By testing the air infiltration rates under different pressure differences, the parameters $C$ and $D$ can be fitted, and then the performance curve of a specific air curtain can be obtained. The accuracy of this model has been verified in [35,36,37]. At the same time, these studies also prove that the model is widely applicable under different geometric dimensions of air curtains, air supply velocities, and installation angles.

$$Q=sign\left({\Delta P}_{oi}\right)C_{D,ave}A\sqrt{\frac{2\left|{\Delta P}_{oi}\right|}{\rho }}+D_{D,ave}A\sqrt{\frac{2}{\rho }}$$

(4)

$$Q=C\sqrt{\left|{\Delta P}_{oi}\right|}+D$$

(5)

The closed space created by ACGS does not have the orifice described by Equation (1). In contrast, there is heat and mass exchange on the whole separating surface where the air curtain is located. We assume that the air curtain can still be regarded as an ‘orifice’ in this case, and $F$ in Equation (1) represents the area of the entire separating surface. Furthermore, when the air curtain is used as an indoor barrier, it does not involve the influence of the door operation process. $C_{D,ave}$ and $D_{D,ave}$ in Equation (4) can be simplified to the steady-state $C_D$ and $D_D$, respectively. At this time, the air exchange quantity $Q$ in the calculation zone can be expressed as the sum of the air exchanges of different air curtains, as shown in Equation (6), where $n$ is the number of air curtains operating in the zone. When creating a rectangular enclosed zone through an air curtain group without any internal wall, n = 4, and so on. $A_i$ is the sectional area corresponding to each air curtain, and $C_{Di}$ and $D_{Di}$ are the flow coefficient and correction coefficient corresponding to each air curtain, respectively.

$$Q=sign\left({\Delta P}_{oi}\right)\sum _{i=1}^n\left(C_{Di}{A}_i\right)\sqrt{\frac{2\left|{\Delta P}_{oi}\right|}{\rho }}+\sum _{i=1}^n\left(D_{Di}{A}_i\right)\sqrt{\frac{2}{\rho }}$$

(6)

Equation (6) shows that the relationship between $Q$ and $\sqrt{{\mathsf{\Delta }P}_{oi}}$ is still linear and can be simplified as Equation (5). However, this relationship depends on the assumption of orifice. Therefore, this paper studies the relationship between the internal and external pressure difference ${\mathsf{\Delta }P}_{oi}$ of the ACGS zone and the air exchange quantity $Q$. We compare the fitting results with Equation (6) to verify the rationality of the mathematical model proposed in this paper.

2.3. Airflow Modeling

Many studies have proved the rationality of computational fluid dynamics (CFD) in describing the operating state of air curtains [33,35]. The simulation in this paper is carried out in ANSYS FLUENT software. The pressure and velocity are coupled by the SIMPLE scheme. The standard $k-\epsilon$ model is used as the turbulence model, which performs well for indoor airflow [10,38,39].

The research object is an open office, which may have a large actual size. In this study, a $24 \mathrm{m}\times 24 \mathrm{m}\times 2.8 \mathrm{m}$ ($\mathrm{L}\times \mathrm{W}\times \mathrm{H}$) internal fluid domain of the building was intercepted and assumed to be unaffected by external heat sources (as shown in Figure 2a). The ACGS divides the whole space into 9 zones of $8\mathrm{m}\times 8\mathrm{m}$. We take the central zone as the research object. This condition represents the most typical mode of partial space occupation (Figure 2b).

The cooling load of the building’s interior zone is mainly affected by the internal heat source. This study considers the equipment (55 W) and personnel heat dissipation (75 W). To reduce the grid number and computational burden, each person and their corresponding equipment are simplified into a $0.5 \mathrm{m}\times 0.5 \mathrm{m}\times 1.4 \mathrm{m}$ cube with a heat dissipation of 130 W, as shown in Figure 2c. The heat transfer caused by lighting and building maintenance structures is calculated assuming 20 $\mathrm{W}/{\mathrm{m}}^2$, and the heat flux density of the upper and lower walls is set to 10 $\mathrm{W}/{\mathrm{m}}^2$ [14]. For non-occupied zones, only this part of the load is considered without occupants and equipment.

Each zone is equipped with an independently controlled MCD (Figure 3a), and its simplified model and geometric dimensions are shown in Figure 3b. The magnitude and direction of velocity can be defined by the horizontal and vertical components, and the feasibility of this method has been shown in [40]. The geometric dimensions of the vents involved can be seen in

Table 1. Geometric parameters of tuyere in CFD model.

Type	Geometric Parameter (m)	Area (m2)	Description
Diffuser—outlet	0.55 × 0.55	0.30	Installed in the center of the ceiling of each ACGS zone
Diffuser—inlet	0.45 × 0.08	0.02	Installed around the outlet
Air curtain—outlet	0.08 × 7.00	0.56	Air curtain installed at the junction of ACGS zones
Air curtain—inlet	0.08 × 7.00	0.56

. The relative positions of the geometric items are shown in Figure 3c.

As shown in Figure 2c, the side surfaces of the fluid domain are set as pressure outlets to indicate the free diffusion of air in the open space to the surrounding area. The air supply vent is set as a velocity inlet. The ceiling return vent is set as a mass flow outlet, and the pressure in the ACGS zone can be adjusted by changing the air return volume.

The air supply temperature is related to the return air, which is initially unknown. In this paper, a “recirc type” opening is created for the air curtain [41]. The return vent of the air curtain is set as the mass flow outlet and given the same mass flow as the supply vent to ensure mass conservation. The supply vent of the air curtain is set as the velocity inlet and is given the same temperature as the return vent to ensure energy conservation. Affected by its own structure, the velocity on the air supply surface is uneven during actual operation [42]. Most previous studies have set the boundary conditions of the air curtain vent section to uniform values [10,30,41], and the simulation results of this method were proved to be acceptable by Goubran et al. [35]. In this study, the velocity and temperature of the air curtain vent section are also simplified in this way.

The turbulence density of the velocity inlet affects the airflow distribution. Navaz et al. [43] have shown that a lower Reynolds number and turbulence intensity can reduce the entrainment rate of air curtains, but this effect is not obvious under low $Re$. Since the low Reynolds jet of air curtains and the indoor airflow pattern are the interests of this paper, the turbulence density factor is not considered and adopts the value in Ref. [10] (as shown in

Table 2. Boundary parameters of the ACGS zone.

Name	Background Inlet	Background Outlet	Air Curtain Inlet	Air Curtain Outlet	ACGS Zone
Size (m)	0.40 × 0.05	0.55 × 0.55	7.00 × 0.08	7.00 × 0.08	8.00 × 8.00
Turbulence intensity	15%	10%	20%	15%	-

).

Due to the symmetry of the model, a quarter of the zone in Figure 2a is taken for calculation. The intercept boundary is set as symmetry. In order to improve the calculation accuracy, the surface grid of the air supply/return vents and the volume grid within 0.5 m of the air curtain jet are densified. The air coming out from the air curtain is vertical, and the grid lines should follow the airflow direction [44]. The number of divisions modeling the width of the air curtain is set as 4. The element size of the lateral 4 m region grid that is less affected by air conditioning and the air curtain is appropriately increased to reduce the computational burden. In this paper, four grid numbers of 5,254,782, 5,902,693, 6,178,045, and 6,637,964 are selected for grid independence verification. The results show that the relative uncertainty of the number of grids of 6,178,045 relative to 6,637,964 is within 5% (as shown in

Table 3. Grid independence testing using three mesh cases.

Grid Type	Element Size (mm)	Number of Elements	Temperature			The Relative Difference with the Previous Grid (P1/P2/P3)
			P1(2,0,0.1)	P2(2,0,1.4)	P3(2,0,2.7)
Mesh 1	120	5,254,782	18.97	23.53	25.05	——
Mesh 2	100	5,902,693	21.62	25.65	26.46	13.97%/9.02%/5.64%
Mesh 3	90	6,178,045	20.75	23.86	25.08	4.02%/6.98%/5.22%
Mesh 4	80	6,637,964	20.91	22.89	24.41	0.77%/4.07%/2.67%

), so the number of grids of 6,178,045 is adopted [30]. The grid diagram can be seen in Figure 4.

2.4. Evaluation Criteria

To evaluate the isolation effect and economy of ACGS in open space, this paper discusses the following indicators of ACGS:

• Temperature distribution;
• Heat exchange capacity;
• Air curtain effectiveness;
• Air curtain COP.

2.4.1. Air Curtain Efficiency

For the building entrance, the air partition efficiency $E$ of the air curtain is defined as the reduction rate of the air exchange volume after installing the air curtain compared with the door-opening situation. In Equation (7), $Q$ and $Q_a$ represent the air exchange volume at the entrance before and after the installation of the air curtain, respectively.

$$E=\frac{Q-Q_a}{Q}$$

(7)

When the air curtain is applied indoors, we are more interested in the blocking of heat and the construction of a stable thermal environment. The heat exchange between zones can be regarded as the sum of two components; the first part is the advective heat transfer caused by the pressure-promoted cross-region flow, and the second part is the diffusive heat transfer caused by molecular and turbulent diffusion [45]. The calculation of these two parts can be unified into Equation (8). $W$ and $H$ represent the width and height of the air exchange section, respectively, and $v_x$ is the velocity component perpendicular to this section. $\rho$ and $c_p$ represent air density and specific heat capacity, respectively, which can be simplified as constant values. $T(x,y)$ is the temperature field of the calculation section. $T_{avg}$ is the average air temperature, as defined in Equation (9), where $T_{in}$ and $T_{out}$ represent the average temperature in the zone and the unconditioned zone on the other side of the curtain, respectively.

$$q={\int }_0^W{\int }_0^H{v}_x\rho c_p\left(T(x,y)-T_{avg}\right)dzdy$$

(8)

$$T_{avg}=\frac{T_{in}+T_{out}}{2}$$

(9)

The air curtain efficiency $\epsilon$ defined by cooling load is illustrated by Equation (10) [46], where $q_m$ is the cooling/heating load of a conventional ventilation system, and $q_{a,m}$ is the cooling load with ACGS under the same background ventilation form.

$$\epsilon =\frac{q_m-q_{a,m}}{q_m}$$

(10)

2.4.2. Air Curtain COP

Energy saving is the key objective of ACGS partition control. In order to consider the power consumption of air curtains and the contribution of air curtains to cooling load reduction, this paper draws on the air curtain COP (${COP}_c$) proposed by Shen et al. [10] to measure the economic performance of the ACGS, as shown in Equation (11), where $N$ represents fan power consumption. When the air curtain increases the heat transfer between different regions ($q_{a,m}$ > $q_m$), ${COP}_c$ < 0.

$${COP}_c=\frac{q_m-q_{a,m}}{N}$$

(11)

The calculation formula of $N$ is shown in Equation (12), where $n$ is the number of air curtains in operation, which is related to the actual operating conditions; $V_i$, $P_i$, and ${\eta }_i$ represent the volume flow rate, pressure head, and fan efficiency of each air curtain, respectively.

$$\begin{array}{c}N={\displaystyle \sum _{i=1}^n}\frac{V_i{P}_i}{{\eta }_i}\end{array}$$

(12)

When the ACGS zone is a regular square and each air curtain has the same operating status, Equation (12) can be simplified to Equation (13).

$$N=\frac{nVP}{\eta }$$

(13)

3. Results and Discussion

3.1. Validation

The verification of numerical simulation is based on the experimental test results of Lo et al. [14]. The research objects in their study are office buildings, which are similar to the heat source distribution and heat dissipation described in Figure 2b. Furthermore, they also adopted the air supply terminal of MCD and arranged it in the center of each air conditioning area. The simulation is carried out under the condition of a diffuser air velocity of 5 m/s and an air supply angle of 45°. The results are compared to those with the velocity at the same position in Ref. [14] as shown in Figure 5b,c.

As shown in Figure 5a, the variation trend of the simulated velocity at different points is consistent with the experimental value. Points 4 and 7 have large velocity deviations, which are located at the furthest extreme of the diffuser jet. This local deviation may be due to the difference in airflow velocity attenuation caused by different turbulence densities of the diffuser [47]. However, it is difficult to accurately obtain the experimental data such as diffuser size and air supply parameters. In addition, the experimental measurement might have some random uncertainties, and the deviation caused for this reason should also be taken into account. Because the velocity variation trend of the simulated data and measured data can be considered consistent, and because the data deviations are small at most positions, the simulation method (turbulence model, mesh density, and tuyere modeling) in this paper can be considered reasonable.

3.2. Airflow Distribution under Different Diffuser Angles and Air Curtain Velocity

The diffuser supply angle directly determines the airflow mode (adherent jet or free jet). At the same time, air curtain jet velocity is the dominant factor affecting environmental isolation. These two factors are discussed in this section. Through the velocity and temperature field, combined with the calculated air curtain efficiency $\epsilon$ and the temperature distribution of the ACGS zone, the optimal airflow pattern can be initially selected. The study conditions involved in this section are shown in

Table 4. Simulation of different diffuser angles and air curtain velocity.

Case Number	Air Curtain Velocity (m/s)	Angle of Diffuser (°)	Case Number	Air Curtain Velocity (m/s)	Angle of Diffuser (°)
1	1	30	6	2	60
2	1	45	7	5	30
3	1	60	8	5	45
4	2	30	9	5	60
5	2	45

. In order to determine the theoretical cooling capacity required, we performed a pre-simulation in an $8 \mathrm{m}\times 8 \mathrm{m}\times 2.8 \mathrm{m}$($\mathrm{L}\times \mathrm{W}\times \mathrm{H}$) enclosed space, which is consistent with the size of the ACGS subzone. The air velocity and temperature of the diffuser are set to 2.9 m/s and 16 °C, respectively.

Only cooling scenarios are considered in this study because (a) air distributions in the cooling and heating state produce completely different results [48], which is beyond the scope of this paper, and (b) the ACGS is mainly for the multi-regional division of LPBs. Due to the existence of internal heat sources, this type of space usually requires annual cooling [14].

The velocity field simulation results for different cases in Table 4 are summarized in Figure 6. The results show that when the diffuser angle is 30°, because of the Coanda effect, all airflow appears as an adherent jet (Case1, Case4, and Case7). This part of the airflow is inhaled by the air curtain return vent after a certain distance of transportation and eventually sent back into the room in the form of a jet, forming a “diffuser—air curtain short circuit”. At this time, the air curtain is equivalent to the role of an induced draft fan. The conditioned air is transported to the non-occupied zone through the curtain jet, resulting in a waste of cooling capacity. This adherent jet condition also proves that the conventional attached air supply ceiling diffuser is not applicable in the ACGS system.

Under the condition of the diffuser at a 45° angle, the air curtain and diffuser jet are shown as intersections. Because of the weak momentum of the air curtain, the airflow has an outflow break-through trend (Case2 and Case5). The increase in the air supply rate of the air curtain strengthens the negative pressure in the return air area and makes the diffuser jet deflect upward. When the negative pressure is strong enough, the 45° outlet airflow of the diffuser also becomes an adherent jet (Case8).

The diffuser angle of 60° shows better results (Case3, Case6, and Case9). Conditioned air is directly sent into the working area, independent of the air curtain jet, and restricted inside the ACGS zone. However, a larger air curtain jet velocity means more air is entrained on both sides. When this airflow is strong enough, it overflows to both sides after hitting the ground. This is also called entrainment—a spill mechanism of the air curtain [46]. As shown in Cases7–9, the airflow overflowing to one side of the occupied zone forms a local vortex, which aggravates the convective heat transfer from the occupied zone to the air curtain.

3.3. Thermal Parameters under Different Diffuser Angles and Air Curtain Velocities

Figure 7a shows the temperature distribution of the occupied zone for each operating scenario. For 30° and 45° conditions, the heat in the zone cannot be effectively removed because the air supply angle is biased to the outside, and the temperature can reach 29–30 °C. Exceptionally, when the air curtain velocity reaches 5 m/s, the temperature distribution is independent of the diffuser angle. Due to the mixing of air caused by the high air supply volume of the air curtain, these conditions show high temperature uniformity. The temperature of the entire space is maintained at 27–28 °C. For the 60° condition, when the air curtain velocities are 1 m/s and 2 m/s, the temperature inhomogeneity is large, which is caused by the cold jet directly into the working space. At the same time, the 60° air supply jet has no lateral force on the air curtain, which avoids damage to the air curtain and reduces the convective heat transfer with the adjacent space. When the air curtain velocity is reasonable (2 m/s), the cooling capacity can be limited inside the zone and effectively utilized. It can make the overall temperature level of the zone reach the set temperature of 26 °C, which represents the optimal cooling effect in the scenarios described in this paper.

Figure 7b shows the air curtain efficiency for each operating scenario. When the air supply angle of the diffuser is 30°, the air curtain changes the original attached airflow to downward airflow, reducing the diffusion of conditioned air to the non-occupied zone. This restriction increases with the increase in air curtain velocity, which is consistent with the variation trend of air curtain efficiency $\epsilon$. For the 45° scenarios, $\epsilon$ is also positively correlated with air curtain velocity. It is mainly because the increase in air curtain jet momentum improves the resistance to lateral force, thus having a stronger restrictive effect on conditioned air. There is an optimal air curtain velocity when the conditioned air is supplied at 60°. This is mainly because excessive jet air entrains more air, increasing the convective heat transfer on both sides.

This paper attempts to analyze the optimal diffuser angle and air curtain velocity combination required for the stable operation of ACGS. In addition to the temperature level and the air curtain efficiency mentioned above, Figure 8 shows the thermal boundary diagram. Case3 and Case6 form a more stable thermal boundary. At this time, conditioned air is confined to the ACGS zone by the air curtain jet, and the temperature difference on both sides of the air curtain can reach 3 °C. Under other working conditions, the failure causes of ACGS can be multifaceted, which can be classified as follows:

(a)

The “diffuser—air curtain short circuit” phenomenon causes the conditioned air to be directly discharged into the non-occupied zone (Case1, Case4, Case7, and Case8). The accumulation of heat can make the occupied zone temperature reach 29–30 °C.

(b)

The air curtain is damaged by the large lateral force produced by the diffuser jet (Case1, Case2, and Case5). The initial jet momentum of the air curtain is low, the conditioned air cannot be constrained inside the ACGS zone, and the air in the non-occupied zone can also be processed to 27 °C. The heat in the occupied zone cannot be effectively removed due to the overflow of cold energy, and the local temperature can reach 29–30 °C.

(c)

Excessive curtain velocity leads to increased heat transfer on both sides (Cases7–9). The air curtain velocity of 5 m/s cannot create a better thermal isolation effect. On the contrary, it makes the whole space tend to a uniform temperature (27 °C). At this time, the air conditioning still uses a full-space mode of air supply and increases the energy consumption of the air curtain.

3.4. Energy-Saving Effect under Different Air Curtain Coverage Ratios

When the ACGS zone boundary is fully covered by the air curtain, it ensures complete separation in the spatial sense, which means more air input and energy consumption. The results of Liu et al. [38] show that a 60% air curtain coverage ratio can make the pollutant isolation efficiency reach 30%. Similarly, this section studies the thermal isolation under some scenarios of air curtain position and coverage ratio, which are shown in

Table 5. Air curtain coverage scenarios.

Scenario ID	Air Curtain Layout		Length Parameter
	Method	Airflow Diagram	Length (m)	Coverage Ratio
6	Midportion 1		7	87.5%
10	Separation 2
11	Midportion		6	75.0%
12	Separation
13	Midportion		5	62.5%
14	Separation
15	Midportion		4	50.0%
16	Separation

¹ Midportion: a single air curtain is arranged in the middle of the interface. ² Separation: two air curtains are evenly arranged on the interface.

.

As shown in Figure 9, the heat exchange of the midportion air curtain is weaker than the separation air curtain, and the air curtain with a high coverage ratio does not achieve the best isolation effect. For the midportion layout method, when the air curtain coverage ratio is above 62.5%, the heat exchange quantity is stable at about 4000 W. The optimal coverage ratio is 50.0%, and the heat exchange quantity is 2192 W, which is reduced by 52.2%. Due to the low air supply under a low coverage ratio, the ${COP}_c$ under this condition is also the highest, which can reach 17.1. For the separation layout method, 87.5% and 75.0% coverage increase the heat exchange of the area on both sides of the air curtain. Compared with the control group of 4582 W, the heat exchange quantity can reach 6696 W and 9420 W, respectively. When the coverage ratio is reduced to 62.5% and 50.0%, the isolation effect of the separation air curtain begins to be reflected. The heat exchange is reduced to 3108 W and 2561 W, respectively. The ${COP}_c$ is 8.4 and 14.4 at this time, respectively.

Figure 10 shows the velocity vector diagrams of different air curtain coverage ratios in Y = 0 m and Y = 2 m planes. The difference in airflow distribution between the two layout methods of midportion and separation is reflected in the Y = 0 plane. The ceiling diffuser is arranged at the center of the ACGS zone. The midportion air curtain can effectively limit the diffuser jet inside the zone. The separation air curtain has no airflow barrier in the middle, resulting in conditioned air jet overflow and cooling loss. This difference explains why the heat exchange capacity of the separation air curtain is larger.

The airflow distributions of different scenarios on the Y = 2 m plane are similar. Under the induction of air curtain airflow, two large vortices are formed in the room. The air curtain airflow blocks a part of the conditioned air with an outward movement tendency and makes this part of the air return to the central area of the zone. However, at the same time, there is convective heat exchange between the two vortices, and some of the cold air is sucked into the air curtain return vent, which is not effectively utilized. The strengths of the two vortices are different under different coverage ratios. At a coverage ratio of 75.0%, more cold air is sucked into the air curtain airflow, and the heat exchange capacity reaches the maximum. When the coverage ratio of the air curtain is reduced to 50.0%, the air entrainment becomes weaker, and a higher proportion of the cooling capacity is limited inside the zone. At this time, the air curtain plays a positive role.

3.5. Infiltration/Exfiltration Characteristics of ACGS

As mentioned above, for the multi-air-curtain operation mode of ACGS, Equation (5) derived from the orifice hypothesis still satisfies the simplified form of Equation (4). To verify this mathematical description, two air curtain jet velocities of 2 m/s and 5 m/s are selected to represent the low- and high-velocity conditions of an indoor air curtain, respectively, and the infiltration/exfiltration curves of air in the range of −5 Pa~5 Pa were fitted, with a total of 50 scenarios. In order to ensure the uniformity of pressure, the upper and lower surfaces inside the ACGS zone are set as pressure—inlet. All scenarios are simulated under the condition of an isothermal jet.

As shown in Figure 11, with a pressure difference in the range of −5 Pa~5 Pa described in this paper, an air curtain velocity of 5 m/s leads to a smaller air exchange capacity than a 2 m/s air curtain velocity, which is reflected in the range of ${\Delta P}_{oi}$ > 0 and ${\Delta P}_{oi}$ < 0. This is because the increase in the momentum of the air curtain jet improves the resistance to lateral force, which can be seen in the deflection modulus method proposed by Hayes and Stoecker [49]. Since MCD is used as the air supply diffuser in this paper, it integrates the air supply and return vents, and the pressure in the ACGS zone is small. In contrast, the influence of the air conditioning jet is dominant, which has been discussed in the previous section.

The curve fitting of 5 m/s and 2 m/s scenarios is carried out by using the form of Equation (4). As shown in

Table 6. Fitting coefficient of different scenarios.

Scenarios	Direction	Parameters in Equation (4)		${\mathit{R}}^2$
		$\mathit{C}$	$\mathit{D}$
2 m/s	outflow	50.93	−4.85	0.9957
	inflow	62.80	−10.67	0.9918
5 m/s	outflow	62.37	−38.19	0.9909
	inflow	61.85	−35.17	0.9944

, for the two different air curtain operation states of inflow and outflow, the fitting coefficient $R^2$ can reach 0.99. This shows that for the closed space created by multiple air curtains, although there is no obvious geometric orifice in the orifice model [34], $Q$ and $\sqrt{{\mathsf{\Delta }P}_{oi}}$ still satisfy the linear relationship, which verifies the rationality of Equation (5) derived in this paper.

3.6. Limitations and Prospects

This subsection first summarizes the limitations of the study. Then, based on the main research results of this paper, it provides guidance and suggestions for air curtain companies and managers.

(1)

The research in this paper is based on numerical simulation. Simplified models are used for tuyeres, personnel, and equipment, which may cause deviations between the results and the actual working conditions. An experimental study needs to be carried out in the future. In addition, the simulation conditions are limited. Only three values were selected for both the diffuser angle and the air curtain velocity, which means that we ignore details in the process of continuous change in variables, and more scenarios need to be considered.

(2)

The positions of occupants in this paper are assumed to be fixed, which deviates from the actual situation. More generally, the indoor air curtain is disturbed by the dynamic movement of pedestrians. The personnel flow can aggravate the heat exchange between adjacent zones. It is necessary to establish a quantitative relationship between “air curtain-foot traffic” and operational efficiency in the future, which directly determines the adaptability of indoor air curtains to different occasions (such as supermarkets, offices, and hospitals).

(3)

The comfort of ACGS is not discussed in this paper. Unreasonable air curtain operating parameters may cause a draught sensation to occupants (such as on the ankle [30]). In addition, more potential air curtain–background ventilation combinations need to be considered, which may lead to different indoor temperature and velocity distributions.

The existing air curtain is mainly applicable to the building entrance. In order to resist thermal pressure and wind pressure, the equipment usually has a large-rated air velocity (6~8 m/s) [22,23], which is not suitable for indoor partitions. It is recommended that relevant companies develop low-volume air curtains suitable for indoor use. Additionally, the air curtain should be light and miniaturized to facilitate hoisting.

4. Conclusions

This paper carried out a numerical simulation to investigate the indoor thermal insulation effect of air curtains. An ACGS air supply mode is created, which divides the LPB space into subzones through air curtains. The effects of diffuser supply angle, air curtain velocity, and boundary coverage ratio on ACGS operation efficiency were studied. Compared with mixed ventilation, ACGS can generate a 2 °C temperature difference between adjacent zones. The combination of a 60° diffuser air supply angle and 2 m/s air curtain velocity shows the best effect in the studied cases, which can maintain the occupied zone at the set temperature (26 °C) and reduce the heat transfer from the adjacent space by 58%. For ACGS design, the air curtain should be arranged in the position opposite the conditioned air jet to limit the outward diffusion of cooling capacity. A 50% air curtain coverage ratio can reduce 52% of the heat exchange for the scenarios addressed in this paper. Moreover, the air infiltration equation under the combined operation of multiple air curtains is established and verified. This study provides a new approach to the air conditioning partition control of LPBs.