Fuel element and full core thermal–hydraulic analysis of the AHTR for the evaluation of the LOFC transient

Annals of Nuclear Energy 64 (2014) 499–510

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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene

Fuel element and full core thermal–hydraulic analysis of the AHTR for the evaluation of the LOFC transient P. Avigni a,b, B. Petrovic a,⇑ a b

Nuclear and Radiological Engineering, Georgia Institute of Technology, 770 State St., Atlanta, GA 30332-0745, United States Dept. of Energy, CeSNEF-Nuclear Engineering Division, Politecnico di Milano, Via La Masa 34, 20156 Milano, Italy

a r t i c l e

i n f o

Article history: Received 13 March 2013 Accepted 21 May 2013 Available online 15 June 2013 Keywords: AHTR Molten salt TRISO fuel LOFC DRACS RELAP5-3D

a b s t r a c t The Advanced High Temperature Reactor (AHTR) is a fluoride-cooled and graphite-moderated reactor concept designed by Oak Ridge National Laboratory (Holcomb et al., 2011). The modeling and optimization of the heat removal system and the core structure is required, in order to obtain an adequate heavy metal loading and to provide effective cooling capability. The single channel MATLAB model provides a simple tool to evaluate the steady state conditions for the coolant and the fuel plate and the effects of the power distribution; sensitivity studies on the main design parameters of the fuel element are performed. A RELAP5-3D single channel model is developed for the validation and comparison with the MATLAB model; this model is the starting point for the development of a full core model, enabling the study of transients. A one-third fuel assembly model is then analyzed, consisting of six fuel plates and modeling the heat conduction of graphite through RELAP5-3D conduction enclosures. Since the assembly model is not suitable for the implementation in a full core model with the same level of detail, several simplifications have been evaluated, involving the modeling of the plate through a single heat structure and the modeling of different plates through a single plate. A SCALE model of the fuel assembly was developed for the evaluation of the reactivity feedback and the power distribution in the core. The results from the neutronic evaluations and the assembly model were implemented in a full core model, involving the core, the main reactor structures, the cooling system and the safety system (DRACS). The RELAP5-3D core model was used for the evaluation of the steady state conditions and the effects of a loss of forced cooling accident (LOFC). Ó 2013 Published by Elsevier Ltd.

1. Introduction The Advanced High Temperature Reactor (AHTR) is a fluoridecooled and graphite-moderated reactor concept designed by Oak Ridge National Laboratory (Holcomb et al., 2011). Several innovative features are introduced with this concept: high temperature molten salt coolant, nearly non-pressurized system, high-temperature resistant TRISO fuel, supercritical steam power cycle. Integration of several different technologies, coming from established or well-known reactor types, (Ingersoll et al., 2004) makes the design of the AHTR credible but challenging. Due to the use of TRISO fuel and graphite as moderator, the core volume limits the allowed heavy metal loading; in order to obtain an adequate heavy metal loading, the heat removal system is required to provide effective cooling capability while occupying the minimum possible core volume fraction. The work presented in this paper intends to assess this aspect through the study and the modeling of the AHTR cooling systems and structures on different levels: single channel, single fuel element and complete reactor system. Moreover, ⇑ Corresponding author. E-mail address: [email protected] (B. Petrovic). 0306-4549/$ - see front matter Ó 2013 Published by Elsevier Ltd. http://dx.doi.org/10.1016/j.anucene.2013.05.029

steady-state conditions are considered for the characterization of the system and the development of parametric studies, but the basis for the study of the transient behavior will be presented in the final part of the work. The MATLAB and RELAP5-3D codes will be used for the modeling of the thermal–hydraulic systems and the SCALE 6.1 code will provide information about the neutronic features.

2. Single-channel analysis In order to prepare a complete core model for the AHTR reactor, the single channel and fuel plate modeling were studied as a first step. Two approaches have been used for the single-channel model assessment:  A steady-state approach, based on a simple MATLAB model; this model is a preliminary tool for steady-state thermal–hydraulic evaluations and parametric studies;  A RELAP5-3D model for the validation of the MATLAB model and the evaluation of both the steady state conditions and transients; this model is the basis on which the core model will be developed.

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2.1. Single channel MATLAB model The single-channel MATLAB model is a steady-state thermal– hydraulic model of the average (or hot) coolant channel and fuel plate; it provides an approximate temperature distribution of the plate and the main coolant thermal–hydraulic features. The primary application of this model is the study of the dependence of the average core thermal–hydraulic performance on design parameters, properties of materials and power density distribution. The baseline design of the fuel assembly and the coolant channel used in this study are provided by ORNL in reference Holcomb et al., 2011, along with dimensions and physical properties. The elevation and the radial coordinate (orthogonal to the plate) are discretized, in order to create a suitable mesh for the calculation. The coolant temperature profile was calculated starting from the bottom of the channel and incrementally adding the temperature increase due to the power delivered by the plate to each single axial interval. Temperature-dependent coolant properties are implemented in the model, but the results show small difference with respect to the case in which properties are considered constant. The calculation of the coolant features, such as flow velocity, heat transfer coefficient and pressure drop is performed assuming the applicability of the Dittus–Boelter correlation for the Nusselt number and the Blasius formula for the friction factor (Holcomb et al., 2011). Regarding the fuel plate temperature distribution, a one-dimensional radial approximation of the heat conduction equation is considered and it is solved for each radial interval. The thermal conductivity is considered constant within every single interval, but it can change from one interval to another, accounting for the temperature dependence; the same consideration applies to the power density, whose profile might depend on the radial coordinate.

2.1.1. Power density distribution The axial power density distribution is approximated through a chopped-cosine profile, whose shape depends on the peaking factor or, equivalently, on the extrapolated length. A reference peaking factor of 1.3 was assumed (Varma et al., 2012); this value correspond to an extrapolated length 1.5 m longer than the core active height (5.5 m). Further evaluations were performed through SCALE, showing that the chopped-cosine profile is a good approximation, but, due to the reflection provided by the upper and lower reflectors, support plates and salt volumes, the peaking factor can be lower than 1.3. Moreover, the profile is not symmetric with respect to the core midplane: compared to the perfect chopped-cosine shape, it is higher for low elevation and lower for high elevation, due to slight coolant density reduction with increasing core elevation. The model requires further optimization, but initial results show that this reactor design can provide a relatively flat axial power profile, with a peaking factor below 1.3. In relation to the radial power density distribution, a uniform profile was initially used for the fuel stripe only; a further development included power generation in the graphite meat and nonuniform power density profile in the fuel stripe. Different radial profiles were tested, looking at the effects produced on the maximum fuel temperature; the main aspect affecting the value of the maximum fuel temperature is the average distance of the fuel from the plate surface. Variations of 1 °C of the maximum fuel temperature were obtained for a 2% variation of the transversal peaking factor. A SCALE simulation was run in order to evaluate the transversal peaking factor, which was found to be about 1.005%, 0.5% different from the uniform case, leading to a practically negligible (0.3 °C) increase in the maximum fuel temperature.

The previous considerations show that the maximum fuel temperature is not strongly affected by the transversal power density profile, for the following reasons:  The fuel stripe is thin (few mm), resulting in low flux depression and low transversal peaking factor;  The effect of the flux depression changes the shape of the power profile, but it does not affect its average distance from the surface of the plate. 2.1.2. Sensitivity studies The MATLAB single-channel model was used to perform sensitivity studies on some parameters of the AHTR fuel assembly, including graphite conductivity, cladding thickness, fuel stripe thickness, fuel packing fraction, and coolant gap thickness. Fig. 1 shows the maximum fuel temperature for the average fuel assembly as a function of the neutron fluence; the model accounts for conductivity dependence on both irradiation and temperature. The decrease of conductivity due to irradiation has a strong impact on the maximum fuel temperature (increase by 80 °C, from 764 °C to 842 °C), but the value that is asymptotically reached for high neutron fluence remains acceptable (Gougar et al., 2010). Fig. 2 shows the maximum fuel temperature as a function of the sleeve thickness. For the hot channel, maximum fuel temperature increases 26 °C per added mm of sleeve thickness. Since the average distance of the power density distribution from the plate surface is directly affected by this quantity, the optimization of the sleeve thickness is important in order to obtain low fuel temperatures. Fig. 3 shows the maximum fuel temperature as a function of the fuel stripe thickness; the derivative of the maximum temperature with respect to the thickness is similar to the case of the sleeve thickness variation, but slightly lower (increasing 25 °C per mm). Fig. 4 shows the fuel temperature dependence on the fuel packing fraction. Two opposing aspects contribute to the shape of the curve: the fuel stripe thickness reduction prevails for low packing fractions, while the fuel conductivity reduction is more important for higher packing fractions. Further sensitivity studies were performed, in order to test the dependence of the maximum fuel temperature on the coolant channel width; a variation of both the coolant channel width and fuel stripe thickness was considered and the results are presented in Figs. 5 and 6. The results presented in Fig. 5 are obtained assuming a constant core mass flow rate; the lowest temperature is obtained for thin fuel stripe and coolant channel, but a small coolant channel causes high core pressure drop. In order to keep the core pressure drop below 1 atm, the coolant channel must be at least 5 mm thick.

maximum fuel temperature (average assembly) 850 840

temperature [°C]

500

830 820 810 800 790 780 770 760

0

1

2

neutron fluence [n/m²]

3 25

x 10

Fig. 1. Maximum fuel temperature in the average assembly for different irradiations.

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maximum temperature [°C] (average assembly)

870

1000

860

980

850

960

840

940

830 0.5

1

1.5

2

2.5

3

ineligible area (sum of coolant and gap thickness limited by the plate pitch)

14

920

sleeve thickness [mm]

fuel stripe thickness [mm]

1020

hottest assembly

average assembly

maximum temperature [°C] 880

Fig. 2. Maximum fuel temperature as a function of the sleeve thickness (with constant plate thickness).

12

90 0

850 10 85

0

800

6

81 5

750

4

77

700

8

5

2

74

78 5

5

5 1100

900

1025

850

950

800

875

10

10

12

fuel stripe thickness [mm] Fig. 3. Maximum temperature as a function of the fuel stripe thickness (with constant plate thickness).

maximum temperature [°C] 1020

870

1000

860

980

850

960

840 20

25

30

35

40

45

50

55

hottest assembly

average assembly

880

10 8

1000

ineligible area (sum of coolant and gap thickness limited by the plate pitch)

800

950

0

8

30

96

6

25

900

0

4

20

650

92

2

15

88 5

maximum temperature [°C] (average assembly)

fuel stripe thickness [mm]

0

85 5

Fig. 5. Maximum fuel temperature as a function of coolant gap and fuel stripe thickness (constant mass flow rate).

14 750

82 0

coolant gap thickness [mm]

hottest assembly

average assembly

maximum temperature [°C] 950

900

850

0

88

800

840

6

750

810

4

790

700

770

2

650

750

5

10

15

20

25

30

coolant gap thickness [mm] Fig. 6. Maximum temperature distribution as a function of coolant gap and fuel stripe thickness (constant pumping power).

940 60

packing fraction [%] Fig. 4. Maximum temperature dependence on TRISO particle packing fraction.

Fig. 6 shows the maximum temperature distribution when the pumping power is constant, instead of the core mass flow rate. In this case, a thin coolant channel means higher core pressure drop and lower mass flow rate, leading to higher coolant temperature and higher fuel temperature. A good compromise between a low fuel temperature and a small coolant volume in the core can be obtained for a coolant channel about 7 mm thick (the design value is 6.2 mm (Holcomb et al., 2011)). The MATLAB model was found to be a useful and simple tool for sensitivity/parametric studies for the preliminary evaluation of the effectiveness of the AHTR core cooling. It was also used as a reference case for the comparison with the RELAP5 model further presented.

2.2. Single channel RELAP3-3D model A RELAP5 model of the AHTR coolant channel and fuel plate was developed, as an initial step for the core modeling; Fig. 7 shows the nodalization diagram of the model. The model is composed of a single channel (101) and a single fuel plate (1011). The salt (FLiBe) is pumped by a time-dependent junction (112) from the inlet plenum (111) at 650 °C to the first volume of the channel; after passing the channel (10 volumes), the coolant flows through a single junction (114) to an exit plenum (115), which keeps a constant atmospheric pressure at the top of the system. The fuel plate is a single heat structure in plane geometry with both sides connected to the channel; 13 transversal intervals are defined: 1 for each sleeve layer, 5 for each fuel stripe and 1 for the graphite meat. The power generation is distributed uniformly in the fuel stripe and the axial profile is a chopped cosine, equal to the profile used for the MATLAB model. The model does not

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The difference between the two models is mainly due to the different power profile. If the power profile implemented in the MATLAB model is modified and adapted to the step cosine profile of the RELAP5 model, the difference could be substantially reduced. Another way to reduce the difference is represented by an increase of the number of axial intervals in which the RELAP5 single channel is subdivided; a 20 intervals model was tested, instead of the standard 10 intervals, and a reduction of the difference was reported. In any case, the error introduced by the RELAP5 model with 10 axial intervals was considered acceptable, and the model was selected as the most valid alternative for the implementation into a full core model. 3. Fuel assembly RELAP5-3D model A RELAP5-3D model of one third of assembly was developed, based on the single channel model previously discussed. Since the AHTR fuel assembly has a threefold symmetry, (Holcomb et al., 2011) only 1/3 of the full structure was modeled (Fig. 9), with appropriate boundary conditions. Fig. 10 shows the nodalization diagram of the assembly model, which consists of:

Fig. 7. Nodalization diagram of the RELAP5 single channel model (red arrows indicate connected surfaces). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

 Inlet components: salt tank (time-dependent volume 112), pump (time-dependent junction 111) and inlet plenum (branch 110);  Assembly: 7 intra-assembly coolant channels (pipe 101–107), 1 inter-assembly coolant channel (pipe 108), 6 fuel plates (heat structures 1012, 1021, 1031, 1041, 1051, 1061), the lower box wall (heat structure 1011), the left box wall (heat structure 1091) and the Y-shape (heat structure 1071);  Outlet components: outlet plenum (branch 113), connection to the outlet tank (single junction 114), outlet tank (time-dependent volume 115). 3.1. Hydrodynamic components of the assembly model

2.2.1. RELAP5 and MATLAB single channel model comparison A comparison between the RELAP5 and MATLAB single channel models was performed, in order to validate the two models. In relation to the axial power profile, the MATLAB model has a higher number of axial mesh points (550), so the shape of the profile is a good approximation of a continuous function, but in the case of the RELAP5 model, only 10 axial intervals were considered, so the shape of the profile is a step approximation of the continuous cosine. This aspect is fundamental in order to understand the difference in the maximum fuel temperature calculation between the two models. A uniform axial profile was first considered: in this condition, from the power distribution standpoint, the two models are equivalent. The following quantities were considered: coolant temperature, heat transfer coefficient, heat flux and plate temperature distribution. The results showed that the two models are equivalent; a small difference (0.3%) was reported for the heat exchange coefficient, resulting in a 1.5 °C difference in the maximum fuel temperature. The chopped cosine profile was then considered; in this condition the power profile of the RELAP5 model is an approximation of the MATLAB case, so the difference in the temperature distributions obtained from the two models was higher. With respect to the MATLAB case, the RELAP5 model resulted in a higher maximum fuel temperature and in a higher position of the maximum, as shown in Fig. 8.

The salt tank keeps the inlet coolant temperature constant at 650 °C. The pump is modeled as a time-dependent junction for which the mass flow rate is set to 37.25 kg/s, equal to one third of the average mass flow rate per assembly. The junction is connected to a branch, which divides the mass flow between the channels; the branch has the same geometrical features of the inlet tank, but temperature and pressure can change with time. The arrows above the branch represent the connections (junctions) to the channels: the form loss coefficient is set to 0.25 for the 7 intra-assembly coolant channels and to 1500 for the interassembly channel.

850 835

temperature [°C]

include the axial reflector and the support plates, which will be further introduced in the full core model.

820 805 790 775 760 745 730 MATLAB RELAP

715 700

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

elevation [m] Fig. 8. Centerline fuel temperature profile for the MATLAB and RELAP5 model (average assembly).

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Fig. 9. AHTR fuel assembly.

The fuel plate is divided into 3 heat structures and 13 total transversal intervals with the composition and dimensions listed in Table 1. Each fuel plate is connected to two different coolant channels, one for the right side and one for the left, as shown in Fig. 10. The heat structures 1091 and 1011 are the left and lower box wall; their thickness is 1 cm and 1.35 cm respectively (both divided into 5 transversal segments). The heat structure 1091 is connected to the outside coolant channel 108 on the left, while the right surface is heated by fuel plates through conduction. The heat structure 1011 is connected to the outside coolant channel 108 on the right side and to the inside coolant channel 101 on the left side. The heat structure 1071 represents both the upper and the right Yshape branches, since the right boundary is connected to the inside coolant channel 107, while the left surface receives conduction heat from plates. The total thickness of this heat structure is 4 cm, divided into 8 transversal segments. 3.2.1. Heat conduction model The conduction between surfaces in RELAP5 can be obtained through the definition of conduction enclosures. A conduction enclosure is a group of surfaces that can exchange heat among them; for each surface belonging to the enclosure, the following features must be defined:  Gap conductance [W/(m2 K)]; the RELAP5 manual suggests to calculate the conductance as (k1k2)/[(k1 + k2)dl], where dl is the distance between the two surfaces and k1 and k2 the conductivities of the two heat structures;  Area factors: fraction of the surface involved in heat conduction;  In this model a conduction enclosure for each axial level has been defined (the model does not account for axial conduction); for each level, the surfaces included into the conduction enclosure are the inner surfaces of the heat structures representing the box wall and the surfaces belonging to the fuel plates, as indicated in Fig. 11. The configuration presented in Fig. 11 is repeated for each fuel plate; other connections are then created to connect the left and the right box walls to the upper and lower box walls.

Fig. 10. Nodalization diagram of the RELAP5-3D assembly model.

The height of the channel is 6 m, divided into 12 axial intervals; the length of the 12 intervals is not constant since the first and the last represent the lower and upper reflector, which is 25 cm long, while the other intervals are 55 cm long. Above the channels there are connections (a junction for each channel) to the outlet plenum, where the mass flows from each channel are mixed together; a single junction connects the plenum to the outlet tank. The outlet tank is a time-dependent volume which keeps the pressure constant at 1 atm at the top of the assembly.

3.2.2. Power density distribution in the fuel assembly The power is distributed axially as a chopped cosine with a 7 m extrapolated length; the reflectors do not generate power, so the total power of a plate is shared among 10 axial active intervals. No power generation occurs in graphite walls and Y-shape and no power is directly absorbed by the inter-assembly channel; this approximation is based on the assumption of low gamma absorption cross section in both graphite and coolant. In this model the power is produced in fuel plates and intraassembly coolant channels only. With reference to a single plate, 2% of power is directly transferred to the coolant channels (1% on the left channel and 1% on the right channel), without passing through the heat structure; the remaining 98% is shared among

3.2. Heat structures of the assembly model Heat structures are used to model fuel plates, assembly wall and Y-shape. Each heat structure consists of 12 axial intervals, of which the first and the last are reflectors, and the material is graphite. The total height is 6 m, the 1st and the 12th intervals are 25 cm long while the remaining are 55 cm long, producing a total active height equal to 5.5 m.

Table 1 Fuel plate model features. Intervals

Zone

Total thickness

Material

Heat structure

1 2–6 7 8–12 13

Sleeve Fuel Meat Fuel Sleeve

1 mm 6.2 mm 11.1 mm 6.2 mm 1 mm

Graphite Fuel Graphite Fuel Graphite

Left stripe Graphite meat Right stripe

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Fig. 11. Top view of the fuel plate structure and conduction enclosure model.

fuel stripes (48% per stripe) and graphite meat (2%). So for each plate we have the following power generation distribution:  96% in the fuel;  2% in the graphite meat;  2% in the coolant channels.

3.3. Results for the fuel assembly RELAP5-3D model Table 2 shows the main hydrodynamic features of the fuel assembly RELAP5 model for a steady-state simulation. As shown in Table 2, the mass flow rate of an intra-assembly channel (neither the first (101), nor the last (107), but one of the middle channels) is 6.3 kg/s. Since the flow area of the first and the last channel is half the flow area of an intermediate channel, we would expect their flow rate to be about half the flow rate of an intermediate channel, but the results show that it is only 2.0 kg/s, 2/3 of the expected value. This means that the expected temperature drop across the first or the last channel will be 50% higher (multiplied by a factor equal to 3/2) than the reference temperature drop (50 °C), that is to say that the outlet temperature of the first and last channel should be at least 725 °C. Looking at Table 2, we can see that this condition is satisfied and that the outlet temperature of these two channels is even higher. In fact the first and the last channel are heated by the respective fuel plate, but also by the lower and higher box walls, respectively; this aspect contribute to a higher temperature increase. Furthermore, the outlet temperature of channel 107 is higher than the outlet temperature of channel 101, because the Y-shape is expected to be hotter than the lower box wall. In relation to the inter-assembly flow, we can see that channel 108 reaches an outlet temperature of 686 °C, lower than the average outlet temperature. The power carried by the inter-assembly flow is about 3.28% of the total thermal power. Tables 3 and 4 show the main temperatures of the heat structures modeling the box wall and the fuel plates; the sixth axial level was selected as reference, corresponding to the middle of the core, but equivalent results are expected for different elevations.

Table 2 Fuel assembly RELAP5 model; hydrodynamic results for a steady-state simulation. Parameter

Value

Units

Outlet plenum temperature Channel 104 outlet temperature Channel 101 outlet temperature Channel 107 outlet temperature Channel 108 outlet temperature Channel 104 mass flow rate Channel 101 and 107 mass flow rate Channel 108 mass flow rate Channel 104 average flow velocity Pressure drop across the core Assembly friction pressure drop

700 697 730 734 686 6.31 2 1.7 2.09 1.793 0.619

°C °C °C °C °C kg/s kg/s kg/s m/s atm atm

Surface

Wall Lower Right Upper Left

Left/lower

Right/upper

706 819 – 747

704 – 709 815

Table 4 Temperature distribution of the fuel plates for the sixth axial level. Temperature (°C)

Lower surface

Maximum value

Upper surface

Plate 1012 1021 1031 1041 1051 1061

746 721 721 721 721 721

839 829 829 829 829 839

721 721 721 721 721 747

Table 3 shows that the temperatures of the surfaces that are in contact with fuel plates (involved in the same conduction enclosure) are only 15 °C lower than the maximum temperature of the fuel plate. Moreover, the left wall is hotter than the lower wall, since it is directly heated by the fuel plates, and the lower wall has similar values of temperature for both the upper and lower surface. The temperature drop across the Y-shape is approximately 100 °C, while the temperature drop across the left wall is 76 °C. All the fuel plates have similar temperature values, 721 °C for the surfaces and 829 °C for the centerline, except for the lower (1012) and the upper (1061) plate, which are in contact with hotter channels 101 and 107. This result in a 10 °C higher maximum fuel temperature. 3.4. Assessment and simplifications of the model The model presented in the previous sections provides a complete description of the fuel assembly features, but it is not suitable for the implementation in a full core model, because it requires a high number of heat structures and hydrodynamic components. Different modifications of the model were tested in order to simplify the model while maintaining accurate results. 3.4.1. Heat conduction through plate surfaces The structure of the fuel plate was simplified, reducing the number of heat structures forming the plate from three to one and adopting the external surfaces of the plate as conduction surfaces in contact with the box walls. This model requires only one heat structure for a plate and a lower number of surfaces involved in the conduction enclosures. For these reasons the model can be considered a simplification, but the number of hydrodynamic volumes and overall heat structures is still high. Moreover an issue is generated by the fact that the conduction surfaces are the external surfaces of the plate. In fact in these conditions the temperature of the box walls results to be lower and consequently the outlet temperature of the inter-assembly coolant is lower, as well as the power carried by the inter-assembly flow. In order to address the issue presented in the last paragraph, two solutions have been tested: the homogenization of the fuel stripe and the sleeve and the artificial modification of the graphite thermal conductivity. The first solution is based on the fact that a thicker heat structure with a single mesh interval allows the use of a higher gap

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conductance for the conduction enclosure model (Code Development Team, 2012). Despite the strong approximation, a slight increase of the box wall temperature was obtained, so an alternative approximation was tempted, consisting of an increase in the thermal conductivity of the wall. This would lead to a wrong temperature distribution of the box wall, but the outlet temperature of the inter-assembly coolant could be adjusted to a higher value. However, the power carried by inter-assembly flow was 2%, which was considered too low (Holcomb et al., 2011). Considering all the previous models, in which the fuel plate is formed by a single heat structure, the main issue is the fact that the box walls are not properly heated by the plate surfaces. So the initial model was considered more suitable than the previous simplifications, even though three heat structures for each fuel plate are required. In order to account for the higher temperature levels of the two thinner intra-assembly channels, the heat exchange coefficient of both the upper face of the lower box wall and the lower face of the upper box wall (corresponding to the right side of the right box wall) were multiplied by a factor 0.3. This resulted in a more accurate temperature distribution for the box walls. The next section (Tables 5–7) presents the main results regarding the heat structures and the hydrodynamic components in steady state conditions.

3.4.2. Single fuel plate and intra-assembly channel Since the six fuel plates have a similar behavior inside the box, the model was simplified by using a single fuel plate with larger heat transfer area. This simplification is required in order to be able to make a full core model, because RELAP5 allows using only up to 100 conduction enclosures. A single intra-assembly channel was also implemented, whose flow area is the sum of the flow areas of all the single intra-assembly channels. Fig. 12 shows a top view of the model, along with convective and conductive connections. A comparison with the results of the complete model presented in Section 3.3 shows that the single fuel plate model is a relatively good approximation. One difference is related to the core friction pressure drop, which results to be 8% higher, as shown in Table 5; the flow distribution is slightly different: the mass flow rate in the inter-assembly channel is 3% higher, so the flow velocity for the intra-assembly channel is smaller. The temperatures of the box wall are consistent with the previous results (few degrees higher, see Table 6), except the temperature of the lower face of the upper box wall, which is 16 °C lower. The reason of this difference is the fact that, in this case, this surface was not included in the conduction enclosure (the model is simpler). Finally, the temperature distribution of the plate (Table 7) is similar to the profile presented in Table 4: the single plate constitutes a sort of average of the initial six fuel plates. A further simplification was tested: the use of a single heat structure to model the box wall; this approximation was shown Table 5 Results for hydrodynamic components; single fuel plate model. Parameter

Value

Units

Outlet plenum temperature Channel 101 outlet temperature Channel 102 outlet temperature

700 702 685

°C °C °C

Channel 101 mass flow rate Channel 102 mass flow rate

35.48 1.75

kg/s kg/s

Channel 101 average flow velocity Pressure drop across the core Assembly friction pressure drop

1.96 1.831 0.669

m/s atm atm

Table 6 Temperature distribution of the box walls; single fuel plate model. Temperature (°C)

Wall Lower Right Upper Left

Surface Left/lower

Right/upper

709 824 – 750

707 – 693 820

Table 7 Temperature distribution of the fuel plate; single fuel plate model. Lower surface

Maximum value

Upper surface

Plate 724 °C

833 °C

824 °C

Fig. 12. Top view of the fuel assembly model with a single fuel plate; convective and conductive connections are indicated by red and blue lines, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

to be too strong, since the power delivered to the inter-assembly channel was substantially different. In summary, the simplified assembly model, with a single fuel plate and a single intra-assembly channel was considered suitable and it was selected for the implementation in a full core model. 4. Neutronic evaluations: fuel assembly SCALE model A SCALE model of the fuel assembly was developed in order to obtain the power density distributions and to calculate the reactivity feedback coefficients, needed as an input for the RELAP5-3D core model. Due to the amount of computational capacity required for full core simulations, the model was developed at the assembly level; a horizontal cross section of the AHTR fuel assembly is presented in Fig. 13. The fuel assembly is formed by 18 fuel plates, the Y-shaped support with the channel for the control rod, the box walls and the inter/intra-assembly channels for the coolant. The boundary conditions are reflective for all the external surfaces. Fig. 14 shows the cross section of a single fuel plate, formed by a sleeve, the fuel stripe and the graphite meat. The configuration of the fuel is presented in Fig. 15, assuming a 40% packing fraction, which is the highest value that can be reliably obtained with currently available technologies. A simple cubic lattice is implemented, even if the real TRISO fuel would probably present a random distribution of particles; we expect this issue to be negligible in relation to the purposes of this work. A second

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The evaluation of the reactivity was performed through the 3D Monte Carlo transport code implemented in SCALE (KENO-VI). The evaluation of the nuclear cross sections is required in order to calculate the reactivity of the fuel assembly and two options are available for the KENO model, the continuous energy library (ce_v7) and the multigroup library (v7-238). Since no approximations for the cross-section evaluation are applied in the continuous energy mode, this would have been the preferable path, but continuous energy cross-sections were available only for several discrete temperature values (600 K, 900 K and 1200 K) and SCALE does not allow cross section interpolation in the continuous energy mode. So the multigroup mode was selected, which allows interpolation, and the Dancoff factor for the TRISO particles was optimized through a comparison with the continuous energy model calculation for a certain set of temperatures, for which the continuous energy libraries were available. 4.1. Reactivity feedback evaluation

Fig. 13. SCALE model of the AHTR fuel assembly; horizontal cross-section.

Two contributions to the reactivity feedback are evaluated in this work: the temperature of the fuel and the temperature of the coolant; a variation of the coolant temperature results also in a variation of the coolant density, so even the coolant density variation is accounted for in this modeling. The evaluation of the reactivity feedback is performed trough the following steps:  Selection of the range of fuel and coolant temperature variation: from 900 K to 1100 K for the coolant and from 900 K to 1500 K for the fuel; the increment was set to 100 K;  Calculation of the k (multiplication factor) for each possible set;  Calculation of the reactivity for each point defined as (k 1)/k;  Calculation of the reactivity coefficient as the slope of the regression line.

Fig. 14. SCALE model of the AHTR fuel plate.

From Fig. 16 it is clear that the k, and so the reactivity, depends mainly on the fuel temperature, while coolant temperature and density play a smaller role. We could expect this, since the amount of coolant, in terms of volumetric fraction, into the core, is small, of the order of 10%. As we can see from Fig. 17, the fuel temperature coefficient is negative; the average value is about -4.5 pcm/K and an increase in the fuel temperature makes the absolute value of the coefficient smaller. In relation to Fig. 18, the coolant temperature coefficient is negative and smaller than the fuel coefficient; its average value is about 0.5 pcm/K and the temperature dependence on both the fuel and coolant temperature is not well defined due to statistical noise. However, for the purpose of this work, the accuracy of the results was considered adequate.

900

1.36

1000

1100

1.35

k

1.34 1.33 1.32 Fig. 15. SCALE model of the TRISO particle and lattice.

1.31 1.3 800

approximation was adopted, which consists of the homogenization of the buffer layer with the inner pyrolitic carbon layer and the outer pyrolitic carbon layer with the graphite matrix.

900

1000

1100

1200

1300

1400

1500

1600

fuel temperature [K] Fig. 16. Multiplication factor as a function of the fuel temperature, for different coolant temperatures.

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Each assembly is modeled as three units connected through the wall of the Y-shape and each unit has the structure presented in Section 3.4.2. The new aspect that must be introduced for a core model description is the characterization of the inter-assembly flow. In our case three inter-assembly channels where associated to each ring:

1000 Linear (900) Linear (1100)

fuel temp. coeff. [pcm/K]

900 1100 Linear (1000)

950

1050

1150

1250

1350

1450

fuel temperature [K] Fig. 17. Fuel temperature coefficient as a function of the fuel temperature, for different coolant temperatures; for each series, the regression line is plotted.

900

1000

1100

1200

1300

1400

 The first channel models the flow that is heated by the reference ring on one side and by the outer ring on the other side;  The second channel is heated by the reference ring on both sides;  The third ring is heated half by the reference ring and half by the inner ring. Each of these inter-assembly channels has a specific flow area, and horizontal cross-flow between channels is allowed, since each channel is modeled as a 3D component. 5.1.2. Piping and structures Various hydrodynamic volumes and heat structures are used to describe the components that operate into the reactor vessel.

1050 Linear (1050)

coolant temp. coeff. [pcm/K]

950 Linear (950)

507

1500

fuel temperature [K] Fig. 18. Coolant temperature coefficient as a function of the fuel temperature, for different coolant temperatures; for each series, the regression line is plotted.

5. RELAP5-3D AHTR core model 5.1. Structure and features of the model A simplified reactor system was modeled in order to account for all the factors that affect the transient behavior; in particular, the model includes the following components:  Reactor core, core channels, permanent and removable radial reflector and lower and upper support plates;  Lower and upper plenum;  Barrel;  Downcomer channels;  Reactor vessel;  Intermediate loop (1/3);  DRACS loop and air circuit (1/3); The following paragraphs give a description of the modeling of these components. 5.1.1. Reactor core The reactor core was modeled as a 9-rings cylinder and each cylinder was modeled as a single fuel assembly; the heat exchange area of the heat structures and the cross-section of the channels were increased by a specific multiplicative factor in order to account for the fact that each modeled assembly represents more than one real assembly.

5.1.2.1. Hydrodynamic components. Starting from the bottom of the vessel, the inlet junctions of the core channels are connected to the lower plenum, a single volume component, shaped as a cylinder with a 10.4 m diameter and 1.2 m height. The lower plenum is connected to the upper plenum through the intra-assembly channels, the inter-assembly channels and the channel associated to the replaceable and permanent reflector. The upper plenum is modeled through two connected parts: the lower part is a single volume cylinder with 9.58 m diameter and 6 m height; the upper part, which is in contact with the Argon plenum, is a cylinder with the following dimensions: 1 m height, 10.4 m diameter (not limited by the barrel). The downcomer region is divided into seven circular sections, and one channel is associated to each region. Each downcomer channel is a 3D component characterized by an inner radius (4.81 m, outer vessel), an outer radius (5.2 m, inner vessel) and an angle (53.85° for the downcomer, 36.5° for the DRACS and 88.95° for the refueling lobe), which defines the arc of circumference. Each DRACS channel is partly connected to a DRACS heat exchanger. 5.1.2.2. Heat structures. Heat structures have been used to model the radial reflector, the barrel and the reactor vessel. The radial reflector is composed of two heat structures, the innermost representing the replaceable reflector and the outermost representing the permanent reflector. The replaceable reflector consists of a cylindrical heat structure with both inner and outer sides connected to a cooling channel; the inner radius is given by the equivalent core radius (3.905 m) and the outer radius is the equivalent radius of the fueled region plus the area of the 60 removable reflector assemblies (4.315 m). The permanent reflector is modeled as a hollow cylinder with inner diameter equal to the outside diameter of the removable reflector and outer diameter equal to the total core diameter, which is 9.56 m (Varma et al., 2012). The barrel is divided into seven sections, corresponding to the seven downcomer regions, and each surface is connected to the two adjacent surfaces through a conduction enclosure, in order to account for the heat conduction of the structure. Each surface is approximated as a plane surface; the thickness is 2 cm and the width is 4.5 m for the downcomer region, 3.05 m for the DRACS region and 7.43 m for the refueling lobe. The total height of the barrel

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is 12.7 m: 6 m for the core, 0.7 m for the upper and lower support plate and 6 m for the upper plenum. The reactor vessel is modeled as a hollow cylinder with two rings: the inner ring is similar to the barrel, since it consists of seven angular sections connected through a conduction enclosure; the outer ring is a single hollow cylinder. The inner diameter of the first ring is 10.4 m, the outer diameter of the first ring is 10.44 m and the outer diameter of the second ring is 10.5 m, so the total vessel thickness is 5 cm; the connection between the two rings is modeled through a conduction enclosure. 5.1.3. Heat removal The primary heat removal during normal reactor operation is provided by three PHXs (primary heat exchanger) located in three different sections of the downcomer, which transfer the heat from the primary circuit to three intermediate loops. The primary piping interior diameter is 1.24 m and the pump, modeled as a time-dependent junction, is located in the middle of the outlet pipe of the exchanger (which is the vessel inlet pipe). The heat exchanger is a straight-tube shell-and-tube counterflow horizontal type exchanger and the piping material is alloy 800H with Hastelloy N lining. The heat exchanger was modeled as a cylindrical heat structure connecting the two sides (primary on the tube side and intermediate on the shell side) of the system. An accurate design of the PHX is not yet available, so dimensions and number of tubes were estimated on the basis of the design of the PB-AHTR IHX (Lim and Peterson, 2009) and the SmAHTR PHX (Greene et al., 2010). The number of tubes was then optimized in order to obtain the correct amount of power removed by the cooling system, which is one third of the total core power per each intermediate loop; a summary of the PHX design features used for this study is given in Table 8. 5.1.4. Safety system: DRACS The DRACS provides heat removal during accidental transients; it is formed by the DRACS loop and the air circuit: the power is removed from the core by the DRACS exchangers, carried by the DRACS loop to the salt-to-air heat exchanger and transferred to the atmosphere, which is the ultimate heat sink. The design of the DRACS of the AHTR is still not well defined so the dimensional parameters were determined looking at the overall description of the system given in the ORNL reports (Holcomb et al., 2011; Varma et al., 2012) and at the design parameters of the DRACS of the SmAHTR (Greene et al., 2010). The pipe diameter for the DRACS loop is 0.62 m (half of the primary piping diameter); the DRACS exchanger is a straight-tube shell-and-tube counterflow vertical type exchanger, with primary fluid (FLiBe) on the shell side and intermediate fluid on the tube side. The dimensional parameters of the DRACS exchanger are given in Table 9.

Table 9 DRACS exchanger parameters. Parameter

Value

Units

Tube outer diameter Tube wall thickness Tube inner diameter Pitch/tube outer diameter Pitch (triangular) Tube-side hydraulic diameter Shell-side hydraulic diameter Tube height Number of tubes

1.27 0.1245 1.021 1.25 1.5875 1.021 0.9192 3.5 5468

cm cm cm – cm cm cm m –

The salt coming out from the DRACS exchanger flows up to the salt-to-air exchanger through a 12 m high pipe which provides the gravitational pressure difference required for natural circulation operation; then it flows downward through the 2 m high salt-toair exchanger and finally it is injected at the entrance of the DRACS exchanger, closing the loop. The dimensional parameters of the salt-to-air exchanger are given in Table 10. Air flows upward in the shell-side and salt flows downward in the tube-side; since air is not implemented in RELAP5 as a working fluid, pure nitrogen was selected for the air loop. The system was set so that, when the temperature of the primary coolant in the downcomer DRACS channel is 700 °C, the power removed is about 8 MW per loop.

5.2. Steady-state conditions The model was run for 100,000 s (27.8 h) at constant thermal and pumping power, in order to evaluate the steady-state conditions of the system. Fig. 19 shows the temperature distribution of the coolant, with respect to the axial and radial positions into the core. As we can see in Fig. 19, the outlet temperature of the core is not uniform and the range goes from 685 °C for the outermost channel to 735 °C for the central channel. While the outlet temperature depends on the radial position, the temperature profile is not affected by the distance from the middle of the core. Although the outlet temperature is not uniform, it spans a relatively small range (50 °C) of temperatures, which means that a redistribution of the mass flow rate might not be required. The flow velocity and the mass flow rate per assembly as functions of the radial position have an almost constant profile (1.8 m/s and 98 kg/s), which slightly increases from the outermost to the central ring, where the coolant is hotter and the buoyancy effects are more effective. In relation to the results obtained from single-assembly or single-channel model studies, the average value for the flow velocity obtained from the reactor model is lower (1.8 m/s, while for the single-channel model it was 1.96 m/s), because a certain fraction of the total reactor mass flow rate does not pass through the core, but forms a by-pass flow through the

Table 8 PHX modeling parameters. Parameter

Value

Units

Tube outer diameter Tube wall thickness Tube inner diameter Pitch/tube outer diameter Pitch (triangular) Tube-side hydraulic diameter Shell-side hydraulic diameter Tube-side flow area Shell-side flow area Tube height Number of tubes

2 0.1 1.8 1.25 2.5 1.8 1.448 2.5434 2.273 22 10000

cm cm cm – cm cm cm m2 m2 m –

Table 10 Salt-to-air exchanger parameters. Parameter

Value

Units

Tube outer diameter Tube wall thickness Tube inner diameter Pitch/tube outer diameter Pitch (triangular) Tube-side hydraulic diameter Shell-side hydraulic diameter Tube height Number of tubes

1.995 0.1652 1.6646 1.25 2.49375 1.6646 1.4439 2 15000

cm cm cm – cm cm cm m –

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Temperature [°C] 6

730

734 5

720

728

710

719 710

700

701 3

692

690

683 680

674

2

665

670

659

1

660

653 0

0.5

1

1.5

2

2.5

3

3.5

Radial position [m] Fig. 19. Coolant temperature distribution.

DRACS downcomer channels. For this reason the outlet temperature of the salt in the upper plenum is 5 °C higher than the design value (700 °C). The pressure of the core has a linear dependence on the elevation; the pressure drop across the core is about 1.75 atm, of which 1.15 atm is the gravitational pressure drop and 0.6 atm is the friction pressure drop. The pressure at the entrance of the core is relatively high because of the height of the salt plenum above the core and the high density of FLiBe, twice the density of water (5.3 m are required to increase the pressure by one atmosphere). Fig. 20 shows the fuel temperature of the plate as a function of the radial and axial position. For a given radial and axial position the value of temperature located at the inner face of the fuel stripe is considered, which is the maximum temperature in the direction transversal to the plate. As it is shown in Fig. 20, the maximum fuel temperature, in the radial direction goes from 800 °C for the outermost ring, to 925 °C for the central ring (the maximum fuel temperature for the average assembly was found to be 843 °C). The location of the axial maximum fuel temperature is not strongly affected by the radial coordinate and it is slightly above the middle of the core.

Temperature [°C] 6 900

Elevation [m]

5 850

4

3

The steady state simulation provides a relevant amount of information about the behavior of the system, but the model is designed for the evaluation of transients; the LOFC transient was selected as a typical accident scenario.(Griveau and Peterson, 2006). The transient has the following features:  The initial conditions are the steady state conditions presented in the last section;  The reactivity is decreased from 0 to 15 $ in 20 s;  The mass flow rate produced by the pumps of the primary and intermediate loop are reduced from the nominal value to 0 in 2 min. The main purpose of the simulation is the verification of the effective cooling capability of the DRACS system. In relation to the coolant temperature, during the initial transient, the outlet temperature decreases, because the core power is reduced. Then, since the cooling capability is initially lower than the core power, the inlet temperature increases, as well as the outlet temperature. The maximum outlet temperature is 714 °C at 21,500 s and the maximum inlet temperature is 688 at 24500 s; the two temperatures decrease after this point.

Temperature profiles in the PHX 800

0

94

20

9

890 2

750

850 800 760

1

700

720 0

5.3. Loss of forced cooling (LOFC) accident

0.5

1

1.5

2

2.5

3

3.5

Radial position [m] Fig. 20. Maximum transversal fuel temperature distribution.

temperature [°C]

Elevation [m]

4

Fig. 21 shows the temperature profiles for the primary and intermediate coolant in the PHX. The inlet and outlet temperatures for both the sides of the exchanger are consistent with the nominal values given by ORNL reports (Holcomb et al., 2011). The temperature profiles for the primary and intermediate coolant in the DRACS exchanger were calculated. During normal operating conditions (as in this case), the flow in the DRACS downcomer channels is directed upward, so the exchanger works in parallel flow configuration, while, when the primary pumps do not work and natural circulation is activated, it works as a counter flow exchanger. The mass flow rate in the primary side is 570 kg/s per channel, which means, considering the three channels, a 1710 kg/s by-pass flow (6% of the total mass flow rate). In the intermediate loop, the mass flow rate is 393 kg/s per channel, for a total of 1179 kg/s. The temperature profiles for the intermediate coolant and air in the salt-to-air exchanger were calculated. This exchanger works in parallel flow configuration and the total mass flow rate is 41.5 kg/ s of nitrogen: since the mass flow rate for the air loop is relatively low, the temperature increase of nitrogen is very high, about 500 °C. The power lost through the DRACS system during normal operation is about 23.4 MW.

710 700 690 680 670 660 650 640 630 620 610 600 590

Primary loop Intermediate loop

0

5

10

15

20

position in the PHX [m] Fig. 21. Temperature profile for primary and intermediate coolant in the PHX.

510

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950 maximum fuel temperature average fuel temperature

temperature [°C]

900 850 800 750 700 650 600

0

2

4

6

8

10 4

time [s]

x 10

Fig. 22. Maximum and average fuel temperature during the LOFC transient.

7

10 9

x 10

total reactor power removed power (DRACS)

8

power [W]

7 6 5 4 3 2 1 0

0

2

4

6

time [s]

8

10

model was developed as a simple tool which can still provide relevant information about the thermal–hydraulic features of the fuel element. Steady state and parametric studies have been performed, showing the capability for an effective heat removal: despite the small volume fraction occupied by the coolant in the core, the maximum temperatures are below the limits for TRISO fuel. The RELAP5 single channel introduces the capability for the modeling of transients, however, due to practical limitations it may result in reducing the accuracy of the results. Nevertheless, the approximations introduced through a coarser discretization of the model was considered acceptable. The RELAP5 fuel assembly model constitutes the intermediate step on the way to the development of a full core model. The model expands the amount of information available from the single channel model, particularly regarding the heat conduction among fuel plates and support structures (box wall, Y-shaped support). The second intermediate step, related to the neutronic modeling of the fuel assembly, provided important information about the reactivity feedback, along with a basic characterization of the power distribution in the fuel stripe and in the core. Further work is required to improve the modeling, but the results obtained in these initial evaluations were considered reliable. The information collected from the single channel and fuel assembly studies was used for the development of a full core model, in order to be able to evaluate the possible transient and accident scenarios and eventually perform the safety analysis of the reactor. The LOFC transient was evaluated; the system was proved very effective in the heat removal. Different types of transient will be evaluated in the future work, as well as the possibility of a potential online refueling procedure.

4

x 10

Acknowledgement

Fig. 23. Total core power and removed power during the LOFC transient.

Fig. 22 shows the maximum and average fuel temperature dependence on time. Similarly to the coolant temperature, the maximum fuel temperature, initially 950 °C, decreases to a minimum (700 °C), reaches the maximum at 21,000 s (721 °C) and then decreases. In relation to the mass flow rates, the primary mass flow rate, driven by natural circulation, is initially 420 kg/s and slightly decreases. The DRACS loop mass flow rate is 1330 kg/s, reaches a maximum at 21,000 s and then decreases. The air mass flow rate is constant during the transient (about 42 kg/s). Fig. 23 shows the total core power and the power removed by the DRACS system during the LOFC transient. The capability of the DRACS system is about 25 MWth; the total core power drops below this value 26,000 s after the beginning of the transient; the power removed by DRACS slightly decreases with time. As we can see from the results of the simulation, the DRACS system provides effective heat removal and the fuel temperature always remains well below the damage limit for TRISO fuel. 6. Conclusions The work presents different aspects regarding the modeling, study and characterization of the AHTR reactor. The MATLAB

This research is being performed using funding received from the DOE Office of Nuclear Energy’s Nuclear Energy University Programs (NEUP). References RELAP5-3D Code Development Team, 2012. RELAP5-3D Code Manual Volume I: Code Structure, System Models and Solution Methods. Idaho National Laboratory, June, 2012. INEEL-EXT-98-00834. Gougar, H. et al., 2010. Prismatic coupled neutronics/thermal fluids transient benchmark of the MHTGR-350 MW core design 12. Greene, S.R., Gehin, J.C., Holcomb, D.E., et al., 2010. Pre-conceptual design of a fluoride-salt-cooled Small Modular Advanced High-Temperature Reactor (SmAHTR). Oak Ridge National Laboratory, ORNL/TM-2010/199. Griveau, A., Peterson, F., 2006. RELAP5-3D Loss of Forced Cooling (LOFC) Transient Response Modeling for the PB-AHTR. In: Berkeley, U.C. September 17, 2006. UCBTH-06-003. Holcomb, D.E., Ilas, D., Varma, V.K., Cisneros, A.T., Kelly, R.P., Ghein, J.C., 2011. Core and refueling design studies for the advanced high temperature reactor. Oak Ridge National Laboratory 30, ORNL/TM-2011/365. Ingersoll, D.T. et al., 2004. Status of preconceptual design of the Advanced HighTemperature Reactor (AHTR). Oak Ridge National Laboratory, ORNL/TM-2004/ 104. Lim, H.J., Peterson, P.F., 2009. Conceptual Design of the Intermediate Heat Exchanger (IHX) for the PB-AHTR. In: Berkeley, U.C., May 20, 2009. UCBTH09-0005. Varma, V.K., Holcomb, D.E., Peretz, F.J., Bradley, E.C., Ilas, D., Qualls, A.L., Zaharia, N.M., 2012. AHTR mechanical, structural, and neutronic preconceptual design. Oak Ridge National Laboratory, ORNL/TM-2012/320.