Evaporative cooler feasibility: the wet-bulb depression decides
An evaporative cooler cools air by evaporating water, with no compressor. How far it cools depends not on the outdoor dry-bulb but on the gap between dry-bulb and wet-bulb, the wet-bulb depression. The same 35 °C gives very different results on a dry day and a humid one, and because a direct unit adds moisture, the room humidity has to be checked as well.
Situation
Say a workshop with a lot of machine heat is looking at an evaporative cooler (outdoor air drawn through wetted pads) to take the edge off summer heat. It brings in 100 % outdoor air, passes it through the space and exhausts it, aiming for a 29 °C room dry-bulb. The sensible load is 60 kW and the latent load from people and the like is 3 kW. Four things to find: how cold the supply gets on a given day, how much airflow handles 60 kW at that supply temperature, what the room RH ends up at, and how much water is used. We repeat the calculation for a two-stage unit with an indirect stage in front. The conditions are illustrative; real decisions use the local design outdoor condition and the product's performance data.
Given conditions
| Item | Value |
|---|---|
| Outdoor O | Representative 35 °C / 40 %. For comparison 35 °C / 20 %, 35 °C / 40 %, 33 °C / 60 %, 30 °C / 80 % |
| Direct evaporative (DEC) | Saturation effectiveness εd = 0.85 (constant wet-bulb process) |
| Indirect evaporative (IEC) | Wet-bulb effectiveness εi = 0.6 (constant humidity ratio process, outdoor air as secondary air) |
| Workshop | Room dry-bulb target 29 °C, sensible 60 kW, latent 3 kW, 100 % outdoor air supply with full exhaust |
| Acceptance (example) | Room RH at most 70 % |
| Pressure | 101.325 kPa (sea level) |
Reading it on the chart
- Plot the outdoor point O (35 °C / 40 %) and read the wet-bulb line through it: 23.93 °C, a wet-bulb depression of 11.07 K.
- Direct evaporation moves from O up and to the left along that wet-bulb line. Going all the way to the saturation curve would reach the wet-bulb temperature; with 0.85 effectiveness it stops at D, 85 % of the way.
- In an indirect unit the water evaporates on the other side of a plate heat exchanger, so no moisture reaches the supply air. It moves horizontally left from O to I. In a two-stage unit it then follows the wet-bulb line through I by direct evaporation to T.
- From the supply point to the room point R is the room load line. The load is mostly sensible, so it runs nearly horizontally to the right, rising slightly with the latent load. Check whether R is below the 70 % RH curve.
Step-by-step calculation
1) Wet-bulb. Outdoor air at 35 °C / 40 % has a humidity ratio of 14.13 g/kg and a wet-bulb of 23.93 °C. The wet-bulb depression 35 − 23.93 = 11.07 K is the most that direct evaporative cooling can take off (an indirect stage in front can go below the outdoor wet-bulb).
2) Direct stage leaving state D. tD = 35 − 0.85 × 11.07 = 25.59 °C. The wet-bulb stays at 23.93 °C, so D has a humidity ratio of 18.10 g/kg and 87.3 % RH; the air picked up 3.97 g/kg of water. Enthalpy goes from 71.47 to 71.87 kJ/kg, almost unchanged (it rises only by the enthalpy of the added water). Evaporative cooling does not remove heat; it turns sensible heat into latent heat.
3) Airflow. Holding the room at 29 °C with 25.59 °C supply leaves a 3.41 K difference. cp = 1.006 + 1.86 × 0.01810 = 1.0397 kJ/kg·K and ṁ = 60 / (1.0397 × 3.41) = 16.946 kg/s. At a supply specific volume of 0.8709 m³/kg that is 53,131 CMH.
4) Room humidity. Adding the 3 kW latent load, WR = 18.10 + 3 / (16.946 × (2501 + 1.86 × 29)) × 1000 = 18.17 g/kg, which is 71.7 % RH at 29 °C. Water evaporated is 16.946 × (18.10 − 14.13) / 1000 × 3600 = 241.9 kg/h.
5) Two-stage (indirect then direct). The indirect stage leaves at tI = 35 − 0.6 × 11.07 = 28.36 °C with the humidity ratio unchanged at 14.13 g/kg, which lowers the wet-bulb to 22.10 °C. Direct evaporation from there gives tT = 28.36 − 0.85 × (28.36 − 22.10) = 23.04 °C at 92.3 %. The temperature difference grows to 5.96 K, airflow drops to 30,097 CMH and the room RH is 65.3 %.
The same calculation for the four outdoor conditions (airflow is what holds the room at 29 °C):
| Outdoor | Wet-bulb (depression) | Direct stage supply | Airflow (CMH) | Room RH | Water (kg/h) |
|---|---|---|---|---|---|
| 35 °C · 20 % | 18.9 °C (16.1 K) | 21.3 °C · 80 % | 23,159 | 51 % | 154 |
| 35 °C · 40 % | 23.9 °C (11.1 K) | 25.6 °C · 87 % | 53,131 | 72 % (over limit) | 242 |
| 33 °C · 60 % | 26.4 °C (6.6 K) | 27.4 °C · 93 % | 114,628 | 85 % (over limit) | 310 |
| 30 °C · 80 % | 27.1 °C (2.9 K) | 27.5 °C · 97 % | 123,537 | 89 % (over limit) | 148 |
| Outdoor | Indirect leaving | Two-stage supply | Airflow (CMH) | Room RH | Water (kg/h) |
|---|---|---|---|---|---|
| 35 °C · 20 % | 25.3 °C | 17.0 °C · 86 % | 14,681 | 43 % | 60 |
| 35 °C · 40 % | 28.4 °C | 23.0 °C · 92 % | 30,097 | 65 % | 78 |
| 33 °C · 60 % | 29.1 °C | 26.0 °C · 96 % | 60,228 | 81 % (over limit) | 90 |
| 30 °C · 80 % | 28.3 °C | 26.9 °C · 98 % | 86,962 | 87 % (over limit) | 57 |
Two-stage water counts only what is added to the supply air. Water evaporated on the secondary side of the indirect stage comes on top of that.
Interpreting the result
Dry outdoor air (35 °C / 20 %) has a 16.1 K wet-bulb depression, so the direct stage alone reaches 21.3 °C supply, 23,159 CMH and 51 % in the room, which is quite workable. At the representative condition (35 °C / 40 %) the supply is 25.6 °C, only 3.4 K below the room, so airflow grows to 53,131 CMH, and the room RH of 72 % exceeds this article's 70 % limit. Humid outdoor air (30 °C / 80 %) has only a 2.9 K depression: supply 27.5 °C and 123,537 CMH, which is not a practical way to cool.
So evaporative cooling suits climates or hours with a low wet-bulb. In a humid summer a direct unit mostly makes the air wetter without cooling it much. Putting an indirect stage in front lowers the wet-bulb without adding moisture, improving the representative case to 23.0 °C supply and 30,097 CMH, but in humid air even two stages only reach 26.9 °C. If days like that are the design condition, pair it with a cooling coil (vapour-compression cooling) or lower the goal to spot cooling around the workers.
The decision starts with one question: what is the wet-bulb of the local design outdoor condition? Picking by dry-bulb alone, the same 35 °C can give 21.3 °C or 25.6 °C supply.
What the calculation leaves out
Saturation effectiveness depends on pad depth and face velocity. The same pad loses effectiveness at higher velocity, so where the table shows airflow growing a lot, 0.85 can no longer be assumed. Read the effectiveness at that velocity from the product's performance data.
Water use is more than evaporation. Evaporation leaves minerals behind and concentrates them, so some water is continuously drained (bleed-off) and replaced. Standing water and wet pads need hygiene maintenance, and the unit should be drained and dried when not in use. With 100 % outdoor air, a restricted exhaust path pushes room humidity higher still; this calculation assumes the exhaust is open enough.
Common mistakes
- Judging performance by dry-bulb. At the same 35 °C the depression can be 16.1 K or 11.1 K, giving 21.3 °C or 25.6 °C supply.
- Looking at supply temperature without sizing airflow. A 3.4 K difference to the room needs 53,131 CMH for 60 kW.
- Forgetting that a direct unit adds moisture. At the representative condition the supply is at 87 % RH and the room at 72 %. Judge the result by room RH.
- Thinking evaporative cooling removes heat. Enthalpy barely changes, from 71.5 to 71.9 kJ/kg. The room heat leaves with the exhaust.
- Recirculating room air. Moisture builds up, so the basic arrangement is outdoor air in and exhaust out. Recirculating raises the wet-bulb and erodes the effect.
Try this calculation on the site
Open the evaporative cooling process on the chart
The chart link plots the outdoor point with its wet-bulb direction line, the direct stage leaving point and the room point with two process cards, so you can follow the wet-bulb line and the room load line. Change the outdoor condition to see how supply and room move. To compare outdoor enthalpies use the enthalpy calculator; for vapour-compression cooling see Summer cooling coil selection and reheat; for another way to use outdoor air see Economizer changeover; and for reading wet-bulb lines see How to read a psychrometric chart.
References
- ASHRAE Handbook Fundamentals 2017 (SI), chapter 1 Psychrometrics: humidity ratio, enthalpy, specific volume, wet-bulb and saturation vapour pressure (Hyland-Wexler). The psychrometric numbers here were computed with this site's engine, which implements those equations at 101.325 kPa.
- The direct saturation effectiveness (to − ts)/(to − twb) and the indirect wet-bulb effectiveness are the definitions used in the Evaporative Air-Cooling Equipment chapter of ASHRAE Handbook HVAC Systems and Equipment. Treating the direct stage as a constant wet-bulb process is the usual approximation, since it is close to adiabatic saturation.
- The 0.85 and 0.6 effectiveness values, the four outdoor conditions, the workshop loads, the 29 °C room and the 70 % RH limit are illustrative. They are not climate statistics for any location or the performance of any product.