The system under consideration consists of two air conditioners"
the main one, in which air is processed for the serviced premises, and the auxiliary one - the cooling tower. The main purpose of the cooling tower is air-evaporative cooling of water feeding the first stage of the main air conditioner during the warm season (surface heat exchanger PT). The second stage of the main air conditioner - irrigation chamber OK, operating in adiabatic humidification mode, has a bypass channel - bypass B to regulate air humidity in the room.
In addition to air conditioners - cooling towers, industrial cooling towers, fountains, spray pools, etc. can be used to cool water. In areas with a hot and humid climate, in some cases, in addition to indirect evaporative cooling, machine cooling is used.
multistage systemsevaporative cooling. The theoretical limit for air cooling using such systems is the dew point temperature.
Air conditioning systems using direct and indirect evaporative cooling have a wider range of applications than systems that use only direct (adiabatic) evaporative cooling.
Two-stage evaporative cooling is known to be most suitable in
areas with dry and hot climates. With two-stage cooling, lower temperatures, fewer air changes and lower relative humidity in rooms can be achieved than with single-stage cooling. This property of two-stage cooling has led to a proposal to switch entirely to indirect cooling and a number of other proposals. However, all other things being equal, the effect of possible evaporative cooling systems directly depends on changes in the state of the outside air. Therefore, such systems do not always ensure the maintenance of the required air parameters in air-conditioned rooms throughout the season or even one day. An idea of the conditions and boundaries of the appropriate use of two-stage evaporative cooling can be obtained by comparing the normalized parameters of indoor air with possible changes in the parameters of outdoor air in areas with a dry and hot climate.
the calculation of such systems should be carried out with using J-d diagrams in the following sequence.
On J-d diagram points with the calculated parameters of external (H) and internal (B) air are plotted. In the example under consideration, according to the design specifications, the following values are accepted: tн = 30 °С; tв = 24 °С; fв = 50%.
For points H and B, we determine the value of the wet thermometer temperature:
tmn = 19.72 °C; tmv = 17.0 °C.
As you can see, the value of tmn is almost 3 °C higher than tmv, therefore, for greater cooling of water, and then external supply air, it is advisable to supply air removed to the cooling tower exhaust systems from office premises.
Note that when calculating a cooling tower, the required air flow may be greater than that removed from the conditioned rooms. In this case, a mixture of external and exhaust air must be supplied to the cooling tower and the wet thermometer temperature of the mixture must be taken as the calculated temperature.
From the calculated computer programs leading cooling tower manufacturers find that the minimum difference between the final water temperature at the outlet of the cooling tower tw1 and the wet thermometer temperature twm of the air supplied to the cooling tower should be at least 2 °C, that is:
tw2 =tw1 +(2.5...3) °C. (1)
To achieve deeper air cooling in the central air conditioner, the final water temperature at the outlet of the air cooler and at the inlet to the cooling tower tw2 is taken to be no more than 2.5 higher than at the outlet of the cooling tower, that is:
tвк ≥ tw2 +(1...2) °С. (2)
Please note that the final temperature of the cooled air and the surface of the air cooler depend on the temperature tw2, since with a transverse flow of air and water, the final temperature of the cooled air cannot be lower than tw2.
Typically, the final temperature of the cooled air is recommended to be 1–2 °C higher than the final water temperature at the outlet of the air cooler:
tвк ≥ tw2 +(1...2) °С. (3)
Thus, if the requirements (1, 2, 3) are met, it is possible to obtain a relationship connecting the wet thermometer temperature of the air supplied to the cooling tower and the final temperature of the air leaving the cooler:
tвк =tвм +6 °С. (4)
Note that in the example in Fig. 7.14 the values taken are tbm = 19 °C and tw2 – tw1 = 4 °C. But with such initial data, instead of the value tin = 23 °C indicated in the example, it is possible to obtain the final air temperature at the outlet of the air cooler not lower than 26–27 °C, which makes the whole scheme meaningless at tn = 28.5 °C.
The invention relates to ventilation and air conditioning technology. The purpose of the invention is to increase the cooling depth of the main air flow and reduce energy costs. Water-irrigated heat exchangers (T) 1 and 2 for indirect evaporative and direct evaporative cooling of air are located in series along the air flow. T 1 has channels 3, 4 of general and auxiliary air flows. Between T 1 and 2 there is a chamber 5 for separating air flows with a bypass channel 6 and a per TiHpyeMbiM valve 7 placed in it. The supercharger 8 with the drive 9 is connected by an input 10 with the atmosphere, and an output 11 with channels 3obp (its air flow Valve 7 through the block control is connected to the air temperature sensor in the room. Channels 4 of the auxiliary air flow are connected by output 12 to the atmosphere, and T 2 by output 13 of the main air flow is connected to the room. Channel 6 is connected to channels 4, and drive 9 has a speed controller 14 connected to. control unit. If it is necessary to reduce the cooling capacity of the device, according to a signal from the air temperature sensor in the room, valve 7 is partially closed through the control unit, and using regulator 14, the speed of the blower is increased, ensuring a proportional reduction in the flow rate of the total air flow by the amount of reduction in the flow rate of the auxiliary air flow. . 1 ill. (L to o 00 to
UNION OF SOVIET
SOCIALIST
REPUBLIC (51)4 F 24 F 5 00
DESCRIPTION OF THE INVENTION
FOR THE AUTHORITY CERTIFICATE
STATE COMMITTEE OF THE USSR
ON INVENTIONS AND DISCOVERIES (2 1) 4 166558/29-06 (22) 12/25/86 (46) 08/30/88. Vyu.t, !! 32 (71) Moscow Textile Institute (72) O.Ya. Kokorin, M.l0, Kaplunov and S.V. Nefelov (53) 697.94(088.8) (56) Copyright certificate of the USSR
263102, cl. F ?4 G 5/00, 1970. (54) DEVICE FOR TWO-STAGE
EVAPORATIVE AIR COOLING (57) The invention relates to ventilation and air conditioning technology. The purpose of the invention is to increase the cooling depth of the main air flow and reduce energy costs.
Water-irrigated heat exchangers (T) 1 and 2 for indirect evaporative and direct evaporative cooling of air are located sequentially along the air flow. T 1 has channels 3, 4 of the general and auxiliary air flows. Between T 1 and 2 there is a chamber 5 for separating air flows with a re„„SU„„1420312 d1. inlet channel 6 and an adjustable valve 7 located in it. Supercharger
8 with drive 9 is connected by input 10 with the atmosphere, and by output 11 with channels
3 total air flow. Valve 7 is connected through the control unit to the indoor air temperature sensor. Channels
4 auxiliary air flows are connected by output 12 with the atmosphere, and T 2 by output 13 of the main air flow with the room. Channel 6 is connected to 4 channels and drive 9 has a regulator
14 speed, connected to the control unit. If it is necessary to reduce the cooling capacity of the device, based on a signal from the air temperature sensor in the room, valve 7 is partially closed through the control unit, and using regulator 14, the speed of the blower is reduced, ensuring a proportional reduction in the flow rate of the total air flow by the amount of reduction in the flow rate of the auxiliary air flow. 1 ill.
The invention relates to ventilation and air conditioning technology.
The purpose of the invention is to increase the cooling depth of the main air flow and reduce energy costs.
The drawing shows circuit diagram devices for two-stage evaporative air cooling. The device for two-stage evaporative air cooling contains 15 indirectly evaporative air cooling heat exchangers 1 and 2, irrigated with water, sequentially located along the air flow, the first of which has channels 3 and 4 of the general and auxiliary air flows. 20
Between the heat exchangers 1 and 2 there is a chamber 5 1 for dividing air flows with an overflow channel 6 and an adjustable valve 7 located in it. drive
9 is connected by input 10 with the atmosphere, and by output 11 - with channels 3 of the general flow ltna;ty;:;3. adjustable valve 7 is connected through the control unit to a room temperature sensor (HP shown). Channels 4 of the auxiliary air flow are connected by an output
12 with the atmosphere, and heat exchanger 2 of direct evaporative air cooling with outlet 13 of the main air flow - with heat exchanger. Bypass channel 6 is connected to valves 4 of the power supply air, and drive 9 of supercharger 8 has a rotation speed regulator 14, connected to control unit 4O (not yet: 3l? . device.g - "d" of two-stage evaporative cooling" l303duhl and; works as follows.
The outside air enters through the inlet 10 and 3-45 into the compressor 8 and through the outlet 11 ttartteT flows into the channels 3 of the general air flow of the heat exchanger for indirect evaporative cooling. When air passes through channels 3 ilpo, there is a decrease in its enthalpy ttpta constant moisture content, after which the total air flow enters chamber 5 rl for the division of air currents.
From chamber 5, part of the pre-cooled air in the place of the auxiliary air flow through the bypass channel 6 enters the auxiliary air flow channels 4 irrigated from above, located in the heat exchanger 1 perpendicular to the direction of the general air flow. In channels 4, evaporative cooling of the stacked air occurs. down the walls of channels 4 there is a film of water and at the same time cooling the general air flow passing through channels 3.
The auxiliary air flow, which has been strengthened and has increased its enthalITHIt3, is removed through outlet 12 into the atmosphere or can be used, for example, for ventilation of auxiliary rooms or cooling of building enclosures under construction. The main air flow comes from the air flow separation chamber 5! 3 direct evaporative cooling heat exchanger 2, where the air is further cooled and cooled at a constant enthalpy and at the same time depleted, after which it is processed. and the main air flow through output 13 is supplied to the displacement. If necessary, reduce the control of the device tet ITT according to the corresponding date signal and the air temperature in the room through the control unit (not shown), the adjustable valve 7 is immediately closed, which leads to a decrease in the consumption of the auxiliary air flow and a decrease in the degree cooling" of the total air flow in the heat exchanger 1 of indirect evaporative cooling. Simultaneously with cover
R. gys!Itpyentoro to:glplnl 7 with use of the ItItett regulator 14 rotation speed!
tot:; the number of revolutions of the blower 8 is increased, ensuring proportional flow rate of the total air flow and:
»ep..tc1t ttãp!I I nogo sweat cl air.
1 srmullieobreteniya u.troystvs; for two-stage evaporative air cooling, containing i os.geggo»l gegpo p,lñ!TOITointed along the air flow, irrigated!30 heat exchangers for indirect evaporative and direct evaporative air cooling, the first of which has channels of common and auxiliary air flows, an air flow separation chamber located between the heat exchangers with a bypass channel and an adjustable adjustable valve located in it, a blower with a drive, communicating Itttt ttt g3x
Compiled by M. Raschepkin
Techred M. Khodanich Proofreader S. Shekmar
Editor M. Tsitkina
Circulation 663 Subscribed
VNIIPI of the USSR State Committee for Inventions and Discoveries
113035, Moscow, Zh-35, Raushskaya embankment, 4/5
Order 4313/40
Production and printing enterprise, Uzhgorod, st. Projectnaya, 4 swarm, and the outlet is with the channels of the general air flow, and the adjustable valve is connected through the control unit to the room air temperature sensor and the auxiliary air flow channels are connected to the atmosphere, and the direct evaporative cooling heat exchanger is connected to the room, from The main thing is that, in order to increase the cooling depth of the main air flow and reduce energy costs, the bypass channel is connected to the auxiliary air flow channels, and the injection drive is equipped with a speed controller connected to the control unit.
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When constructing processes on an i - d diagram and selecting technological scheme air treatment must strive to rational use energy, ensuring economical consumption of cold, heat, electricity, water, as well as saving construction space occupied by equipment. For this purpose, it is necessary to analyze the possibility of saving artificial cold by using direct and indirect evaporative cooling of air, using a scheme with regeneration of heat from exhaust air and recycling heat from secondary sources, if necessary, using first and second air recirculation, a bypass scheme, as well as controlled processes in heat exchangers.
Recirculation is used in rooms with significant excess heat, when the supply air flow rate determined to remove excess heat is greater than the required outside air flow rate. In the warm season of the year, recirculation makes it possible to reduce cold costs compared to a direct-flow scheme of the same productivity, if the enthalpy of the outside air is higher than the enthalpy of the removed air, and also to eliminate the need for second heating. During the cold period, significantly reduce heat costs for heating the outside air. When using evaporative cooling, when the enthalpy of the outdoor air is lower than that of the indoor and exhaust air, recirculation is not practical. The movement of recirculation air through a network of air ducts is always associated with additional energy costs and requires a building volume to accommodate recirculation air ducts. Recirculation will be advisable if the costs of its design and operation are less than the resulting savings in heat and cold. Therefore, when determining the supply air flow rate, you should always strive to bring it closer to the minimum required value of outside air, adopting the appropriate air distribution scheme in the room and the type of air distributor and, accordingly, a direct-flow scheme. Recirculation is also not compatible with heat recovery from exhaust air. In order to reduce heat consumption for heating the outside air during the cold season, it is necessary to analyze the possibility of using secondary heat from low-potential sources, namely: the heat of exhaust air, exhaust gases of heat generators and technological equipment, heat of condensation refrigeration machines, heat of lighting fixtures, heat Wastewater etc. Heat exchangers for regenerating the heat of the removed air also make it possible to slightly reduce the cold consumption in warm time years in areas with hot climates.
To do right choice, you need to know the possible air treatment schemes and their features. Let's consider the most simple processes changes in air condition and their sequence in central air conditioners serving one large room.
Typically, the determining mode for choosing a processing flow chart and determining the performance of an air conditioning system is the warm period of the year. During the cold period of the year, they strive to maintain the supply air flow rate determined for the warm period of the year and the air treatment scheme.
The wet bulb temperature of the main air flow after cooling in the indirect evaporative cooling surface heat exchanger has a lower value compared to the wet bulb temperature of the outdoor air, as a natural limit for evaporative cooling. Therefore, when subsequent processing of the main flow in a contact apparatus using the direct evaporative cooling method, lower air parameters can be obtained compared to the natural limit. This scheme of sequential air processing of the main air stream by indirect and direct evaporative cooling is called two-stage evaporative cooling. The layout of the central air conditioner equipment, corresponding to two-stage evaporative air cooling, is presented in Figure 5.7 a. It is also characterized by the presence of two air flows: main and auxiliary. Outdoor air, which has a lower wet-bulb temperature than the indoor air in the room being served, enters the main air conditioner. In the first air cooler, it is cooled using indirect evaporative cooling. Next, it enters the adiabatic humidification unit, where it is cooled and humidified. Evaporative cooling of water circulating through the surface air coolers of the main air conditioner is carried out when it is atomized in the adiabatic humidification unit in the auxiliary flow. Circulation pump takes water from the sump of the adiabatic humidification unit of the auxiliary flow and supplies it to the air coolers of the main flow and then to spraying in the auxiliary flow. The loss of water from evaporation in the main and auxiliary flows is replenished through float valves. After two stages of cooling, air is supplied to the room.
In modern climate control technology Much attention is paid to the energy efficiency of equipment. This explains the increased Lately interest in water evaporative cooling systems based on indirect evaporative heat exchangers (indirect evaporative cooling systems). Water evaporative cooling systems may be effective solution for many regions of our country, the climate of which is characterized by relatively low air humidity. Water as a refrigerant is unique - it has a high heat capacity and latent heat of vaporization, is harmless and accessible. In addition, water has been well studied, which makes it possible to fairly accurately predict its behavior in various technical systems.
In indirect evaporative systems, the air can be cooled to point “3” (Fig. 1). Process diagram in in this case goes vertically down the line of constant moisture content. As a result, the resulting temperature is lower, and the moisture content of the air does not increase (remains constant).
In addition, water evaporation systems have the following positive qualities:
Cooling systems that use the effect of heat absorption during water evaporation have been known for a very long time. However, at the moment, water evaporative cooling systems are not widespread enough. Almost the entire niche of industrial and domestic cooling systems in the region of moderate temperatures is filled with refrigerant vapor compression systems.
This situation is obviously associated with problems in the operation of water evaporation systems when negative temperatures and their unsuitability for operation at high relative humidity of outside air. It was also affected by the fact that the main devices of such systems (cooling towers, heat exchangers), previously used, had large dimensions, weight and other disadvantages associated with working in conditions high humidity. In addition, they required a water treatment system.
However, today, thanks to technological progress, highly efficient and compact cooling towers have become widespread, capable of cooling water to temperatures that are only 0.8 ... 1.0 ° C different from the wet-bulb temperature of the air flow entering the cooling tower.
Here it is worth special mentioning the cooling towers of the companies Muntes and SRH-Lauer. Such a low temperature difference was achieved mainly due to original design cooling tower nozzles with unique properties - good wettability, manufacturability, compactness.
After the heat exchanger, the main air flow is divided into two: auxiliary and working, directed to the consumer.
The auxiliary flow simultaneously plays the role of both a cooler and a cooled flow - after the heat exchanger it is directed back towards the main flow (Fig. 2).
At the same time, water is supplied to the auxiliary flow channels. The point of supplying water is to “slow down” the rise in air temperature due to its parallel humidification: as is known, the same change in thermal energy can be achieved either by changing only the temperature or by changing temperature and humidity simultaneously. Therefore, when the auxiliary flow is humidified, the same heat exchange is achieved by a smaller temperature change.
In indirect evaporative heat exchangers of another type (Fig. 3), the auxiliary flow is directed not to the heat exchanger, but to the cooling tower, where it cools the water circulating through the indirect evaporative heat exchanger: the water is heated in it due to the main flow and cooled in the cooling tower due to the auxiliary one. Water moves along the circuit using a circulation pump.
The calculation methodology is based on the following assumptions:
The procedure for engineering calculation of the system under consideration is as follows (Figure 4):
1. Using the I d diagram or using the program for calculating moist air, additional parameters of the ambient air are determined (point “0” in Fig. 4): specific enthalpy of air i 0, J/kg and moisture content d 0, kg/kg.
2. The increment in the specific enthalpy of air in the fan (J/kg) depends on the type of fan. If the fan motor is not blown (cooled) by the main air flow, then:
If the circuit uses a duct-type fan (when the electric motor is cooled by the main air flow), then:
Where:
η dv — electric motor efficiency;
ρ 0 — air density at the fan inlet, kg/m 3
Where:
B 0 — ambient barometric pressure, Pa;
R in is the gas constant of air, equal to 287 J/(kg.K).
3. Specific enthalpy of air after the fan (point “1”), J/kg.
i 1 = i 0 +∆i in; (3)
Since the “0-1” process occurs at a constant moisture content (d 1 =d 0 =const), then using the known φ 0, t 0, i 0, i 1 we determine the air temperature t1 after the fan (point “1”).
4. The dew point of the ambient air t dew, °C, is determined from the known φ 0, t 0.
5. Psychrometric temperature difference of the main flow air at the outlet of the heat exchanger (point “2”) ∆t 2-4, °C
∆t 2-4 =∆t x +∆t wgr; (4)
Where:
∆t x is assigned based on specific operating conditions in the range ~ (0.5…5.0), °C. It should be borne in mind that small values of ∆t x will entail relatively large dimensions of the heat exchanger. To ensure small values of ∆t x it is necessary to use highly efficient heat transfer surfaces;
∆t wgr is selected in the range (0.8…3.0), °C; Lower values of ∆t wgr should be taken if it is necessary to obtain the minimum possible cold water temperature in the cooling tower.
6. We accept that the process of humidifying the auxiliary air flow in the cooling tower from state “2-4”, with sufficient accuracy for engineering calculations, proceeds along the line i 2 =i 4 =const.
In this case, knowing the value of ∆t 2-4, we determine the temperatures t 2 and t 4, points “2” and “4” respectively, °C. To do this, we will find a line i=const such that between point “2” and point “4” the temperature difference is the found ∆t 2-4. Point “2” is located at the intersection of the lines i 2 =i 4 =const and constant moisture content d 2 =d 1 =d OS. Point “4” is located at the intersection of the line i 2 =i 4 =const and the curve φ 4 = 100% relative humidity.
Thus, using the above diagrams, we determine the remaining parameters at points “2” and “4”.
7. Determine t 1w - the water temperature at the outlet of the cooling tower, at point “1w”, °C. In the calculations, we can neglect the heating of water in the pump, therefore, at the entrance to the heat exchanger (point “1w’”) the water will have the same temperature t 1w
t 1w =t 4 +.∆t wgr; (5)
8. t 2w - water temperature after the heat exchanger at the inlet to the cooling tower (point “2w”), °C
t 2w =t 1 -.∆t m; (6)
9. The temperature of the air discharged from the cooling tower into the environment (point “5”) t 5 is determined by the graphic-analytical method using an i d diagram (with great convenience, a set of Q t and i t diagrams can be used, but they are less common, therefore in this i d diagram was used in the calculations). The specified method is as follows (Fig. 5):
10. We compose a system of equations to find the unknown mass flow rates of air and water. Thermal load of the cooling tower by auxiliary air flow, W:
Q gr =G in (i 5 - i 2); (7)
Q wgr =G ow C pw (t 2w - t 1w); (8)
Where:
C pw is the specific heat capacity of water, J/(kg.K).
Thermal load of the heat exchanger along the main air flow, W:
Q mo =G o (i 1 - i 2); (9)
Thermal load of the heat exchanger by water flow, W:
Q wmo =G ow C pw (t 2w - t 1w) ; (10)
Material balance by air flow:
G o =G in +G p ; (11)
Heat balance for cooling tower:
Q gr =Q wgr; (12)
The heat balance of the heat exchanger as a whole (the amount of heat transferred by each flow is the same):
Q wmo =Q mo ; (13)
Combined thermal balance of the cooling tower and water heat exchanger:
Q wgr =Q wmo; (14)
11. Solving equations from (7) to (14) together, we obtain the following dependencies:
mass air flow along the auxiliary flow, kg/s:
mass air flow along the main air flow, kg/s:
G o = G p ; (16)
Mass flow of water through the cooling tower along the main flow, kg/s:
12. The amount of water required to recharge the water circuit of the cooling tower, kg/s:
G wn =(d 5 -d 2)G in; (18)
13. Power consumption in the cycle is determined by the power spent on the fan drive, W:
N in =G o ∆i in; (19)
Thus, all the parameters necessary for structural calculations of the elements of the indirect evaporative air cooling system have been found.
Note that the working flow of cooled air supplied to the consumer (point “2”) can be additionally cooled, for example, by adiabatic humidification or any other method. As an example in Fig. 4 indicates the point “3*”, corresponding to adiabatic humidification. In this case, points “3*” and “4” coincide (Fig. 4).
If we compare cooling by adiabatic and indirect evaporative methods, then from the I d-diagram it can be seen that in the first case, air with a temperature of 28 ° C and a relative humidity of 45% can be cooled to 19.5 ° C, while in the second case - up to 15°C (Fig. 6).
As mentioned above, an indirect evaporative cooling system can achieve lower temperatures than a traditional adiabatic humidification system. It is also important to emphasize that the moisture content of the desired air does not change. Similar advantages compared to adiabatic humidification can be achieved through the introduction of an auxiliary air flow.
There are currently few practical applications of indirect evaporative cooling systems. However, devices of a similar, but slightly different operating principle have appeared: air-to-air heat exchangers with adiabatic humidification of the outside air (systems of “pseudo-indirect” evaporation, where the second flow in the heat exchanger is not some humidified part of the main flow, but another, completely independent circuit).
Such devices are used in systems with a large volume of recirculated air that needs cooling: in air conditioning systems for trains, auditoriums for various purposes, data processing centers and other facilities.
The purpose of their implementation is to reduce the operating time of energy-intensive compressor refrigeration equipment as much as possible. Instead, for outside temperatures up to 25°C (and sometimes higher), an air-to-air heat exchanger is used, in which the recirculated room air is cooled by the outside air.
For greater efficiency of the device, the outside air is pre-humidified. In more complex systems, humidification is also carried out during the heat exchange process (water injection into the heat exchanger channels), which further increases its efficiency.
Thanks to the use of such solutions, the current energy consumption of the air conditioning system is reduced by up to 80%. Annual energy consumption depends on the climatic region of operation of the system; on average, it is reduced by 30-60%.
Yuri Khomutsky, technical editor of Climate World magazine
The article uses the methodology of MSTU. N. E. Bauman for calculating the indirect evaporative cooling system.
For servicing individual small rooms or their groups, local air conditioners with two-stage evaporative cooling, based on an indirect evaporative cooling heat exchanger made of aluminum rolling tubes, are convenient (Fig. 139). The air is purified in filter 1 and supplied to fan 2, after the discharge hole of which it is divided into two flows - main 3 and auxiliary 6. The auxiliary air flow passes inside the tubes of the indirect evaporative cooling heat exchanger 14 and provides evaporative cooling of the water flowing down the inner walls of the tubes. The main air flow passes from the fin side of the heat exchanger tubes and transfers heat through their walls to the water, cooled by evaporation. Recirculation of water in the heat exchanger is carried out using pump 4, which takes water from pan 5 and supplies it to irrigation through perforated tubes 15. The indirect evaporative cooling heat exchanger plays the role of the first stage in combined two-stage evaporative cooling air conditioners.
