CFD analysis of suspended debris during postulated severe core damage accident of PHWR

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CFD analysis of suspended debris during postulated severe core damage accident of PHWR Nitesh Dutta, Ankit R. Singhb, Pradeep K. Sahoob,

⁎

a b

Department of Mechanical Engineering, College of Engineering Roorkee, Roorkee, India Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, Roorkee, India

ARTICLE INFO

ABSTRACT

Keywords: IPHWR LOCA LCDA SCDA Suspended debris

A steady state CFD analyses for suspended debris with two different configurations are carried out for heat transfer assessment. Very low frequency postulated accident without mitigation can lead to fuel channels exposure for Pressurized Heavy Water Reactor (PHWR). The exposed fuel channels constitute suspended debris. The debris configuration changes from regular to a disassembled configuration with accident progression. Each fuel channel consists of nineteen pin bundles, sagged Pressure Tube (PT) and Calandria Tube (CT). The study shows an asymmetric heat distribution from fuel bundle to surroundings for debris with disassembled channels. This is due to contact among the channels and among the components of an individual fuel channel. The asymmetric heat distribution leads to higher peak fuel pin, PT and CT temperatures as compared to debris with regular configuration. It also increases the circumferential temperature gradient in constituting components of a fuel channel. Radiative heat transfer from fuel channel surface constitutes the major heat transfer for both the debris configurations; the debris bed with disassembled channels radiates 71% of its total energy dissipation as compared to 65.3% for regular configuration. A good extent of convective heat transfer takes place for regular configuration as space among channels allows the steam flow to take place. The analyses shows that predicted temperatures of the debris bed is limited with convective and radiative cooling, thus a large scale of component oxidation is not anticipated. Radiation heat transfer is found to be the major mode of heat transfer. Hence, a numerical study of the effect of emissivity (0.3–0.8) variation on fuel channel heat up is also studied. The maximum temperature variation of 164.5 °C is observed at the bottom (0°) of CT with emissivity variation.

1. Introduction The Indian Pressurized Heavy Water Reactor (IPHWR) 220 MWe design core comprises of horizontally placed fuel channels (Bajaj and Gore, 2006). Each fuel channel (Total 306 channels) has two concentric tubes. The inner tube is named as Pressure Tube (PT) while outer tube is termed as Calandria Tube (CT). Twelve fuel bundles, each of 0.495 m length are housed inside and along the length of PT. The annulus of PT and CT is filled with an insulating gas, CO2. The primary function of this filling gas is to limit the heat transfer to moderator during normal operation. Fig. 1 shows a schematic of Primary Heat Transport System (PHTS), half of the fuel channels are connected to one inlet header. The coolant flows through these connected fuels channels and takes away the fission heat from the fuel bundles inside the fuel channels. The coolant exchanges heat inside the steam generator. This coolant again gets connected to remaining 153 fuel channels, then flows in the

opposite direction to first 153 fuel channels. The fluid temperature at the inlet and outlet of the fuel channel is at 249 °C and 293 °C, respectively. Calandria houses moderator (heavy water) at atmospheric pressure and all the fuel channels. The channels1 are organized in square pitch of 229 mm. Calandria is further submerged into a large pool of vault water housed in concrete rectangular vault. PHWR comprises of various engineering, safety guidelines to mitigate any Design Basis Accidents (BDAs) and Beyond Design Basis Accidents (BDBAs) progression with the associated consequences. In PHWR, postulated accidents are segregated into two categories, as Limited Core Damage Accident (LCDA) and Severe Core Damage Accident (SCDA) (Majumdar et al., 2014). BDBAs which do not cause gross fuel melting and channel dislocation are categorized as LCDAs, whereas fuel melting and channel dislocation (loss of core geometry) are considered under SCDA category. The postulated LCDA scenario can be initiated with the Loss of

Corresponding author. E-mail addresses: [email protected] (N. Dutt), [email protected] (A.R. Singh), [email protected] (P.K. Sahoo). 1 Pradeep K Sahoo is on leave and working as professor in Botswana international university of Science and Technology, Palapye, Botswana, [email protected]. ⁎

https://doi.org/10.1016/j.nucengdes.2019.110390 Received 24 February 2019; Received in revised form 20 September 2019; Accepted 14 October 2019 0029-5493/ © 2019 Elsevier B.V. All rights reserved.

Please cite this article as: Nitesh Dutt, Ankit R. Singh and Pradeep K. Sahoo, Nuclear Engineering and Design, https://doi.org/10.1016/j.nucengdes.2019.110390

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Nomenclature

a b C d Dst DCT D PT e E Gr h I k L n Q p Pr Ra RaDi RaDo Re Ri q r s s S s t

v T Ti To Te T amb T CT T PT V

absorption coefficient (m−1) body force vector specific heat (J/kg.K) oxide layer thickness (m) characteristic length for steam flow outside CT diameter of CT (m) diameter of PT (m) total specific energy [h + u2/2 + gz ] (J/kg) experimental Grashof number heat transfer coefficient (W/m2.K) radiation intensity, which depends upon position (r ) and direction (s )(J/m2.rad) thermal conductivity (W/m.K) characteristic length for air flow in CT-PT annulus refractive index volumetric heat generation (W/m3) pressure (Pa) Prandtl number Rayleigh number Rayleigh number based on inner diameter Rayleigh number based on outer diameter Reynolds number Richardson number heat flux vector position vector direction vector scattering direction vector simulation path length (m) time (s)

velocity (m/s) local temperature (K) temperature of inner cylinder (°C) temperature of outer cylinder (°C) temperature (°C) ambient temperature of steam (°C) temperature of the CT (°C) temperature of the PT (°C) velocity vector

Greek symbols

µ

s

θ

density (kg/m3) dynamic viscosity (N.s/m2) kinematic viscosity (m2/s) coefficient of volumetric expansion (1/K) hemispherical emissivity Stefan-Boltzmann constant (5.67 × 10−8 W/m2. K4) scattering coefficient (m−1) angular position in degree phase function solid angle (rad) stress tensor

Subscripts

i o st a NC C CO2

inner surface outer surface steam air non-contact contact carbon dioxide

uncovering of few top rows of fuel channels (Singh et al., 2011, Mathew et al., 2008). The exposed channels in steam environment form suspended debries. These channels sag due to high temperature creep and stack one on another. A higher order of channel sagging can lead to channel disassembly (failure from both ends). Figs. 2 and 3 depict the layout of suspended debris in which fuel channels are arranged for intact and disassembled configurations in the steam environment. The first configuration indicates beginning of fuel channel heat up and the second configuration indicates post disassembly heat up. As the fuel channels are exposed to steam, it is assumed that PT has sagged and in contact with CT. The pitch is 229 mm in horizontal and vertical directions. The suspended debris with or without disassembled channels eventually grows and impart load to the submerged fuel channels. A column wise core collapse may take place once suspended debris load exceeds the threshold value of a pullout load of CT to Calandria tube sheet rolled joints for still submerged channels. The collapsed channels constitute a terminal debris bed (Dutt et al., 2015). Presence of moderator in Calandria delays the heat up of the terminal debris. The decay heat of terminal debris bed is eventually removed by vault water heat up and boil-off, which prevent the heat up and failure of Calandria. Failure of Calandria is likely to take place once the vault water gets vaporized, leaving the Calandria exposed to steam condition. Termination of accident progression as described is planned through measures taken through Severe Accident Management Guidelines (SAMGs). Addition of Fire Fighting Water into different places like steam generators, PHTS, Calandria and vault through hookup up points are the measures taken for residual heat removal from the core. In this paper, a numerical simulation is presented with the study of heat up behavior of suspended debris bed. The study is carried out using

Coolant Accident (LOCA). A feeder pipe or header pipe break proceeds to the postulated LOCA conditions causing a decrease in the coolant flow rate and system depressurization. Termination of LOCA condition is achieved with Emergency Core Cooling System (ECCS) water injection by filling the PHTS and reflooding fuel channels with coolant. With the failure of ECCS system, fuel channels would experience very low flow conditions leading to degraded convective cooling, which in turn increases the temperature of fuel channel. Stratified flow inside the fuel channel may be established after a long time and even fuel channel may be fully voided (Sharma et al., 2018; Yadav et al., 2014). Depending on PT internal pressure and temperature, the PT may either balloon or sag as a result of high temperature creep. Ballooning of PT is evidently under high internal pressure, whereas sagging takes place under the fuel bundle weight. In either case, the PT contacts the CT establishes a heat transfer path to surrounding moderator (Nandan et al., 2010; Gupta and Dutta, 1996). Ballooning contact produces more uniform heat transfer over CT owing to large contact area between PT and CT. On the contrary, a small area of contact between PT and CT during sagging contact leads to localized heating on CT. Using numerical simulation, Singh and Sahoo (2018) has shown that the severe circumferential temperature gradient are restricted to the small sector around the contact area between PT and CT. In either case of deformation, the moderator plays as a heat sink and limits the severe heat up of core and its degradation. With postulating LOCA and unavailability of ECCS with the failure of the moderator cooling unit, moderator presents in Calandria is expected to boil off continuously. Moderator boil-off will result in high pressure inside the Calandria, which eventually leads to rupture of Over Pressure Rupture Disks (OPRDs). Expulsion of moderator through OPRDs depressurizes Calandria (Nitheanandan et al., 2017) leads to 2

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channel lying in the top three rows of Calandria. Dutt and Sahoo (2018) conducted experiments for the single exposed channel and also validated the numerical results with experimental results at average decay heat (4.16 kW/m) in the steam environment as shown in Fig. 5. Temperature profile inside the fuel channel at average decay heat is shown in Fig. 6 in which maximum temperature is observed for the central fuel pins. Fig. 7 shows the non-scaled 2D layout of the exposed channel in steam environment. The horizontal distance between the centers of fuel pin to the symmetry boundary is 114.5 mm. Velocity is of 20 cm/s is applied at the bottom of the fuel channel. CAD modelling and meshing is carried out on ANSYS Fluent software. The compact forms of continuity, momentum, energy and radiation equations for the present flow system are given below by Eqs. (1)–(4), respectively. Continuity equation

dt

+

. ( V) = 0

(1)

Momentum Equation

( V) + dt

. ( VV ) =

p+

.

+ b

(2)

. (V . )

(3)

Energy Equation

( e) + dt

. ( eV ) = Q

.q+

In the above equations , t , V , p , , b , e , Q and q are the fluid density at specific temperature, time, velocity vector, pressure, stress tensor, body force vector, total specific energy, volumetric heat generation and heat flux vector. The radiative transfer equation (RTE) is

dI (r , s ) T4 + (a + s ) I (r , s ) = an2 + s ds 4 Absorption

Fig. 1. Indian Pressurized Heavy Water Reactor.

4 0

I (r , s ) ( s . s ) d

Emission

Scattering

(4)

ANSYS Fluent software in which exposed fuel channels in two configurations, namely the intact core configuration and disassembled conditions are simulated. The effect of variation of emissivity, in the range of 0.3–0.8, on radiation heat dissipation and channel component heat up is also investigated. The analyses helps to understand the complex heat transfer of the suspended debris bed and assessment of the state of debris bed which can undergo in-Calandria injection as a part of the SAMGs measure as described.

(a + s ) is the optical thickness of the medium. The refractive index (n), is important when considering radiation in semi-transparent media. In the above equation a , s , s , s , , , T are absorption coefficient, scattering coefficient, scattering direction vector, path length, phase function, solid angle, and local temperature in Kelvin, respectively. Table 1 provides the dimensions for fuel channel components (CT, PT and Clad). Fig. 8 depicts the mixed mesh (Triangular and Quad) approach in which triangular elements are used for the curvilinear geometry and quad elements used where temperature gradients are low. Minimum orthogonal quality of 0.36 and the maximum aspect ratio of 5.8 achieved. In simulation, DO model is used. It is postulated that during SCDA, steam purges inside the CT-PT annulus. In numerical simulation, it is considered that, the space between PT and fuel pin is also filled with steam. Buoyancy effect is considered and temperature dependent thermal properties of steam are used. Hydrogen generation is neglected in the analysis. Pressure based solver, SIMPLE algorithm, second order upwind scheme for momentum, energy and radiation is used.

2. Emissivity sensitivity analysis of single exposed channel In a postulated accident scenario, the emissivity of the exposed channel may vary in the range of 0.3–0.8. In this section an emissivity sensitivity analysis is carried out to predict the behaviour of the exposed fuel channels. Fuel channels in the Calandria have different power. Fig. 4 shows a 3D view of Calandria in which fuel channels are submerged into moderator and top three rows of fuel channels are exposed to steam environment. Steam is produced by the decay heat of submerged fuel channels. Exposed fuel channels interact with the steam generated inside Calandria. The power in the fuel channel varies in the core of a nuclear reactor. At 1% decay heat, the channel that has maximum power in the top three row is 4025.2 kW/m. This power is used in the simulation because it takes care of the worst scenario. The first case is studied in which CT, PT and the fuel pins emissivity is 0.3, while the 2nd and 3rd cases are simulated for emissivities of 0.5 and 0.8, respectively. Comparative study is carried out to observe the effect of change in emissivity on temperature of fuel channel components. Results are also plotted for the heat flux through the CT outer surface. In a 220 MWe IPHWR reactor, 1% average decay heat of 306 channels is 4.16 kW/m, which is higher than the maximum power in a

2.1. Boundary conditions and flow model selection To study the effect of the neighbouring channels, array of single exposed channel is simulated. The channels are kept in horizontal pitch of 229 mm. The symmetric boundary condition is applied at a distance of 114.5 mm from the centre of the fuel channel and is shown in Fig. 7. Steam inlet velocity of 0.20 cm/s is applied at the bottom of fuel channel. Pressure outlet boundary condition is used at the outlet of steam domain. It is postulated that during LOCA, emissivity of unoxidized and oxidized fuel channel components (CT, PT and fuel pins) 3

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Fig. 2. Suspended debris with original core configuration in steam environment.

been carried out for Grashof number using the maximum observed temperature of the CT outer surface is (669.4 °C), which appears at the bottom-most part. Thermal properties of steam are calculated by considering constant temperature of the CT and bulk mean temperature of the steam (Minkowycz and Sparrow, 1966).

may vary in the range of 0.3–0.8. To simulate the postulated accident scenario, three cases are studied with different emissivity of (0.3, 0.5 and 0.8) of the fuel channel. For this problem, experimental data is not available to know whether the flow is laminar or turbulent. Initially numerical simulation is carried out, in which laminar model is used. After that, numerical simulation is carried out in which different turbulence models (standard k-omega and epsilon) are used. Turbulent intensity of 5% is added at steam inlet. Second order turbulent viscosity is used. Table 2 gives the results of the grid independence study having area weighted average (AWA) temperature of fuel channel components outer surface, obtained by using laminar and turbulent models in Fluent. Fuel pins numbering is shown in Fig. 5. In all cases, 102,624 elements are found to be adequate to make results independent of the mesh size. Grid independence test (GIT) results are compared at emissivity 0.3, because the simulation at low emissivity results in high temperature of the fuel channel components. High temperature of the fuel channel increases the probability of turbulent flow. Laminar and turbulent model results are compared and observed that there is insignificant variation in temperature of fuel channel components. It is because at high temperature radiation dominant mode of heat transfer. The maximum value of y+ is observed on the outer side of the CT and it is 0.16 for k-omega and 0.17 for kepsilon model. To study the flow of steam outside the CT surface, dimensionless numbers are calculated which indicates the flow is laminar and natural convection dominated. Above grid independence study shows that insignificant variation in temperature of fuel channel components by using laminar or turbulent model in simulation. For the simulation, laminar model is used. Fig. 9 depicts the results of circumferential temperature variation at CT and PT outer surfaces. A calculation has

Grst =

Dst3

CT st g (To 2 st

T amb)

=

0. 11053 × 0.001459 × 9.8 × (669.4 (7.078 × 10 5) 2

(5)

= 2.19 × 106 Prst =

µst × Cst 2.36 × 10 5 × 2384.6 = = 0.94 kst 0.05111

Rast = Grst × Prst = 2.19 ×

100)

106

× 0.94 = 2.05 ×

(6) (7)

106 (Laminar) 4

8

Calculated Rayleigh number lies between 10 < Rest < 10 , which confirms the flow is laminar (Kuehn and Goldstein, 1980) The Reynolds number is calculated for inlet steam velocity 0.2 m/s at 100 °C.

Rest = Rist =

vst

0.2 × 0.595 × 0.1105 st Dst = = 1019.3 (Laminar) µst (1.29 × 10 5)

Grst 2.19 × 106 = = 2.10 2 Rest (1019.3)2

(9)

Richardson number is found to be more than one, indicates the dominance of natural convection over forced convection. Grashof number is calculated for CT-PT annulus. PT temperature varies circumferentially from bottom to top. In calculation, maximum temperature of the PT and minimum temperature of the CT is used. This assumption takes care of the extreme condition that may arise in the system. 4

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Fig. 3. Suspended debris with disassembled channel configuration in steam environment.

Fig. 5. CT and PT temperature profile for 4160 W/m (Dutt and Sahoo 2018).

Fig. 4. Non scaled exposed fuel channels in steam environment (Dutt and Sahoo 2018).

5

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Table 1 Dimensions of fuel channel components.

CT PT Clad

Prst =

Outer Diameter (mm)

Inner Diameter (mm)

Thickness (mm)

110.5 90.0 15.2

107.8 83.0 14.4

1.35 3.50 0.41

µst × Cst 3.23 × 10 5 × 2230.8 = = 0.89 kst 0.0811

(11)

Rast = Grst × Prst = 997.35 × 0.89 = 887.6 (Laminar) As the Rayleigh number (Rast ) is less than 106 (Francis et al., 2002), laminar viscous model is used in the simulation. Analysis shows that at 0.3 emissivity of the fuel channel, flow is in laminar zone inside CT-PT annulus and outside CT surface. Lower emissivity 0.3 results show that flow is laminar. Higher emissivity 0.5 and 0.8 results would also be in laminar flow. Table 3 shows the grid independence test in which results are shown in case of 0.5 and 0.8 emissivity.

Fig. 6. Temperature contour (°C) of the test section (Dutt and Sahoo 2018).

2.2. Results and discussion of single exposed fuel channel Fig. 9 shows the circumferential temperature profile at CT and PT outer surface for different emissivity (0.3, 0.5 and 0.8). The channel with 0.3 emissivity attains highest temperature for the CT and PT, while 0.8 emissivity channel attains the lowest temperature. Comparing results of 0.3 emissivity and 0.8 emissivity channels show that the maximum deviation in temperature is observed at the bottom of CT and it is 164.5 °C. For PT, the maximum deviation of temperature is observed at 170° and it is 202.7 °C. Eccentricity of PT with CT increases the localized view factor near CT-PT contact area. This results in higher radiation heat transfer from PT outer surface to CT inner surface and higher temperature at the bottom of the CT. As expected, PT attains minimum temperature at the bottom. In addition to radiation heat transfer, local gas conduction in the narrow space between PT and CT, and conduction at the contact region of CT-PT, leads to better heat transfer. At the top of the PT, the gap between CT and PT is the maximum. This increases the convective heat transfer resistance and reduces radiation view factor that results in poor heat transfer from PT outer surface to CT inner surface and higher temperature of PT at the top of fuel channel. Fig. 10(a–c) depicts the temperature contour of the test section at emissivity of 0.3, 0.5 and 0.8, respectively. It is observed that fuel channel having 0.3 emissivity attains maximum temperature, while the channel with 0.8 emissivity attains lowest temperature. Another observation is that a thermal boundary layer is formed around the CT outer surface due to natural and forced convection. Steam absorbs heat from the CT outer surface and becomes superheated. Superheated steam is at higher temperature results in low density. This results in natural convection and thermal boundary formation over CT outer surface. Moderator boils off in Calandria results in upward movement of steam, which acts as a coolant for the high temperature CT through forced convection. Steam participates in radiation and dissipate heat to the low temperature steam. Steam temperature increases after crosses CT. From the temperature contour one can observe that for emissivity of 0.3, the surrounding steam above the fuel channel are less affected than the other two case. This is most affected for emissivity of 0.8. This could be attributed to higher velocity of rising stream and lower contact time with the nearby fluid. Fig. 11(a–c) shows the velocity profile of superheated steam. The steam velocity range is maximum for channel having an emissivity of 0.3, while the steam velocity range is minimum for channel of emissivity 0.8. Fuel channel of emissivity 0.3 has a maximum CT temperature, which increases the steam temperature near CT outer surface. Higher degree of superheat steam around CT outer surface result in

Fig. 7. Layout of exposed channel.

Grst = =

L3

PT st g (To 2 st

(0.1078

TiCT )

=

(DiCT

DoPT )3

PT st g (To 2 st

0.090)3 × 0.00106 × 9.8 × (798.1 (1.38 × 10 4)2

= 997.35 (Laminar)

TiCT ) 535) (10) 6

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Fig. 8. Non-uniform computational grid structure. Table 2 Grid independence test for 0.3 emissivity. (0.3)

(0.3)

(0.3)

Laminar model Te (°C) Elements CT 49,190 559.5 88,679 549.4 102,624 549.6 231,033 549.6

Te (°C) PT 781.4 767.4 767.5 767.5

Te (°C) Pin (01) 968.1 954.7 954.7 954.8

Te (°C) Pin (06) 928.0 918.3 918.4 918.4

Te (°C) Pin (14) 1017.7 1006.5 1006.7 1006.7

Te (°C) Pin (19) 1033.4 1023.1 1023.3 1023.3

Turbulent model k-omega Te (°C) Te (°C) Elements CT PT 49,190 558.6 780.9 88,679 548.7 767.0 102,624 548.9 767.1 231,033 548.9 767.1

Te (°C) Pin (01) 967.8 954.4 954.5 954.5

Te (°C) Pin (06) 927.7 918.1 918.1 918.2

Te (°C) Pin (14) 1017.4 1006.3 1006.4 1006.4

Te (°C) Pin (19) 1033.1 1022.8 1023.0 1023.0

Turbulent model k-epsilon Te (°C) Te (°C) Elements CT PT 49,190 547.5 774.8 88,679 538.1 761.1 102,624 542.2 763.3 231,033 542.2 763.3

Te (°C) Pin (01) 963.2 950.1 951.6 951.6

Te (°C) Pin (06) 923.4 914.1 915.5 915.5

Te (°C) Pin (14) 1013.3 1002.4 1003.9 1003.9

Te (°C) Pin (19) 1029.2 1019.1 1020.5 1020.5

Fig. 9. Temperature profile CT and PT. Table 3 Grid independence test for 0.5 and 0.8 emissivity.

higher buoyancy force on steam. This increases natural convection resulting higher velocity of steam.

(0.5)

2.2.1. Temperature profile of fuel pins The temperature contour of fuel pins for different emissivity are presented in Figs. 12–14. In a 19 pins fuel bundle, power is distributed in a ratio of 1:1.1:1.4 for central, middle and outer fuel pins respectively. In each case, central fuel pin attains the maximum temperature and outer fuel pins of the fuel bundle have lowest temperature. Centre fuel pin is surrounded by middle and outer fuel pins. The temperature difference between the centre pin and surround pins is small. This reduces heat transfer resulting highest temperature among all fuel pins. Outer fuel pins have better heat sink through PT, CT and steam, results in lower temperature than middle fuel pins. Outer circle fuel pins temperature decreases from top (fuel pin 01) to bottom (fuel pin 06). In simulation, fuel bundle is placed concentrically with PT. The fuel pins temperature is largely influenced by PT circumferential temperature. A similar trend of temperature profile is also observed in middle circle fuel pins (fuel pin 13–16). Outer fuel pins temperatures influences the temperature of central fuel pins.

(0.8)

Laminar viscous model Te (°C) Te (°C) Elements CT PT 49,190 489.9 673.9 88,679 487.4 669.3 102,624 487.6 669.4 231,033 487.6 669.4

Te (°C) Pin (01) 836.2 831.2 831.3 831.4

Te (°C) Pin (06) 804.1 801.5 801.6 801.6

Te (°C) Pin (14) 885.7 881.8 882.0 882.0

Te (°C) Pin (19) 901.6 898.2 898.3 898.3

Laminar viscous model Te (°C) Te (°C) Elements CT PT 49,190 431.3 575.5 88,679 432.2 577.0 102,624 432.4 577.2 231,033 432.4 577.2

Te (°C) Pin (01) 709.3 712.0 712.0 712.1

Te (°C) Pin (06) 685.3 688.5 688.6 688.7

Te (°C) Pin (14) 757.3 759.6 759.7 759.7

Te (°C) Pin (19) 772.9 775.4 775.4 775.4

surface. It represent combined heat transfer having radiation and convection. Fig. 15 shows that, heat transfer is maximum at the bottom of the channel, varies circumferentially and marginally increases near 180°. As discussed earlier, CT-PT contact region and narrow zone increases conduction and radiation between the CT-PT. Heat transfer rate is enhanced due to vortex formation at the top of CT outer surface, which is shown in Fig. 16. Total heat flux (4.03 kW/m) is constant. Low emissivity (0.3) fuel channel has more heat transfer at the bottom and less heat transfer from 50 to 300°.

2.2.2. Heat flux profile of CT Numerical study has been carried out at different emissivity (0.3, 0.5, and 0.8) for the circumferential heat transfer from the CT outer 7

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Fig. 10. (a). Temperature contour (°C) for ε = 0.3. (b). Temperature contour (°C) for ε = 0.5. (c). Temperature contour (°C) for ε = 0.8.

Fig. 11. (a). Velocity contour (m/s) for ε = 0.3. (b). Velocity contour (m/s) for ε = 0.5. (c). Velocity contour (m/s) for ε = 0.8.

3. Suspended debris bed problem formulation

3.1. Flow model selection and result discussion of multiple exposed fuel channels

To study the effect of the neighbouring channels, array of exposed channels is simulated by applying symmetry boundary conditions. Steam velocity is calculated assuming 1% decay heat of submerged reactor channels. Figs. 17 and 18 illustrate the configuration of suspended debris beds (intact and disassembled configuration) used for computational purposes. The power distribution in each channel is different. It varies from top to bottom and also varies in a horizontal row. The top most channel power is least as per actual power distribution in 220 MWe IPHWR. Power used for simulation is 2735.6 W, 3412.4 W and 4025.2 W for top, middle and bottom fuel channels respectively. The channel arrangement and its power is shown in Figs. 17 and 18. Steam inlet boundary conditions are used for simulation.

For non-contact (intact core configuration) suspended debris analysis, it is considered that channels are not detached from Calandria and CO2 is available inside the eccentric annulus CT-PT. Inside PT space between PT-fuel pin is flooded with steam. Pressure based solver and Discrete Ordinate (DO) mode is used. 2D-steady state analysis has been carried out using SIMPLE algorithm with second order upwind scheme for momentum, energy and radiation. Fig. 19 shows the mesh of the computational domain in which triangular and quad elements are adopted. In simulation, non-uniform computational grid of minimum orthogonal quality 0.33 and maximum aspect ratio 6.5 is obtained. In the reactor, linear horizontal pitch between fuel channels is 229 mm. Hence symmetric boundary conditions are applied at a distance of 114.5 mm from centre of fuel channel and is shown in Figs. 17 8

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Fig. 12. AWA temperature of fuel pin surface for 4025.2 W/m heating rate (ε = 0.3).

Fig. 15. Heat flux at CT outer surface.

independent (GI) test for non-contact channels are given in Tables 4–6 that shows 198,531 elements provide acceptable results. It is observed that there is insignificant variation in temperature of channel components using laminar model and turbulent model (standard k-omega and epsilon model). It is observed that in all cases radiation heat transfer is the dominant heat transfer mode, fuel channels, component temperatures are high, results in the dominant mode of heat transfer. Hence, grid independence test results are almost similar for any flow model, either laminar or turbulent. Dimensionless numbers are calculated for the fluid flow using numerical results of laminar model, which also shows the flow to be laminar. The maximum temperature of the CT is used to calculate the Grashof number. Fluid properties evaluated at the mean temperature of steam and constant temperature of the CT. 3.2. Fluid flow analysis outside CT surface of non-contact fuel channels

Fig. 13. AWA temperature of fuel pin surface for 4025.2 W/m heating rate (ε = 0.5).

Grst =

Dst3 g (ToCT

T amb)

2 st

=

0. 11053 × 0.001575 × 9.8 × (613.3 (6.48 × 10 5) 2

(13)

= 2.5 × 106

Prst =

µst × Cst 2.3 × 10 5 × 2020.5 = = 0.95 kst 0.04841

Rist =

vst

(14)

106 (Laminar)

(15)

0.20 × 0.595 × 0.1105 st Dst = = 1019.3 (Laminar) µst (1.29 × 10 5)

16)

Rast = Grst × Prst = 2.5 ×

Rest =

100)

106

× 0.95 = 2.37 ×

106

Grst 2.5 × = = 2.4 Re2st 1019. 32

(17)

3.3. Fluid flow analysis inside CT-PT annulus Grashof number is calculated for CT-PT annulus. In calculation, maximum temperature of the PT and minimum temperature of the CT is used.

Fig. 14. AWA temperature of fuel pin surface for 4025.2 W/m heating rate (ε = 0.8).

and 18. Emissivity of Zircaloy increases after oxidation. Clad or fuel pin is expected to attain high temperature and exposure to steam environment that oxidizes it. In numerical simulation, the emissivity of fuel pin (clad) is assumed to be 0.6. Emissivity of 0.5 and 0.4 is considered for PT and CT. At the inlet, steam velocity of 20 cm/s is applied. To predict the flow is laminar or turbulent, three simulations are carried out for non-contact channels, in which all boundary conditions are same, except the flow model (laminar or turbulent). Grid

GrCO2 = =

(0.1078

PrCO2 = 9

L3

PT CO2 g (To 2 CO2

TiCT )

=

(DiCT

DoPT )3

0.090)3 × 0.001136 × 9.8 × (720.1 (6.4 × 10 5) 2

µCO2 × CCO2 kCO2

=

PT CO2 g (To 2 CO2

494.2)

3.7 × 10 5 × 1183.05 = 0.7 0.06127

TiCT ) (18)

= 3372.2

(19) (20)

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Fig. 16. Velocity vector (m/s) and temperature (°C) contour at the top of CT outer surface.

Fig. 17. Layout of non-contact exposed fuel channels of suspended debris bed.

Fig. 18. Layout of contact exposed fuel channels of suspended debris bed.

10

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RaCO2 = GrCO2 × PrCO2 = 3372.2 × 0.7 = 2360.54 (Laminar) Temperature contours for the non-contact fuel channels are shown in Fig. 20. It can be seen that central fuel pin of the bottom fuel channel attains the highest temperature. The maximum temperature of the noncontact fuel channels reaches to 905.8 °C, which is below the melting point. It can be visualized that as steam moves upward, gets superheated by absorbing heat from CTs. Steam temperature is higher near CT and diminishes in a horizontal direction from CTs. Fig. 21 depicts the natural convection inside the annulus of CT2NC and PT2NC. PT2NC temperature is higher than CT2NC temperature. After receiving heat from PT, the currents move in an upward direction and after reaching the top of the CT, the convection currents moves in downward direction due to cooler CT inner surface. Fig. 22 represents temperature profile of all three channels CT1NC attains 613.2 °C at the bottom. CT1NC temperature varies circumferentially from bottom to top and attains 509 °C at the top. The temperature profile of PT1NC shows that the temperature at the point of contact at the bottom is 628.8 °C and at the top is 720 °C. Factors that control the circumferential temperature of CT, PT are eccentricity of the PT, localized view factor, buoyancy driven motion of the fluid between CT-PT annulus and available space between PT-fuel pins. Change in steam temperature near CTs outer surfaces also influence the fuel channel temperature. Steam generated through submerged channels moves upward by absorbing heat of CT1NC and acts as a coolant for second CT2NC. As steam temperature rises, its cooling capacity decreases.

Fig. 19. Non-uniform computational grid structure for multiple channels. Table 4 Grid independence test for non-contact channels for laminar model. Non-Contact channels simulation using laminar model Elements CT1NC outer surface temperature (°C) CT2NC outer surface temperature (°C) CT3NC outer surface temperature (°C) PT1NC outer surface temperature (°C) PT2NC outer surface temperature (°C) PT3NC outer surface temperature (°C) Fuel pin(1NC) (No. 01) outer surface temperature Fuel pin(2NC) (No. 01) outer surface temperature Fuel pin(3NC) (No. 01) outer surface temperature Fuel pin(1NC) (No. 06) outer surface temperature Fuel pin(2NC) (No. 06) outer surface temperature Fuel pin(3NC) (No. 06) outer surface temperature Fuel pin(1NC) (No. 19) outer surface temperature Fuel pin(2NC) (No. 19) outer surface temperature Fuel pin(3NC) (No. 19) outer surface temperature

(°C) (°C) (°C) (°C) (°C) (°C) (°C) (°C) (°C)

GIT 79,062 514.2 499.4 487.1 698.9 664.3 629.8 843.1 800.4 750.5 816.1 771.0 725.2 901.4 852.9 797.7

126,452 515.1 501.3 488.2 699.4 665.5 630.8 843.3 801.1 750.9 816.6 772.2 726.4 901.8 853.8 798.4

198,531 515.3 501.8 488.8 699.5 665.8 631.3 843.4 801.2 751.2 816.7 772.5 727.0 901.9 854.0 798.7

287,844 515.2 501.8 488.8 699.3 665.7 631.2 843.2 801.2 751.1 816.6 772.5 726.9 901.8 853.9 798.6

Table 5 Grid independence test for non-contact channels for k-omega model. Non-Contact channels simulation using k-omega model Elements CT1NC outer surface temperature (°C) CT2NC outer surface temperature (°C) CT3NC outer surface temperature (°C) PT1NC outer surface temperature (°C) PT2NC outer surface temperature (°C) PT3NC outer surface temperature (°C) Fuel pin(1NC) (No. 01) outer surface temperature Fuel pin(2NC) (No. 01) outer surface temperature Fuel pin(3NC) (No. 01) outer surface temperature Fuel pin(1NC) (No. 06) outer surface temperature Fuel pin(2NC) (No. 06) outer surface temperature Fuel pin(3NC) (No. 06) outer surface temperature Fuel pin(1NC) (No. 19) outer surface temperature Fuel pin(2NC) (No. 19) outer surface temperature Fuel pin(3NC) (No. 19) outer surface temperature

(°C) (°C) (°C) (°C) (°C) (°C) (°C) (°C) (°C)

GIT 79,062 513.4 500.0 489.3 698.4 664.7 631.5 842.8 800.7 751.6 815.7 771.3 726.7 901.1 853.2 798.8

126,452 514.3 501.6 490.2 698.9 665.7 632.3 843.0 801.3 752.0 816.2 772.3 727.6 901.5 853.9 799.3

11

198,531 514.6 502.0 490.7 699.0 665.9 632.5 843.1 801.4 752.2 816.3 772.6 727.9 901.6 854.1 799.6

287,844 514.5 502.2 490.9 698.9 665.9 632.6 843.0 801.5 752.3 816.2 772.6 727.9 901.6 854.1 799.6

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Table 6 Grid independence test for non-contact channels for k-epsilon model. Non-Contact channels simulation using k-epsilon model Elements CT1NC outer surface temperature (°C) CT2NC outer surface temperature (°C) CT3NC outer surface temperature (°C) PT1NC outer surface temperature (°C) PT2NC outer surface temperature (°C) PT3NC outer surface temperature (°C) Fuel pin(1NC) (No. 01) outer surface temperature Fuel pin(2NC) (No. 01) outer surface temperature Fuel pin(3NC) (No. 01) outer surface temperature Fuel pin(1NC) (No. 06) outer surface temperature Fuel pin(2NC) (No. 06) outer surface temperature Fuel pin(3NC) (No. 06) outer surface temperature Fuel pin(1NC) (No. 19) outer surface temperature Fuel pin(2NC) (No. 19) outer surface temperature Fuel pin(3NC) (No. 19) outer surface temperature

(°C) (°C) (°C) (°C) (°C) (°C) (°C) (°C) (°C)

GIT 79,062 505.4 488.0 479.9 693.5 656.8 624.6 838.8 794.9 746.8 812.4 765.5 721.2 897.8 848.0 794.0

126,452 508.4 491.0 482.5 695.3 658.6 626.2 840.1 796.4 748.4 813.7 766.8 722.3 899.1 849.3 795.2

198,531 509.8 492.6 484.1 696.1 659.5 627.3 840.7 797.1 748.9 814.3 767.5 723.2 899.7 849.9 796.0

287,844 510.4 493.8 485.1 696.4 660.2 627.9 841.0 797.6 749.3 814.6 768.0 723.7 899.9 850.4 796.4

Fig. 21. Velocity vector inside annulus of CT2NC and PT2NC, m/s.

Fig. 20. Temperature contours of non-contact channels, °C.

Fig. 22. Temperature profile of non-contact channels.

Temperature of CT2NC is found to be 578.3 °C at the bottom and varies circumferentially up to 180° and is 491.5 °C at the top. The PT2NC temperature at the point of contact is 592.6 °C and 687.6 °C at the top. It is observed that temperature of CT2NC and PT2NC is less than CT1NC and PT1NC despite steam having lower cooling capacity is less for fuel channel (2NC). It is attributed due lower heating power of the channel than the bottom one. A similar trend is also observed for the CT3NC with little variation in results. High temperature steam glides over the CT2NC and acts as coolant for CT3NC. The CT3NC temperature at the bottom is

found to be 561.3 °C. The temperature profile of CT3NC varies circumferentially and reaches 473.4 °C at the top. Temperature of PT3NC at the bottom and top are 572.6 °C and 649.2 °C, respectively. It is desirable because the moderator boils off during the postulated SCDA scenario, top channel in the Calandria vessel will be exposed first. Hence less temperature of top channel is desirable. As soon as top fuel channel rows uncovers with time, the percentage of decay heat would also get reduced. Further analysis is carried out for contact channels (disassembled 12

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configuration). Tables 7–9 gives the grid independence test carried out for laminar and turbulent (standard k-omega and epsilon) models. As expected, insignificant change in results is observed. For 154,399 elements, mesh minimum orthogonal quality of 0.36 achieved with a maximum aspect ratio of 5.9. Dimensionless numbers are calculated for the fluid flow using numerical results of laminar model, which also shows the flow to be

laminar. All three CTs are in contact, temperature varies circumferentially. Grashof number is calculated using maximum temperature of the CT outer surface and saturated steam temperature is taken as 100 °C. Steam thermal properties are evaluated at the bulk mean temperature of the steam and constant temperature of the CT.

Table 7 Grid independence test for contact channels for laminar model. Contact channel simulation using laminar model Elements CT1C outer surface temperature (°C) CT2C outer surface temperature (°C) CT3C outer surface temperature (°C) PT1C outer surface temperature (°C) PT2C outer surface temperature (°C) PT3C outer surface temperature (°C) Fuel pin(1C) (No. 01) outer surface temperature Fuel pin(2C) (No. 01) outer surface temperature Fuel pin(3C) (No. 01) outer surface temperature Fuel pin(1C) (No. 06) outer surface temperature Fuel pin(2C) (No. 06) outer surface temperature Fuel pin(3C) (No. 06) outer surface temperature Fuel pin(1C) (No. 19) outer surface temperature Fuel pin(2C) (No. 19) outer surface temperature Fuel pin(3C) (No. 19) outer surface temperature

(°C) (°C) (°C) (°C) (°C) (°C) (°C) (°C) (°C)

GIT 83,624 569.9 597.8 536.4 726.9 739.7 679.2 873.6 852.8 776.7 828.8 839.3 780.0 920.0 903.2 831.2

130,092 570.7 598.5 536.7 727.7 740.4 679.7 874.1 853.3 776.9 829.5 839.9 780.4 920.6 903.8 831.6

154,399 570.7 598.5 537.0 727.7 740.4 680.0 874.2 853.3 777.1 829.5 840.0 780.6 920.6 903.8 831.7

195,263 570.8 598.6 537.1 727.8 740.4 680.0 874.3 853.4 777.2 829.6 840.0 780.7 920.7 903.9 831.9

Table 8 Grid independence test for contact channels for k-omega model. Contact channels simulation using k-omega model Elements CT1C outer surface temperature (°C) CT2C outer surface temperature (°C) CT3C outer surface temperature (°C) PT1C outer surface temperature (°C) PT2C outer surface temperature (°C) PT3C outer surface temperature (°C) Fuel pin(1C) (No. 01) outer surface temperature Fuel pin(2C) (No. 01) outer surface temperature Fuel pin(3C) (No. 01) outer surface temperature Fuel pin(1C) (No. 06) outer surface temperature Fuel pin(2C) (No. 06) outer surface temperature Fuel pin(3C) (No. 06) outer surface temperature Fuel pin(1C) (No. 19) outer surface temperature Fuel pin(2C) (No. 19) outer surface temperature Fuel pin(3C) (No. 19) outer surface temperature

(°C) (°C) (°C) (°C) (°C) (°C) (°C) (°C) (°C)

GIT 83,624 569.4 597.8 536.6 726.6 739.7 679.4 873.4 852.9 776.8 828.5 839.4 780.1 919.8 903.3 831.4

130,092 570.2 598.5 537.0 727.3 740.3 679.9 873.9 853.3 777.1 829.1 839.9 780.5 920.4 903.8 831.8

154,399 570.2 598.7 537.4 727.4 740.5 680.2 874.0 853.5 777.4 829.2 840.0 780.9 920.5 904.0 832.0

195,263 570.3 598.6 537.5 727.4 740.4 680.2 874.0 853.4 777.4 829.3 840.0 780.8 920.5 903.9 832.0

Table 9 Grid independence test for contact channels for k-epsilon model. Contact channels simulation using k-epsilon model Elements CT1C outer surface temperature (°C) CT2C outer surface temperature (°C) CT3C outer surface temperature (°C) PT1C outer surface temperature (°C) PT2C outer surface temperature (°C) PT3C outer surface temperature (°C) Fuel pin(1C) (No. 01) outer surface temperature Fuel pin(2C) (No. 01) outer surface temperature Fuel pin(3C) (No. 01) outer surface temperature Fuel pin(1C) (No. 06) outer surface temperature Fuel pin(2C) (No. 06) outer surface temperature Fuel pin(3C) (No. 06) outer surface temperature Fuel pin(1C) (No. 19) outer surface temperature Fuel pin(2C) (No. 19) outer surface temperature Fuel pin(3C) (No. 19) outer surface temperature

(°C) (°C) (°C) (°C) (°C) (°C) (°C) (°C) (°C)

GIT 83,624 561.3 588.0 523.0 721.5 733.0 670.4 869.2 847.4 769.4 825.1 834.2 773.3 916.3 898.5 824.9

130,092 564.4 590.9 528.6 723.7 735.1 673.8 870.9 849.1 772.6 826.7 835.9 775.5 917.9 899.1 827.4

13

154,399 564.9 591.3 526.4 724.0 735.5 672.9 871.2 849.4 771.5 826.9 836.2 775.3 918.1 900.4 826.9

195,263 565.2 591.5 527.7 724.2 735.6 673.6 871.4 849.5 772.1 827.1 836.3 775.6 918.3 900.4 827.3

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Grst = =

Dst3 0.

CT T amb) st g (To 2 st 11053 × 0.001466 ×

9.8 × (706.22 (7.5 × 10 5)2

100)

= 2.1 × 106

(22)

µst × Cst 2. 4 × 10 × 2050. 92 = = 0. 93 kst 0. 0530

(23)

Rast = Grst × Prst = 2.1 × 106 × 0.93 = 1.95 × 106

(24)

Prst =

Rest =

Rist =

5

vst

0.20 × 0.595 × 0.1105 st Dst = = 1019.3 (Laminar) µst (1.29 × 10 5)

Grst 2.1 × 106 = = 2.0 Re2st 1019. 32

(25) (26)

Grashof number inside the annulus for contact debris is calculated by taking the maximum temperature of the PT and minimum temperature of the CT.

Grst = =

L3

(0.1078

Prst =

PT st g (To 2 st

TiCT )

=

(DiCT

DoPT )3

PT st g (To 2 st

0.090)3 × 0.001087 × 9.8 × (720.1 (1.3 × 10 4) 2

Fig. 24. Velocity vector inside annulus of CT2C and PT2C.

TiCT )

494.2)

(27)

= 854 (Laminar)

µst × Cst 3.2 × 10 5 × 2214.9 = = 0.9 kst 0.0787

Rast = Grst × Prst = 854 × 0.9 = 768.6 (Laminar)

(28) (29)

Temperature contours of debris in contact are shown in Fig. 23. As expected, steam temperature rises on moving upward against gravity. Fig. 24 shows the natural convection of steam inside the annulus of CT2C and PT2C. The temperature profile of the three exposed channels in contact is shown in Fig. 25. At the bottom, CT1C attains 628.7 °C. As one moves circumferentially from bottom to top of the CT1C, Fig. 25. Temperature profile CTC and PTC.

temperature initially decreases and finally increases to 700.6 °C at the top. It is observed that the temperature of CT1C is more than CT1NC. The high temperature of CT1C than CT1NC is attributed to contact between fuel channels (1-2-3), which obstruct the path of upward moving steam. The channels also exchange of heat with each other. Superheated steam glides over the outer surface of CT1C and acts as coolant of CT2C. It can be noticed that the CT2C temperature at the bottom is 700.6 °C, which is same for CT1C at the top. A similar trend of temperature profile is also observed for CT2C. Initially, CT2C temperature is higher at 0°, then decreases and again increases to 667 °C at the top of CT2C. The PT2C temperature at the point of contact is found to be 714.4 °C and at the top is 756.2 °C. The CT3C temperature at 0° is found to be 667 °C, which is same as for top surface of the CT2C. The temperature profile of CT3C varies circumferentially and reaches a value of 496 °C at the top of CT3C. The PT3C temperature at the bottom is 671.1 °C and reaches 676.2 °C at the top. Results of temperature at the bottom and top of CTs and PTs are summarized in Table 10. Table 10 Temperature of CTs and PTs at bottom and top position.

Fig. 23. Temperature contours of contact channels, °C. 14

Parameters

0°

180°

Parameters

0°

180°

CT1NC (°C) CT1C (°C) CT2NC (°C) CT2C (°C) CT3NC (°C) CT3C (°C)

613.2 628.7 578.3 700.6 561.3 667

509 700.6 491.5 667 473.4 496

PT1NC (°C) PT1C (°C) PT2NC (°C) PT2C (°C) PT3NC (°C) PT3C (°C)

628.8 647.4 592.6 714.4 572.6 677.1

720.2 770.3 687.6 756.2 649.2 676.2

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Figs. 26 and 27 represents and compares the AWA temperature of the outer surface of fuel pins. Due to symmetry of the fuel bundle about the Y-axis, results are plotted only for 11 fuel pins out of 19 fuel pins. In all case (contact and non-contact channels), central fuel pin (number 19) attains the highest temperature in the fuel bundle. The AWA temperature of fuel pin outer surface (number 19) of fuel channel (NC) (1, 2, and 3) are 901.8 °C, 853.9 °C, and 798.6 °C, respectively. Similarly for fuel channel(C) (1-2-3) are 920.5 °C, 903.7 °C, and 831.6 °C, respectively. While fuel pin (number 06) achieves minimum temperature in

Fig. 27. (a). AWA temperature of fuel pins of fuel channel (1C). (b). AWA temperature of fuel pins of fuel channel (2C). (c). AWA temperature of fuel pins of fuel channel (3C).

Fig. 26. (a). AWA temperature of fuel pins of fuel channel (1NC). (b). AWA temperature of fuel pins of fuel channel (2NC). (c). AWA temperature of fuel pins of fuel channel (3NC).

Fig. 27. (continued)

Fig. 26. (continued)

Fig. 27. (continued)

the fuel bundle except fuel channel3C. The lowest temperature of fuel pin (number 06) can be attributed to the eccentricity of PT, position of fuel pins, steam temperature outside CTs, buoyancy driven movement of fluid between the annulus of CT-PT and space between PT-fuel pins. While in case of fuel channel3C, all middle fuel pins attains almost equal temperature with little variation. As there is no other exposed channel above CT3C, the heat transfer from top of CT is higher which reduce the temperature of the top fuel pins of fuel-channel3C. The variation of steam temperature outside CT3C is lower which promotes uniform heat transfer through CT.

Fig. 26. (continued) 15

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Fig. 28. Heat flux of CT1NC.

Fig. 29. (continued)

The distribution of heat flux of non-contact channels is shown in Fig. 28. It can be clearly seen that in all the cases, heat transfer rate is maximum at the contact point (0°) of CT and PT. For CT1NC, the highest heat transfer rate is at the bottom and it is 20.2 kW/m2. Heat transfer rate varies circumferentially and reaches up to 9.4 kW/m2 at the top of the CT. A similar trend is also observed in the case of CT2NC and CT3NC. The heat fluxes of exposed CT2NC at the bottom and top are 19.44 kW/ m2 and 9.1 kW/m2, respectively. Similarly, heat flux of CT3NC at 0° is

13.5 kW/m2 and is 7.6 kW/m2 at the top. It is observed that in all the above cases, CT3NC has the lowest heat transfer rate. One can observe that steam has higher temperature outside the CT3NC in comparison to CT1NC and CT2NC. This reduces the cooling capacity of steam. Reason for low temperature of fuel channel 3NC is the lowest power inside the fuel bundle 3NC. Heat transfer characteristics of contact channels are different from non-contact channels. Fig. 29(a–c) show that in some places, heat transfer from CT to steam is negative. It is evident from Fig. 29(a) that maximum heat transfer through the outer surface of CT1C is 21.4 kW/ m2, which takes place at the bottom. Heat flux changes

Fig. 29. (a). Heat flux of CT1C. (b). Heat flux of CT2C. (c). Heat flux of CT3C.

Fig. 30. Velocity vector (m/s) and temperature (°C) contour at the top of CT2NC.

Fig. 29. (continued) 16

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In the narrow zone of CT2C and CT3C, trapped superheated steam temperature is higher thanCT2C. Hence, reverse heat transfer from CT3C to CT2C takes place. At the bottom of CT2C, trapped steam temperature is lower than CT2C. Therefore, positive heat transfer from CT2C of steam takes place. Fig. 29(c) represents the circumferential heat flux of CT3C, having a positive heat flux trend from bottom to top. At the bottom of CT3C, heat flux is low due to the existence of the narrow zone between CT2C and CT3C, where high temperature superheated steam is present. Temperature difference near contact point CT2C and CT3C is also low which decreases localized radiation heat transfer. Fig. 29(c) shows that the localized heat fluxes to be 610.4 W/m2 and 8130.5 W/m2 at the bottom and top, respectively. Figs. 28 and 29(c) shows that localized heat flux increases suddenly nearby 180°. This trend of increase in heat transfer at the top of CTs is due to vortex formation. Vortex formation contributes in enhancement of heat transfer rate. To have more insight of vortex formation and heat transfer, result is shown for one fuel channel2NC in Fig. 30. It can be seen that vortex formation at the top of the CT2NC. Hence, the temperature is low near 180° and heat transfer is more. Circumferential variation of heat flux of CTs for non-contact and contact fuel channels is already discussed above. To get more information of heat flux at the top and bottom of the CTs, data are presented in Table 11. In case of non-contact fuel channels, heat flux is positive along the circumference of the CTs. But for contact fuel channels, heat flux varies in positive and negative direction. Table 12 provides simulations results of total heat flux of three fuel channels. For regular configuration, it is 10173.2 W and for disassembled channels is also 10170.3 W. Heat generated through three fuel channels, shown in Figs. 17 and 18, is also 10173.2 W. This satisfies convergence criterion. Radiation is found to be the dominant mode of heat transfer. It is 65.3% for regular configuration and 71% for disassembled channels.

Table 11 Heat flux parameters for contact and non-contact debris. Angle

CT1NC Heat flux (W/m2)

CT2NC Heat flux (W/m2)

CT3NC Heat flux (W/m2)

CT1C Heat flux (W/m2)

CT2C Heat flux (W/m2)

CT3C Heat flux (W/m2)

0° 180°

20244.2 9426.2

19434.3 9072.1

13509.2 7652.7

21430.2 −1358

1294.8 0.0193

610.4 8130.5

circumferentially and at the top of CT1C is (-1358) W/m2. It is interesting to note that as we move from 172.8° to 180°, the heat flux is negative. It represents that heat is transferred to CT1C from localized superheated steam trapped between narrow domains of CT1C- CT2C and also radiation heat transfer from CT2C to CT1C. Heated steam glides over the outer surface of CT1C and acts as coolant for CT2C. Heat absorbed by steam from CT1C reduces the cooling capacity of steam for CT2C. However, the power of fuel channel2C is less than fuel channel1C. The circumferential heat transfer of fuel channel2C is shown in Fig. 29 (b). At the bottom of CT2C, heat flux is 1294.8 W/m2. Reason for low heat flux at the bottom of CT2C can be attributed to a narrow zone between the outer surface of CT1C and CT2C in which temperature difference is low. this results in a low radiation heat transfer. As the angle increases from zero to the positive side, the gap between CT1C and CT2C increases and more heat transfer takes place. An interesting phenomenon of heat transfer is observed for CT2C in between 172° to 180°. The heat flux sharply decreases and even goes in negative direction up to −0.0193 W/m2 at the top of CT2C. A negative heat transfer indicates that heat transfer to CT2C takes place from localized superheated steam available near the contact point of CT2C and CT3C. Radiation heat transfer also takes place from CT3C to CT2C. However, heat flux of CT2C at the bottom is observed to be positive and at the top it is negative. This type of opposite behaviour of heat transfer is due to following reasons: Table 12 Comparison of temperature and heat flux of contact and non-contact fuel channels. Parameters

Circumferential temperature gradient range (°C)

Radiative heat flow at CT outer surface (W/m2)

Total convective heat flow at CT outer surface (W/m2)

Total heat transfer at CT outer surface (W/m2)

Uranium dioxide Pellet (19) 1NC Uranium dioxide Pellet (19) 2NC Uranium dioxide Pellet (19) 3NC Outer surface of Fuel Pin (19) 1NC Outer surface of Fuel Pin (19)2NC Outer surface of Fuel Pin (19) 3NC PT1NC outer surface PT2NC outer surface PT3NC outer surface CT1NC outer surface CT2NC outer surface CT3NC outer surface Total CT heat transfer for regular configuration Uranium dioxide Pellet (19) 1C Uranium dioxide Pellet (19) 2C Uranium dioxide Pellet (19) 3C Outer surface of Fuel Pin (19) 1C Outer surface of Fuel Pin (19)2C Outer surface of Fuel Pin (19) 3C PT1C outer surface PT2C outer surface PT3C outer surface CT1C outer surface CT2C outer surface CT3C outer surface Total CT heat transfer for regular configuration

901.1–905.7 853.1–857.2 797.9–801.2 900.9–902.8 853.0–854.9 797.9–799.4 628.8–720.1 596.2–687.5 572.6–649.2 494.2–613.2 486.7–578.3 473.4–561.3

X X X X X X X X X 2625.8 2209.8 1805.4 6641

X X X X X X X X X 1399.4 1202.6 930.2 3532.2

X X X X X X X X X 4025.2 3412.4 2735.6 10173.2

919.2–924.7 903.6–907.2 831.8–834.4 919.1–922.3 903.5–904.4 831.7–832.0 642.8–770.5 714.6–756.3 675.4–684.5 520.7–700.7 544.5–706.4 495.8–669.9

X X X X X X X X X 2804.1 2478.6 1934.4 7217.1

X X X X X X X X X 1290 897.1 766.1 2953.2

X X X X X X X X X 4094.1 3375.7 2700.5 10170.3

17

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4. Conclusion

References

A Numerical simulation study has been carried out for single exposed channel at 1% decay heat with different emissivity 0.3, 0.5 and 0.8. The work is further extended to three channels having different configuration. In the first case, the channels are intact and there is no deformation. In the second case, the channels are deformed and are in contact with each other.

Bajaj, S.S., Gore, A.R., 2006. The Indian PHWR. Nucl. Eng. Des. 236, 701–722. Dutt, N., Sahoo, P.K., 2018. Experimental and numerical study of phwr specific suspended debris. Nucl. Eng. Des. 330, 344–355. Dutt, N., Sahoo, P.K., Mukhopadhyay, D., 2015. Experimental investigation of transient behaviour of IPHWR under heat up condition. Nucl. Eng. Des. 289, 278–286. Francis, N.D. Jr., Itamura, M.T., Webb, S.W., James, D.L., 2002.CFD Calculation of Internal Natural Convection in the Annulus between Horizontal Concentric Cylinders. Sand Report, Prepared by Sandia National Laboratories Albuquerque, New Mexico 871 85 and Livermore, California 94550. Gupta, S.K., Dutta, B. K., Raj, V.V., 1996. A study of the Indian PHWR reactor channel under prolonged deteriorated flow conditions. Proceedings of a Technical committee meeting on advances in heavy water reactor technology; Mumbai (India); 29 Jan – 1 Feb 1996, 331–359. Kuehn, T., Goldstein, R., 1980. Numerical solution to the Navier-Stokes equations for laminar natural convection about a horizontal isothermal circular cylinder. Int. J. Heat Mass Transfer 23, 971–979. Majumdar, P., Chatterjee, B., Lele, H.G., Guillard, G., Fichot, F., 2014. ASTEC adaptation for PHWR limited core damage accident analysis. Nucl. Eng. Des. 272, 273–286. Mathew, P., Nitheanandan, T., Bushby, S.J., 2008. Severe core damage accident progression within a CANDU 6 Calandria vessel. Europian Review Meeting on Severe Accidents Research. (ERMSAR-2008). Minkowycz, W.J., Sparrow, E.W., 1966. Free convection heat transfer to steam under variable property conditions. Int. J. Heat Mass Transf. 9, 1145–1147. Nandan, G., Sahoo, P.K., Kumar, R., Chatterjee, B., Mukhopadhyay, D., Lele, H.G., 2010. Experimental investigation of sagging of a completely voided pressure tube of Indian PHWR under heatup condition. Nucl. Eng. Des. 240, 3504–3512. Nitheanandan, T., Cao, X., Choi, J.-H., Dupleac, D., Kim, D.-H., Lele, H.G., Nayak, A.K., Rammohan, H.P., 2017. Benchmarking severe accident computer codes for heavy water reactor applications. J. Nucl. Eng. Radiat. Sci. 3, 020903-1–11. Sharma, M., Kumar, R., Majumdar, P., Mukhopadhyay, D., 2018. Effect of eccentricity of pressure tube on circumferential temperature distribution of PHWR fuel bundle under postulated accident condition. Nucl. Eng. Des. 331, 274–281. Singh, A.R., Sahoo, P.K., 2018. Investigation of the channel disassembly behaviour of Indian 200 MWe PHWR – a numerical approach. Nucl. Eng. Des. 339, 137–149. Singh, R.J., Ravi, K., Gupta, S.K., 2011. Methodology for developing channel disassembly criteria under severe accident conditions for PHWRs. Ann. Nucl. Energy 38, 1884–1890. https://doi.org/10.1016/j.anucene.2011.05.011. Yadav, A.K., Kumar, R., Gupta, A., Chatterjee, B., Mukhopadhyay, D., Lele, H.G., 2014. Experimental investigation on circumferential and axial temperature gradient over fuel channel under LOCA. Heat Mass Transfer 50, 737–746.

• The maximum temperature of the single channel for 0.3 emissivity is 1027.4 °C. • The maximum area weighted temperature (AWA) of fuel pin for • • •

non-contact channels is 905.8 °C and it is 924.7 °C for contact channels. Radiative heat transfer from fuel channel surface is the major heat transfer mode for both the debris configurations. However, a good extent of convective heat transfer takes place for debris with regular configuration due to space availability among the channels. Total radiative heat transfer from the CTs outer surface is 65.3% for regular configuration and 71% for disassembled channels. The CFD analysis shows that at 1% decay heat, predicted temperatures of the debris is limited to below 1050 °C with convective and radiative cooling. This is well below the melting point of the component materials.

Acknowledgements The authors acknowledge Reactor Safety Division, Bhabha Atomic Research Centre, Trombay, Mumbai, India to provide the technical support. The authors are thankful to the Institute Computer Centre (ICC), Roorkee for providing the computer software facility.

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