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A thermal environmental analysis method for data centers
International Journal of Heat and Mass Transfer 62 (2013) 579–585
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
A thermal environmental analysis method for data centers Xiaodong Qian, Zhen Li, Zhixin Li ⇑ Key Laboratory of Thermal Science and Power Engineering of Ministry of Education, School of Aerospace, Tsinghua University, Beijing 100084, China
a r t i c l e
i n f o
Article history: Received 23 March 2012 Received in revised form 17 December 2012 Accepted 14 March 2013 Available online 11 April 2013 Keywords: Data center Airflow organization optimization Entransy dissipation Minimum thermal resistance
a b s t r a c t The rapidly growing of data center energy consumption rates are contributing to concern about energy conservation. Reasonable airflow organization is an effective way to reduce the cooling system energy consumption and to upgrade the energy utilization efficiency. Comprehensive and accurate analyses are important for airflow organization optimization. This paper presents the entransy dissipation analysis method to analyze the influences of hot and cold air mixing and cooling air distributions on data center heat transfer process. The thermal resistance based on entransy dissipation is used to define three indexes to evaluate hot and cold air mixing, cooling air distributions and the integrated heat transfer performance. A sample data center is studied with the analytical results showing that the smaller the entransy-dissipation-based thermal resistance is, the lower the average heat source temperature will be. Thus, the minimum thermal resistance principle is applicable to the analysis and optimization of data center heat transfer process. The three indexes can be used to guide the improvement and optimization of airflow organization. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction The 21st century is the era of networks and information. With the huge increment of data processing demands, data center energy consumption has dramatically increased in recent years. A statistical report from Lawrence Berkeley National Laboratory in 2007 showed that the US data center energy consumption had a high growth rate of 15% per year and global data center energy consumption doubled every 5 years [1]. With the rapid growth of data center energy consumption and continuously increasing energy costs, energy conservation in data centers is more and more concerned by governments, companies and academia. Data centers consume energy in the IT equipment, cooling systems, UPS and other systems. The data center cooling systems always account for a high proportion of the total energy consumption. Research has indicated that the cooling system energy consumption usually accounts for more than 30–50% of the total energy consumption [2,3]. Therefore, the cooling system energy conservation plays an important role in high-efficiency energy utilization and energy conservation in data centers. Optimization of the data center airflow organization is one of the most effective ways to reduce the cooling system energy consumption. Previous studies have developed some ways to improve the airflow organization and equipment layout in data centers. For example, the raised-floor design is commonly used in large data
⇑ Corresponding author. Tel.: +86 10 62772919; fax: +86 10 62781610. E-mail address: [email protected] (Z. Li). 0017-9310/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.03.037
centers with cold and hot aisles [4–8]. However, there are still inefficient data center airflow patterns. Fig. 1 shows a typical raisedfloor data center. The cooling air is pumped into the plenum below the raised floor from the cooling system, flows into the cold aisle through perforated tiles, is heated in the racks, and finally flows back to the air conditioning. Air mixing and inefficient cooling air distributions often occur between racks in data centers [9,10]. The three main types of air mixing phenomena are recirculation air mixing, bypass air mixing and negative pressure air mixing. Air mixing will reduce the cooling ability and poor cooling air distributions between racks will result in local hot spots. Therefore, a more comprehensive method is needed to evaluate the thermal environment and to optimize the airflow organization. In recent years, there have been many studies of data center thermal environments with various analysis methods and evaluation indexes. Sharma et al. [11] defined a Supply Heat Index (SHI) and a Return Heat Index (RHI) based on the rack input and output air temperatures. The sum of SHI and RHI is equal to unity and both indexes can be used to measure the air recirculation in data centers. Larger SHI or smaller RHI corresponds to stronger recirculation air mixing and lower cooling efficiency. Herrlin [12] introduced the Rack Cooling Index (RCI), which is also named as the data center health index. RCI is divided into two types, RCIHI and RCILO, describing the overheating and overcooling of the data center equipments. A lager RCI indicates a better thermal environment. Herrlin [13] also proposed a Return Temperature Index (RTI) to measure the level of bypass airflow and recirculation airflow to evaluate the cooling air utilization. RTI above 100% suggests mainly air recirculation, while RTI below 100% suggests mainly air bypass.
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Nomenclature C cv G G/ g/ K k kn q Q R/ r
heat capacity rate, W K1 specific heat at constant volume, J kg1 K1 entransy, J K entransy dissipation rate, W K entransy dissipation rate per unit volume, W K m3 thermal conductance, W K1 thermal conductivity, W m1 K1 air distribution ratio of the nth rack group heat flux, W m2 heat transfer rate, W entransy-dissipation-based thermal resistance, K W1 air mixing ratio
Greek symbol q density, kg m3
DC ex h i max mix m1 m2 npa nm o opt ra RM sys tot
data center heat exchanger heat source or hot flow inlet maximum mixing middle airflow 1 middle airflow 2 negative pressure air no mixing outlet optimal recirculation air rack module system total
Subscripts ba bypass air c cold flow
VanGilder and Shrivastava [14] introduced the dimensionless Capture Index (CI), which is a cooling performance metric at the equipment rack level. Tozer et al. [15] also discussed air mixing in data centers. The main airflow organization problems in a data center are air mixing and poor cooling air distributions. Hot and cold air mixing reduces the cooling air utilization efficiency, and poor cooling air distribution between racks results in hot spots in high thermal load equipment. Both of these problems will degrade the thermal environment and affect the operation of IT equipment. The existing analyses and evaluation indexes of data center thermal environment mainly belong to empirical methods. Most of them are mainly focused on one or two air mixing problems in local position of the data center. For instance, SHI, RHI and CI are only concerned with the airflow at the rack level. And some analysis methods and evaluation indexes cannot accurately reflect the airflow organization problems. For example, RTI actually describes the relative strength of bypass airflow and recirculation airflow rather than the absolute extent of the mixing phenomena and the influence on the data center heat transfer. In addition, the indexes come from empirical methods, so they cannot give enough information to show the energy efficiency of data center cooling process and cannot well guide solutions to airflow organization. In light of the deficiencies of the empirical methods, approaches based on the Second
Law of thermodynamics are proposed to analyze the data center cooling system. Shah et al. [16–18] use the concept of exergy to analyze the data center thermal management system and optimize the parameters of computer room air-conditioning units. Their researches are more comprehensive and can give better guidance for the data center cooling system design. While researchers found that the thermodynamic analysis does not always work well on some pure heat transfer process. For an example, Shah and Skiepko [19] indicated that minimum entropy generation does not always correspond to higher heat exchanger effectiveness. Data center cooling is actually a heat transfer process, and a more suitable method needs to be studied. Guo et al. [20] introduced a new physical quantity, entransy, to analyze and optimize heat transfer processes. Entransy represents the heat transfer ability of an object and depends not only on the internal energy stored in the object but also on its thermodynamic temperature.
G ¼ Q h T=2
ð1Þ
where Qh is the internal thermal energy stored in an object and T is the object’s absolute temperature. The entransy of an object describes its heat transfer ability, as the electrical energy in a capacitor describes its charge transfer ability. During an irreversible heat transfer process, the thermal energy is conserved, but the entransy will be partially dissipated. The entransy balance equation is obtained by multiplying the heat conduction equation by T,
qcv T
@T ¼ r ðqTÞ þ q rT: @t
ð2Þ
The left hand side of Eq. (2) represents the entransy variation with time, the first term on the right hand side is the entransy flux, and the last term is the entransy dissipation rate due to heat conduction. It can be written as,
g / ¼ q rT ¼ kðrTÞ2
ð3Þ
and the entransy-dissipation-based thermal resistance can be expressed as,
R/ ¼
Fig. 1. Airflow schematic in a typical data center.
G/ Q2
ð4Þ
where G/ is the entransy dissipation rate during the heat transfer process, and Q is the heat transfer rate.
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Studies have shown that entransy dissipation and the entransydissipation-based thermal resistance are widely applicable for optimization of heat transfer processes. Guo et al. [21] proposed the extremum entransy dissipation principle for heat conduction. The definition of the entransy-dissipation-based thermal resistance was used by Zhu [22] to develop the minimum thermal resistance principle for optimizing the volume-to-point problem. Wu et al. [23] and Chen and Ren [24] respectively used the entransy dissipation extremum principle for laminar and turbulent flow heat transfer optimization. Wu and Liang [25] and Cheng and Liang [26] both did entransy dissipation analyses and defined the radiation thermal resistance for thermal radiation process. The entransy dissipation analysis method and the minimum thermal resistance principle have also been used in many engineering heat transfer problems. Chen et al. [27–29] optimized the heat transfer in channels using the entransy dissipation minimization principle. Liu et al. [30] introduced the entransy-dissipation-based thermal resistance for heat exchangers and used the minimum thermal resistance principle for heat exchanger optimization. Guo et al. [31,32] defined an entransy dissipation number for heat exchangers and introduced the principle of entransy dissipation equi-partition for heat exchanger design. Qian and Li [33] compared and proved that the minimum thermal resistance principle is more applicable than the minimum entropy generation principle to the optimization of heat exchangers. In researches of heat exchanger networks, Qian et al. [34] analyzed two-stream heat exchanger networks using the entransy-dissipation-based thermal resistance, while Cheng et al. [35] optimized parallel thermal networks of a spacecraft thermal control system. In this paper, the heat transfer in a data center is analyzed using the entransy dissipation analysis method. Three indexes are presented according to the entransy-dissipation-based thermal resistance of data center to evaluate the air mixing, cooling air distribution and integrated heat transfer performance.
2. Data center entransy dissipation and thermal resistance The airflow model given by Tozer et al. [15] can be used to abstract the airflow and heat transfer processes in data center into a two-dimensional heat transfer network shown in Fig. 2. The airflow cycle is shown in Fig. 2 with cooling air delivered into data center from the cooling system, flowing into the racks through perforated tiles, absorbing heat from the IT equipment, and finally flowing back to the cooling system. Poor airflow organization causes significant air mixings in data centers, such as recirculation air mixing, bypass air mixing and negative pressure air mixing. The three air mixing phenomena are quantified by the recirculation air mixing ratio, bypass air mixing ratio and negative pressure air
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mixing ratio given in Eqs. (5)–(7) [15]. The three air mixing ratios all vary from 0 to 1. In these equations, C is the heat capacity rate of airflows and the subscripts ra, ba, npa, RM, m1 mean recirculation air, bypass air, negative pressure air, rack module, middle airflow1 respectively.
rra ¼ C ra =C RM
ð5Þ
rba ¼ C ba =C m1
ð6Þ
rnpa ¼ C npa =C m1
ð7Þ
As the cooling air flows into the racks, poor air distributions will lead to hot spots in some high-load racks. The impact of the air distribution on the rack cooling is analyzed using the actual racks layout in the data center as the parallel model shown in Fig. 2 with the cooling air distribution ratio defined as,
kn ¼ C RM;n =C RM
ð8Þ
For a given data center, the equipment heat loads, flow rates and cooling system supply air temperature are all fixed. The entransy dissipation of heat transfer process in the data center includes the rack module heat transfer entransy dissipation, the recirculation air mixing entransy dissipation, the bypass air mixing entransy dissipation and the negative pressure air mixing entransy dissipation. The heat transfer in the racks can be approximated as heat transfer in a heat exchanger. For a two-stream heat exchanger shown in Fig. 3, Liu et al. [26] formulated the entransy dissipation rate,
G/;ex ¼
1 1 1 1 C h T 2h;i þ C c T 2c;i C h T 2h;o þ C c T 2c;o 2 2 2 2
ð9Þ
The entransy dissipation rate of the heat exchanger is equal to the difference between the total entransy rates of the fluids entering and leaving the heat exchanger. In the heat transfer process of racks, one side is the heat source while the other side is the cooling air. The entransy dissipation rate in the rack module can then be expressed as,
1 G/;h ¼ ðQ 1 T h1 þ Q 2 T h2 þ þ Q n T hn Þ þ C RM T 2RM;i T 2RM;o 2
ð10Þ
where Qn is the heat load and Thn is the heat source temperature of the nth rack. CRM, TRM,i and TRM,o are the heat capacity rate, the inlet temperature and the outlet temperature for air flow through the rack module. Recirculation air mixing, bypass air mixing and negative pressure air mixing are all non-isothermal mixing processes, so their entransy dissipation rates can be expressed by the entransy dissipation of mixing processes. For the mixing process shown in Fig. 4, the entransy dissipation rate can be defined as, G/;mix ¼
1 1 1 1 C 1 T 21;i þ C 2 T 22;i þ þ C n T 2n;i ðC 1 þ C 2 þ þ C n ÞT 2mix 2 2 2 2
ð11Þ
According to Eq. (11), the entransy dissipation rate due to recirculation air mixing, bypass air mixing and negative pressure air mixing shown in Fig. 2 can be expressed as follows: The entransy dissipation rate due to recirculation air mixing,
Fig. 2. Two-dimensional model of data center heat transfer network.
Fig. 3. Schematic of heat exchanger.
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3. Data center entransy dissipation analysis
Fig. 4. Schematic of a mixing process.
G/;ra ¼
1 C m2 T 2m2 þ C ra T 2ra C RM T 2RM;i 2
ð12Þ
The entransy dissipation rate due to bypass air mixing,
G/;ba ¼
1 C m2 T 2RM;o þ C ba T 2ba C m1 T 2DC;o 2
ð13Þ
The entransy dissipation rate due to negative pressure air mixing,
G/;npa ¼
1 C DC T 2DC;i þ C npa T 2npa C m1 T 2m1 2
ð14Þ
The entransy dissipation rate for the entire data center is then the sum of the four parts,
1 G/;sys ¼ ðQ 1 T h1 þ Q 2 T h2 þ þ Q n T hn Þ C DC T 2DC;o T 2DC;i 2
ð15Þ
The total data center heat load is,
Q sys ¼ Q 1 þ Q 2 þ þ Q n
ð16Þ
Define the average heat source temperature as,
Th ¼
Q1 Q sys
T h1 þ
Q2 Q sys
T h2 þ þ
Qn T hn Q sys
ð17Þ
And also define the average cooling air temperature as,
T DC ¼
T DC;i þ T DC;o 2
ð18Þ
Then the data center entransy dissipation rate can be simplified using Eqs. (17) and (18) as,
G/;sys ¼ Q sys ðT h T DC Þ
ð19Þ
Equation (19) indicates that the entransy dissipation rate due to the data center heat transfer is equal to the product of the heat load and the temperature difference in the data center. Here, Th is the heat load weighted average temperature of the heat sources and TDC is the arithmetic average temperature of the cooling air flowing. TDC is a fixed value when the data center and cooling system are given. When the entransy dissipation rate and heat load are known, the entransy-dissipation-based thermal resistance of data center can be defined as,
Rsys ¼
G/;sys Q 2sys
¼
T h T DC Q sys
Hot and cold air mixing and poor cooling air distribution between the racks are the major problems for data center airflow organization. Among the three air mixing phenomena, recirculation air mixing and bypass air mixing are more serious and the air mixing ratios are normally more than 0.5 in data centers. Negative pressure air mixing only occurs in some data centers and the air mixing ratio is usually less than 0.1. The cooling air distribution is affected by the heat load and the air flow rate in the racks. The current data center designs do not have effective rack level cooling air distribution control, so there are problems with ineffective cooling air distributions between racks. The influence of the airflow organization problems on the data center heat transfer was analyzed using the entransy dissipation analysis method. The data center racks are divided into two groups. The heat transfer network is shown in Fig. 5 and the parameters are listed in Table 1. The air mixing analyses assumed that the cooling air flow rates in the two group racks are the same and only one of the three mixing phenomena accrues. The analysis used recirculation air mixing ratios and bypass air mixing ratios of 0–0.8 and negative pressure air mixing ratios of 0–0.2. The analytical results for the recirculation air mixing, bypass air mixing and negative pressure air mixing are shown in Figs. 6–8. The figures show that the entransy dissipation, the entransy-dissipation-based thermal resistance and the average rack module heat source temperature increase with the increased air mixing. The results in Figs. 6 and 8 show that both the data center entransy-dissipation-based thermal resistance and the average rack module heat source temperatures increase linearly with increasing recirculation air mixing ratio and negative pressure air mixing ratio. For bypass air mixing as seen in Fig. 7, the thermal resistance and the average heat source temperature grow exponentially with increasing bypass air mixing ratio. Thus, in the three air mixing phenomena, bypass air mixing has a larger influence than the others under the same air mixing ratio. The effect of the cooling air distribution on the data center heat transfer was analyzed with all the air mixing ratios set at their maximum values, while the cooling air distribution ratio in the first rack group was varied from 0.1 to 0.7. The analytical results in Fig. 9 show that with increasing cooling air distribution ratio, the entransy dissipation in the rack module, the data center thermal resistance and the average rack module heat source temperature first decrease and then increase. Thus, the cooling air distribution can be optimized by minimizing the entransy-
ð20Þ
The temperature difference between the heat source and the cooling air is the driving force. The heat transfer performance in the data center can be characterized by the entransy-dissipationbased thermal resistance. For a given data center, the heat load and the average cooling air temperature are fixed. Thus Eq. (20) shows that a smaller thermal resistance will give a lower rack module temperature and a better thermal environment in the data center.
Fig. 5. Data center heat transfer network with two group racks.
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X. Qian et al. / International Journal of Heat and Mass Transfer 62 (2013) 579–585 Table 1 Data center parameters. Cooling air (cooling system)
Racks
Return temperature TDC,o
24 °C
#1
Heat capacity rate CDC
3700 W/K
#2
Thermal conductance Kh1 Heat load Q1 Thermal conductance Kh2 Heat load Q2
480 W/K 10 kW 720 W/K 20 kW
Fig. 6. Normalized G/,ra, Th, Rsys for various recirculation air mixing ratios.
Fig. 8. Normalized G/,npa, Th, Rsys for various negative pressure air mixing ratios.
Fig. 7. Normalized G/,ba, Th, Rsys for various bypass air mixing ratios.
Fig. 9. Normalized G/,h, Th, Rsys for various cooling air distribution ratios.
dissipation-based thermal resistance to give the lowest average rack module heat source temperature. These results show that how the entransy dissipation analysis method can be used to analyze the heat transfer of the data center cooling system. A smaller entransy-dissipation-based thermal resistance will improve the data center thermal environment, i.e., the minimum thermal resistance principle can be used to optimize the data center heat transfer.
Table 2 Working conditions of data center. Operating condition
Description
Thermal resistance
Original No mixing Optimal
Actual operating condition in the data center No air mixing happened in the data center No air mixing + optimal air distribution
Rsys Rnm Ropt
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Table 3 Data center airflow parameters. Negative pressure air mixing ratio
Bypass air mixing ratio
Recirculation air mixing ratio
Cooling air distribution ratio of the first rack group
rNPa = 0.03
rBa = 0.61
rRa = 0.51
k1 = 0.5
ADI can be used to evaluate the effects of ineffective cooling air distribution on data center cooling system. A larger ADI corresponds to a better cooling air distribution. When the cooling air distribution between racks is optimal, Rnm = Ropt and ADI = 1. The integrated heat transfer index (IHTI) is defined as the thermal resistance ratio of the optimal condition to the original condition.
IHTI ¼ ð1 AMIÞ ADI ¼
Ropt Rsys
ð23Þ
IHTI can be used to assess the data center heat transfer efficiency relative to the optimal condition. The IHTI actually indicates the potential for improvement of the data center airflow organization. Since IHTI is equal to the product of 1-AMI and ADI, a smaller AMI and a larger ADI result in a larger IHTI, and therefore, a better thermal environment in the data center. When the data center integrated heat transfer index equals to 1, the thermal resistance reaches the minimum value and the thermal environment is close to optimal condition.
Fig. 10. Entransy dissipation ratio in a data center.
4. Evaluation of data center airflow organization
4.2. Case study
4.1. Evaluation indexes based on the thermal resistance
The entransy dissipation analysis method and the evaluation indexes were used to analyze the thermal environment of a data center. For a given data center, the heat loads and cooling system parameters are fixed. The air mixing ratio and the cooling air distribution ratio can be obtained by testing or CFD simulations. The data center cooling system conditions for the case studied here are given in Fig. 5 and Tables 1 and 3. The air mixing ratios were taken from the results given by Tozer et al. [15] with a cooling air distribution ratio of 0.5. The entransy dissipations for the three kinds of air mixings and the heat transfer in racks were calculated for the parameters listed in Table 3. As seen in Fig. 10 and 698% of the data center heat transfer entransy dissipation is due to the racks heat transfer with the three kinds of air mixing contributing 30.2%. The entransy dissipation due to the bypass air mixing is the largest of the three kinds of air mixing phenomena with the negative pressure air mixing the smallest. The thermal resistances and heat source temperatures for the original, no mixing and optimal operating conditions are listed in Table 4. For this case, AMI is 0.307, ADI is 0.981 and IHTI is 0.679. The evaluation indexes show that the air mixing is quite serious in this data center and the improvement of air mixing is more helpful to the data center heat transfer. If the air mixing is eliminated, the thermal resistance of the data center will be significantly reduced, the cooling temperature difference will be decreased by 11.64 °C, and the data center thermal environment will be greatly improved. Furthermore, by comparing the entransy dissipations of the three air mixing phenomena, it is found that the bypass air mixing
The aim of the thermal environment analysis is to understand the airflow organization and the heat transfer of the data center. The entransy dissipation analysis is used to evaluate the influences of the air mixing and cooling air distribution on the data center cooling system. The data center entransy-dissipation-based thermal resistance can be minimized by optimizing the airflow organization. In the following, three evaluation indexes are presented based on a system with no air mixing, a system with no air mixing and the optimal cooling air distribution between racks, and the original working condition as listed in Table 2. The air mixing index (AMI) is defined as.
AMI ¼
Rsys Rnm Rsys
ð21Þ
where the numerator is the thermal resistance difference between the original condition and the no mixing condition, and the denominator is the thermal resistance of original condition. AMI can be used to evaluate the effects of air mixing on the data center cooling system. A larger AMI means that the air mixing phenomena are more serious and have stronger effects on data center cooling system. When the data center is working in no mixing condition, Rsys = Rnm and AMI = 0. The air distribution index (ADI) is defined as the thermal resistance ratio of the optimal condition to the no mixing condition.
ADI ¼
Ropt Rnm
ð22Þ
Table 4 Thermal resistances and heat source temperatures for different operating conditions.
Original No mixing Optimal
rNPa
rBa
rRa
k1
Rsys K/W
DT °C
Th1 °C
Th2 °C
0.03 0 0
0.61 0 0
0.51 0 0
0.5 0.5 0.335
1.261 103 0.873 103 0.856 103
37.83 26.19 25.68
50.72 39.54 41.02
61.30 49.42 47.93
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should be first improved due to its largest impact on data center heat transfer. Optimization of the cooling air distribution will also improve the data center cooling system heat transfer. Although the optimization potential of this case is small, the uniformity of the rack module temperature can be improved by optimizing the air distribution. 5. Concluding remarks The entransy dissipation analysis method has been presented to analyze the thermal environment of the data center. The entransy dissipation analyses of the air mixings and the cooling air distribution showed that the minimum thermal resistance principle is applicable to data center heat transfer optimization. Based on the entransy dissipation analysis of the data center thermal environment, the air mixing index (AMI), the air distribution index (ADI) and the integrated heat transfer index (IHTI) are defined by using the thermal resistances of the original, no mixing and optimal operating conditions. AMI and ADI reflect the effects of air mixing and the cooling air distribution on the data center heat transfer, while IHTI is an integrated parameter to evaluate the data center heat transfer conditions. A sample data center was analyzed with the results indicating that the evaluation indexes accurately reflect the data center thermal environment, where the bypass air mixing has the largest impact on data center heat transfer. This method can guide optimization to the airflow organization in data centers. Acknowledgements This work was financially supported by the National Natural Science Foundation of China (51138005) and the National Basic Research Program of China (2013CB228301). References [1] J.G. Koomey, Estimating total power consumption by servers in the US and the World, Technical report, Lawrence Berkeley National Laboratory, 2007. [2] S. Greenberg, E. Mills, B. Tschudi, Best practices for data centers: results from benchmarking 22 data center, ACEEE Summer Study Energy Effic. Buildings 3 (2006) 76–87. [3] A. Shah, C. Patel, C. Bash, R. Sharma, R. Shih, Impact of rack-level compaction on the data center cooling ensemble, in: 11th Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems, 2008), pp. 1175–1182. [4] V. Sorell, S. Escalante, J. Yang, Comparison of overhead and underfloor air delivery systems in a data center environment using CFD modeling, ASHRAE Trans. 111 (2) (2005) 756–764. [5] R.R. Schmidt, M. Iyengar, Comparison between underfloor supply and overhead supply ventilation designs for data center high-density clusters, ASHRAE Trans. 113 (1) (2007) 115–125. [6] R.R. Schmidt, M. Iyengar, Best practices for data center thermal and energy management – review of literature, ASHRAE Trans. 113 (1) (2007) 206–218. [7] R.F. Sullivan, Alternating cold and hot aisles provides more reliable cooling for server farms, White Paper by the Uptime Institute, Santa Fe, NM, 2003. [8] S.V. Patankar, Airflow and cooling in a data center, J. Heat Transfer 132 (7) (2010) 1–17. [9] R.F. Sullivan, K.G. Brill, L. Strong, Reducing bypass airflow is essential for reducing computer room hot spots, White Paper by the Uptime Institute, Santa Fe, NM, 2004.
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[10] R.F. Sullivan, Some worst case practices in data centers, ASHRAE Trans. 114 (1) (2008) 3–7. [11] R.R. Sharma, C.E. Bash, C.D. Patel, Dimensionless parameters for evaluation of thermal design and performance of large-scale data centers, in: Proceeding of the Eighth ASME/AIAA Joint Thermophysics and Heat Transfer Conference, St Louis, MO, 2002. [12] M.K. Herrlin, Rack cooling effectiveness in data center and telecom central offices: the rack cooling index (RCI), ASHRAE Trans. 111 (2) (2005) 1–11. [13] M.K. Herrlin, Improved data center energy efficiency and thermal performance by advanced airflow analysis, in: Digital Power Forum, San Francisco, CA, 2007. [14] J.W. VanGilder, S.K. Shrivastava, Capture index: an airflow-based rack cooling performance metric, ASHRAE Trans. 113 (1) (2007) 126–136. [15] R. Tozer, C. Kurkjian, M. Salim, Air management metrics in data centers, ASHRAE Trans. 115 (1) (2009) 63–70. [16] A.J. Shah, V.P. Carey, C.E. Bash, C.D. Patel, Exergy analysis of data center thermal management systems, J. Heat Transfer 130 (2) (2008) 021401– 021410. [17] A.J. Shah, V.P. Carey, C.E. Bash and C.D. Patel, Exergy-based optimization strategies for multi-component data center thermal management: part I, analysis, in: Proceedings of International Electronic Packaging Technical Conference and Exhibition (IPACK2005-73137), San Francisco, CA, 2005. [18] A.J. Shah, V.P. Carey, C.E. Bash and C.D. Patel, Exergy-based optimization strategies for multi-component data center thermal management: part II, Application and validation, in: Proceeding of International Electronic Packaging Technical Conference and Exhibition (IPACK2005-73138), San Francisco, CA, 2005. [19] R.K. Shah, T. Skiepko, Entropy generation extrema and their relationship with heat exchanger effectiveness – number of transfer unit behavior for complex flow arrangements, J. Heat Transfer 126 (6) (2004) 994–1002. [20] Z.Y. Guo, H.Y. Zhu, X.G. Liang, Entransy-a physical quantity describing heat transfer ability, Int. J. Heat Mass Transfer 50 (13–14) (2007) 2545–2556. [21] Z.Y. Guo, X.G. Cheng, Z.Z. Xia, Least dissipation principle of heat transport potential capacity and its application in heat conduction optimization, Chin. Sci. Bull. 48 (4) (2003) 406–410. [22] H.Y. Zhu, The minimum thermal resistance principle based on entransy dissipation. Ph.D. thesis, Tsinghua University, Beijing, 2007. [23] J. Wu, X.G. Cheng, J.A. Meng, Potential capacity dissipation extremum and entropy generation minimization in laminar convective heat transfer, J. Eng. Thermophys. 27 (1) (2006) 100–102. [24] Q. Chen, J.X. Ren, Generalized thermal resistance for convective heat transfer and its relation to entransy dissipation, Chin. Sci. Bull. 53 (23) (2008) 3753– 3761. [25] J. Wu, X.G. Liang, Application of entransy dissipation extremum principle in radiative heat transfer optimization, Sci. Chin. Technol. Sci. 51 (8) (2008) 1306–1314. [26] X.T. Cheng, X.G. Liang, Entransy flux of thermal radiation and its application to enclosures with opaque surfaces, Int. J. Heat Mass Transfer 54 (1–3) (2011) 269–278. [27] Z.H. Xie, L.G. Chen, F.R. Sun, Constructal optimization on T-shaped cavity based on entransy dissipation minimization, Chin. Sci. Bull. 54 (23) (2009) 4418– 4427. [28] S.H. Wei, L.G. Chen, F.R. Sun, Constructal optimization of discrete and continuous-variable cross-section conducting path based on entransy dissipation rate minimization, Sci. Chin. Technol. Sci. 53 (6) (2010) 1666–1677. [29] Q.H. Xiao, L.G. Chen, F.R. Sun, Constructal entransy dissipation rate and flowresistance minimizations for cooling channels, Sci. Chin. Technol. Sci. 53 (9) (2010) 2458–2468. [30] X.B. Liu, J.A. Meng, Z.Y. Guo, Entropy generation extremum and entransy dissipation extremum for heat exchanger optimization, Chin. Sci. Bull. 54 (6) (2009) 943–947. [31] J.F. Guo, L. Cheng, M.T. Xu, Entransy dissipation number and its application to heat exchanger performance evaluation, Chin. Sci. Bull. 54 (15) (2009) 2708– 2713. [32] J.F. Guo, M.T. Xu, L. Cheng, Principle of equipartition of entransy dissipation for heat exchanger design, Sci. Chin. Technol. Sci. 53 (5) (2010) 1309–1314. [33] X.D. Qian, Z.X. Li, Analysis of entransy dissipation in heat exchangers, Int. J. Therm. Sci. 50 (4) (2011) 608–614. [34] X.D. Qian, Z. Li, Z.X. Li, Entransy-dissipation- based thermal resistance analysis of heat exchanger networks, Chin. Sci. Bull. 56 (31) (2011) 3289–3295. [35] X.T. Cheng, X.H. Xu, X.G. Liang, Application of entransy to optimization design of parallel thermal network of thermal control system in spacecraft, Sci. Chin. Technol. Sci. 54 (4) (2011) 964–971.
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
A thermal environmental analysis method for data centers Xiaodong Qian, Zhen Li, Zhixin Li ⇑ Key Laboratory of Thermal Science and Power Engineering of Ministry of Education, School of Aerospace, Tsinghua University, Beijing 100084, China
a r t i c l e
i n f o
Article history: Received 23 March 2012 Received in revised form 17 December 2012 Accepted 14 March 2013 Available online 11 April 2013 Keywords: Data center Airflow organization optimization Entransy dissipation Minimum thermal resistance
a b s t r a c t The rapidly growing of data center energy consumption rates are contributing to concern about energy conservation. Reasonable airflow organization is an effective way to reduce the cooling system energy consumption and to upgrade the energy utilization efficiency. Comprehensive and accurate analyses are important for airflow organization optimization. This paper presents the entransy dissipation analysis method to analyze the influences of hot and cold air mixing and cooling air distributions on data center heat transfer process. The thermal resistance based on entransy dissipation is used to define three indexes to evaluate hot and cold air mixing, cooling air distributions and the integrated heat transfer performance. A sample data center is studied with the analytical results showing that the smaller the entransy-dissipation-based thermal resistance is, the lower the average heat source temperature will be. Thus, the minimum thermal resistance principle is applicable to the analysis and optimization of data center heat transfer process. The three indexes can be used to guide the improvement and optimization of airflow organization. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction The 21st century is the era of networks and information. With the huge increment of data processing demands, data center energy consumption has dramatically increased in recent years. A statistical report from Lawrence Berkeley National Laboratory in 2007 showed that the US data center energy consumption had a high growth rate of 15% per year and global data center energy consumption doubled every 5 years [1]. With the rapid growth of data center energy consumption and continuously increasing energy costs, energy conservation in data centers is more and more concerned by governments, companies and academia. Data centers consume energy in the IT equipment, cooling systems, UPS and other systems. The data center cooling systems always account for a high proportion of the total energy consumption. Research has indicated that the cooling system energy consumption usually accounts for more than 30–50% of the total energy consumption [2,3]. Therefore, the cooling system energy conservation plays an important role in high-efficiency energy utilization and energy conservation in data centers. Optimization of the data center airflow organization is one of the most effective ways to reduce the cooling system energy consumption. Previous studies have developed some ways to improve the airflow organization and equipment layout in data centers. For example, the raised-floor design is commonly used in large data
⇑ Corresponding author. Tel.: +86 10 62772919; fax: +86 10 62781610. E-mail address: [email protected] (Z. Li). 0017-9310/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.03.037
centers with cold and hot aisles [4–8]. However, there are still inefficient data center airflow patterns. Fig. 1 shows a typical raisedfloor data center. The cooling air is pumped into the plenum below the raised floor from the cooling system, flows into the cold aisle through perforated tiles, is heated in the racks, and finally flows back to the air conditioning. Air mixing and inefficient cooling air distributions often occur between racks in data centers [9,10]. The three main types of air mixing phenomena are recirculation air mixing, bypass air mixing and negative pressure air mixing. Air mixing will reduce the cooling ability and poor cooling air distributions between racks will result in local hot spots. Therefore, a more comprehensive method is needed to evaluate the thermal environment and to optimize the airflow organization. In recent years, there have been many studies of data center thermal environments with various analysis methods and evaluation indexes. Sharma et al. [11] defined a Supply Heat Index (SHI) and a Return Heat Index (RHI) based on the rack input and output air temperatures. The sum of SHI and RHI is equal to unity and both indexes can be used to measure the air recirculation in data centers. Larger SHI or smaller RHI corresponds to stronger recirculation air mixing and lower cooling efficiency. Herrlin [12] introduced the Rack Cooling Index (RCI), which is also named as the data center health index. RCI is divided into two types, RCIHI and RCILO, describing the overheating and overcooling of the data center equipments. A lager RCI indicates a better thermal environment. Herrlin [13] also proposed a Return Temperature Index (RTI) to measure the level of bypass airflow and recirculation airflow to evaluate the cooling air utilization. RTI above 100% suggests mainly air recirculation, while RTI below 100% suggests mainly air bypass.
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Nomenclature C cv G G/ g/ K k kn q Q R/ r
heat capacity rate, W K1 specific heat at constant volume, J kg1 K1 entransy, J K entransy dissipation rate, W K entransy dissipation rate per unit volume, W K m3 thermal conductance, W K1 thermal conductivity, W m1 K1 air distribution ratio of the nth rack group heat flux, W m2 heat transfer rate, W entransy-dissipation-based thermal resistance, K W1 air mixing ratio
Greek symbol q density, kg m3
DC ex h i max mix m1 m2 npa nm o opt ra RM sys tot
data center heat exchanger heat source or hot flow inlet maximum mixing middle airflow 1 middle airflow 2 negative pressure air no mixing outlet optimal recirculation air rack module system total
Subscripts ba bypass air c cold flow
VanGilder and Shrivastava [14] introduced the dimensionless Capture Index (CI), which is a cooling performance metric at the equipment rack level. Tozer et al. [15] also discussed air mixing in data centers. The main airflow organization problems in a data center are air mixing and poor cooling air distributions. Hot and cold air mixing reduces the cooling air utilization efficiency, and poor cooling air distribution between racks results in hot spots in high thermal load equipment. Both of these problems will degrade the thermal environment and affect the operation of IT equipment. The existing analyses and evaluation indexes of data center thermal environment mainly belong to empirical methods. Most of them are mainly focused on one or two air mixing problems in local position of the data center. For instance, SHI, RHI and CI are only concerned with the airflow at the rack level. And some analysis methods and evaluation indexes cannot accurately reflect the airflow organization problems. For example, RTI actually describes the relative strength of bypass airflow and recirculation airflow rather than the absolute extent of the mixing phenomena and the influence on the data center heat transfer. In addition, the indexes come from empirical methods, so they cannot give enough information to show the energy efficiency of data center cooling process and cannot well guide solutions to airflow organization. In light of the deficiencies of the empirical methods, approaches based on the Second
Law of thermodynamics are proposed to analyze the data center cooling system. Shah et al. [16–18] use the concept of exergy to analyze the data center thermal management system and optimize the parameters of computer room air-conditioning units. Their researches are more comprehensive and can give better guidance for the data center cooling system design. While researchers found that the thermodynamic analysis does not always work well on some pure heat transfer process. For an example, Shah and Skiepko [19] indicated that minimum entropy generation does not always correspond to higher heat exchanger effectiveness. Data center cooling is actually a heat transfer process, and a more suitable method needs to be studied. Guo et al. [20] introduced a new physical quantity, entransy, to analyze and optimize heat transfer processes. Entransy represents the heat transfer ability of an object and depends not only on the internal energy stored in the object but also on its thermodynamic temperature.
G ¼ Q h T=2
ð1Þ
where Qh is the internal thermal energy stored in an object and T is the object’s absolute temperature. The entransy of an object describes its heat transfer ability, as the electrical energy in a capacitor describes its charge transfer ability. During an irreversible heat transfer process, the thermal energy is conserved, but the entransy will be partially dissipated. The entransy balance equation is obtained by multiplying the heat conduction equation by T,
qcv T
@T ¼ r ðqTÞ þ q rT: @t
ð2Þ
The left hand side of Eq. (2) represents the entransy variation with time, the first term on the right hand side is the entransy flux, and the last term is the entransy dissipation rate due to heat conduction. It can be written as,
g / ¼ q rT ¼ kðrTÞ2
ð3Þ
and the entransy-dissipation-based thermal resistance can be expressed as,
R/ ¼
Fig. 1. Airflow schematic in a typical data center.
G/ Q2
ð4Þ
where G/ is the entransy dissipation rate during the heat transfer process, and Q is the heat transfer rate.
X. Qian et al. / International Journal of Heat and Mass Transfer 62 (2013) 579–585
Studies have shown that entransy dissipation and the entransydissipation-based thermal resistance are widely applicable for optimization of heat transfer processes. Guo et al. [21] proposed the extremum entransy dissipation principle for heat conduction. The definition of the entransy-dissipation-based thermal resistance was used by Zhu [22] to develop the minimum thermal resistance principle for optimizing the volume-to-point problem. Wu et al. [23] and Chen and Ren [24] respectively used the entransy dissipation extremum principle for laminar and turbulent flow heat transfer optimization. Wu and Liang [25] and Cheng and Liang [26] both did entransy dissipation analyses and defined the radiation thermal resistance for thermal radiation process. The entransy dissipation analysis method and the minimum thermal resistance principle have also been used in many engineering heat transfer problems. Chen et al. [27–29] optimized the heat transfer in channels using the entransy dissipation minimization principle. Liu et al. [30] introduced the entransy-dissipation-based thermal resistance for heat exchangers and used the minimum thermal resistance principle for heat exchanger optimization. Guo et al. [31,32] defined an entransy dissipation number for heat exchangers and introduced the principle of entransy dissipation equi-partition for heat exchanger design. Qian and Li [33] compared and proved that the minimum thermal resistance principle is more applicable than the minimum entropy generation principle to the optimization of heat exchangers. In researches of heat exchanger networks, Qian et al. [34] analyzed two-stream heat exchanger networks using the entransy-dissipation-based thermal resistance, while Cheng et al. [35] optimized parallel thermal networks of a spacecraft thermal control system. In this paper, the heat transfer in a data center is analyzed using the entransy dissipation analysis method. Three indexes are presented according to the entransy-dissipation-based thermal resistance of data center to evaluate the air mixing, cooling air distribution and integrated heat transfer performance.
2. Data center entransy dissipation and thermal resistance The airflow model given by Tozer et al. [15] can be used to abstract the airflow and heat transfer processes in data center into a two-dimensional heat transfer network shown in Fig. 2. The airflow cycle is shown in Fig. 2 with cooling air delivered into data center from the cooling system, flowing into the racks through perforated tiles, absorbing heat from the IT equipment, and finally flowing back to the cooling system. Poor airflow organization causes significant air mixings in data centers, such as recirculation air mixing, bypass air mixing and negative pressure air mixing. The three air mixing phenomena are quantified by the recirculation air mixing ratio, bypass air mixing ratio and negative pressure air
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mixing ratio given in Eqs. (5)–(7) [15]. The three air mixing ratios all vary from 0 to 1. In these equations, C is the heat capacity rate of airflows and the subscripts ra, ba, npa, RM, m1 mean recirculation air, bypass air, negative pressure air, rack module, middle airflow1 respectively.
rra ¼ C ra =C RM
ð5Þ
rba ¼ C ba =C m1
ð6Þ
rnpa ¼ C npa =C m1
ð7Þ
As the cooling air flows into the racks, poor air distributions will lead to hot spots in some high-load racks. The impact of the air distribution on the rack cooling is analyzed using the actual racks layout in the data center as the parallel model shown in Fig. 2 with the cooling air distribution ratio defined as,
kn ¼ C RM;n =C RM
ð8Þ
For a given data center, the equipment heat loads, flow rates and cooling system supply air temperature are all fixed. The entransy dissipation of heat transfer process in the data center includes the rack module heat transfer entransy dissipation, the recirculation air mixing entransy dissipation, the bypass air mixing entransy dissipation and the negative pressure air mixing entransy dissipation. The heat transfer in the racks can be approximated as heat transfer in a heat exchanger. For a two-stream heat exchanger shown in Fig. 3, Liu et al. [26] formulated the entransy dissipation rate,
G/;ex ¼
1 1 1 1 C h T 2h;i þ C c T 2c;i C h T 2h;o þ C c T 2c;o 2 2 2 2
ð9Þ
The entransy dissipation rate of the heat exchanger is equal to the difference between the total entransy rates of the fluids entering and leaving the heat exchanger. In the heat transfer process of racks, one side is the heat source while the other side is the cooling air. The entransy dissipation rate in the rack module can then be expressed as,
1 G/;h ¼ ðQ 1 T h1 þ Q 2 T h2 þ þ Q n T hn Þ þ C RM T 2RM;i T 2RM;o 2
ð10Þ
where Qn is the heat load and Thn is the heat source temperature of the nth rack. CRM, TRM,i and TRM,o are the heat capacity rate, the inlet temperature and the outlet temperature for air flow through the rack module. Recirculation air mixing, bypass air mixing and negative pressure air mixing are all non-isothermal mixing processes, so their entransy dissipation rates can be expressed by the entransy dissipation of mixing processes. For the mixing process shown in Fig. 4, the entransy dissipation rate can be defined as, G/;mix ¼
1 1 1 1 C 1 T 21;i þ C 2 T 22;i þ þ C n T 2n;i ðC 1 þ C 2 þ þ C n ÞT 2mix 2 2 2 2
ð11Þ
According to Eq. (11), the entransy dissipation rate due to recirculation air mixing, bypass air mixing and negative pressure air mixing shown in Fig. 2 can be expressed as follows: The entransy dissipation rate due to recirculation air mixing,
Fig. 2. Two-dimensional model of data center heat transfer network.
Fig. 3. Schematic of heat exchanger.
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3. Data center entransy dissipation analysis
Fig. 4. Schematic of a mixing process.
G/;ra ¼
1 C m2 T 2m2 þ C ra T 2ra C RM T 2RM;i 2
ð12Þ
The entransy dissipation rate due to bypass air mixing,
G/;ba ¼
1 C m2 T 2RM;o þ C ba T 2ba C m1 T 2DC;o 2
ð13Þ
The entransy dissipation rate due to negative pressure air mixing,
G/;npa ¼
1 C DC T 2DC;i þ C npa T 2npa C m1 T 2m1 2
ð14Þ
The entransy dissipation rate for the entire data center is then the sum of the four parts,
1 G/;sys ¼ ðQ 1 T h1 þ Q 2 T h2 þ þ Q n T hn Þ C DC T 2DC;o T 2DC;i 2
ð15Þ
The total data center heat load is,
Q sys ¼ Q 1 þ Q 2 þ þ Q n
ð16Þ
Define the average heat source temperature as,
Th ¼
Q1 Q sys
T h1 þ
Q2 Q sys
T h2 þ þ
Qn T hn Q sys
ð17Þ
And also define the average cooling air temperature as,
T DC ¼
T DC;i þ T DC;o 2
ð18Þ
Then the data center entransy dissipation rate can be simplified using Eqs. (17) and (18) as,
G/;sys ¼ Q sys ðT h T DC Þ
ð19Þ
Equation (19) indicates that the entransy dissipation rate due to the data center heat transfer is equal to the product of the heat load and the temperature difference in the data center. Here, Th is the heat load weighted average temperature of the heat sources and TDC is the arithmetic average temperature of the cooling air flowing. TDC is a fixed value when the data center and cooling system are given. When the entransy dissipation rate and heat load are known, the entransy-dissipation-based thermal resistance of data center can be defined as,
Rsys ¼
G/;sys Q 2sys
¼
T h T DC Q sys
Hot and cold air mixing and poor cooling air distribution between the racks are the major problems for data center airflow organization. Among the three air mixing phenomena, recirculation air mixing and bypass air mixing are more serious and the air mixing ratios are normally more than 0.5 in data centers. Negative pressure air mixing only occurs in some data centers and the air mixing ratio is usually less than 0.1. The cooling air distribution is affected by the heat load and the air flow rate in the racks. The current data center designs do not have effective rack level cooling air distribution control, so there are problems with ineffective cooling air distributions between racks. The influence of the airflow organization problems on the data center heat transfer was analyzed using the entransy dissipation analysis method. The data center racks are divided into two groups. The heat transfer network is shown in Fig. 5 and the parameters are listed in Table 1. The air mixing analyses assumed that the cooling air flow rates in the two group racks are the same and only one of the three mixing phenomena accrues. The analysis used recirculation air mixing ratios and bypass air mixing ratios of 0–0.8 and negative pressure air mixing ratios of 0–0.2. The analytical results for the recirculation air mixing, bypass air mixing and negative pressure air mixing are shown in Figs. 6–8. The figures show that the entransy dissipation, the entransy-dissipation-based thermal resistance and the average rack module heat source temperature increase with the increased air mixing. The results in Figs. 6 and 8 show that both the data center entransy-dissipation-based thermal resistance and the average rack module heat source temperatures increase linearly with increasing recirculation air mixing ratio and negative pressure air mixing ratio. For bypass air mixing as seen in Fig. 7, the thermal resistance and the average heat source temperature grow exponentially with increasing bypass air mixing ratio. Thus, in the three air mixing phenomena, bypass air mixing has a larger influence than the others under the same air mixing ratio. The effect of the cooling air distribution on the data center heat transfer was analyzed with all the air mixing ratios set at their maximum values, while the cooling air distribution ratio in the first rack group was varied from 0.1 to 0.7. The analytical results in Fig. 9 show that with increasing cooling air distribution ratio, the entransy dissipation in the rack module, the data center thermal resistance and the average rack module heat source temperature first decrease and then increase. Thus, the cooling air distribution can be optimized by minimizing the entransy-
ð20Þ
The temperature difference between the heat source and the cooling air is the driving force. The heat transfer performance in the data center can be characterized by the entransy-dissipationbased thermal resistance. For a given data center, the heat load and the average cooling air temperature are fixed. Thus Eq. (20) shows that a smaller thermal resistance will give a lower rack module temperature and a better thermal environment in the data center.
Fig. 5. Data center heat transfer network with two group racks.
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X. Qian et al. / International Journal of Heat and Mass Transfer 62 (2013) 579–585 Table 1 Data center parameters. Cooling air (cooling system)
Racks
Return temperature TDC,o
24 °C
#1
Heat capacity rate CDC
3700 W/K
#2
Thermal conductance Kh1 Heat load Q1 Thermal conductance Kh2 Heat load Q2
480 W/K 10 kW 720 W/K 20 kW
Fig. 6. Normalized G/,ra, Th, Rsys for various recirculation air mixing ratios.
Fig. 8. Normalized G/,npa, Th, Rsys for various negative pressure air mixing ratios.
Fig. 7. Normalized G/,ba, Th, Rsys for various bypass air mixing ratios.
Fig. 9. Normalized G/,h, Th, Rsys for various cooling air distribution ratios.
dissipation-based thermal resistance to give the lowest average rack module heat source temperature. These results show that how the entransy dissipation analysis method can be used to analyze the heat transfer of the data center cooling system. A smaller entransy-dissipation-based thermal resistance will improve the data center thermal environment, i.e., the minimum thermal resistance principle can be used to optimize the data center heat transfer.
Table 2 Working conditions of data center. Operating condition
Description
Thermal resistance
Original No mixing Optimal
Actual operating condition in the data center No air mixing happened in the data center No air mixing + optimal air distribution
Rsys Rnm Ropt
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Table 3 Data center airflow parameters. Negative pressure air mixing ratio
Bypass air mixing ratio
Recirculation air mixing ratio
Cooling air distribution ratio of the first rack group
rNPa = 0.03
rBa = 0.61
rRa = 0.51
k1 = 0.5
ADI can be used to evaluate the effects of ineffective cooling air distribution on data center cooling system. A larger ADI corresponds to a better cooling air distribution. When the cooling air distribution between racks is optimal, Rnm = Ropt and ADI = 1. The integrated heat transfer index (IHTI) is defined as the thermal resistance ratio of the optimal condition to the original condition.
IHTI ¼ ð1 AMIÞ ADI ¼
Ropt Rsys
ð23Þ
IHTI can be used to assess the data center heat transfer efficiency relative to the optimal condition. The IHTI actually indicates the potential for improvement of the data center airflow organization. Since IHTI is equal to the product of 1-AMI and ADI, a smaller AMI and a larger ADI result in a larger IHTI, and therefore, a better thermal environment in the data center. When the data center integrated heat transfer index equals to 1, the thermal resistance reaches the minimum value and the thermal environment is close to optimal condition.
Fig. 10. Entransy dissipation ratio in a data center.
4. Evaluation of data center airflow organization
4.2. Case study
4.1. Evaluation indexes based on the thermal resistance
The entransy dissipation analysis method and the evaluation indexes were used to analyze the thermal environment of a data center. For a given data center, the heat loads and cooling system parameters are fixed. The air mixing ratio and the cooling air distribution ratio can be obtained by testing or CFD simulations. The data center cooling system conditions for the case studied here are given in Fig. 5 and Tables 1 and 3. The air mixing ratios were taken from the results given by Tozer et al. [15] with a cooling air distribution ratio of 0.5. The entransy dissipations for the three kinds of air mixings and the heat transfer in racks were calculated for the parameters listed in Table 3. As seen in Fig. 10 and 698% of the data center heat transfer entransy dissipation is due to the racks heat transfer with the three kinds of air mixing contributing 30.2%. The entransy dissipation due to the bypass air mixing is the largest of the three kinds of air mixing phenomena with the negative pressure air mixing the smallest. The thermal resistances and heat source temperatures for the original, no mixing and optimal operating conditions are listed in Table 4. For this case, AMI is 0.307, ADI is 0.981 and IHTI is 0.679. The evaluation indexes show that the air mixing is quite serious in this data center and the improvement of air mixing is more helpful to the data center heat transfer. If the air mixing is eliminated, the thermal resistance of the data center will be significantly reduced, the cooling temperature difference will be decreased by 11.64 °C, and the data center thermal environment will be greatly improved. Furthermore, by comparing the entransy dissipations of the three air mixing phenomena, it is found that the bypass air mixing
The aim of the thermal environment analysis is to understand the airflow organization and the heat transfer of the data center. The entransy dissipation analysis is used to evaluate the influences of the air mixing and cooling air distribution on the data center cooling system. The data center entransy-dissipation-based thermal resistance can be minimized by optimizing the airflow organization. In the following, three evaluation indexes are presented based on a system with no air mixing, a system with no air mixing and the optimal cooling air distribution between racks, and the original working condition as listed in Table 2. The air mixing index (AMI) is defined as.
AMI ¼
Rsys Rnm Rsys
ð21Þ
where the numerator is the thermal resistance difference between the original condition and the no mixing condition, and the denominator is the thermal resistance of original condition. AMI can be used to evaluate the effects of air mixing on the data center cooling system. A larger AMI means that the air mixing phenomena are more serious and have stronger effects on data center cooling system. When the data center is working in no mixing condition, Rsys = Rnm and AMI = 0. The air distribution index (ADI) is defined as the thermal resistance ratio of the optimal condition to the no mixing condition.
ADI ¼
Ropt Rnm
ð22Þ
Table 4 Thermal resistances and heat source temperatures for different operating conditions.
Original No mixing Optimal
rNPa
rBa
rRa
k1
Rsys K/W
DT °C
Th1 °C
Th2 °C
0.03 0 0
0.61 0 0
0.51 0 0
0.5 0.5 0.335
1.261 103 0.873 103 0.856 103
37.83 26.19 25.68
50.72 39.54 41.02
61.30 49.42 47.93
X. Qian et al. / International Journal of Heat and Mass Transfer 62 (2013) 579–585
should be first improved due to its largest impact on data center heat transfer. Optimization of the cooling air distribution will also improve the data center cooling system heat transfer. Although the optimization potential of this case is small, the uniformity of the rack module temperature can be improved by optimizing the air distribution. 5. Concluding remarks The entransy dissipation analysis method has been presented to analyze the thermal environment of the data center. The entransy dissipation analyses of the air mixings and the cooling air distribution showed that the minimum thermal resistance principle is applicable to data center heat transfer optimization. Based on the entransy dissipation analysis of the data center thermal environment, the air mixing index (AMI), the air distribution index (ADI) and the integrated heat transfer index (IHTI) are defined by using the thermal resistances of the original, no mixing and optimal operating conditions. AMI and ADI reflect the effects of air mixing and the cooling air distribution on the data center heat transfer, while IHTI is an integrated parameter to evaluate the data center heat transfer conditions. A sample data center was analyzed with the results indicating that the evaluation indexes accurately reflect the data center thermal environment, where the bypass air mixing has the largest impact on data center heat transfer. This method can guide optimization to the airflow organization in data centers. Acknowledgements This work was financially supported by the National Natural Science Foundation of China (51138005) and the National Basic Research Program of China (2013CB228301). References [1] J.G. Koomey, Estimating total power consumption by servers in the US and the World, Technical report, Lawrence Berkeley National Laboratory, 2007. [2] S. Greenberg, E. Mills, B. Tschudi, Best practices for data centers: results from benchmarking 22 data center, ACEEE Summer Study Energy Effic. Buildings 3 (2006) 76–87. [3] A. Shah, C. Patel, C. Bash, R. Sharma, R. Shih, Impact of rack-level compaction on the data center cooling ensemble, in: 11th Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems, 2008), pp. 1175–1182. [4] V. Sorell, S. Escalante, J. Yang, Comparison of overhead and underfloor air delivery systems in a data center environment using CFD modeling, ASHRAE Trans. 111 (2) (2005) 756–764. [5] R.R. Schmidt, M. Iyengar, Comparison between underfloor supply and overhead supply ventilation designs for data center high-density clusters, ASHRAE Trans. 113 (1) (2007) 115–125. [6] R.R. Schmidt, M. Iyengar, Best practices for data center thermal and energy management – review of literature, ASHRAE Trans. 113 (1) (2007) 206–218. [7] R.F. Sullivan, Alternating cold and hot aisles provides more reliable cooling for server farms, White Paper by the Uptime Institute, Santa Fe, NM, 2003. [8] S.V. Patankar, Airflow and cooling in a data center, J. Heat Transfer 132 (7) (2010) 1–17. [9] R.F. Sullivan, K.G. Brill, L. Strong, Reducing bypass airflow is essential for reducing computer room hot spots, White Paper by the Uptime Institute, Santa Fe, NM, 2004.
585
[10] R.F. Sullivan, Some worst case practices in data centers, ASHRAE Trans. 114 (1) (2008) 3–7. [11] R.R. Sharma, C.E. Bash, C.D. Patel, Dimensionless parameters for evaluation of thermal design and performance of large-scale data centers, in: Proceeding of the Eighth ASME/AIAA Joint Thermophysics and Heat Transfer Conference, St Louis, MO, 2002. [12] M.K. Herrlin, Rack cooling effectiveness in data center and telecom central offices: the rack cooling index (RCI), ASHRAE Trans. 111 (2) (2005) 1–11. [13] M.K. Herrlin, Improved data center energy efficiency and thermal performance by advanced airflow analysis, in: Digital Power Forum, San Francisco, CA, 2007. [14] J.W. VanGilder, S.K. Shrivastava, Capture index: an airflow-based rack cooling performance metric, ASHRAE Trans. 113 (1) (2007) 126–136. [15] R. Tozer, C. Kurkjian, M. Salim, Air management metrics in data centers, ASHRAE Trans. 115 (1) (2009) 63–70. [16] A.J. Shah, V.P. Carey, C.E. Bash, C.D. Patel, Exergy analysis of data center thermal management systems, J. Heat Transfer 130 (2) (2008) 021401– 021410. [17] A.J. Shah, V.P. Carey, C.E. Bash and C.D. Patel, Exergy-based optimization strategies for multi-component data center thermal management: part I, analysis, in: Proceedings of International Electronic Packaging Technical Conference and Exhibition (IPACK2005-73137), San Francisco, CA, 2005. [18] A.J. Shah, V.P. Carey, C.E. Bash and C.D. Patel, Exergy-based optimization strategies for multi-component data center thermal management: part II, Application and validation, in: Proceeding of International Electronic Packaging Technical Conference and Exhibition (IPACK2005-73138), San Francisco, CA, 2005. [19] R.K. Shah, T. Skiepko, Entropy generation extrema and their relationship with heat exchanger effectiveness – number of transfer unit behavior for complex flow arrangements, J. Heat Transfer 126 (6) (2004) 994–1002. [20] Z.Y. Guo, H.Y. Zhu, X.G. Liang, Entransy-a physical quantity describing heat transfer ability, Int. J. Heat Mass Transfer 50 (13–14) (2007) 2545–2556. [21] Z.Y. Guo, X.G. Cheng, Z.Z. Xia, Least dissipation principle of heat transport potential capacity and its application in heat conduction optimization, Chin. Sci. Bull. 48 (4) (2003) 406–410. [22] H.Y. Zhu, The minimum thermal resistance principle based on entransy dissipation. Ph.D. thesis, Tsinghua University, Beijing, 2007. [23] J. Wu, X.G. Cheng, J.A. Meng, Potential capacity dissipation extremum and entropy generation minimization in laminar convective heat transfer, J. Eng. Thermophys. 27 (1) (2006) 100–102. [24] Q. Chen, J.X. Ren, Generalized thermal resistance for convective heat transfer and its relation to entransy dissipation, Chin. Sci. Bull. 53 (23) (2008) 3753– 3761. [25] J. Wu, X.G. Liang, Application of entransy dissipation extremum principle in radiative heat transfer optimization, Sci. Chin. Technol. Sci. 51 (8) (2008) 1306–1314. [26] X.T. Cheng, X.G. Liang, Entransy flux of thermal radiation and its application to enclosures with opaque surfaces, Int. J. Heat Mass Transfer 54 (1–3) (2011) 269–278. [27] Z.H. Xie, L.G. Chen, F.R. Sun, Constructal optimization on T-shaped cavity based on entransy dissipation minimization, Chin. Sci. Bull. 54 (23) (2009) 4418– 4427. [28] S.H. Wei, L.G. Chen, F.R. Sun, Constructal optimization of discrete and continuous-variable cross-section conducting path based on entransy dissipation rate minimization, Sci. Chin. Technol. Sci. 53 (6) (2010) 1666–1677. [29] Q.H. Xiao, L.G. Chen, F.R. Sun, Constructal entransy dissipation rate and flowresistance minimizations for cooling channels, Sci. Chin. Technol. Sci. 53 (9) (2010) 2458–2468. [30] X.B. Liu, J.A. Meng, Z.Y. Guo, Entropy generation extremum and entransy dissipation extremum for heat exchanger optimization, Chin. Sci. Bull. 54 (6) (2009) 943–947. [31] J.F. Guo, L. Cheng, M.T. Xu, Entransy dissipation number and its application to heat exchanger performance evaluation, Chin. Sci. Bull. 54 (15) (2009) 2708– 2713. [32] J.F. Guo, M.T. Xu, L. Cheng, Principle of equipartition of entransy dissipation for heat exchanger design, Sci. Chin. Technol. Sci. 53 (5) (2010) 1309–1314. [33] X.D. Qian, Z.X. Li, Analysis of entransy dissipation in heat exchangers, Int. J. Therm. Sci. 50 (4) (2011) 608–614. [34] X.D. Qian, Z. Li, Z.X. Li, Entransy-dissipation- based thermal resistance analysis of heat exchanger networks, Chin. Sci. Bull. 56 (31) (2011) 3289–3295. [35] X.T. Cheng, X.H. Xu, X.G. Liang, Application of entransy to optimization design of parallel thermal network of thermal control system in spacecraft, Sci. Chin. Technol. Sci. 54 (4) (2011) 964–971.