A thermal environmental analysis method for data centers

Abstract

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.

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 centers with cold and hot aisles [4], [5], [6], [7], [8]. However, there are still inefficient data center airflow patterns. Fig. 1 shows a typical raised-floor 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, RCI_HI and RCI_LO, 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. 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], [17], [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.

$$G=Q_{h}T/2$$

where Q_h 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,

$$\rho c_{v}T\frac{\partial T}{\partial t}=-\nabla ·(\mathit{qT})+q·\nabla T\text{.}$$

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,

$$g_{\varphi }=-q·\nabla T=k(\nabla T{)}^2$$

and the entransy-dissipation-based thermal resistance can be expressed as,

$$R_{\varphi }=\frac{G_{\varphi }}{Q^2}$$

where G_ϕ is the entransy dissipation rate during the heat transfer process, and Q is the heat transfer rate.

Studies have shown that entransy dissipation and the entransy-dissipation-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], [28], [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.