Effect of spacer on the dryout of BWR fuel rod assemblies

Nuclear Engineering and Design 294 (2015) 262–273

Contents lists available at ScienceDirect

Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes

Effect of spacer on the dryout of BWR fuel rod assemblies D.K. Chandraker ∗ , A.K. Nayak, P.K. Vijayan Reactor Design and Development Group, Bhabha Atomic Research Centre, Hall-7, Trombay, Mumbai 400085, Maharashtra, India

h i g h l i g h t s • • • •

Modeling of spacer for nuclear fuel assembly. A brief review of the existing approaches for spacer effect on dryout of BWR fuel assemblies. A methodology for BWR fuel spacer proposed. Dryout analysis for untested 54 rod bundle design of AHWR with the proposed spacer model.

a r t i c l e

i n f o

Article history: Received 7 September 2015 Accepted 18 September 2015 Available online 23 October 2015

a b s t r a c t Spacer is used in the fuel rod bundle of a nuclear reactor to maintain appropriate gaps among the fuel pins ensuring adequate heat transfer to the coolant. Hence, the design of such spacing devices is an important consideration to arrive at the acceptable configuration of the fuel bundle. The analysis of the flow behavior around the spacer is necessary to find its effect on the important phenomena like the pressure drop, dryout and heat transfer due to enhanced turbulence caused by the flow obstruction. Both experimental and analytical studies have been carried out in the past to investigate these phenomena. However, most of the experiments have been conducted under air–water conditions and the mechanism of the spacer effect has not been adequately modeled and validated due to the underlying complexity of the phenomena. In addition, the phenomenological based dryout modeling for the determination of thermal margins in BWR requires spacer model to be incorporated for evaluating the critical power of a fuel assembly. The present study briefly reviews the existing approaches and proposes a simple approach for incorporating the spacer effect on the dryout of the BWR rod bundle by analyzing the flow field near the spacer with the CFD application. In this study, a methodology for the formulation of a spacer model for BWR fuel assembly has been proposed and incorporated in the phenomenological dryout code (FIDOMRod). Thus, the paper briefly discusses the FIDOM-Rod approach, spacer modeling, its application to the for untested 54 rod bundle design for AHWR. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Spacer is a vital component in the nuclear fuel rod assembly which maintains appropriate gap between the rods allowing coolant to perform its assigned function. The spacers cause additional pressure drop and affect the liquid film flow rates (hence the dryout) on the rods in a fuel rod bundle of BWR. Hence, the spacer plays an important role in the thermal hydraulic performance of the rod bundle in terms of pressure drop and the Critical Heat Flux (CHF). A large amount of test data is required for the optimum design of the spacer in absence of the mechanistic modeling of the spacer. Hence the development of a model for the spacer based

∗ Corresponding author. Tel.: +91 22 25593976; fax: +91 22 25519613. E-mail address: [email protected] (D.K. Chandraker). http://dx.doi.org/10.1016/j.nucengdes.2015.09.004 0029-5493/© 2015 Elsevier B.V. All rights reserved.

on the study of the flow behavior downstream of the spacer is an important aspect of the spacer design and this would also facilitate analysis of the liquid film dryout mechanistically to arrive at the critical bundle power. The literature review on the spacer effect in BWR assemblies indicates that the droplet deposition is generally enhanced downstream of the fuel spacer because of change in the velocity profiles in the narrow passage and wider passage at the spacer location. The process of velocity recovery downstream of the spacers results into the lateral velocity components causing liquid droplets to be transported on the fuel rod (drift velocity phenomenon). In addition, the liquid film is deposited on the spacer wall which gets dislodged at the spacer edge and joins the core flow affecting the film flow on the rods (run-off effects). The liquid film flow on the rod is obstructed at the spacer location (narrow channel effect). Thus, drift velocity, run-off effect and narrow channel effects are three major mechanisms to be considered for

D.K. Chandraker et al. / Nuclear Engineering and Design 294 (2015) 262–273

D g k m N P q w

diameter (m) gravitational constant (m/s2 ) mass transfer coefficient (m/s) mass transfer rate (kg/m2 s) viscosity number perimeter of the heated surface heat flux (MW/m2 ) mass flow rate (kg/s)

Greek symbol density (kg/m3 )   viscosity (N s/m2 )  surface tension (N/m) Subscripts ld liquid droplet deposition d e entrainment evaporation ev eq value at equilibrium lf liquid film scl subchannel liquid scld subchannel drop subchannel liquid film sclf sclfi at onset of annular flow lfi at onset of annular flow cf cross flow liquid cross flow lcf gcf gas cross flow g gas phase liquid phase l rld total liquid flow in a rod k liquid film number

the deposition of the droplets in BWR assemblies as described by Yano et al. (2000, 2001a,b). BWR vendors have developed fuel spacers using large-scale test loops simulating actual bundle geometry which yields critical power and pressure drop data under BWR operating conditions. However, such testing requires long periods of operation involving high cost as a large amount of data is required to optimize the spacer geometry. Thus, mechanistic model for a spacer will be useful for the design optimsation by focusing on phenomenon involving droplet deposition on the rod and the liquid film entrainment from the liquid film of the rod. In addition, the dryout analysis in a rod bundle needs the spacer effect to be modeled to arrive at the thermal margin. It has been investigated that the turbulence intensity enhancement downstream of spacer is a driving force for the droplet deposition. In the present study, a numerical analysis of a gas flow through a simple spacer has been carried out and the results compared with the experimental data of the literature to confirm the predictive capability of this approach for the spacer effect. Further to this the analysis to the BWR spacer is carried out to determine the distribution of the turbulence kinetic energy downstream of the spacer. Kinetic energy enhancement has a direct impact on the droplet deposition on the fuel rod. Hence this analysis has been carried at various flow rates to explore the possibility of correlating the enhancement in the turbulence kinetic energy with the enhancement in the droplet deposition coefficients. Thus, the droplet enhancement deposition model for the spacer can be embedded in the dryout modeling approach to account for the spacer effect. The dryout model with the spacer effect has been subsequently applied to the AHWR design.

263

Advanced Heavy Water Reactor (AHWR) (Sinha and Kakodkar, 2006) is a vertical pressure tube type and boiling light water cooled reactor and depends on the natural circulation for the removal of heat generated in the fuel assemblies. AHWR has a 54 fuel rods having 3.5 m active fuel length and rods are spaced by six spacers. The critical power of AHWR needs to be predicted in absence of the experimental data at the design stage. Chandraker et al. (2012) developed a phenomenological based dryout code, FIDOMRod for the Liquid Film Dryout (LFD) analysis to ascertain the power corresponding to the dryout of CHF occurrences (critical power). The dryout prediction of FIDOM-Rod has been validated with the 16, 19 and 37 rod clusters as discussed in the reference paper by Chandraker et al. (2012). However, spacer effect needs to be incorporated in this code. The present work proposes methodology to evaluate the spacer effect for BWR fuel assemblies. Finally, based on the above studies a spacer model for the AHWR fuel assembly has been worked out for incorporation in FIDOM-Rod for analyzing the spacer effect.

2. Review on the spacer modeling Considering the complexity of the spacer effect, at first, the previous studies on spacer effect has been reviewed. Spacer has a strong influence on the critical power of a bundle and the effect is geometric specific. The modeling approach for the spacer is evolving and many models are based on the simple spacer geometry which accounts for the phenomena partly only. The validation is also limited to air–water conditions. Thus extension of these models to the high pressure and high temperate condition of BWRs with the prototype geometry is a challenge. However, a simple approach can be worked out based on the enhancement in the turbulence intensity downstream of the spacer. Before proceeding ahead, these models have been reviewed as shown briefly in Table 1 . Previous models are (Lahey et al., 1972; Lahey, 1977) basically based on the eddy diffusivity. Recently some numerical approaches have been performed by considering the turbulence of gas phase induced by the spacer. Kanazawa et al. (1995) obtained the deposition rate numerically downstream of the spacer under the gas single-phase condition for ring type spacers as it increases in proportion to the ratio between the turbulence intensity with and without spacer. Yamamoto et al. (1997) calculated droplet trajectories adopting large eddy simulation in a vapor phase and obtained droplet deposition rates assuming that droplets were transferred by turbulence diffusivity which is considered as the driving force for enhancement of the droplet deposition rate. The approach of Kanazawa et al. (1995) and Yamamoto et al. (1997) has many unknown factors and many assumptions, such as the diameter of the droplet and droplet distribution. In previous studies, basically the effect of spacer on the film flow has been studied on air–water experiments; for example by Yano et al. (2011). Their application to the actual spacer is not well recommended. However, some of the useful information regarding the deposition trend with respect to the spacer geometry is obtained in such experiments. It was noted from the review that the analytical approach to capture the spacer geometry for the droplet deposition is to use the particle tracking analysis in a gas flow dispersed with the droplets. The number of droplets deposited on the rod is computed analytically to quantify the droplet deposition rate. However, the effect of spacer on the liquid film flow has not been accounted and hence the phenomenon is modeled partly. Yano et al. (2000, 2001a,b) proposed analytical models for the specific effect of the spacer like drift flow, narrow channel and run-off effect in a round tube with a ring spacer and validated for the air–water conditions. However, it has not been applied and validated for the rod bundle application under BWR conditions.

264

Table 1 Previous study on the spacer effect and spacer models. Source

Details

Fluid considered

Geometry

Model proposed

Remarks

1

Okawa et al. (2004)

Air–water

Nishida et al. (1994)

Simple ring spacer in a round tube 4 × 4 and 9 × 9 bundle

Film flow rate increased by 50%. No generalized model proposed

2

Deposition rate measured by double film extraction Film thickness measured

K values evaluated for the spacer geometry under consideration Eddy enhancement model used and the characteristics length defined is a geometric specific Using this model dryout in 36 rod bundle was predicted within 7%

Air–water (constant air velocity of 10 m/s)

Based on eddy diffusivity of a droplet, spacer downstream divided ⎧ into three regions.(see Fig. 1(a)) 5  ⎪ 0
εSP

3

Yano et al. (2000, 2001a,b)

4

Nagayoshi and Nishida (1998)

Models for the narrow channel effect, drift effect and run-off effect Radial component of velocity measured

Analytical approach for a simple spacer Air–water

1  ⎪ ⎪ ⎩ 42 UGC z 2

5


Region-2 and Region-3

182 2 De



f/2

De UGC f/2 εB = 72 To be verified for the BWR application. Limited verification in air–water. test subchannel

Turbulence intensity enhancement as a function of blockage ratio and distance. Velocity fluctuation was correlated with the prandtl’s mixing length (l) and the channel averaged eddy (ε) viscosity

v¯ 2 = ε¯ /l. ε¯ = 0.04vRef 0.5 f is the friction factor in a channel

5

Nagayoshi and Nishida (2001a,b)

Lahey’s diffusivity model

Analytical model for steam-water

Tube

Deposition multiplier is the ratio of the eddy diffusivity with and without spacer ksp εsp = sp = k0 ε0 f Gd ε0 = 72m 2 G 5 0 ≤ Zsp < 2 20m  εsp ( Zsp ) = 2 2  5  G G ≤ Zsp < × × 2 m ε0 4 4 m ( Zsp ) 

Droplet enhancement factor is not directly given for rod bundle application. Radial velocity fluctuation was worked out as a function of blockage ratio () based on the data experimental  





v¯2SP /

v¯2O

= −0.27(z/De )

1.0 + 6.54 × e The Prandl’s mixing length (l) is assumed to be 0.08 times the hydraulic equivalent diameter However, the droplet enhancement factor was not provided for BWR application The characteristic length,  for each spacer design is optimized based on the data obtained from critical power experiments Thus this model cannot be applied arbitrarily for any spacer design since  needs to be tuned based on the experimental data on the critical power 2

D.K. Chandraker et al. / Nuclear Engineering and Design 294 (2015) 262–273

S. no

6

Tomiyama and Yokomizo (1988)

Film thickness measured and film flow enhancement derived from this with certain assumptions

Air–water

Exp. with the 9 rod bundle

K as a function of the flucturational part of the velocity depends on the eddy  diffusivity  /VB ksp = kB VSP



VB = const.

fin Ugc ,

and Vsp = ε/l where l is Prandtl’s mixing length as given by l = 0.18b, , ε = 0.882bUgc KL De /x

Yamamoto et al. (1997)

Dispersed droplets in gas

LES for turbulence analysis

Droplet motion is tracked Droplet diameter and distribution is assumed

8

Kanazawa et al. (1992, 1995)

3D flow analysis and particle tracking of method for droplets considering non-viscous flow

Rod bundle subchannels considered

Incorporated in SILFEED code

Particle tracking and a code HIZET-AFIMA which provides enhanced value of K behind the spacer Flow is considered to be inviscid Does not consider the effect of spacer on the liquid film. Thus phenomenon is only partly modeled

9

Naitoh et al. (2002)

Lagrangian method for particle tracking (k − ε model used for the turbulence)

Exp. In a plate spacer and model validated

PLASHY-CRT code for droplet behavior

Particle tracking method. K value suggested for a typical BWR for ferrule and grid type spacer (see Fig. 1(b and c). PLASHY-CRT is similar to HIJET-AFIMA but viscid flow considered

10

Adamsson and Le Corre (2008)

Based on kinetic energy enhancement

Derived analytically

Maximum K.E. is given  by:



regions defined (see. Fig. 1(d) Region-1 (ZG  = 0, Z2 = 0.05) 

MAX = B + 1 Kenh dep

Kenh

dep

=

D + 1 Based on kinetic energy. Three

MAX 0.95kenhl

dep

−1



(z − zG ) / (z2 − zG ) + 1Region

2(ZG =0.05,Z2 =0.15);  Kenh

dep

=

Kenh

dep

=

MAX kenh

 dep 1/

1−

and the region 3 (Z4 = 0.15, Z5 = 0.45);



1 0.95kMAX enh dep

z−z4 z5 −z4



+

1 0.95kMAX enh dep

D.K. Chandraker et al. / Nuclear Engineering and Design 294 (2015) 262–273

7

b Is the width of the wake region, KL is the spacer loss coefficients, x distance from spacer and De is the equivalent diameter Model constants depends on the spacer geometry. Film thickness enhancement was modeled using SILFEED No critical power prediction was made • K is not given directly (only droplet no. Density) • Liquid film effect is not considered in the analysis • It has not been applied for the dryout analysis of rod bundle • HIZET-AFIMA does not treat viscosity, so droplet transfer caused by eddy diffusion cannot be considered • Dryout compared for the rod bundle. Effect of spacer geometry accounted • Droplet diameter and distribution is assumed Dryout prediction compared with bundle (8 × 8) and (4 × 4) bundle Effect of spacer geometry accounted in the subchannel code CAPE-BWR • Used in the LFD code and dryout compared with the data • Max. K.E. behind the spacer and three regions of variation considered and the constants depend on the blockage ratio • For a atypical BWR spacer as suggested by Adamsson: B = 7.898 from CFD calculations from three values of blockage ratio and D = 4.791 from CFD calculation from a typical value of BWR spacer blockage ratio

Note: K is the deposition coefficients for droplets and is an important parameter for the Liquid Film Dryout (LFD) modeling, f: interfacial friction factor, UGC : gas core velocity, De : equivalent diameter, : characteristic length which depends on the spacer geometry. 265

266

D.K. Chandraker et al. / Nuclear Engineering and Design 294 (2015) 262–273

Fig. 1. Deposition models proposed for typical BWR spacers.

Akiba et al. (2005) conducted experiments in the 16 rod bundles for the spacers using air–water and film flow measurements were made at various axial locations. The difference of the film flow at these two axial locations (50 mm and 150 mm from the spacer) was utilized for estimating the deposition coefficient. The film flow rate was measured for the inner, corner and central rods at different axial and azimuthal locations using open slit methods. Minimum value of the deposition coefficients calculated for different circumferential locations was used to find the minimum value of the enhancement factor for the corner, side and central rods to be used for the critical power calculation. Minimum value for the deposition enhancement factor due to space for the central rod was found to be 2.14. The maximum value of enhancement factor is not reported in the paper. The experimental values were used in the modeling and a good agreement was obtained but a generic enhancement factor has not been proposed. Most of the experiments are for the air water and a simple/model spacer. Thus the application of the experimental data of a simple spacer cannot be applied for the spacer of a reactor bundle. The models proposed by Lahey et al., 1972, Naitoh et al. (2002) and Adamsson and Le Corre (2008) indicate that the deposition enhancement attains maximum behind the spacer and then decays to the background value. For a typical BWR spacer the enhancement

is almost 3 to 5 times higher than the upstream values as shown in Fig. 1. This information has been utilized for the spacer model of AHWR fuel assembly using the turbulence intensity calculation. Most of the models proposed earlier like that of Nishida et al. (1994) deal with the gas part of the flow for the deposition factor and the droplet effects are neglected. In the other methods like a particle tracking methods, the droplets are also considered and these are tracked to quantify their deposition on to the rod surface. In these models the maximum peak is obtained at the spacer face. However, the particle tracking method considered by Naitoh et al. (2002) shows that the maximum peak in the deposition is away from the spacer as shown in Fig. 1. In none of these methods, direct interaction of the liquid film with the spacer is modeled.

3. Analysis of a simple spacer and comparison with the measurements A simple ring spacer in a round channel has been considered to investigate the effect of spacer on the lateral velocity profile and turbulent kinetic energy using the CFD code. In general, any CFD code can be used for the single phase analysis for charactering the flow to study the turbulence enhancement across the spacer.

D.K. Chandraker et al. / Nuclear Engineering and Design 294 (2015) 262–273

267

Fig. 2. Geometry considered for the analysis with a ring type spacer.

Fig. 5. Lateral velocity contours in the downstream of a ring spacer (present study).

Fig. 3. Velocity profile in the narrow and the wider channel due to the flow obstruction.

3.1. Spacer geometry considered for the analysis and experimental data A simple geometry considered by Yano et al. (2011) for the experiments on a spacer having following dimensions is shown in Fig. 2. The channel diameter, spacer thickness, spacer length and spacer wall to wall gap are 20 mm, 1.4 mm, 30 mm and 1.3 mm, respectively. The superficial gas velocity considered is 85 m/s. Yano et al. (2011) carried out experiments to measure the lateral velocity at different axial location behind the spacer using Dual Phase Doppler Anemometer to verify the drift model proposed by Yano et al. (2000). The measurement was taken along the axis passing through the centre of the spacer thickness. This spacer has been analyzed to find the lateral velocity profile and the turbulent kinetic energy variation. 3.2. Simulation of simple spacer geometry Fig. 3 depicts a typical lateral velocity profile expected downstream of the spacer. Results of the velocity profile for this simple spacer geometry and the typical gas (air) velocity of 85 m/s is shown in Fig. 4. It can be seen that the wider channel has a higher velocity

Fig. 4. Velocity profile in the upstream and down stream of a ring spacer (present study).

due to flow blockage. The velocity profile recovers along the length in the narrow channel. Thus, the narrow channel and wide channel attains different velocity profiles. The velocity profiles merges gradually in the downstream of the spacer and in the process, the lateral component of the velocity gets enhanced. This is called the ‘drift’ flow effect caused by the recovery process of flow splits which is among the other phenomena (like run-off effect, narrow channel effect) responsible for influencing the rate of droplet deposition in the annular flow. The lateral velocity profile depends on the geometrical details of the obstruction like spacer thickness, clearance between wall and gap, spacer length and operating parameters like velocity at the upstream of the spacer. Fig. 5 shows the contours of the lateral velocity profile with the maximum value downstream of the spacer which shows that the deposition rate is expected to be higher in this region.

3.2.1. Comparison with the experimental data of Yano et al. (2001a,b) The lateral velocity profile is depicted in Fig. 6 along with a typical data of Yano et al. (2011) for the same geometry and superficial gas velocity of 85 m/s. The peak values of the lateral velocity prediction and experiments at the location of measurement are comparable. However, the trend is not exactly produced. This could be because of the fact that the droplets have not been simulated in the analysis. Also, the location of the maximum value of the lateral velocity is close to the spacer thickness. The lateral velocity effect decays away from the spacer location as shown in Fig. 6. The higher lateral velocity due to the presence of spacer has important role in increasing the deposition rate of entrained droplets in case of annular two phase flow.

3.2.2. Variation of turbulent kinetic energy due to the spacer Fig. 7 shows that the kinetic energy is enhanced behind the spacer depending upon the radial position. After attaining the peak value the kinetic energy tends to decay to the background value. As postulated by the investigators, the enhancement in the droplet deposition is expected to be driven by the turbulent kinetic energy of the flow. Present analysis has been performed considering the effect of liquid droplet on the kinetic energy enhancement to be insignificant owing to very small droplet sizes. Fig. 7 shows that the kinetic energy is greatly enhanced by the presence of spacer. The kinetic energy is found to be enhanced very close to the spacer and its effect is negligible towards centre of the channel. Higher thickness of the spacer is expected to influence the wider area as compared to the lower thickness. The above analysis indicated that the CFD analysis can be helpful in determining the trend of the velocity profile and the kinetic energy due to the spacer and hence this information is expected to be useful for application to the rod bundle application.

268

D.K. Chandraker et al. / Nuclear Engineering and Design 294 (2015) 262–273

Fig. 6. Lateral velocity (present study) along the channel length and comparison with the experimental data of Yano et al. (2011).

Fig. 7. Turbulent kinetic energy along the channel length for three different radial locations.

4. Evaluation of the spacer model for BWR assemblies The spacer effect needs to be considered for the dryout prediction of a new design of AHWR. Hence, based on the existing approaches and the flow behavior of the bundle, a simplified model has been proposed for the spacer of 54 rod bundle having a central unheated rod (Fig. 8). The channel diameter and fuel rod diameter

are 120 mm and 11.2 mm, respectively. The channel length is 3.5 m with six grid type spacers having 15 mm length spaced at 550 mm. 4.1. Turbulent intensity factor and vapor velocity for the analysis The dryout quality in BWR is expected to be in the range of 40 to 90% depending upon the mass flux and the gas velocity will be in the range of 5 to 15 m/s. The Analysis was done for the velocities of 1 m/s, 5 m/s, 10 m/s, 15 m/s and 22 m/s. However, it will be shown later that the enhancement factor is not sensitive to the gas velocity. The following two cases have been analyzed. (a) With spacer. (b) Without spacer.

Fig. 8. (a) cross section of the bare bundle showing the central rod, fuel pins and channel inside diameter, (b) 1/4th sector of cross section of spacer.

The cross sectional average kinetic energy computed for the values of above gas velocity has been normalized with respect to the bare bundle. The ratio is regarded as the turbulence enhancement factor. The turbulent kinetic energy has been determined to estimate the spacer effect on its enhancement for the AHWR bundle. The average kinetic energy across the cross section can

D.K. Chandraker et al. / Nuclear Engineering and Design 294 (2015) 262–273

269

Fig. 9. 1/4th symmetry sector of AHWR fuel cluster considered for analysis (a) the spacer grid shown along with the region of the bundle consisting of bearing pads, (b) The complete assembly of spacer and rod cluster, (c) 90 × 90 computational grid across the cross section of bundle.

be computed with the spacer and without the spacer and the enhancement ratio (TKEF) is defined as follow: Turbulent Kinetic Energy Enhancement Factor (TKEF) =

(TKE with spacer) (TKE without spacer)

4.3. Comparison with other spacer models Adamsson et al. (2011a,b) suggested droplet enhancement factors for three regions downstream of the spacer in the code MAFISTO for the mechanistic prediction of dryout in BWR bundle. The droplet deposition rate is assumed to be proportional to the turbulent kinetic energy we obtain:



MAX Kenh = B + 1 dep

4.2. Turbulent kinetic energy variation due to AHWR spacer The geometry for the rod bundle, spacer bearing pads and spacer was created using solid modeling software and used in PHOENICS. As the structured grid is used in PHOENICS, a Cartesian mesh was considered. The total number of cells used for computation was 1215,000. The number of cells is large due to the use of a structured mesh. Fig. 9 shows the modeled bundle along with the spacer and spacer bearing pads. Since Cartesian coordinates have been considered, the channel inside diameter has been simulated by considering a solid block. For the purpose of modeling, first a bare bundle has been modeled and the length for the flow to become fully developed has been evaluated. This length has been found to be ∼130 mm. Since this length is smaller than the spacer pitch, it can be expected that the flow disturbed after flowing over a spacer will be fully developed before reaching the next spacer. Considering this, the simulation length for flow over bundle containing spacer was taken to be sufficiently larger than the developing length. For the simulation, a 1/4th symmetry sector of the cluster was used. The spacer causes enhanced turbulence level which increases the deposition of the liquid droplets on the liquid film and hence the flow of the liquid film over the rods is also increased. The enhancement in the droplet deposition is found to be proportional to the turbulent kinetic energy of the gas which depends on the spacer design. There has been various studies in the past on the modeling of spacer each having assumptions and limitations or only part of the phenomena is dealt with for simplicity. However, review of previous work shows that the kinetic energy enhancement factor is almost of the same order of magnitude as of the deposition enhancement of the droplets as calculated by the particle tracking methods of droplets for a typical BWR spacer (2001). The average kinetic energy across the cross section has been computed with the spacer and without the AHWR spacer and the enhancement ratio (TKEF) is evaluated. The results of the analysis of the TKEF for various velocities of gas and liquid are shown in Fig. 10. Considering the dryout quality range of 0.4 to 0.90, the gas velocity of AHWR is expected to be in the range of 5 to 15 m/s (typical BWR value). The enhancement factor is found to be almost same for these values of the gas velocity.



D + 1

where B and D depend on the spacer geometry and  is a blockage ratio. A typical deposition trend for BWR conditions is shown in Fig. 1(d). Kanazawa et al. (1995) used HIJET-AFIMA (1994) for the three dimensional flow analysis to take into account the behaviors of liquid droplets in gas flow. In their calculation, the peak of droplet deposition rate on a liquid film appeared in the spacer region, although the experiments indicate that a liquid film thickened downstream form spacer. Also, the flow was assumed to be inviscid around the spacer. Naitoh et al. (2002) incorporated the spacer model for the dryout code, CAPE-BWR with the similar approach as that of HIJET-AFIMA code. However, the fluid was considered viscid and the effect of spacer incorporated in the sub-module called PLASHY-CRT and the turbulence enhancement was predicted with the good accuracy in a simple test spacer (Fig. 1(b)). Here the peak is observed downstream of the spacer unlike the prediction of HIJETAFIMA. Thus, the peak is expected at some distance from the spacer. 4.4. Evolution of a spacer model for AHWR The depositions enhancement factor for different velocity has been obtained for AHWR spacer. As mentioned above, most of the

Fig. 10. Enhancement factor for a turbulence kinetic energy in a bundle for various gas velocities.

270

D.K. Chandraker et al. / Nuclear Engineering and Design 294 (2015) 262–273

Fig. 11. A simplified model for AHWR spacer.

previous models evaluate the peak value of turbulent enhancement at the spacer as the droplet effect on the turbulent kinetic energy is not modeled. However, when the droplet effect is also considered using the particle tracking method, the peak is found to lie at some distance from the spacer. Since the droplets have not been modeled in the present study, the delay in the peak value is not observed in the results. However, similar to Adamsson model a plateau is provided for the delay in the deposition with the peak value calculated by the analysis of AHWR spacer. The maximum value of the enhancement factor is attained within 50 mm downstream of the spacer (can be considered a typical trend of BWR spacer). The maximum value of the deposition is maintained for 100 mm and subsequently, the decay curve is followed as shown in Fig. 1(d). Also, the background value of TKE is achieved within 350 mm from the spacer. As discussed earlier, the decay curve is expected to follow the TKE profile obtained in the analysis of AHWR spacer which is a function of the spacer geometry. Here the peak value and the decay profile is obtain from the analysis of the actual spacer of AHWR and only the delay in the droplet deposition is assumed based on the literature data. Thus a simple model for AHWR is presented in the form shown in Fig. 11. The above proposed model has been considered for the spacer effect which will be validated as the prototype dryout data on AHWR becomes available. The proposed spacer model has been incorporated in the mechanistic code, FIDOM-Rod for the dryout out analysis of AHWR fuel assembly as discussed subsequently. 5. Critical power analysis of BWR fuel assemblies with spacer model A phenomenological approach based on the liquid film dryout modeling has been adopted to evaluate the critical power of AHWR. The modeling details of the computer code FIDOM-Rod developed for this purpose has been described comprehensively in the reference paper (2012). In this paper, only relevant information has been described very briefly for the sake of completeness and continuity. 5.1. Description of the LFD analysis code (FIDOM-Rod) The code FIDOM-Rod (Film Dryout Modeling in Rod Bundle) is the extended version of the code, FIDOM (2011) which was developed and validated for a dryout in a tube. The code, FIDOM-Rod uses the subchannel conditions determined by the subchannel code and initiates the film analysis as soon as the annular flow pattern prevails in the subchannels. COBRA-IV-I has been used as the driver module to determine the subchannel conditions and the film dryout code (FIDOM-Rod) analyses the liquid film dryout over various rods. In general any subchannel code can be used to provide the local conditions of the rod bundle to the dryout code, FIDOM-Rod. The modeling is based on the entrainment and deposition of the

droplet in an annular flow regime. The important aspects of the modeling are the mass exchange at the interface between the liquid film and the vapor core region (Fig. 12a). Fig. 12b shows that the film flow rate in the rod facing different subchannels varies azimuthally. However, the complex process of the liquid film flow around the rod has been simplified by making it uniform as the calculation proceeds along the fuel length which has been found to be acceptable when compared with the experimental data (Chandraker et al., 2012). In the code, FIDOM-Rod, the constitutive correlations for the entrainment, deposition and onset of annular flow have been considered which are same as that incorporated in the FIDOM. The conservation equations for the three fields namely the liquid film flow, droplets and vapor are described below along with the constitutive models for entrainment and deposition. The equations of conservation of mass and energy are as follows: Mass balance of the liquid film (k) in a subchannel is given by dwlfk cf dwlfk (1) = P k (md − me − mev )k + dz dz Liquid film mass conservation for the subchannel having n liquid films

dwsclf = dz n 

P k (md − me − mev )k +

dwsclf dz

cf

Similarly, the cross flow of the liquid (liquid film and droplets) dwscl cf dwsclf cf dwscld cf = + (5) dz dz dz The droplet flow rate in a subchannel is estimated using the results of subchannel module and dryout module given by dwscl dwsclf dwscld = − (6) dz dz dz

(2)

k=1

For the droplets in a subchannel surrounded by n number of liquid films



For the gas

n

dwscld = dz

P k (me − md )k +

dwscld dz

cf

(3)

dwg dz

=

k=1

n 

P k mev +

dwgcf dz

(7)

k=1

Total liquid flow composed of liquid film and droplets is computed by the subchannel module as given by the following equation: dwsclf dwscld dwscl = + dz dz dz

(4)

Energy balance in a given subchannel is

mev =

n  q

k

hfg

(8)

k=1

The loss of liquid due to evaporation of each film is taken into account in the liquid film dryout analysis (FIDOM-ROD) depending upon the rod peaking factor and axial peaking factor. However, the gas flow is dictated by the subchannel analysis code. After calculating the film flow rate in the rod surfaces for all the subchannels, the film flow rate around the rod is averaged circumferentially at each axial location before proceeding for the analysis for the next node. Thus film flow rate is averaged considering l number of liquid film around the rod as given below:

wrlf =

l 

wlfk

(9)

k=1

wlfk

 updated

where wlfk

=



w Pk

nrlf

k=1

updated

Pk

(10)

is the updated value of film flow rate in the

surface (k) of the rod. In addition, the mass transfer correlations for the entrainment and deposition of the liquid droplets proposed by Whalley (1977) are given below: me = KCeq md = KC without the spacer and md = Kenh KC with the spacer

(11)

(12)

D.K. Chandraker et al. / Nuclear Engineering and Design 294 (2015) 262–273

271

Fig. 12. Schematic of film dryout process in a tube/a rod and extension of LFD methodology to the rod bundle.

where Kenh is equal to TKEF described above and is incorporated in FIDOM-Rod to account for the spacer effect.where K is the mass transfer coefficient and C is the droplet concentration prevailing in subchannel. Ceq is the liquid concentration at equilibrium which is related to the entrainment. E is the entrainment fraction defined as the ratio of the entrained liquid droplets to the total liquid in the subchannel. The entrainment fraction in a subchannel is calculated considering the quality and the liquid film flow rate in the subchannel. This ensures that the cross flow information is passed on to LFD module in terms of the droplet concentration. The droplet entrainment fraction (the fraction of liquid entrained in the gas core) and the droplet mass per unit volume are is given by C=

l jld l jl E = jg + jld jg + jl E

(13)

and

Rel =

l jl D l

(17)

For the mass transfer coefficient or deposition coefficient (K): The model of Paleev and Filippovich was modified by Utsuno and Kaminaga (1998) to achieve better prediction in the BWR operating range and diabatic conditions. K = 41.2

g Re0.15 g D g



C g

−0.36 (18)

where Reg is the Reynolds number for gas defined by Ishii and Grolmes (1975) have suggested a simple model for the inception of entrainment droplets in the annular flow. The initial entrainment fraction right after the transition to the annular-mist flow is assumed to be at equilibrium. E = Eeq

J E = ld Jl

(14)

(19)

The equilibrium droplet concentration in a subchannel is given by

where jg and jl are the superficial velocities for the gas and liquid droplets in the subchannel, respectively. The constitutive correlations for the deposition coefficient and entrainment are the important for the dryout prediction and hence validated models for a tube (FIDOM) has been incorporated in the present approach. Modified form of the entrainment model for Ishii and Mishima (1981) has been used. The modified form was proposed by Utsuno and Kaminaga (1998) for the BWR operating range and diabatic conditions. Eeq = tan h

Rel is the liquid Reynolds number defined by

0.16 0.16We0.08 Rel



− 1.2

(15)

where We is the Weber number defined as g jg D We = 



 g

1/2 (16)

Ceq =

l jl Eeq jg + jl Eeq

(20)

The total film flow rate in the subchannel at the onset of the annular flow gets distributed to the associated rod surfaces of the subchannel in the proportion of the surface area facing the subchannel, that is,



k wlfi =

w

sclfi n

Pk

k=1

Pk

(21)

Once the initial film flow rate is set at the onset of the annular flow rate, the flow rate of individual films on the rod and the droplet concentration depends on the film evaporation, entrainment and deposition. The film flow rate in each rod is examined and if none of the rod has zero film flow rate indicating that dryout is not attained, the power of the channel is further increased

272

D.K. Chandraker et al. / Nuclear Engineering and Design 294 (2015) 262–273 1.8

Fig. 13. 1/12th symmetry sector of AHWR fuel assembly showing rod no. and subchannel no. and axial power profile.

Critical Power Ratio (CPR)

1.7 1.6 1.5

5.2. Incorporation of the spacer model in FIDOM-Rod and the results The spacer model proposed in section has been considered to account for the droplet enhancement due to the spacer. The enhancement factor (TKEF) for the droplet due to the spacer is indicated as given in the profile of Fig. 11. Thus the droplet deposition rate with the spacer effect is expressed as Md = TKEF × (K × C) Adamsson and Le Corre (2011a,b) proposed to adjust the values of K in different channels to tune the prediction. But it is mentioned that the K values for each subchannel must be considered for a better prediction. However, a general approach has not been proposed. Diana (2009) and Diana et al. (2009) also study the spacer effect on the flow field but a model for BWR for the steam-water condition has not been proposed. The present methodology for the spacer modeling would be helpful to analyze the spacer effect. 5.3. Critical power of AHWR with the spacer effect The radial and axial power profile for AHWR bundle is shown in Fig. 13. The film flow rate variation with the spacer and without spacer is shown in Fig. 14. At the spacer locations the droplet deposition is enhanced resulting into higher film flow rates downstream of the spacer as depicted in Fig. 14. The variation of the critical power ratio with the mass flux is shown in Fig. 15 and the channel flow rate variation with the power is also plotted. The critical

Fig. 14. Variation of liquid film flow rates over various fuel pins of AHWR and the spacer effect.

CPR in Reactor=1.425

1.4

CPR with mass flux

1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6

and subchannel condition is obtained to feed the Liquid Film Dryout Module (LFD) module. This iteration is repeated till the dryout condition is achieved.

CPR=1.52(with spacer)

Without Spacer Model With Spacer Model Mass flux reduction with the powerfor a max. Pressure=70 bar Inlet Subcooling = 25 deg. C rated channel

0.5 400

500

600

700

800

900 2

1000

1100

1200

Mass Flux(kg/m s) Fig. 15. Critical power of 54 rod bundle of AHWR consideirng the spacer model.

power ratio values are also shown without considering the spacer effect. The spacer effect is found to enhance the critical power ratio of AHWR from 1.425 to 1.51 due to enhanced droplet deposition. Thus spacer effect plays an important role to ascertain the critical power of BWR assemblies.

6. Conclusions In the present study, a brief review on the previous investigation on the effect of spacer on dryout has been carried out and a methodology to formulate the spacer model for a fuel assembly has been proposed for BWR application. The following points are important in this study. (1) Most of the experimental measurements carried out previously are based on air–water data and hence their extension to the BWR conditions can not yield accurate prediction of the spacer effect on the droplet deposition enhancement. Also, most of the analytical model is based on the diffusivity of the gas and the interaction of the liquid film with the spacer is neglected due to the complexity of the mechanism. (2) The kinetic energy enhancement can be related to the deposition enhancement rate and the present investigation shows that the enhancement factor remains almost same for the wide range of vapor velocity. Thus, the turbulent flow analysis with the spacer can provide information about the deposition enhancement factor. A model with the assumed delay in the peak droplet deposition can be worked out for a given spacer design. The decay profile and the peak value of turbulent kinetic energy factor depend on the spacer design and needs to be analyzed for a fuel assembly for formulating the spacer model. (3) The model proposed for AHWR spacer has been incorporated in the dryout analysis code, FIDOM-Rod to arrive at the critical power. With the spacer model the critical power ratio is found to be enhanced from 1.425 to 1.51. This approach of spacer modeling is useful to compare the effectiveness of different spacer design on the performance of nuclear fuel assembly from view point of critical power. (4) Further research needs to be focused to generate data under steam-water conditions for the validation of spacer modeling approaches. The analytical models for the narrow channel effect and run-off effects should be evolved and validated for steam water conditions for a good prediction.

D.K. Chandraker et al. / Nuclear Engineering and Design 294 (2015) 262–273

References Adamsson, C., Le Corre, J.M., 2008. MEFISTO: a mechanistic tool for the prediction of critical power in BWR fuel assemblies. In: 16th Int. Conf. on Nucl. Eng. (ICONE16), Orlando, USA. Adamsson, C., Le Corre, J.M., 2011a. Modeling and validation of a mechanistic tool (MEFISTO) for the prediction of critical power in BWR fuel assemblies. Nucl. Eng. Des. 241, 2843–2858. Adamsson, C., Le Corre, J.M., 2011b. Modeling and validation of a mechanistic tool (MEFISTO) for the prediction of critical power in BWR fuel assemblies. Nucl. Eng. Des. 241 (8), 2843–2858. Akiba, M., et al., 2005. Prediction method of critical power by film flow rate measurement and subchannel analysis. Heat Transfer—Asian Res. 34 (5), 309–323. Chandraker, D.K., Vijayan, P.K., Sinha, R.K., Aritomi, M., 2012. A mechanistic approach for the prediction of critical power in BWR fuel bundles. JSME: J. Power Energy Syst. 6 (2), 35–50. Diana, C.G., Henryk, A.t., WiktorFrid, 2009. Experimental investigation of turbulent flow through spacer grids in fuel rod bundles. Nucl. Eng. Des. 239 (10), 2013–2021. Diana, C.G., (Thesis) 2009. Experimental Study and Modeling of Spacer Grid Influence on Flow in Nuclear Fuel Assemblies. KTH Engg. Sciences, Stockholm, Sweden, ISBN 978-91-7415-229-6. Ishii, M., Grolmes, M.A., 1975. Inception criteria for droplet entrainment in twophase concurrent film flow. AICHE J. 21 (2), 308–318. Ishii, M., Mishima, K., 1981. Correlation for liquid entrainment in annular two-phase flow of low-viscous fluid. In: ANL/RAS/LWR81-2. Kanazawa, T., Nishida, K., Nagayoshi, T., et al., 1995. Critical power evaluation with consideration of differences in droplet behavior due to spacer shape influence. J. Nucl. Sci. Technol. 32 (4), 301–312. Kanazawa, T., Nishida, K., Yokomizo, O., Kawabe, O.R., 1992. Analysis on deposition characteristics of coolant droplets in fuel assembly-effect of spacer (flow tab) shape. J. Nucl. Sci. Technol. 29 (21), 75–178. Lahey, R.T., et al., 1972. Out-of pile subchannel measurements in a nine-rod bundle for water at 10000 psia. Progress in Heat and Mass Transfer, vol. 4. Pergamon Press, New York, NY.

273

Lahey, R.T., 1977. The Thermal-Hydraulics of Boiling Water Nuclear Reactor. ANS Monograph. Naitoh, M., Ikeda, T., Nishida, K., Okawa, T., Kataoka, I., 2002. Critical power analysis with mechanistic models for nuclear fuel bundles, (I). J. Nucl. Sci. Technol. 39 (1), 40–52. Nishida, K., Kanazawa, T., et al., 1994. Spacer effect on liquid film flow and critical power in BWR fuel bundles. J. Nucl. Sci. Technol. 31 (3), 213–221. Nagayoshi, T., Nishida, K., 2001/1998. Spacer effect model for subchannel analysisturbulence intensity enhancement due to spacer. J. Nucl. Sci. Technol. 35 (6), 399–405. Nagayoshi, T., Nishida, K., 2001b. Development of transient boiling transition analysis method based on a film flow model. Nucl. Sci. Technol. 38 (10), 819–825. Okawa, T., Kotani, A., Kataoka, I., Naitoh, M., 2004. Prediction of the critical heat flux in annular regime in various vertical channels. Nucl. Eng. Des. 229, 223–236. Sinha, R.K., Kakodkar, A., 2006. Design and development of the AHWR—the Indian thorium fuelled innovative nuclear reactor. Nucl. Eng. Des. 236, 7–8. Tomiyama, O., Yokomizo, O., 1988. Spacer effects on film flow in BWR fuel bundle. J. Nucl. Sci. Technol. 25 (2), 94. Utsuno, H., Kaminaga, F., 1998. Prediction of liquid film dryout in two-phase annular mist flow in an uniformly heated narrow tube: development of analytical method under BWR conditions. J. Nucl. Sci. Technol. 35 (9), 643–653. Whalley, P.B., 1977. The calculation of dryout in a rod bundle. Int. J. Multiphase Flow 3, 501–515. Yamamoto, Y., Hoshide, A., Mitsutake, T., Morooka, S., 1997. Analytical study on effects of BWR fuel spacer on droplet deposition. Nucl. Eng. Des. 175, 119–129. Yano, T., Komori, Y., Aritomi, M., 2011. Droplet deposition distribution equation downstream of a BWR fuel spacer in a circular channel. J. JSEM 11 (Special issue), 177–188. Yano, T., Kodama, E., Aritomi, M., et al., 2000. Mechanistic modeling for ring-type BWR fuel spacer design—(1) Drift flow model. Nucl. Eng. Des. 201, 177–188. Yano, T., Aritomi, M., Kikura, H., Obata, H., 2001a. Mechanistic modeling for ringtype BWR fuel spacer design—(2) Local pressure drop and narrow channel effect. Nucl. Eng. Des. 205, 297–305. Yano, T., Aritomi, M., Kikura, H., Obata, H., 2001b. Mechanistic modeling for ringtype boiling water reactor fuel spacer design—(3) Run-off effect and model formulation. Nucl. Eng. Des. 210, 21–36.