Data center high sensible heat ratio load: a nearly horizontal process and the dry coil

Situation

Say a server room with 100 kW of IT heat has air handlers whose humidity control alternates between humidifying and dehumidifying, burning power. Server inlet is 20 °C, air leaving the servers is 32 °C, and the humidity ratio hardly changes. The only moisture source is 0.5 kW of latent load such as people, so the sensible heat ratio is 0.995. Three things to find: the airflow needed, what coil surface temperature avoids dehumidification, and how much airflow falls if the server temperature rise is increased. The conditions are illustrative; real decisions use equipment data and the site's chilled-water temperature.

Given conditions

Reading it on the chart

1. Plot return R (32 °C, 8.36 g/kg) and supply S (20 °C, 8.33 g/kg). The two sit at almost the same height, so the room load line from S to R is horizontal.
2. Going left from R at constant humidity ratio to the saturation line gives the dew point of the return air, 11.3 °C. If the coil surface is below it, condensation occurs.
3. The coil line runs from R toward the saturation point at the coil's mean surface temperature ADP, and the point on it at 20 °C dry-bulb is the coil leaving state C. If the ADP is below the dew point, the line slopes downward and C has a lower humidity ratio than S.
4. Check that S is inside the 18 to 27 °C, dew point at most 15 °C envelope.

Step-by-step calculation

1) Airflow. The target 24 °C / 45 % has W = 8.36 g/kg, so moist air c_p = 1.006 + 1.86 × 0.00836 = 1.0215 kJ/kg·K. Dry air mass flow ṁ = 100 / (1.0215 × 12) = 8.158 kg/s. At the supply specific volume of 0.8416 m³/kg that is 24,715 CMH.

2) Supply humidity ratio. The 0.5 kW latent load rides on ṁ: W_S = W_R − 0.5 / (8.158 × (2501 + 1.86 × 32)) = 8.332 g/kg. It differs from the return by only 0.024 g/kg, which is why the two points sit at the same height.

3) Return dew point. The return air at 32 °C / 28.2 % has a dew point of 11.35 °C. The RH looks low, but the humidity ratio is the same and only the dry-bulb is higher. Condensation starts if the coil surface is below 11.3 °C.

4) ADP 8 °C coil. To get 20 °C supply the bypass factor is BF = (20 − 8) / (32 − 8) = 0.50. The saturation humidity ratio at the ADP is 6.66 g/kg, and the leaving humidity ratio is W_out = 6.66 + 0.50 × (8.36 − 6.66) = 7.51 g/kg. That is 0.85 g/kg below the return, so the coil condenses 25.0 kg per hour. To restore the target humidity ratio the same amount must be humidified, which with steam is 18.1 kW.

5) Raising the ADP. With the ADP at or above the return dew point (11.3 °C) there is no dehumidification, since the line is horizontal. The coil that still delivers 20 °C then has a smaller BF, falling from 0.54 at ADP 6 °C to 0.40. A smaller BF means the air must come closer to the coil surface temperature, so it needs more coil surface (rows, area), in exchange for a higher chilled-water temperature.

Interpreting the result

Supply at 20 °C / 57.3 %, dew point 11.3 °C, is inside the recommended envelope (dry-bulb 18 to 27 °C, dew point at most 15 °C, RH at most 60 %). The return at 32 °C has a low RH of 28.2 %, but that is the server outlet, not the inlet, so it is not judged against the envelope. Managing humidity by dew point (humidity ratio) is better, because it does not change with temperature.

The ADP 8 °C coil makes 25.0 kg/h of condensate and the humidifier wastes energy putting it back. With the ADP at or above the dew point of 11.3 °C the coil is dry and there is no such waste. That is why server rooms use a higher chilled-water supply temperature than ordinary air conditioning (here, such that the mean coil surface stays at or above 11.3 °C). A higher chilled-water temperature also improves chiller efficiency.

A bigger server temperature rise moves the same 100 kW with less airflow (return held at 32 °C).

Going from ΔT 8 K to 15 K cuts airflow from 37,579 CMH to 19,570 CMH and fan power drops a lot. However, a lower supply reaches the 18 °C lower limit and a higher return raises server internal temperatures, so check the equipment specification first.

What the calculation leaves out

This assumes all the heat goes into air that passes through the servers. In reality there is bypass and recirculation where cold and hot air mix, so the server inlet runs warmer than the supply. Aisle containment reduces that mixing and allows a higher return temperature at the same supply. Outdoor air through floor gaps and doors, and moisture leaking through the room walls, add to the humidification and dehumidification loads separately.

A dry coil only reduces condensate; with outdoor air intake, the moisture it carries becomes a problem again. A room that uses free cooling should check that the outdoor dew point stays inside the recommended range. The recommended range here applies to the server inlet.

Common mistakes

• Using an office coil (7 °C chilled-water class) as is. At ADP 8 °C it condenses 25.0 kg/h and the humidifier puts the same amount back.
• Humidifying because the return RH looks low. The 28.2 % at 32 °C has the same humidity ratio as the supply. Judge by the server inlet dew point of 11.3 °C.
• Choosing airflow without regard to server ΔT. Between ΔT 8 K and 15 K the airflow differs by a factor of 1.92.
• Ignoring the sensible heat ratio and sizing for latent load. A process line at SHR 0.995 is horizontal. Holding humidity means leaving the humidity ratio alone rather than balancing dehumidifying and humidifying.
• Applying the envelope to the return point. The recommended range is for the server inlet.

Try this calculation on the site

Open the server room process on the chart

The chart link plots the return and supply points with a process card, so you can check the horizontal sensible-only process and the airflow. For coil selection and reheat see Summer cooling coil selection and reheat, for humidification see Winter office humidification load, for flow conversions see unit conversion, and for plotting see How to read a psychrometric chart.

References

• ASHRAE Handbook Fundamentals 2017 (SI), chapter 1 Psychrometrics: humidity ratio, enthalpy, specific volume 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.
• ASHRAE TC 9.9, Thermal Guidelines for Data Processing Environments: the recommended server inlet envelope of 18 to 27 °C dry-bulb, -9 to 15 °C dew point and at most 60 % RH. The allowable ranges are wider and depend on the equipment class. This article uses only the recommended range; check the equipment maker's specification and the relevant edition of that guideline.
• The ADP and bypass factor method is the usual way to analyse a cooling coil on the chart. The steam humidification balance follows the Humidifiers chapter of ASHRAE Handbook HVAC Systems and Equipment; the steam enthalpy of 2676 kJ/kg is the 100 °C saturated steam value (IAPWS-IF97 2675.6) and the feed water heating uses 4.186 kJ/kg·K.
• The IT load of 100 kW, latent 0.5 kW, supply and return temperatures and the room target 24 °C / 45 % are example values.