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Entransy and exergy analyses of airflow organization in data centers
International Journal of Heat and Mass Transfer 81 (2015) 252–259
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Entransy and exergy analyses of airflow organization in data centers Xiaodong Qian, Zhen Li, Zhixin Li ⇑ Key Laboratory of Thermal Science and Power Engineering of Ministry of Education, School of Aerospace Engineering, Tsinghua University, Beijing 100084, China
a r t i c l e
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Article history: Received 8 July 2013 Received in revised form 6 March 2014 Accepted 29 September 2014
Keywords: Data center Airflow organization Entransy analysis Exergy analysis
a b s t r a c t The cooling system plays an important role in high-efficiency energy utilization for data centers and airflow improvement is one of the most effective ways to reduce cooling system energy consumption. In this paper, the applicability of entransy analysis method is studied and compared with the exergy analysis method. The results show that the minimum entransy-dissipation-based thermal resistance for the heat transfer between the cooling air and the racks always corresponds to the optimal system parameters for the data center cooling system, but the exergy analysis method is not always effective. Therefore, the entransy-dissipation-based thermal resistance is more suitable as the object parameter to optimize the airflow organization in a data center. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Data centers are service platforms for data processing, storage, transmission and exchange. These data centers are densely equipped with IT equipments and consume large amounts of energy. In recent years, the development of the global information industry has greatly increased demands for large data centers and their energy consumption has grown rapidly. Statistics indicate that the global energy consumption of data centers doubles every 5 years [1], so energy savings in data centers are becoming more and more important. The main equipment in data centers are the IT systems, the cooling systems, the UPS and other auxiliary equipments. For the same energy consumption, a larger ratio of the IT equipment energy use to the total energy consumption is referred to as higher data center energy use efficiency. At present, the energy consumption by the data center cooling system usually accounts for more than 30% of the total energy consumption, and is even larger than the energy use of the IT systems in some data centers, though for some cutting-edge facilities, this percentage is less than 10% [2–4]. Therefore, the cooling system energy efficiency needs to be improved. Optimization of the airflow can efficiently enhance the cooling efficiency and reduce the cooling system energy consumption. The high density arrangements of the IT equipments leads to very complex airflows and heat transfer processes in data centers. In recent years, many studies have been conducted on how to improve the airflow [5–12]. Nevertheless, more airflow problems ⇑ Corresponding author. Tel./fax: +86 10 62772919. E-mail address: [email protected] (Z. Li). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.09.078 0017-9310/Ó 2014 Elsevier Ltd. All rights reserved.
still need to be solved. For example, air mixing will raise the cooling air temperature and reduce the cooling efficiency. Moreover, unreasonable distributions of the cold airflow will result in hot spots in the data center. Thus, analysis methods are needed to further improve the airflow organization. Existing airflow analysis and evaluation methods can be categorized as empirical and second law based methods. The empirical methods usually use system parameters such as temperature to as evaluation indexes. For instance, the Supply Heat Index (SHI) and the Return Heat Index (RHI) given by Sharma [13] and the Rack Cooling Index (RCI) and Return Temperature Index (RTI) by Herrlin [14,15]. These empirical analysis and evaluation methods reflect the airflow conditions to some degree, but the empirical indexes generally just reflect one or two aspects of the air mixing problems at one position, e.g., SHI and RHI are mainly concerned with the airflow at the rack level and cannot accurately describe the airflow problems. For example, RTI only gives the relative strength of the bypass airflow and the recirculation airflow rather than the absolute value. Thus, the empirical indexes cannot give enough information about the cooling energy efficiency to effectively evaluate the system. Hence, they cannot be effectively used to optimizing the data center airflow. In view of the deficiencies of the empirical methods, approaches based on the Second Law of Thermodynamics have been introduced to analyze data center airflows. Exergy analyses are widely used to analyze thermodynamic processes. For data center cooling systems, Shah et al. [16–20] related exergy losses to the air-conditioning unit parameters. The optimal parameters could be obtained by minimizing the cooling system exergy loss. The entransy analysis method proposed by Guo [21] can be also used to analyze and optimize heat
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253
Nomenclature C Ex
UG H I i K kn q Q R r S T T0
heat capacity rate, W K1 exergy, W entransy dissipation, W K enthalpy, W exergy loss, W exergy loss per unit cooling capacity thermal conductance, W K1 air distribution ratio for the nth rack group heat flux, W m2 heat transfer rate, W entransy-dissipation-based thermal resistance, K W1 air mixing ratio entropy, W K1 temperature, °C or K the reference temperature
DC ex h i max mix m1 m2 Npa o Ra RM sys tot
data center heat exchanger heat source, hot flow inlet maximum mixing middle airflow 1 middle airflow 2 negative pressure air outlet recirculation air rack module system total
Subscripts Ba bypass air c cold flow
transfer processes. Entransy, is a new physical quantity, which represents the heat transfer ability of an object in heat transfer process. It is defined as the product of 0.5T and Q. Where Q is the internal thermal energy stored in an object and T is the object’s absolute temperature. During an irreversible heat transfer process, the thermal energy is conserved, but the entransy will be partially dissipated. This method also follows the Second Law and has been successfully used in analyses of heat conduction [22,23], heat convection [24,25], heat exchangers and heat exchanger networks [26–29]. Qian et al. [30] related the rack heat source temperatures to the entransy-dissipation-based thermal resistance and defined three indexes to evaluate data center thermal environment. The purpose of improving the data center airflow is to reduce the cooling system energy consumption and to optimize the data center thermal environment by changing the system parameters. This paper relates the cooling system parameters to the entransy-dissipation-based thermal resistance or the exergy loss per unit cooling capacity and to demonstrate the applicability of the entransy and exergy analysis methods.
The air mixing phenomena, recirculation air mixing ratio, bypass air mixing ratio and negative pressure air mixing ratio are given by Tozer et al. [31],
rRa ¼ C Ra =C RM
ð1Þ
rBa ¼ C Ba =C m1
ð2Þ
rNPa ¼ C NPa =C m1
ð3Þ
where C is the heat capacity rate and subscript, Ra refers to the recirculation air, Ba refers to the bypass air, NPa refers to the negative pressure air, RM refers to the rack module and m1 refers to middle airflow 1. All the three air mixing ratios vary from 0 to 1. Inappropriate cooling air distributions result in hot spots in locally high-load racks. The influence of the cooling air distribution is analyzed by abstracting the rack layout into the parallel model shown in Fig. 2 with the cooling air distribution ratio defined as [30],
kn ¼ C RM;n =C RM
ð4Þ
2.2. Impacts of air mixing and the cooling air distribution 2. Relationship between the airflow and the system parameters 2.1. Analysis model Fig. 1 shows the airflow pattern in a typical data center. The cooling air is blown from the air conditioning units into the cold aisles through the floor plenum, flows through the racks to remove heat from the rack heat sources, and then flows back to the air conditioning units. This airflow path includes significant air mixing and air distribution problems. Air mixing in data centers can be divided into recirculation air mixing, bypass air mixing and negative pressure air mixing. As seen in Fig. 1, recirculation air mixing occurs when the heated air flows back into the racks and mixes with the cooling air, bypass air mixing occurs when the cooling air flows straight back to the air-conditioning units and does not cool the heat sources, while the negative pressure air mixing occurs when the hot air is sucked back into the floor plenum and mixes with the cooling air. The airflow model given by Tozer et al. [31] simplifies the airflow and heat transfer processes in the data center into a two-dimensional heat transfer network as shown in Fig. 2.
The four system operating parameters in the data center cooling system are the rack heat source temperature, Th, the data center heat load, Qsys, the cooling air temperature, TDC,in, and the cooling air heat capacity rate, CDC. The rack heat source temperature describes the thermal environment while the other system parameters reflect the energy usage of the data center cooling system. To study the influences of the airflow organization on these four system parameters, four schemes listed in Table 1 are arranged. The heat load and heat source temperature are both fixed in schemes 3 and 4, so the effects of the air mixing can only be analyzed for the condition that all the racks are the same. As seen in Fig. 3, the racks in each rack module are assumed to be the same when discussing the air mixing effects. The analyses of each scheme in Table 1 are based on the base case system parameters listed in Table 2. During the analyses, the system parameters are varied by separately varying the recirculation air mixing ratio, bypass air mixing ratio and negative pressure air mixing ratio. In general, the recirculation air mixing and bypass air mixing are more serious in data centers, so their variations were both set as 0–0.6, while the variation of the negative pressure air mixing ratio was set as 0–0.2 because it has a relatively weak effect.
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Fig. 1. Schematic of the airflow in a typical data center.
Fig. 2. Two-dimensional data center heat transfer network model.
Table 1 Analysis schemes. Schemes
Variable parameter
Fixed parameters
1 2 3 4
Th Qsys TDC,in CDC
TDC,in TDC,in Th Th
The impacts of the recirculation air mixing, bypass air mixing and negative pressure air mixing on the system parameters are shown in Figs. 4–6. For scheme 1, the rack heat source temperature is increased as the temperature and heat capacity rate of the cooling air and the heat load are held constant. For scheme 2, the data center heat load is reduced as the temperature and heat capacity rate of the cooling air and the heat source temperature are held constant. For scheme 3, the cooling air temperature is reduced as the cooling air heat capacity rate, the heat source temperature and the heat load are held constant. For scheme 4, the cooling air heat capacity rate is increased while the cooling air temperature,
Airflow problems CDC CDC CDC TDC,in
Qsys Th Qsys Qsys
Air Air Air Air
mixing, air distribution mixing, air distribution mixing mixing
heat source temperature and heat load remain unchanged. It is seen that the system parameters vary linearly with the recirculation air mixing ratio and negative pressure air ratio (Figs. 4 and 6), and vary exponentially with the bypass air mixing ratio (Fig. 5). Thus, for the same air mixing ratio, the bypass air mixing has a larger impact on the system parameters than the others. The influence of the cooling air distribution is analyzed using the simplified model shown in Fig. 7 with two groups of racks. The analyses use the schemes in Table 1 with the analysis parameters selected from Table 3. In schemes 3 and 4, the heat source temperature and heat load are fixed, so there is no air distribution problem.
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Fig. 3. Air mixing analysis model.
Table 2 Analysis parameters for air mixing analysis. Cooling system
Rack module
Cooling air temperature TDC,in (°C) Cooling air heat capacity rate CDC (W K
18 1
)
4000
Thermal conductance KAh (W K1) Heat load Q (kW) Heat source temperature Th (°C)
1500 30 42
Fig. 4. System parameter variations with the recirculation air mixing ratio.
Fig. 5. System parameter variations with the bypass air mixing ratio.
The effect of the cooling air distribution on the system parameters was analyzed with all the air mixing ratios set to zero while the cooling air distribution ratio in the first group of racks is varied from 0.1 to 0.7. For scheme 1, the heat source temperature is defined as the arithmetic mean temperature of the racks. The results shown in Fig. 8 indicate that the heat source temperature first decreases and then increases with increasing cooling air distribution ratio, with a minimum at k1 = 0.42, where k1 represents the ratio of the cooling airflow rate into the first group of racks to the total flow rate. For scheme 2, as the cooling air distribution ratio increases, the heat load first increases and then decreases, with a maximum at k1 = 0.52, as is shown in Fig. 9. Thus, the thermal process can be optimized by optimizing the cooling air distribution ratio.
These analysis results for the impacts of the air mixing and cooling air distributions on the system parameters show that the cooling system thermal and energy consumption performance can be improved by improving the airflow organization. The heat source temperature can be reduced and the thermal environment can be improved for the same energy consumption in scheme 1, while the energy consumption per unit cooling capacity can be reduced in schemes 2 and 3 because the evaporation temperature is increased by the increased heat load and cooling air temperature, which improves the cooling efficiency. For scheme 4, the reduced cooling air heat capacity, which is a reduced cooling airflow rate, not only raises the evaporation temperature but also reduces the energy used to driving the
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Fig. 6. System parameter variations with the negative pressure air mixing ratio.
air flow, both of which lower the energy consumption per unit cooling capacity. 3. Entransy and exergy analyses 3.1. Entransy-dissipation-based thermal resistance The evaluation indexes used in the empirical methods are related to only one or two system parameters, which is usually a limitation when they are used to analyze the airflow in a data
Fig. 8. Heat source temperature variations with the cooling air distribution ratio (scheme 1).
center. Thus, more comprehensive methods which include all the four system parameters are needed. Entransy analyses have been successfully used to analyze many heat transfer processes and thermal devices. In general, the rack heat sources temperatures are different, so the data center heat transfer problem is similar to a multi-stream heat transfer network. The traditional entransy analysis method is reasonable for analyzing two-stream heat transfer processes but not suitable for multi-stream heat transfer network. Qian [32] extended the method to multi-stream heat transfer processes by including virtual distribution and mixing at inlets and outlets. This entransy
Fig. 7. Analysis model for the cooling air distribution effect.
Table 3 Analysis parameters for the cooling air distribution analysis. Cooling system Cooling air temperature TDC,in (°C)
Cooling air heat capacity flow rate CDC (W K1)
Rack module 18
4000
Thermal conductance 1 KAh1 (W K1) Heat load 1 Q1 (kW) Heat source temperature 1 Th1 (°C) Thermal conductance 2 KAh2 (W K1) Heat load 2 Q2 (kW) Heat source temperature 2 Th2 (°C)
900 10 30 600 20 40
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The arithmetic average temperature of the rack heat sources is,
Th ¼
T h1 þ T h2 þ þ T hn n
ð12Þ
The arithmetic average temperature of the cooling air is,
T DC ¼
T DC;in þ T DC;out 2
ð13Þ
Then, Eq. (10) can be simplified as,
UG;sys ¼ Q sys ðT h T DC Þ
ð14Þ
Eq. (14) shows that the entransy dissipation of the data center heat transfer network is the product of the heat load and the average temperature difference between the rack heat source and the cooling air. Then, the entransy-dissipation-based thermal resistance can be written as,
Rsys ¼ Fig. 9. Heat load variations with the cooling air distribution ratio (scheme 2).
analysis method is used here to analyze the airflow organization in a data center. The entransy dissipation of the airflow heat transfer processes in a data center includes five parts. The first is caused by unequal rack heat source temperatures; the second is due to the heat transfer between the airflow and the rack module, while the others are due to the three kinds of air mixing. The entransy analysis method for multi-stream heat transfer problems first simplifies the problem to an equivalent two-stream heat transfer process with the additional entransy dissipation resulting from the unequal heat source temperatures written as:
T h1 þ T h2 þ þ T hn n
UG;v ¼ ðQ 1 þ Q 2 þ þ Q n Þ
ð5Þ
where Qn is the heat transfer rate and Thn is the temperature of the nth heat source. The entransy dissipation due to the heat transfer between the airflow and the rack module can be expressed:
1 2
ð6Þ
where CRM is the heat capacity rate of the air flowing through the rack module and TRM,in and TRM,out are the air temperatures flowing into and out of the rack module. The entransy dissipation rates due to the recirculation air mixing, bypass air mixing and negative pressure air mixing are:
1 C m2 T 2m2 þ C Ra T 2Ra C RM T 2RM;in 2 1 UG;Ba ¼ C m2 T 2RM;out þ C Ba T 2Ba C m1 T 2DC;out 2 1 UG;NPa ¼ C DC T 2DC;in þ C NPa T 2NPa C m1 T 2m1 2
UG;Ra ¼
ð7Þ ð8Þ ð9Þ
The five parts are summed to give the total entransy dissipation in the data center airflow heat transfer processes:
UG;sys
T h1 þ T h2 þ þ T hn ¼ ðQ 1 þ Q 2 þ þ Q n Þ n 1 C DC T 2DC;out T 2DC;in 2
Q 2sys
¼
T h T DC Q sys
ð15Þ
Eq. (15) shows that the temperature difference between the heat source and the cooling air is the heat transfer driving force and the thermal performance of the data center cooling system can be characterized by the entransy-dissipation-based thermal resistance. Using the inlet temperature to replace the average cooling air temperature, Eq. (15) can be expressed as,
Rsys ¼
T h T DC;in 1 C DC Q sys
ð16Þ
Thus, the entransy-dissipation-based thermal resistance is a function of the four system parameters and the entransydissipation-based thermal resistance can be used to evaluate the airflow organization. 3.2. Exergy loss
ðQ 1 T h1 þ Q 2 T h2 þ þ Q n T hn Þ
UG;h ¼ ðQ 1 T h1 þ Q 2 T h2 þ þ Q n T hn Þ þ C RM T 2RM;in T 2RM;out
UG;sys
The exergy analysis method has been widely used to analyze various thermodynamic processes. Based on the research of Shah et al.’s [16–20], the exergy losses of heat transfer processes in data centers include the exergy losses due to the heat transfer between the airflow and the rack modules and the exergy losses resulting from the three air mixing processes. The exergy loss due to the airflow from state 1–2 without work is:
Ex;1 Ex;2 ¼ H1 H2 T 0 ðS1 S2 Þ
ð17Þ
where H is the enthalpy, S is the entropy and T0 is the reference temperature (environment temperature). The exergy loss due to the heat transfer, Q, for a constant temperature heat source is,
T0 Q Ix;Q ¼ 1 T
ð18Þ
Combining Eqs. (17) and (18) gives the exergy loss for the heat transfer between the airflow and the rack modules as:
T0 T0 T0 T RM;out þ T 0 C RM ln Ih ¼ Q 1 þ Q2 þ þ Qn T h1 T h2 T hn T RM;in
ð19Þ
The exergy loss due to the recirculation air mixing is,
ð10Þ
IRa ¼ T 0 C m2 ln
T RM;in T RM;in þ T 0 C Ra ln T m2 T Ra
where CDC is the heat capacity rate of the airflow through data center and TDC,in and TDC,out are the air temperatures flowing into and out of the data center. The total data center heat load is then:
The exergy loss due to the bypass air mixing is,
Q sys ¼ Q 1 þ Q 2 þ þ Q n
IBa ¼ T 0 C m2 ln
ð11Þ
T DC;out T DC;out þ T 0 C Ba ln T RM;out T Ba
ð20Þ
ð21Þ
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The exergy loss due to the negative pressure air mixing is,
INPa ¼ T 0 C DC ln
T m1 T m1 þ T 0 C NPa ln T DC;in T NPa
ð22Þ
The total exergy loss for all of the heat transfer processes is the sum of the four parts,
T0 T0 T0 T DC;out þ T 0 C DC ln Isys ¼ Q 1 þ Q2 þ þ Qn T h1 T h2 T hn T DC;in
ð23Þ
When the heat load or the cooling capacity is not fixed, the exergy loss per unit cooling capacity is usually used to evaluate the airflow organization as:
isys ¼
Isys Q sys
ð24Þ
Similar to the entransy-dissipation-based thermal resistance, exergy loss per unit cooling capacity is also a function of the four system parameters, but the relationship between them are not as clear as for the entransy-dissipation-based thermal resistance.
Fig. 10. Variations of Th, Rsys and isys with the cooling air distribution ratio (scheme 1).
3.3. Analyses by entransy and exergy analysis methods The expressions for the entransy-dissipation-based thermal resistance and the exergy loss per unit cooling capacity for the data center airflow heat transfer processes are used to evaluate the data center airflow organization. The relationships between the two evaluation indexes and the system parameters are studied here for the four analysis schemes to demonstrate the applicability of the two analysis methods. To improve the air mixing, the system parameters were varied with the changes in the entransy-dissipation-based thermal resistance and exergy loss per unit cooling capacity calculated by Eqs. (16) and (24). The results in Table 4 show that without the air mixing, the entransy-dissipation-based thermal resistance and exergy loss per unit cooling capacity both decrease for the system parameter variations for all the four schemes. Correspondingly, the energy use also decreases and the data center thermal environment is improved. The variations of the two evaluation indexes (the entransydissipation-based thermal resistance and the exergy loss per unit cooling capacity) with the cooling air distribution ratio are shown in Figs. 10 and 11. As seen in Fig. 10, when the cooling air distribution ratio in the first rack group increases from 0.1 to 0.7, the rack heat source temperature, the entransy-dissipation-based thermal resistance and the exergy loss per unit cooling capacity all initially decrease and then increase. The minimum rack heat source temperature and the minimum entransy-dissipation-based thermal resistance occur at k1 = 0.42. The minimum exergy loss per unit cooling capacity occurs at k1 = 0.48. The results in Fig. 11 show that with increasing cooling air distribution ratio, the allowed data center heat load first increases and then decreases, and the entransy-dissipation-based thermal resistance also first decreases and then increases. Both have their extremes at k1 = 0.52. However, the exergy loss per unit cooling capacity decreases continuously within the given air distribution ratio range. These case studies indicate that the minimum exergy loss per unit cooling capacity
Fig. 11. Variations of Qsys, Rsys and isys with the cooling air distribution ratio (scheme 2).
does not correspond to the largest heat load. In fact, what we discussed is a pure heat transfer problem, where heat-work conversion is not included. Entransy represents the heat transfer ability of a body, entransy analysis is more suitable for analyzing heat transfer problem than exergy method. In addition, the heat transfer between cooling air and racks is similar to a multi-stream heat transfer network due to the different rack temperatures, the additional entransy dissipation resulting from the unequal heat source temperatures should be considered in the entransy analysis. If heat-work conversion exists, for example in a thermodynamic process the exergy analysis will be better. Thus, the entransydissipation-based thermal resistance is more suitable for evaluating the effect of the cooling air distribution on the system parameters.
Table 4 Rsys and isys vary with eliminating air mixing. Airflow organization
Schemes
System parameters
Energy use and thermal environment
Rsys
isys
Eliminate air mixing
1 2 3 4
Th; Qsys" TDC,in" CDC;
Better thermal environment Energy use decreases Energy use decreases Energy use decreases
; ; ; ;
; ; ; ;
X. Qian et al. / International Journal of Heat and Mass Transfer 81 (2015) 252–259
4. Concluding remarks The airflow organization plays an important role in reducing the energy consumption and improving the thermal environment of data centers. The airflow heat transfer was modeled as a multi-stream heat transfer network to relate the entransy-dissipation-based thermal resistance for the airflow heat transfer to the data center system parameters. The airflow was then analyzed based on the entransy and exergy analyses. For air mixing analyzing, the smaller of the entransy-dissipation-based thermal resistance or the exergy loss per unit cooling capacity can both reflect the better energy using and thermal environment of data centers. In cooling air distribution analyses, a lower entransy-dissipation-based thermal resistance can improves the thermal environment and the energy conservation in data centers. However, the minimum exergy loss per unit cooling capacity does not correspond to the optimal system parameters. Therefore, entransy analysis method is more applicable then exergy analysis method in the analysis and optimization of data center airflow organization. Conflict of interest None declared. Acknowledgements This work was financially supported by the National Key Basic Research Program of China (2013CB228301) and the National Natural Science Foundation of China (51138005). 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] TC 9.9 Committee, Datacom Equipment Power Trends and Cooling Applications, Atlanta: ASHRAE, 2005. [3] 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. [4] C. Belady, In the data center, power and cooling costs more than the IT equipment it supports, Electronics Cooling, February 2007. [5] 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. [6] M. Iyengar, R.R. Schmidt, A. Sharma, et al., Thermal characterization of nonraised floor air cooled data centers using numerical modeling, in: International Electronic Packaging Technical Conference and Exhibition, San Francisco, CA, 2005. [7] 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. [8] R.F. Sullivan, Alternating cold and hot aisles provides more reliable cooling for sever farms, a White Paper From the Uptime Institute, Incorporated, Santa Fe, New Mexico, 2002.
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Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Entransy and exergy analyses of airflow organization in data centers Xiaodong Qian, Zhen Li, Zhixin Li ⇑ Key Laboratory of Thermal Science and Power Engineering of Ministry of Education, School of Aerospace Engineering, Tsinghua University, Beijing 100084, China
a r t i c l e
i n f o
Article history: Received 8 July 2013 Received in revised form 6 March 2014 Accepted 29 September 2014
Keywords: Data center Airflow organization Entransy analysis Exergy analysis
a b s t r a c t The cooling system plays an important role in high-efficiency energy utilization for data centers and airflow improvement is one of the most effective ways to reduce cooling system energy consumption. In this paper, the applicability of entransy analysis method is studied and compared with the exergy analysis method. The results show that the minimum entransy-dissipation-based thermal resistance for the heat transfer between the cooling air and the racks always corresponds to the optimal system parameters for the data center cooling system, but the exergy analysis method is not always effective. Therefore, the entransy-dissipation-based thermal resistance is more suitable as the object parameter to optimize the airflow organization in a data center. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Data centers are service platforms for data processing, storage, transmission and exchange. These data centers are densely equipped with IT equipments and consume large amounts of energy. In recent years, the development of the global information industry has greatly increased demands for large data centers and their energy consumption has grown rapidly. Statistics indicate that the global energy consumption of data centers doubles every 5 years [1], so energy savings in data centers are becoming more and more important. The main equipment in data centers are the IT systems, the cooling systems, the UPS and other auxiliary equipments. For the same energy consumption, a larger ratio of the IT equipment energy use to the total energy consumption is referred to as higher data center energy use efficiency. At present, the energy consumption by the data center cooling system usually accounts for more than 30% of the total energy consumption, and is even larger than the energy use of the IT systems in some data centers, though for some cutting-edge facilities, this percentage is less than 10% [2–4]. Therefore, the cooling system energy efficiency needs to be improved. Optimization of the airflow can efficiently enhance the cooling efficiency and reduce the cooling system energy consumption. The high density arrangements of the IT equipments leads to very complex airflows and heat transfer processes in data centers. In recent years, many studies have been conducted on how to improve the airflow [5–12]. Nevertheless, more airflow problems ⇑ Corresponding author. Tel./fax: +86 10 62772919. E-mail address: [email protected] (Z. Li). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.09.078 0017-9310/Ó 2014 Elsevier Ltd. All rights reserved.
still need to be solved. For example, air mixing will raise the cooling air temperature and reduce the cooling efficiency. Moreover, unreasonable distributions of the cold airflow will result in hot spots in the data center. Thus, analysis methods are needed to further improve the airflow organization. Existing airflow analysis and evaluation methods can be categorized as empirical and second law based methods. The empirical methods usually use system parameters such as temperature to as evaluation indexes. For instance, the Supply Heat Index (SHI) and the Return Heat Index (RHI) given by Sharma [13] and the Rack Cooling Index (RCI) and Return Temperature Index (RTI) by Herrlin [14,15]. These empirical analysis and evaluation methods reflect the airflow conditions to some degree, but the empirical indexes generally just reflect one or two aspects of the air mixing problems at one position, e.g., SHI and RHI are mainly concerned with the airflow at the rack level and cannot accurately describe the airflow problems. For example, RTI only gives the relative strength of the bypass airflow and the recirculation airflow rather than the absolute value. Thus, the empirical indexes cannot give enough information about the cooling energy efficiency to effectively evaluate the system. Hence, they cannot be effectively used to optimizing the data center airflow. In view of the deficiencies of the empirical methods, approaches based on the Second Law of Thermodynamics have been introduced to analyze data center airflows. Exergy analyses are widely used to analyze thermodynamic processes. For data center cooling systems, Shah et al. [16–20] related exergy losses to the air-conditioning unit parameters. The optimal parameters could be obtained by minimizing the cooling system exergy loss. The entransy analysis method proposed by Guo [21] can be also used to analyze and optimize heat
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Nomenclature C Ex
UG H I i K kn q Q R r S T T0
heat capacity rate, W K1 exergy, W entransy dissipation, W K enthalpy, W exergy loss, W exergy loss per unit cooling capacity thermal conductance, W K1 air distribution ratio for the nth rack group heat flux, W m2 heat transfer rate, W entransy-dissipation-based thermal resistance, K W1 air mixing ratio entropy, W K1 temperature, °C or K the reference temperature
DC ex h i max mix m1 m2 Npa o Ra RM sys tot
data center heat exchanger heat source, hot flow inlet maximum mixing middle airflow 1 middle airflow 2 negative pressure air outlet recirculation air rack module system total
Subscripts Ba bypass air c cold flow
transfer processes. Entransy, is a new physical quantity, which represents the heat transfer ability of an object in heat transfer process. It is defined as the product of 0.5T and Q. Where Q is the internal thermal energy stored in an object and T is the object’s absolute temperature. During an irreversible heat transfer process, the thermal energy is conserved, but the entransy will be partially dissipated. This method also follows the Second Law and has been successfully used in analyses of heat conduction [22,23], heat convection [24,25], heat exchangers and heat exchanger networks [26–29]. Qian et al. [30] related the rack heat source temperatures to the entransy-dissipation-based thermal resistance and defined three indexes to evaluate data center thermal environment. The purpose of improving the data center airflow is to reduce the cooling system energy consumption and to optimize the data center thermal environment by changing the system parameters. This paper relates the cooling system parameters to the entransy-dissipation-based thermal resistance or the exergy loss per unit cooling capacity and to demonstrate the applicability of the entransy and exergy analysis methods.
The air mixing phenomena, recirculation air mixing ratio, bypass air mixing ratio and negative pressure air mixing ratio are given by Tozer et al. [31],
rRa ¼ C Ra =C RM
ð1Þ
rBa ¼ C Ba =C m1
ð2Þ
rNPa ¼ C NPa =C m1
ð3Þ
where C is the heat capacity rate and subscript, Ra refers to the recirculation air, Ba refers to the bypass air, NPa refers to the negative pressure air, RM refers to the rack module and m1 refers to middle airflow 1. All the three air mixing ratios vary from 0 to 1. Inappropriate cooling air distributions result in hot spots in locally high-load racks. The influence of the cooling air distribution is analyzed by abstracting the rack layout into the parallel model shown in Fig. 2 with the cooling air distribution ratio defined as [30],
kn ¼ C RM;n =C RM
ð4Þ
2.2. Impacts of air mixing and the cooling air distribution 2. Relationship between the airflow and the system parameters 2.1. Analysis model Fig. 1 shows the airflow pattern in a typical data center. The cooling air is blown from the air conditioning units into the cold aisles through the floor plenum, flows through the racks to remove heat from the rack heat sources, and then flows back to the air conditioning units. This airflow path includes significant air mixing and air distribution problems. Air mixing in data centers can be divided into recirculation air mixing, bypass air mixing and negative pressure air mixing. As seen in Fig. 1, recirculation air mixing occurs when the heated air flows back into the racks and mixes with the cooling air, bypass air mixing occurs when the cooling air flows straight back to the air-conditioning units and does not cool the heat sources, while the negative pressure air mixing occurs when the hot air is sucked back into the floor plenum and mixes with the cooling air. The airflow model given by Tozer et al. [31] simplifies the airflow and heat transfer processes in the data center into a two-dimensional heat transfer network as shown in Fig. 2.
The four system operating parameters in the data center cooling system are the rack heat source temperature, Th, the data center heat load, Qsys, the cooling air temperature, TDC,in, and the cooling air heat capacity rate, CDC. The rack heat source temperature describes the thermal environment while the other system parameters reflect the energy usage of the data center cooling system. To study the influences of the airflow organization on these four system parameters, four schemes listed in Table 1 are arranged. The heat load and heat source temperature are both fixed in schemes 3 and 4, so the effects of the air mixing can only be analyzed for the condition that all the racks are the same. As seen in Fig. 3, the racks in each rack module are assumed to be the same when discussing the air mixing effects. The analyses of each scheme in Table 1 are based on the base case system parameters listed in Table 2. During the analyses, the system parameters are varied by separately varying the recirculation air mixing ratio, bypass air mixing ratio and negative pressure air mixing ratio. In general, the recirculation air mixing and bypass air mixing are more serious in data centers, so their variations were both set as 0–0.6, while the variation of the negative pressure air mixing ratio was set as 0–0.2 because it has a relatively weak effect.
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Fig. 1. Schematic of the airflow in a typical data center.
Fig. 2. Two-dimensional data center heat transfer network model.
Table 1 Analysis schemes. Schemes
Variable parameter
Fixed parameters
1 2 3 4
Th Qsys TDC,in CDC
TDC,in TDC,in Th Th
The impacts of the recirculation air mixing, bypass air mixing and negative pressure air mixing on the system parameters are shown in Figs. 4–6. For scheme 1, the rack heat source temperature is increased as the temperature and heat capacity rate of the cooling air and the heat load are held constant. For scheme 2, the data center heat load is reduced as the temperature and heat capacity rate of the cooling air and the heat source temperature are held constant. For scheme 3, the cooling air temperature is reduced as the cooling air heat capacity rate, the heat source temperature and the heat load are held constant. For scheme 4, the cooling air heat capacity rate is increased while the cooling air temperature,
Airflow problems CDC CDC CDC TDC,in
Qsys Th Qsys Qsys
Air Air Air Air
mixing, air distribution mixing, air distribution mixing mixing
heat source temperature and heat load remain unchanged. It is seen that the system parameters vary linearly with the recirculation air mixing ratio and negative pressure air ratio (Figs. 4 and 6), and vary exponentially with the bypass air mixing ratio (Fig. 5). Thus, for the same air mixing ratio, the bypass air mixing has a larger impact on the system parameters than the others. The influence of the cooling air distribution is analyzed using the simplified model shown in Fig. 7 with two groups of racks. The analyses use the schemes in Table 1 with the analysis parameters selected from Table 3. In schemes 3 and 4, the heat source temperature and heat load are fixed, so there is no air distribution problem.
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Fig. 3. Air mixing analysis model.
Table 2 Analysis parameters for air mixing analysis. Cooling system
Rack module
Cooling air temperature TDC,in (°C) Cooling air heat capacity rate CDC (W K
18 1
)
4000
Thermal conductance KAh (W K1) Heat load Q (kW) Heat source temperature Th (°C)
1500 30 42
Fig. 4. System parameter variations with the recirculation air mixing ratio.
Fig. 5. System parameter variations with the bypass air mixing ratio.
The effect of the cooling air distribution on the system parameters was analyzed with all the air mixing ratios set to zero while the cooling air distribution ratio in the first group of racks is varied from 0.1 to 0.7. For scheme 1, the heat source temperature is defined as the arithmetic mean temperature of the racks. The results shown in Fig. 8 indicate that the heat source temperature first decreases and then increases with increasing cooling air distribution ratio, with a minimum at k1 = 0.42, where k1 represents the ratio of the cooling airflow rate into the first group of racks to the total flow rate. For scheme 2, as the cooling air distribution ratio increases, the heat load first increases and then decreases, with a maximum at k1 = 0.52, as is shown in Fig. 9. Thus, the thermal process can be optimized by optimizing the cooling air distribution ratio.
These analysis results for the impacts of the air mixing and cooling air distributions on the system parameters show that the cooling system thermal and energy consumption performance can be improved by improving the airflow organization. The heat source temperature can be reduced and the thermal environment can be improved for the same energy consumption in scheme 1, while the energy consumption per unit cooling capacity can be reduced in schemes 2 and 3 because the evaporation temperature is increased by the increased heat load and cooling air temperature, which improves the cooling efficiency. For scheme 4, the reduced cooling air heat capacity, which is a reduced cooling airflow rate, not only raises the evaporation temperature but also reduces the energy used to driving the
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Fig. 6. System parameter variations with the negative pressure air mixing ratio.
air flow, both of which lower the energy consumption per unit cooling capacity. 3. Entransy and exergy analyses 3.1. Entransy-dissipation-based thermal resistance The evaluation indexes used in the empirical methods are related to only one or two system parameters, which is usually a limitation when they are used to analyze the airflow in a data
Fig. 8. Heat source temperature variations with the cooling air distribution ratio (scheme 1).
center. Thus, more comprehensive methods which include all the four system parameters are needed. Entransy analyses have been successfully used to analyze many heat transfer processes and thermal devices. In general, the rack heat sources temperatures are different, so the data center heat transfer problem is similar to a multi-stream heat transfer network. The traditional entransy analysis method is reasonable for analyzing two-stream heat transfer processes but not suitable for multi-stream heat transfer network. Qian [32] extended the method to multi-stream heat transfer processes by including virtual distribution and mixing at inlets and outlets. This entransy
Fig. 7. Analysis model for the cooling air distribution effect.
Table 3 Analysis parameters for the cooling air distribution analysis. Cooling system Cooling air temperature TDC,in (°C)
Cooling air heat capacity flow rate CDC (W K1)
Rack module 18
4000
Thermal conductance 1 KAh1 (W K1) Heat load 1 Q1 (kW) Heat source temperature 1 Th1 (°C) Thermal conductance 2 KAh2 (W K1) Heat load 2 Q2 (kW) Heat source temperature 2 Th2 (°C)
900 10 30 600 20 40
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The arithmetic average temperature of the rack heat sources is,
Th ¼
T h1 þ T h2 þ þ T hn n
ð12Þ
The arithmetic average temperature of the cooling air is,
T DC ¼
T DC;in þ T DC;out 2
ð13Þ
Then, Eq. (10) can be simplified as,
UG;sys ¼ Q sys ðT h T DC Þ
ð14Þ
Eq. (14) shows that the entransy dissipation of the data center heat transfer network is the product of the heat load and the average temperature difference between the rack heat source and the cooling air. Then, the entransy-dissipation-based thermal resistance can be written as,
Rsys ¼ Fig. 9. Heat load variations with the cooling air distribution ratio (scheme 2).
analysis method is used here to analyze the airflow organization in a data center. The entransy dissipation of the airflow heat transfer processes in a data center includes five parts. The first is caused by unequal rack heat source temperatures; the second is due to the heat transfer between the airflow and the rack module, while the others are due to the three kinds of air mixing. The entransy analysis method for multi-stream heat transfer problems first simplifies the problem to an equivalent two-stream heat transfer process with the additional entransy dissipation resulting from the unequal heat source temperatures written as:
T h1 þ T h2 þ þ T hn n
UG;v ¼ ðQ 1 þ Q 2 þ þ Q n Þ
ð5Þ
where Qn is the heat transfer rate and Thn is the temperature of the nth heat source. The entransy dissipation due to the heat transfer between the airflow and the rack module can be expressed:
1 2
ð6Þ
where CRM is the heat capacity rate of the air flowing through the rack module and TRM,in and TRM,out are the air temperatures flowing into and out of the rack module. The entransy dissipation rates due to the recirculation air mixing, bypass air mixing and negative pressure air mixing are:
1 C m2 T 2m2 þ C Ra T 2Ra C RM T 2RM;in 2 1 UG;Ba ¼ C m2 T 2RM;out þ C Ba T 2Ba C m1 T 2DC;out 2 1 UG;NPa ¼ C DC T 2DC;in þ C NPa T 2NPa C m1 T 2m1 2
UG;Ra ¼
ð7Þ ð8Þ ð9Þ
The five parts are summed to give the total entransy dissipation in the data center airflow heat transfer processes:
UG;sys
T h1 þ T h2 þ þ T hn ¼ ðQ 1 þ Q 2 þ þ Q n Þ n 1 C DC T 2DC;out T 2DC;in 2
Q 2sys
¼
T h T DC Q sys
ð15Þ
Eq. (15) shows that the temperature difference between the heat source and the cooling air is the heat transfer driving force and the thermal performance of the data center cooling system can be characterized by the entransy-dissipation-based thermal resistance. Using the inlet temperature to replace the average cooling air temperature, Eq. (15) can be expressed as,
Rsys ¼
T h T DC;in 1 C DC Q sys
ð16Þ
Thus, the entransy-dissipation-based thermal resistance is a function of the four system parameters and the entransydissipation-based thermal resistance can be used to evaluate the airflow organization. 3.2. Exergy loss
ðQ 1 T h1 þ Q 2 T h2 þ þ Q n T hn Þ
UG;h ¼ ðQ 1 T h1 þ Q 2 T h2 þ þ Q n T hn Þ þ C RM T 2RM;in T 2RM;out
UG;sys
The exergy analysis method has been widely used to analyze various thermodynamic processes. Based on the research of Shah et al.’s [16–20], the exergy losses of heat transfer processes in data centers include the exergy losses due to the heat transfer between the airflow and the rack modules and the exergy losses resulting from the three air mixing processes. The exergy loss due to the airflow from state 1–2 without work is:
Ex;1 Ex;2 ¼ H1 H2 T 0 ðS1 S2 Þ
ð17Þ
where H is the enthalpy, S is the entropy and T0 is the reference temperature (environment temperature). The exergy loss due to the heat transfer, Q, for a constant temperature heat source is,
T0 Q Ix;Q ¼ 1 T
ð18Þ
Combining Eqs. (17) and (18) gives the exergy loss for the heat transfer between the airflow and the rack modules as:
T0 T0 T0 T RM;out þ T 0 C RM ln Ih ¼ Q 1 þ Q2 þ þ Qn T h1 T h2 T hn T RM;in
ð19Þ
The exergy loss due to the recirculation air mixing is,
ð10Þ
IRa ¼ T 0 C m2 ln
T RM;in T RM;in þ T 0 C Ra ln T m2 T Ra
where CDC is the heat capacity rate of the airflow through data center and TDC,in and TDC,out are the air temperatures flowing into and out of the data center. The total data center heat load is then:
The exergy loss due to the bypass air mixing is,
Q sys ¼ Q 1 þ Q 2 þ þ Q n
IBa ¼ T 0 C m2 ln
ð11Þ
T DC;out T DC;out þ T 0 C Ba ln T RM;out T Ba
ð20Þ
ð21Þ
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The exergy loss due to the negative pressure air mixing is,
INPa ¼ T 0 C DC ln
T m1 T m1 þ T 0 C NPa ln T DC;in T NPa
ð22Þ
The total exergy loss for all of the heat transfer processes is the sum of the four parts,
T0 T0 T0 T DC;out þ T 0 C DC ln Isys ¼ Q 1 þ Q2 þ þ Qn T h1 T h2 T hn T DC;in
ð23Þ
When the heat load or the cooling capacity is not fixed, the exergy loss per unit cooling capacity is usually used to evaluate the airflow organization as:
isys ¼
Isys Q sys
ð24Þ
Similar to the entransy-dissipation-based thermal resistance, exergy loss per unit cooling capacity is also a function of the four system parameters, but the relationship between them are not as clear as for the entransy-dissipation-based thermal resistance.
Fig. 10. Variations of Th, Rsys and isys with the cooling air distribution ratio (scheme 1).
3.3. Analyses by entransy and exergy analysis methods The expressions for the entransy-dissipation-based thermal resistance and the exergy loss per unit cooling capacity for the data center airflow heat transfer processes are used to evaluate the data center airflow organization. The relationships between the two evaluation indexes and the system parameters are studied here for the four analysis schemes to demonstrate the applicability of the two analysis methods. To improve the air mixing, the system parameters were varied with the changes in the entransy-dissipation-based thermal resistance and exergy loss per unit cooling capacity calculated by Eqs. (16) and (24). The results in Table 4 show that without the air mixing, the entransy-dissipation-based thermal resistance and exergy loss per unit cooling capacity both decrease for the system parameter variations for all the four schemes. Correspondingly, the energy use also decreases and the data center thermal environment is improved. The variations of the two evaluation indexes (the entransydissipation-based thermal resistance and the exergy loss per unit cooling capacity) with the cooling air distribution ratio are shown in Figs. 10 and 11. As seen in Fig. 10, when the cooling air distribution ratio in the first rack group increases from 0.1 to 0.7, the rack heat source temperature, the entransy-dissipation-based thermal resistance and the exergy loss per unit cooling capacity all initially decrease and then increase. The minimum rack heat source temperature and the minimum entransy-dissipation-based thermal resistance occur at k1 = 0.42. The minimum exergy loss per unit cooling capacity occurs at k1 = 0.48. The results in Fig. 11 show that with increasing cooling air distribution ratio, the allowed data center heat load first increases and then decreases, and the entransy-dissipation-based thermal resistance also first decreases and then increases. Both have their extremes at k1 = 0.52. However, the exergy loss per unit cooling capacity decreases continuously within the given air distribution ratio range. These case studies indicate that the minimum exergy loss per unit cooling capacity
Fig. 11. Variations of Qsys, Rsys and isys with the cooling air distribution ratio (scheme 2).
does not correspond to the largest heat load. In fact, what we discussed is a pure heat transfer problem, where heat-work conversion is not included. Entransy represents the heat transfer ability of a body, entransy analysis is more suitable for analyzing heat transfer problem than exergy method. In addition, the heat transfer between cooling air and racks is similar to a multi-stream heat transfer network due to the different rack temperatures, the additional entransy dissipation resulting from the unequal heat source temperatures should be considered in the entransy analysis. If heat-work conversion exists, for example in a thermodynamic process the exergy analysis will be better. Thus, the entransydissipation-based thermal resistance is more suitable for evaluating the effect of the cooling air distribution on the system parameters.
Table 4 Rsys and isys vary with eliminating air mixing. Airflow organization
Schemes
System parameters
Energy use and thermal environment
Rsys
isys
Eliminate air mixing
1 2 3 4
Th; Qsys" TDC,in" CDC;
Better thermal environment Energy use decreases Energy use decreases Energy use decreases
; ; ; ;
; ; ; ;
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4. Concluding remarks The airflow organization plays an important role in reducing the energy consumption and improving the thermal environment of data centers. The airflow heat transfer was modeled as a multi-stream heat transfer network to relate the entransy-dissipation-based thermal resistance for the airflow heat transfer to the data center system parameters. The airflow was then analyzed based on the entransy and exergy analyses. For air mixing analyzing, the smaller of the entransy-dissipation-based thermal resistance or the exergy loss per unit cooling capacity can both reflect the better energy using and thermal environment of data centers. In cooling air distribution analyses, a lower entransy-dissipation-based thermal resistance can improves the thermal environment and the energy conservation in data centers. However, the minimum exergy loss per unit cooling capacity does not correspond to the optimal system parameters. Therefore, entransy analysis method is more applicable then exergy analysis method in the analysis and optimization of data center airflow organization. Conflict of interest None declared. Acknowledgements This work was financially supported by the National Key Basic Research Program of China (2013CB228301) and the National Natural Science Foundation of China (51138005). 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] TC 9.9 Committee, Datacom Equipment Power Trends and Cooling Applications, Atlanta: ASHRAE, 2005. [3] 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. [4] C. Belady, In the data center, power and cooling costs more than the IT equipment it supports, Electronics Cooling, February 2007. [5] 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. [6] M. Iyengar, R.R. Schmidt, A. Sharma, et al., Thermal characterization of nonraised floor air cooled data centers using numerical modeling, in: International Electronic Packaging Technical Conference and Exhibition, San Francisco, CA, 2005. [7] 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. [8] R.F. Sullivan, Alternating cold and hot aisles provides more reliable cooling for sever farms, a White Paper From the Uptime Institute, Incorporated, Santa Fe, New Mexico, 2002.
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