Cabinet Cooling Using Water & Refrigeration

Case Study:
Cabinet Cooling Using a Water and Refrigeration system
Escalating computing capabilities and shrinking chip
packages are leading to corresponding increases in server
and rack power densities. Cooling the new higher-powered
racks is a serious challenge to system designers and data
center managers. In the past, designers tried such methods
as cabinets with better airflow configurations, adding central
air conditioning systems, raising floors and using coldaisle and hot-aisle layouts. Today, engineers are turning
their attention to water-cooled techniques and refrigeration
technology to solve cabinet overheating problems.
Many liquid-cooled cabinets are available on the market,
based on different cooling methods. IBM has a patented
rear door heat exchanger design. Emerson manufactures
both water-cooled and refrigeration-cooled cabinets. HP’s
Modular Cooling System uses chilled water to dissipate
heat. This paper will not discuss which company has the
best technique for cabinet cooling; rather, it addresses the
concept of a liquid-cooled cabinet by simple calculation and
comparison.
Consider a cabinet, with dimensions of 2200 x 800 x 1200
mm, containing multiple servers which generate 30 kW of
waste heat. The cabinet has a fan tray which delivers 5000
m3/h (2940 CFM) of airflow to the servers and dissipates 1
kW of heat to move the air. The air temperature at the cabinet
inlet is 20˚C (68˚F). The cabinet is supplied with chilled water
whose temperature is 12˚C (54˚F) at the inlet. To cool this
cabinet, what are the requirements for the heat exchanger
and water supply system? If the refrigeration system is used,
what are its advantages?
1. A Cabinet with an Integrated Air-Water Heat
Exchanger
This configuration sets the baseline of liquid cooling and
includes the following cases:
1)A rear-door, air-water heat exchanger which cools the hot
air from the cabinet to 20˚C (Figure 1(a)).
2)A sealed cabinet with an air-water heat exchanger inside
(Figure 1(b)).
Figure 1 shows the simplest water-cooled cabinet. The
rear door heat exchanger design was developed by IBM
Corporation. The Figure 1(b) represents the water-cooled
cabinet with internal air circulation.
Figure 1. Schematics of a Cabinet with Different Integrated Air-Water Heat Exchangers.
The total heat dissipation of the cabinet (from servers and fan
tray) is 31 kW. The average air temperature at the servers’
exit is
Ta _ o 
18
q
31000
 2 0  3 8 .5 C
 Ta _ i 
m V C
1 .2  5 0 0 0 / 3 6 0 0 1 0 0 5
Assuming the water temperature at the outlet is 18˚C
(64.5˚F), the water flow rate needed to cool the cabinet is,
mV 
q
31000

 0 .0 0 1 2 3m 3 / s(1 9 .5G P M )
C(T w _ o  T w _ i ) 1 0 0 0  4 2 0 0  (1 8  1 2 )
The efficiency of the air-water heat exchanger depends on
both air and water properties and on the temperature.
For air:
C a  m V C  1 .2  (5 0 0 0 / 3 6 0 0 ) 1 0 0 5  1 6 7 5 W / C
The heat transfer coefficient of tube is:
hw 
N u k 2 1 1  0 .6

 1 2 6 6 0 W / m 2 . C
D
0 .0 1
The total surface area needed for the tubes is:
Aw 
C w N T U 5 1 6 6 1 .7

 0 .6 9m 2
hw
12660
The length of each tube is:
L
Aw /4
0 .6 9 / 4

 5 .4 9m
D
3 .1 4  0 .0 1
The friction factor of the tube is:
For water:
f  0 .1 8 4 R e 1 / 5  0 .1 8 4  3 2 5 0 0 0 .2  0 .0 2 3
C w  m V C  1 0 0 0  0 .0 0 1 2 3  4 2 0 0  5 1 6 6 W / C
So the maximum heat the heat exchanger can dissipate is:
q m a x  C a (Ta _ i  T w _ i )  1 6 7 5  (3 8 .5  1 2 )  4 4 .4k W
The heat exchanger’s effectiveness is:
 
q
31000

 0 .7 0
qm ax 4 4 4 0 0
With
Ca 1675

 0 .3 2
C w 5166
The estimated pressure drop for each straight tube is:
P 
1
L 1
5 .4 9
V 2 f  1 0 0 0  3 .9 2  0 .0 2 3 
 9 6 0 0 0P a(1 3 .9P S I)
0 .0 1
2
D 2
From the calculation we find that a total of 0.00123 m3/s
(19.5GPM) of water is needed to cool this cabinet. The
estimated water pressure drop across the heat exchanger
is 96000 Pa (13.9 PSI). This cooling solution has minimum
impact on the CRAC (Computer Room Air Condition) system
because, in theory, there is no heat dissipation from cabinet
to the ambient.
The NTU (number of transfer units) of the heat exchanger
(according to [1]) is:
NTU 
ha A a hw A w

 1 .7
C w
Ca
Assuming the average heat transfer coefficient between air
and heat exchanger fin is:
h a  5 0 W / m 2 . C
The total surface area needed for the fins is:
V 
mV
0 .0 0 1 2 3

 3 .9m / s
4 A tu b e 4  3 .1 4  0 .0 0 5 2
For the water, assume four parallel tubes with internal diameter
of 10 mm are used for the air-water heat exchanger.
The average water velocity inside tube is:
V 
mV
0 .0 0 1 2 3

 3 .9m / s
4 A tu b e 4  3 .1 4  0 .0 0 5 2
The Reynolds number is:
Re 
V D 3 .9  0 .0 1

 32500

1 .2 1 0 6
The Nusselt number for fully developed turbulent flow is:
N u  0 .0 2 3 R e 4 / 5 P r 0 .4  0 .0 2 3  3 2 5 0 0 4 / 5  7 .6 0 .4  2 1 1
Figure 2. Schematic of a Cabinet with a Front Integrated Air-Water
Heat Exchanger.
In general, it is not advisable to put an air-water heat
exchanger in the front of a cabinet, as shown in Figure 2.
This configuration has very low heat exchanger efficiency
because the temperature difference between the inlet air
and inlet water is very small. In this case, it is only 8˚C. In
the best scenario, the air can only be cooled down to about
12˚C after passing through the heat exchanger.
February 2010 |Qpedia
19
2. A Cabinet with an Integrated Refrigeration System
Using a refrigeration system to cool electronic components
has been applied in the field for long time. Today, this technique
is used by companies such as Emerson Corporation for
cabinet cooling. It gives the cabinet more flexibility and more
potential to reach higher power densities. It also makes the
cabinet more complex and adds cost.
In this study, the integrated refrigeration system calculation
covers the following cases:
1) A rear-door air-refrigerant heat exchanger which cools the
hot air from the cabinet to 20˚C (Figure 3(a)).
2) A sealed cabinet with an air-refrigerant heat exchanger
and an refrigerant-water heat exchanger inside (Figure
3(b)).
Assume R134a is used as refrigerant. The refrigeration
system can be simplified as a heat transfer system with two
heat exchangers, as shown in Figure 4.
For this system, assume the coefficient of performance
(COP) of refrigeration is 4:
COP 
q
4
Wc
Figure 4, Illustration of a Cabinet with a Refrigeration System.
The flow rate of refrigerant R-134a needed is:
mr 
For R134a in the air-refrigerant heat exchanger:
So the power of compressor is:
Wc 
q
31

 7 .8k W
COP
4
q
31

 0 .1 9 1k g / s
h 1 6 2 .6
C r  m C  0 .1 9 1 1 9 8 6 0 0  3 7 9 3 0 W / C
So maximum heat the heat exchanger can dissipate is:
The total power generated by cabinet and compressor is
38.8kW.
q m a x  C a (Ta _ i  Tr _ i )  1 6 7 5  (3 8 .5  0 )  6 4 .5k W
The effectiveness of air-refrigerant heat exchanger is:
 
q
31

 0 .4 8
q m a x 6 4 .5
With
Ca
1675

 0 .0 4 4
Cr 37930
The NTU (number of transfer units) of the air-refrigerant heat
exchanger (according to [1]) is:
NTU 
ha A a hr A r

 1 .7
C r
Ca
Assume the average fin heat transfer coefficient is:
h a  5 0 W / m 2 . C
The total surface area needed for the fins is:
Aa 
Figure 3. Schematics of Cabinets with Integrated Air-Refrigerant
Heat Exchangers.
20
C a N T U 1 6 7 5  0 .7

 2 3 .5m 2
ha
50
Compared to the air-water heat exchanger, the required fin
surface area of the air-refrigerant heat exchanger is reduced
by more than half. A more compact heat exchanger can be
used for this configuration.
For the refrigerant-water heat exchanger, the total heat
transferred from R134a to water is 38.8 kW. Assume that
the temperature of the water leaving the tube-to-tube heat
exchanger is 25˚C.
The water flow rate needed is:
mV 
q
C(T w _ o
38800

 7 .1 1 0 4 m 3 / s(1 1 .3G P M )
 T w _ i ) 1 0 0 0  4 2 0 0  (2 5 1 2 )
And:
The length of each tube is:
L
The friction factor is:
f  0 .1 8 4 R e 1 / 5  0 .1 8 4 1 9 1 7 0 0 .2  0 .0 2 6
The estimated pressure drop for straight tube is:
P 
C w  m V C  1 0 0 0  0 .0 0 0 7 1  4 2 0 0  2 9 8 2 W / C
For R134a at condenser:
C r  m C  0 .1 9 1  8 2 8 3  1 5 8 2 W / C
So the maximum heat the refrigerant-water heat exchanger
can dissipate is:
q m a x  C r (Tr _ i  T w _ i )  1 5 8 2  (5 0  1 2 )  6 0k W
Heat sink effectiveness is:
 
q
3 8 .8

 0 .6 5
60
qm ax
With:
Cr
1582

 0 .5 3
C w 2982
The NTU (number of transfer units) of the refrigerant-water
heat exchanger (according to [1]) is:
NTU 
Aw /4
0 .6 1 / 4

 4 .8 6m
D
3 .1 4  0 .0 1
1
L 1
4 .8 6
V 2 f  1 0 0 0  2 .3 2  0 .0 2 6 
 3 3 4 0 0P a( 4 .8P S I)
0 .0 1
2
D 2
In this configuration, 7.1 x 10-4 m3/s (11.3 GPM) of water are
needed to cool this cabinet. The estimated pressure drop for
water is 33400 Pa (4.8 PSI). Compared to the cooling system
illustrated in Figure 1, this system requires less water and
pumping power. But, it requires a bigger chiller at the data
center’s cooling system.
One possible configuration for the refrigeration system is to
put the air-refrigerant heat exchanger in front of the servers,
as shown in Figure 5. This design will enable the cabinet
to provide sub-ambient temperature airflow to the servers.
Because the air-refrigerant heat exchanger works as an
evaporator for R134a, the air temperature after the heat
exchanger can be very uniform irrespective of location. The
air-refrigerant can be quite efficient because the refrigerant
evaporating temperature is regulated by a compressor.
h w A w hr A r

 1 .7
C r
Cw
For water, assume four parallel tubes with an internal diameter of 10 mm are used for tube-to-tube refrigerant-
water heat exchanger.
The average water velocity is:
V 
mV
0 .0 0 0 7 1

 2 .3m / s
4 A tu b e 4  3 .1 4  0 .0 0 5 2
The Reynolds number is:
Re 
V D 2 .3  0 .0 1

 19170

1 .2 1 0 6
The Nusselt number for fully developed turbulent flow is:
N u  0 .0 2 3 R e 4 / 5 P r 0 .4  0 .0 2 3 1 9 1 7 0 4 / 5  7 .6 0 .4  1 3 8
The heat transfer coefficient of tube is,
hw 
N u k 1 3 8  0 .6

 8 2 8 0 W / m 2 . C
D
0 .0 1
The total surface area needed for the tubes is:
Aw 
C w N T U 2 9 8 2 1 .7

 0 .6 1m 2
8280
hw
Figure 5. Schematic of a Cabinet with a Front-Integrated
Air-Refrigerant Heat Exchanger.
February 2010 |Qpedia
21
Compared with other liquid-cooled cabinets, the cabinet
with a simple air-water heat exchanger is the most energy
efficient. It transfers the waste heat from the cabinet to a
central chiller, with no additional work required for cooling. A
cabinet with a refrigeration system adds an extra heat load to
central chiller, but it also brings advantages of better cabinet
cooling, a less sophisticated heat exchanger design and
less requirements of the water delivery system. Choosing
a liquid-cooled cabinet with the right cooling technique and
configuration depends on the customer’s requirements,
including the rack power density, water supply system, CRAC
system and budget. The configuration must be selected on
an individual basis. With the continuing increase of power
dissipation we are sure to see more liquid-cooled cabinets
in data centers.
Reference
1. Incropera F. and DeWitt D., Fundamentals of Heat and
Mass Transfer, 5th Edition, John Wiley & Sons, 2002.
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