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Applied Thermal Engineering 30 (2010) 2347e2356

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Applied Thermal Engineering

journal homepage: www.elsevier .com/locate/apthermeng

The steady-state modeling and optimization of a refrigeration system for highheat flux removal

Rongliang Zhou a,*, Tiejun Zhang b, Juan Catano b, John T. Wen a,b, Gregory J. Michna c, Yoav Peles b,Michael K. Jensen b

aDept. of Electrical, Computer, & Systems Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180, United StatesbDept. of Mechanical, Aerospace, & Nuclear Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180, United StatescMechanical Engineering Department, South Dakota State University, 100 Administration Lane, Brookings, SD 57007, United States

a r t i c l e i n f o

Article history:Received 19 August 2009Accepted 19 May 2010Available online 2 June 2010

Keywords:High heat fluxVapor compression cycleCHFCOPPareto optimization

* Corresponding author. Center of AutomationRensselaer Polytechnic Institute, 8th Floor, CII, 110United States. Tel.: þ1 518 466 8098; fax: þ1 518 276

E-mail addresses: zhour@rpi.edu (R. Zhou), zhangtrpi.edu (J. Catano), wenj@rpi.edu (J.T. Wen), gregMichna), pelesy@rpi.edu (Y. Peles), jensem@rpi.edu (M

1359-4311/$ e see front matter � 2010 Elsevier Ltd.doi:10.1016/j.applthermaleng.2010.05.023

a b s t r a c t

Steady-state modeling and optimization of a refrigeration system for high heat flux removal, such aselectronics cooling, is studied. The refrigeration cycle proposed consists of multiple evaporators, liquidaccumulator, compressor, condenser and expansion valves. To obtain more efficient heat transfer andhigher critical heat flux (CHF), the evaporators operate with two-phase flow only. This unique operatingcondition necessitates the inclusion of a liquid accumulator with integrated heater for the safe operationof the compressor. Due to the projected incorporation of microchannels into the system to enhance theheat transfer in heat sinks, the momentum balance equation, rarely seen in previous vapor compressioncycle heat exchangers modeling efforts, is utilized in addition to the mass and energy balance equationsto capture the expected significant microchannel pressure drop witnessed in previous experimentalinvestigations. Using the steady-state model developed, a parametric study is performed to study theeffect of various external inputs on the system performance. The Pareto optimization is applied to findthe optimal system operating conditions for given heat loads such that the system coefficient ofperformance (COP) is optimized while satisfying the CHF and other system operation constraints. Initialvalidation efforts show the good agreement between the experimental data and model predictions.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Since their invention in the early 19th century, refrigerationsystems have been used in numerous applications ranging fromfood storage to metal processing industries. In the most widelyused applications such as refrigerators, automobiles, and residen-tial and public buildings, the enclosure temperatures are regulated.In recent years, however, there has been an increasing demand forrefrigeration systems targeted at high heat flux removal. Spurred bythe ever-increasing packaging density and, hence, power density inelectronic systems, heat flux dissipated from semiconductordevices could reach as high as 0.1e10 kW/cm2 [1e7] for suchdiverse applications as active radars, all-electric ships, high-powerlight emitting diodes (LED), hybrid electric vehicles (HEV), and

Technologies and Systems,8th Street, Troy, NY 12180,4897.

6@rpi.edu (T. Zhang), catanj@ory.michna@sdstate.edu (G.J..K. Jensen).

All rights reserved.

semiconductor lasers. More than ever, high heat flux dissipationhas become the bottleneck toward compact higher performanceelectronic systems, and heat flux management is becoming morechallenging to maintain product reliability and desired life time.The thermal challenges have spawned the so-called thermal-awaredesign in the electronics industry, and a number of innovativecooling techniques have been proposed which include refrigerationsystems with microchannel heat sinks [8], thermoelectric coolers[9], and liquid impingement cooling [10e12]. Among these newcooling techniques, refrigeration systems with microchannel heatsinks have been shown to be particularly promising. Lee andMudawar [8], for example, have shown that a heat flux of840 W/cm2 can be successfully removedwithout triggering the CHFcondition by using a refrigeration system with microchannels.

Tremendous efforts have been devoted to the modeling ofconventional vapor compression cycles. In dynamic modeling, themoving boundary approach is used tomodel the heat exchangers inthe early work of Wedekind et al. [13]. This approach is lateradopted in the work of Grald and MacArthur [14], He et al. [15] andthe recent development of the vapor compression cycles simulationtool “Thermosys” [16,17] by Rasmussen. The finite volume approach

Nomenclature

cp constant pressure specific heat (kJ/kg K)cv constant volume specific heat (kJ/kg K)h enthalpy (kJ/kg)_m mass flow rate (kg/s)p pressure (kPa)q heat transfer rate (W)q00 heat flux (kW/m2)z flow length (m)A heat exchanger cross-sectional area (m2)Av valve opening (%)Kv valve orifice coefficient (m2)Lc length of condenser (m)M refrigerant charge (kg)P heat exchanger cross-sectional perimeter (m)S heat exchanger surface area (m2)T temperature (�C)U overall heat transfer coefficient (W/m2 K)Vd compressor displacement volume (m3/rpm)W power (W)

hs isentropic efficiencyhv volumetric efficiencyu compressor speed (rpm)r density (kg/m3)

Subscripta accumulatoract active chargec condensercool the second fluide evaporatorf frictionali inletm compressoro outletr refrigerantsatliq saturated liquidsatvap saturated vaportotal cycle totalv valve

R. Zhou et al. / Applied Thermal Engineering 30 (2010) 2347e23562348

is used to model heat exchangers in [18]. In steady-state modeling,which is more related to the present work, Richardson et al. [19,20]develop the simulation tool “VapCyc” for the steady-state analysisof vapor compression cycles that allows the optimization ofrefrigerant charge and design for different components configura-tions. A correlation is used to capture the pressure drop in the heatexchangers; therefore the momentum balance equation is notincluded. Lin and Yeh [21] briefly introduce the steady-state opti-mization of an air-conditioning system based on COP. The optimaloperating conditions are obtained by adjusting the compressorspeed and the expansion valve opening through constrainednonlinear optimization. Corberán et al. develop a computer code“ART” [22] for the steady-state design of refrigeration and air-conditioning equipments, and the momentum balance equation isused in the modeling of the heat exchangers.

In recent years, therehasbeenan increasing interest inusingvaporcompression cycles for high heat flux cooling [8,23e26]. The systemdesigners, however, are not armed with the appropriate design oroptimization tools to help them select the components for eachparticular high heat flux cooling system or determine the ideal oper-ating conditions for given heat loads. Targeting conventional air-conditioning systems, themodeling and optimizationwork discussedabove either neglects the momentum balance equation in themodeling of heat exchangers [16,17,19,20] or is restricted to a super-heated condition at the exit of the evaporator [18,21,22]. These twofundamental deficiencies limit the application of the previousmodeling and optimization work in the high heat flux removalscenarios because the significant pressure drop in the presentmicrochannelswillnotbecaptured, andasuperheatedevaporatorexitwill most probably lead to unacceptably high device temperatures.

Aiming to bridge this gap, the current work introduces a generalmodeling and optimization framework for high heat flux elec-tronics cooling. A refrigeration system structure for high heat fluxremoval is proposed, and the corresponding steady-state systemmodeling and optimization are investigated. The CHF considerationis a fundamental difference between the present refrigerationsystem targeted at high heat flux removal and the conventionalrefrigeration systems designed for temperature regulation. In ourcase, the evaporator is designed to operate with two-phase flowonly for more efficient heat transfer and higher CHF, and, thus,a liquid accumulator with an integrated heater is placed

downstream of the evaporator to ensure the safe operation of thecompressor. Compared with the conventional refrigerationsystems, which are designed to operate within a small rangearound a fixed operating point, the refrigeration system proposedhere for high heat flux removal needs to cover a wide range ofoperating conditions, as the heat generating device could operateanywhere from the standby mode to full load mode and result invarious levels of heat fluxes. The varying active charge of therefrigeration system corresponding to the wide range of operatingconditions is accommodated by the liquid level change in theaccumulator, and the active charge here is defined as the totalrefrigerant holdup in the heat exchangers and piping.

The rest of this paper is structured as follows. Section 2 presentsthe refrigeration system structure for high heatflux removal and thedetailed modeling of individual cycle components. In Section 3, thesteady-steady cycle simulation setup is described and a parametricstudy is performed to investigate theeffectof variousexternal inputson system performance. In Section 4, the Pareto optimizationapproach is applied to find the optimal steady-state operatingconditions to remove the given heat fluxes, and the optimizationresults are interpreted in details. The experimental testbed andinitial model validation results are discussed in Section 5. Finally,Section 6 concludes the present work and provides suggestions forfuture work.

It is expected that the system structure and designmethodologyproposed in this paper are applicable to high heat flux removalapplications of various scales, and that the modeling, simulation,and optimization framework will aid throughout the system designprocess from component sizing to subsequent steady-state opera-tion optimization. By varying the system setup, the same approachis also readily applicable to the design of traditional refrigerationcycles for temperature regulation. Table 1 compares the presentstudy and related work, highlighting the CHF and momentumbalance considerations in the present study which are essential inhigh heat flux removal applications using microchannels.

2. Modeling of refrigeration system for high heat fluxremoval

The present refrigeration system structure for high heat fluxremoval is depicted in Fig. 1. The five components of the system are

Table 1Comparison of vapor compression cycle simulation tools.

RPI VapCyc [19] ART [22] ThermoSys[16,17]

Optimization O(COP/CHF)

O(COP/Totalcharge)

� �

CHFconsideration

O � � �

Accumulator O � � OPressure drop

in heatexchangers

O(momentumbalance)

O(algebraiccorrelation)

O(momentumbalance)

�

R. Zhou et al. / Applied Thermal Engineering 30 (2010) 2347e2356 2349

evaporator, liquid accumulator with integrated heater, variablespeed compressor, condenser, and electronic expansion valve(EEV). For simplification, pressure drop and refrigerant storage inthe piping are not considered.

The fundamental feature that differentiates the present refrig-eration system in Fig. 1 from other vapor compression cyclesproposed for high heat flux removal is that the evaporator operateswith two-phase flow only. In the high heat flux scenario, the highheat transfer coefficient associated with two-phase flow helps keepthe surface temperature of heat generating device low. In compar-ison, other high heat flux electronics cooling work [23,24,26] hassuperheated vapor at the evaporator exit. The low heat transfercoefficient of superheated vapor, together with an imposed highheat flux, will inevitably lead to unacceptably high device temper-atures and, thus, the heat generating device has to be placed incontact with the two-phase flow region of the evaporator only. Inaddition to the device placement issue, the big difference in heattransfer coefficients between the two-phase and superheated flowregions will also result in less uniformity in the device temperaturedistribution, which induces more thermally induced strain.

For the protection of the compressor, a liquid accumulator isincluded downstream of the evaporator. Heat from the integratedaccumulator heater fully evaporates the two-phase flow comingout of the evaporator, and, thus, only saturated vapor enters thecompressor at steady state. Through its liquid level change, theaccumulator also has the important role of cycle active refrigerantcharge regulation to accommodate a wide range of operatingconditions.

The external inputs of the refrigeration system are heat load ofthe evaporator qe, heat provided to the accumulator from theintegrated heater qa, compressor speed u, temperature of thesecond fluid to which the heat is rejected Tcool, and EEV percentageopening Av. The steady state of the system is fully represented bythe pressure and enthalpy at the exit of each cycle component,together with the cycle mass flow rate. As shown in the detailedcomponent modeling below, each cycle component is described bytwo equations except the accumulator. The accumulator, in

Fig. 1. Refrigeration system structure for high flux removal.

addition to the two equations representing energy balance andpressure, has a third equation stating that the accumulator exit issaturated vapor in steady state. With this third accumulatorequation, the loop of interconnected cycle components is closedand cycle steady state can be solved. In comparison, the conven-tional vapor compression cycle without accumulator uses the cyclerefrigerant charge conservation equation to close the loop.

2.1. Compressor

The compressor mass flow rate is given by:

_m ¼ uVdrhv (1)

where u, Vd, r, and hv are compressor speed (rpm), displacementvolume, inlet refrigerant density, and volumetric efficiency,respectively. The volumetric efficiency hv can be approximated by[18]:

hv ¼ 1þ cr � drðpo=piÞcv=cp (2)

where cr and dr are coefficients to be identified from the actualcompressor, po and pi are the compressor outlet and inlet pressures,and cv and cp are constant volume and constant pressure specificheats evaluated at the compressor inlet condition.

The compressor exit enthalpy is given by:

ho ¼ hi þ ðhis � hiÞ=hs (3)

where ho, hi, and his are compressor outlet, inlet, and isentropicenthalpy, respectively. The compressor isentropic efficiency hsvaries with operating conditions and can be described with thefollowing polynomial approximation [27]:

hs ¼ c0 þ c1uþ c2u2 þ c3ðpo=piÞ þ c4ðpo=piÞ2 (4)

where the coefficients c0, c1, c2, c3 and c4 can be identified from theactual compressor.

Assuming the compression process is adiabatic, the work doneby the compressor Wm can be calculated using the mass flow rate,and inlet and outlet enthalpies:

Wm ¼ _mðho � hiÞ (5)

2.2. Electronic expansion valve (EEV)

The cross-sectional area of the EEV can be electronicallycontrolled and can be translated into a percentage opening denotedby Av (ranging from 0 to 100%). It is assumed that the expansionprocess is an adiabatic constant enthalpy process with ho¼ hi,where ho and hi are the expansion valve’s outlet and inletenthalpies.

The pressure drop across the expansion valve is:

Dp ¼ _m2

K2vA2

vri(6)

where Kv is the expansion valve orifice coefficient obtained fromthe manufacturer (or through experiments), and ri is refrigerantdensity at the inlet of the expansion valve.

2.3. Liquid accumulator

Both the inlet and the outlet of the liquid accumulator arelocated at its top. At steady state, only saturated vapor leaves theaccumulator and thus:

R. Zhou et al. / Applied Thermal Engineering 30 (2010) 2347e23562350

po ¼ pi (7)

ho ¼ hsatvapðpoÞ (8)

where po and pi are the outlet and inlet pressures of the accumu-lator, ho is the accumulator exit enthalpy, and hsatvap(po) is thesaturated vapor enthalpy at pressure po.

At steady state, the accumulator level does not change, and theincoming two-phase flow at the accumulator inlet is fully evapo-rated into saturated vapor leaving the accumulator by qa, heatsupplied to the accumulator heater. Assuming that the accumulatoris insulated, from the energy balance we have:

qa ¼ _mðho � hiÞ (9)

where hi is the refrigerant enthalpy at the accumulator inlet. Asexplained earlier, this energy balance equation plays the importantrole of closing the loop in later cycle simulations.

With a known total refrigerant charge of the vapor compressioncycle Mtotal, and the active charge Mact calculated from theexchangers and piping, the total refrigerant holdup in the liquidaccumulator Ma is Ma¼Mtotal�Mact. Once the geometry of theliquid accumulator is given,Ma can be easily converted to the liquidlevel of the accumulator.

2.4. Heat exchangers

A one-dimensional homogeneous model is used to characterizeboth the evaporator and condenser. The steady-state behavior ofthe refrigerant inside the heat exchangers can be described by themass, energy, and momentum balance equations:

v _mvz

¼ 0 (10)

v�_mh�

vzþ q00p ¼ 0 (11)

1A

v�_m2=r

�vz

þ Avpvz

þ Ff ¼ 0 (12)

where z stands for the location measured from the inlet of the heatexchangers, A is the flow cross-sectional area, p is the perimeter ofthe cross-sectional area, q00 is the incoming heat flux (negative inthe case of condenser), and Ff is the term introduced to describe thefriction inside the channels of the heat exchangers.

At steady state, the energy and momentum balance equationscan be integrated along the heat exchanger length to obtain thefollowing two algebraic equations:

ho ¼ hi þq_m

(13)

Dpbpi � po ¼�

_mA

�2� 1ro

� 1ri

�þ Dpf (14)

where hi, ri, and pi are the enthalpy, density and pressure at theheat exchanger inlet, while ho, ro, and po are the enthalpy, densityand pressure at the heat exchanger outlet. The pressure drop acrossthe heat exchanger Dp is the sum of the acceleration pressure dropð _m=AÞ2ðð1=roÞ � ð1=riÞÞ and the frictional pressure drop Dpfcalculated using the Martinelli correlation [28].

The rate of heat transferred by the heat exchanger q is calculatedaccording to the different boundary conditions in the evaporatorand condenser, and established correlations are used to predict the

heat transfer coefficients in different flow regimes. In the single-phase region of the heat exchangers, the Petukhov and Popovcorrelation [29], Gnielinski correlation [30], and Kandlikar corre-lation [31] are used for highly turbulent, turbulent, laminar andtransitional flow, respectively. In the two-phase region, the Kand-likar correlation [31] is used for boiling, and the correlation by Shah[32] is used for condensation.

2.4.1. EvaporatorA uniform heat flux q00 is applied to the evaporator, and the heat

transfer rate into the evaporator qe is:

qe ¼ q00Se (15)

where Se is the evaporator surface area.The evaporator wall temperature Twall at any specific location is:

Twall ¼ Tr þ q00

U(16)

where Tr and U [29e31] are the locally evaluated refrigeranttemperature and overall heat transfer coefficient, respectively.

2.4.2. CondenserDepending on the operation conditions, the condenser can

operate with two zones (superheated and two-phase) or threezones (superheated, two-phase, and subcooled). It is thus describedby amulti-zonemoving boundarymodel inwhich both the numberof zones in the condenser and the length of each zone may vary.

In each zone of the condenser, the integrated energy andmomentum balance equations are:

ho;k ¼ hi;k �qc;k_m

(17)

Dpc;kbpi;k � po;k ¼�

_mAc

�2

1ro;k

� 1ri;k

!þ Dpf ;k (18)

where Ac is the cross-sectional area of the condenser, and (hi,k, ri,k,pi,k) and (ho,k, ro,k, po,k) are the enthalpy, density and pressureevaluated at the inlet and outlet of the kth zone, respectively. Thepressure drop across the kth zone Dpc,k is the sum of the acceler-ation pressure drop ð _m=AcÞ2ð1=ro;k � 1=ri;kÞ and the frictionalpressure drop Dpf,k.

The rate of heat rejected in the kth zone to the second fluid qc,k is:

qc;k ¼ UkSk

�To;k � Tcool

�� �Ti;k � Tcool�

lnhTo;k�TcoolTi;k�Tcool

i (19)

where Uk [29,30,32], Sk, Tcool, Ti,k, and To,k are the overall heattransfer coefficient, surface area, second fluid temperature, andinlet and outlet refrigerant temperatures of the kth zone.

The rate of total heat rejected by the condenser qc is:

qc ¼XNk¼1

qc;k (20)

where N (2 or 3) is the total number of zones existing in thecondenser. The length of each zone Lc,k should be greater than zeroand add to the total length of the condenser Lc:

Lc ¼XNk¼1

Lc;k (21)

Note that at the boundary between the superheated and two-phase regions h¼ hsatvap(p), in which hsatvap(p) stands for thesaturated vapor enthalpy at pressure p. Similarly, h¼ hsatliq(p) holds

Fig. 2. Effect of Tcool on system performance (peh plot).

R. Zhou et al. / Applied Thermal Engineering 30 (2010) 2347e2356 2351

true at the boundary between the two-phase and subcooledregions, in which hsatliq(p) stands for the saturated liquid enthalpyat pressure p.

3. System simulation setup and parametric study

3.1. Cycle setup

In an effort to reflect the testbed built at RPI for high heat fluxremoval, the refrigeration system simulated has exactly the samestructure shown in Fig. 1, except that the single evaporator inFig. 1 is replaced by three identical evaporators in parallelconfiguration. Each evaporator is equipped with an EEV of thesame model to regulate its mass flow rate. R134a is chosen to bethe cycle refrigerant because of its wide use, but other refrigerantscan also be easily used in the simulation if their thermophysicalproperty tables are available. On the condenser side, water ischosen to be the second fluid, and its temperature is denotedas Tcool.

The three evaporators are configured to have the same oper-ating conditions; thus, qe,1¼ qe,2¼ qe,3¼ qe, Av,1¼ Av,2¼ Av,3¼ Av,and _m1 ¼ _m2 ¼ _m3 ¼ _m=3. Cycle simulation results with non-equal evaporator heat loads have also been obtained but are notincluded here because of space limitations.

3.2. System performance indices

For the present refrigeration system targeted at high heat fluxremoval, CHF is the safety index and COP is the efficiency index.

3.2.1. Coefficient of performanceFor refrigeration cycles, COP can be defined as the ratio of the

heat transfer rate received by the system undergoing the cycle fromthe cold body, q, to the net power into the system to accomplish thiseffect, Wcycle [33].

COP ¼ qinWcycle

(22)

Thus, for the cycle setup with three identical evaporators of thesame heat load qe:

COP ¼ 3qeqa þWm

(23)

3.2.2. Critical heat fluxIn the present refrigeration system for high flux removal

applications, knowledge of the CHF condition is vital for safesystem operation. When the imposed heat flux exceeds the CHF,the high heat flux together with the sudden decrease in heattransfer coefficient will cause the temperature of the heat dissi-pating device to rise high enough and eventually destroy thedevice.

The Katto correlation [34] is a well established correlation forCHF prediction in tubular channels, and it is expressed as:

qCHF ¼ qco

1þ KDhi

hfg

!(24)

where qco is the basic CHF, K is the inlet subcooling parameter,Dhi isthe inlet subcooling enthalpy, and hfg is the latent heat of evapo-ration. Detailed interpretation of these terms can be found in Kat-to’s original paper [34], and the CHF generally has an increasingtrend with increasing mass flow rate and inlet subcooling.

3.3. Parametric study

To gain more insight into the present refrigeration system forhigh heat flux removal, a parametric study is conducted to studythe effect of second fluid temperature Tcool, evaporator heat load qe,compressor speed u, EEV percentage opening Av, and accumulatorheat qa on system performance.

3.3.1. Second fluid temperature TcoolIn the simulation setup, cooling water is chosen to be the second

fluid of the condenser to which the heat load is rejected. It isassumed that its temperature Tcool can vary from 25 �C to 35 �C,reflecting the possible weather and seasonal changes. Fig. 2 showsthe cycle peh plot for Tcool¼ 25 �C, 30 �C, and 35 �C, respectively,with qe¼ 2500 W, qa¼ 2000 W, u¼ 3000 rpm, and Av¼ 20%.

It is shown in Fig. 2 that as the cooling water temperatureincreases, the cycle steady states shift upward on the peh plot,indicating an increase in the whole system pressure level and,hence, increased evaporation and condensation temperature. Theincreased condenser temperature is necessary to maintain a suffi-cient temperature difference between the refrigerant and coolingwater to reject the heat load. Also revealed in Fig. 2 is the largerpressure difference across the compressor as the Tcool increases,which leads to more compressor power and hence a decreasingsystem COP. It is observed in Fig. 2 that the refrigerant quality in theevaporator increases with Tcool and thus results in lower CHF.

3.3.2. Evaporator heat load qeAlthough specifically designed for high heat flux removal, the

present refrigeration system is also expected to handle the low heatloads and corresponding low heat fluxes when the heat generatingdevice is at standby mode. Fig. 3 shows the cycle steady states onthe peh plot for qe¼ 500 W, 1500 W, and 2500 W, respectively,with qa¼ 2000W, u¼ 3000 rpm, Av¼ 20%, and Tcool¼ 30 �C.

It can be observed from Fig. 3 that a higher heat load will bringan increase in the pressure level of the evaporator and, hence,higher evaporation temperature. As the heat load increases, the exitquality of the evaporator also increases correspondingly. The widerange of heat loads from 500W to 2500W are all successfullyremoved without triggering the CHF condition, but higher systemCOPs are achieved for higher heat loads, implying that the presentrefrigeration system is more efficient in high heat flux removal.

Fig. 5. Effect of Av on system performance (peh plot).Fig. 3. Effect of qe on system performance (peh plot).

R. Zhou et al. / Applied Thermal Engineering 30 (2010) 2347e23562352

3.3.3. Compressor speed u

Compressor power is a major part of the power consumption ofthe refrigeration cycle for high heat flux removal, which directlyaffects the system COP. Fig. 4 shows the cycle steady states on thepeh plot for u¼ 2000 rpm, 3000 rpm, and 4000 rpm, respectively,with qe¼ 2500 W, qa¼ 2000 W, Av¼ 20%, and Tcool¼ 30 �C.

With increasing compressor speed u, the cycle mass flow rate _mincreases accordingly and, thus, lower evaporation temperaturesand higher CHFs are achieved as shown in Fig. 4. On the other hand,compressor power Wm increases with the compressor speed u andresults in decreased COP.

3.3.4. EEV percentage opening AvFig. 5 shows the cycle steady states on the peh plot for Av¼ 12%,

20%, and 28%, respectively, with qe¼ 2500W, qa¼ 2000W,u¼ 3000 rpm, and Tcool¼ 30 �C.

Fig. 4. Effect of u on system performance (peh plot).

It can be observed from Fig. 5 that the pressure differencebetween the condensation side and the evaporation side of thecycle experiences a bigger change when Av is changed from 20% to12%, compared with the case when Av is changed from 20% to 28%.This means that the cycle steady state is more sensitive to the valveopening changes in the lower range. This observation agrees withequation (6), which states that the pressure drop across the valveDpf 1/Av2. Another important trend in Fig. 5 is that a smaller valveopening helps reduce the evaporator inlet quality and, thus,increase the CHF as shown in Fig. 5. The larger pressure dropresulted from the smaller valve opening Av, however, will requirethe compressor to do more work and, hence, reduce the systemCOP. The conflicting trend in CHF and COP as Av varies suggests thata trade-off has to be made between these two objectives in thesteady-state system operation.

3.3.5. Heat supplied to the accumulator qaBased on the accumulator equations (7)e(9), heat supplied to

the accumulator, qa, affects the exit quality of the evaporator atsteady state. Higher qa will naturally decrease the system COP, but italso lowers the evaporator exit quality. With a given heat load, theevaporator inlet quality will drop accordingly and a higher CHF canbe achieved in the evaporator since CHF increases with inletsubcooling.

Fig. 6 shows the cycle steady states on the peh plot forqa¼ 1000 W, 2000 W, and 3000 W, respectively, with qe¼ 2500 W,u¼ 3000 rpm, Av¼ 20%, and Tcool¼ 30 �C. It can be seen from Fig. 6that as qa increases, the refrigerant qualities at both the inlet andoutlet of the evaporator decrease, which lead to increased CHF. Thesystem COP, however, will decrease because of the higher powerconsumption of the cycle brought by larger qa. Once again, weobserve the necessary trade-off between the conflicting objectivesof COP and CHF.

4. Investigation of steady-state operation optimization

4.1. Problem formulation

The present refrigeration system is designed for the efficient andsafe removal of high heat fluxes, thus the system COP has to be

Fig. 6. Effect of qa on system performance (peh plot).

R. Zhou et al. / Applied Thermal Engineering 30 (2010) 2347e2356 2353

maximized while avoiding the CHF condition. Although it isa natural thought to post the CHF condition as a constraint in thesystem operation optimization, we must acknowledge that all theCHF correlations available are only accurate to a certain extent, andsome safety margin has to be reserved to prevent the deviceburnout. With this concern in mind, the CHF condition can betreated as an additional objective to be maximized along with thesystem COP, thus giving the system designer the freedom to choosethe CHF safety margin.

Of the external system inputs discussed earlier, the second fluidtemperature Tcool is usually determined by the environment andnot directly controllable. The steady-state optimization of therefrigeration system with given heat load qe and second fluidtemperature Tcool can thus be formulated as the followingbi-objective constrained optimization problem:

maximizeu;Av;qa

�COPCHF

subject to : umin � u � umax

0 � Av � 1000 � qa � qa max

Tmin � Twall � Tmax

The physical limitations of the compressor, EEV, and the accu-mulator embedded heater are specified in the first threeconstraints. In the fourth constraint, the evaporator wall tempera-ture Twall (representing the heat generating device temperature) ismaintained below Tmax to avoid device burnout, and at the sametime above Tmin to prevent moisture condensation on the devicesurface that may cause an electrical short or other adverse effects.Tmin can be set to be well above the room dew point temperature toleave some safety margin. This approach is adopted in IBM’s eSer-ver z990 [26] to replace the airtight metal enclosure used in IBM’sS/390 server [23], which lowers costs and system complexity.

Fig. 7. Pareto frontier for [COP CHF]T optimization.

4.2. Optimization approach and results

For multiobjective optimization (MO) problems, Pareto solutionis a well accepted approach. A Pareto solution is one for which anyimprovement in one objective can only take place if at least oneother objective worsens. The Pareto frontier of a MO problem

consists of the Pareto solutions, and it gives the system designer theinformation needed to make a trade-off between the conflictingobjectives according to varying conditions and requirements.Among the many methods to obtain the Pareto frontier of a MOproblem, the normalized normal constraint method [35] is used forthe present bi-objective (COP and CHF) optimization problembecause its performance is entirely independent of the designobjective scales.

For the simulation setupwith the same systemstructure as shownin Fig. 1 and three identical evaporators of the same heat load andvalve opening in parallel configuration, the Pareto frontiers of the[COP CHF]T optimization with qe¼ 2500W (q00 imposed¼ 156.6 kW/m2) and qe¼ 1500W (q00imposed¼ 94.0 kW/m2) are shown in Fig. 7.The optimization constraints are 2000 rpm�u� 5000 rpm,0� Av� 100%, 0 W� qa� 5000W, 25 �C� Twall� 60 �C.

Each point along the Pareto frontiers in Fig. 7 corresponds to the[COP CHF]T of a Pareto solution obtained by optimizing the systeminput (u, Av, qa) for a specific heat load qe, and the conflict betweenCOP and CHF can be easily observed since the CHF decreases assystem COP increases. To prevent the device burnout, solutionsalong the Pareto frontier with CHF higher than the imposed heatflux q00imposed can be chosen for the steady-state operation.Although it is desirable to select an operating point with a higherCHF and, hence, a larger safety margin, it is observed in Fig. 7 thatsuch an operating point will have a lower COP. The system designerthus has to make a trade-off between the system COP and CHF.

Fig. 7 reveals that the refrigeration system is more efficient inhandling higher heat fluxes. The highest system COPs achievedwithout violating the CHF condition are around 2.5 for qe¼ 2500 Wand 1.8 for qe¼ 1500 W, respectively. The reason can be attributedto the fact that a heated accumulator is used in the system to fullyvaporize the two-phase flow leaving the evaporator, and it can befound from Eqn. (23) that for the same system power input(qaþWm) a larger heat load qe results in a higher system COP.Another important fact shown in Fig. 7 is the slower slope of thePareto frontier of qe¼ 2500 W compared with that of qe¼ 1500 W,indicating that the system COP can be improved without compro-mising CHF a lot when handling higher heat fluxes. In Fig. 7 bothPareto frontiers have decreasing slope with increasing system COP,a feature amenable to the steady-state system operation

Table 2Pareto solutions for qe¼ 2500W (q00 imposed¼ 156.6 kW/m2).

CHF(kW/m2)

COP Twall,i/Twall,o

(�C)qa (W) u (rpm) Av (%)

198 1.0 41.4/50.6 5000 2000 8.6194 1.1 37.8/49.4 5000 2000 12.5190 1.2 35.5/48.4 5000 2000 19.1186 1.3 34.4/47.0 4550 2000 20.9182 1.5 33.4/50.9 3932 2000 19.2178 1.7 32.5/50.6 3346 2000 17.5174 1.9 31.6/55.9 2785 2000 16.3170 2.2 30.8/56.2 2262 2000 15.2166 2.6 30.0/60.0 1962 2000 16.6

Fig. 8. Experimental testbed.

R. Zhou et al. / Applied Thermal Engineering 30 (2010) 2347e23562354

optimization since the system suffers less CHF degradation as thesystem COP increases in its higher range.

Tables 2 and 3 list the optimized system operation conditions(qa, u, Av) and main system performance indices for the two Paretofrontiers shown in Fig. 7, in which Twall,i and Twall,o are the evapo-rator wall temperatures at the inlet and outlet. Because of theincreasing refrigerant quality and associated decreasing heattransfer coefficient along the flow direction of the evaporator, Twall,iand Twall,o are the lowest and highest evaporator wall temperatures,respectively, when a uniform heat flux is applied. The systemtrends revealed in the parametric study of Section 3.3 are alsomanifested in the Pareto optimization results shown in Tables 2and 3 for qe¼ 2500W and qe¼ 1500 W, respectively. As qadecreases, the system COP increases because of less energyconsumption, and at the same time the evaporator exit qualityincreases which leads to lower CHF. For both Pareto frontiers,higher CHFs are achieved with smaller EEV opening and higherheat input supplied to the accumulator. It is also noted that all thePareto solutions in Tables 2 and 3 have the compressor speed at thelower bound of the optimization constraint. One possible expla-nation is that for the two heat loads considered the compressorrunning at this speed is capable of delivering sufficient refrigerantmass flow rate, but is less energy efficient than the accumulatorheater in regulating the CHF, and thus the compressor is main-tained at this low speed to achieve better system COP.

Although the present study is specifically targeted at high heatflux removal and the optimization results above show that higherefficiency is attained with higher heat flux, the possibility ofremoving low heat fluxes using the same system structure is alsoinvestigated. It is found that for much lower heat loads and heatfluxes (qe¼ 500 W and q00imposed¼ 31.3 kW/m2, for example), themain challenge is tomaintain the evaporator wall temperature highenough (not lower than 25 �C in the optimization) to avoid ambientmoisture condensation. To achieve this goal, either the accumulatorheat input qa can be increased or the system mass flow rate can bedecreased, and apparently the latter option is more energy efficient.This implies that either a compressor capable of delivering a wide

Table 3Pareto solutions for qe¼ 1500W (q00 imposed¼ 94.0 kW/m2).

CHF(kW/m2)

COP Twall,i/Twall,o

(�C)qa (W) u (rpm) Av (%)

176 0.6 36.1/41.9 5000 2000 6.4169 0.7 29.1/35.8 5000 2000 13.2161 0.9 27.1/36.0 4108 2000 13.1147 1.0 25.0/37.8 3385 2000 18.5130 1.2 25.0/41.5 2799 2000 25.3114 1.4 25.0/46.1 2291 2000 29.9101 1.6 25.0/51.8 1855 2000 33.390 1.8 25.0/56.0 1483 2000 35.880 2.0 30.0/59.1 1290 2000 40.1

range of mass flow rate is required, or parallel compressors ofvarying capacities can be used to cover the wide range of mass flowrate needed.

5. Experimental setup and model validation

The experimental testbed built in Rensselaer Polytechnic Insti-tute for high heat flux removal investigation is shown in Fig. 8. Inthe three evaporators, the imposed heat fluxes come from thecartridge heaters immersed in the refrigerant and each cartridgeheater can provide up to 2.5 kW heat output. Using the EEVsupstream of each evaporator, the system can be reconfigured tooperate with one, two, or three evaporators simultaneously. Thetestbed is equipped with two compressors (small and medium) toallow for a wide range of operating conditions and is also fullyinstrumented with temperature, pressure, and mass flow ratesensors.

While the parameter identification of system components(compressors and EEVs) is still underway, preliminarily modelvalidation against the testbed has been undertaken using the initialparameter identification results. Fig. 9 shows the cycle steady-state

Fig. 9. Comparison between experimental data and modeling prediction (case 1:qe¼ 1200 W, Av¼ 6%, Tcool¼ 25.0 �C, u¼ 4050 rpm, case 2: qe1¼ qe2¼1500 W,Av1¼ Av2¼ 35%, Tcool¼ 26.7 �C, u¼ 4200 rpm).

R. Zhou et al. / Applied Thermal Engineering 30 (2010) 2347e2356 2355

comparison between the experiments and model prediction. Incase 1, the testbed operates with only one evaporator and the smallcompressor, while in case 2 two identical evaporators and themedium compressor are in operation.

It can be seen from the peh plots that the modeling predictionmatches the experimental data well in both cases, with onlynoticeable differences at the exits of the accumulator andcompressor. The discrepancy at the accumulator and compressorexits can be attributed to the efficiency correlations used in thecompressor model and the 20 inches of piping connecting theaccumulator and the compressor. It is found through modeling thatthe compressor exit temperature is sensitive to the isentropicefficiency and hence an accurate correlation is desired. Also foundthrough experiments is the fact that although the piping connect-ing the accumulator and the compressor is insulated, some heat canstill be gained from the ambient and thus slightly superheat the exitof the accumulator, which is assumed to be saturated vapor in thesteady-state modeling. To solve this problem, more accuratecorrelations are being developed to better model the compressorand pipemodel will be included in futuremodelingwork to capturethe heat transfer process and pressure change in the piping.

6. Conclusions and future work

In this paper, the steady-state modeling and operation optimi-zation of a refrigeration system for high heat flux removal is pre-sented. To deal with the CHF condition in high heat flux removal,the evaporator is designed to operate with two-phase flow only,and thus a liquid accumulator with embedded heater is included inthe cycle for the safe operation of the compressor and cycle activecharge regulation. Using the steady-state model, the effect ofvarious external system inputs on the system performance isinvestigated, and Pareto optimization is applied to optimize thesystem steady-state operation for given heat loads. The initialexperimental data from the testbed show good prediction ability ofthe model, and validation of the steady-state system operationoptimization approach is also underway.

Acknowledgements

This work is supported in part by the Office of Naval Research(ONR) under the Multidisciplinary University Research Initiative(MURI) Award N00014-07-1-0723 entitled “System-LevelApproach for Multi-Phase, Nanotechnology-Enhanced Cooling ofHigh-Power Microelectronic Systems.” This work is also supportedin part by the Center for Automation Technologies and Systems(CATS) under a block grant from the New York State Foundation forScience, Technology and Innovation (NYSTAR). John Wen is sup-ported in part by the Outstanding Overseas Chinese Scholars Fundof Chinese Academy of Sciences (No. 2005-1-11).

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