Using a simple air recirculation model to explore computer rack cooling
Robert E. Simons, Associate Technical Editor
Figure 1. Schematic diagram of simple computer rack air recirculation
model.
Figure 2. Schematic diagram of computer rack air recirculation model
with heat exchanger in rear of computer rack.
In an article in the November 2006 issue of ElectronicsCooling it was noted that “advances in computer clusters have resulted in the introduction of higher density server equipment that consumes significant amounts of electrical power and produces an extraordinary amount of heat” [1]. Such advances are taxing the ability of many data centers to provide sufficient air conditioning capacity to handle the associated heat loads. The same article and an earlier one [2] discussed the use of air-to-water heat exchangers at the rear of high power computer racks to cool the hot air exiting these racks. This approach helps to reduce the demand on computer room air cooling (CRAC) units and to alleviate “hot spot” problems associated with recirculation of hot exhaust air [3]. This Calculation Corner article will illustrate how a simple air recirculation model may be used to explore the relative effectiveness of this approach.
Air Recirculation Model (without Heat Exchanger)
We will first consider air recirculation without a heat exchanger in place. To do this, consider the schematic of the simple model illustrated in Figure 1. In this model air flows through the computer rack with a mass flow rate, m , entering the rack at temperature Ti and exiting at temperature To due to the heat load, q, within the rack or as given by the following equation,
A fraction, Φ, of the air exiting the rack recirculates and mixes with the cool room air at temperature, Tr, supplied by the CRAC units. It is assumed that the recirculating air flow rate, Φm , and cool room air flow rate, (1-Φ)m , fully mix to satisfy equation [2],
Combining equations [1] and [2] it is found that the temperature of the air entering the electronics compartment is given by,
The temperature of the heated air leaving the rack is given by,
Air Recirculation Model (with Rear Heat Exchanger)
Next, we will consider the same air recirculation model, but with a water-cooled air-to-liquid heat exchanger in the rear of the computer rack as shown in Figure 2. It is assumed that the heat exchanger has an effectiveness, ε, and is cooled with water at temperature, Tci. In this case air enters the electronics compartment at temperature Ti, and then enters the heat exchanger at temperature Thi, as given by equation [5],
Figure 3. Schematic diagram of computer rack air recirculation model
with heat exchanger at front of computer rack.
Figure 4. Effect of air recirculation on electronics compartment
air inlet temperature with and without water-cooled heat exchanger.
The quantity of heat, qhtx, extracted from the air by the heat
exchanger is given by
and
where Cmin in equation [6] is the smaller of the air or water heat
capacity rates (m cp) and m cp in equation [7] is the air heat capacity
rate. Using equations [2], [5], [6], and [7], after a bit of algebraic
manipulation we can arrive at the equation for the temperature of the
air entering the electronics compartment, which is,
Air Recirculation Model (With Front Heat Exchanger)
Last, we again consider the same air recirculation model, but, now
with a water-cooled air-to-liquid heat exchanger in the front of the computer rack as shown in Figure 3. In this case, the recirculating
air at temperature To, and the fresh room air at temperature Tr, mix
to enter the heat exchanger at temperature Thi, as given by,
The quantity of heat, qhtx, extracted from the air by the heat
exchanger is given by equation [6] and also by,
The temperature, To, of the air exiting the computer rack is again
determined by equation [1]. Using equations [1], [6], [9], and [10],
and again after a bit of algebraic manipulation we can arrive at the
equation for the temperature of the air entering the electronics
compartment, which in this case is,
Figure 5. Effect of air recirculation on computer rack exit air
temperature with and without water-cooled heat exchanger.
Figure 6. Effect of air recirculation on percent of total
heat load rejected to water.
Example Results
Now, to illustrate the utility of the simple
recirculation model and the resulting equations
with and without a water-cooled heat exchanger,
we will consider the following representative
values of the relevant quantities:
Rack heat load (q) – 20 kW
Rack air flow rate (m) – 1.37 kg/s
(2500 CFM)
Room air temperature – 25°C
Water flow rate – 0.94 kg/s (15 gpm)
Water inlet
temperature (Tci) – 20°C
Heat exchanger
effectiveness (ε) – 0.5
Using the above values and the equations
discussed in this article the inlet air
temperature to the electronics compartment
was calculated for air recirculation values
ranging from 0 to 100%. As shown in Figure 4
without the water-cooled heat exchanger, inlet
air temperature increases dramatically as air
recirculation increases. Of course this rise in
cooling air temperature will be directly
reflected in increased component temperatures.
With the water-cooled heat exchanger in place
(rear or front) air temperatures entering the
rack are well controlled. It may be noted that in
this case for values of recirculation below
35%, the heat exchanger in the front actually
cools incoming air below the room air
temperature. It may also be noted that at 100%
recirculation whether the heat exchanger is in
the front or back gives the same result. The
results for 100% air recirculation are the same
as would result for closed-loop air cooling with
a water-cooled heat exchanger within the rack.
Figure 5 illustrates the results obtained in
terms of the exit air temperature from the rack.
Again, as might be expected the exhaust air
temperature rises significantly with increasing
air recirculation. It may also be noted that the
exit air temperature is under much better control
with the heat exchanger in the rear of the rack
rather than the front of the rack. This is because
the heat exchanger in this position “sees”
warmer air than a heat exchanger in the front of
the rack. As is shown by equation [6], the
amount of heat extracted by the heat exchanger
is directly proportional to the difference between
the temperature of the “hot” fluid (i.e., air)
entering the heat exchanger and the temperature
of the “cold” fluid (i.e., water) entering the heat
exchanger. This is clearly demonstrated in Figure 6, which shows the percent of the total
heat load rejected to water depending upon whether the heat exchanger is in the rear or front
of the rack. These results show that the heat exchanger in the rear is much more effective in
reducing the heat load to room air than a heat exchanger in the front of the rack.
It is hoped that this article has not only demonstrated the effectiveness of using a
water-cooled heat exchanger to reduce the heat load to room air; but, has also
demonstrated how effective even a simple model can be in providing meaningful results.
References
LaPlante, S.R., Aubry, N., Rosa, L., Levesque, P., Abroumrad, B., Porter, D., Cavanaugh, C., and Johnston, J.,“Liquid Cooling of a High-Density Computer Cluster,” ElectronicsCooling, Vol. 12, No. 4, November 2006.
Schmidt, R., “Liquid Cooling is Back,” ElectronicsCooling, Vol. 11, No. 3, August 2005.
Schmidt, R., “Hot Spots in Data Centers,” ElectronicsCooling, Vol. 9, No. 3, August 2005.
