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Applied Thermal Engineering 48 (2012) 436e445

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Applied Thermal Engineering

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

Experimental and numerical study on the enhanced effect of spiral spacer to heattransfer of supercritical pressure water in vertical annular channels

Han Wang, Qincheng Bi*, Zhendong Yang, Wu Gang, Richa HuState Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xianning West Road #28, Xi’an 710049, China

h i g h l i g h t s

< Enhanced effects of spacer to heat transfer of water were investigated.< Spiral spacer has local and global effects on heat transfer.< Spiral spacer has positive effect on eliminating heat transfer deterioration.< The mechanisms for the enhanced effect of spacer were obtained.

a r t i c l e i n f o

Article history:Received 10 March 2012Accepted 8 May 2012Available online 14 May 2012

Keywords:Supercritical pressure waterHeat transferAnnular pipeSpiral spacer

* Corresponding author. Tel.: þ86 29 8266 5287; faE-mail address: qcbi@mail.xjtu.edu.cn (Q. Bi).

1359-4311/$ e see front matter � 2012 Elsevier Ltd.doi:10.1016/j.applthermaleng.2012.05.010

a b s t r a c t

Heat transfer characteristics of supercritical pressure water in annular channel have been investigatedexperimentally and numerically. The gap of the annular channel was 6 mm and a spiral spacer witha length of 100 mmwas arranged on the inner test section. Experimental parameters included pressuresof 23e28 MPa, mass fluxes of 350e1000 kg/m2 s and heat fluxes up to 1000 kW/m2. Special attention hasbeen focused on the effect of spacer on heat transfer characteristics of water. In the experiments, anenhanced effect of the spiral spacer on heat transfer has been observed. It was found that the affecteddistance of the spacer depends strongly on flow conditions. Moreover, it was also observed that the spiralspacer has a positive effect on eliminating heat transfer deterioration which occurred at high ratios ofheat flux to mass flux. Numerical simulation was carried out with a Computational Fluid Dynamics (CFD)method to obtain a deep insight of how the spiral spacers affect heat transfer. Calculated heat transfercoefficients captured the experimental data pretty well, with a largest deviation of 14.33% shows up atthe vicinity of the pseudo-critical temperature. The mechanisms for the enhanced effect of spacer onheat transfer have been discussed based on the physical profiles obtained from numerical results.

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1. Introduction

The Supercritical Water-cooled Reactor (SCWR) has beenselected as one of the six Generation IV nuclear reactors by theGeneration IV International Forum (GIF) in 2002 [1]. The designs ofSCWRs aim to achieve a safe, reliable and economic operation witha low power cost. A SCWR power plant may have a thermal effi-ciency of 45% by operating its coolant at a higher temperature(500 �C) and pressure (25 MPa) compared to the efficiency ofcurrent Light Water-cooled Reactor (LWR) power plants of about33% [2]. Moreover, since the reactor coolant experiences noliquidevapor transition beyond the critical pressure, a SCWR powerplant system can become more compact by eliminating the coolantrecirculation pump, steam generator and steamewater separation,

x: þ86 29 8266 9033.

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which will further lower the capital cost. Although there is nophase change at supercritical pressure and the boiling crisis can beeliminated in a SCWR, the thermophysical properties of supercrit-ical water experience strong variations at the vicinity of thepseudo-critical temperature (Fig. 1). These drastic variations causelarge non-uniformity of buoyancy over the flow channel and resultin unusual heat transfer behaviors. Therefore, a thorough knowl-edge of heat transfer characteristics of supercritical water ingeometries relevant to nuclear reactor, such as annular or bundlechannels, is essential for the design of SCWR fuel bundle.

Heat transfer characteristics of water at supercritical pressureshavebeeninvestigatedbymanyresearchers since the1950s. Swensonet al. [3] and Yamagata et al. [4] investigated forced convection heattransfer in vertical upward tubes. They found that heat transfer wasenhanced within the pseudo-critical enthalpy region but the peakheat transfer coefficient decreases with the increase of heat flux.Jackson andHall [5] conducted experiments on heat transfer of water

Nomenclature

cp specific heat [kJ/kg K]G mass flux [kg/m2 s]h heat transfer coefficient [kW/m2 K]k turbulent kinetic energy [m2/s2]K temperature [K]P pressure [MPa]q heat flux [kW/m2]t temperature [�C]U velocity [m/s]

Greek lettersl thermal conductivity [W/m K]m dynamic viscosity [Pa s]r density [kg/m3]

Subscriptsb bulkcal calculatedexp experimentalin inletpc pseudo-criticalw wall

Abbreviationsms measuring positionSCWR Supercritical Water-Cooled Reactor

H. Wang et al. / Applied Thermal Engineering 48 (2012) 436e445 437

in vertical and horizontal tubes and provided a criterion for buoyancyeffect.With thedevelopmentofnuclear powerplants since the 1970s,heat transfer in fuel bundleswithgrid spacers attractsmore andmoreinterests. Cluss [6] conducted experimental study on the effect ofspacer to post critical heat flux heat transfer in a vertical tube. Heobserved a promoted heat transfer phenomenon at the spacer andconcluded that this phenomenon may be caused by the increasedflowvelocityat the spacer and the radiation to liquiddepositedon thespacer. Yoder [7] carried out single and two-phase heat transferinvestigations in rod bundles. He found that heat transfer wasimproved beyond the spacer range and the affected zone dependedonflowconditions. Hassan andRehme [8] performed gas-cooledheattransfer experiments in rod bundles with grid spacer. Based on the

Fig. 1. Thermophysical property variation of water as a function of temperature at25 MPa.

measurements, empirical correlations for the influence of spacer onheat transfer were established. Other studies dealing with spacereffect to heat transfer were presented by Cesna and Valincius [9] andLeeetal. [10]. The results showed that spacereffect in rodbundleswasvery limited and related closely to mass velocity. Nematollahi andNazifi [11] studied the enhancement of heat transfer in LWR by gridspacer andobtainedanoptimumspacer shapewithCFDanalysis. Zhuand Laurien [12] conducted numerical simulation of water coolingchannel with a wrapped wire single rod. The effect of wrapped wireon heat transfer was discussed in detail. Investigation on the optimaldesign and structure reliability of spacer has also been performed bymany other researchers with CFD methods [13e15].

Although much work has been done on the enhanced heattransfer effect of spacer, the mechanisms have not been fully solveddue to the difference in spacer shape and flow conditions. More-over, previous studies were mainly restricted to single and two-phase heat transfer under sub-critical pressures, little researchhas been devoted to the effect of spacer on heat transfer of water atsupercritical pressures. Under the background of developing SCWR,it is essential to study the effect of spacer in SCWR fuel bundle.Therefore, heat transfer experiments of supercritical water in singlerod channel were carried out at Xi’an Jiaotong University. Theenhanced heat transfer effect of spacer to supercritical water wasobserved in the experiments and the mechanisms for thisphenomenon were studied by numerical methods.

2. Experimental materials and methods

2.1. Experimental facility and procedure

The experiments were carried out in the high-temperature andhigh-pressure steamewater test loop shown in Fig. 2. Distilled andde-ionized feed water in the water tank was driven through a filterby a high-pressure plunger pump operating at pressure up to40 MPa. Part of the water was returned to the water tank througha bypass and the rest part of the water flowed through measuringorifices and adjusting valves into a heat exchanger to absorb theheat of the hot fluid coming from the test section. Then this part ofwater was heated to the test state by the pre-heater and test sectiontransformer, using electrical AC power supplies with maximumcapacities of 760 kW and 250 kW, respectively. The heat of testsection was removed first by the above-mentioned heat exchangerand then by a condenser, and finally the feed water flowed back to

Fig. 2. Schematic diagram of the supercritical pressure water test loop.

Fig. 4. Thermocouple arrangements and the schematic diagram of spiral spacer.

H. Wang et al. / Applied Thermal Engineering 48 (2012) 436e445438

the water tank. The pressure and mass flux in the test section werecontrolled by adjusting the main valve and bypass valve.

The geometry of the test section is shown in Fig. 3. The annularchannel was made up of a heated F8 � 1.5 mm stainless steel(0Cr18Ni9) circular pipe within a F25 � 2.5 mm circular pipe,forming an annular gap of 6.0 mm and a hydraulic diameter of12.0 mm. The length of the test section was 1400 mm and waselectrically-heated by low-voltage AC current so that variable heatfluxcanbeobtained. The outerpipewasunheatedandwas thermallyinsulated to minimize heat loss. As illustrated in Fig. 3, a sealingstructure was used on the ends of the test section to guarantee thehermetic demand and ensure the electric insulation between theinner and outer pipes. A double sealing structure was performed forthe test section with a flat seal structure adopted between Flange 1and Flange 2 with a gasket seal. There was a stuffing box betweenFlange 1 and the inner pipe so that a packing seal can be obtained bysqueezing the hold-down bolt to the stuffing graphite.

The thermocouple arrangements and the schematic diagram ofspacer are shown in Fig. 4. The current design permits the use of sixthermocouples to measure the wall temperature of the test section.The spiral spacer arranged on the inner heated pipe was a string of6 mm long ceramic tubes with an outside diameter of 3 mm. Onepitchof the spiral spacerwas50mmand the full length along the testsection was 100 mm. It should be emphasized that the spiral spacerwas arranged exactly at the first measuring position (ms for short).Furthermore, in order to better evaluate the effect of spacer on heattransfer characteristic ofwater, a bare test sectionwith identicalflowgeometry which has no spacer on inner test section has also beenconducted. The wall temperatures were measured using F0.2 mmstandard NiCreNiSi thermocouples while the fluid temperaturesweremeasured byF3mmK-type sheathed thermocouples. Thefluidpressure at the inlet of the test sectionwas measured by Rosemount3051 capacitance-type pressure transmitter and the pressure drop ofthe test section was measured with a Rosemount 3051 capacitance-

Fig. 3. Geometry structure of the annular test section.

type differential pressure transducer. All data were collected andrecorded by an IMP 3595 data acquisition system. Estimated uncer-tainties in measured and calculated parameters are summarized inTable 1. In the present paper, the thermophysical properties of waterwere obtained from the NIST table [16].

The experiments were performed at the following steady-stateconditions: pressures at the inlet of the test section varied from23 to 28 MPa, mass fluxes ranged from 350 to 1000 kg/m2 s andheat fluxes on the outside wall of the heated pipe varied from 200to 1000 kW/m2. The experimental procedure was as follows. Ineach of the test condition, the pressure, mass flux and heat fluxwere firstly adjusted to given values, and then raised the heatingpower of the pre-heater to increase the bulk enthalpy at the inlet ofthe test section. The test was done once the wall temperature wasover 700 �C or when the heating power reached the maximum.

2.2. Experimental results and discussion

2.2.1. Effect of spacer on local heat transferFig. 5(a) and (b) shows the effect of spacer on wall temperature

and heat transfer coefficients plotted against bulk enthalpy. At thefirst measuring position seen in Fig. 5, wall temperatures of annularflow channel with spacer are lower than that without spacer.Consequently, heat transfer coefficients with spacer are higher thanthat without spacer, suggesting that the spiral spacer has a positiveeffect on enhancing local heat transfer. This phenomenon has alsobeen found in the post dryout heat transfer experiment in annuli byKoizumi et al. [17]. In the lowandhigh enthalpy regions, heat transfercoefficientswith spacerarehigher than thatwithout spacernearly by

Table 1Uncertainties in measured and calculated parameters.

Parameter Uncertainty

Pressure (MPa) 0.44%Electrically-heated power (kW) 6.25%Mass flux (kg/s) 1.02%Fluid temperature (�C) 0.4Wall temperature (�C) 6.14%Heat transfer coefficient (kW/m2 K) 8.83%

Fig. 6. Wall temperature distributions along the heated length (a) tin ¼ 232.1 �Cwithout spacer; (b) tin ¼ 217.9�Cwith spacer; (c) tin ¼ 429.4�Cwith spacer.

Fig. 5. Comparison of heat transfer characteristics with and without spacers (a) walltemperature; (b) heat transfer coefficient.

H. Wang et al. / Applied Thermal Engineering 48 (2012) 436e445 439

a fixed value of about 2.5 kW/m2 K. The possible reason is that thethermophysical properties variations of supercritical water in thetwo regions are rather gentle, which is similar to constant-propertyflow. However, at a bulk temperature slightly lower than thepseudo-critical temperature, the test section with spacer givesa maximum heat transfer coefficient of about 16 kW/m2 K, which ishigher than that of 9 kW/m2 K for the test sectionwithout spacer bya factor of 1.8. This suggests that the spiral spacer can significantlyimprove local heat transfer of water, especially at the vicinity of thepseudo-critical temperature.

Another evidence for the enhanced effect of spacer on local heattransfer can be observed from the wall temperature distributionsalong the heated length at a given inlet bulk temperature. In orderto get a better evaluation for the enhanced effect of spacer, only thewall temperature in low and high enthalpy regions are displayed tominimize the effect of property change on heat transfer. Fig. 6(aec)illustrates the wall temperature distributions along the heatedlength with and without spacers. As clearly shown in Fig. 6a,without the spacers, the linearity of the wall temperatures alongthe heated length is pretty well, indicating that the flow is fullydeveloped and free from entrance effect. Fig. 6b displays the walltemperature distribution with spacers. It is evident that the walltemperatures increase almost linearly from tw-2 to tw-6, whereastw-1 is significantly lower than tw-2. Taking no account of the effectof spacer, tw-1 is expected to be linearly with the wall temperatures

of the other fivemeasuring positions, as tw-10 shows. However, tw-1is lower than tw-10 by about 15 �C, suggesting that the spiral spacerhas a significant effect on decreasing local wall temperature andconsequently, improving local heat transfer. From Fig. 6c we can seea similar wall temperature distribution at a higher inlet bulktemperature compared to Fig. 6b, signifying that the spacers alsohave an enhanced effect in high enthalpy region.

H. Wang et al. / Applied Thermal Engineering 48 (2012) 436e445440

2.2.2. Effect of spacer on heat transfer over the whole flow channelFig. 7 displays the heat transfer coefficients plotted against bulk

enthalpy at four measuring positions (ms-1, ms-2, ms-3 and ms-5)along the flow direction. At a high mass flux and heat flux conditionshown in Fig. 7(a), it is clear that heat transfer coefficient of ms-1is higher than that of the other three measuring positions overthe whole range of bulk enthalpy, which further proves theabove-mentioned conclusion that spacer has a significant effect onenhancing local heat transfer. In addition, it can be seen from Fig. 7(a)that heat transfer coefficients decrease gradually fromms-1 to ms-5along the flow direction. The reason for this interesting feature isthat although the spacer has a positive effect on enhancing local heattransfer, this effect is gradually weakened as the flow develops to thedownstream. Therefore, heat transfer coefficients behavea decreasing trend fromms-1where the spacerwas arranged toms-5whichwas far from the spacer.Moreover, it can also beobserved fromFig. 7(a) that heat transfer coefficients of ms-3 and ms-5 are almostidentical, indicating that the affected distance of spacer terminates atms-3 at the current mass flux of 1000 kg/m2 s. This observation isconsistent with the study of Yao et al. [18] who found that theenhancementof heat transfer is relatively short-livedanddecayswiththe increasing distance downstream from the spacer.

The variations of heat transfer coefficients plotted against bulkenthalpy at the four measuring positions under a relative lowmassflux and heat flux are shown in Fig. 7(b). Similar to the variation at

Fig. 7. Effect of spacer on heat transfer coefficients (a) at q/G ¼ 0.6; (b) at q/G ¼ 1.14.

high mass flux, heat transfer coefficient of ms-1 is significantlylarger than that of the other three measuring positions. However,unlike the case of high mass flux, heat transfer enhanced effect ofthe spacer at low mass flux terminates very quickly. Because theheat transfer coefficients of ms-2, ms-3 and ms-5 become nearlycoincident within the whole enthalpy region, it is concluded thatthe enhanced effect of spacer could not even spread to ms-2.Comparing the heat transfer coefficients in Fig. 7(a) and (b)comes to the conclusion that the affected distance of the spiralspacer depends strongly on flow conditions. This conclusion is inagreement with the findings of Unal et al. [19].

2.2.3. Effect of spacer on heat transfer deteriorationFig. 8 gives the wall temperature distributions plotted against

bulk enthalpy under a relative high ratio of heat flux to mass fluxcondition of 1.71. A transverse comparison was made for the walltemperature at the first measuring position under the condition ofwith and without spacer. As clearly shown in line-1 and line-2, inthe case of disusing spacer, heat transfer deterioration occurs at thefirst measuring position with a rapid wall temperature incrementfrom 400 �C to 500 �C, whereas no deteriorated heat transfer isobserved at the same positionwhen the spacer is used, as shown byline-2. A vertical comparisonwas also made by line-2 and line-3 forthe wall temperatures at the first and second measuring positionsunder the circumstance of using spacer. Wall temperature of tw-2behaves rather unusual, with a rapid increase prior to the pseudo-critical temperature, a recover back in the pseudo-critical regionand a sudden rise in high enthalpy region. It is clear that heattransfer deterioration occurs at tw-2 but does not appear at tw-1.Taking the transverse and vertical wall temperature comparisonsinto consideration, it is concluded that the spiral spacer hasa positive effect on eliminating local heat transfer deterioration.

In this study, we believed that heat transfer deterioration iscaused by the combined effects of strong variations in thermo-physical properties of supercritical water near the pseudo-criticaltemperature. Under the condition of high ratio of heat flux tomass flux, there remains a large radial gradient in fluid temperatureover a cross section. A thin fluid boundary layer close to the heatedwall absorbs enough heat and firstly enters into the pseudo-criticalregion, while the fluid adjacent to the outer pipe remains relativelycold. Thus, a drastic reduction of fluid density, viscosity and thermalconductivity from the outer cold fluid to the inner hot boundarylayer is formed. The strong reduction of viscosity in the hot

Fig. 8. Comparison of wall temperature at deteriorated heat transfer condition.

Fig. 9. Comparison of experimental and calculated heat transfer coefficient in verticalupward circular tube.

H. Wang et al. / Applied Thermal Engineering 48 (2012) 436e445 441

boundary layer reduces the shear stress between the hot layer andthe mainstream cold water, which impairs the turbulent diffusivity.A large decrease in fluid density causes buoyancy effect whichreduces the velocity gradient and consequently, impairs turbulenceproduction [20]. The decrease in thermal conductivity furtherweakens heat transfer by reducing heat conduction from theheated wall to the boundary layer. The combined effects of theabove-mentioned factors make the heated wall covers by light andhot fluid, which eventually results in heat transfer deterioration.However, because of the disturbance and swirling effect of thespacer, the turbulence is enhanced, the mixing in the boundarylayer is promoted and temperature gradient in the radial directionis decreased. Therefore, heat transfer deterioration does not occur,as can be seen in tw-1 with spacer.

3. Numerical simulation

In the following discussions, heat transfer of supercritical waterin an annular upward channel has been calculated using the CFDcode Fluent 6.3. Moreover, numerical results were also comparedwith our test data to verify the performance of the selectedturbulence model and to get more understanding about thephenomena happening in supercritical water.

3.1. Turbulence model

The main difficulties in numerical analysis are related to theturbulence model under supercritical pressure [21]. There is a strongbuoyancy and thermal acceleration near the heated wall due to thelarge variation of thermophysical properties, especially at the vicinityof the pseudo-critical point. In the present analysis, three k-ε turbu-lence models, i.e. the Standard k-ε turbulence model, the RNG k-εturbulencemodel and the Realizable k-ε turbulencemodel, are testedagainst the experimental data of Yamagata et al. [4] to obtain the bestone in predicting heat transfer of supercritical water. Calculationgeometry is a vertical upward tube with a length of 1500 mm and aninside diameter of 7.5mm. The turbulencemodel equation and valuesof the constant are shown in Eq. (1) and Table 2 [22], respectively.

uivε

vxi¼ v

vxi

��nþ nt

sε

�vε

vxi

�þ c1Sε� c2

ε2

kþ ffiffiffiffiffinε

p (1)

Fig. 9 shows the numerical results and experimental heattransfer coefficients plotted against bulk temperature. It is clearthat predictions of the three turbulence models are acceptableagainst experimental data in low and high bulk temperatureregions. However, numerical heat transfer coefficients vary greatlyat the vicinity of the pseudo-critical temperature. The result of RNGk-ε turbulence model gives more reasonable predictions comparedwith experimental data, while the predictions of Standard k-εturbulence model and Realizable k-ε turbulence model are signifi-cantly lower than experimental data. This conclusion is consistentwith the findings of Kim et al. [23] who examined more than 10first-order turbulence models in Fluent. Therefore, the RNG k-εturbulence model with enhanced wall treatment is recommendedin predicting heat transfer of supercritical water and is adopted forthe following study of annular channel.

Table 2Values of constant in the k-ε turbulence models.

k-ε Modeltype

c1 c2 cm sk sε

Standard 1.44 1.92 0.09 1.0 1.3RNG 1:42� ðhð1� h=h0Þ=1þ bh3Þ 1.68 0.085 0.7179 0.7179Realizable max {0.43, h/(5 þ h)} 1.92 1=ðA0 þ AsU*k=εÞ 1.0 1.2

3.2. Computational methods

Calculation geometry is the same as that carried out in ourexperimental investigation,which is anannularupwardchannelwitha lengthof1400mmandan insideandoutsidediameters of 8mmand20mm, respectively. It should bementioned that the spacer which ismade upof a stringof ceramic tubes in the experimentwas simplifiedby a continuous spiralmodel. The schematic geometry of the annularchannel with spiral spacer is displayed in Fig. 10 and the calculatedboundaryconditionsare listed inTable3. Thepresentanalysis isunder

Fig. 10. Geometry and boundary conditions for annular pipe.

Table 3Calculated boundary conditions for heat transfer in annular channel.

Boundary Property Value Unit

Inlet Constant mass flux 1000 kg/m2 sTurbulence intensity 5 %Turbulence length scale 0.012 m

Outlet Pressure 25 MPaInner wall Constant heat flux 600 kW/m2

Outer wall Constant heat flux 0 kW/m2

Table 4Mesh systems used for sensitive study.

Meshes With spacer Without spacer

1 656,150 326,2002 946,220 683,6603 1,458,000 844,600

H. Wang et al. / Applied Thermal Engineering 48 (2012) 436e445442

steady-state forconvergedcomputationwhen themaximumresidualRmf after m iterations and the summed residual at the nth iterationsatisfy the following criterions:

Rnf=Rmf < 10�3 (2)

Rnf*=Rmf* < 10�6 (3)

where f represents u, v, w, k, ε and f* represents T.

3.3. Mesh validation

In this study, the values of turbulence model constants are thedefault values of Fluent 6.3. In addition, the size of the first meshclose to thewall surface plays an important role in the simulation ofheat transfer. Roelofs [24] has carried out some near wall meshrefinement studies and it was concluded that the yþ value has to beless than 1.0 with enhanced wall treatment in order to inspire thefull function of RNG k-ε turbulence model. In this numericalsimulation, three-dimensional grid systems were employed toexamine the heat transfer of water. In the r-direction, the boundary

Fig. 11. Local meshes partition (a) at the inlet

layer mesh adjacent to the wall had the minimum width of8� 10�4 mm to ensure the non-dimensional yþ is lower than 1.0 atthe largest Reynolds number. The mesh width was enlarged by 1.2within the total 15 boundary layers. Consequently, the radial meshcount was 45. The meshes of the inlet cross section and near thespacer are illustrated in Fig. 11.

Three meshes used in this study are listed in Table 4. Fig. 12displays the calculated heat transfer coefficients of the threemeshes with spacer against our test data at ms-5. It is clear that thepredictions from the threemeshes collapsedwell, with amaximumerror of about 0.12% shown in the sub-figure, suggesting that thecalculations are approximately mesh independent. Similar resultscan also be obtained for the case without spacer. Taking thecomputational time and cost into consideration, mesh 2 areadopted to conduct the numerical calculation.

3.4. Numerical results and discussion

3.4.1. Comparison of numerical results with annular test dataFigs. 13 and 14 show respectively the comparison of calculated

and measured heat transfer coefficients and their relative errors atthe cross section of Z ¼ 500 mm. In order to get an objectivecomparison with experimental data, the calculated heat transfer

cross section; (b) near the spiral spacer.

Fig. 12. Calculated heat transfer coefficients by three mesh systems.Fig. 14. Relative errors in heat transfer coefficients.

H. Wang et al. / Applied Thermal Engineering 48 (2012) 436e445 443

coefficients were obtained by the averaged circumferential walltemperature and bulk temperature. It is seen in Fig. 13 thatcomputed result captures the experimental data pretty well, 87.5%of the data are captured within an accuracy of 8%, suggesting thatthe selected RNG k-ε turbulence model is also applicable in pre-dicting heat transfer of supercritical water in annuli. The largestdeviation of 14.33% exists in the pseudo-critical enthalpy region, asshown in Fig. 14. The possible reason is that the thermophysicalproperties of water experience a drastic variation at the vicinity ofthe pseudo-critical temperature, whereas the RNG k-ε turbulencemodel cannot absolutely simulate the actual physical change.

3.4.2. Mechanisms of the enhanced heat transfer effect of spiralspacer

Since the spacer is spirally arranged in the flow channel, thefluid is strongly rotated and disturbed due to the swirling effect ofspacer. Hence, the turbulence intensity near the spacer is expectedto be higher than that without spacer. Fig. 15 gives the radialdistribution of turbulent kinetic energy at the cross section ofZ ¼ 570 mm which is 20 mm downstream from the spacer. It isclearly seen that the near wall turbulent kinetic energy with spaceris almost 5 times larger than that without spacer, indicating the

Fig. 13. Comparison of measured and calculated heat transfer coefficients.

turbulence intensity is greatly promoted after the fluid flowsthrough the spacer, which might be the main reason for theenhanced heat transfer effect of the spiral spacer. Fig. 16 displaysthe averaged turbulent kinetic energy along the flow directionunder three mass fluxes. We can see that the turbulent kineticenergy increases sharply from the end of the spacer, reaches a peakvalue soon afterwards and then gradually drops and finally, achievea constant value at certain locations. Moreover, it seems that theturbulence intensity and the affected distance depend strongly onmass flux. The higher the mass flux is, the higher the turbulentkinetic energy and the longer the affected distance will be.

Apart from examining the turbulence intensity near the spacer,numerical study also observes other physical profile distributions ata cross section and near wall regions. Fig. 17 illustrates the velocityand temperature profiles along the r-direction at the axial positionof Z ¼ 570 mm. As seen clearly in Fig. 17(a), the near wall velocitywith spacer experiences a faster increase and reaches a highervalue in a short distance compared to that without spacer. Thepossible reason is that the velocity is increased as the flow adjustsfor the reduced flow area at the spacer location, which might alsoincrease the velocity shortly afterwards the spacer. The combinedeffects of higher velocity and stronger turbulence intensity lead to

Fig. 15. Radial distribution of turbulent kinetic energy (P ¼ 25 MPa, G ¼ 600 kg/m2 s,q ¼ 200 kW/m2).

Fig. 16. Axial distribution of area-weighted average turbulent kinetic energy(P ¼ 25 MPa, q ¼ 200 kW/m2).

H. Wang et al. / Applied Thermal Engineering 48 (2012) 436e445444

a quicker heat exchange between the heated wall and the main-stream fluid. Thus, heat transfer is enhanced while the boundarylayer temperature remains relatively low, as shown in Fig. 17(b).The boundary layer temperature with spacer is lower than thatwithout spacer of about 6 �C.

Fig. 17. Radial distributions across a section: (a) velocity; (b) temperature (P ¼ 25 MPa,G ¼ 700 kg/m2 s, q ¼ 400 kW/m2).

Fig. 18. Radial property distributions across a section: (a) density; (b) thermalconductivity (P ¼ 25 MPa, G ¼ 700 kg/m2 s, q ¼ 400 kW/m2).

As mentioned previously, thermophysical properties of watervary greatly with the change of temperature. Fig. 18 gives the radialdistributions of density and thermal conductivity profiles with andwithout spacers. It is clearly seen in Fig. 18(a) that the radial densitywithout spacer rises from 450 kg/m3 to 620 kg/m3, forming a radialdensity gradient of 170 kg/m3 between the heated wall and themainstream. Thus, natural convection caused by density differencemay bring about considerable buoyancy effect and impair heattransfer. However, the spiral spacer lowered the radial densitydifference to 80 kg/m3, which weakens the buoyancy effect andenhances heat transfer of water compared to the case withoutspacer. In addition, Fig. 18(b) illustrates that the thermal conduc-tivity with spacer is higher than that without spacer in the nearwall region, which enhances the heat conduction from the heatedwall to the boundary layer fluid. Therefore, heat transfer withspacer is further promoted.

4. Conclusions

This paper focuses on the effect of spiral spacer on heat transferof supercritical water in an annular channel by experimental andnumerical methods. The reasons for the enhanced heat transferof spacer have been discussed based on the physical profilesdistributions obtained by numerical simulation. According to theexperimental data and numerical results, the following conclusionscan be drawn.

H. Wang et al. / Applied Thermal Engineering 48 (2012) 436e445 445

(1) The spiral spacer has an enhanced effect on local heat transfer,especially at the vicinity of pseudo-critical temperature. Itappears that heat transfer enhancement of the spacer and itsaffected distance depend strongly on flow conditions. At a lowmass flux condition (e.g. 350 kg/m2 s), the effect of spacer onlyplays its role within the local region.

(2) Heat transfer deterioration is caused by the drastic change inthermophysical properties of water near the pseudo-criticaltemperature. However, because of the swirling and disturbingeffect of the spiral spacer, heat transfer deterioration is elimi-nated at the location where the spacer is arranged.

(3) Numerical results have a good agreement with experimentaldata, except a relatively higher deviation shows up at thevicinity of the pseudo-critical temperature, indicating that theRNG k-ε turbulence model is applicable in predicting heattransfer of supercritical water in annular channels.

(4) The turbulent kinetic energy downstream from the spacer issignificantly larger than that without spacer, which is the mainreason for its enhanced heat transfer effect. Moreover, theturbulence kinetic energy increases with increasing mass flux.

(5) The near wall velocity downstream from the spacer is muchlarger than that without spacer, which is another main factorfor heat transfer enhancement. The combined effect of highervelocity and stronger turbulence intensity leads to a lowerboundary layer temperature. A smaller radial density gradientweakens buoyancy effect while a higher thermal conductivityin the near wall region enhances heat conduction, both ofwhich contribute to the improvement of heat transfer.

Acknowledgements

This research was financially supported by the Atomic Energy ofCanada Limited.

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