1、Kishor Khankari is a Associate Partner at Syska Hennessy Group in Ann Arbor, Michigan. Rate of Heating Analysis of Data Centers during Power Shutdown Kishor Khankari, PhD Member ASHRAE Abstract During power outages servers in the data centers are generally powered by uninterruptible power supplies (
2、UPS). At the same time the sources for active cooling such as CRACs, CRAHs, and chillers stop operating for a period until powered by alternate power sources. During this period servers continue to generate heat without any active cooling. This results in increase in the room air temperature within
3、a short period that can be detrimental to the servers. This paper, with the help of a mathematical model, indicates that the rate of heating of a data center can start initially at a certain maximum level, and can then gradually reduce to a certain minimum level, which is the lowest possible rate of
4、 heating that a data center can attain. The rate of such exponential decay is a function of the time constant, which is the characteristic of a data center design and layout. The time constant depends on the heat capacity ratio and the specific surface area of racks in a data center. This paper anal
5、yzes various factors that affect these parameters and demonstrates how the time constant can be employed as a matrix to compare the thermal performance of data centers during the power outage period. INTRODUCTION Provision of continuous cooling to mission critical facilities is essential to maintain
6、 supply air temperatures to servers within the recommended range of 64.4 F (18 C) to 80.6 F (27 C) (as recommended by ASHRAE, 2008). During power outages servers continue to operate with the power provided by the uninterruptible power supply (UPS) units while the supply of cooling air is completely
7、halted until alternate means of powering the cooling system are activated. During this time servers continue to generate heat and the server fans continue to circulate room air several times though the servers. This can result in sharp increase in the room air temperature to undesirable levels, whic
8、h in turn can lead to automatic shutdown of servers, and in some cases can even cause thermal damage to servers. Provisions for making continuous cooling available during this period by alternate means are generally expensive and tedious. Data centers contain a large number of rack enclosures constr
9、ucted out of rolled carbon steel. Before considering the other expensive options for continuous cooling it would be valuable to analyze whether rack thermal mass can help in reducing or eliminating the need for provisional cooling. Previous analysis by Khankari (2010) showed that thermal mass of rac
10、k enclosures can play a crucial role in attenuating the temperature rise of room air during the power shutdown period. However, availability of this thermal mass depends on the extent of the exposed surface area of the racks, which in turn, depends on the number of racks and number of rack rows in a
11、 data center. It was further demonstrated that data centers with low heat load densities are less likely to experience automatic server shut off due to increased air temperatures and can provide more time for starting alternate power systems. In addition to the temperature, the rate of heating of ro
12、om air during the power outage period is also an important factor. Not only the temperature levels in the room be maintained within the recommended range but the rate of heating should also be kept at a minimum level. During a power outage the temperature of the room air as well as the rate of tempe
13、rature rise vary with time. If the rate of heat generation from servers remains constant, the temperature levels in the room would LV-11-C026212 ASHRAE Transactions2011. American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions
14、, Volume 117, Part 1. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAES prior written permission.continue to rise and not reach a steady state during the power shutdown period. However, the rate of temperatu
15、re rise can reach a steady state and attain a constant rate, which can also be the lowest rate of heating that a data center can attain. This lowest rate of heating and the rate at which it can be reduced from the maximum rate are the characteristics of the design and layout of a data center. This p
16、aper with the help of a heat transfer model evaluates this phenomenon and analyzes various parameters that can affect the thermal performance of a data center during the power shutdown period. DESCRIPTION OF HEAT TRANSFER MODEL The heat transfer analysis presented in this study is based on the heat
17、transfer model developed during the previous study ( Khankari.2010). Unlike the previous heat transfer model, which was mainly related to study the variation of room air temperature with time, the present model is developed to study the variation of rate of air temperature rise or the rate of heat t
18、ransfer between the air and rack mass with time. The previous model was based on the hypothesis that the total heat generated by servers during the off cooling period is primarily dissipated to the surrounding air through active recirculation induced by the server fans. Air then dissipates part of t
19、his heat to the surroundings through several pathways that includes rack enclosure mass, mass of the cold air trapped under the raised floor, and to the outside world through the building envelop. However, the previous analysis showed that about 98 percent of the total heat generated by the servers
20、is absorbed by the room air and rack enclosures and less than 2 percent is dissipated to the other components. Therefore, in this analysis the heat transfer model is modified to assume that the total generated heat is dissipated among the room air and the rack enclosures only. This is described by t
21、he equation (1) (Table 1). The rate of heat transfer mechanism between the air and the rack enclosures, as shown in the equation (2b), depends on the heat transfer coefficients (U), exposed rack surface area (Arack), and the temperature differences (T) between the rack mass and the room air. It shou
22、ld be noted that the exposed rack surface area depends not only on the number of racks but also on the number of rack rows. The assumptions related to the previous analysis are still valid and are mentioned here for reference. The heat transfer model considered in this analysis is a zero dimensional
23、 model and assumes that all spatial variations within the data center are negligible. The air in the data center room is assumed to be well mixed, and hence, assumes a single mixed temperature. Since the air is rapidly moved by the server fans this assumption is quite reasonable. Also all the rack e
24、nclosure mass assumes a single temperature. The resistance to heat transfer within the rack mass is assumed to be small due to large thermal conductivity compared to the heat transfer coefficient on the surfaces. The rate of heat generation from servers is assumed to be constant during the power shu
25、t down period. Mathematical analysis of the heat transfer model and the development of various equations are presented in Table 1. RATE OF HEATING ANALYSIS After the active cooling completely stops, the air and rack temperature start rising due to the heat generated from the servers. Figure 1a shows
26、 a hypothetical trend of room air and rack temperature rise. Effect of various factors that can affect these trends is discussed in detail in Khankari (2010). Figure 1b shows the corresponding trend of rate of heating or rate of temperature rise with time. These trends reveal two important facts a)
27、after an initial rapid rise, both the air and rack temperatures tend to vary at constant rate; and b) this rate is equal for both the air and the rack mass. As shown in Figure 1b the rate of heating of air starts at a certain maximum level (Rmax), and then, gradually reduces to a certain minimum lev
28、el (Rmin), which is the lowest possible rate of heating that a data center can attain. Thus, Rmin can be an important characteristic of a data center design. The heat transfer analysis presented in Table 1 indicates that with increasing time, the difference between Rmax and Rmin gradually approaches
29、 zero while the room air temperature continues to increase at a constant rate of Rmin. For the purpose of this analysis a non-dimensional rate of heating () is introduced. According to equation (6), initially when the rate of heating, R, is at Rmax, is equal to 1. Similarly, when R approaches the Rm
30、in, and theoretically at time equal to infinity, will approach to zero. Thus, the non-dimensional rate of heating varies exponentially from 1 to 0 as shown in Figure 1c. This 2011 ASHRAE 213parameter is helpful in analyzing the extent of the rate of heating (R) from reaching the potential minimum ra
31、te of heating (Rmin) at any given time during the power outage period. As shown in equation (6), the rate of such exponential decay depends on the time constant () of the data center. Figure 1 (a) Variation of temperature with time. Figure 1 (b) Variation of rate of heating with time. Figure 1 (c) V
32、ariation of non-dimensional rate of heating () with time. The time constant () of the data center depends on the heat transfer coefficient (U), the specific heat of rack mass (Cprack), the specific surface area of the rack (As), and on the heat capacity ratio (Cr). Thus, the time constant is a chara
33、cteristic of the design and layout of the data center. A good design of a data center should not only try to reduce the minimum rate of heating (Rmin) to the lowest possible level but should also reduce the time constant (), which determines the rate at which the initial maximum rate of heating redu
34、ces to the minimum rate. MAXIMUM AND MINIMUM RATE OF HEATING It is assumed that initially (at time t=0), right after the power outage, room air and rack mass are in thermal equilibrium and both assume a certain average initial temperature. According to this assumption at time t=0, there is no exchan
35、ge of heat between the air and the rack mass. This assumption leads to equation (4a) for the initial rate of heating, Rmax. This initial Temperature Time AirRackRate of Temperature Rise(dT/dt) Time AirRackRmaxRmin0.00.10.20.30.40.50.60.70.80.91.0Non-dimensional rate of heating() Time 36.8 % line214
36、ASHRAE Transactionsmaximum rate of heating increases with the heat load in the data center and decreases with the room heat capacity. The heat capacity of the room depends on the volume of a data center. Thus, the maximum rate of heating decreases with an increase in the floor area and/or height of
37、a data center room. In other words, data centers with larger floor area and/or larger height will have lower Rmax. This mathematical analysis also leads to another important conclusion, as indicated by equation (4b), that at steady state when the rate of heat transfer between the air and rack mass b
38、ecomes constant, the rate change of air and rack temperature become equal (Figure 1b). This analysis leads to the equation (4c) for Rmin, which is the lowest possible rate of heating the room air can attain. Equation 4c indicates that the minimum rate of heating also varies directly with the heat lo
39、ad, but unlike the maximum rate, it decreases with the total heat capacity of the system, which is the sum of the room and rack mass heat capacities. As thermal mass increases, Rmin decreases. In other words, data center with larger thermal mass, for example, due to more number of racks will have a
40、lower Rmin than an identical data center with a fewer racks. Similar to Rmax, the minimum rate of heating also decreases with an increase in the heat capacity of a data center room. Table 1: Mathematical Model g1843g4662g3034g3032g3041 g3404g1843g4662g3028g3036g3045 g3397g1843g4662g3045g3028g3030g30
41、38 (1) g1843g4662g3028g3036g3045 g3404g3435g2025g1848g1855g3043g3439g3028g3036g3045 g3031g3021g3276g3284g3293g3031g3047 (2a) g1843g4662g3045g3028g3030g3038 g3404g1847g1827g3045g3028g3030g3038 g1846g3404g3435g1865g1855g3043g3439g3045g3028g3030g3038 g3031g3021g3293g3276g3278g3286g3031g3047 (2b) From t
42、he equations (1) and (2) g3435g2025g1848g1855g3043g3439g3028g3036g3045 g3031g3031g3047g4672g3031g3021g3276g3284g3293g3031g3047 g4673g3404g3398 g3435g1865g1855g3043g3439g3045g3028g3030g3038 g3031g3031g3047g4672g3031g3021g3293g3276g3278g3286g3031g3047 g4673 (3a) g3435g1865g1855g3043g3439g3045g3028g303
43、0g3038 g3031g3031g3047g4672g3031g3021g3293g3276g3278g3286g3031g3047 g4673g3404g1847g1827g4674g3031g3021g3276g3284g3293g3031g3047 g3398g3031g3021g3293g3276g3278g3286g3031g3047 g4675 (3b) Initial and final conditions for the equation (3a) are g3031g3021g3276g3284g3293g3031g3047 g3404g3421g1844g3040g30
44、28g3051, g1872g34040g1844g3040g3036g3041, g1872g3404g1 (4) At time t = 0, T = 0, and therefore, from equation (1) and (2a) g1844g3040g3028g3051 g3404 g3018g4662g3282g3280g3289g3435g3096g3023g3030g3291g3439g3276g3284g3293(4a) At steady state (time t = ), the equation (3b) reduces to g3031g3021g3276g3
45、284g3293g3031g3047 g3404g3031g3021g3293g3276g3278g3286g3031g3047 (4b) Therefore, from equation (1) and (2) g1844g3040g3036g3041 g3404 g3018g4662g3282g3280g3289g4674g3435g3096g3023g3030g3291g3439g3276g3284g3293g2878g3435g3040g3030g3291g3439g3293g3276g3278g3286g4675(4c) From equation (4a) and (4c) g30
46、19g3288g3276g3299g3019g3288g3284g3289 g3404g46661g3397g1829g3045g4667 (4d) g1829g3045 g3404 g3435g3040g3030g3291g3439g3293g3276g3278g3286g3435g3096g3023g3030g3291g3439g3276g3284g3293g3404 g3428g3015g3293g3276g3278g3286g3002g3281g3432g4674g3050g3009g4675g3428g3004g3291g3293g3276g3278g3286g3435g3096g3
47、030g3291g3439g3276g3284g3293g3432 (5) With the initial and final conditions described above, the solution of the equation (3) is g2016g3404 g3019g2879 g3019g3288g3284g3289g3019g3288g3276g3299g2879 g3019g3288g3284g3289g3404g1857g2879g3047/g3099 (6) where, Time constant g4666g2028g4667g3404 g3428g3436
48、 g3022g3002g3294g3004g3291g3293g3276g3278g3286g3440g46661g3397g1829g3045g4667g3432g2879g2869(7) and the specific surface area of rack g1827g3045g3028g3030g3038 g34042g1830g4666g1840g3045g3028g3030g3038g1849g3397g1840g3045g3042g3050g1834g4667 (8a) g1827g3046 g34042g1830g4666g1849g3397g1834/Ng2928g292
49、6g2928g4667/g1875 (8b) TIME CONSTANT As mentioned before the time constant () of a data center is an important design parameter that determines its ability to reduce the initial maximum rate of heating, Rmax, to the final minimum rate of Rmin. Data centers with a large time constant will take relatively long time to reach the minimum level of heating compared to those with lower time constant. According to equation (6) and as shown in the Figure 1c, when the physical time, after the power outage, reaches the value of the time con
