Annals of Nuclear Energy 45 (2012) 37–45

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Annals of Nuclear Energy

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Development of sub-channel code SACoS and its application in coupledneutronics/thermal hydraulics system for SCWR

Khurrum Saleem Chaudri a,b, Yali Su a, Ronghua Chen a, Wenxi Tian a, Guanghui Su a, Suizheng Qiu a,⇑a School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an 710049, Chinab Pakistan Institute of Engineering and Applied Sciences (PIEAS), Nilore 45650, Islamabad, Pakistan

a r t i c l e i n f o a b s t r a c t

Article history:Received 28 September 2011Received in revised form 16 January 2012Accepted 19 February 2012Available online 22 March 2012

Keywords:Sub-channelHPLWRSCWRCoupled analysis

0306-4549/$ - see front matter � 2012 Elsevier Ltd. Adoi:10.1016/j.anucene.2012.02.014

⇑ Corresponding author. Tel.: +86 29 82668648; faxE-mail address: szqiu@mail.xjtu.edu.cn (S. Qiu).

Supercritical Water Reactor (SCWR) is one of the promising reactors from the list of fourth generation ofnuclear reactors. High thermal efficiency and low cost of electricity make it an attractive option in the eraof growing energy demand. An almost seven fold density variation for coolant/moderator along the activeheight does not allow the use of constant density assumption for design calculations, as used for previousgenerations of reactors. The advancement in computer technology gives us the superior option of per-forming coupled analysis. Thermal hydraulics calculations of supercritical water systems present extrachallenges as not many computational tools are available to perform that job. This paper introduces anew sub-channel code called Sub-channel Analysis Code of SCWR (SACoS) and its application in coupledanalyses of High Performance Light Water Reactor (HPLWR). SACoS can compute the basic thermalhydraulic parameters needed for design studies of a supercritical water reactor. Multiple heat transferand pressure drop correlations are incorporated in the code according to the flow regime. It has the addi-tional capability of calculating the thermal hydraulic parameters of moderator flowing in water box andbetween fuel assemblies under co-current or counter current flow conditions. Using MCNP4c and SACoS,a coupled system has been developed for SCWR design analyses. The developed coupled system is veri-fied by performing and comparing HPLWR calculations. The results were found to be in very good agree-ment. Significant difference between the results was seen when Doppler feedback effect was included inthe coupled calculations. This difference is due to the use of different values of fuel temperature toinclude Doppler feedback in our and reference coupled systems. This also lays emphasis on the use of truerepresentative values of critical parameters in the design calculations to get the real picture of conditionsrather than over or under estimated values.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Supercritical Water Reactor (SCWR) is an emerging 4th genera-tion reactor. Higher thermal efficiency so cheap electricity, simpli-fied system due to one phase coolant/moderator flow so lowcapital cost, absence of boiling crisis during normal operationdue to no change of phase, low flow rate as compared to Pressur-ized Water Reactor (PWR) and Boiling Water Reactor (BWR) dueto large specific heat around pseudo critical point, developed sec-ondary side due to experience with supercritical water fossil fueledpower plants and small containment size are few of the advantagesthat SCWR can bring to the table. Thermal (Liu and Cheng, 2009;Oka et al., 1992; Squarer et al., 2003), fast (Oka and Koshizuka,1998) and mixed (Liu and Cheng, 2007) spectrum kind of reactorconcepts are being studied for SCWR. Pressure vessel (Liu andCheng, 2009; Oka et al., 1992; Squarer et al., 2003) and pressure

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tube (Shan et al., 2009) kind of reactor designs are under study.Major work about SCWR is being done in Japan, Europe, China,Canada and Korea. European design is known as High PerformanceLight Water Reactor (HPLWR) (Squarer et al., 2003).

In supercritical phase of liquids, thermal hydraulic behavior ofthe system is quite different from normal PWR or BWR system.For example, due to operation under supercritical pressure, therewill be no Onset of Nucleate Boiling (ONB) or Departure fromNucleate Boiling (DNB) in SCWR. Instead, the phenomena of Onsetof Heat Transfer Deterioration or Heat Transfer Deterioration (HTD)are encountered. Heat transfer correlations are different from sub-critical water reactor. Due to large and abrupt variation of modera-tor and coolant density, both thermal hydraulics and neutronicsproperties vary drastically over the active length of the fuel. Thenumber of thermal hydraulics codes being used in nuclear industryfor research regarding supercritical water reactor are very few e.g.(Shan et al., 2009; Yoo et al., 1999) Conventionally used thermalhydraulics codes like COBRA (Basile et al., 1987) are being modifiedto work with supercritical water reactors but still are in developing

Nomenclature

m axial mass flow rate (kg/s)v cross flow rate (kg/s)s length faced into neighboring channel (m)Dz length of control volume (m)A flow area (m2)g gravitational acceleration (m/s2)f friction coefficienth specific enthalpy (J/kg)k pressure drop coefficient of grid spacer/2 two-phase friction multiplierw coolant velocity (m/s)G mass flux (kg/m2 s)p pressure (Pa)

D fuel rod outer diameter (m)l turbulence length (m)Kg frictional pressure drop coefficient for transverse flowq linear power density (W/m)t temperature (K)q density (kg/m3)a void fractionb turbulence factoru fuel rod fraction included in the channeli, j, k sub-channel subscriptsl liquid phasev vapor phase

axiallevel j-1

j

j+1channel i channel n=l+l'-i

h ρij axial

interval j

m

m ij-1

q"ij

v kj

v'kj

P ij

P ij-1

Δz

ij

ijα

ij T ij

j+1

gap k

Fig. 1. Basic quantities sub-channel nomenclature.

38 K.S. Chaudri et al. / Annals of Nuclear Energy 45 (2012) 37–45

phases (Ammirabile, 2010). Hence the scarcity of computationalcodes for thermal hydraulic analyses of supercritical water systemspresents a potential challenge and opportunity for research.

The recent advancements in the field of computer sciences haveopened new horizons for scientific community. Calculations whichtook days or weeks can now be done in a matter of minutes orhours. Availability of high computational capability systems havestarted many new activities focusing on the better understandingand inclusion of interaction between neutron kinetics and thermalhydraulics in the field of nuclear reactor design and safety. A pro-ject named CRISSUE-S was launched by Europe in 2002–2003. Themain emphasis of the program was to re-evaluate critical issues innuclear reactor design and safety by implementing 3D neutronics/thermal hydraulics coupled systems. The reports presenting thefindings of this project have strongly suggested the use of coupledcalculations for safety evaluation of LWRs (Partners, 2004a,b,c).

Design studies of the supercritical water fuel assemblies needcoupled analysis using 3D neutronics and thermal hydraulics cal-culations. This is due to the fact that density of coolant can varyfrom a value of above 700 kg/m3 to less than 100 kg/m3 over theactive fuel length. Conventional design studies use the approachof constant coolant/moderator density throughout the fuel assem-bly (Oka et al., 1992). Looking at the magnitude of density variationof SCWR, the best approach is to perform the coupled neutronics/thermal hydraulics analyses. Studies conducted have shown thedifference between coupled and non-coupled systems is very large(Waata, 2006). Design and safety studies for all kinds of SCWR areadopting the coupled calculations methodology. For HPLWR, vari-ous studies have been performed on the recent 3-pass core design(Schulenberg et al., 2008). Analyses about finding the equilibriumcore (Maráczy et al., 2011; Monti, 2009), doing the burn-up calcu-lations (Reiss et al., 2008) or performing the safety analyses (Mará-czy et al., 2010) are being performed using coupled calculations. Anew design for HPLWR is also proposed by the name of SimplifiedSuper Critical Water Reactor (SSCWR) by using zirconium hydrideto compensate for under moderation present in SCWR (Reiss et al.,2010). The account of Japanese SCWR (thermal and fast) designmethodology, design calculations and safety studies can be foundin this reference (Oka et al., 2010). Studies about pressure tubetype SCWR design using coupled analyses can be found in thiswork (Shan et al., 2009). Design of a new fuel assembly using cou-pled calculations for thermal SCWR is proposed by Chineseresearchers (Liu and Cheng, 2009). A new kind of SCWR reactoris also proposed by the same team known as mixed spectrumSCWR (Liu and Cheng, 2010). All these research activities empha-size the need and importance of coupled analyses for SCWRsystems.

The selection of MCNP code in coupled calculation system offerscertain clear advantages to perform neutron kinetics calculations.A very detailed 3D geometry modeling is one of them. We do nothave to use approximations to model the geometry as is the prac-tice with diffusion theory and transport theory codes (Monti,2009). Quite complex cross section modeling techniques are tobe used for coupled calculations with diffusion and transport the-ory codes (Watson and Ivanov, 2002). For MCNP higher tempera-ture cross section modeling, we just need to prepare new crosssection libraries. To avoid generating a large number of librariesat each possible temperature, mixture technique can be used tointerpolate the cross section value between two available libraries(Bernnat et al., 2000).

In this paper, first the development of SACoS code is explainedbriefly. Then, a coupled system using Monte Carlo N-Particle(MCNP) code (Briesmeister, 2000) version 4c and SACoS is intro-duced which can perform coupled design calculations of SCWR fuelassembly.

2. Sub-channel Analysis Code of Supercritical reactor (SACoS)

Using the basic theory of sub-channel analyses, Sub-channelAnalysis Code of SCWR (SACoS) has been developed. Fig. 1 repre-sents the sub-channel nomenclature used for basic conserved

Begin

Read input data

Axial momentum

Lateral momentum

Energy balance

Coolant velocity

Crossflow rate

Enthalpy

Convergence

End

Update

Update

Update

Output

N

Y

Maximum fuel Temperature, DNBR

Mass flow rate, temperature distribution

Mass balance

Update dP

N

Y

Mass balance

Update dP

Y

N

Fig. 2. SACoS calculation flowchart.

Table 1Heat transfer models used in SACoS.

Flow/heat transfer regime Heat transfer correlation

Single phase flowRe < 2500 Collier correlationRe < 2500 Dittus–Boelter correlationSub-cooled boiling Jens–Lottes correlationSaturated nucleate boiling Chen correlationSuper critical water Bishop correlation

Dittus–Boelter correlationWatts and Chou correlation

K.S. Chaudri et al. / Annals of Nuclear Energy 45 (2012) 37–45 39

quantities. A coolant centered sub-channel scheme is used. Thebasic parameters are initialized in the main code while the geo-metric parameters of the assembly, to be thermal hydraulicallyevaluated, along with initial and boundary conditions are suppliedin the input files. The basic equations used in SACoS code to get thesolution for thermal hydraulic parameters are given here.

Mass conservation equation:

mijþ1 �mij ¼ �DzXni

k¼1

v ijþ1;kslkqik;j ð1Þ

Energy conservation equation:

mijþ1hijþ1 �mijhij

Dz¼Xmi

k¼1

uik

qkjþ1 þ qkj

2�

Xni

k¼1

bGiksikðhij � hkjÞ þ kcijsikðtij � tkjÞ

likþ

hijqij þ hkjqkj

2

� �v ijþ1;ksik

� �

ð2Þ

Axial momentum balance equation:

mijþ1wijþ1�mijwij¼�Ai Pijþ1�Pij� �

�AiqijgDz�Xni

k¼1

Dzsikv ijþ1;kGik;j

�bXni

k¼1

DzsikGik;jðwij�wkjÞ�12

fDz/2

Dhqlþ k

qijþ 1

qijþ1� 1

qij

! !mij� �2

Ai

ð3Þ

Lateral momentum balance equation:

v ijþ1;kGik;jþ1�v ij;kGik;j¼DzPij�Pkj

lik�1

2KgDzðqijþqkjÞðv ij;kÞ2

2lik

!ð4Þ

Eqs. (1)–(4) are solved numerically to get the basic thermalhydraulics parameters. The calculation flow chart for SACoS isshown in Fig. 2. This figure illustrates the calculation methodologyof the code. Axial momentum and lateral momentum equations aresolved first and with each of them, the mass conservation ischecked. After the conservation of basic quantities (mass andmomentum), the energy balance is performed. This process goeson until the convergence is achieved. After the convergence, veloc-ity, mass flow rate and temperature are printed out in separateoutput files.

Specific channels needed for thermal hydraulic calculation ofSCWR i.e. sub-channels adjacent to water box along with conven-tional sub-channels can be modeled in this code. Heat transfer ofcoolant with moderator can also be calculated. Both co-currentand counter-current flow modes can be simulated using SACoScode. Different heat transfer models and flow friction correlationsused for different flow regimes used in SACoS code are given inTables 1 and 2 respectively. In the case of supercritical water re-gime, heat transfer is calculated by Bishop Correlation (Bishopet al., 1965) as suggested by research review and application toHPLWR work carried out by researchers (Cheng and Schulenberg,2001).

To check SACoS performance, geometry shown in Fig. 3 wassolved with both COBRA and SACoS. The description of the problembeing referred to in Fig. 3 is a 17 � 17 PWR fuel rod bundle with 25unheated rods. Here, unheated rods refer to thimble guide tubeswhich can be used for control rod and instrumentation. Data forthis assembly is given in Table 3. Due to symmetry present, only1/8th assembly is modeled in COBRA and SACoS. The steady statecalculations are performed at 50% increase of nominal power.

The comparison of results obtained from both the codes isshown in Figs. 4–6. Fig. 4 shows the void fraction along the activeheight in sub-channel 10 and 26 calculated by COBRA and SACoS.Fig. 5 shows the coolant temperature profile along axial length cal-

culated by both codes for sub-channel 9, 10 and 45. Fig. 6 showscenterline fuel temperature calculated by the two codes for fuelrods 10, 32 and 45.

The results shown in Figs. 4–6 justify the statement that SACoSand COBRA are in excellent agreement with each other and that theSACoS can be used safely with other systems also.

3. Coupled MCNP and SACoS system

The large density variation axially in a SCWR makes it almostcompulsory to carry out coupled calculations for design and safetycalculations. The recent advancement in computational capabilityhas enabled us to perform coupled calculations even for computa-tionally expensive systems i.e. Monte Carlo and Computational

Table 2Flow friction correlations used for different flow regimes.

Flow regimes Darcy friction coefficient correlations

Re < 2000 f = C/Re different values for C for various geometricalchannels

2000 < Re < 3000 f = 0.048Re > 3000 Blausius correlation or McAdams correlationSuper critical

pressureBlausius correlation

Fig. 3. 1/8th Fuel assembly solved by COBRA and SACoS.

Table 3PWR fuel assembly data for comparing COBRA and SACoS.

Parameter Unit Value

Assembly side m 0.215Vertical length m 4.267Fuel rod array 17 � 17Number of fuel rods 264Number of water rods 25Rod diameter m 0.95 � 10�3

Fig. 4. Void fraction comparison between COBRA and SACoS.

Fig. 5. Coolant temperature profile along active height.

40 K.S. Chaudri et al. / Annals of Nuclear Energy 45 (2012) 37–45

Fluid Dynamics (CFD) systems (Seker et al., 2007). In this paper, wewill present the coupled MCNP and SACoS system used for designcalculations of HPLWR.

An external coupling is established between MCNP4c and SACoScode. A master module controls the coupling and transfer of rele-vant data between neutronics and thermal hydraulics codes. Smallmodules perform the duty of data transfer in successive iterations.The coupling procedure carries on until a reasonably convergedpower profile is achieved. An under-relaxation factor of 0.2 is ap-plied to dampen out the fluctuations and get a converged profilemore quickly. A flow chart depicting the coupling process is shownin Fig. 7.

3.1. Reference system

The HPLWR assembly used for testing the performance of cou-pled system is the same as designed by Hofmeister et al. (2007)

except that a fully square assembly is used rather than using onewith round corners. The main design parameters of the assemblyare given in Table 4.

Cross sectional view of the HPLWR fuel assembly being used forcalculations is shown in Fig. 8a. Due to the symmetry present, only1/8th fuel assembly is modeled in MCNP4c and SACoS. Fig. 8bshows the 1/8th assembly modeled in MCNP. The boundary condi-tions used for thermal hydraulic calculations in SACoS code aredescribed in Table 5 and boundary conditions used for neutronicscalculations in MCNP4c are given in Table 6. Along with theseboundary conditions, the coupled calculation is run for 10,000 par-ticles and 700 cycles from which first 50 cycles are discarded. Crosssection data for higher temperatures was used from ENDF-B VIIlibrary. For simulation of fuel temperatures between the availablelibraries, mixing technique (Bernnat et al., 2000) was used. Mixingtechnique provides a mean for a linear interpolation for the crosssection of fuel to simulate the Doppler broadening effect in fuel.The active length (4.20 m) of fuel is divided into 21 equal parts. Fueland coolant/moderator properties like density and temperature areconsidered constant over one axial part during one iteration.

4. Results and discussion

Using the coupled system of MCNP4c and SACoS, calculationswere performed for aforementioned HPLWR reference system.

Fig. 6. Centerline fuel temperature along the active fuel height.

Start

Run MCNP

Run SACoS

PowerConvergence

?

Stop

No

Yes

Linear Power Density

Coolant/Moderator Density & Temperature, Fuel Temperature

Fig. 7. Flowchart describing the coupling procedure.

Table 4Geometric parameters for HPLWR assembly (Hofmeister et al.,2007).

Parameter Unit Value

Diameter of fuel pellet mm 6.9Inner cladding diameter mm 7Outer cladding diameter mm 8.0Cladding thickness mm 0.5Active height mm 4200Pitch/Diameter (P/D) 1.15Gap between fuel rod and box wall mm 1.01/2 gap around one fuel assembly mm 5.0

Fuel assembly boxInner Side Length mm 65.2Wall thickness mm 1Outer side length mm 67.2

Moderator boxOuter side length mm 26.8Wall thickness mm 0.3Inner side length mm 26.2

K.S. Chaudri et al. / Annals of Nuclear Energy 45 (2012) 37–45 41

The basic parameter to look out for was k-effective value for thesystem. The results of k-effective value are shown in Table 7. Thedifference in k-effective values can be explained as difference ofcross section libraries being used. For the reference work (Waata,2006), JEFF 2.2 library was used for the calculation while we usedENDF-B VII library. The second reason can be the absence of inac-tive part of 255 mm on top and bottom of active fuel length in thereference case which was not modeled in our calculation. Also theauthor has mentioned that all results are preliminary and they in-clude an error of 7%. The value of multiplication factor in our cal-culation is showing the correct trend i.e. for partially coupledsystem the value is less than that of uncoupled system which isdue to reduction in density of water. The value used for uncoupledcase is 0.6 g/cm3 for coolant and moderator as indicated in Table 6.In case of partially coupled system, the density of coolant fromconverged solution comes out to be 0.3 g/cm3. In case of fully

coupled system, the value of multiplication factor is greater thanthat of partially coupled system but less than that of uncoupledsystem. This is due to smaller fuel temperature as compared touncoupled or partially coupled system. For uncoupled and partiallycoupled system, the fuel temperature used is 1500 K. For fully cou-pled system, the average fuel temperature value comes out to be1000 K which explains the increase in multiplication factor. Thisalso indicates that the Doppler coefficient of reactivity is negative.

The variation of linear power density averaged over fuel rodsalong the active fuel height is shown in Fig. 9. This figure also laysemphasis on the use of coupled analyses for a supercritical waterreactor. The linear power density varies drastically for uncoupledand coupled cases.

The results for linear power density for uncoupled, partiallycoupled and fully coupled cases are compared with the referencevalues in Figs. 10–12. Fig. 10 shows the comparison of linear powerdensity for uncoupled case for calculated and reference values.Both curves match quite well. The little difference can be explainedas the absence of top and bottom reflector in our calculations.

The inclusion of feedback effect from coolant/moderator tem-perature and density changes the shape of linear power densityquite dramatically. Fig. 11 depicts the linear power density com-parison of coupled case without Doppler feedback effect. The dif-ference in values is due to absence of top and bottom reflector.Same reason for similar results has been quoted by Reiss et al.(2008). The reason for two peaks is the counter current flow ofcoolant and moderator i.e. higher moderator density gives a peakat the top of fuel rod and higher coolant density gives a peak nearthe bottom of fuel rod.

The result which shows the most deviation from reference caseis shown in Fig. 12. When we include the Doppler feedback effectin our calculations, we seem to get a result which show quite flatprofile as compared to the reference case. In our case, we have usedthe average temperature for the fuel pellet as fuel pellet is modeledas a single lump. The formula used to calculate the average tem-perature of the fuel is Tavg = 4/9Tcenterline + 5/9Tsurface (Rowlands,1962). This formula has been shown to work very well in case ofboth low and high power cases (Greifenkamp et al., 2008). The var-iation of fuel temperature (averaged over the seven rods) along theactive height of fuel rod is presented in Fig. 13. This figure clearlyshows that the maximum temperature along the height of fuel isclose to 1100 K whereas, in the uncoupled case or coupled casewithout Doppler feedback effect, the constant temperature usedis 1500 K. Hence due to negative nature of Doppler feedback effecti.e. higher temperature introduces negative reactivity and lower

Fig. 8. (a) Reference fuel assembly (Waata, 2006). (b) 1/8th Assembly modeled in MCNP.

Table 5Boundary conditions for SACOS code (1/8th assembly) (Waata, 2006).

Parameters Unit Value

Total power of the 1/8th assembly kW 327.5Inlet pressure of the moderator channels MPa 25Inlet temperature of the moderator

channels�C 280

Total coolant mass flow rate kg/s 0.167Mass flow rate in the moderator tube kg/s 0.0278 (16.65% of total

flow)Mass flow rate for inter assembly gap kg/s 0.0139 (8.32% of total

flow)

Table 6Boundary conditions used in MCNP.

Parameters Density(kg/m3)

Temperature of the crosssection library (K)

Fuel – UO2 (5% enrichment and 4%in the corner rod)

10600 1500

Cladding-Alloy 316 7450 800Moderator 769 600Coolant 769 600

Table 7Comparison of k-effective values.

Uncoupled Coupled withoutDoppler feedback

Coupled withDoppler feedback

Referencecase

1.16619 ± 0.00022 1.16365 ± 0.00022 1.17112 ± 0.00023

Calculated 1.12019 ± 0.00022 1.07043 ± 0.00022 1.09101 ± 0.00023

Fig. 9. Linear power density variation along active fuel height.

42 K.S. Chaudri et al. / Annals of Nuclear Energy 45 (2012) 37–45

temperature introduces positive reactivity, we are having a highervalue of linear power density due to smaller temperature values.Our calculations show a much flatter fuel temperature along activeheight leading to a much flatter linear power density profile. Fig. 14gives the comparison of fuel temperature for corner fuel rod be-tween calculated and reference values. Reference value for fueltemperature is showing two peaks which is the reason for twopeaks in the power profile and hence supports our conclusion.Monti (2009) has used the same formula to calculate the averagefuel temperature and has shown that the variation of power alongactive height for an HPLWR exhibits a similar trend as our calcula-tions near the center of the core.

The average density variation for coolant and moderator alongactive height is shown in Fig. 15. Coolant density is averaged overthe fuel rods and moderator density is averaged over water boxand inter-assembly gap value. As shown in Table 5, 25% of totalflow at the inlet of pressure vessel goes through moderator chan-nels (water boxes and gap between assemblies) in the downwarddirection. At the lower plenum, it mixes with the rest of 75% oftotal flow and then travels upward acting as coolant. The mixingwith 75% water, which is still at inlet conditions i.e. 280 Celsiusat the lower plenum, tends to increase the density of moderatora little bit. This increase in moderator density is visible in Fig. 15.The density profile is for the fully coupled system i.e. includingDoppler feedback effect. A similar profile is exhibited in the caseof partially coupled system i.e. without Doppler feedback effectwhich gives rise to two peaks as shown in Fig. 10.

Fuel centerline temperature distribution for the seven fuel rodsis shown in Fig. 16 for the converged solution. We can see that fuelrod 1 showing less temperature as compared to other rods. This isdue to the fact that fuel rod 1 is a corner rod and so we are using anenrichment of 4% for that to avoid hotspot factor. The maximumtemperature reached is 1440 K in fuel rod 6 which is well withinsafe operating limits of UO2 fuel.

Coolant temperature distribution in sub-channels is shown inFig. 17. We can see that, similar to the profile for fuel centerline

Fig. 10. Linear power density comparison for uncoupled case.

Fig. 11. Linear power density comparison of coupled case without Dopplerfeedback.

Fig. 12. Linear power density comparison of coupled case with Doppler feedback.

Fig. 13. Variation of linear power density and fuel temperature along active height.

Fig. 14. Comparison of fuel temperature used as feedback for corner fuel rod.

Fig. 15. Average density profile for coolant and moderator.

K.S. Chaudri et al. / Annals of Nuclear Energy 45 (2012) 37–45 43

temperature, sub-channel 1 shows the minimum value for temper-ature among all the sub-channels. The reason is 4% enrichment forcorner fuel rod. The maximum coolant temperature is 778 K forsub-channel 8 at exit.

Clad surface temperature value is a very important design andsafety criteria which must be satisfied in order to avoid the phe-nomenon of Heat Transfer Deterioration (HTD) in supercriticalwater systems. For nickel based alloys, the value for MaximumClad Surface Temperature (MCST) must be limited below 650Celsius. Fig. 18 shows the average clad surface temperature for fuel

Fig. 16. Fuel centerline temperature for fuel rods.

Fig. 17. Coolant temperature distribution in sub-channels.

Fig. 18. Average clad surface temperature comparison for fully and partiallycoupled systems.

44 K.S. Chaudri et al. / Annals of Nuclear Energy 45 (2012) 37–45

rods in case of fully coupled and partially coupled systems. Due tomore uniform axial power distribution, the value of clad surfacetemperature will rise more uniformly for fully coupled system ascompared to the partially coupled system. Near the top of the fuelrod, the average clad temperature for fully coupled system is

showing a slightly higher value as compared to partially coupledsystem. This is due to higher value of linear power density in theupper part of fuel rod shown by fully coupled system. However,in both the cases, the MCST criterion is satisfied.

5. Conclusions

The aim of the study was to develop a coupled analyses tool forSCWR. To do that, we need a thermal hydraulics code capable ofcalculating thermal hydraulic parameters for supercritical watersystems. A sub-channel analyses code called Sub-channel AnalysisCode of SCWR (SACoS) has been developed and verified. UsingSACoS and MCNP4c, a coupled system for calculation have beendeveloped. To check the validity of our coupled system, the resultsare compared with that of HPLWR calculations. The results showquite good agreement. The striking difference between the resultswas seen in the case of coupled system with Doppler feedback ef-fect. The reason for the difference is use of different fuel tempera-ture as feedback in calculation. The results obtained lay emphasison use of correct simulation parameters as variation of parameterscan lead to large difference in the simulation results obtained. Onone hand, overestimation can lead to a safer system but can hurtthe prospects of cheap power. On the other hand, underestimationcan increase the danger of nuclear catastrophe. So a true picture ofthe actual phenomena is quite necessary to built a safe and yet eco-nomically feasible system.

Acknowledgments

I would like to thank Prof. Liangzhi Cao (Xi’an JiaotongUniversity), Dr. T. Reiss (Budapest University of Technology andEconomics) and my friend Mr. Zeeshan Anjum for their guidanceand encouragement during this work.

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