Masters Thesis – Degree Project in Energy Engineering, 30 hp
CHIMNEY EFFECT IN DATA CENTERS
On the possibility to achieve natural draft through servers
Sebastian Fredriksson
EN1739
my gratitude to the people that supported me in completing this thesis. My supervisor Gireesh Nair at Ume˚a University brought many insightful thoughts and good guidance throughout the work and for that I am thankful and direct much appreciation. Many thanks goes to my supervisors at RISE SICS North, Jonas Gustafsson and Tor Bj¨orn Minde for their support and guidance.
which use large amounts of electrical energy. Electrical energy is converted to heat by the data processing units in servers and therefore demand cooling. In large scale data centers, air is tradi- tionally used as cooling medium where heat from the server components are transferred to the air as it flows through the server. Free cooling utilizes the cold outside air to avoid the use of chillers as cold source and therefore reduce energy consumption significantly. However, some facility energy and ventilation fan energy is still required to move the air. In addition, each server is commonly equipped with several small fans to move air through the server to keep CPU temperature at a safe operational level.
The purpose of this paper was to study if fan energy consumption can be decreased due to an innovative server room layout. The idea was to connect a chimney to the backside of a server rack and route the air through the chimney and out to the ambient. The purpose of the chimney was to allow the heated exhaust air to rise upwards, due to buoyancy forces, and through this obtain natural draft through the servers. The induced air flow could potentially replace internal fans for moving the air through the servers and thus, reduce energy consumption. A mathematical model was developed and implemented in Simulink where simulations was performed on the system. The effect on temperatures and air flow in the system was studied by several simulations as different input parameters such as chimney dimension, server power and outdoor temperature was varied.
Separate parts of the model were firstly validated against results presented in literature where good agreement was found. The complete model was assessed to be able to provide estimations on temperature and air flow to fulfill the general goal of the paper. The results showed reasonable values in most of the simulated cases despite lack of research to compare with. It could be concluded that low outdoor temperatures provided better air flow rates and hence, also better cooling abilities.
A chimney height of 20 m and radius of 0.4 m was estimated to cover the cooling need for 160 servers where each server was assumed to consume 150 W. The induced flow from the chimney would be sufficient to replace all the internal fans based on climate data from Lule˚a, Sweden.
The simulations provided interesting and promising results on the studied system. To further strengthen the findings, experimental measurements could be performed on small scale with real server hardware. The model could then be tested and compared to experimental values as the innovative configuration implied limited research similar to the system studied in the present paper.
servrar, switchar och annan n¨atverksutrustning. Servrar kr¨aver kylning eftersom de omvandlar elektrisk energi till v¨arme i samband med att de utf¨or ber¨akningar. Vanligen anv¨ands luft som kylmedium i stora traditionella data center. N¨ar luft str¨ommar genom servrarna, ¨overg˚ar v¨armen fr˚an komponterna till luften. Genom att anv¨anda kall utomhusluft kan energif¨orbrukningen i ett data center kraftigt reduceras. Detta kallas frikyla och inneb¨ar att anv¨andningen av kylmaskiner kan undvikas. ¨Aven om frikyla anv¨ands, kr¨avs det ¨and˚a energi f¨or att driva ventilationens fl¨aktar och anl¨aggningen i ¨ovrigt. F¨orutom stora fl¨aktar tillh¨orande ventilationen sitter det ¨aven ett flertal sm˚a fl¨aktar i varje server f¨or att flytta luften genom servern. Dessa fl¨aktar s¨akerst¨aller ett bra luftfl¨ode genom varje server s˚a att dess CPU-temperatur h˚alls p˚a en s¨aker niv˚a under drift.
Syftet med detta arbete var att unders¨oka om energianv¨andningen fr˚an fl¨aktar kan minska genom en innovativ placering av servrarna. Den huvudsakliga id´en var att ansluta en skorsten till baksidan servrarna f¨or att p˚a s˚a vis leda den varma luften genom skorstenen och ut. Syftet med skorstenen var att l˚ata den varma luften att stiga upp˚at p˚a grund av densitetsskillnader mellan luft i skorstenen och omgivningens luft. P˚a s˚a s¨att finns m¨ojligheten till att sj¨alvdrag skulle kunna uppst˚a som eventuellt skulle kunna ers¨atta de sm˚a fl¨aktarna monterade i varje server och d¨armed leda till minskad energianv¨andning. En matematisk modell utvecklades och implementerades i Simulink d¨ar simuleringar utf¨ordes p˚a det t¨ankta systemet. Temperaturer och luftfl¨ode utv¨arderades utifr˚an en m¨angd olika simuleringar d¨ar parametrar s˚asom skorstensdimension, utomhustemperatur och effektf¨orbrukning hos servrarna ¨andrades.
Separata delar av modellen validerades mot litteraturen d¨ar modellen st¨amde v¨al ¨overens med presenterade resultat. Det bed¨omdes att den kompletta modellen kunde estimera temperaturer och luftfl¨oden f¨or att tillf¨orlitligt kunna besvara denna studies fr˚agest¨allningar. Resultaten fr˚an de flesta simuleringarna visade p˚a rimliga v¨arden trots brist p˚a artiklar att j¨amf¨ora med. Utifr˚an resultaten kunde det konstateras att l˚ag utomhustemperatur medf¨orde st¨orre luftfl¨oden i systemet och d¨armed ocks˚a b¨attre kylning av servrarna. En 20 m h¨og skorsten med 0.4 m radie ber¨aknades kunna t¨acka hela kylbehovet f¨or 160 servrar d¨ar varje server antogs f¨orbruka 150 W. Det sj¨alvdrag som uppstod fr˚an skorstenen var tillr¨ackligt f¨or att ers¨atta alla sm˚a serverfl¨aktar baserat p˚a klimatet f¨or Lule˚a.
Simuleringarna visade p˚a intressanta och lovande resultat f¨or det studerade systemet. Resultatens v¨arde och tillf¨orlitlighet skulle kunna f¨orst¨arkas genom att utf¨ora experimentalla m¨atningar i en sm˚askalig f¨ors¨oksuppst¨allning d¨ar riktiga servrar anv¨ands. Modellen skulle d˚a kunna vidare testas och j¨amf¨oras mot experimentella m¨atresultat d˚a den innovativa id´en medf¨or att forskningen ¨annu
¨
ar begr¨ansad inom detta specifika omr˚ade som detta arbete behandlade.
1.1 Scope of this paper . . . 2
1.2 Limitations and assumptions . . . 3
2 System description 4 2.1 Open Compute Project server . . . 4
2.2 Modeled system . . . 5
2.3 PUE as an energy metric . . . 5
3 Theory 7 3.1 Compact server model . . . 7
3.2 Induced air flow in vertical round duct . . . 8
3.3 Heat transfer in a round duct . . . 10
4 Methodology 12 4.1 Details on the server model . . . 13
4.2 Details on the chimney model . . . 14
4.3 Complete model . . . 15
4.4 MATLAB - Simulink R . . . 15
4.5 Model validation . . . 16
4.5.1 Server model . . . 16
4.5.2 Analytical mass flow rate relation . . . 16
4.6 Required dimension - static case . . . 17
4.7 Simulations . . . 17
4.7.1 Complete model simulation . . . 17
4.7.2 Chimney height . . . 17
4.7.3 Increased server power . . . 18
4.7.4 Transient simulation . . . 18
4.7.5 Effect of outdoor temperature . . . 18
4.7.6 Energy reductions . . . 18
5.2 Validation of analytical mass flow rate relation . . . 21
5.3 Chimney dimension - static solution . . . 22
5.4 Complete model . . . 23
5.5 Chimney height evaluation . . . 23
5.6 Effect of increased power . . . 25
5.7 Transient simulation of four racks . . . 26
5.8 Outdoor temperature . . . 29
5.9 Energy savings potential . . . 30
6 Discussion 32 6.1 Discussion on model validation results . . . 32
6.2 Discussion on the simulation results . . . 32
6.3 Discussion on energy reduction possibilities . . . 34
6.4 General discussion . . . 34
7 Conclusions 34
8 Future work 35
References 37
Thermal effectiveness λ Friction factor
ξ Pressure loss coefficient cp specific heat [J/kg K]
Cs Thermal mass of server [J/K]
cp,s Specific heat of server [J/kg K]
Ctot Total thermal mass [J/K]
D Chimney diameter [m]
F ACe Facility energy [J]
g Gravitational acceleration [m/s2] H Chimney height [m]
ITe,o IT energy without server fans [J]
kw Thermal conductivity of chimney wall [W/m K]
mR Server rack mass [kg]
ms Server mass [kg]
rc Chimney radius [m]
SFe Internal fan energy [J]
T∞ Ambient temperature around chimney [K]
Ta,in Temperature of air at chimney inlet or chimney section inlet [K]
Ta,out Temperature of air at chimney outlet or chimney section outlet [K]
Tc,is Temperature of chimney inside surface [K]
Tc,os Temperature of chimney outside surface [K]
Ti,avg Average temperature of air inside chimney [K]
Ts,i Server inlet temperature [K]
Ts,o Server exhaust temperature [K]
Ts Server temperature [K]
1 Introduction
The world’s resources of fossil fuels are used in an non-sustainable way and are becoming depleted.
Energy reductions and efficiency measures must be considered in all sectors at a higher rate than today to mitigate the threat that entails climate change. There is a general interest in the environ- mental impacts of energy consumption, where the attention has specifically increased for electricity consumption related to Information and Communications Technology (ICT) equipment [1]. One of the categories of ICT is data centers which has experienced a rapid growth in recent years in num- ber, size and power densities with an accompanying increased demand for energy [2]. Essentially, data centers are facilities that houses large number of data processing equipment such as servers and switches [3]. Data centers are used by industries and society where large data processing is required for sectors such as banking, telecommunications, stock market, search engines and social networks [3].
Data centers use large amount of electrical energy in data processing units and therefore, contribute to global warming through emission of green house gases and air pollution in fossil fuel based electrical power production. Statistics reported in 2014 showed that data centers in the US was responsible for more than 2 % of the country’s total electricity consumption. Furthermore, the share of the power consumption by data centers are expected to increase for the foreseeable future driven by a growing data center (DC) market and higher power density server components [4].
The global energy demand for DCs between year 2010 and 2030 was studied in a recent paper where estimations showed an energy use of 325 TWh in 2013 [5]. In 2030, the energy demand was predicted to increase to 1100 TWh for the best case scenario and close to 2900 TWh for the expected scenario [5].
As depicted by Ebrahimi, Jones, and Fleischer, the server is considered to be the smallest data processing unit in a DC. Several servers are typically aligned horizontally in a standardized metal frame enclosure called server rack. A modern data center have several racks arranged next to each other forming lines with every other row facing opposite directions. Cold air is supplied to the front of the servers, by the computer room air conditioning (CRAC) unit, and forced to move through the racks by internal fans on servers. The IT related equipment in a data center are the main source of heat production. Electrical power for data processing is converted to heat which is dissipated and transferred to the the air [4].
DCs have high demands on continuous operation and availability at all times which require thermal management systems to maintain the temperature of the sensitive electronics components at a safe level [4]. Capozzoli et al. stated that the energy for cooling constitutes a large fraction, up to 40
%, of the total energy use which implies large operational costs [2]. Large quantities of energy are used by traditional cooling systems due to work done by fans and pumps to transport cold water or air [6]. This provide strong incentives to conduct research associated to overhead infrastructure of a DC. Air movement for cooling are provided by large ventilation fans, fans integrated in the CRAC units and small internal fans mounted on the server. The work of this project aimed to investigate if energy consumption of the internal fans can be decreased. The main idea was to study if a vertical duct connected to server racks could serve as a chimney and induce natural draft air flow through the servers.
The research field associated to the energy use in data centers encompass several approaches.
Fulpagare and Bhargav provided a review of recent advances in the thermal management systems of data centers where it is stated that numerical, experimental and Computational Fluid Dynamics (CFD) analysis methods are used in several different areas [7]. For air cooled data centers, by pass and recirculation of air are two major challenges in the air management system. The former problem occurs due to excessive flow rates or leaks through cable cutouts and the latter arises when cold air intake to the IT equipment is not sufficient and a fraction of the hot return air flows through the server causing raised inlet temperatures [8].
A comprehensive review on free cooling of data centers was conducted by Zhang, Shao, Xu, et al. Here, the strategies of utilizing cold outdoor air in the cooling of a DC was explained. Free
air-side cooling can significantly reduce energy consumption related to cooling in comparison to a traditional DC since the use of chillers and cooling towers are avoided [6]. As described by Capozzoli and Primiceri, air-side free cooling (also called economizer mode) can be both direct and indirect where the former blows outdoor air directly into the server room and the latter use air-to-air heat exchanger to cool the server room air. The strategy of utilizing free air-side cooling avoids any particulate or gaseous contamination which may be harmful to the sensitive IT equipment. Furthermore, the geographical location of a DC utilizing economizer mode becomes of large importance [2].
The work of VanGilder, Pardey, Healey, et al. proposed a compact server model for server and rack level simulations to capture the thermal mass effects from server hardware. CFD simulations typically ignores these effects and therefore, are overly conservative when estimating transient scenarios such as a sudden unexpected loss of cooling. The developed compact server model calculates server air exhaust temperatures based on rate of internal IT power consumption and server inlet air temperature and requires the mass and specific heat of the server as input [9]. The model has been experimentally validated and further developed with independent measurements on several different server hardware [10], [11].
The demand for data processing and storage is predicted to increase in the future with a growing demand for data centers. On a global scale, ICT has a carbon footprint but also provides a platform in which a number of sectors may decrease their footprint. The ICT sector has a footprint corresponding to 2.3 GtCO2e but provides an abatement potential 7 times higher [12].
When new data centers are planned by global Internet companies such as Google or Facebook, the location is chosen with great precision. Many have turned their eyes towards Scandinavia when higher demands for sustainability of new data centers are to be met. The circumstances of the northern part of Sweden are unique with regards to sustainable electrical energy production with low energy costs, political stability in a low mean temperature region providing energy- and environmental saving opportunities [13].
There are substantial economic values due to the data center business in Sweden. The Boston Consulting Group estimated in their report that the Swedish data center industry in 2015 generated upward 13 billion SEK in full economic impact for construction and operation and predicts that Sweden has the potential of increasing this number to 50 billion SEK by 2025 [14]. There are strong incentives to locate data center in the northern part of Sweden. The net energy consumption can significantly be reduced if new data centers are located in a region with colder climate with the advantage of free cooling possibilities.
As described above, there are many studies which aim to increase energy efficiency of data centers and decrease energy usage. However, most of them investigate different air flow management schedules based on the somewhat static template with server rack rows separating hot and cold air aisles. Efforts in reducing energy in data centers are important from both environmental and economical perspectives when todays hyper scale data centers may consume over 100 MW where cooling related energy contributions are always present.
1.1 Scope of this paper
The work of this paper aimed to study if fan energy usage could be decreased by an innovative configuration in a server room or data center. The main idea was to route the air exiting at the back of a server to a vertical duct. The purpose of the duct was to act as a chimney allowing the hot air, by buoyancy forces, to rise and disseminate to the outdoor atmosphere. Natural draft air flows may potentially arise from this system configuration and thus decrease fan energy demand to move air through the server.
Is it possible to achieve natural draft air flow by routing the exhaust air from servers to a chimney?
If natural draft do occur, how does the input parameters chimney height, chimney radius, server power and outdoor temperature affect the air flow in the system? Is it possible to reduce fan
energy usage due to the air flow induced by the chimney? If so, how much energy can be saved?
The goal of this study was to establish a theoretical model of the setup based on the physical relations that dictates the heat transfer and air flow in the system. The model of the setup should be able to calculate the server temperature, server exhaust air temperature, average chimney tem- perature and induced air flow. Based on simulations, the effect on mass flow rate and temperatures was studied when the dimensions of the chimney changed. The possible energy reductions due to induced air flow by the chimney was finally estimated.
A server room utilizing free air-side cooling was considered as the hypothetical system. The considered layout included four server racks populated with servers organized in a plus formation.
A chimney was connected on top of the empty space that arise at the center.
1.2 Limitations and assumptions
The work of this study focused on calculating the induced air flow in the vertical duct acting as a chimney. The air inlet temperature to the servers were assumed to be the same as provided to the existing data center (about 20◦C). In a system utilizing free air-side cooling, the temperature provided to the front of the servers is commonly controlled through air-to-air heat exchangers.
However, the intended system in this study disregarded how this practically would be solved. The intention was to conduct simulations to provide the stakeholder company RISE SICS North with estimations on the potential of obtaining natural draft. Hence, the system boundary was limited to server racks, servers and the connected chimney. The boundary limits can be expanded in a future work where inlet air conditioning can be integrated.
Except for servers mounted in server racks, the server room also accommodates switchboard, fire extinguishing and humidification equipment. The server room IT equipment furthermore demand backup power, called uninterruptible power supply (UPS), in the event of a abrupt, unexpected power loss. All these units and devices contribute with thermal mass to the server room but was not considered in this study as it is the servers and server racks that constitute the major part of thermal mass and power consumption in a data center.
Servers accommodated in data centers demand environmental control beyond temperature. More specifically, the equipment require a suitable humidity to avoid electrostatic discharges and con- densation along with dust control for safe and continuous operation [4]. A comprehensive study conducted by [15], concluded that energy due to humidification may play a role on the total en- ergy consumption of a DC [15]. The work of this project focused on air temperature and air flow rates through the server racks and disregarded humidity and dust control for simplification. For a study with a wider perspective on energy consumption in data centers, the energy related to humidification of air should be included.
A chimney with a outer surface temperature higher than the surrounding surfaces will experience heat transfer through radiation. This phenomena is affected by the emissivity of the surface and the surrounding surfaces’ temperature. Moreover, a chimney in a outdoor ambient climate will be exposed to wind which enhances the heat loss. Air flow across a cylinder will introduce heat transfer due to forced convection which according to heat transfer theory influences the heat transfer coefficient. Both of these effects was omitted in this thesis as a simplification as it would include significantly more theory and in some cases, complex relations. Despite this assumption, it was assessed that the model could provide meaningful results about the system.
At the time of the thesis work, the Facebook OCP servers was not fully operational and no data collecting services were yet installed. However, the technical specifications from these servers was used because of the intention of using OCP servers in a future experimental setup.
2 System description
2.1 Open Compute Project server
The server hardware used for this study was the servers developed in the Open Compute Project (OCP) called Windmill. Except for the server, seen in figure 1, the server cradle also hosts fans, drive bay and power supply unit. The server specifications provide the range of air flows that the server may function properly, based on reasonable inlet temperatures. When the server is idle, 12 cubic feet per minute (CFM) is suggested to be sufficient and under 100 % load, an air flow of 103 CFM [16]. The technical specifications also states that the maximum CFM is expected to be less than 60 for almost every system loading [16]. Air flow levels of around 20-30 CFM may be sufficient for a server with a power usage of 200 W [17]. This power usage can be considered reasonable since the maximum server power of one Windmill-server is 350 W [18].
Figure 1. To the right, a Windmill-server taken out from its cradle. The black plastic cover seen to the left is the air flow hood that goes onto the server.
It is important to remember that the critical quantity that dictates if the cooling of a server is sufficient or not is the temperature of server components. In reality, the upper temperature limit is related to the temperature of the CPU which should not exceed 85◦C for Windmill-servers [18]. The server intelligence does not know of the air flow and for this reason, the control system regulates the fan speeds as a function of CPU temperature.
The Windmill-servers mounts in non-standard server racks called Triplet Cabinets with three columns hosting 40 servers in each column [16]. One server holds two CPUs with a height close to 1.5U where 1 U = 44.5 mm (U is a industry standard measure correlated to the height of a standard server). In one of the three columns, each horizontal level provides space for two servers, internal fans, power supply unit and drive bay all placed in a server cradle [16]. Each server has two internal fans and one additional fan shared by the two servers on the same horizontal level.
The shared fan provide cooling for the hard drives and power supply unit [16], [18].
The technical specification for the fan states that the maximum power consumption for one fan is about 27 W [19]. However, it is known that the power consumption is not linear when changing the fan speed. Experimental measurements was performed by staff at the stakeholder company RISE
SICS North where the power consumption of the fan was measured at fan speeds between 1200 RPM and 16500 RPM which corresponded to 10 % and 100 % duty cycle, respectively. Through the measurements, a relation between power as a function of fan speed was obtained.
Except for high performance computing data centers, the majority of servers in a data center operate at or below 20 % of their capacity and rarely reach maximum at the same time as the power drawn from the grid may reach 60 - 100 % of maximum power during idle (no load) [4]. A measurement test week was conducted at the research facility in 2016 where server loads of 50 % corresponded to internal fan speeds of approximately 5500 RPM. By using the relation between power and fan speed, one fan was concluded to consume about 2.5 W at these fan speeds.
The OCP server specification further states the system pressure drop that hardware make up. At idle and 100 % load, the corresponding system pressure drops was 1.2 Pa and 60 Pa, respectively.
One server weighs around 10 kg and one of the triplet rack vertical columns is approximated to weigh 100 kg based on the technical specification [16].
2.2 Modeled system
In this thesis, a server room was considered where free air-side cooling provided inlet air temper- ature suitable for servers. A schematic view of the system is seen in figure 2. A more detailed view of the intended server rack layout is depicted in figure 3. The system does not include how the inlet air temperature, Ts,i was conditioned. Furthermore, the dust control and humidification units would be located before the air is allowed to go through the servers but for this study, not accounted for as a simplification. The setup shown in figure 3 show a plus-formation arrangement of the server racks. The concept of connecting a vertical chimney can also be applied to a setup with only one server without a rack or a fully populated server rack.
Heat is transfered to the air as it flows through the servers. The air, now of higher temperature as indicated by the darker colored arrow in figure 2, flow out of the servers and into the bottom of the chimney. The temperature decrease of the air between the server outlet and the stack inlet was assumed negligible. As time progress, more and more hot air will be contained in the chimney and start to rise due to the decreased density in comparison to the ambient air. The rate of air flow out of the chimney at the top, must be the same as the air flow rate into the servers due to the conservation of mass under the assumption that there are no leakages in the system.
Figure 2. Schematic view of the system. Figure 3. Server rack layout.
As the air flow along the vertical duct the air temperature gradually decrease, as indicated by the vertical gradient filled arrow in figure 2, due to a lower ambient temperature surrounding the chimney. This temperature decrease was caused by heat transfer through the chimney wall and indicated as a black curved arrow.
The server racks could be arranged in a plus-formation where the backside of the four racks faced each other leaving an empty space in the middle, see figure 3. The heated air from all the servers would meet in the middle where a vertical duct could be connected allowing the air to rise and disseminate to the outdoor.
2.3 PUE as an energy metric
Energy usage in a DC can be divided into categories where IT equipment energy constitute a large percentage. Lighting, battery management systems, security and other miscellaneous subsystems
is commonly included in the facility energy [6]. Cooling related energy include ventilation fan and pump energy and can also be added to the facility energy category. Within the sector, different DC facilities are assessed and compared through different metrics. Power Usage Effectiveness (PUE) has become the industry standard metric and defined as
PUE = T otal f acility energy IT energy
where the numerator consist of all purchased energy to the facility i.e., the sum of IT equipment energy and other facility related energy [20]. The IT equipment energy is present both in numerator and denominator and defined as the electrical energy usage of servers, switches or other devices located in server racks. The PUE metric can be useful as it presents the proportion of energy actually used to operate the IT equipment with respect to the total energy usage of a DC. The IT equipment is the core service of a DC whereas all the other subsystems exists to support a reliable and safe operation.
PUE as an energy efficiency metric has been criticized due to the large amount of data required to calculate PUE, as multiple parameters need to be measured over an entire year [20]. In addition, another problem with the PUE metric was revealed when considering an air-side free cooling DC which have fans in the ventilation system. Traditionally, the IT equipment energy include all energy consumed by a server but in fact, consists of both energy strictly related to IT (CPU, memory and storage) and energy consumed by internally mounted fans. These fans are small and of low efficiency. As per the traditional definition of PUE, the value would decrease and imply better energy efficiency if air movement was shifted from larger ventilation fans to the internal fans on servers. The PUE value would decrease even though the total energy consumption would increase.
A simple example can illustrate the weakness to the traditional PUE metric, where no separation of internal fan energy is done, compared to net energy consumption. In a 1 MW data center, about 10 % can be estimated to be facility energy where ventilation fans are included. According to the definition, the PUE value becomes 1.1. Internal server fan energy constitute about 5 % of the IT equipment energy. A modified PUE (called SPUE) was derived where internal server fans was separated from other server IT. SPUE can be calculated as
SPUE = ITe,o+ F ace+ SFe ITe,o
where ITe,odenotes IT energy without internal fans, F acedenotes facility energy and SFedenotes internal server fan energy. The numerator is the total f acility energy where the sum of ITe,o and SFe is the IT energy also found in the PUE equation. As presented in table 1, if a DC changes from calculating PUE to SPUE without any other energy reduction measures taken, the value increases.
Table 1. The effect on PUE and SPUE values when reducing fan power usage in a exemplified DC utilizing free air-side cooling.
Fan reduction PUE SPUE Total power
0 % 1.1 1.157 1.1
50 % 1.102 1.131 1.07
80 % 1.104 1.115 1.06
100 % 1.105 1.105 1.05
Based on the example, the values in table 1 show a weakness in the industry standard PUE metric where a decrease in total energy consumption naturally is desirable but affects the traditional PUE
value negatively. Moreover, even for the case of no actual energy saving measure taken, a transition to SPUE would naturally meet resistance as a increased PUE value impair the DC energy efficiency and hence, the technical ”status” of the facility in comparison to others. Separating the internal fan energy from the remaining IT energy can be done but not included in standard servers.
3 Theory
The theory involved in this paper is essentially devided into three sections. The first section describe the heat transfer within the servers. The second section described how the calculation of air mass flow rate was derived. In the last section, the theory of heat transfer through the chimney wall was explained.
3.1 Compact server model
A loss of cooling or varied server loads are examples of transient events that can occur in data centers. The thermal mass of the servers populating a DC highly contribute to the transient scenarios. Computational Fluid Dynamics (CFD) is widely used to model steady state conditions of DC facilities but concluded impractical to catch the behavior of such transient events [11]. A compact server model was proposed to capture the effects of thermal mass without the need for providing explicit details of all server component [21]. The theory proposed for the concept of compact server model was adopted from [11] and described below.
The physical nature of real server hardware are complex but can be approximated as a lumped thermal capacity model under the assumption that spatially temperature variations within the body are neglected. The criteria for lumped system analysis is related to the dimensionless Biot number (Bi) which essentially describe the relation between heat convection and heat conduction [22]. Normally, a lumped system can be assumed if Bi ≤ 0.1 and calculated using the heat transfer coefficient [22]. However, this value is unknown as the surface of the server is complex.
Lumped capacity heating and cooling is expressed as
qlc= mcdT
dt (1)
where qlcis the rate of internal heat generation, m is the mass of the solid, c is the specific heat and dT is the difference in temperature during the time dt. The temperature of the solid will continue to rise according to equation 1 if no external cooling is available [23]. Heat can continuously be transfered from a body to a fluid (that does not undergo any phase change) which will result in a increase in the coolant temperature from inlet to outlet. This can be described as
qf r= ˙mcp(T2− T1) (2)
where qf r denotes flow resistance, ˙m is the mass flow, cp is the specific heat at constant pressure [23]. The subscripts 1 and 2 in this general case correspond to inlet and outlet temperature, respectively. By expanding the lumped-capacity model for transient heating to include cooling, equation 3 is obtained
qlc= qgen− qf r (3)
where qgen is the rate of internal heat generation and qf r is the flow resistance. In a steady state, the right hand side of equation 3 must be zero. However, time delay can occur due to the mass and specific heat of the body.
Consider model of a server as in figure 4, where air flows through and increases in temperature
from inlet to exhaust with a mass flow rate ˙m. All sides of the server are assumed to be perfectly insulated only allowing thermal communication with the surroundings through the air flow stream [11]. The model does not depend on any heat transfer coefficient but rather the mass of the server hardware ms, and its specific heat, cp,s.
Figure 4. Schematic view of a compact server model and essential parameters.
With the server taken as the control volume and performing an energy balance, the relation can be written as
˙
qs= mscp,s
dTs
dt + ˙mcp,air(Ts,o− Ts,i) (4)
where Tsdenotes the average server temperature, ˙qsis the rate of electrical power that is consumed by the server equipment and msis the mass of the server. In accordance with the proposed model developed in [11] and [24], the variable is introduced and defined as
≡ q˙s
˙ qmax
=mc˙ p(Ts.o− Ts,i)
˙
mcp(Ts− Ts,i) = (Ts,o− Ts,i)
(Ts− Ts,i) . (5)
depicts the fraction of the actual rate of heat transfered from the server to the air, ˙qs to the maximum possible rate of heat transfer from the server to the air, ˙qmax. may take values between 0 and 1 where the latter corresponds to a ideal heat transfer corresponding to Ts,o= Ts. Using equation 4 together with equation 5 and rearranging, a ordinary differential equation is obtained as
mscp,s
dTs
dt = ˙qs− ˙mcp,air(Ts− Ts,i). (6)
3.2 Induced air flow in vertical round duct
Much research has been done on natural draft in the application of solar chimney power plants.
Except for the turbine converting kinetic energy to electrical energy, there are similarities to the application of a vertical duct intended in this thesis. The scale of large solar chimney power plants considered in case studies modeled by various research groups, reach heights of several hundred meters, diameters between 40-80 meters and solar collector radii up to 2 km [25]. Since the scale of the chimney for the application studied in this thesis was assumed to be significantly smaller, the pressure and temperature lapse rate was neglected.
The driving force in a solar chimney power plant stem from the difference in air density as described in [26] and [27]. Air situated in the solar collector area is heated by the solar radiation and move towards the center of the collector, where the chimney is located, due to its decrease in density. Hot air in the chimney rise as it has lower density than the ambient air. As the hot air disseminates to the atmosphere at the chimney outlet, ambient air enters at the collector perimeter. A continuous air flow is attained through the collector and the chimney. A solar chimney power plant hosts turbine connected to a generator in the lower part of the chimney. A considerable pressure drop
occurs when air flows across the turbine where kinetic energy of the hot air flow is converted into power.
For the application in this thesis, the thermal engine is provided by electricity used in servers which is converted to heat of in the server component. A mathematical expression estimating the mass flow rate of air in a vertical duct due to the natural draft effect was derived. The model originates from the same fundamental theory as in solar chimney power plants as presented in [26], [27] and [25] but with turbine and solar collector left out as it was out of this paper’s scope and intended application.
The pressure difference between the chimney and the ambient air can be expressed as
∆p = g Z H
0
ρ∞(h) − ρ(h)dh (7)
where g is the gravitational acceleration, H is the total chimney height and ρ∞ is the density of the ambient air at elevation h [27]. Pressure and temperature vary with elevation but in modest ranges, the effect can be neglected. The temperature drop with elevation inside the chimney can be considered small so ρ is independent of the height. Hence, equation 7 simplifies to
∆p = g(ρ∞− ρ)H (8)
where ρ is the density of the gas.
Air can be assumed to follow the ideal gas law under standard ambient climate conditions. With the density at some reference temperature known, air density at any temperature can be expressed in terms of the reference case, i.e air density at 0◦C is 1.293 kg/m3, the density at any other temperature can be expressed as
ρair= 1.293 · p 1· 273
T ' 1.293 ·273
T . (9)
Note that the density of a gas depends on both pressure and temperature according to the ideal gas law. However, a 250 Pa pressure increase only affects the density 0.25 %. A temperature decrease of 10◦C gives a density decrease of 3.5 %. Density can be assumed to only change with temperature as equation 9 suggests. The density in equation 8 can be replaced by temperature using the same analogy to obtain
∆p = gρTi,avg− T∞
T∞
H (10)
where Ti,avg denotes the average temperature of the air inside the chimney and T∞ denotes the air temperature of the surroundings. The pressure difference of the air inside the pipe and the outdoor ambient air must overcome the pressure losses in the pipe. The pressure losses is the sum of friction losses, entrance and exit pressure losses and described as
∆ploss= ∆pf+ ∆pin+ ∆pout. (11)
Here, ∆pf is the pressure loss due to friction between the fluid and the pipe surface, ∆pin is the entrance pressure loss and ∆pout is the exit pressure loss [27]. Equation 11 can be rewritten as
∆ploss= λH D · ρV2
2 + Σ ξ ·ρV2
2 (12)
where λ is the friction factor, V is the average velocity of the fluid and ξ is the minor loss coefficient [27]. Equation 10 set equal to equation 12 become
gρTi,avg− T∞
T∞
H = λH D ·ρV2
2 + Σ ξ ·ρV2
2 . (13)
Rearranging equation 13 allowed the average velocity of the air inside the chimney to be expressed as
V =
s 2gH
λHD+ Σ ξ ·Ti,avg− T∞ T∞
. (14)
The pressure drop coefficient ξ for the pipe exit is unit when a flow from a vertical pipe end is directly discharged to the ambient [28].
A fluid flowing in a pipe of average velocity V is related to the flow rate according to
˙
m = ρAV (15)
where A is the cross sectional area of the pipe. Hence, the mass flow rate can be expressed as
˙ m = ρA
s 2gH
λHD+ Σ ξ ·Ti,avg− T∞ T∞
. (16)
3.3 Heat transfer in a round duct
A hot fluid flowing in a pipe will decrease in temperature along the pipe if the inner surface of the pipe is colder than the fluid. The pipe may be divided into a number of smaller sections along the pipe for improved accuracy. The pipe itself can involve heat transfer resistance depending on the insulation abilities, i.e the pipe material characteristics. Consider air flowing at a steady state in a pipe as in figure 5 with insulated walls.
A mathematical relation of heat loss from a fluid flowing in a pipe was developed in accordance with theory described in [29] and [30]. Some general assumptions of importance are firstly mentioned.
For a pipe section, no heat transfer within the fluid in radial direction or in the direction of flow are considered. Moreover, a homogeneous wall surface temperature was employed in each section of the pipe (both inside and outside wall). Average temperature of a pipe section was calculated as the arithmetical average temperature of the sections’ inlet and outlet temperatures. Finally, the heat loss through the pipe wall was approximated as heat loss through a vertical plane wall justified by a small ratio of pipe wall thickness to pipe diameter.
Figure 5. Cross section of a pipe wall of thickness L describing the temperature decrease.
An energy balance over the air in the pipe requires that
macp,air
dTout
dt = ˙macp,air(Ta,in− Ta,out) − hinAin
Ta,in+ Ta,out
2 − Tc,is
(17)
where hinis the heat transfer coefficient between the air and the inside pipe wall, Ainis the inside surface area of the pipe wall and Tc,isdenotes the temperature of the chimney’s inside surface [30].
The above equation can also be written as
qlc = qf r− qcv,in (18)
where the index lc, f r and cv, in denotes lumped capacity, flow resistance and convection on the inside wall, respectively. Moving the control volume to the pipe wall, the energy balance requires that
qlc= qcv,in− qcd (19)
where the subscript cd denotes conduction in the pipe wall. This can also be written as
mwcp,w
dTc,is
dt = hinAin
Ta,in+ Ta,out
2 − Tc,is
−kwA
L (Tc,is− Tc,os). (20) where kwis the thermal conductivity of the wall, A is the area which the heat transfer is perpen- dicular towards and L is the thickness of the pipe wall. The control volume can further be moved outwards so that the energy balance becomes
qlc= qcd− qcv,out (21)
where qcv,out is rate of heat transfer due to convection on the outside pipe wall. Following the same analogy as above, this can be written as
mwcp,wdTc,os
dt =kwA
L (Tc,is− Tc,os) − houtAout(Tc,os− T∞) (22)
where hout denotes the heat transfer coefficient between the pipe outside surface and the ambient air. The differential equations stated in equations 17, 20 and 22 can be implemented in each vertical section of the pipe.
The heat transfer coefficient, hin, between the inside surface of a pipe and a fluid flowing in a pipe is related to the Nusselt number as
Nu = hinD
k (23)
where D is the diameter of the cylinder and k is the thermal conductivity of the fluid. The empirical relation for the Nusselt number for turbulent flow in tubes is
Nu = 0.023Re0.8Pr1/3 (24)
where Pr is the dimensionless Prandtl number [22].
A vertical cylinder can be approximated as a vertical plate if D ≥35L/Gr1/4. The heat transfer coefficient due to natural convection is related to the dimensionless Nusselt number through
Nunatural=hH
k (25)
where k is the thermal conductivity of the fluid and H is the cylinder height [22]. Furthermore, the Nusselt number can be obtained through the empirical relation
Nu = 0.1Ra1/4 (26)
which holds for Rayleigh numbers in the range of Ra = 104− 109. The empirical relation
Nu = 0.59Ra1/3 (27)
hold for Raleigh numbers in the range of Ra = 1010− 1013 [22].
4 Methodology
The intended system described in section 2.2 was divided into three essential parts; 1. the server model which calculated the server exhaust temperature based on the server power usage, air flow and inlet air temperature; 2. the chimney model that accounted for heat loss through the pipe walls and calculated the chimney outlet and average temperature and 3. the analytical mass flow rate relation which calculated the mass flow rate in the system. The three separate parts of the model emerged from the development process. Each part of the model originated from separate theories and applications and was for this reason developed separately. This allowed the models to be tested individually and then, gradually connected to each other.
The details on the server and chimney models are presented in sections 4.1 and 4.2 below. Further information about the complete model and how they were connected to each other is described in section 4.3. Details regarding the simulation software is stated in section 4.4. The server model and the analytical mass flow rate relation was tested and validated separately against results found in literature. Details regarding the experiments found in literature are presented section 4.5.
Only few papers was found in literature with experimental or modeled results of air flow rates due to natural draft in a vertical pipe acting as a chimney. Hence, the complete model was firstly tested under similar conditions (such as chimney dimensions and other constants) as those presented in literature, see section 4.7.1. As seen in section 3, a number of parameters dictate and influence the behavior of a complete system. The complete model was simulated with different parameters changed one at a time, see table 2. Details about the simulations of the simulation plan is described in 4.7. A final set of simulations was performed beyond simulation E, where energy reduction potential was evaluated and described in section 4.7.6.
The general purpose of the simulation plan was to start out in a smaller scale of power and chimney radius and study the behavior of the system. Simulations B and C expanded the scale to include one server rack populated with servers and thereafter, perform simulations D and E which correspond to four server racks populated with 160 servers.
Table 2. Schedule over the different simulations and the corresponding conditions.
Simulation Server power [W] Radius [m] Height [m] T∞[◦C]
A1 400 0.05 2 to 60 17
A2 400 0.05 to 0.15 2 to 60 17
B 150 to 6000 0.05 20 17
C 150 to 6000 0.5 20 17
D 24000 to 32000* 0.4 30 17
E 24000 0.4 30 -20 to 20
Simulation D indicated with * represents an instant increase in server power usage where the simulation results was studied as function of simulation time.
4.1 Details on the server model
By using the compact model approach, the server exhaust air temperature was successfully pre- dicted as function of the air flow rate and server power in the work of [9]. Some experimental measurements was performed on actual server hardware [9]–[11]. Their experiments was per- formed with one server in an wind tunnel setup where the server’s properties was determined by temperature measurements. The compact server model approach was implemented in this study for its simplicity yet good accuracy in predicting the server exhaust air temperature. Another pos- itive aspect was the evaded estimation of the heat transfer coefficient between the server hardware surfaces and the air flow.
The thermal mass of a server, denoted Cs, can be determined by a experimental measurement method described in [10] and [11]. The specifications for the Open Compute Project server hard- ware provide information regarding power consumption, required air flow and internal pressure loss. However, the specific heat or weight of the server was not included since the weight of the server may vary with the amount of memory and number of hard drives installed.
The compact server model approach may be further expanded so that a server rack populated with several servers can be simulated. According to [9], the total mass of the server rack cabinets will contribute to the total thermal mass, which is the product of mass and specific heat capacity. The contribution of the server rack is accounted for in the calculation of the total specific heat
cp,tot= 1 mtot
n
X
s=1
mscp,s+ mRcp,R
(28)
where n equals the number of servers mounted in one server rack and mtot is the sum of all the server’s mass and the mass of the server rack cabinet. Some references to a reasonable value for the
specific heat of a server cp,s, was found in the literature as technical specifications rarely include information about this value. As stated in [31], the server can be approximated to be composed of 50 % copper and 50 % steel with an average specific heat of 438 J/kg◦C and an average density of 8390 kg/m3. Based on experimental measurements, an average server specific heat was given in [11] as 644 J/kg◦C ( based on fully configured servers). A broader interval of the specific heat for a server ranging between 400 J/kg◦C to 800 J/kg◦C was stated in [9]. The adopted value for this thesis was cp,s = 460 J/kg◦C. Furthermore, an assumed value of the server rack specific heat of cp,R = 500 J/kg◦C was provided in [9] which was adopted in this thesis in the simulations where needed.
Several different server models has been evaluated experimentally by various research groups to determine the thermal effectiveness, . A correlation between thermal effectiveness and server mass per U, (called ρ0), was adopted from [11] as
= 1 − 13ρ0−1.87. (29)
Experimental measurements was performed on server hardware in the work of [10] where the thermal effectiveness was correlated to the server’s mass density. The technical specifications did not include the volume of a OCP server so the the former correlation based on the server height in U was used to obtain the thermal effectiveness. It was suggested that would be unaffected when expanding from a single server to several servers mounted in a rack [9].
The critical server CPU temperature, was discussed in section 2.1. The level of detail of the server model used in the present study calculated the average server temperature, Ts, assuming that a server can be modeled as a lumped system. In reality, the CPU temperature would be somewhat higher than the average temperature of the server. Here, the CPU temperature was assumed to be 15◦C higher than the average server temperature Ts. To include an extra layer of operational security, it was assumed that the CPU temperature should not exceed 75◦C (10◦C lower than the value stated in the technical specification, see 2.1).
4.2 Details on the chimney model
The chimney model was developed by implementing the theoretical equations governing heat loss through a pipe wall described in section 3.3. By calculating the heat loss through the chimney wall, the chimney outlet temperature was obtained and hence, the arithmetical average chimney temperature Ti,avg, was calculated and provided as an input to the analytical mass flow rate relation. The chimney was divided into three sections, see figure 6 where the outlet temperature from one section was fed as an input to the oncoming section. Besides this, the air mass flow and outdoor temperature T∞ was required as input. Three sections was assumed to provide sufficient level of accuracy yet keep simulation time short.
Figure 6. Overview of the chimney model where all three vertical sections had the same heat loss equations implemented.
Air flowing in a vertical pipe will gradually loose heat through the chimney walls if the temperature of the wall surface is lower than the air flow as depicted in figure 5. The heat loss through the
chimney wall depend on the material constants and thickness. A layer with no significant thermal resistance in contact with the air flow will not affect the heat loss through the pipe wall. A vertical pipe constructed of a galvanized steel may be neglected in the heat loss calculations as the pipe thickness L is small and the thermal conductivity is big causing a very low temperature drop across the material.
To reduce the heat loss from the air flow inside the pipe, mineral wool was used in [28] as the insulating material around a galvanized steel pipe. The galvanized steel pipe was neglected in the this paper for thermal analysis considerations, as it only slightly would increase the thermal mass of the chimney. The thermal conductivity of the insulating material was set to kw= 0.05 W/mK with a corresponding cp,w= 800 J/kg◦C and ρ = 15 kg/m3 [22].
The heat transfer coefficient between air flowing inside a pipe and the pipe wall can be estimated using empirical relations that depends on the temperature of the fluid and the fluid’s flow velocity.
The heat transfer coefficient is related to the dimensionless Nusselt Number which in turn have empirical correlations. The empirical correlations was implemented in the chimney model to obtain the Nusselt number and finally also the heat transfer coefficient. The heat transfer coefficient between outdoor ambient air and the surface of the vertical duct was assumed to only depend on natural convection.
4.3 Complete model
When the server model, chimney model and analytical mass flow rate relation was connected to each other, the model was called complete model. For each time step in a simulation with the complete model, the server model calculated the air temperature flowing out of the server, Ts,o
which was fed to the chimney model as an input, see figure 7. Here, the assumption of no heat loss between server exhaust and chimney inlet implied that Ts,o= Ta,in. The chimney model calculated the average air temperature inside the chimney Ti,avg, which in turn was fed to the analytical mass flow rate relation. In this part, the mass flow rate induced through the system was calculated.
The system was assumed not to have any leakages and hence, the air flow rate out of the chimney was equal to the air flow at the server inlet. The calculated mass flow rate was therefore fed back to the server model as an input. The mass flow rate was also fed back to the chimney model as it was needed in the calculations of heat loss.
Figure 7. The server and chimney model together with the analytical mass flow rate relation and how they were connected to each other in Simulink.
Steady state was reached in the simulation when the temperatures and air flow rate did not change with time.
4.4 MATLAB - Simulink
RSimulink is a add-on to the software program MATLAB. The model was built in this environment because of the user friendly interface and its great possibilities to solve differential equations such as equation 6. Simulink provides a number of different algorithms to solve differential equations and the possibility to chose fixed or variable-step size for the simulation time. The detailed description on how the Simulink software works was beyond the scope of this thesis but more information can be found in the Simulink reference documentation.
Throughout all simulations, the automatic solver selection setting was chosen combined with vari- able time step. The integrator block from the Simulink Library was used for solving differential equations. The block requires an initial condition where the simulation starts, in all instances, as a temperature property. The initial condition temperatures were chosen to reasonable temperatures which did not interfere with the direction of heat flow. For example, the initial temperature at the inner surface was higher than the initial temperature on the outside surface of the chimney.
4.5 Model validation
4.5.1 Server model
Before combining and connecting the models developed in this study, some tests and comparisons was performed with results found in literature. The behavior of the server model was compared with the work of [10] and [11] where the inlet and outlet temperatures of a server were studied as a function of time with no internal heat generation in the server. To simulate a similar test in the present study, Ts,i was configured as a ramp function, both as linearly increasing and decreasing.
The behavior of the exhaust air temperature Ts,o as a function of time was monitored to validate the server model. Equation 6 was implemented in Simulink for simulations with ˙qs = 0 and a constant mass flow rate of 30 CFM, see figure 8. With Tsknown, equation 5 was used to calculate the exhaust air temperature.
Figure 8. The server model implemented in Simulink. Notice how the average server temperature Ts ultimately was fed back to the start of the equation.
Another experimental test was performed on a server which was contained in a wind tunnel by VanGilder, Healey, Pardey, et al. Here, the server power was held constant at ˙qs = 103 W and an electrical heater was turned on to increase the temperature of the inlet air to the server. The exhaust air temperature was studied as the inlet temperature was approximately linearly increased from 22.5◦C to 40◦C during 100 seconds [24]. A similar server power and ramp function on the inlet air temperature was configured to the server model. The air flow rate was set to 36 CFM and = 0.8 in accordance with the aforementioned paper.
4.5.2 Analytical mass flow rate relation
The derived relation stated in 16, called analytical mass flow rate relation, was compared to results presented in two separate papers.
A first comparison was made to the results from a performed study by Rahimi and Bayat, on a vertical duct where temperatures and velocities were measured within the pipe [28]. The chimney height was varied between 1 m and 5 m, with increments of 1 m, according to what was tested experimentally in the paper. T∞ and Ti,avg was set according to the data given in the paper for each height of the chimney. The analytical mass flow rate relation stated in equation 16 was implemented in a Matlab-script where constants was configured in accordance with the values given in the paper at each chimney height.
Natural draft in a chimney was studied in the work of Maia, Ferreira, Valle, et al. where experi- mental measurements was performed on a 12.3 m high, 1.0 m diameter wide prototype chimney.
The measured data for temperatures and velocities was used to validate their theoretical model.
The temperature, mass flow rate and velocities inside the tower was studied when varying both tower height and tower radius. The ambient temperature around the chimney was 303 K [32].
The paper did not give values for the friction factor λ or the loss coefficient ξin at the entrance.
Values was found for a large scale solar collector chimney of 10 m diameter given as λ = 0.00842 and ξ = 0.056 [27]. The magnitude of the entrance loss coefficient is correlated to the ratio of how rounded the pipe entrance is to the diameter of the pipe where a squared edge inlet corresponds to an entrance loss coefficient of 0.5 [33]. The adopted values were ξin= 0.1 and λ = 0.005. The analytical mass flow rate relation was compared to the results presented in [32] by a Matlab-script where equation 16 was implemented.
4.6 Required dimension - static case
Consider a static case where the server inlet temperature was provided and set to constant 20◦C.
The exhaust temperature was assumed to be maintained below 40◦C to ensure that the CPU tem- perature does not exceed the critical temperature. For the static case, ∆T = 20◦C was obtained.
For any given power supplied to a server, the required mass flow rate ˙m was analytically obtained by rearranging equation 2. What are the chimney dimensions that would theoretically provide sufficient air flow rates to cover the cooling of the servers?
A chimney was considered fully exposed to a constant outdoor temperature of 1◦C (approximately the yearly average temperature in Lule˚a, Sweden) [34]. For this case, the chimney was assumed as to be well insulated which implied no heat loss through chimney walls. By this assumption, Ts,o = Ti,avg. These assumptions introduced the opportunity to solve which chimney dimensions would suffice to cover the required air mass flow rate. Mathematically, this corresponded to set the rearranged equation 2 equal to equation 16. Constants was set to λ = 0.0365, Σξ = 13. The server power was increased up to 24 kW and chimney heights up to 76 m was considered. Furthermore, chimney radii was considered between 0.2 - 0.4 m.
As mentioned in section 2.1, the server contribute to the system pressure drop which depend on the air flow and thus, another pressure loss term was added to equation 11. Effectively, this contributed to an increased value for Σ ξ and thus decreased the induced air flow rate, see equation 14.
4.7 Simulations
4.7.1 Complete model simulation
Because of the detailed data presented by Rahimi and Bayat, simulations with the complete model was performed with these given parameters and dimensions. The chimney height was varied between 1 m and 5 m and the server power was held constant at ˙qs = 400 W, similar to the conditions in [28]. Here, the simulations was performed with the complete model consisting of the server model connected to the chimney model which in turn was connected to the analytical mass flow rate relation.
A sensitivity analysis on the impact of the constant Σξ was performed. This was done since the contribution from a server, to the total pressure loss coefficient was estimated based the values on pressure drop from the technical specifications [18] which only allowed rough calculations for the pressure loss coefficient. Subsequent simulations adopted the value on the pressure loss coefficient based on the results on this simulation.
4.7.2 Chimney height
As seen in equation 16, the mass flow is dependent on both the chimney height and diameter.
Simulation A1 was performed where the effect of increased height was investigated. The ambient temperature, and chimney radius was held constant at T∞= 17◦C and rc= 0.05 m, respectively.
The ambient temperature around the chimney was kept at 17◦C so that the start of the simulations emanated from previous results and then expanded. Furthermore, for the geographical location of Lule˚a, this ambient temperature almost correspond to a worst case scenario since only a small fraction of the hours of a year has higher temperatures in combination with the fact that low ambient temperatures provide better draft according to the analytical mass flow rate relation, see
equation 16.
Server power was held constant at ˙qs= 400 W during a simulation until steady state was reached.
The chimney wall thickness was set to L = 0.025 m. Temperatures and air mass flow rate was extracted from the simulation model. The chimney’s height was incremented, before another simulation run was started. The purpose of these simulations was to see if the theoretical mass flow of air would increase unhindered along with increased chimney height given a fixed radius and server power usage.
Simulations was expanded to also include changes of chimney radius as stated in table 2 for simulation A2. The simulation model was investigated for a range of radii between rc = 0.05 m and rc = 0.15 m.
4.7.3 Increased server power
In reference to the simulation plan in table 2, simulation B and C was considered here. The range of power usage corresponded to turning on servers sequentially so that during a simulation, one server to a full rack of servers was simulated.
Simulation B was performed with a chimney radius of 0.05 m and simulation C was performed with a chimney radius of 0.5 m. The height was held constant in both simulation B and simulation C. The purpose was to test the robustness of the model when subjected to deviances of server powers in combination with both small and large chimney diameters. The chimney wall thickness was in both simulation B and C set to L = 0.025 m. Values for mass flow and temperature were extracted at steady state.
4.7.4 Transient simulation
Four server racks populated with 160 Windmill-servers was considered in Simulation D, where the transient behavior of temperature and mass flow was investigated. Here, the servers was set to first draw 150 W and then 200 W. cp,tot was calculated according to equation 28 (the mass of four racks was adjusted for). The weight of one server together with the height of the server corresponded to = 0.65 according to equation 29. The inlet temperature to the servers was set to 20◦C, which is commonly found in todays DCs. The simulation time was set to eight hours where an instantaneous increase in power consumption was implemented through a step function in Simulink and set to occur at four hours. The thickness of the chimney wall was set to L = 0.1 m.
The magnitude of the mass flow rate was compared to the required air flow which was assumed to be 25 CFM per server. Chimney height and radius was kept constant. The chimney dimensions was set to 0.4 m radius and a height of 30 m.
4.7.5 Effect of outdoor temperature
As indicated in table 2, the ambient temperature was varied in simulation E. T∞was varied between
−20◦C and 20◦C. The purpose was to study how variations of outdoor temperature affected the mass flow rate and server temperature for a given chimney size. The server power was held constant at 24 kW which corresponded to 160 servers each consuming 150 W. The chimney height was set to 30 m with 0.4 m radius. Here, the chimney wall thickness was set to L = 0.1 m.
4.7.6 Energy reductions
Servers in data centers operate continuously, regardless of time at day or time of year so the cooling need is constant. Direct energy savings due to decreased use of internal fan usage was studied.
As a base for these calculations, previous experimental measurements performed by staff at RISE SICS North showed that the total power consumption for the internal fans use about 250 W for one server rack (assumed 2.5 W for each fan where two servers share five fans). Four racks populated with 40 servers each, hence consume 1000 W of power continuously and assumed sufficient for keeping the CPU temperature on a safe operational level.
