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2017 International Nuclear Atlantic Conference - INAC 2017 Belo Horizonte, MG, Brazil, October 22-27, 2017 ASSOCIAÇÃO BRASILEIRA DE ENERGIA NUCLEAR – ABEN

THERMAL-HYDRAULIC CODE FOR ESTIMATING SAFETY LIMITS OF NUCLEAR REACTORS WITH PLATE TYPE FUELS Duvan A. Castellanos1, João L. Moreira2, Jose R. Maiorino3, Pedro R. Rossi4 and Pedro Carajilescov5 1,2,3,4,5

Centro de Engenharias, Modelagem e Ciências Sociais Aplicadas, Pós-Graduação em Energia Universidade Federal do ABC Avenida dos Estados, 5001 09210-508 Santo André, SP 1 [email protected] 2 [email protected] 3 [email protected] 4 [email protected] 5 [email protected]

ABSTRACT To ensure the normal and safe operation of PWR type nuclear reactors is necessary the knowledge of nuclear and heat transfer properties of the fuel, coolant and structural materials. The thermal-hydraulic analysis of nuclear reactors yields parameters such as the distribution of fuel and coolant temperatures, and the departure from nucleated boiling ratio. Usually computational codes are used to analyze the safety performance of the core. This research work presents a computer code for performing thermal-hydraulic analyses of nuclear reactors with platetype fuel elements operating at low pressure and temperature (research reactors) or high temperature and pressure (naval propulsion or small power reactors). The code uses the sub-channel method based on geometric and thermal-hydraulic conditions. In order to solve the conservation equations for mass, momentum and energy, each sub-channel is divided into control volumes in the axial direction. The mass flow distribution for each fuel element of core is obtained. Analysis of critical heat flux is performed in the hottest channel. The code considers the radial symmetry and the chain or cascade method for two steps in order to facilitate the whole analysis. In the first step, we divide the core into channels with size equivalent to a fuel assembly. From this analysis, the channel with the largest enthalpy is identified as the hot assembly. In the second step, we divide the hottest fuel assembly into subchannels with size equivalent to one actual coolant channel. As in the previous step, the sub-channel with largest final enthalpy is identified as the hottest sub-channel. For the code validation, we considered results from the chinese CARR research reactor. The code reproduced well the CARR reactor results, yielding detailed information such as static pressure in the channel, mass flow rate distribution among the fuel channels, coolant, clad and centerline fuel temperatures, quality and local heat and critical heat fluxes.

1. INTRODUCTION The plate type fuel assemblies (FA) are used for applications in research reactors and naval propulsion reactors, because such geometry provides some advantages in comparison with rod FA like compact cores with high power density and greater resistance to external dynamic loads [1, 2, 3]. The analysis of nuclear reactors involves the study of neutronic, thermal-hydraulic and structural behavior, coupled to each other. These studies help define the safety basis for the parts, which are important to ensure that the general design and the operational conditions of the plant is capable to avoid nuclear accidents; normally this study is done through adequate analysis tools [4].

The neutronic and thermal-hydraulic analyses are strongly bonded. The microscopic neutron cross-section of the core materials are dependent on temperature and the heat generation distribution, necessary to developed the thermal-hydraulic calculus, is furnished by the neutronic analysis [5]. In practice, the limit of the core operational power is given by thermalhydraulic study that furnishes the operational condition to avoid deterioration of the structures and fuel [6, 7]. The fuel plate consists of the fuel meat between a metallic cladding. This geometry allows the reactor core to achieve a high power density as possible, thus reducing the core volume required for a desired thermal output [8]. To maintain the integrity of the core, the fuel, cladding and coolant temperatures and the surface heat flux must obey the design limits [2, 6]. Thus, the design and safety analysis of nuclear installations are dependent of the thermalhydraulic analysis [9], executed by computers codes that calculate the core behavior at different safety and operational conditions. The more widely used codes for these purposes are the COBRA and the THINC codes [10]. Many other codes are available in addition to the above, such as COBRA-3C/RERTR, PARET, COOLOD-N and [11, 12, 13]. The models developed in these codes consider a detailed analysis of the mass, momentum and energy transfer equations. However, the sub-channel method is widely spread to perform the solution of the conservation equation [9]. In the present work, a new computational code named “COTENP” was developed to estimate the thermal-hydraulic safety limits and to calculate detail operational data in research or small PWR reactor used in naval propulsion (in steady state conditions).

2. METHODS AND DATA The code COTENP was developed to represent the tridimensional behavior of whole core, combining the sub-channel approach [9, 14], and the cascade or multistep method for two steps with two-channel sizes [2, 7], the first equivalent to a fuel assembly and second equal to one channel. Each sub-channel was divides axially into volumes control. In order to obtain the coolant behavior, the conservation equations were applied for the control volumes and solved simultaneously taking into account the operational conditions. The following assumptions were adopted in the code: • Steady-state power and coolant flow • Uniform inlet and outlet pressure distribution • Single-phase and two-phase flows • Material thermal properties independent of temperature. • One-dimensional steady-state heat flow with uniform heat generation [16]. • Thermal conductivities of the fuel kf and the cladding kc are constant independent of temperature [16] 2.1. Conservation equation of Mass, Momentum and Energy Figure 1 shows schematically the sub-channel approach used to represent the coolant behavior, each sub-channel is divided into control volumes distributed axially.

INAC 2017, Belo Horizonte, MG, Brazil.

Figure 1: Balance equations in a control volume of a sub-channel, where H is the length, L is the side length, and d is the distance between plates. The balance equations are established to the kth sub-channel and ith volume control. The basic conservation equation in volume control form are the following. Mass balance equation:

 k ,i  m  k ,i 1  0 m

(1)

 k ,i    k ,i uk ,i dA  k ,i uk ,i AK , m

(2)

A

 is the mass flow rate (kg/s), ρ is the specific mass of the coolant (kg/m3), u is the where m coolant speed, and A is the cross section area of the sub-channel (m2). Momentum balance equation: ( zk ,i 1  zk ,i ) k ,i (uk ,i ) 2 k ,iuk2,i m k2 1 1 Pk ,i  f k ,i  kk , i   k ,i g ( zk ,i 1  zk ,i )  ( 2  2) Dh 2 2 2 k ,i Ai 1 Ai f k ,i 

64 Re k ,i

f k ,i  0,36 Re k 0,i, 25

(3) (4) (5)

where P is the total pressure drop in the volume control, f is the friction coefficient, z is the node elevation in the sub-channel, Dh is the hydraulic diameter of the sub-channel and, kk,i is the localized form loss coefficient. The friction coefficient is calculated by the HangenPoiseulle correlation for laminar flow, Eq. (4), and by the Blasius correlation for turbulent flows, Eq. (5) [15]. Energy balance equation:


m k (hk ,i 1  hk ,i )  qx pa dz ,

(6)

where h is the coolant enthalpy (J/kg), q is the heat flux across the surface area of the fuel plate (W/m2), and Pa is the heated perimeter of the sub-channel (m). The power density distribution in different sub-channels can be represent by the axial and radial factors distribution to account the different position in the core [6]. The code give the heat flux in the kth sub-channel and ith volume control by:

 FzN,i FRN,k , qx_ k ,i  qmax

(7)

N N where Fz ,i is the axial power distribution factor in the volume control e FR ,k is the radial power

distribution factor in the sub-channel. Coolant temperature: The main coolant temperature limitation is in order to achieve the suitable coolant behavior like to keep the bulk coolant temperature below its saturation temperature and to maintain the temperature rise in the core [8]. The coolant temperature are given by Eq. (8). Tck ,i 1  Tck ,i  _

_

hk ,i Ck ,i

(8)

_

where Tc is the coolant temperature,  h k ,i  h k 1,i  h k ,i is the enthalpy gain in the kth node, C is the heat capacity of the coolant. 2.2. Heat transfer calculations The description of the temperature field in the reactor core and reactor structures is necessary to calculate the lifetime behavior of the reactor components [6]. Several simplifying assumptions are made to treat the problem of heat removal from an individual element in a reactor.

Figure 2: Temperature profile in plate type fuel.


The temperature profile across the plate fuel element is shown in Figure 2. It was assumed perfect contact between fuel and cladding. The heat-transfer coefficient between plate fuel and coolant h is calculate from the empirical correlation. Clad temperature: The most critical clad limit is the heat flux that can be transferred from the clad to the coolant [8]. The clad temperature Tclad is calculate from the heat flux described by equation (9).

TClad k ,i 

qx_ k ,i hc _ k ,i

 Tck ,i 1

(9)

where hc_k,i is the heat transfer coefficient of coolant. This parameter is usually expressed in term of the thermal conductivity of the fluid kcool, hydraulic diameter of the channel and the Nusselt number Nu, as show Eq. (10) [8]. Nu is given by Eq. (11) [17].

hc _ k ,i 

kCool_ k ,i Dh

Nu

Nu  0.0058 Re0.9383 Pr 0.4

(10) (11)

Fuel Temperature: Another limit requires that the fuel temperature Tf , at any point in the core, does not reach the melting point. The fuel temperature is calculate from Eq. (12

 s sc  T f _ k ,i  TClad k ,i  q' ' ' k ,i     2k f 2k c 

(12)

where q' ' ' is the power density, s is the half thickness of fuel and c is the cladding thickness, as shown in Figure 2. 2.3. Critical heat flux calculations The safety heat transfer condition is given by the departure from nucleate boiling ratio (DNBR) defined as: q  DNBR  DNB , (13)  qlocal

 is the critical heat flux and qlocal  is the local heat flux. For safe operation during where qDNB normal conditions and operational transients, the protection of reactor core must be performed using the right bases. A more critical limitation is the critical heat flux (in which the coolant temperature is allowed to approach the boiling point). Usually, a DNBR limit is established based on the standard deviation of the correlation, thus there will be a probability of 95% that DNB will not occur when the value of DNBR calculated to the critical fuel element is equal to


the limit of DNBR [2, 6]. The critical heat flux is usually obtained from a correlation based on experiments that reproduce the reactor core operation conditions. We adopt EPRI correlation mainly because it fits well typical PWR conditions and is compatible with the thermalhydraulic calculation scheme implemented in the COTENP code [2]. 2.4. Multichannel analysis. One of main objectives in the reactor design is to analyze the whole core to ensure that the thermal-hydraulic limits are not exceeded. Usually, a more common approach used to investigate this state is the “hot channel” or the “hot assembly”, this approach analyzes the coolant channel in which the core heat flux and enthalpy rise is maximum [8]. In order to identify the hot channel, the multichannel considers the radial symmetry and the chain or cascade method with two steps as show in Figure 3 [2, 14, 18].

Figure 3: The chain method for two steps adopted in the code. The chain or cascade method considers two steps: in the first step, the core is divided into subchannels with size equivalent to a fuel assembly. From this analysis, the sub-channel with the largest enthalpy rise is identified as the hot assembly. In the second step, the hot fuel assembly is divided into sub-channels with size equivalent to an actual coolant channel. As in the previous step, the sub-channel with largest final enthalpy rise is identified as the hottest subchannel. For this sub-channel, a detailed analysis, including critical heat flux calculations and DNBR, is undertaken. To ensure that the thermal-hydraulic calculation is accurate, it requires a good estimate of the flow distribution among the channels [7, 12]. To adjust the flow distribution, the coolant velocity of each fuel assembly (or channel) is adjust imposing the same pressure drop for all fuel assemblies. From the conservation equations, it are obtained Eqs. 14 and 15, representing the coolant velocity and pressure drop relation between the parallel channels.

u j 

  Pi ,0  u j ,0  u j ,0  Pi ,0   u  1     P  u  i ; Pi ,0  Pj ,0 2  Pj ,0   j ,0  i ,0 


(14)

   1  N ui      i i u j  i i  j 1   j i   u max i  i  ui

    

(15) (16)

Where, ui is the coolant speed change, u i is the coolant speed, ui , 0 is the initial coolant speed; Pi ,0 is the initial pressure drop,  i is the specific mass of the coolant,  i is the area relation Ai /AT, Ai is the cross section area of the ith sub-channel, AT is the total cross section area of all sub-channels, and ϵ is the convergence criterion. These equations are solved by an iterative method for N different sub-channels and the procedure is halted when the convergence criterion, given by equation (16) is reached. 2.5. Numerical solution procedure. The code was developed using FORTRAN language to perform a modular programming which allows an easy modification of implemented routines. The main structure has one main routine and five operation five subroutines. The main program controls the following five subroutines: I.) Input parameters; II.) Geometrical parameter calculations; III) Calculation subroutine (Estimated velocity, conservation equation and velocity adjustment); IV) Critical heat flux calculation and V) output results.

Figure 4: The chain method for two steps adopted in the code.


The solution of the conservation equations and heat transfer behavior are performed in subroutine III. The flow chart of the solution procedure are shown in Figure 4, the state properties of water and steam are furnishes from PROPAGUA code.

3. RESULTS AND DISCUTIONS To validate the developed code COTENP, it was applied to simulate the thermal conditions of the 50 MW CARR, research reactor, a multipurpose research reactor for different applications. This reactor core contains 24 plate-type fuel assemblies with an U3Si2-Al dispersion type fuel meat, with two types of fuel assemblies: 17 standard assemblies and 4 open assemblies [19, 20]. Table 1 present the main thermal-hydraulic data for the CARR reactor, the geometrical data and the thermal properties of the plate fuels come from [17, 20, 21]. Table 1: Main thermal-hydraulic data of CARR reactor Parameter

Value

Unit

Thermal power reactor Flow rate Inlet pressure Inlet temperature Average power density in the core Height of the active area

56.4 2650 0.62 45 568 0.85

MW m3/h MPa °C W/cm3 m

Figure 5 shows the details used as input data. Fig. 5a presents the arrangement and the radial power factor for each fuel assembly in the reactor core, Fig. 5b presents the axial power distribution for both types of fuel assemblies. The analysis was performed dividing the axial channel length into 17 control volumes.

Figure 5: Arrangement of the FAs in the core. (a)Location and radial power factors of FA. (b) Axial power factor of standard and open FA.


The results for steady-state are shown in Figs. 6 to 9. The flow distribution among the several fuel assemblies is presented in Figure 6 compared to the results from [20]. It can be observed that the two curves have a similar behavior, with negligible differences between both calculations. The maximum discrepancy is about 0.74%. The coolant average speed calculated by COTENP is 10,5 m/s, with a discrepancy of about 3,9%, compared with the results given by [20].

Figure 6: Mass flow rate distribution for the CARR reactor. As a result of the first step analysis, Fig. 7 shows that the FA with largest enthalpy rise is the fuel element number 9. Then the second step analysis was performed in this FA. Figure 8 shows the core temperature field for coolant and fuel, the Average Relative Derivation (ADV) [22] was calculate for the discrepancy between code calculation and [20]. The ADV for the coolant temperature calculation is 1.41 % and the highest temperature discrepancy is 3.18 %. To the cladding temperature, the ADV is 1.25 % and the maximum discrepancy is 3.89%. Finally, the centerline temperature in the fuel presented a ADV equal to 4,45% and with the highest discrepancy of 8,6%.

Figure 7: Enthalpy rise of the fuel elements (CARR reactor).


Figure 8: Temperature field in nuclear reactor core (CARR). TCC is the centerline temperature, CFT is the cladding temperature and CT is the coolant temperature. Figure 9 shows the critical heat flux analysis in the hot Fuel Assembly. The results obtained present similar trend with the reference data, for the region with of lower DNB. The code results present minimum DNBR equal to 10 while the reference work present a minimum DNBR of 11. The differences can be attributed to different CHF correlations, since the W-3 correlation was adopted by the reference work. 90 80 70

COTENP

DNBR

60

CARR

50 40 30 20 10 0 0

2

4

6

8

10

12

14

16

18

Number of control Volume

Figure 9: DNBR in the hottest sub-channel. The core analysis performed by COTENP code present good results. However the temperature field results could be improved performing more accurate calculations of thermal conductivity to the fuel meat and cladding, since to the code are used average values for this parameters, which vary depending on the temperature.

4. CONCLUSIONS COTENP code is a computational tool for estimating safety limits of nuclear reactors that contain plate type fuel assemblies. The thermal-hydraulic analysis developed can be represent the core behavior based in the physics and mathematical models adopted, in this way can be furnished detail information to the safety analysis like pressure drop, average speed coolant, coolant temperature, cladding temperature, fuel meat temperature, and departure from boiling


ratio (DNBR). The COTENP code was evaluated using operational data of research reactor CARR, the results were compared with similar analysis provide in the literature. The COTENP code performers quite well the results, the fuel meat temperature present a maximum discrepancy of ADV (4.45%), this can be improve using a variable thermal conductivity (kf) as function of the temperature. More comparisons should be carried out in order to obtain a better estimation of uncertainties of the models employed in the COTENP code like the critical velocity into the coolant channels.

ACKNOWLEDGMENTS This research was supported by the Federal University of ABC – UFABC, Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq) and Eletrobras-Eletronuclear.

REFERENCES 1. Thomas. D, Effects of Variation of Uranium Enrrichment On Nuclear Submarine Reactor Desing. MSc. thesis, Massachusetts Institute of Tecnology, United States (1990). 2. Tong. L. S, Weisman. J, Thermal Analysis of Pressurized Water Reactor. La Grange Park, Illions, American Nuclear Society, United States of America (1996). 3. Andrezejewski. C, Avaliação de Alternativas de Combustível Tipo placa Para Reatores De Pequeno Porte. MSc. thesis, Instituto de Pesquisas Energéticas e Nucleares,USP, São Paulo & Brazil (2005). 4. Petrangeli. G, Nuclear safety, Butterworth Heinemann, Oxford, United Kingdom (2010). 5. A. G. Mylonakis, M. Varvayanni, N. Catsaros, P. Savva, D.G.E. Gridoriadis, “Multiphysics and multi-scale methods used in nuclear reactor analysis,” Annals of Nuclear Energy, Vol. 72, pp.104-119 (2014). 6. Todreas. N. E, Kazimi. M. S, Nuclear Systems I, Thermal Hydraulic Fundamentals. Taylor & Francis, United States of America (1990). 7. Cuervo. G, Análisis termohidráulico de núcleos PWR con modelizacion de flujo bifásico para acoplamiento con la neutrónica. Ph.D. thesis, Universidad Politécnica de Madrid, Madrid & Spain (2007). 8. Duderstadt. James. J, Hamiltom. Louis. J, Nuclear Reactor Analysis, JOHN WILEY & SONS, Inc, United States of America (1976). 9. Imke. U, Sanchez. V, “Validation of the Subchannel Code SUBCHANFLOW Using the NUPEC PWR Test. (PSBT),” Science and Technology of Nuclear Installations, Vol. 2012, pp.12 (2012). 10. Carajilescov. P, Bastos, “ Experimental Analysis of Pressure Droop and Flow Redistribution In Axial Flows in rod Bundles,” Journal of Brazilian Society of Mechanical Sciences, Vol .22, (2000). 11. Kaminaga, and Masanori, COOLOD-N A Computer code, for yhe Analyses of Steady-state Thermal-hydraulic in Plate-Type Research Reactors. Japan Atomic Energy Research Institute, Ibaraki-ken & Japão (1990). 12. Umbehaun. P. H, Metodologia para Análise Termo-hidráulica de Reatores de Pesquisa Tipo Piscina com Combustível Tipo Placa. MSc. thesis, Instituto de Pesquisas Energéticas e Nucleares, USP, São Paulo & Brazil (2000).


13. Hainoun, Ghazi, and Mansour, “Safety Anlalysis of the IAEA Reference Research Reactor During Loss of Flow Accident Using the Code MERSAT”. Journal of Nuclear Engineering and Design, Vol. 240, pp. 1132–1138 (2010). 14. Todreas. N. E, and Kazimi. M. S, 2001. Nuclear Systems II, Elements of Thermal Hydraulic Desing, Taylor & Francis, United States of America (2001). 15. Incropera. F. P, and Dewitt. D. P, Fundamentos de Transferencia de Calor, 4th ed. PEARSON Pretince Hall, Mexico (1999). 16. EL-Wakil. M. M, Nuclear heat transport, International Textbook Company, Pennsylvania & United States of America (1971). 17. Gong. D, Huang. S, Wang. G, Wang. K, “Heat Transfer Calculation on Plate-Type Fuel Assembly of High Flux Research Reactor,” Science and Technology of Nuclear Installations, Vol. 2015, pp.13 (2015). 18. Chelemer. H, Weisman. J, and Tong. L, “Subchannel Thermal Analysis of Rod Bundle Cores,” Journal of Nuclear Engineering And Desing, Vol.21, (1972). 19. Shen. F, Yuan. L, “Conceptual Study of cold-neutron source in China Advanced Research Reactor,” Physica B, Vol. 311, pp. 152-157 (2002). 20. Lei. L, Zhang. Z, “Development of Thermal;Hydraulic Analysis Code for Plate Type Fuel Reactor,” Journal Institute of Electrical and Electronics Engineers, Harvin, China (2010) 21. W. X. Tian, S. Z. Qiu, Y. Guo, G. H Su, D. N. Jia, “Development of a termal-hydraulic code for CARR,” Annals of Nuclear Energy, Vol.32, pp.261-279 (2005). 22. A. Hainoun, A. Doval, P. Umbehaum, S. Chatzidakis, N. Ghazi, S. Park, M. Mladin, A. Shokr, “International benchmark study of advance thermal hydraulic safety analysis codes against measurements on IEA-R1 research reactor,” Nuclear Engineering and Design, Vol. 280, pp. 233-250 (2014).
