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Thermal Hydraulics: General—II

Transient Analysis in a Supercritical Water Reactor Concept with Multiple Heat-Up Steps A. M. Barragán-Martínez1,*, G. Espinosa-Paredes2, A. Vázquez-Rodríguez2, C. Martin-del-Campo1, J.L. François1 1* PhD student, Posgrado de Ingeniería, Universidad Nacional Autónoma de México. [email protected] 2 Area de Ingeniería en Recursos Energéticos, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186 Col. Vicentina, México, D.F., C.P. 09340 México, [email protected]; [email protected] 1 Departamento de Sistemas Energéticos, Facultad de Ingeniería, Universidad Nacional Autónoma de México, Paseo Cuauhnáhuac 8532, 62550 Jiutepec, Mor., México, [email protected]; [email protected]

INTRODUCTION

TRANSIENT ANALYSIS OF THE HPLWR

The European version of a supercritical water reactor (SCWR) is the High Performance Light Water Reactor (HPLWR). Previous work has contributed to the understanding of thermal-hydraulics phenomena in HPLWR, Renz [1] showed that the heat transfer enhancement occurs at low heat fluxes and at a bulk fluid temperature close to the pseudo-critical region, which is mainly due to the increase in the specific heat capacity. Dobashi [2] found that a downward flow of moderator water can flatten the high density of the power variation in the core. On the other hand, Cheng [3] and Pioro [4] observed that the heat transfer enhancement occurs at high mass flux and relatively low heat flux, whereas the deterioration was observed at low mass flux and relatively high heat flux, for the circular geometry and the same region. For the square annular geometry with helical wirewrapped spacer, Hongzhi [5] shared the same observations. When it comes to the core design, in order to achieve higher core exit temperatures, and thus a higher specific turbine power and a higher net efficiency, Schulenberg [6] proposed following the concept for supercritical fossil fired power plants and then in the case of this reactor to include a second superheater, resulting in the three-pass concept of the HPLWR, in which the coolant enters the core three times in three different radial positions. Recently, a steady state numerical analysis of heat transfer in the nuclear fuel rod and the thermalhydraulics in the HPLWR core was studied by Barragan [7] using a model that consists of a three-pass core design for heating-up the water. Results showed that the thermalhydraulic behavior of water at supercritical conditions (SCC) differs strongly from sub-critical conditions, due to a rapid change of the thermal-physical properties of water in the vicinity of the pseudo-critical point, and particularly at SCC. For this reason, it is a challenge to avoid excessive hot spots of local coolant temperature and, subsequently of local cladding temperature at SCC. We applied a numerical analysis of a transient in which the power decreases from 100% to 25%. We found that this transient produces a peak temperature in the wall that exceeds the safety clad temperature limit.

In the present study Barragán’s model [7] was applied to analyze the transient analysis behavior of the heat transfer in the rod of fuel as well as the thermalhydraulics in the core of the HPLWR. The thermalhydraulics analysis uses a three-pass core design with multiple heat-up steps. Each step was simulated using an average channel. A transient one-dimensional radial conduction model was applied in the fuel rod for each cell in the axial coordinate. Energy balances for the coolant have been made using a steady state and one-dimensional model for the axial coordinate. Reactor Core Design For the HPLWR, a special core layout has been designed in which the coolant water, as the working fluid, is guided three times through the core (up, down and up again) until the water is heated up to 800K. For this reason, it is called the three-pass core concept. The first pass, called evaporator, is situated in the center of the core. In this region, the moderator water flows downward in gaps between assembly boxes and inside of the moderator tubes. The moderator water, as it is heated-up on its path downward to the lower plenum, is mixing with the coolant coming from the downcomer reaching an inlet temperature of around 583K. The evaporator heats the coolant up to 663.5K, flowing upward around the fuel rods, resulting in an outlet temperature of 5.8K higher than the pseudo-critical temperature of 557.7K at a pressure of 25MPa. An inner steam plenum above the core will eliminate hot streaks. The second pass, called superheater, with a downward flow, heats the coolant up to 712.4K. After a second mixing in an outer mixing plenum below the core, the coolant is finally heated up to 807K with an upward flow in a second superheater (the third pass) located at the core periphery. All the channels, the evaporator and both superheaters, are built of 52 fuel assembly clusters as described by Schulenberg [6]. The complete HPLWR core consists of 156 assembly clusters. The square arrangement design proposed by Hofmeister [8] of 40 fuel rods with an outer diameter of 8mm distributed into dual rows, and a single water tube replacing 9 fuel rods is used as an assembly. The fuel rods

Transactions of the American Nuclear Society, Vol. 109, Washington, D.C., November 10–14, 2013

Thermal Hydraulics: General—II and the water tube are housed within an assembly box and grouped in a cluster of 9 assemblies, with common head and foot pieces to facilitate handling during revisions. This allows for a reduction in number of individual control rod drivers and makes it similar in dimensions to a PWR assembly. As in the PWR, control rods are inserted from the core top into 5 of the 9 water tubes of a cluster. The structural material for cladding, assembly boxes and water tubes is stainless steel. The model conditions considered are: (a) the core inlet coolant temperature is set at 553K which is then heated through the downcomer to 583K; (b) the total mass flow rate is calculated to satisfy the criterion of the maximum cladding surface temperature of 893K; and (c) given this thermal-hydraulic criterion, the core outlet temperature in the second superheater is 807K. Conceptual Model The conceptual model of the core is composed of three different vertically oriented circular tubes. In the first and third steps (channel 1 and 3) the coolant flows upward, while in the second step (channel 2) the coolant flows downward as shown in Fig. 1.

1727 was applied for each of the twenty one hydraulic axial nodes in the core. A detailed multi-node fuel pin model was developed for this study. The fuel heat transfer formulation is based on the following assumptions: (i) axis-symmetric radial heat transfer, (ii) the heat conduction in the axial direction is negligible with respect to the heat conduction in the radial direction, (iii) the volumetric heat rate generation in the fuel is uniform in each radial node, and iv) storage of the heat in the fuel cladding and gap is negligible. The fuel element is represented by a one-dimensional mesh-centered grid consisting of a variable number of radial elements, as is illustrated in Fig. 2, at each axial position. The differential equations of the model were transformed into discrete equations using the control volume formulation technique in an implicit form [10]. Application of the control volume formulation enables the equations for the fuel, the gap and the cladding to be written as a single set of algebraic equations for the sweep in the radial direction; see eq. (1). t t +∆t t a jT jt−+∆ + c jT jt++∆ 1 + b jT j 1 = dj

(1)

t +∆t and t t where T jt−+∆ T jt++∆ 1 , Tj 1 are unknowns, a j , b j , c j and d j are coefficients that are computed at the time

t . When the equations are put into a matrix form, the coefficient matrix is tri-diagonal. Because the coefficients a j , b j and c j that depend on thermal Fig. 1. Three-pass core heat-up model. In heated channels with supercritical fluids there exists a sudden change in the fluid density. However, it remains a single-phase fluid due to supercritical conditions; a phase change does not occur during the heat-up process. For this reason, the heat transfer analysis takes into account that it is a single supercritical fluid. To get a better understanding of the thermalhydraulic behavior in the fuel bundles, determining the flow conditions in sub-channels is required, due to the changes of properties (such as density and the specific heat) of the coolant all along the axial fuel assembly. Mathematical model and numerical solution The simulation of the heat transfer processes in the fuel element of the HPWR was obtained using the numerical model of Espinosa-Paredes [9]. This model was used for the supercritical water reactor and is composed of cylindrical fuel elements which contain ceramic pellets inside the metallic cladding. The fuel assembly temperature distribution is calculated for each of the eight radial nodes as shown in Fig. 2. This nodal arrangement

conductivity, density and specific heat capacity at least one iteration is needed since they are also a function of

T jt +∆t ,

Fig. 2. Nodal grid and half control volume near the boundary; radial nodes 1, 2, 3, 4, and 5 for the fuel; radial node 6 for the gap; radial nodes 7 and 8 for the clad. Nodes 1 and 8 are used for the boundary condition. The heat transfer coefficient (HTC) has a large effect on the prediction of the wall temperature of the fuel rod. Several authors have studied the correlations for supercritical water conditions and it would be necessary to continue making a detailed study to establish the most suitable correlation. However, the scope of our study does not cover this uncertainty analysis and would be the topic of another paper. The HTC was calculated with the Dittus–Boelter correlation [11] as a first approximation. The connection of the convective heat transfer coefficients with the fuel heat transfer model is the clad

Transactions of the American Nuclear Society, Vol. 109, Washington, D.C., November 10–14, 2013

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Thermal Hydraulics: General—II

GCp

∂Tco q′′ PH = Af ∂z

(2)

where T is the temperature, q′′ is the heat transfer from the wall to the coolant, PH is the heated perimeter, A f is the flow area. The equation was simplified because work due to pressure on the fluid and work due to viscous effects are negligible with respect to the term q′′ PH / A f , and an incompressible flow was assumed, i.e., the mass flux (G ) is constant. The temperature in each node of the channel is obtained numerically as: § dT · (Tco ) j +1 = (Tco ) j + ¨ co ¸ ∆z © dz ¹ j

(3)

where ∆z is the node length and j is the node number. The arrangement of the computational nodes of the thermo-hydraulics model was illustrated in figures 1 and 2. Transient Simulation Each channel in the core was based on a hydraulic unit cell whose parameters are: PH = 0.025m , De = 0.054m , and A f = 0.34 ×10−4 m 2 . The active height

of the fuel cell (4.2m) was divided into 21 equidistant axial nodes; then ∆z = 0.2m . The axial distribution of power in each channel takes into account that the heat flux is not uniform. The thermal physical properties used in this work were taken from Wagner [12]. The core thermal-hydraulic transient behavior has been analyzed for a power reduction from 100% to 25%. The power reduction was instantaneous in the simulation time equal to zero. The heat transfer from the wall to the coolant was obtained using Newton’s law of cooling. It is important to note that the physical interpretation of our discussion assumes that the system pressure and mass flux are constants at 25MPa and at 621.6 kg/m2s, respectively. Channels 1, 2 and 3 contain 73, 48 and 35 assemblies respectively. The heat transfer coefficient is a function of the Reynolds number and the Prandtl number. Prandtl number depends on the fluid properties, is the ratio of momentum diffusivity (kinematic viscosity) and thermal diffusivity, ie, a function of the supercritical fluid properties such as, viscosity, thermal conductivity, density and specific heat. The specific heat (thermal conductivity as well) presents an unusual behavior at supercritical pressure, that directly affects the value of the Prandtl number. The changes in

the HTC are due to changes in the thermal-physical properties as result of the power reduction. The numerical experiments were executed for each channel and for different values of mass-flow rate in the inlet of the core, whose range was from 1100 to 1300 kg/s. RESULTS The numerical results showed the transient behavior of the heat flux, the heat transfer coefficients, and the coolant and wall temperatures for each one of the heat-up steps. Analysis of Channel 1 Fig. 3 shows the 21 curves (one for each axial node) of coolant temperatures as a function of time during a power reduction from 100% to 25%. In this graph the lower curve corresponds to axial node 1, whose temperature is 588K at time equal to zero.

Channel 1

720

Coolant Temperature (K)

temperature. The governing equations for describing the thermal hydraulic behavior in the three representative heated channels (one channel for each pass core) assuming the supercritical fluid as single phase fluid, is given by:

EŽĚĞϮϭ EŽĚĞϮϬ EŽĚĞϭϵ EŽĚĞϭϴ EŽĚĞϭϳ EŽĚĞϭϲ EŽĚĞϭϱ EŽĚĞϭϰ EŽĚĞϭϯ EŽĚĞϭϮ EŽĚĞϭϭ EŽĚĞϭϬ EŽĚĞϵ EŽĚĞϴ EŽĚĞϳ EŽĚĞϲ EŽĚĞϱ EŽĚĞϰ EŽĚĞϯ EŽĚĞϮ EŽĚĞϭ

700 680 660 640 620 600 580 560 0

10

20

30

40

50

60

70

Time (s)

Fig. 3. Coolant temperature behavior in channel 1. Analysis of Channel 2 The exit coolant temperature of channel 1 is the input temperature of channel 2. Fig. 4 shows a peak of the coolant temperature in all nodes at 5s. In this graph the upper curve corresponds to axial node 1 and the coolant temperature maximum is 867K. The peak wall temperature is 878K. which is close to the maximum temperature of 893K that the cladding should not exceed. Analysis of Channel 3 The exit coolant temperature of channel 2 is the input temperature of channel 3. In this channel the coolant temperature maximum is 943K as is observed in Fig. 5. The peak wall temperature is 947K at node 17 and that exceeds the temperature limit for the cladding materials available today. Under these conditions there is a risk of cladding failure with the resulting release of radioactive material. To avoid this risk we agree with Schulenberg

Transactions of the American Nuclear Society, Vol. 109, Washington, D.C., November 10–14, 2013

Thermal Hydraulics: General—II

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[13] who proposed a concept where the cooling water is mixed in two mixing chambers in between each of the three heat-up regions.

Channel 2

Coolant Temperature (K)

910

EŽĚĞϭ EŽĚĞϮ EŽĚĞϯ EŽĚĞϰ EŽĚĞϱ EŽĚĞϲ EŽĚĞϳ EŽĚĞϴ EŽĚĞϵ EŽĚĞϭϬ EŽĚĞϭϭ EŽĚĞϭϮ EŽĚĞϭϯ EŽĚĞϭϰ EŽĚĞϭϱ EŽĚĞϭϲ EŽĚĞϭϳ EŽĚĞϭϴ EŽĚĞϭϵ EŽĚĞϮϬ EŽĚĞϮϭ

860 810 760 710 660 610 560 0

10

20

30

40

50

60

70

Time (s)

Fig. 4. Coolant temperature behavior in channel 2.

Channel 3

Coolant Temperature (K)

960

EŽĚĞϮϭ EŽĚĞϮϬ EŽĚĞϭϵ EŽĚĞϭϴ EŽĚĞϭϳ EŽĚĞϭϲ EŽĚĞϭϱ EŽĚĞϭϰ EŽĚĞϭϯ EŽĚĞϭϮ EŽĚĞϭϭ EŽĚĞϭϬ EŽĚĞϵ EŽĚĞϴ EŽĚĞϳ EŽĚĞϲ EŽĚĞϱ EŽĚĞϰ EŽĚĞϯ EŽĚĞϮ EŽĚĞϭ

910 860 810 760 710 660 610 560 0

10

20

30

40

50

60

70

Time (s)

Fig. 5. Coolant temperature behavior in channel 3. With this numerical analysis we found that a decrease in power from 100% to 25% produces a peak temperature in the wall that exceeds the safety clad temperature limit. We also found that it is not recommended to use an inlet mass-flow rate lower than 1150 kg/s in order to avoid exceeding the safety clad temperature of the HPLWR. In the pseudo-critical zone the wall temperature exhibits a pronounced peak in the heat-up step 2 and step 3, where the heat transfer coefficient is reduced drastically. It is interesting to note that current empirical heat transfer correlations are not capable of predicting the heat transfer of water at supercritical conditions due to its strong physical property variations, so these results are preliminary.

REFERENCES 1. U. RENZ, R. BELLINGHAUSEN, “Heat transfer in a vertical pipe at supercritical pressure,” 8th International Heat Transfer Conference 3, 957–962 (1986). 2. K. DOBASHI et al., “Conceptual design of a high temperature power reactor cooled and moderated by supercritical light water,” Annals of Nuclear Energy 25: 487–505 (1998). 3. X. CHENG, and T. SCHULENBERG, “Heat transfer at supercritical pressure - literature review and application to a HPLWR,” Scientific Report FZKA6609 (2001). 4. I.L. PIORO, and R.B. DUFFEY, “Heat transfer and hydraulic resistance at supercritical pressures in power engineering applications,” ASME Press, New York, NY, USA (2007). 5. L. HONGZHI et al., “Experimental investigation on heat transfer from a heated rod with a helically wrapped wire inside a square vertical channel to water at supercritical pressures,” Nuclear Engineering and Design, 239, 2004-2012 (2009). 6. T. SCHULENBERG, J. STARFLINGER, “Core design concepts for high performance light water reactors,” Nuclear Engineering and Technology, 39, 249256 (2007). 7. A. BARRAGAN-MARTINEZ et al., “Diseño y optimización de combustible de un reactor nuclear de agua supercrítica” PhD thesis. Posgrado en Ingeniería. Universidad Nacional Autónoma de México (2013). 8. J. HOFMEISTER, “Fuel assembly design study for a reactor with supercritical water,” Nuclear Engineering and Design, 237, 1513-1521 (2007). 9. G. ESPINOSA-PAREDES, E. G. ESPINOSAMARTÍNEZ, “Fuel rod model based on Non-Fourier heat conduction equation,” Annals of Nuclear Energy , 36, 680-693 (2009). 10. S.V. PATANKAR, “Numerical Heat Transfer and Fluid Flow”, McGraw-Hill, New York. (1980). 11. F.W. DITTUS, L.M. BOELTER, “Heat transfer in automobile radiators of the tubular type,” University of California, Publications in Engineering, 2, 443-461 (1930). 12. W. WAGNER, H.J. KRETZSCHMAR, International Steam Tables. Properties of Water and Steam based on the Industrial Formulation IAPWS-IF97, Springer, Second Edition (2008). 13. T. SCHULENBERG et al., “Three pass core design proposal for a high performance light water reactor,” Progress in Nuclear Energy, 50, 526–531(2008).

ACKNOWLEDGEMENTS Special thanks to the National Council for Science and Technology (CONACYT) for the scholarship provided to PhD student Alejandra Barragan, and to the National Autonomous University of Mexico for the PAPIIT IN113213 project funds.

Transactions of the American Nuclear Society, Vol. 109, Washington, D.C., November 10–14, 2013