Modeling of a Thermosiphon to Recharge a Phase Change ...evaporator cv tube cv pcm conductor pcm capacitor pcm container refrigerant tube downcomer air inlet boundary conditions Heat

Modeling of a Thermosiphon to Recharge a Phase Change MaterialBased Thermal Battery for a Portable Air Conditioning Device

Rohit Dhumane Jiazhen Ling Vikrant Aute Reinhard Radermacher

Center for Environmental Energy Engineering, University of Maryland, College Park, 4164 Glenn L. Martin HallBldg., MD 20742, USA

{dhumane,jiazhen,vikrant,raderm}@umd.edu

AbstractClosed loop two phase thermosiphons have a broad rangeof applications due to their simplicity, reliability, low costand the ability to dissipate high heat fluxes from minimaltemperature differences. The present study focuses on onethermosiphon operation which solidifies a phase changematerial (PCM) based thermal battery for a portable airconditioner called Roving Comforter (RoCo). RoCo usesvapor compression cycle (VCC) to deliver cooling andstores the heat released from the condenser into a com-pact phase change material (PCM) based thermal battery.Before its next cooling operation, the PCM needs to bere-solidified. This is achieved by the thermosiphon, whichoperates within the same refrigerant circuitry with the helpof a pair of valves. The molten PCM which acts as heatsource affects the dynamics of the thermosiphon which inturn affects the solidification process. Thus the dynamicsof both the PCM and thermosiphon are coupled. For ac-curate transient modeling of this process, the PCM modelconsiders the solidification over a temperature range, vari-able effects of conduction and natural convection duringthe phase change and variable amounts of heat releaseat different temperatures within the temperature range ofphase change. The paper discusses component modelingfor this transient operation of thermosiphon and its valida-tion with experimental data.Keywords: Thermosiphon, Thermosyphon, Phase ChangeMaterials

1 IntroductionA thermosiphon is an energy transfer device capable oftransferring heat from a heat source to a heat sink overa relatively long distance, without the use of active con-trol instrumentation and any mechanically moving partssuch as pumps (Dobson and Ruppersberg, 2007). Ther-mosiphons are used in diverse applications like coolingof electronic components, light water reactors, solar wa-ter heating systems, geothermal systems, and thermoelec-tric refrigeration systems due to simple designs, simpleoperating principles and high heat transport capabilities(Franco and Filippeschi, 2011). Lack of moving com-ponent for pumping refrigerant also leads to higher reli-ability of the system. Thermosiphons may operate with

single phase fluid or two phase fluid, may consist of aco-current or counter-current flow (Haider et al., 2002)and have open or closed loops (Benne and Homan, 2009).The counter-current thermosiphons are also referred to asheat pipes. Industrial applications typically involve theco-current thermosiphons and the term thermosiphon usedhenceforth in this paper, will refer to these co-current ther-mosiphons.

A closed-loop two-phase thermosiphon consists of aclosed circuit of refrigerant tube filled with a working fluid(referred to as refrigerant in this paper) and oriented in avertical plane. The refrigerant evaporates in the lower por-tion of the loop (called evaporator) due to a heat input.The resultant vapor then travels upwards through a verti-cal tube called as the riser to reach the condenser, whereit rejects its latent heat. The condenser is located verti-cally above the evaporator and the condensed refrigerantfrom its outlet trickles down into the evaporator by gravitythrough the downcomer tube. The cycle repeats until theheat source is exhausted.

The current study is motivated by a need to understandthe dynamics of a thermosiphon used to recharge the ther-mal battery of a portable air conditioning device calledRoving Comforter (RoCo) (Du et al., 2016). The dynamicmodel is expected to aid the improvement of design anddevelopment of controls. A brief description of RoCo isgiven in the next section.

2 System DetailsTraditional HVAC (Heating, Ventilation and Air Condi-tioning) systems consume significant amounts of energyto maintain a uniform temperature in the buildings withina narrow range, neither of which is necessary for deliv-ering comfort (Hoyt et al., 2015). Personal condition-ing systems like RoCo provide an opportunity to save thebuilding energy by relaxing the building thermostat set-tings without compromising occupant thermal comfort.

RoCo uses vapor compression cycle (VCC) to delivercooling for building occupants and stores the waste heatfrom the condenser in a compact PCM based thermal bat-tery. The schematic of the two modes of operation ofRoCo is shown in Figure 1. When the PCM is molten,the VCC operation is terminated. Due to the poor ther-mal conductivity of PCM, the molten PCM cannot solid-

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459

Figure 1. Schematic of two modes of operation of RoCo withthe thermal battery marked in grey box

ify by itself within a reasonable time duration by reject-ing heat to ambient air. Consequently, to enable a fasterrecharge of the thermal battery (i.e. PCM solidification),a thermosiphon is used. The thermosiphon operation isideal in this situation because of its high rate of heat dissi-pation even from relatively small temperature differencesbetween the heat source and the heat sink. The refrigerantcircuitry is designed to enable a single direction flow ofrefrigerant. By operating a pair of valves, the refrigerantcircuit switches from VCC circuit to thermosiphon circuit.

The PCM selected for the current application isparaffin-based, with the midpoint of its solidification tem-perature range at 35°C. The temperature choice is basedon a trade-off between two opposing factors. The temper-ature should be high enough so that the PCM does not so-lidify at typical room temperatures (< 26°C). At the sametime, the temperature should also be low enough so thatthe condenser temperature for VCC operation is not veryhigh. Higher condenser temperature leads to poor coeffi-cient of performance (COP). Thus, a very narrow range oftemperature range is applicable for the solidification tem-perature of PCM in RoCo. Paraffin based PCM is chosenbecause as a class paraffin is safe, reliable, predictable,less expensive and non-corrosive. It melts and freezes re-peatedly without phase segregation and consequent degra-dation of its latent heat of fusion (Sharma et al., 2009). Itcrystallizes with little or no supercooling (Sharma et al.,2009). The only major disadvantage of paraffin basedPCM is its low thermal conductivity. To address this issue,the thermal battery consists of helical coils of refrigeranttubing enclosed within PCM volume (See Figure 2). Thisarrangement enables higher surface area of heat transferand better reach within the PCM volume.

Figure 2. The thermal battery of RoCo in the experimental setup(Du et al., 2016)

3 Model DevelopmentThe system model for the thermosiphon consists of severalcomponents which are shown in Figure 3. The evaporator(See Figure 2) consists of four symmetric refrigerant cir-cuits and to save computational effort, only one of themis modeled. The splitter and mixer components areused to scale the dynamic behavior of a single refriger-ant circuit to the complete evaporator. The splitter di-vides refrigerant mass flow rates equally into four, whilethe mixer combines them. The refrigerant then flows intothe riser, condenser, refrigerant tube and downcomer be-fore flowing back to the evaporator. The refrigerant tube isa non-adiabatic flow passage for the refrigerant. The PCMblocks are connected to a tube control volume, which is asimple model of circular wall for pipes. The tube controlvolume component is also used to model the pcm con-tainer. Finally, the heat losses by natural convection andradiation from the pcm container to the ambient are incor-porated. Detailed description of the component models isprovided in this section.

3.1 Phase Change MaterialRecall that the PCM Heat Exchanger (PCM-HX) consistsof helical refrigerant tubes surrounded by PCM. The PCMsolidification is a complex phenomenon due to the fact thatthe solid-liquid boundary moves depending on the rate ofheat transfer and hence its position with time forms partof the solution (Zalba et al., 2003). The rate of heat trans-fer varies progressively during the phase change due tothe varying effects of conduction and natural convectionwhich depends on the state of PCM. Thus, the dynamicsof PCM and thermosiphon are coupled. The helical natureof the refrigerant tube further increases the complexity bymaking the problem three-dimensional.

Modeling of a Thermosiphon to Recharge Phase Change Material Based Thermal Battery for a Portable AirConditioning Device

460 Proceedings of the 12th International Modelica ConferenceMay 15-17, 2017, Prague, Czech Republic

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pCMCapacitor

C

pCMConductor

Condenser

RH

duration=0Tair

duration=0mdot

duration=0

Splitter

Mixer

convection

Gc

fixedTemperature

T=299.35

K

const

k=0.2322

bodyRadiation

Gr=0.073215

condenser

riser

evaporator cv

tube cv

pcm conductor

pcm capacitor

pcm container

refrigerant tube

downcomer

air inlet boundary conditions

Heat losses from PCMcontainer to surroundings

Figure 3. Schematic of System Model for Thermosiphon.

The model used in the current work is a trade-off for ac-curacy, complexity and usability. The PCM block is takenas a lumped control volume to eliminate the modeling ofmomentum equation for the molten PCM flow from natu-ral convection. Two components are used to model PCM:PCMConductor to model the rate of heat transfer from thePCM and PCMCapacitor to model the PCM heat storage.

3.1.1 PCM CapacitorThe PCM-HX is the heat source for the thermosiphon andconsequently dictates its dynamics. Very accurate descrip-tion of its solidification is required. The energy equationapplied to PCM control volume gives rise to:

mpcmdhdt

= Q (1)

where, mpcm [kg] is the mass of PCM, h [Jkg−1] is thespecific enthalpy, t [s] is the time and Q [W] is the rate ofheat transfer.

The enthalpy method by Voller (1990) is used to modelthe energy equation. This method requires an inputof enthalpy-temperature function of PCM solidificationwhich is created using data from DSC readings of thePCM. This ensures accurate temperature prediction of thePCM state during solidification. The benefit of the en-thalpy method is that it allows calculations on a fixedgrid with implicit treatment of the phase change boundary.

Modelica.Blocks.Sources.CombiTable1D block isused for input of enthalpy-temperature profile.

The enthalpy-temperature profile is calculated as shownin equation (2)

h(T ) =

∫ TA

T csdT, solid∫ TATB

c(T )dT, two phaseh f g +

∫ TBT cLdT, liquid

(2)

h f g [Jkg−1] is the latent heat of melting, the PCM meltsfrom temperature TA [K] to TB [K], cs [Jkg−1 K−1], c(T )[Jkg−1 K−1] and cL [Jkg−1 K−1] are specific heat capaci-ties of PCM in the respective phases.

The melt fraction (λ ) of PCM is calculated from its en-thalpy by the following equation:

λ = max(0,min(1,hhl)) (3)

where hl [Jkg−1] is the enthalpy at the point where thePCM just turns liquid. The equation is simplified becauseof the fact that the enthalpy scale is defined as zero for thepoint where the PCM starts to melt. The melt fraction ismade available for the PCM capacitor block through theRealOutput interface.

Session 7B: Thermodynamic Systems

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461

3.1.2 PCM Conductor

The PCM Conductor block captures the variable effectsof conduction and natural convection during the solidifi-cation of PCM. It calculates heat transfer coefficient as afunction of melt fraction.

PCM Conductor block connects the re-frigerant control volume of the condenserto the PCM Capacitor block. It extendsModelica.Thermal.HeatTransfer.Interfaces.Element1D block and provides for the heat flow, whichis calculated using CombiTable1D fitted function forheat transfer coefficient as a function of melt fraction.The RealInput interface is used to obtain melt fractioninput from PCM Capacitor.

Table 1 contains the anchor points given to the Com-biTable block used as input for the normalized heat trans-fer coefficient as a function of melt fraction. The con-stant value used to multiply the normalized function toobtain heat transfer coefficient (HTC) is 116 Wm2 K−1.These numbers are obtained by matching the condenserpressure from simulation to the experiment since there areno correlations to capture the behavior in literature. Paland Joshi (2001) discuss the heat transfer variation in thefour regimes captured by Table 1. The initial heat trans-fer occurs in a conduction dominated regime. Then thereis a reduction in heat transfer coefficient with the appear-ance of small melt layer because the velocity of the liquidPCM due to buoyancy force is small. The melting thenprogresses to a convection dominated regime where thevelocity of liquid PCM increases causing a higher rate ofheat transfer. Finally, the magnitude of velocity decreasesas the temperature in the molten PCM becomes more uni-form with time due to natural convection stirring, leadingto decreased buoyancy force for convection.

Table 1. Input table for PCM Conductor block.

Melt Fraction Normalized HTC

0 10.2 0.90.4 10.7 0.91 0.8

3.1.3 PCM-HX Refrigerant Control Volume

The PCM is modeled using a lumped control volume (CV)and accordingly a lumped control volume on the refriger-ant side is required. These two CVs are connected usingModelica.Thermal.HeatTransfer.Interfaces.HeatPort interface.

The liquid refrigerant from the downcomer reachesthe bottom header of the PCM-HX (See Figure 2).Then it absorbs heat from the PCM, vaporizes andrises up into the riser. The flow of refriger-ant into and out from the CV, is modeled using

Modelica.Fluid.Interfaces.FluidPort interface.To define the state of refrigerant inside the lumped con-

trol volume two properties are required. The average den-sity, ρavg [kgm−3] for the two phase refrigerant can beobtained as shown below:

Vtot =Vv +Vl (4)m = ρvVv +ρlVl (5)

ρavg =m

Vtot(6)

V [m3] refers to the volume of the refrigerant, m [kg]its mass. The subscripts v and l refer to vapor and liquidphases while tot stands for total.

The pressure of the refrigerant is the average of thepressure at its inlet and outlet fluid ports.A medium recordfor the refrigerant is created and these thermodynamicproperties are set to determine its state.

medium.d = rho_avg;medium.p = 0.5*(port_a.p+port_b.p);

The net pressure drop between the inlet and outlet portsis assumed to equal to the gravitational head offered bythe refrigerant column.

The evaporator CV consists of liquid refrigerant withvapor escaping from the top after absorbing heat from thesurrounding PCM. If the flow were to reverse, liquid re-frigerant will leave out from the inlet port. Thus the streamvariable of enthalpy in the fluid connectors are equated tothe enthalpies of saturated liquid and vapor.

port_a.h_outflow = h_f;port_b.h_outflow = h_g;

The heat flow term of the HeatPort is calculated by mul-tiplying heat transfer coefficient by the product of surfacearea and temperature difference between HeatPort temper-ature and medium temperature.

heatPort.Q_flow = htc * A * (heatPort.T -medium.T);

The two phase heat transfer coefficient for the refrig-erant inside the helical coils is calculated first by usingSchmidt (1967) correlation to obtain single phase liquidonly heat transfer coefficient which is then used in ShahChart correlation (Shah, 1982).

Finally, the mass and energy balance equations are writ-ten down and state transformations applied to update thevalues of pressure and enthalpy of the refrigerant CV. Thisapproach is pretty standard in two phase refrigerant sys-tem and is discussed in Tummescheit et al. (2000). Theequations for energy, however, involve stream connectorvariations as described in Franke et al. (2009).

3.2 CondenserThe condenser in the system is a standard air to refriger-ant heat exchanger. It is modeled using the heat exchangerdeveloped by Qiao et al. (2015). The model neglects grav-itational pressure drops. Thus, it can be visualized as if



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it is placed in a horizontal plane as opposed to verticalin the real case. However, the height of the condenser issmall compared to the riser and gravitational effects canhence be ignored for model simplicity. The refrigerantside heat transfer coefficients for two phase flow are cal-culated using Shah (2016) correlation. The airside heattransfer coefficient is calculated using (Wang et al., 2000)correlation.

3.3 RiserRecall that the riser is that portion of the refrigerant cir-cuit where the refrigerant vapor rises from the evaporatorinto the condenser. The timescale over which its dynam-ics evolves is much faster than the heat exchangers. As aresult, it is modeled as what is described as Flow Modelin literature (Tummescheit et al., 2000). Only the momen-tum equation is used in the model and the mass and energystorage in the control volume are ignored. The momentumequation for riser contains balances for the pressure force,frictional force and gravitational force as shown in Equa-tion 7 in which Lt [m] is the length of the riser, dm

dt [kgs−2]is the rate of change of refrigerant mass flow rate, A [m2]is the cross-section area for refrigerant flow in the tube,pin [Pa] and pout [Pa] are inlet and outlet pressures, f isfriction factor, S [m] is the perimeter of the flow section ofthe tube, ρ [kgm−3] is refrigerant density and g [ms−2] isthe acceleration due to gravity.

Ltdmdt

= A(pin − pout)−12

m2

ρA2 f SLt +AρgLt (7)

The friction factor equation incorporates laminar andturbulent flow regimes by merging Hagen-Poiseuille andBlasius equations. Both these equations are taken fromBergman and Incropera (2011).

3.4 DowncomerThe model for downcomer is similar to that of riser exceptfor the momentum equation in which the direction of grav-itational effects are reversed. The momentum equation fordowncomer is shown in Equation 8.

Ltdmdt

= A(pin − pout)−12

m2

ρA2 f SLt −AρgLt (8)

3.5 Heat LossesThe PCM loses heat by natural convection and radiationwith the surroundings. The heat loss by these modes areabout 15-20% of the heat removed by the thermosiphon.For accurate prediction of solidification time, it is neces-sary to include these heat losses.

The PCM is contained in a PVC container. A simpleTube model of circular wall with one-dimensionalheat conduction and capacitance lumped at arithmeticmean temperature is used. The equations for thismodel can be found in Modelica.Fluids.Examples.

25

30

35

40

45

50

0 100 200 300 400 500

Tem

per

atu

re [°C

]

Time [min]

Expt_axis Expt_wall Sim_PCM

Figure 4. Comparison of PCM temperature prediction with ex-perimental data

HeatExchanger.BaseClasses.WallConstProps.The Tube model has two HeatPort interfaces, oneof which is connected to the PCM Capacitorblock. The second HeatPort is connected to aModelica.Thermal.HeatTransfer.Sources.FixedTemperature block whichhas surrounding temperature, viaModelica.Thermal.HeatTransfer.Components.Convection and Modelica.Thermal.HeatTransfer.Components.BodyRadiation blocks to model the heatlosses.

The heat transfer coefficient by convection from thecontainer walls is obtained using Churchill and Chu(1975) correlation for natural convection for verticalplates. Radiation is calculated by taking a value of emis-sivity ε = 0.9 for the material. The container is assumedto be a convex body in a large enclosure. The heat transfercoefficient from the top surface of the container is calcu-lated using Lloyd and Moran (1974) correlation. However,this value is negligible in comparison to the net heat lossand omitted from the simulation.

4 Results and DiscussionFigure 3 shows the thermosiphon model with all the com-ponents described in the previous section. The boundaryconditions and initial state points are provided using theexperimental results from Du et al. (2016).

Figure 4 shows a comparison of PCM temperaturesfrom the experiment with the model. There are two pointsfrom the experiment with subscripts axis and wall. Thesubscript axis refers to temperature probe near the PCMcontainer wall while the subscript axis refers to tempera-ture probe at the axis of the helical coil. The dotted linein the Figure 4 shows the lumped PCM temperature fromthe model. As can be observed, the overall prediction isgood until roughly 430 minutes. The results deviate sig-nificantly from this point. This deviation can be attributedto the assumption of the adiabatic riser. In the experiment,there is heat loss from the refrigerant vapor as it passesthrough the riser leading to its condensation. The heat ab-sorption from PCM drops significantly when the PCM is


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463

0

0.2

0.4

0.6

0.8

1

0 100 200 300 400 500

Mel

t F

ract

ion

[-]

Time [min]

Figure 5. Percentage of PCM Molten with time

solidified. The model predicts a small rate of the massflow rate at this point, but in reality there is no mass flowrate. The refrigerant vapor rises up but gets condensed andfalls back down. This phenomenon is not captured by themodel.

The recharge time calculated by the model is 489 min-utes when the PCM fully solidifies (See Figure 5). How-ever, 94% percent of PCM is solidified at the 400 minutemark. For a good overall cycle COP for RoCo, the ther-mosiphon can be operated for only 400 minutes and VCCoperation started at this point.

Figure 6 shows the temperatures on the airside of thecondenser. The prediction of air outlet temperature isslightly lower in the initial 20 minute interval. This canbe attributed to the receiver present in the circuit which isfilled with hot liquid refrigerant. For the setup, the receiveris sized in such a way that the downcomer is completelyfilled with liquid refrigerant. This results in larger thermalmass of refrigerant to be cooled.

5 ConclusionsA fully transient model for two phase closed loop ther-mosiphon is developed from first principles and used tostudy the dynamics of a thermosiphon used to rechargethe thermal battery of a portable air conditioner. Equa-tions to model various components of the thermosiphon

25

26

27

28

29

30

0 100 200 300 400 500

Tem

per

atu

re [°C

]

Time [min]

Expt_in Expt_out Sim_out Sim_in

Figure 6. Comparison of air inlet and outlet temperatures at thecondenser

are discussed. The heat source of the thermosiphon is fi-nite and the coupled dynamics is successfully predicted bythe model. It is observed that solidifying 94% of PCM isbetter than full solidification for better system COP. Themodel is expected to be an invaluable tool in designingthe future versions of the portable air conditioning devicewith different requirements.

6 AcknowledgmentThis research was supported by the Advanced ResearchProjects Agency - Energy (ARPA-E) with Award NumberDE-AR0000530. We thank the members of Center for En-vironmental Energy Engineering (CEEE) and team mem-bers of the Roving Comforter Project for their support.

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Modeling of a Thermosiphon to Recharge a Phase Change ...evaporator cv tube cv pcm conductor pcm capacitor pcm container refrigerant tube downcomer air inlet boundary conditions Heat