CHIMNEY EFFECT IN DATA CENTERS - DiVA portal1113628/... · 2017. 6. 22. · Nair at Ume a University brought many insightful thoughts and good guidance throughout the work and for

Masters Thesis – Degree Project in Energy Engineering, 30 hp

Master of Science Programme in Energy Engineering, 300 hp

Spring term 2017

CHIMNEY EFFECT IN

DATA CENTERS

On the possibility to achieve natural draft through servers

Sebastian Fredriksson

EN1739

AcknowledgementsThis thesis was completed during the spring term of 2017 as the final degree project course in theMaster of Science Programme in Energy Engineering at Ume̊a University. I would like to expressmy gratitude to the people that supported me in completing this thesis. My supervisor GireeshNair at Ume̊a University brought many insightful thoughts and good guidance throughout the workand for that I am thankful and direct much appreciation. Many thanks goes to my supervisors atRISE SICS North, Jonas Gustafsson and Tor Björn Minde for their support and guidance.

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AbstractData centers has in recent years experienced a rapid growth in numbers and size. Essentially, datacenters are facilities housing IT equipment such as servers, switches and other network deviceswhich use large amounts of electrical energy. Electrical energy is converted to heat by the dataprocessing 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 airas it flows through the server. Free cooling utilizes the cold outside air to avoid the use of chillers ascold source and therefore reduce energy consumption significantly. However, some facility energyand ventilation fan energy is still required to move the air. In addition, each server is commonlyequipped with several small fans to move air through the server to keep CPU temperature at asafe operational level.

The purpose of this paper was to study if fan energy consumption can be decreased due to aninnovative server room layout. The idea was to connect a chimney to the backside of a server rackand route the air through the chimney and out to the ambient. The purpose of the chimney wasto allow the heated exhaust air to rise upwards, due to buoyancy forces, and through this obtainnatural draft through the servers. The induced air flow could potentially replace internal fans formoving the air through the servers and thus, reduce energy consumption. A mathematical modelwas developed and implemented in Simulink where simulations was performed on the system. Theeffect on temperatures and air flow in the system was studied by several simulations as differentinput 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 wheregood agreement was found. The complete model was assessed to be able to provide estimationson temperature and air flow to fulfill the general goal of the paper. The results showed reasonablevalues in most of the simulated cases despite lack of research to compare with. It could be concludedthat 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 160servers where each server was assumed to consume 150 W. The induced flow from the chimneywould be sufficient to replace all the internal fans based on climate data from Lule̊a, Sweden.The simulations provided interesting and promising results on the studied system. To furtherstrengthen the findings, experimental measurements could be performed on small scale with realserver hardware. The model could then be tested and compared to experimental values as theinnovative configuration implied limited research similar to the system studied in the presentpaper.

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SammanfattningUnder de senaste åren har data center-sektorn haft en snabb tillväxttakt, b̊ade gällande antaloch storlek. Ett data center är väsentligen en annläggning som inrymmer IT utrustning s̊asomservrar, switchar och annan nätverksutrustning. Servrar kräver kylning eftersom de omvandlarelektrisk energi till värme i samband med att de utför beräkningar. Vanligen används luft somkylmedium i stora traditionella data center. När luft strömmar genom servrarna, överg̊ar värmenfr̊an komponterna till luften. Genom att använda kall utomhusluft kan energiförbrukningen i ettdata center kraftigt reduceras. Detta kallas frikyla och innebär att användningen av kylmaskinerkan undvikas. Även om frikyla används, krävs det änd̊a energi för att driva ventilationens fläktaroch anläggningen i övrigt. Förutom stora fläktar tillhörande ventilationen sitter det även ettflertal sm̊a fläktar i varje server för att flytta luften genom servern. Dessa fläktar säkerställer ettbra luftflöde genom varje server s̊a att dess CPU-temperatur h̊alls p̊a en säker niv̊a under drift.

Syftet med detta arbete var att undersöka om energianvändningen fr̊an fläktar kan minska genomen innovativ placering av servrarna. Den huvudsakliga idén var att ansluta en skorsten till baksidanservrarna för att p̊a s̊a vis leda den varma luften genom skorstenen och ut. Syftet med skorstenenvar att l̊ata den varma luften att stiga upp̊at p̊a grund av densitetsskillnader mellan luft i skorstenenoch omgivningens luft. P̊a s̊a sätt finns möjligheten till att självdrag skulle kunna uppst̊a someventuellt skulle kunna ersätta de sm̊a fläktarna monterade i varje server och därmed leda tillminskad energianvändning. En matematisk modell utvecklades och implementerades i Simulinkdär simuleringar utfördes p̊a det tänkta systemet. Temperaturer och luftflöde utvärderades utifr̊anen mängd olika simuleringar där parametrar s̊asom skorstensdimension, utomhustemperatur ocheffektförbrukning hos servrarna ändrades.

Separata delar av modellen validerades mot litteraturen där modellen stämde väl överens medpresenterade resultat. Det bedömdes att den kompletta modellen kunde estimera temperaturer ochluftflöden för att tillförlitligt kunna besvara denna studies fr̊ageställningar. Resultaten fr̊an de flestasimuleringarna visade p̊a rimliga värden trots brist p̊a artiklar att jämföra med. Utifr̊an resultatenkunde det konstateras att l̊ag utomhustemperatur medförde större luftflöden i systemet och därmedocks̊a bättre kylning av servrarna. En 20 m hög skorsten med 0.4 m radie beräknades kunna täckahela kylbehovet för 160 servrar där varje server antogs förbruka 150 W. Det självdrag som uppstodfr̊an skorstenen var tillräckligt för att ersätta alla sm̊a serverfläktar baserat p̊a klimatet för Lule̊a.Simuleringarna visade p̊a intressanta och lovande resultat för det studerade systemet. Resultatensvärde och tillförlitlighet skulle kunna förstärkas genom att utföra experimentalla mätningar i ensm̊askalig försöksuppställning där riktiga servrar används. Modellen skulle d̊a kunna vidare testasoch jämföras mot experimentella mätresultat d̊a den innovativa idén medför att forskningen ännuär begränsad inom detta specifika omr̊ade som detta arbete behandlade.

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Contents

1 Introduction 1

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

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5 Results 19

5.1 Server model validation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

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

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Nomenclature

q̇s Rate of server power [W]

� 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]

FACe 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]

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Ume̊a UniversityDegree Project in Energy Engineering Sebastian Fredriksson

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 thantoday 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 electricityconsumption related to Information and Communications Technology (ICT) equipment [1]. One ofthe 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 serversand switches [3]. Data centers are used by industries and society where large data processing isrequired for sectors such as banking, telecommunications, stock market, search engines and socialnetworks [3].

Data centers use large amount of electrical energy in data processing units and therefore, contributeto global warming through emission of green house gases and air pollution in fossil fuel basedelectrical power production. Statistics reported in 2014 showed that data centers in the US wasresponsible for more than 2 % of the country’s total electricity consumption. Furthermore, theshare of the power consumption by data centers are expected to increase for the foreseeable futuredriven 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 paperwhere estimations showed an energy use of 325 TWh in 2013 [5]. In 2030, the energy demandwas predicted to increase to 1100 TWh for the best case scenario and close to 2900 TWh for theexpected scenario [5].

As depicted by Ebrahimi, Jones, and Fleischer, the server is considered to be the smallest dataprocessing unit in a DC. Several servers are typically aligned horizontally in a standardized metalframe enclosure called server rack. A modern data center have several racks arranged next to eachother forming lines with every other row facing opposite directions. Cold air is supplied to thefront of the servers, by the computer room air conditioning (CRAC) unit, and forced to movethrough the racks by internal fans on servers. The IT related equipment in a data center are themain source of heat production. Electrical power for data processing is converted to heat which isdissipated and transferred to the the air [4].

DCs have high demands on continuous operation and availability at all times which require thermalmanagement systems to maintain the temperature of the sensitive electronics components at a safelevel [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 areused by traditional cooling systems due to work done by fans and pumps to transport cold wateror air [6]. This provide strong incentives to conduct research associated to overhead infrastructureof a DC. Air movement for cooling are provided by large ventilation fans, fans integrated in theCRAC units and small internal fans mounted on the server. The work of this project aimed toinvestigate if energy consumption of the internal fans can be decreased. The main idea was tostudy if a vertical duct connected to server racks could serve as a chimney and induce naturaldraft 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 systemsof 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 passand recirculation of air are two major challenges in the air management system. The formerproblem occurs due to excessive flow rates or leaks through cable cutouts and the latter ariseswhen cold air intake to the IT equipment is not sufficient and a fraction of the hot return air flowsthrough the server causing raised inlet temperatures [8].

A comprehensive review on free cooling of data centers was conducted by Zhang, Shao, Xu, etal. Here, the strategies of utilizing cold outdoor air in the cooling of a DC was explained. Free

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air-side cooling can significantly reduce energy consumption related to cooling in comparison toa traditional DC since the use of chillers and cooling towers are avoided [6]. As described byCapozzoli and Primiceri, air-side free cooling (also called economizer mode) can be both directand indirect where the former blows outdoor air directly into the server room and the latteruse air-to-air heat exchanger to cool the server room air. The strategy of utilizing free air-sidecooling avoids any particulate or gaseous contamination which may be harmful to the sensitive ITequipment. Furthermore, the geographical location of a DC utilizing economizer mode becomes oflarge importance [2].

The work of VanGilder, Pardey, Healey, et al. proposed a compact server model for server andrack level simulations to capture the thermal mass effects from server hardware. CFD simulationstypically ignores these effects and therefore, are overly conservative when estimating transientscenarios such as a sudden unexpected loss of cooling. The developed compact server modelcalculates server air exhaust temperatures based on rate of internal IT power consumption andserver inlet air temperature and requires the mass and specific heat of the server as input [9]. Themodel has been experimentally validated and further developed with independent measurementson several different server hardware [10], [11].

The demand for data processing and storage is predicted to increase in the future with a growingdemand for data centers. On a global scale, ICT has a carbon footprint but also provides aplatform in which a number of sectors may decrease their footprint. The ICT sector has a footprintcorresponding 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 Scandinaviawhen higher demands for sustainability of new data centers are to be met. The circumstances ofthe northern part of Sweden are unique with regards to sustainable electrical energy productionwith low energy costs, political stability in a low mean temperature region providing energy- andenvironmental saving opportunities [13].

There are substantial economic values due to the data center business in Sweden. The BostonConsulting Group estimated in their report that the Swedish data center industry in 2015 generatedupward 13 billion SEK in full economic impact for construction and operation and predicts thatSweden has the potential of increasing this number to 50 billion SEK by 2025 [14]. There are strongincentives to locate data center in the northern part of Sweden. The net energy consumption cansignificantly be reduced if new data centers are located in a region with colder climate with theadvantage of free cooling possibilities.

As described above, there are many studies which aim to increase energy efficiency of data centersand decrease energy usage. However, most of them investigate different air flow managementschedules based on the somewhat static template with server rack rows separating hot and coldair aisles. Efforts in reducing energy in data centers are important from both environmental andeconomical perspectives when todays hyper scale data centers may consume over 100 MW wherecooling related energy contributions are always present.

1.1 Scope of this paperThe work of this paper aimed to study if fan energy usage could be decreased by an innovativeconfiguration in a server room or data center. The main idea was to route the air exiting at theback of a server to a vertical duct. The purpose of the duct was to act as a chimney allowing thehot air, by buoyancy forces, to rise and disseminate to the outdoor atmosphere. Natural draft airflows may potentially arise from this system configuration and thus decrease fan energy demandto 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, serverpower and outdoor temperature affect the air flow in the system? Is it possible to reduce fan

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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 physicalrelations that dictates the heat transfer and air flow in the system. The model of the setup shouldbe 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 temperatureswas studied when the dimensions of the chimney changed. The possible energy reductions due toinduced air flow by the chimney was finally estimated.

A server room utilizing free air-side cooling was considered as the hypothetical system. Theconsidered 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 assumptionsThe work of this study focused on calculating the induced air flow in the vertical duct acting asa chimney. The air inlet temperature to the servers were assumed to be the same as provided tothe existing data center (about 20◦C). In a system utilizing free air-side cooling, the temperatureprovided 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. Theintention was to conduct simulations to provide the stakeholder company RISE SICS North withestimations on the potential of obtaining natural draft. Hence, the system boundary was limitedto server racks, servers and the connected chimney. The boundary limits can be expanded in afuture work where inlet air conditioning can be integrated.

Except for servers mounted in server racks, the server room also accommodates switchboard, fireextinguishing and humidification equipment. The server room IT equipment furthermore demandbackup power, called uninterruptible power supply (UPS), in the event of a abrupt, unexpectedpower loss. All these units and devices contribute with thermal mass to the server room but wasnot considered in this study as it is the servers and server racks that constitute the major part ofthermal mass and power consumption in a data center.

Servers accommodated in data centers demand environmental control beyond temperature. Morespecifically, 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 studyconducted 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 flowrates through the server racks and disregarded humidity and dust control for simplification. Fora study with a wider perspective on energy consumption in data centers, the energy related tohumidification of air should be included.

A chimney with a outer surface temperature higher than the surrounding surfaces will experienceheat transfer through radiation. This phenomena is affected by the emissivity of the surfaceand the surrounding surfaces’ temperature. Moreover, a chimney in a outdoor ambient climatewill be exposed to wind which enhances the heat loss. Air flow across a cylinder will introduceheat transfer due to forced convection which according to heat transfer theory influences the heattransfer coefficient. Both of these effects was omitted in this thesis as a simplification as it wouldinclude 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 datacollecting services were yet installed. However, the technical specifications from these servers wasused because of the intention of using OCP servers in a future experimental setup.

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2 System description

2.1 Open Compute Project serverThe 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 theserver 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 flowof 103 CFM [16]. The technical specifications also states that the maximum CFM is expected tobe less than 60 for almost every system loading [16]. Air flow levels of around 20-30 CFM maybe sufficient for a server with a power usage of 200 W [17]. This power usage can be consideredreasonable 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 seento 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 issufficient or not is the temperature of server components. In reality, the upper temperature limitis 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 systemregulates the fan speeds as a function of CPU temperature.

The Windmill-servers mounts in non-standard server racks called Triplet Cabinets with threecolumns hosting 40 servers in each column [16]. One server holds two CPUs with a height closeto 1.5U where 1 U = 44.5 mm (U is a industry standard measure correlated to the height of astandard 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 hastwo 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 isabout 27 W [19]. However, it is known that the power consumption is not linear when changing thefan speed. Experimental measurements was performed by staff at the stakeholder company RISE

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SICS North where the power consumption of the fan was measured at fan speeds between 1200RPM and 16500 RPM which corresponded to 10 % and 100 % duty cycle, respectively. Throughthe 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 centeroperate at or below 20 % of their capacity and rarely reach maximum at the same time as thepower drawn from the grid may reach 60 - 100 % of maximum power during idle (no load) [4]. Ameasurement 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 betweenpower 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. Atidle 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 toweigh 100 kg based on the technical specification [16].

2.2 Modeled systemIn 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 detailedview of the intended server rack layout is depicted in figure 3. The system does not include howthe inlet air temperature, Ts,i was conditioned. Furthermore, the dust control and humidificationunits would be located before the air is allowed to go through the servers but for this study, notaccounted for as a simplification. The setup shown in figure 3 show a plus-formation arrangementof the server racks. The concept of connecting a vertical chimney can also be applied to a setupwith 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 temperatureas indicated by the darker colored arrow in figure 2, flow out of the servers and into the bottomof the chimney. The temperature decrease of the air between the server outlet and the stack inletwas assumed negligible. As time progress, more and more hot air will be contained in the chimneyand start to rise due to the decreased density in comparison to the ambient air. The rate of airflow out of the chimney at the top, must be the same as the air flow rate into the servers due tothe 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 bythe vertical gradient filled arrow in figure 2, due to a lower ambient temperature surrounding thechimney. This temperature decrease was caused by heat transfer through the chimney wall andindicated as a black curved arrow.

The server racks could be arranged in a plus-formation where the backside of the four racks facedeach other leaving an empty space in the middle, see figure 3. The heated air from all the serverswould meet in the middle where a vertical duct could be connected allowing the air to rise anddisseminate to the outdoor.

2.3 PUE as an energy metricEnergy usage in a DC can be divided into categories where IT equipment energy constitute a largepercentage. Lighting, battery management systems, security and other miscellaneous subsystems

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is commonly included in the facility energy [6]. Cooling related energy include ventilation fan andpump energy and can also be added to the facility energy category. Within the sector, different DCfacilities are assessed and compared through different metrics. Power Usage Effectiveness (PUE)has become the industry standard metric and defined as

PUE =Total facility energy

IT energy

where the numerator consist of all purchased energy to the facility i.e., the sum of IT equipmentenergy and other facility related energy [20]. The IT equipment energy is present both in numeratorand denominator and defined as the electrical energy usage of servers, switches or other deviceslocated in server racks. The PUE metric can be useful as it presents the proportion of energyactually used to operate the IT equipment with respect to the total energy usage of a DC. The ITequipment is the core service of a DC whereas all the other subsystems exists to support a reliableand safe operation.

PUE as an energy efficiency metric has been criticized due to the large amount of data required tocalculate 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 DCwhich have fans in the ventilation system. Traditionally, the IT equipment energy include allenergy 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 andof low efficiency. As per the traditional definition of PUE, the value would decrease and implybetter energy efficiency if air movement was shifted from larger ventilation fans to the internalfans on servers. The PUE value would decrease even though the total energy consumption wouldincrease.

A simple example can illustrate the weakness to the traditional PUE metric, where no separationof 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. Accordingto the definition, the PUE value becomes 1.1. Internal server fan energy constitute about 5 % ofthe IT equipment energy. A modified PUE (called SPUE) was derived where internal server fanswas separated from other server IT. SPUE can be calculated as

SPUE =ITe,o + Face + SFe

ITe,o

where ITe,o denotes IT energy without internal fans, Face denotes facility energy and SFe denotesinternal server fan energy. The numerator is the total facility energy where the sum of ITe,o andSFe is the IT energy also found in the PUE equation. As presented in table 1, if a DC changesfrom calculating PUE to SPUE without any other energy reduction measures taken, the valueincreases.

Table 1. The effect on PUE and SPUE values when reducing fan power usage in a exemplified DCutilizing free air-side cooling.

Fan reduction PUE SPUE Total power

0 % 1.1 1.157 1.150 % 1.102 1.131 1.0780 % 1.104 1.115 1.06100 % 1.105 1.105 1.05

Based on the example, the values in table 1 show a weakness in the industry standard PUE metricwhere a decrease in total energy consumption naturally is desirable but affects the traditional PUE

6


value negatively. Moreover, even for the case of no actual energy saving measure taken, a transitionto SPUE would naturally meet resistance as a increased PUE value impair the DC energy efficiencyand hence, the technical ”status” of the facility in comparison to others. Separating the internalfan 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 sectiondescribe the heat transfer within the servers. The second section described how the calculation ofair mass flow rate was derived. In the last section, the theory of heat transfer through the chimneywall was explained.

3.1 Compact server modelA loss of cooling or varied server loads are examples of transient events that can occur in datacenters. The thermal mass of the servers populating a DC highly contribute to the transientscenarios. Computational Fluid Dynamics (CFD) is widely used to model steady state conditionsof DC facilities but concluded impractical to catch the behavior of such transient events [11]. Acompact server model was proposed to capture the effects of thermal mass without the need forproviding explicit details of all server component [21]. The theory proposed for the concept ofcompact server model was adopted from [11] and described below.

The physical nature of real server hardware are complex but can be approximated as a lumpedthermal capacity model under the assumption that spatially temperature variations within thebody are neglected. The criteria for lumped system analysis is related to the dimensionless Biotnumber (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 transfercoefficient [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 qlc is the rate of internal heat generation, m is the mass of the solid, c is the specific heat anddT is the difference in temperature during the time dt. The temperature of the solid will continueto rise according to equation 1 if no external cooling is available [23]. Heat can continuously betransfered from a body to a fluid (that does not undergo any phase change) which will result in aincrease in the coolant temperature from inlet to outlet. This can be described as

qfr = ṁcp(T2 − T1) (2)

where qfr denotes flow resistance, ṁ 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 − qfr (3)

where qgen is the rate of internal heat generation and qfr 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 massand specific heat of the body.

Consider model of a server as in figure 4, where air flows through and increases in temperature

7


from inlet to exhaust with a mass flow rate ṁ. All sides of the server are assumed to be perfectlyinsulated 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 serverhardware 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 canbe written as

q̇s = mscp,sdTsdt

+ ṁcp,air(Ts,o − Ts,i) (4)

where Ts denotes the average server temperature, q̇s is the rate of electrical power that is consumedby the server equipment and ms is the mass of the server. In accordance with the proposed modeldeveloped in [11] and [24], the variable � is introduced and defined as

� ≡ q̇sq̇max

=ṁcp(Ts.o − Ts,i)ṁcp(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, q̇s to themaximum possible rate of heat transfer from the server to the air, q̇max. � may take valuesbetween 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 isobtained as

mscp,sdTsdt

= q̇s − ṁcp,air�(Ts − Ts,i). (6)

3.2 Induced air flow in vertical round ductMuch 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 theapplication of a vertical duct intended in this thesis. The scale of large solar chimney power plantsconsidered in case studies modeled by various research groups, reach heights of several hundredmeters, diameters between 40-80 meters and solar collector radii up to 2 km [25]. Since the scaleof 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 describedin [26] and [27]. Air situated in the solar collector area is heated by the solar radiation and movetowards the center of the collector, where the chimney is located, due to its decrease in density. Hotair in the chimney rise as it has lower density than the ambient air. As the hot air disseminates tothe atmosphere at the chimney outlet, ambient air enters at the collector perimeter. A continuousair flow is attained through the collector and the chimney. A solar chimney power plant hoststurbine connected to a generator in the lower part of the chimney. A considerable pressure drop

8


occurs when air flows across the turbine where kinetic energy of the hot air flow is converted intopower.

For the application in this thesis, the thermal engine is provided by electricity used in servers whichis converted to heat of in the server component. A mathematical expression estimating the massflow rate of air in a vertical duct due to the natural draft effect was derived. The model originatesfrom 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 intendedapplication.

The pressure difference between the chimney and the ambient air can be expressed as

∆p = g

∫ H0

(ρ∞(h)− ρ(h)

)dh (7)

where g is the gravitational acceleration, H is the total chimney height and ρ∞ is the density ofthe ambient air at elevation h [27]. Pressure and temperature vary with elevation but in modestranges, the effect can be neglected. The temperature drop with elevation inside the chimney canbe 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. Withthe density at some reference temperature known, air density at any temperature can be expressedin terms of the reference case, i.e air density at 0◦C is 1.293 kg/m3, the density at any othertemperature can be expressed as

ρair = 1.293 ·p

1· 273T' 1.293 · 273

T. (9)

Note that the density of a gas depends on both pressure and temperature according to the idealgas law. However, a 250 Pa pressure increase only affects the density 0.25 %. A temperaturedecrease of 10◦C gives a density decrease of 3.5 %. Density can be assumed to only change withtemperature as equation 9 suggests. The density in equation 8 can be replaced by temperatureusing the same analogy to obtain

∆p = gρ(Ti,avg − T∞

T∞

)H (10)

where Ti,avg denotes the average temperature of the air inside the chimney and T∞ denotes theair temperature of the surroundings. The pressure difference of the air inside the pipe and theoutdoor ambient air must overcome the pressure losses in the pipe. The pressure losses is the sumof 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 theentrance pressure loss and ∆pout is the exit pressure loss [27]. Equation 11 can be rewritten as

9


∆ploss = λH

D· ρV

2

2+ Σ ξ · ρV

2

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

gρ(Ti,avg − T∞

T∞

)H =

λH

D· ρV

2

2+ Σ ξ · ρV

2

2. (13)

Rearranging equation 13 allowed the average velocity of the air inside the chimney to be expressedas

V =

√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 isdirectly discharged to the ambient [28].

A fluid flowing in a pipe of average velocity V is related to the flow rate according to

ṁ = ρAV (15)

where A is the cross sectional area of the pipe. Hence, the mass flow rate can be expressed as

ṁ = ρA

√2gH

λHD + Σ ξ· Ti,avg − T∞

T∞. (16)

3.3 Heat transfer in a round ductA hot fluid flowing in a pipe will decrease in temperature along the pipe if the inner surface of thepipe is colder than the fluid. The pipe may be divided into a number of smaller sections along thepipe for improved accuracy. The pipe itself can involve heat transfer resistance depending on theinsulation abilities, i.e the pipe material characteristics. Consider air flowing at a steady state ina 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 withtheory 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 floware considered. Moreover, a homogeneous wall surface temperature was employed in each sectionof the pipe (both inside and outside wall). Average temperature of a pipe section was calculatedas 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 walljustified by a small ratio of pipe wall thickness to pipe diameter.

10


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,airdToutdt

= ṁacp,air(Ta,in − Ta,out)− hinAin(Ta,in + Ta,out

2− Tc,is

)(17)

where hin is the heat transfer coefficient between the air and the inside pipe wall, Ain is the insidesurface area of the pipe wall and Tc,is denotes the temperature of the chimney’s inside surface [30].The above equation can also be written as

qlc = qfr − qcv,in (18)

where the index lc, fr and cv, in denotes lumped capacity, flow resistance and convection on theinside wall, respectively. Moving the control volume to the pipe wall, the energy balance requiresthat

qlc = qcv,in − qcd (19)

where the subscript cd denotes conduction in the pipe wall. This can also be written as

mwcp,wdTc,isdt

= hinAin

(Ta,in + Ta,out

2− Tc,is

)− kwA

L(Tc,is − Tc,os). (20)

where kw is 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 movedoutwards 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 thesame analogy as above, this can be written as

mwcp,wdTc,osdt

=kwA

L(Tc,is − Tc,os)− houtAout(Tc,os − T∞) (22)

11


where hout denotes the heat transfer coefficient between the pipe outside surface and the ambientair. The differential equations stated in equations 17, 20 and 22 can be implemented in eachvertical section of the pipe.

The heat transfer coefficient, hin, between the inside surface of a pipe and a fluid flowing in a pipeis 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 empiricalrelation 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 transfercoefficient 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 servermodel which calculated the server exhaust temperature based on the server power usage, air flowand inlet air temperature; 2. the chimney model that accounted for heat loss through the pipewalls and calculated the chimney outlet and average temperature and 3. the analytical mass flowrate relation which calculated the mass flow rate in the system. The three separate parts of themodel emerged from the development process. Each part of the model originated from separatetheories and applications and was for this reason developed separately. This allowed the modelsto 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. Furtherinformation about the complete model and how they were connected to each other is described insection 4.3. Details regarding the simulation software is stated in section 4.4. The server modeland the analytical mass flow rate relation was tested and validated separately against results foundin literature. Details regarding the experiments found in literature are presented section 4.5.

12


Only few papers was found in literature with experimental or modeled results of air flow ratesdue to natural draft in a vertical pipe acting as a chimney. Hence, the complete model wasfirstly tested under similar conditions (such as chimney dimensions and other constants) as thosepresented in literature, see section 4.7.1. As seen in section 3, a number of parameters dictate andinfluence the behavior of a complete system. The complete model was simulated with differentparameters changed one at a time, see table 2. Details about the simulations of the simulation planis described in 4.7. A final set of simulations was performed beyond simulation E, where energyreduction 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 chimneyradius and study the behavior of the system. Simulations B and C expanded the scale to include oneserver rack populated with servers and thereafter, perform simulations D and E which correspondto 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 17A2 400 0.05 to 0.15 2 to 60 17B 150 to 6000 0.05 20 17C 150 to 6000 0.5 20 17D 24000 to 32000* 0.4 30 17E 24000 0.4 30 -20 to 20

Simulation D indicated with * represents an instant increase in server power usage where thesimulation results was studied as function of simulation time.

4.1 Details on the server modelBy 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 experimentalmeasurements 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 bytemperature measurements. The compact server model approach was implemented in this studyfor 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 hardwaresurfaces and the air flow.

The thermal mass of a server, denoted Cs, can be determined by a experimental measurementmethod 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 pressureloss. However, the specific heat or weight of the server was not included since the weight of theserver 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 withseveral servers can be simulated. According to [9], the total mass of the server rack cabinets willcontribute to the total thermal mass, which is the product of mass and specific heat capacity. Thecontribution of the server rack is accounted for in the calculation of the total specific heat

cp,tot =1

mtot

n∑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 theserver’s mass and the mass of the server rack cabinet. Some references to a reasonable value for the

13


specific heat of a server cp,s, was found in the literature as technical specifications rarely includeinformation about this value. As stated in [31], the server can be approximated to be composedof 50 % copper and 50 % steel with an average specific heat of 438 J/kg◦C and an average densityof 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 fora server ranging between 400 J/kg◦C to 800 J/kg◦C was stated in [9]. The adopted value for thisthesis was cp,s = 460 J/kg

◦C. Furthermore, an assumed value of the server rack specific heat ofcp,R = 500 J/kg

◦C was provided in [9] which was adopted in this thesis in the simulations whereneeded.

Several different server models has been evaluated experimentally by various research groups todetermine the thermal effectiveness, �. A correlation between thermal effectiveness and server massper U, (called ρ′), was adopted from [11] as

� = 1− 13ρ′−1.87. (29)

Experimental measurements was performed on server hardware in the work of [10] where thethermal effectiveness was correlated to the server’s mass density. The technical specifications didnot include the volume of a OCP server so the the former correlation based on the server height inU was used to obtain the thermal effectiveness. It was suggested that � would be unaffected whenexpanding 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 servermodel used in the present study calculated the average server temperature, Ts, assuming that aserver can be modeled as a lumped system. In reality, the CPU temperature would be somewhathigher than the average temperature of the server. Here, the CPU temperature was assumed tobe 15◦C higher than the average server temperature Ts. To include an extra layer of operationalsecurity, it was assumed that the CPU temperature should not exceed 75◦C (10◦C lower than thevalue stated in the technical specification, see 2.1).

4.2 Details on the chimney modelThe chimney model was developed by implementing the theoretical equations governing heat lossthrough a pipe wall described in section 3.3. By calculating the heat loss through the chimneywall, the chimney outlet temperature was obtained and hence, the arithmetical average chimneytemperature Ti,avg, was calculated and provided as an input to the analytical mass flow raterelation. The chimney was divided into three sections, see figure 6 where the outlet temperaturefrom one section was fed as an input to the oncoming section. Besides this, the air mass flow andoutdoor temperature T∞ was required as input. Three sections was assumed to provide sufficientlevel of accuracy yet keep simulation time short.

Figure 6. Overview of the chimney model where all three vertical sections had the same heat lossequations implemented.

Air flowing in a vertical pipe will gradually loose heat through the chimney walls if the temperatureof the wall surface is lower than the air flow as depicted in figure 5. The heat loss through the

14


chimney wall depend on the material constants and thickness. A layer with no significant thermalresistance in contact with the air flow will not affect the heat loss through the pipe wall. A verticalpipe constructed of a galvanized steel may be neglected in the heat loss calculations as the pipethickness L is small and the thermal conductivity is big causing a very low temperature drop acrossthe material.

To reduce the heat loss from the air flow inside the pipe, mineral wool was used in [28] as theinsulating material around a galvanized steel pipe. The galvanized steel pipe was neglected in thethis paper for thermal analysis considerations, as it only slightly would increase the thermal massof the chimney. The thermal conductivity of the insulating material was set to kw = 0.05 W/mKwith 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 estimatedusing 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 haveempirical correlations. The empirical correlations was implemented in the chimney model to obtainthe Nusselt number and finally also the heat transfer coefficient. The heat transfer coefficientbetween outdoor ambient air and the surface of the vertical duct was assumed to only depend onnatural convection.

4.3 Complete modelWhen the server model, chimney model and analytical mass flow rate relation was connected toeach other, the model was called complete model. For each time step in a simulation with thecomplete model, the server model calculated the air temperature flowing out of the server, Ts,owhich was fed to the chimney model as an input, see figure 7. Here, the assumption of no heat lossbetween server exhaust and chimney inlet implied that Ts,o = Ta,in. The chimney model calculatedthe average air temperature inside the chimney Ti,avg, which in turn was fed to the analytical massflow 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 chimneywas equal to the air flow at the server inlet. The calculated mass flow rate was therefore fed backto the server model as an input. The mass flow rate was also fed back to the chimney model as itwas needed in the calculations of heat loss.

Figure 7. The server and chimney model together with the analytical mass flow rate relation andhow they were connected to each other in Simulink.

Steady state was reached in the simulation when the temperatures and air flow rate did not changewith time.

4.4 MATLAB - Simulink R©Simulink is a add-on to the software program MATLAB. The model was built in this environmentbecause of the user friendly interface and its great possibilities to solve differential equations such asequation 6. Simulink provides a number of different algorithms to solve differential equations andthe possibility to chose fixed or variable-step size for the simulation time. The detailed descriptionon how the Simulink software works was beyond the scope of this thesis but more information canbe found in the Simulink reference documentation.

15


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 differentialequations. The block requires an initial condition where the simulation starts, in all instances, as atemperature property. The initial condition temperatures were chosen to reasonable temperatureswhich did not interfere with the direction of heat flow. For example, the initial temperature at theinner 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 comparisonswas performed with results found in literature. The behavior of the server model was comparedwith the work of [10] and [11] where the inlet and outlet temperatures of a server were studied asa function of time with no internal heat generation in the server. To simulate a similar test in thepresent 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 validatethe server model. Equation 6 was implemented in Simulink for simulations with q̇s = 0 and aconstant mass flow rate of 30 CFM, see figure 8. With Ts known, equation 5 was used to calculatethe exhaust air temperature.

Figure 8. The server model implemented in Simulink. Notice how the average server temperatureTs 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 byVanGilder, Healey, Pardey, et al. Here, the server power was held constant at q̇s = 103 W andan electrical heater was turned on to increase the temperature of the inlet air to the server. Theexhaust air temperature was studied as the inlet temperature was approximately linearly increasedfrom 22.5◦C to 40◦C during 100 seconds [24]. A similar server power and ramp function on theinlet air temperature was configured to the server model. The air flow rate was set to 36 CFMand � = 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 resultspresented in two separate papers.

A first comparison was made to the results from a performed study by Rahimi and Bayat, on avertical duct where temperatures and velocities were measured within the pipe [28]. The chimneyheight was varied between 1 m and 5 m, with increments of 1 m, according to what was testedexperimentally in the paper. T∞ and Ti,avg was set according to the data given in the paperfor each height of the chimney. The analytical mass flow rate relation stated in equation 16 wasimplemented in a Matlab-script where constants was configured in accordance with the valuesgiven 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.

16


The temperature, mass flow rate and velocities inside the tower was studied when varying bothtower 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 = 0.00842and ξ = 0.056 [27]. The magnitude of the entrance loss coefficient is correlated to the ratio of howrounded the pipe entrance is to the diameter of the pipe where a squared edge inlet correspondsto an entrance loss coefficient of 0.5 [33]. The adopted values were ξin = 0.1 and λ = 0.005. Theanalytical mass flow rate relation was compared to the results presented in [32] by a Matlab-scriptwhere equation 16 was implemented.

4.6 Required dimension - static caseConsider 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 ṁ was analytically obtainedby rearranging equation 2. What are the chimney dimensions that would theoretically providesufficient air flow rates to cover the cooling of the servers?

A chimney was considered fully exposed to a constant outdoor temperature of 1◦C (approximatelythe yearly average temperature in Lule̊a, Sweden) [34]. For this case, the chimney was assumedas 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 dimensionswould suffice to cover the required air mass flow rate. Mathematically, this corresponded to set therearranged equation 2 equal to equation 16. Constants was set to λ = 0.0365, Σξ = 13. The serverpower 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 theair flow and thus, another pressure loss term was added to equation 11. Effectively, this contributedto 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 modelwas performed with these given parameters and dimensions. The chimney height was variedbetween 1 m and 5 m and the server power was held constant at q̇s = 400 W, similar to theconditions in [28]. Here, the simulations was performed with the complete model consisting of theserver model connected to the chimney model which in turn was connected to the analytical massflow rate relation.

A sensitivity analysis on the impact of the constant Σξ was performed. This was done since thecontribution from a server, to the total pressure loss coefficient was estimated based the values onpressure drop from the technical specifications [18] which only allowed rough calculations for thepressure loss coefficient. Subsequent simulations adopted the value on the pressure loss coefficientbased 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 ambienttemperature, 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 simulationsemanated from previous results and then expanded. Furthermore, for the geographical locationof Lule̊a, this ambient temperature almost correspond to a worst case scenario since only a smallfraction of the hours of a year has higher temperatures in combination with the fact that lowambient temperatures provide better draft according to the analytical mass flow rate relation, see

17


equation 16.

Server power was held constant at q̇s = 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 wasextracted from the simulation model. The chimney’s height was incremented, before anothersimulation run was started. The purpose of these simulations was to see if the theoretical massflow of air would increase unhindered along with increased chimney height given a fixed radius andserver power usage.

Simulations was expanded to also include changes of chimney radius as stated in table 2 forsimulation A2. The simulation model was investigated for a range of radii between rc = 0.05 mand 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 rangeof power usage corresponded to turning on servers sequentially so that during a simulation, oneserver to a full rack of servers was simulated.

Simulation B was performed with a chimney radius of 0.05 m and simulation C was performedwith a chimney radius of 0.5 m. The height was held constant in both simulation B and simulationC. The purpose was to test the robustness of the model when subjected to deviances of serverpowers in combination with both small and large chimney diameters. The chimney wall thicknesswas in both simulation B and C set to L = 0.025 m. Values for mass flow and temperature wereextracted at steady state.

4.7.4 Transient simulation

Four server racks populated with 160 Windmill-servers was considered in Simulation D, wherethe transient behavior of temperature and mass flow was investigated. Here, the servers was setto first draw 150 W and then 200 W. cp,tot was calculated according to equation 28 (the massof four racks was adjusted for). The weight of one server together with the height of the servercorresponded to � = 0.65 according to equation 29. The inlet temperature to the servers was setto 20◦C, which is commonly found in todays DCs. The simulation time was set to eight hourswhere an instantaneous increase in power consumption was implemented through a step functionin Simulink and set to occur at four hours. The thickness of the chimney wall was set to L = 0.1m.

The magnitude of the mass flow rate was compared to the required air flow which was assumed tobe 25 CFM per server. Chimney height and radius was kept constant. The chimney dimensionswas 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 themass flow rate and server temperature for a given chimney size. The server power was held constantat 24 kW which corresponded to 160 servers each consuming 150 W. The chimney height was setto 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 coolingneed 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 RISESICS North showed that the total power consumption for the internal fans use about 250 W for oneserver rack (assumed 2.5 W for each fan where two servers share five fans). Four racks populatedwith 40 servers each, hence consume 1000 W of power continuously and assumed sufficient forkeeping the CPU temperature on a safe operational level.

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The potential of reduced energy was estimated by comparing simulation results to climate datafrom SMHI for Lule̊a (hourly data for 2016) [35]. A set of simulations was performed whereoutdoor ambient temperature was varied in a similar manner as in section 4.7.5. Here, of specialinterest was the assumed CPU temperature and at what ambient temperature it exceeded its uppertemperature limit of 75◦C. The outdoor temperature at which the CPU temperature exceed itslimit was called T ′∞. This outdoor temperature was then used together with the climate data sortedfrom lowest to highest to calculate for how many hours in a year that the ambient temperaturewas lower than T ′∞. For all these hours, the cooling demand was assumed to be covered so thatthe internal fans could be turned off completely. As a simplification, the fans was only expectedto be either on or off.

The effect of reduced energy if scaled to a 1 MW data center was investigated briefly. Thiscorresponded to the example in section 2.3 where 10 % of the total energy consumption wasassumed to be related to facility energy. Instead of assuming the internal fan energy as a fractionof the total IT energy, the fan energy was set to 1000 W for the 160 servers and then scaled. Theeffect on both PUE and SPUE was investigated along with the total energy consumption.

5 Results

5.1 Server model validation resultsAs described in section 4.5.1, experimental tests was performed on a server placed in flow benchsetup where the server was turned off [11]. The authors of the paper performed these tests todetermine the server’s thermal mass and thermal effectiveness. A similar system was simulated inthe present paper where the constants was obtained from literature and implemented in the servermodel. The exhaust air temperature response lagged behind when the inlet air temperature waschanged linearly, see figure 9. The inlet air temperature was changed due to two ramp functionblocks implemented in Simulink. The two ramp functions was introduced at two arbitrary timesin the simulation from a steady state. Here, lower and upper temperatures of the inlet air was alsoconfigured arbitrarily because no explicit values was given in the paper [11].

0 50 100 150 200 250 30015

20

25

30 Inlet temperature

Exhaust air temperature

Figure 9. Server inlet and exhaust temperatures as function of time where the exhaust temperatureshows a time lag behind the inlet temperature.

It could be concluded that the exhaust air temperature reactions predicted by the model matchedthe behavior found in literature, when subjected to an increasing inlet temperature [11].

The results from another simulation is seen in figure 10. In contrast to 9 where the server wasturned off, these simulations was conducted with a constant power of 103 W which cause a gapbetween inlet and outlet temperatures. Here, the resulting exhaust temperature was compared toexplicit temperatures from experiments performed on a server in a flow bench. Again the rampfunction was introduced at an arbitrary simulation time step but configured to have the same slope

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and same initial and final temperatures as described in [24]. Results from the simulation modelshowed good agreement with nearly exact same values of the exhaust air temperature found inliterature, both before and after the ramp function was introduced [24].

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Figure 10. Exhaust air temperature provided by the simulation model when the inlet air temper-ature was configured to linearly increase.

A clear effect of the server thermal mass is shown in figure 10 as the exhaust air temperature lagsbehind the inlet temperature when the ramp function is introduced. In the case of no thermalmass, the difference between inlet and exhaust air temperature would remain constant throughoutthe simulation.

A final comparison of the compact server model was performed where the inlet air temperaturewas held constant and instead, the server power usage was increased linearly from 97 W to 117W during 100 seconds. Again, good agreement was found when the simulation model resultswas compared with specific temperature measurements presented in literature [24]. Steady statetemperatures, before and after the power increase was underestimated by about 3 % by the model.Before reaching steady state, the exhaust air temperature increases from 18 to 28◦C during thefirst 25 minutes of the simulation, see figure 11. This corresponds to the establishment period ofthe simulation since the Simulink solver require a initial ”guess” where it starts the simulation.

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er [

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Power usage

Figure 11. Exhaust air temperature response for the case where inlet air temperature was heldconstant and the server power usage was configured as a ramp function increasing from 97 W to117 W.

In general, simulation results showed good agreement with the behavior and temperatures found

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in literature. The simulation model was found robust and simulation time was in the range ofseconds when simulating a whole day.

5.2 Validation of analytical mass flow rate relationThe developed analytical mass flow rate relation was compared to results presented in two papers.The results from the analytical mass flow rate relation was first compared to the results presentedin [28]. Here, the height was varied between 1 m and 5 m on a chimney with rc = 0.05m. Theanalytical mass flow rate relation used the same values for T∞, ρair and average air temperatureinside the chimney as given in [28] for each chimney height. Similarly, values for λ, ξin and ξoutwas also matched to data given in [28]. Good agreement was found between the results presentedin the paper by Rahimi and Bayat and results provided by the analytical mass flow rate relation,see table 3.

For example, a chimney with a height of 5 meter and the constant chimney radius of rc = 0.05m was estimated to induce a mass flow rate of 8.7 g/s according to the analytical mass flow raterelation. This value was compared to the experimental result of 8.25 g/s presented in [28]. Inthis case, the average air temperature inside the chimney, Ti,avg and ambient temperature T∞ was36.2◦C and 17◦C, respectively.

Table 3. Comparison of model results from the analytical mass flow rate relation and experimentalresults by Rahimi et al., [28] for chimneys with several different heights and a constant radius ofrc = 0.05 m.

Height [m] 1 2 3 4 5

Mass flow rate [g/s] (model) 4.8 6.7 7.6 8.2 8.7Mass flow rate [g/s] (Rahimi et al.) 5.50 6.75 7.5 8.01 8.25Average velocity [m/s] (model) 0.6 0.8 0.9 1.0 1.1Average velocity [m/s] (Rahimi et al.) 0.74 0.91 1.0 1.05 1.1

The analytical mass flow rate relation followed the experimental results well when the height ofthe chimney was varied. Small differences was seen between predictions from the analytical massflow rate relation and the experimental values reported in [28].

The analytical mass flow rate was furthermore compared to a second paper which studied naturaldraft through a chimney [32]. Here, the tower height was kept constant at 12.3 m and varied theradius of the chimney. In a similar manner as in the previous comparison, the average air flowtemperature in the chimney presented in [32] was inserted in the analytical mass flow rate relationfor each chimney radius. The ambient temperature was set to T∞ = 30

◦C. Velocity and mass flowrate was compared, see table 4. Some values for required constants was not given in the referredpaper and was therefore assumed.

The values predicted by the model was compared to values presented in [32]. As an example, themodel estimated that a chimney of height 12.3 m and radius of 0.5 m would induce a mass flowrate of 1.3 kg/s which was compared to the value 1.5 kg/s found in [32]. For this case, the averageair temperature inside the chimney was set to Ti,avg = 33.5

◦C.

Table 4. Comparison between the analytical mass flow rate relation and results from Maia et al.[32] with constant chimney height and varied chimney radius.

Radius [m] 0.125 0.25 0.5

Mass flow rate [kg/s] (model) 0.1 0.3 1.3Mass flow rate [kg/s] (Maia et al.) 0.13 0.49 1.5Average velocity [m/s] (model) 2.0 1.8 1.5Average velocity [m/s] (Maia et al.) 2.5 2.3 1.85

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The analytical mass flow rate relation developed in the present paper showed some differencesbetween the predicted mass flow rate compared with the results presented in [32]. The values wasin all cases lower than the values presented in [32] and possibly affected by the unknown constants.

The purpose of these comparisons was to validate the analytical mass flow rate relation. Here,the analytical mass flow rate relation showed good agreement when compared to some resultsin smaller scale (table 3) and bigger differences when larger chimneys was considered (table 4).Despite these differences, the analytical mass flow rate relation was assessed as sufficiently reliablein providing predictions on mass flow rate in order to fulfill the purpose of this thesis. As of this,simulations results should be interpreted as estimations and awareness of possible deviances in areal experimental situation.

The data in table 3 and 4 indicated a general trend where increased dimensions of a chimney,increased the air flow through the system. For the intended application of the present study, highair flow induced by a chimney would imply good cooling of server components which is desirable.

5.3 Chimney dimension - static solutionTo obtain the required air flow rate for any given server power, ∆T = 20◦C across a server wasassumed to be constant where Ts,in = 20

◦C and Ts,out = 40◦C. The dashed line in figure 12 show

the required mass flow rate as a function of server power (plotted against the lower horizontalaxis). The remaining solid lines in figure 12 corresponds to equation 16 where mass flow rate wasplotted as function of chimney height H for five different chimney radii. These lines was plottedagainst the upper horizontal axis. Here, one should remember that the dashed line called requiredflow was not based on any assumed air flow rate in CFM. Instead one should rather interpret it asrequired flow to keep the server exhaust air temperature at Ts,out = 40

◦C.

A solution was provided in figure 12 with a range of power up to 24 kW which correspond tofour server racks populated with 160 server, assuming each server consumed 150 W. The ambienttemperature was assumed to be T∞ = 1

◦C.

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2.5

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0

0.5

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Figure 12. The graphical solution was found in points where the dashed line crossed the linesderived from the analytical mass flow relation for different radii.

Note that a chimney with rc = 0.25 m and a height of approximately 65 m can cover the requiredcooling need for a power consumption of 7 kW equally as good as a chimney of rc = 0.3 m with a

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chimney height of approximately 22 m.

5.4 Complete modelSimulation runs was performed on the complete model. The server model was connected to thechimney model which in turn provided the average temperature to the analytical mass flow raterelation. The induced mass flow rate was calculated and fed back as an input to the servermodel. When the simulation reached steady state, the mass flow rate was extracted. Moreover,the simulations was based on one server with a constant power of q̇s = 400W. Simulations wasperformed for five different chimney heights, see figure 13. Conditions and constants, such asambient temperature and pressure loss coefficients for the pipe, was set equal to values found in[28]. A sensitivity analysis was performed on different pressure loss coefficients, ξs in order tostudy the impact on mass flow rate.

Figure 13. Results from the complete model where different chimney heights and different pressureloss coefficients was simulated.

The mass flow rate estimations using the value ξs = 0 corresponded to no pressure loss from theserver. Effectively, the simulations constituting the solid line in figure 13 corresponded to a similarsetup as in [28] where a server with no pressure loss can be viewed as an electrical resistanceheater. Consequently, the complete model simulation results should match the results from theexperimental measurements in [28] (also presented in table 3). Here, some differences was foundwhere the complete model showed higher mass flow rates in comparison to the experimental valuespresented in [28]. More discussion on the possible cause of the differences was given in section 6.Despite the differences between the complete model and the reported experimental results, it wasassessed that the model still could provide estimations on the system to fulfill the purpose of thethesis.

With high values on the pressure loss coefficient ξs, the mass flow rate decreased below valuesfound in 3. The calculated pressure loss coefficient for a Windmill-server was based on the technicalspecification and estimated to ξs = 12 which was also adopted in subsequent simulations.

5.5 Chimney height evaluationSimulation A1 was performed based on a constant server power of 400 W and a chimney radiusof 0.05 m. The chimney height was increased from 2 to 60 m and the predictions on mass flowrate was studied at steady state for the different heights. An increased chimney height resultedin increased mass flow rates, see figure 14. The obtained results suggested that no considerablychange in mass flow rate occurred for chimney heights beyond 30 m.

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0 10 20 30 40 50 60

6

8

10

12

14

Figure 14. Air mass flow rate as function of chimney height with constant server power andrc = 0.05 m.

The dimensions of the chimney was further investigated in simulation A2, where both chimneyradius and chimney height was varied between 0.05-0.15 m and 2-60 m, respectively. Figure 15show the mass flow rate as function of chimney height for five different chimney diameters atconstant power (400 W). Note that the scale of the y-axis changed in figure 15 compared to theprevious figure 14 causing the shape of curve to almost diminish. As rc increased, the mass flowrate of air through the system increased.

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Figure 15. Air mass flow rate as function of the stack height.

Exhaust air temperatures was obtained for the same set of simulations and presented in figure 16.As the air mass flow rate increased for greater values of rc, the exhaust air temperature decreased.

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0 10 20 30 40 50 60

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20

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Figure 16. Exhaust air temperature as function of the stack height for radii between 0.05 - 0.15 m.

These set of simulations expanded the range of heights that was investigated in [28] under similarconditions. The strength in using simulation models becomes obvious as the range of simulationcombinations and conditions is endless and expands beyond what is realistically possibly to mea-sure. At the same time, interpretation must be done with caution and knowledge of underlyingassumptions.

5.6 Effect of increased powerResults from simulations B and C are presented in figure 17 and 18 for radii of 0.05 m and 0.5 m,respectively. In the lower left corner of figure 17 where low power was provided, the mass flow andtemperature followed known values given in literature. As the power increased, both mass flowand temperature increased.

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