heat transfer in nuclear reactor

8/10/2019 heat transfer in nuclear reactor

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hand, significant efforts have been directed by investigators (Elligot et al., 2006; Jackson et al.,

2012) in developing a criterion for the onset of HTD, which has been helpful in identifying the

conditions favorable for HTD to occur. Although an overwhelming number of articles areavailable in this area, currently there still exists a lack of clear understanding on:

The pressure dependency of HTE and HTD, and

An HTD onset criterion that can be successfully applied to rod bundles.

Each of these phenomena (HTD, HTE) has a distinct character and exhibit variability between

the cases. This, in turn, presents a challenge for existing correlations (that were generally

developed using a certain set of experiments) to successfully predict the flow and heat transfercharacteristics for SC flows. In recent years, CFD has been increasingly used for simulation of

supercritical flows and has been assessed against data for smooth pipes (Cheng and Schulenberg,

2001; Saha et al., 2013). Similar to subcritical flows, the case-by-case suitability of the

turbulence model to be used for SC flows still remains a topic of active research (Cheng andSchulenberg, 2001). Due to the availability of the experimental data for smooth pipe flows,

several investigators (He et al., 2008; Zhu, 2010; Gang et al., 2011; Zhang et al., 2012; Liu et al.,

2013; Angelucci et al., 2013) have tested the suitability of the existing turbulence models to

predict the experimentally reported HTD phenomenon. It was found that the SST k-turbulencemodel (Menter, 1994), along with wally

+set to lower than one, was able to capture the reported

HTD trends to a certain extent. Here it is worthwhile to point out that, although the SST k-turbulence model could capture the qualitative trends of the HTD reasonably well, the ability topredict the exact quantitative degree of temperature rise varied amongst investigations. Apart

from using the original formulation of SST k-, attempts have been made at University of

Stuttgart (Zhu, 2010) to modify this model to be better suited for modeling SC flows. Recently,

with an aim to find suitable turbulence models and develop guidelines for using CFD forsimulation of SC flows, international consortiums such as THINS project in EU (Schulenberg

and Visser, 2013) have tested the suitability of the STAR-CCM+CFD code. The outcome of

their attempts was documented by various investigators (Ambrosini, 2009; De Rosa et al., 2011;Angelucci et al., 2013) which provided some guidance on the applicability of the existingturbulence models and potential areas of development in order to improve the CFD capability for

SC flows. In spite of these efforts, a fit-to-purpose turbulence model for SC flows could not

be formulated and remains an area for improvement.

Understanding the possibility of occurrence of HTD in the proposed SCWR fuel bundles is ofkey interest to the conceptual fuel design. At AECL, our primary focus is to understand the fluid

flow and heat transfer characteristics for the proposedbarefuel bundle design. The overall work

is divided into phases. Phase 1 of the investigation focuses on the development of a bundle heattransfer correlation suitable for the proposed bundle design. This is an ongoing task which is

performed by mainly using the subchannel code ASSERT-PV (Rao et al, 2013). Since HTD is

a boundary layer phenomenon, which cannot be dealt with by the current ASSERT-PV, theSTAR-CCM+CFD code is used for simulating the fuel bundle to determine the conditions

favorable for occurrence of HTD. This forms the subject of the current investigation.

In order to accomplish the objective, a broad set of flow conditions over three operational

pressures (23.5, 25 and 28 MPa) are simulated using a fine computational mesh with wally+< 1.

Two mass flow rates, five inlet fluid temperatures, along with bundle powers proportional to the

inlet mass flow rate based on the nominal operating power/flow conditions, are considered in the


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current simulations. Taking advantage of the un-staggered bundle design, only 1/32 section and

0.4m long bundle is simulated in the current work to limit computational time and obtain

relatively quick solutions. A step-wise methodology along with ASME CFD best practiceguidelines was adopted to execute this investigation. The work presented in this manuscript

presents the first step in the application of CFD approach to the newly developed fuel bundle

design by AECL. In this investigation, sensitivity analysis on the effect of the existingturbulence models was not performed. Instead, the aim was to use the recommendations madeby the previous investigators as a starting point to judge the capability of the suggested model to

predict HTD for rod bundles. Unlike majority of the previous investigations that simulated

smooth pipe flows, rod bundle geometry was considered in the present study, a subject that is ofimportance to the nuclear industry for which publications are scarce. As discussed earlier, the

GEN-IV project at AECL is currently in its conceptual phase (Phase 1) for which the

experimental data does not exists. Hence, the assessment of CFD predictions against

measurements is currently not possible. In this paper, the mesh generation and solutionmethodology adopted for the current simulation is discussed in section 2, followed by sensitivity

analysis and CFD predictions in sections 3 and 4 respectively.

2.

Methodology

STAR-CCM+ v 7.04(referred to as STAR hereinafter) was used in this study instead of the

ANSYS CFDcode due to its relative ease in meshing complex geometries, and the flexibility of

power session license to execute on multiple nodes. In addition, participants involved ininternational consortiums such as CASL (CASL, 2013) and THINS (Angelucci et al., 2013;

THINS, 2013) have tested the suitability of this code for modeling rod bundle geometries with

complex spacers in both subcritical and SC flows within their respective project frame work.

2.1 Development of computational domain

The fuel bundle geometry comprised of 64 elements in two un-staggered rings and one large

centre flow tube. The surface for the sub-assembly geometries was created using ANSYSDesign Modeler, with the model dimensions listed inTable 1. As discussed earlier in

section 1, to reduce the computational effort, the geometry used in the current investigation wasa 1/32 section with an overall length of 0.4 m (Figure 1).

Table 1 Geometric model dimensions used for developing CAD

Pressure tube inner diameter 0.144 m

Centre flow tube diameter 0.094 m

# of elements in inner and outer ring 32 each

Inner ring element diameter, Pitch circle diameter 0.0095 m, 0.108 mOuter ring element diameter, Pitch circle diameter 0.001m, 0.1315 m

Length of the simulation domain 0.40 m

The bare rod bundle geometry was created by extruding the two dimensional circular cross

section in the flow direction. This solid geometry of fuel elements was exported into a parasolid

format. The solid fuel elements model developed in CAD was then imported into STAR to


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extract internal fluid volume and mesh the fluid domain. The fluid model of the bare rod

geometry was subsequently used for meshing as shown inFigure 2.

The meshing domains (fluid part) for the geometry were developed by extracting the internal

fluid volume from the CAD representation of the fuel elements. The resulting surfaces from thisoperation were automatically triangulated and used as the base for discretizing the computational

domain. The initial surface mesh was improved using a surface remesher during volumemeshing.

Considerable computational efforts were required to resolve the near wall region and reduce thecomputational uncertainty in capturing HTD. The wall thickness option, which enables a STAR

user to specify the first-node-point distance away from the wall, was selected as the stretching

mode. Boundary layers were used on the walls (fuel elements, pressure tube and centre tube),with the first node point set to respect the constraint of wally

+< 1 (typically in the range of 0.6

to 0.9). This resulted in the first node point to be typically set at ~2.7 to 3.2 m away from the

wall. The mesh growth factor was maintained at 1.3 as recommended by STAR (CD-Adapco,

2013).

A minimum of ten boundary layers were used to capture the large variation of fluid properties in

the near-wall region that may contribute to the occurrence of heat transfer deterioration

phenomenon. Three volume meshing models, prism layer mesher, surface remesher and trimmer

option, were used to generate hexahedral cells with boundary layers on the walls of the fuelelements (seeFigure 2). Using this meshing strategy, three computational meshes were

developed for the current investigation, which typically comprised of a total cell count of 3.5 to

11.3 million cells. For the current investigation, the computational mesh to be used was basedon a detailed mesh independence study (described in section 2.4) based on ASME CFD best

practise guidelines (ASME, 2009).

Figure 1 Computational domain for bare bundle(colors are used only to distinguish model

elements)

Figure 2 Mesh on a section for bare bundleshowing boundary layers on the

elements

2.2 Implementation of supercritical fluid properties

Unlike subcritical flows, the thermophysical properties of supercritical water may vary drastically with

temperature at a given pressure (Figure 3). For all properties, specific heat in particular, it can be seeninFigure 3 that an increase in pressure results in reduction in magnitude of property variation.


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STAR has built-in steam tables (IAPWS-IF97) to define the thermophysical properties of water which

are only valid for sub-critical conditions, i.e., conditions below the critical point (22.1 MPa and 374 C).Consequently, STAR cannot be directly used to simulate flows subjected to supercritical conditions.

Hencefor the three system pressures (23.5, 25 and 28 MPa) tested, the SCW properties were obtained fromthe NIST online database (Lemmon et al., 2013) and implemented in STAR. Similar to the previousinvestigations (Palko and Anglart, 2008; Ambrosini, 2009; Angelucci et al., 2013), properties of SCW

were assumed to be only temperature dependent (under a specific system pressure). The dependencyon the pressure (under a specific system pressure) was usually small and hence neglected. Currently,

most CFD solvers do not include the option to consider thermophysical properties as a function of bothpressure and temperature. In order for these properties to vary simultaneously with both pressure and

temperature, a different approach such as a look-up table may be considered in future analyses.

The SCW properties obtained from the online NIST database were fitted using higher orderpolynomials (cubic splines) as a function of temperature. In order to ensure accuracy, the polynomials

were specified in a piece-wise fashion. They were divided into many temperature interval ranges,

including small ranges for the pseudo-critical region which required significant effort. For density and

specific heat, the resulting polynomial equations were introduced in STAR through a GUI hook-up.The variations of the thermal conductivity and viscosity with the temperature were introduced through

tables as STAR does not currently provide a GUI hook-up capability for incorporating them. Theproperties implemented in the current work are valid only for the three system pressures tested. The

procedure stated above should be repeated if the operational pressure changes.

(a)

(b)

(c)

Figure 3 Variation of thermophysical properties for SC water at: (a) 23.5MPa; (b) 25 MPa; (c) 28 MPa

2.3 Governing equations and turbulence models

In the present CFD analysis, the finite volume approach was used to discretize and numerically solve

the Reynolds Averaged Navier-Stokes (RANS) and turbulence model equations simultaneously with

the continuity and temperature form of the energy balance equations in STAR. The turbulence model

equations are presented and discussed below regarding their impact on prediction of HTD. However,for the RANS, continuity and energy equations, the reader is referred to the STAR user manual

(CD-Adapco, 2013) since these equations are standard and their use does not depend on the choice of

models by a CFD user.

Although a general consensus on the choice of turbulence models for SC flows is currently notavailable, previous studies (Palko and Anglart, 2008; Zhu, 2010; Liu et al., 2013; Schulenberg and

Visser, 2013) reported that amongst the existing turbulence models, the SST (shear stress transport)

model can qualitatively predict HTD. Hence, Menters SST k-model with low Reynolds number


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modification as implemented in STAR along with lowy+

approach for the near wall treatment was used

in the present study to better capture the occurrence of HTD in the proposed fuel bundle.

Menter (1994) formulated a hybrid two equation model, the SST k- model, which was designed to

yield the best behaviour of the k- model by Wilcox (for Wilcoxs model formulations refer

Wilcox, 2010) and the standard k- model. This model utilizes the original k-model in the near wall

region (sub and log layer) and gradually switches to the standard k-model in the fully turbulent region

far away from the wall. This switch was facilitated through a blending function. The transportequations for the SST k-turbulence model are:

kx

u

x

u

x

u

x

k

xku

xt

k

i

j

j

i

j

it

j

tk

j

j

j

*

(1)

)(

21

)(

2

)()(

112

IV

jj

III

II

i

j

j

i

j

it

I

j

t

j

j

j

x

w

x

kF

x

u

x

u

x

u

kxxu

xt

(2)

The first three terms (I to III) on the right hand side of the Eq. 2 represent the conservative diffusion,eddy viscosity production and dissipation of turbulence respectively. The last term (IV) represents the

additional non conservative cross diffusion term which is not included in Wilcoxs k-model. All the

coefficients in the model were calculated using a blending function as in Eq. 3. The blending function

was set to a value of zero close to walls (leading to a standard equation) and a value of one away

from the walls (which corresponds to a standard equation).

2111 1 FF (3)

where, 1 and 2 are the two sets of values for each variable listed inTable 2. The coefficient 1k hasbeen modified by STAR to 0.85 (CD-Adapco, 2013) from 0.5 as originally proposed by Menter. The

blending function was computed as:

411 argtanhF (4)

with:

)(

2

2

)(

2

)(

1

4;

500;

09.0maxminarg

III

k

III

yDC

k

yy

k

(5)

and, to prevent the build-up of turbulence in the stagnation regions, a turbulence production limiter was

introduced in the SST model as:

202 10;

12max

jj

kxx

kDC

(6)

In Eq. 5., the first term represents the turbulent length scale divided by the shortest distance to the nextsurface, the second term becomes important in the viscous sub layer and ensures that F1does not tend


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to zero in that region while the last one prevents a possible freestream-dependent solution. The

turbulent viscosity was computed as:

SSFkt

3

6.0,

31.0,max

1min

2

*

(7)

and S is the modulus of mean strain rate tensor. The function F2was evaluated as:

222 argtanhF (8)

22

500;

09.0

2maxarg

yy

k

(9)

Table 2 Coefficients present in the SST k-turbulence model

Coefficients

for Set 1Set 1

1 Coefficients

for Set 2Set 2

2

1 0.075 2 0.0828

*

1 0.09 *

2 0.09

1k 0.85 2k 1

1 0.5 2 0.856

*

1 1 *

2 1

1 0.41 2 0.41

1

*

1

2

1*

1

1

k 2

*

2

2

2*

2

2

k

Note that in the SST model by Menter (1994),*

1 = *

2 = * ;

*

1 = *

2 = * and 1 = 2 =

It should be noted that, the wall functions used in the current investigation neglected any

thermophysical property changes for SC water within the viscous sub-layer. Also, to better capture thenear wall effects, low Reynolds damping functions were considered with the SST model.

As described earlier, in the current investigation, the low-Reynolds number modification (low-Re

approach) implemented in STAR was used to capture the occurrence of HTD. The term low

Reynolds number refers to the turbulent Reynolds number which is related to turbulence kineticenergy and dissipation as:

t

t

k~Re

2

(10)

which is usually low near the wall (Menter, 2009) and should not be confused with the channel

Reynolds number. In the low-Re model, some of the coefficients previously used ( *

1 , 1 ,*

) for the

SSTk- model were replaced as:

4

4

*

2

*

Re,1ReRe1

ReRe154

t

t

low (11)


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*

01Re,1

1

ReRe1

ReRe

t

tlow (12)

kt

ktlow

ReRe1

ReRe3*Re,1

(13)

where: 0 = 9

1

and =125

9.

The three coefficients,Re =8; Re =2.95; kRe =6; in Eq.s 11, 12 and 13 control the rate at which the

closure coefficients approach their fully-turbulent values.

2.4 Solution approach and models used

In all the simulations, the entrance and exit of the flow channel were modeled with uniform velocity

inlet and pressure outlet boundary conditions. The fuel elements, centre and pressure tubes were set as

solid walls with no-slip conditions. Symmetry boundary conditions were applied along the sides

(Figure 2). A uniform heat flux boundary condition was imposed at the surface of the inner- and outer-ring elements. The effect of conjugate heat transfer was not included in the current investigation.

Following the recommendations made by Kao et al., 2010 and Liu et al., 2013, the gravity (buoyancy

force) was included in all the simulations to capture a sharp increase in the sheath temperature whenHTD occurs under test conditions considered in the current investigation. However, in order to

confirm the recommendations made by previous investigators (Kao et al., 2010; Liu et al., 2013), a

sensitivity analysis to buoyancy was also performed (refer to section 3.2).

In the current study, the equations were solved using a steady-state segregated solver with Rhie and

Chow type pressure velocity coupling (CD-Adapco, 2013) combined with a SIMPLEtype algorithm.

The segregated solver was chosen over the coupled solver because it uses less memory, and improves

solution convergence for some cases. Considering the recommendation made in ASME CFD

numerical accuracy guidelines (ASME, 2009), all the equations were solved using second order

differential schemes. A convergence strategy was adopted for some cases where numerical simulationfailed to converge. First, a fully converged solution was obtained by solving only the flow equations

with URF set to a value of zero. Using the converged flow solution, the energy equation was enabledand the solution was iterated till convergence was achieved again. The URF values for flow, pressure

and energy were set to 0.7, 0.3 and 0.99 respectively. However, for some of the run conditions,

especially at a lower pressure (23.5MPa) and when the inlet temperature is close to the pseudo-criticalpoint, it was found necessary to further lower the flow URF to 0.2 to ensure stability and avoiddivergence of the numerical solution.

Convergence was monitored for each run and the solution was iterated till the scaled residuals dropped

at least by three orders of magnitude and fluctuated in a steady manner. In addition, fluid temperatures

were monitored in the cross-plane sections near the outlet (0.38 m) and in the middle (0.2 m) portion of

the bundle geometries. The solution was judged to be converged once the residuals had dropped bythree orders of magnitude and steady-state fluid temperatures at the monitored sections were achieved.

A wide range of test conditions as listed inTable 3 were simulated to test the possibility of occurrence

of HTD for the current fuel bundle design. An overall of 53 test cases were simulated based on thecurrent test matrix, of which selected results are presented in this paper. In general HTD is more likely

to occur at lower mass fluxes and prior to pseudo-critical temperature (bulk) (Cheng and Schulenberg,

2001). Hence, the current paper focuses on the results obtained for low-mass-flow test cases in greaterdetail.


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Table 3 Test matrix used for the current investigation

Operational pressure 23.5, 25, 28 MPa

Mass flux 0.438, 1.095 Mg/m -s

Inlet fluid temperature 300-400C

Heat flux 0.2-1.2 MW/m

Power 1.97-11.87 MW

3. Sensitivity Analysis

3.1 Computational mesh and wall y+treatment

The grid sensitivity and effect of wally+is investigated as follows. Of the three system (or operational)

pressures considered for testing (Table 3), the mesh sensitivity was performed at 23.5 MPa to check theaccuracy of the computational mesh size used in the current simulations. As seen inFigure 3,the

thermophysical properties (especially the specific heat capacity) vary with temperature more

significantly at lower pressures than at higher pressures. This necessitates the need to examine thesuitability of the mesh size and determine if it can be used for capturing the occurrence of HTD. In

principle, similar exercise should be performed at 25 and 28 MPa. However, at 25 and 28 MPa, the

current study utilizes, presumably conservatively, a computational mesh derived from the meshsensitivity analysis of lower pressure condition (23.5 MPa). For the grid-sensitivity study, the mesh

count was increased by changing the base size of the meshes. The mesh refinement ratio between

consecutive meshes was maintained at 1.3 as per ASME V&V 20 guidelines (ASME, 2009). Asdiscussed in section 2.1, the computational model used at least ten boundary layers on the elements

with the first node point set to a corresponding wally+value of ~1.0. The simulations were performed

using the low-Re SST k-turbulence model, described in section 2.3, to capture the occurrence of

HTD. The finest mesh used in the current analysis was designated as mesh#1 followed by coarser

meshes as shown inTable 4. All the three meshes presented a well behaved convergence. As seen inFigure 4,the sheath temperature did not significantlychange for the three meshes. Hence, the

mesh #3 with 3.5 million cells is used as the base case for the current simulations. In this work, the

variation of sheath temperature was plotted along the fuel channel at a radial location where themaximum sheath temperature was observed. The radial location for the maximum sheath temperature

changes case-by-case.

Table 4 Mesh characteristics and refinement ratios for bare bundle

Mesh i Total mesh

count (millions)

Average

base meshsize (mm)

Mesh

refinementratio, r

1 11.3 0.22 -

2 6.0 0.29 1.3

3 3.5 0.38 1.3


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Figure 4Mesh sensitivity analysis for the current investigation at 23.5 MPa

(G= 0.438Mg/m2-s, Q=3.95MW, q= 0.405 MW/m

2, Tin=370C)

As discussed in section 2.1, a computational mesh with y+30) and low y

+ (y

+


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cannot be used directly. Hence, wall temperature was considered to be a key variable to judge the

occurrence of HTD in the current analysis.

For the lower operating pressure (23.5 MPa) and lower mass flux, as seen inFigure 6a, buoyancy playsa significant role in the predicted sheath-temperature distribution, resulting in a sharp rise in

temperature in the upstream section and a steady decrease in the downstream section. In comparison,

when the buoyancy effect was not accounted for, the sheath temperature increased gradually along the

length, indicating HTD in the upstream section and HTE in the downstream section due to buoyancy.For a given operating pressure, the temperature difference between cases with and without buoyancy is

larger for the case of lower mass flux than for the case of higher mass flux. The results clearly indicatethat buoyancy is an important contributor to the occurrence of HTD, especially at lower pressures and

lower mass fluxes. Similar findings have been reported for flows in smooth pipes and annular channels

by previous investigators (Palko and Anglart, 2008; Liu et al., 2013; Kao et al., 2013).

For 25 MPa and 28 MPa at low mass flux condition, the sharp increase in the predicted sheath

temperatures were found to be lower compared to that of 23.5MPa. In addition, a gradual increase intemperature was observed across the length of the rod bundle (Figure 6a throughFigure 6c) without

inclusion of the buoyancy force. For all the test cases in Figure 6 and Figure 7, the sharp spike in the

predicted temperature close to the entrance region of ~3 cm can be regarded as a result of theassumption of uniform flow at the entrance without including a non-heated part that would develop the

turbulent flow upstream of the entrance. Therefore, the spike (Figures 6b, 6c) is judged to have no

practical importance to this study. On the other hand, considering buoyancy force for 25 MPa yielded

a taper off of the temperature increase (at ~0.2m), compared to the case without the buoyancy.Similarly, for 28 MPa, a flatter sheath temperature was predicted with buoyancy than without it.

For high mass flux conditions at 23.5 MPa, a small step increase in temperature was predicted at

~10cm (Figure 7a) for which no explanation is currently available. For all three pressures, no HTD

was predicted (seeFigure 7bandFigure 7c). However, as a result of neglecting buoyancy, thepredicted sheath temperatures were higher in the downstream half of the test section compared to the

simulations that included the buoyancy. Based on the six conditions included in Figures 6 and 7, it can

be inferred that buoyancy cannot be ignored, especially for the lowest pressure combined with thelower mass flux (Figure 6a).

(a) (b) (c)

Figure 6 Effect of buoyancy at low mass flux test conditions for the three operating pressures(G= 0.438Mg/m

2-s, Q=3.95MW, q= 0.405 MW/m

2)


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(a) (b) (c)

Figure 7 Effect of buoyancy at high mass flux test conditions for the three operating pressures

(G=1.095 Mg/m2s, Q=9.89MW, q= 1.012 MW/m

2)

4. CFD predictions and discussion

For the test matrix shown inTable 3,simulation results were obtained using mesh#3 (3.5 million cells)

with wally+


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temperatures (Zhang et al., 2012). Also, the conjugate heat transfer (CHT) that considers conduction of

heat through the fuel rod cladding was not included in the computational model. The incorporation ofthe wall conduction model is expected to result in reduced wall temperatures without impacting the

occurrence of heat transfer deterioration thereby leaving the qualitative trends unaffected. In an

attempt to address the limitations of the existing low-Returbulence models in overepredicting the walltemperature (Rosa et al, 2011), Amoako et al., 2013 used high wally

+wall treatment instead of

detailed wall treatments along with the low-Returbulence models. However, based on the sensitivityof wall treatment approach discussed earlier in section 3.1, low wally+treatment was used in this study

to qualitatively determine if HTD could exist for the flow conditions listed in Table3.

(a) (b) (c)

Figure 8 Effect of inlet temperature on axial sheath temperature variation (G= 0.438Mg/m2-s,

Q=3.95MW, q=0.405 MW/m2: (a) 23.5 MPa; (b) 25 MPa; (c) 28 MPa)

4.2 Effect of operational pressure and mass flux on heat transfer

The variations with bulk fluid temperature of the maximum sheath temperature and corresponding heat

transfer coefficients for the low (0.438Mg/m2-s) and high mass fluxes (1.095 Mg/m

2-s) at the three

operational pressures are presented inFigure 9 andFigure 10 respectively. In general, deviations from

the normal heat transfer have been found to occur when the sheath temperature is greater than thepseudo-critical temperature and the bulk temperature is less than the pseudo-critical temperature(Tsh > Tpc>Tb) (Cheng and Schulenberg, 2001).

At 23.5MPa and at bulk temperature near pseudo-critical temperature the simulations predicted HTD

for low mass flux (Figure 9a) and HTE for higher mass flux (Figure 10a). For this study, occurrence of

HTD at 23.5 MPa for low mass flux is in line with the findings by previous investigators (Cheng andSchulenberg, 2001; Gang et al., 2011).

However, it was observed that the simulations behaved differently at 25 and 28 MPa when compared to

that of 23.5 MPa. This behaviour was also observed by Kim and co-workers (Kim et al., 2007) thereby

suggesting the occurrence of HTD and/or HTE depend also on the operational pressure. For the low

mass flux at 25 and 28MPa, the wall temperature exhibited a dip when approaching the pseudo-criticaltemperature region resulting in an increase in the heat transfer coefficient as predicted inFigure 9b and

Figure 9c. This change in trend is attributed to the HTE for the simulated test case. In addition, for the

pressure of 28 MPa at the lower mass flux, HTD was also observed at lower bulk temperatures. On theother hand, for higher mass flux conditions at 25 and 28 MPa, normal heat transfer behaviour was

observed (Figure 10b andFigure 10c).


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(a) (b) (c)

Figure 9 Variation of maximum sheath temperature and heat transfer coefficient with the bulktemperature (G= 0.438Mg/m

2-s, Q=3.95MW, q= 0.405 MW/m

2)

(a) (b) (c)

Figure 10 Variation of maximum sheath temperature and heat transfer coefficient with the bulk

temperature (G= 1.095 Mg/m2s, Q=9.89MW, q= 1.012 MW/m

2)

5.

Limitations and ChallengesThe first step on the application of CFD approach to identify the conditions favorable for theoccurrence of HTD in the newly developed fuel bundle design by AECL is presented in this work. The

simulations performed were for a short domain length compared to the full length of the fuel element

(~6m) primarily to reduce the computational run time and fit within the computational resources

available for this project. The results obtained from this study present trends which provideinformation on the possibility of occurrence of HTD at the test conditions considered.

One of the uncertainties associated with this work is the use of a single turbulence model for all the

inlet temperature conditions (i.e. inlet temperatures close to and away from pseudo-critical conditions).

The CFD predictions, especially of the sheath temperature, may change significantly with the use of adifferent turbulence model and wall treatment approach. However, given the current limited

understanding of the application of the turbulence models for SC bundle flows, it was decided to use a

turbulence model that was generally agreed upon by previous investigators. It should be noted that the

sheath temperature variations predicted in this analysis are only qualitative in nature and may varysignificantly with turbulence models as discussed above. However, the trends obtained in this analysis

are indicative of the expected heat transfer behaviour for the test conditions considered in the current

investigation.


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6. Summary

The possibility of occurrence of heat transfer deterioration in the proposed SCWR fuel bundles was

numerically examined by solving conservation laws of mass, momentum, and energy with the low-Re

SST k-turbulence model and wally+


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THINS Thermalhydraulics of Innovative Nuclear Systems

URF Under Relaxation Factor

General symbols

CDk Production limiter in Eq. 7cp Specific heat (kj/kg-C)

F1, F2 blending function in Menters SST k-turbulence model (-) in Eq. 3 and 8G Mass flux (Mg/m2-s)

k Thermal conductivity (W/m-C)k Turbulence kinetic energy (m

-2s

-2)

P Operating pressure (MPa)

Q Power (MW)q Heat flux (MW/m

2)

Re Reynolds Number (-)

t Time (s)

T Temperature (C)u velocity field (m/s)

y Distance to the nearest wall in Eq. 5

y+ non-dimensional distance from wall (-)

Greek letters

Constant in the blending function of the SST model

Constants 1 and 2 in the blending function of the SST model

Constant in the SST k-model

* Constant in the SST k-model

Constant in the SST k-model

Dynamic viscosity (Pa-s)

Kinematic viscosity (m2/s)

Density (kg/m3) Schmidt number (-)

Specific dissipation rate (s-1

)

Subscripts/ Over- bars

b Bulk

in inleti, j, k velocity components

k Turbulence kinetic energy

pc Pseudo-critical

sh Sheath

t Turbulent Specific dissipation rate

- over-bar used for average

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