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Exergy Analysis of Data Center Thermal Management Systems

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Energy Efficient Thermal Management of Data Centers

Abstract

Data center thermal management systems exist to maintain the computer equipment within acceptable operating temperatures. As power densities have increased in data centers, however, the energy used by the cooling infrastructure has become a matter of growing concern. Most existing data center thermal management metrics provide information about either the energy efficiency or the thermal state of the data center. There is a gap around a metric that fuses information about each of these goals into a single measure. This chapter addresses this limitation through an exergy analysis of the data center thermal management system. The approach recognizes that the mixing of hot and cold streams in the data center airspace, which is often a primary driver of thermal inefficiency in the data center, is an irreversible process and must therefore lead to the destruction of exergy. Experimental validation in a test data center confirms that such an exergy-based characterization in the cold aisle reflects the same recirculation trends as suggested by traditional temperature-based metrics. Further, by extending the exergy-based model to include irreversibilities from other components of the thermal architecture, it becomes possible to quantify the amount of available energy supplied to the cooling system which is being utilized for thermal management purposes. The energy efficiency of the entire data center cooling system can then be collapsed into the single metric of net exergy consumption. When evaluated against a ground state of the external ambience, this metric enables an estimate of how much of the energy emitted into the environment could potentially be harnessed in the form of useful work. The insights availed from the above analysis include a wide range of considerations, such as the viability of workload placement within the data center; the appropriateness of airside economization as well as containment; the potential benefits of reusing waste heat from the data center; as well as the potential to install additional compute capacity without needing to increase the data center cooling capacity. In addition, the analysis provides insight about how local thermal management inefficiencies in the data center can be mitigated. The chapter concludes by suggesting that the proposed exergy-based approach can provide a foundation upon which the data center cooling system can be simultaneously evaluated for thermal manageability and energy efficiency.

Credit: Portions of this chapter (particularly related to Sects. 9.2, 9.3.1, 9.3.3, and 9.3.4) are reproduced, with permission, from the work of Shah A, Carey V, Patel C, Bash C (2008) Exergy analysis of data center thermal management systems. J Heat Transfer 130(2), Article No. 021401, © American Society of Mechanical Engineers.

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Abbreviations

\( A \) :

Availability or available energy (exergy) [J]

\( \bar{A} \) :

Area [m2]

\( C \) :

Coefficient matrix (9.67)

\( {C_{\rm{p}}} \) :

Specific heat at constant pressure [J/kg K]

\( {\hbox{CFD}} \) :

Computational fluid dynamics

\( {\hbox{cfm}} \) :

Cubic feet per minute

\( {\hbox{const}} \) :

Arbitrary constant value

\( {\hbox{COP}} \) :

Coefficient of performance defined as the heat removed by a cooling system normalized to the work input to the cooling system for removal of heat

\( {\hbox{CRAC}} \) :

Computer room air conditioning unit

\( E \) :

Energy stored in system [J]

\( e \) :

Energy transported per unit massflow [J/kg]

\( f \) :

Function

\( F \) :

Matrix defining flow conditions at boundaries (9.67)

\( g \) :

Acceleration due to gravity [m/s2]

\( H \) :

Enthalpy of a system [J]

HVAC:

Heating, Ventilation, and Air-Conditioning system

\( h \) :

Specific enthalpy (enthalpy per unit mass) [J/kg]

\( \bar{h} \) :

Convection coefficient [W/m2K]

\( i \) :

Counter in summation

\( J \) :

Joule unit of energy

\( {\hbox{KE}} \) :

Kinetic energy [J]

\( M \) :

Mass stored in system [kg]

\( {\hbox{Ma}} \) :

Mach number

\( m \) :

Mass flow [kg]

\( N \) :

Number especially as a limit for the counter in summation

\( n \) :

Number especially as a limit for the counter in summation

\( \hat{n} \) :

Normal (unit) vector in a direction perpendicular to the plane of consideration

\( P \) :

Pressure [Pa or N/m2]

\( {\hbox{PE}} \) :

Potential energy [J]

\( Q \) :

Amount of heat transferred [J]

\( q \) :

Heat dissipation [J]

\( R \) :

Universal gas constant [J/kg-K]

\( {\hbox{RHI}} \) :

Return heat index (9.49) non-dimensional measure of recirculation

\( S \) :

Entropy in system [J/K]

\( s \) :

Specific entropy (entropy per unit mass) [J/kg K]

\( {\hbox{SHI}} \) :

Supply heat index (9.48) non-dimensional measure of recirculation

\( {\hbox{SOR}} \) :

Successive over relaxation

\( T \) :

Absolute temperature [K]

\( t \) :

Time [s]

\( U \) :

Internal energy [J]

\( u \) :

Component of velocity nominally in the direction of x-axis [m/s]

\( \rlap-{V} \) :

Volume [m3]

\( V \) :

Velocity [m/s]

\( v \) :

Component of velocity nominally in the direction of y-axis [m/s]

\( W \) :

Amount of work transferred [J] nominally in the form of electricity or mechanical work

\( w \) :

Component of velocity nominally in the direction of z-axis [m/s]

\( x \) :

Distance in the direction of x-axis [m]

\( y \) :

Distance in the direction of y-axis [m]

\( z \) :

Height or distance in the direction of z-axis [m]

\( \alpha \) :

Thermal diffusivity defined as the ratio of thermal conductivity to the volumetric thermal capacity (\( \rho {C_{\rm{p}}} \))

\( \beta \) :

Nondimensional measure of recirculation (9.50) at the rack inlet

\( \Delta \) :

Change in value or state

\( \delta \) :

Incremental (infinitesimally small) change

\( \Phi \) :

Exergy of a closed system [J]

\( \varphi \) :

Potential flow function (9.60, 9.61)

\( \eta \) :

Efficiency

\( \rho \) :

Density [kg/m3]

\( \omega \) :

Relaxation factor for Gauss–Seidel iteration (9.70)

\( \Psi \) :

Stream exergy for flow through an open system [J]

\( \psi \) :

Specific stream exergy (stream exergy per unit mass) [J/kg]

0:

Ground state

1:

State of a system (nominally initial state) or arbitrary index value (e.g., in summation)

2:

State of a system (nominally final state) or arbitrary index value (e.g., in summation)

II:

Related to second law (such as second-law efficiency)

a:

Ambient

airspace:

related to the airspace within a data center

b:

At the boundary of a control volume nominally the boundary of a cell in a finite volume mesh

C:

Carnot

CRAC:

Related to the CRAC units in a data center

cv:

Control volume

cycle:

Integrated over an entire cycle i.e., final and initial states are identical

d:

Destroyed or irreversibly consumed

f:

Related to the faces (surfaces) of a cell within a finite volume mesh

gen:

Generated

H:

Related to high-temperature reservoir (source)

i:

Inlet or counter in summation, often for variables relating to the x-direction

in:

Inlet or flowing into a given control volume

j:

Counter in summation often for variables relating to the y-direction

k:

Counter in summation often for variables relating to the z-direction

KE:

Related to the transfer of kinetic energy

L:

Related to low-temperature reservoir (sink)

max:

(Theoretical) maximum value

o:

Outlet

out:

Outlet or flowing out of a given control volume

P:

Related to the processor within a computer system

PE:

Related to the transfer of potential energy

Q:

Related to the transport of heat

sup:

Supply state

rack:

Related to the computer racks in a data center

rec:

Recoverable

ret:

Return state

rev:

Reversible

t, th:

thermal

W:

Related to work

.:

Rate (i.e., per unit time)

′″:

Per unit volume

→:

Vector

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Authors and Affiliations

  1. Hewlett Packard Laboratories, 1501 Page Mill Road, M/S 1183, Palo Alto, CA, 94304-1126, USA

    Amip J. Shah, Cullen E. Bash, Chandrakant D. Patel & Ratnesh K. Sharma

  2. Department of Mechanical Engineering, University of California, Berkeley, CA, 94720-1740, USA

    Van P. Carey

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  1. Amip J. Shah
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  3. Cullen E. Bash
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  1. George W. Woodruff School of, Mechanical Engineering, Georgia Institute of Technology, Ferst Dr. 771, Atlanta, 30332, Georgia, USA

    Yogendra Joshi

  2. George W. Woodruff School of, Mechanical Engineering, Georgia Institute of Technology, Ferst Dr. 771, Atlanta, 30332, Georgia, USA

    Pramod Kumar

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Shah, A.J., Carey, V.P., Bash, C.E., Patel, C.D., Sharma, R.K. (2012). Exergy Analysis of Data Center Thermal Management Systems. In: Joshi, Y., Kumar, P. (eds) Energy Efficient Thermal Management of Data Centers. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-7124-1_9

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