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A thermal-fluid assessment of a cooled-vessel concept for a VHTR
Nuclear Engineering and Design 238 (2008) 3360–3369
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A thermal-fluid assessment of a cooled-vessel concept for a VHTR Min-Hwan Kim ∗ , Hong-Sik Lim, Won-Jae Lee Korea Atomic Energy Research Institute, 1045 Daedeokdaero, Yoseong, Daejeon 304-353, South Korea
a r t i c l e
i n f o
Article history: Received 20 December 2007 Received in revised form 29 May 2008 Accepted 25 June 2008
a b s t r a c t Flow distribution and thermal analyses of a conceptual design of a cooled vessel for a very high temperature reactor (VHTR), which has a forced vessel cooling with an internal coolant path through a permanent side reflector, have been performed. A computational fluid dynamics (CFD) code was employed to investigate flow distributions at inlet and upper plenums of the proposed cooled-vessel concept. Thermal-fluid analyses of the cooled vessel during a normal operation were carried out by using the CFD code with the boundary conditions provided by the GAMMA system analysis code. The transient analyses during postulated accidents were conducted by the GAMMA code itself. According to the results, the flow deviation at the riser holes due to a change of the inlet flow path to the core inlet is about ±20% which results in about a 3–7% core flow deviation from the average value depending on the upper plenum height. The pressure drops in the inlet and upper plenums are estimated to be from 13 to 25 kPa with a change of the upper plenum height. A cooling flow of more than 4 kg/s is sufficient to maintain the RPV temperature within the required limit during a normal operation. Transient analysis reveals that the reactor vessel is exposed to a temperature above its limit of 371 ◦ C but this duration is shorter than the allowable time for a creep region with a sufficient safety margin. The results suggest that the cooled-vessel concept considered in this paper has the potential to be used for a VHTR but further and more detailed studies are required to realize the proposed concept. © 2008 Elsevier B.V. All rights reserved.
1. Introduction The very high temperature (gas-cooled) reactor (VHTR) has become of great interest in connection with a process heat application such as a hydrogen production. The Nuclear Hydrogen Development and Demonstration (NHDD) project has been launched at KAERI (Korea Atomic Energy Research Institute). The NHDD plant is a VHTR coupled to a hydrogen production plant using a sulfur–iodine process via an intermediate loop (Chang et al., 2007). It has not been determined yet whether the reactor type should be a pebble bed reactor (PBR) or a prismatic modular reactor (PMR). However, the design of the reactor pressure vessel (RPV) is very important, and is of interest (Hoffelner, 2004; Gougar et al., 2006), regardless of the reactor type because the operating temperature of the RPV in a VHTR is much higher than that in a light water reactor. The cooled-vessel concept makes it possible to use conventional SA-508/533 steel (ASME, 2001) as the material for the RPV of a VHTR. The PBMR in South Africa (Matzner, 2004) adopts a conventional SA-508 cooled-vessel design in which the coolant flow is
∗ Corresponding author. Tel.: +82 42 868 8102; fax: +82 42 868 8767. E-mail address: [email protected] (M.-H. Kim). 0029-5493/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2008.06.022
directed through internal graphite structures, and a vessel cooling system is used to cool the RPV inner wall. The GT-MHR by General Atomics selected a creep-resistant material for their RPV, which has not been manufactured on a large scale as yet, and also its welding procedure has not been established, so they have considered an alternative design (Reza et al., 2006) for their VHTR for a hydrogen production, which uses conventional steel instead of a creep-resistant material. Therefore, it is meaningful to consider an alternative design for a NHDD prismatic reactor. In this paper, we propose a cooled-vessel concept applicable to a NHDD prismatic reactor, which is characterized by an internal flow path and a vessel cooling, and then we carried out thermo-fluid analyses by using the CFX (ANSYS, 2005) and GAMMA codes (Lim and No, 2006) to establish whether this concept has the potential for a future use. The analyses include an analysis of the flow distribution through an internal flow path and an assessment of the vessel cooling performance during a normal operation and accidents. 2. Description of the cooled-vessel concept The GT-MHR is selected as a reference PMR to apply the proposed cooled-vessel concept. Coolant thermo-fluid design conditions of both the GT-MHR and the NHDD are given in Table 1.
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Table 1 Thermo-fluid design conditions of GT-MHR and the present MHR Parameter
GT-MHR
NHDD
Core power (MW) Core inlet temperature (◦ C) Core outlet temperature (◦ C) Operating pressure (MPa) Helium mass flow (kg/s)
600 490 850 7 320
600 590 950 7 320
The reactor power, operating pressure, and helium mass flow of the NHDD reactor are the same as those of the GT-MHR but its core outlet temperature is increased to 950 ◦ C for efficient hydrogen production. Without changing the core design of the GT-MHR, the increase of the coolant outlet temperature results in an increase of the coolant inlet temperature up to 590 ◦ C. In the GT-MHR, the inlet coolant flow is routed through the coolant channels between the core barrel and the RPV as shown in Fig. 1. With the GT-MHR inlet configuration, the elevated inlet temperature of the NHDD would result in an increase of the reactor vessel temperature which would exceed the operating limit of the creep-resistant material. To reduce the influence of the increase in the inlet temperature on the reactor vessel temperature, the inlet flow path through the channels is routed to cylindrical riser holes through a permanent side reflector. A modified inlet flow configuration of the cooled vessel is shown in Figs. 2 and 3. The inlet flow coming from the outside of the coaxial duct is supplied to the inlet plenum, a large annular space below the permanent side reflector, in which the flow is distributed into the riser holes. After passing through the riser holes, the flow gathers at the upper plenum and is supplied to the core. The diameter of a riser hole is determined to maintain a total area comparable to that of the coolant channels of the GT-MHR in Fig. 1, 1.6417 m2 (Reza et al., 2006). The number of riser holes is 54, and the diameter of a hole is 0.2 m. At the upper plenum, three riser holes are grouped to buffer the non-uniform flow from the riser, and then the flow is supplied to the upper part of the core through the slits in the graphite structure. A vessel cooling flow is supplied to the annular gap between the RPV and the core barrel, where the coolant channels of the GT-MHR are installed. Cold helium for the vessel
Fig. 1. GT-MHR inlet flow path and cross-section at the middle plane.
cooling flow can be supplied by using a slipstream flow from the helium purification system which removes chemical and radioactive impurities from the primary helium coolant. If the required amount of cooling flow is too large to be supplied by the helium
Fig. 2. Configuration of the cooled-vessel design concept.
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M.-H. Kim et al. / Nuclear Engineering and Design 238 (2008) 3360–3369 Table 2 Coolant conditions at the inlet plenum Parameter
Value ◦
Temperature ( C) Pressure (bar) Mass flow (kg/s) Density (kg/m3 ) Viscosity (N s/m2 )
Fig. 3. Cross-section of the middle plane of the cooled vessel.
purification system, a dedicated vessel cooling system needs to be installed. 3. Analyses of flow distributions 3.1. Inlet plenum An analysis using a computational fluid dynamics (CFD) code, CFX-10 (ANSYS, 2005), is performed to establish how the flow is distributed at the riser holes. Fig. 4 shows the geometric configuration and the applied boundary conditions. The inlet plenum connects the outer annulus of the hot duct and the 54 riser holes. The coolant from the annular inlet duct is supplied to the plenum and sent to
Fig. 4. Inlet plenum domain and boundary conditions.
590 70 320 (160 for the half inlet) 3.868 4.111 × 10−5
the upper side of the reactor core through the riser holes. The inlet plenum has a symmetrical shape, so only a half of the plenum is selected for the CFD analysis. For the mesh generation, the domain was divided into three regions which are the inlet pipe, the plenum and the riser, respectively. The mesh extrusion method that creates prism meshes for the center region and hexahedral meshes for the boundary layer region was used for the inlet pipe and the riser, respectively. Due to the complexity of the flow field, tetrahedral meshes were used for the plenum with prism meshes for the wall boundary region. The total number of nodes was 1,205,002. This number is considered to be sufficient enough for the present study because a previous study for the inlet plenum of a pebble-bed reactor (Ahmad et al., 2007) indicated that a node number of more than 400,000 was sufficient enough to resolve the flow distribution at their inlet plenum. The three-dimensional Navier–Stokes equations were integrated for the inlet plenum analysis in which an isothermal flow was assumed because there is no large temperature variation at the inlet plenum. Table 2 shows the coolant conditions at the inlet plenum. A constant mass flow is set for the inlet boundary condition. At the outlet boundary of the 27 riser holes, a constant static pressure is applied because the length of the riser, 15 times that of the riser hole diameter, is sufficient enough so that the flow in the plenum cannot be affected by the static pressure condition at the riser outlet. Symmetric and wall conditions are applied for the other boundaries. The Reynolds number based on the hydraulic diameter of the inlet duct is 2.52 × 106 , which means the flow is turbulent. The shear stress transport (SST) model with an automatic near-wall treatment (Vieser et al., 2002) was adopted for a turbulence closure in this complex geometry. A turbulence intensity of 5% was assumed at the inlet boundary. Fig. 5 shows the streamline distribution at the inlet plenum. The flow coming from the annular inlet duct expands rapidly at the inlet plenum and the maximum velocity increases by nearly up to twice that of the inlet velocity. The expanded and accelerated flow is spread throughout the whole plenum, and is distributed to each riser hole. Recirculation flow is observed at the riser holes near the inlet duct. Fig. 6 shows the pressure distribution at the inlet plenum for three horizontal planes (z = −1 m, z = 0 m, z = +1 m) and a mid-surface of the annular plenum. High pressure occurs at the wall where the inlet flow impinges on it, whereas a low pressure occurs at the riser holes, where a flow separation is observed. It should be noted that a high pressure comparable to that of the inlet region occurs at the opposite side of it, which is expected to result in a higher flow rate in a riser further from the inlet duct. Total pressure drop at the plenum region is estimated to be about 7.9 kPa. Mass flow at each riser hole is computed by averaging the exit velocities over their area. Fig. 7 shows the mass flow distribution at a riser. The horizontal axis represents an assigned number for each riser hole. Number 1 corresponds to the nearest hole to the inlet duct and Number 27 to the farthest riser hole from the inlet duct. The vertical axis is a mass flow deviation (Si ) normalized by
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Fig. 5. Streamlines at the inlet plenum.
an average value, defined as Si =
mi − mavg mavg
(1)
where mi is the mass flow rate at each riser, mavg is the average mass flow rate computed by dividing the inlet mass flow rate by the total number of riser holes, and subscript i corresponds to the assigned number of the riser varying from 1, near to the inlet duct, to 27, the opposite side of it. The holes near to the inlet duct, in which a flow separation occurs, have a relatively lower flow rate and those far from the inlet duct have a higher flow rate. There is about a ±20% flow deviation from the mean value. Considering that the flow deviation level of the PBMR with one inlet pipe was about ±60% (Kim et al., 2006), we can postulate that the current configuration can provide a better flow distribution. The reason is that the hydraulic diameter of the inlet duct of the present plenum is smaller than that of the PBMR, that is, larger ratios of the plenum width and height to the hydraulic diameter, and it provides a sufficient space for an inlet flow expansion. If a configuration using two inlet pipes is introduced such as in the PBMR (Kim et al., 2006), the resultant flow deviation and pressure drop are expected to be reduced further.
Fig. 6. Static pressure contours at the inlet plenum.
occurs in the plenum. As the height increases, the magnitude of the maximum velocity decreases and the flow distribution becomes more uniform. Fig. 10 shows the distribution of the static pressure. Although the location of the high-pressure region does not change,
3.2. Upper plenum To establish how the flow distribution in the riser affects the core flow, CFD analyses were conducted for the upper plenum. A symmetrical half of the upper plenum was modeled including 27 riser holes and a core as shown in Fig. 8. For a simple modeling, an isothermal flow was assumed, in which the core was modeled to be a porous media with a pressure drop of 50 kPa (Reza et al., 2006). Inlet condition at each riser hole was obtained from the result of the inlet plenum analysis. Other boundary conditions were treated in the same manner as those for the inlet plenum. The height of the upper plenum was selected as a design parameter for a sensitivity study. The considered ratios of the plenum height to riser diameter (Hplenum /Driser ) are 1.0, 2.0, 3.0 and 4.0. Fig. 9 shows the velocity vectors at the mid-plane of the upper plenum in the cases of the height ratios of 1.0 and 3.0. A complex flow mixing
Fig. 7. Mass flow distribution at each riser hole.
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Fig. 8. Upper plenum geometry and boundary conditions.
Fig. 10. Static pressure distributions at the core inlet. (a) Hplenum /Driser = 0.1 and (b) Hplenum /Driser = 0.3.
the maximum pressure decreases the static pressure distribution becomes more uniform with an increase of the height. The effect of a height change is represented well in Fig. 11. It reveals pressure drops in the upper plenum and a normalized velocity variation at the core exit. Both the pressure drop and the velocity variation reduce and converge at a certain value as the plenum height increases. These results imply that a plenum height taller than three times the diameter of a riser hole is sufficient enough to obtain a minimized pressure drop and velocity variation in the present configuration.
Fig. 9. Velocity vector profiles at the upper plenum. (a) Hplenum /Driser = 0.1 and (b) Hplenum /Driser = 0.3.
Fig. 11. Pressure drop at the upper plenum and the velocity deviation at the core exit.
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Table 3 Physical properties of helium Properties Density (kg/m3 ) Conductivity (W/(m K)) Viscosity (N s/m2 )
Fig. 12. Meshes and boundary conditions for the RPV temperature analysis during a normal operation.
4. Analysis of vessel cooling effects 4.1. Normal operation The CFD code was employed to investigate the effect of a forced vessel cooling on the RPV temperature during a normal operation condition. Fig. 12 shows a computational domain selected for the RPV temperature analysis in a steady state, which is a 1/54 model of the entire domain consisting of a permanent side reflector (PSR), a riser, a core barrel, a gap between the RPV and the barrel, and the RPV. The inner and outer radii of the PSR are 2.415 and 3.425 m. The thickness of the core barrel, the gap, and the RPV are 75, 113, and 216 mm, respectively. The diameter of the riser is 200 mm. Three radial locations of the riser from the center axis of the core are used. The reference location is 3.223 m and the others are moved from it by ±60 mm. The height of the domain is 10.305 m which corresponds to 1 lower reflector block, 10 core blocks, and 2 upper reflector blocks. Uniform inlet velocity and constant static pressure conditions are used at the inlet and exit of the riser and the gap. The inlet mass flow rate at the riser is 5.925 kg/s at 590 ◦ C. The cooling flow rate of the cold helium to the gap is selected as a variable while its temperature and pressure conditions are fixed at 140 ◦ C and 7 MPa, respectively. Periodic conditions are applied in the circumferential direction. The heat transfer between the solid and fluid domains is treated by a so-called conjugate heat transfer method which solves the equations for a heat transfer in solid regions with no flow, so the heat flux at a wall is not provided by using a boundary condition but is computed implicitly from a numerical solution. General grid interface (GGI) connections in the ANSYS CFX (ANSYS, 2005) are used for the fluid–solid and solid–solid interfaces. K– turbulence model is selected for a turbulence closure with a scalable wall func-
Polynomial Expressions 39.881 − 0.18041T + 4.04423 × 10−4 T 2 −4.90968 × 10−7 T 3 + 3.27067 × 10−10 T 4 −1.1211410−13 T 5 + 1.5425710−17 T 6 0.05027 + 3.515110−4 T − 3.00999 × 10−8 T 2 5.42994 × 10−6 + 5.44595 × 10−8 T − 1.63587 × 10−11 T 2 + 2.8945210−15 T 3
tion method of the ANSYS CFX (ANSYS, 2005). The values of y+, the dimensionless wall distance, for the first mesh from the wall are set to be less than 50 for both the gap and riser regions. The discrete transfer model of the CFX code is used to consider a radiation heat transfer. Temperature distribution from the GAMMA system analysis code (Lim and No, 2006) is fixed for the inner wall of the PSR. In the thermal analysis, the physical properties of not only the helium but also the barrel, the PSR and the RPV are changed and dependent on the temperature. Tables 3 and 4 present the properties of the helium and solid materials used in the thermal analysis. There is a parasitic heat loss through the RPV during a normal operation due to a passive operation of the air-cooled reactor cavity cooling system (RCCS), which is designed to remove the residual heat during an accident. In order to model the parasitic heat loss to the RCCS, the CFD calculation was iterated with the GAMMA calculation. From the CFD calculation, the core barrel temperature was obtained by using an assumed heat loss, then, the GAMMA model as shown in Fig. 13 was used to calculate the heat loss from the barrel to the RCCS using the CFD results. This procedure was repeated three or four times to obtain a converged heat loss to the RCCS. Figs. 14 and 15 show the computed temperature contours at the middle plane and the temperature distribution along the centerline of the middle plane for the reference riser location. Both cases of with and without a vessel cooling flow were compared. It is shown that the RPV temperature can be reduced to the desired temperature by adjusting the vessel cooling flow conditions. It should be noted that there is a large amount of radiation heat transfer through the gap, which results in the RPV temperature being higher than the gap fluid temperature. To examine the effects of a convection and radiation on the heat transfer from the core to the RPV, the heat balance in the gap region for the cases with and without a vessel cooling are summarized in Table 5. When there is no vessel cooling, all of the heat coming from the barrel wall is fully transferred to the RPV wall. With a vessel cooling, however, the heat transfer from the barrel is increased by the heat removal of the cold helium flow but the heat transfer to the RPV is decreased when compared to the case of no vessel cooling. The radiation effect on the heat transfer to the RPV is very large, with amounts to 82.2% of the total heat flux in the case of
Table 4 Conductivity of the solid materials Alloy 800H (core barrel)
H451 (PSR)
SA-508 (RPV)
Temperature (K)
Conductivity (W/(m K))
Temperature (K)
Conductivity (W/(m K))
Temperature (K)
Conductivity (W/(m K))
294.3 366.5 477.6 588.7 699.8 810.9 922 1033.1 1144.3 1255.4
11.6 12.8 14.9 16.6 18.4 20.1 22.0 24.0 26.1 30.9
811.1 950.0 1088.9 1227.8 1366.7 1505.6
28.97 32.28 34.58 36.89 39.19 41.5
294 366 477 589 700 873
37.7 38.7 38.6 37.2 35.3 32.3
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Fig. 13. GAMMA model from the core barrel to the RCCS.
Fig. 15. Temperature distribution along the centerline of the middle plane. Fig. 14. Temperature contours at the middle plane.
Table 5 Heat balance in the gap region for the cases with and without a forced cooling Cooling
Location
Total
Convection
Radiation
No
Barrel wall RPV wall
−29.2 kWa (100%) 29.2 kW (100%)
−5.2 kW (17.8%) 5.2 kW (17.8%)
−24.0 kW (82.2%) 24.0 kW (82.2%)
6.4 kg/s
Barrel wall RPV wall
−65.4 kW (100%) 11.5 kW (39.0%)
−35.4 kW (54.1%) −18.0 kW (61.0%)
−30.0 kW (45.9%) 29.5 kW (100%)
a
The “−” sign means heat flux removed from the wall while no sign means that transferred to the wall.
M.-H. Kim et al. / Nuclear Engineering and Design 238 (2008) 3360–3369
Fig. 16. Maximum temperatures of the RPV according to a change of the cooling mass flow and riser location.
no cooling. Although there is no vessel cooling, a natural convection flux occurs, which transfers 17.8% of the total heat. For the case of a vessel cooling, the amount of radiation heat transfer increases due to the increased temperature difference between the walls as shown in Fig. 15 but its proportion decreases to 45.9% due to the increased amount of convective heat transfer. The effects of not only the cooling flow rate but also the riser location were investigated. Figs. 16 and 17 show the maximum temperatures of the RPV and the heat losses to the RCCS according to a change of the cooling flow rate and the riser location. The result for the case without a vessel cooling flow indicates the effect of changing the inlet flow configuration in the proposed cooledvessel concept. The maximum vessel temperature for the case with the original GT-MHR design was estimated to be about 577 ◦ C by the GAMMA code. By changing the coolant flow path direction into the graphite structure, that is, by precluding a direct contact of the coolant with the vessel wall, the RPV temperatures are reduced by 100–120 ◦ C and the consequent heat losses are also reduced. However, this reduction is not enough to maintain the temperature below the limit of SA-508/533 steel which is 371 ◦ C (ASME, 2001). When introducing a small amount of a vessel cooling flow, 3.2 kg/s, the temperature is reduced by 100 ◦ C. To ensure a temperature below 371 ◦ C, more than 4 kg/s of a vessel cooling flow is required. Moving the riser location closer to the core also reduces the resultant RPV temperature and heat losses. However, the shape
Fig. 17. Heat losses to the RCCS according to a change of the cooling mass flow and riser location.
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Fig. 18. Grid system of the 1/2 model for the thermal-fluid analysis of the cooled vessel.
of the original temperature variation due to a change of the vessel cooling flow is preserved. The validity of the 1/54 model used in this paper should be verified because the flow distribution at the riser is not uniform as revealed by the inlet plenum analysis of Section 3.1, which might result in a different convective heat transfer through the riser. So, a half domain model, a 1/2 model, was constructed as shown in Fig. 18. The model has 27 riser holes and their inlet condition was fixed as the mass flow distribution in Fig. 7. The other boundary conditions are the same as the 1/2 model except for the symmetric condition at the surface cutting the domain in a half. Fig. 19 shows the temperature contours at three arbitrary horizontal planes of the computational domain. Although a different inlet mass flow passes through each riser, the flow variation at the inlet plenum does not reveal a perceivable effect on the heat transfer from the core to the RPV. The maximum RPV temperatures between the 1/54 and the 1/2 models are compared in the Fig. 20.
Fig. 19. Temperature contours at the arbitrary planes of the computational domain.
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Fig. 20. Comparison of the maximum vessel temperature between the 1/54 and the 1/2 models.
Fig. 22. Maximum fuel temperature variation during the HPCC accident.
When the vessel cooling flow is zero, the two results present nearly the same results. As the cooling flow is introduced, the 1/2 model results in slightly higher values but the difference is not much more than 0.7%. The above results indicate that the flow distribution at the riser has little influence on the RPV temperature so that the 1/54 model is suitable for the thermo-fluid assessment of the proposed cooled vessel. 4.2. Accidents In this section, safety aspect of the cooled-vessel concept is investigated to examine if the integrity of the RPV is maintained during accident conditions. Two of the most limiting events are analyzed using the GAMMA code: the high-pressure conduction cooling (HPCC) and the low-pressure conduction cooling (LPCC) events. The HPCC event is initiated by a complete loss of a forced convection in a reactor coolant loop and a simultaneous failure of a shutdown cooling system. It is assumed that the initial vessel cooling flow at 3 kg/s and 140 ◦ C is lost with the occurrence of an event. Fig. 21 shows the maximum RPV temperature variation during the HPCC accident. It shows that the RPV temperature reaches its maximum of 463 ◦ C within 70 h and decreases to below the creep limit of 371 ◦ C in 186 h after reaching a peak temperature. According to
the ASME Section III Subsection NB with Code Case N-499-2, the SA-508/533 steel can be used for a temperature up to 538 ◦ C with a 1000 h limit. The exposure duration of the RPV above a temperature of 371 ◦ C during the HPCC event is 250 h, which is less than
Fig. 21. Maximum RPV temperature variation during the HPCC accident.
Fig. 24. Maximum fuel temperature variation during the LPCC accident.
Fig. 23. Maximum RPV temperature variation during the LPCC accident.
M.-H. Kim et al. / Nuclear Engineering and Design 238 (2008) 3360–3369
the 1000 h limit; however, it should be noted that the 1000 h limit accounts for a total exposure time during the lifetime of a reactor. The fuel temperature during the HPCC event is maintained below its limit of 1600 ◦ C with a sufficient margin, as shown in Fig. 22. Figs. 23 and 24 show the maximum RPV and fuel temperature variations during the LPCC accident. The RPV temperature increases to 517 ◦ C at 82 h and decreases to below 371 ◦ C at 488 h. The peak temperature is still below 538 ◦ C but the duration above 371 ◦ C is increased to 488 h when compared to the HPCC event. The peak fuel temperature during the LPCC event is 1516 ◦ C, which is still below its safety limit of 1600 ◦ C. 5. Conclusions A cooled-vessel concept has been assessed in view of its steady state operational performance and safety during accidents. In the proposed cooled-vessel concept, the riser flow path is directed through the permanent side reflector and then collected in the upper plenum which is also inside the upper part of the graphite core structure. Additional vessel cooling system is provided between the core barrel and the reactor vessel wall. The assessment of a conceptual design of the cooled vessel for a VHTR, which uses proven LWR steels as a material for the reactor vessel, was performed by computational methods. From the steady state CFD analysis, the flow distributions at the inlet and upper plenums and the thermal analysis for the effectiveness of a vessel cooling flow were performed. From the results, it was found that the flow distribution to the riser holes from the inlet plenum had a deviation of about ±20%, however, the flow distribution to the core became more uniform, that is, 3–7% of a deviation due to a mixing effect in the upper plenum. The recommended plenum height is about three times that of the riser diameter. The pressure drop through the inlet and upper plenums was estimated to be from 13 to 25 kPa with a height change. Analysis of the vessel cooling flow reveals that the modified inlet configuration, routing the coolant flow paths inside the permanent side reflector, can effectively reduce the RPV temperature; however, an additional vessel cooling system is required to reduce the RPV temperature further to meet the material limit of the SA508/533 conventional steel vessel. A vessel cooling flow of more than 4 kg/s at 140 ◦ C is sufficient enough to maintain the RPV temperature within the required limit during a normal operation. Moving the riser location inside the core also contributes to a reduction in the RPV temperature.
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For the safety assessment of the proposed cooled-vessel concept, the HPCC and LPCC events were analyzed. It was found that in both events the peak RPV temperatures were below the required limit, 538 ◦ C, and their durations above 371 ◦ C were 250 and 480 h, which are still below the required limit, 1000 h. The peak fuel temperature was also below the safety limit in both events, 1600 ◦ C. In conclusion, the proposed cooled-vessel concept is a feasible option for VHTR applications. However, further and more detailed studies are required to realize this concept, which are how to manufacture the required graphite blocks and pile them up to create the desired configuration, how to reduce or prevent a direct leakage flow from the riser to the core through the vertical gaps between the permanent side reflector blocks, and how to examine the influence of the proposed cooled-vessel concept on a plant’s safety and economy. Acknowledgement The authors gratefully acknowledge the financial support of The Korean Ministry of Science and Technology. References Ahmad, I., Kim, K.Y., Lee, W.J., and Park, G.C., 2007. Numerical study on flow field in inlet plenum of a pebble-bed modular reactor. Nucl. Eng. Deg. 237, 565–574. ANSYS Inc., 2005. CFX, release 10.0, reference manual. ASME, 2001. Use of SA-533 grade B, class 1 plate and SA-508 class 3 forgings and their weldments for limited elevated temperature service, Section III, Division 1, Case N-499-2. Chang, J., Kim, Y.W., Lee, K.Y., Lee, Y.W., Lee, J.L., Noh, J.M., Kim, M.H., Lim, H.S., Shin, Y.J., Bae, K.K., Jung, K.D., 2007. A study of a nuclear hydrogen production demonstration plant. Nucl. Eng. Technol. 39 (2), 111–122. Gougar, H.D., Davis, C.B., Hayner, G., Weaver, K., 2006. Reactor pressure vessel temperature analysis of candidate very high temperature reactor designs. In: Proceedings of the Third International Topical Meeting on High Temperature Reactor Technology, Johannesburg, South Africa, October 1–4. Hoffelner, W., 2004. High temperature materials—the challenge for future advanced gas cooled reactors. In: Proceedings of the International Congress on Advanced in Nuclear Power Plants (ICAPP), Pittsburgh, PA, USA, June 13–17. Kim, M.H., Lee, W.J., Chang, J., 2006. A computational study on an inlet plenum flow for a NHDD Plant. In: Proceedings of the International Congress on Advances in Nuclear Power Plants, Reno, NV, USA, June 4–8. Lim, H.S., No, H.C., 2006. GAMMA multi-dimensional multi-component mixture analysis to predict air ingress phenomena in an HTGR. Nucl. Sci. Eng. 152, 87–97. Matzner, D., 2004. PBMR project status and the way ahead. In: Second International Topical Meeting on High Temperature Reactor Technology, Beijing, China, September 20–24. Reza, S.M., Harvego, E.A., Richards, M., Shenoy, A., Peddicord, K.L., 2006. Design of an alternative coolant inlet flow configuration for the modular helium reactor. In: Proceedings of the International Congress on Advances in Nuclear Power Plants, Reno, NV, USA, June 4–8. Vieser, W., Esch T., Menter, F., 2002. Heat transfer predictions using advanced twoequation turbulence models. CFX technical memorandum, CFX-VAL10/0602.
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Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
A thermal-fluid assessment of a cooled-vessel concept for a VHTR Min-Hwan Kim ∗ , Hong-Sik Lim, Won-Jae Lee Korea Atomic Energy Research Institute, 1045 Daedeokdaero, Yoseong, Daejeon 304-353, South Korea
a r t i c l e
i n f o
Article history: Received 20 December 2007 Received in revised form 29 May 2008 Accepted 25 June 2008
a b s t r a c t Flow distribution and thermal analyses of a conceptual design of a cooled vessel for a very high temperature reactor (VHTR), which has a forced vessel cooling with an internal coolant path through a permanent side reflector, have been performed. A computational fluid dynamics (CFD) code was employed to investigate flow distributions at inlet and upper plenums of the proposed cooled-vessel concept. Thermal-fluid analyses of the cooled vessel during a normal operation were carried out by using the CFD code with the boundary conditions provided by the GAMMA system analysis code. The transient analyses during postulated accidents were conducted by the GAMMA code itself. According to the results, the flow deviation at the riser holes due to a change of the inlet flow path to the core inlet is about ±20% which results in about a 3–7% core flow deviation from the average value depending on the upper plenum height. The pressure drops in the inlet and upper plenums are estimated to be from 13 to 25 kPa with a change of the upper plenum height. A cooling flow of more than 4 kg/s is sufficient to maintain the RPV temperature within the required limit during a normal operation. Transient analysis reveals that the reactor vessel is exposed to a temperature above its limit of 371 ◦ C but this duration is shorter than the allowable time for a creep region with a sufficient safety margin. The results suggest that the cooled-vessel concept considered in this paper has the potential to be used for a VHTR but further and more detailed studies are required to realize the proposed concept. © 2008 Elsevier B.V. All rights reserved.
1. Introduction The very high temperature (gas-cooled) reactor (VHTR) has become of great interest in connection with a process heat application such as a hydrogen production. The Nuclear Hydrogen Development and Demonstration (NHDD) project has been launched at KAERI (Korea Atomic Energy Research Institute). The NHDD plant is a VHTR coupled to a hydrogen production plant using a sulfur–iodine process via an intermediate loop (Chang et al., 2007). It has not been determined yet whether the reactor type should be a pebble bed reactor (PBR) or a prismatic modular reactor (PMR). However, the design of the reactor pressure vessel (RPV) is very important, and is of interest (Hoffelner, 2004; Gougar et al., 2006), regardless of the reactor type because the operating temperature of the RPV in a VHTR is much higher than that in a light water reactor. The cooled-vessel concept makes it possible to use conventional SA-508/533 steel (ASME, 2001) as the material for the RPV of a VHTR. The PBMR in South Africa (Matzner, 2004) adopts a conventional SA-508 cooled-vessel design in which the coolant flow is
∗ Corresponding author. Tel.: +82 42 868 8102; fax: +82 42 868 8767. E-mail address: [email protected] (M.-H. Kim). 0029-5493/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2008.06.022
directed through internal graphite structures, and a vessel cooling system is used to cool the RPV inner wall. The GT-MHR by General Atomics selected a creep-resistant material for their RPV, which has not been manufactured on a large scale as yet, and also its welding procedure has not been established, so they have considered an alternative design (Reza et al., 2006) for their VHTR for a hydrogen production, which uses conventional steel instead of a creep-resistant material. Therefore, it is meaningful to consider an alternative design for a NHDD prismatic reactor. In this paper, we propose a cooled-vessel concept applicable to a NHDD prismatic reactor, which is characterized by an internal flow path and a vessel cooling, and then we carried out thermo-fluid analyses by using the CFX (ANSYS, 2005) and GAMMA codes (Lim and No, 2006) to establish whether this concept has the potential for a future use. The analyses include an analysis of the flow distribution through an internal flow path and an assessment of the vessel cooling performance during a normal operation and accidents. 2. Description of the cooled-vessel concept The GT-MHR is selected as a reference PMR to apply the proposed cooled-vessel concept. Coolant thermo-fluid design conditions of both the GT-MHR and the NHDD are given in Table 1.
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Table 1 Thermo-fluid design conditions of GT-MHR and the present MHR Parameter
GT-MHR
NHDD
Core power (MW) Core inlet temperature (◦ C) Core outlet temperature (◦ C) Operating pressure (MPa) Helium mass flow (kg/s)
600 490 850 7 320
600 590 950 7 320
The reactor power, operating pressure, and helium mass flow of the NHDD reactor are the same as those of the GT-MHR but its core outlet temperature is increased to 950 ◦ C for efficient hydrogen production. Without changing the core design of the GT-MHR, the increase of the coolant outlet temperature results in an increase of the coolant inlet temperature up to 590 ◦ C. In the GT-MHR, the inlet coolant flow is routed through the coolant channels between the core barrel and the RPV as shown in Fig. 1. With the GT-MHR inlet configuration, the elevated inlet temperature of the NHDD would result in an increase of the reactor vessel temperature which would exceed the operating limit of the creep-resistant material. To reduce the influence of the increase in the inlet temperature on the reactor vessel temperature, the inlet flow path through the channels is routed to cylindrical riser holes through a permanent side reflector. A modified inlet flow configuration of the cooled vessel is shown in Figs. 2 and 3. The inlet flow coming from the outside of the coaxial duct is supplied to the inlet plenum, a large annular space below the permanent side reflector, in which the flow is distributed into the riser holes. After passing through the riser holes, the flow gathers at the upper plenum and is supplied to the core. The diameter of a riser hole is determined to maintain a total area comparable to that of the coolant channels of the GT-MHR in Fig. 1, 1.6417 m2 (Reza et al., 2006). The number of riser holes is 54, and the diameter of a hole is 0.2 m. At the upper plenum, three riser holes are grouped to buffer the non-uniform flow from the riser, and then the flow is supplied to the upper part of the core through the slits in the graphite structure. A vessel cooling flow is supplied to the annular gap between the RPV and the core barrel, where the coolant channels of the GT-MHR are installed. Cold helium for the vessel
Fig. 1. GT-MHR inlet flow path and cross-section at the middle plane.
cooling flow can be supplied by using a slipstream flow from the helium purification system which removes chemical and radioactive impurities from the primary helium coolant. If the required amount of cooling flow is too large to be supplied by the helium
Fig. 2. Configuration of the cooled-vessel design concept.
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M.-H. Kim et al. / Nuclear Engineering and Design 238 (2008) 3360–3369 Table 2 Coolant conditions at the inlet plenum Parameter
Value ◦
Temperature ( C) Pressure (bar) Mass flow (kg/s) Density (kg/m3 ) Viscosity (N s/m2 )
Fig. 3. Cross-section of the middle plane of the cooled vessel.
purification system, a dedicated vessel cooling system needs to be installed. 3. Analyses of flow distributions 3.1. Inlet plenum An analysis using a computational fluid dynamics (CFD) code, CFX-10 (ANSYS, 2005), is performed to establish how the flow is distributed at the riser holes. Fig. 4 shows the geometric configuration and the applied boundary conditions. The inlet plenum connects the outer annulus of the hot duct and the 54 riser holes. The coolant from the annular inlet duct is supplied to the plenum and sent to
Fig. 4. Inlet plenum domain and boundary conditions.
590 70 320 (160 for the half inlet) 3.868 4.111 × 10−5
the upper side of the reactor core through the riser holes. The inlet plenum has a symmetrical shape, so only a half of the plenum is selected for the CFD analysis. For the mesh generation, the domain was divided into three regions which are the inlet pipe, the plenum and the riser, respectively. The mesh extrusion method that creates prism meshes for the center region and hexahedral meshes for the boundary layer region was used for the inlet pipe and the riser, respectively. Due to the complexity of the flow field, tetrahedral meshes were used for the plenum with prism meshes for the wall boundary region. The total number of nodes was 1,205,002. This number is considered to be sufficient enough for the present study because a previous study for the inlet plenum of a pebble-bed reactor (Ahmad et al., 2007) indicated that a node number of more than 400,000 was sufficient enough to resolve the flow distribution at their inlet plenum. The three-dimensional Navier–Stokes equations were integrated for the inlet plenum analysis in which an isothermal flow was assumed because there is no large temperature variation at the inlet plenum. Table 2 shows the coolant conditions at the inlet plenum. A constant mass flow is set for the inlet boundary condition. At the outlet boundary of the 27 riser holes, a constant static pressure is applied because the length of the riser, 15 times that of the riser hole diameter, is sufficient enough so that the flow in the plenum cannot be affected by the static pressure condition at the riser outlet. Symmetric and wall conditions are applied for the other boundaries. The Reynolds number based on the hydraulic diameter of the inlet duct is 2.52 × 106 , which means the flow is turbulent. The shear stress transport (SST) model with an automatic near-wall treatment (Vieser et al., 2002) was adopted for a turbulence closure in this complex geometry. A turbulence intensity of 5% was assumed at the inlet boundary. Fig. 5 shows the streamline distribution at the inlet plenum. The flow coming from the annular inlet duct expands rapidly at the inlet plenum and the maximum velocity increases by nearly up to twice that of the inlet velocity. The expanded and accelerated flow is spread throughout the whole plenum, and is distributed to each riser hole. Recirculation flow is observed at the riser holes near the inlet duct. Fig. 6 shows the pressure distribution at the inlet plenum for three horizontal planes (z = −1 m, z = 0 m, z = +1 m) and a mid-surface of the annular plenum. High pressure occurs at the wall where the inlet flow impinges on it, whereas a low pressure occurs at the riser holes, where a flow separation is observed. It should be noted that a high pressure comparable to that of the inlet region occurs at the opposite side of it, which is expected to result in a higher flow rate in a riser further from the inlet duct. Total pressure drop at the plenum region is estimated to be about 7.9 kPa. Mass flow at each riser hole is computed by averaging the exit velocities over their area. Fig. 7 shows the mass flow distribution at a riser. The horizontal axis represents an assigned number for each riser hole. Number 1 corresponds to the nearest hole to the inlet duct and Number 27 to the farthest riser hole from the inlet duct. The vertical axis is a mass flow deviation (Si ) normalized by
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Fig. 5. Streamlines at the inlet plenum.
an average value, defined as Si =
mi − mavg mavg
(1)
where mi is the mass flow rate at each riser, mavg is the average mass flow rate computed by dividing the inlet mass flow rate by the total number of riser holes, and subscript i corresponds to the assigned number of the riser varying from 1, near to the inlet duct, to 27, the opposite side of it. The holes near to the inlet duct, in which a flow separation occurs, have a relatively lower flow rate and those far from the inlet duct have a higher flow rate. There is about a ±20% flow deviation from the mean value. Considering that the flow deviation level of the PBMR with one inlet pipe was about ±60% (Kim et al., 2006), we can postulate that the current configuration can provide a better flow distribution. The reason is that the hydraulic diameter of the inlet duct of the present plenum is smaller than that of the PBMR, that is, larger ratios of the plenum width and height to the hydraulic diameter, and it provides a sufficient space for an inlet flow expansion. If a configuration using two inlet pipes is introduced such as in the PBMR (Kim et al., 2006), the resultant flow deviation and pressure drop are expected to be reduced further.
Fig. 6. Static pressure contours at the inlet plenum.
occurs in the plenum. As the height increases, the magnitude of the maximum velocity decreases and the flow distribution becomes more uniform. Fig. 10 shows the distribution of the static pressure. Although the location of the high-pressure region does not change,
3.2. Upper plenum To establish how the flow distribution in the riser affects the core flow, CFD analyses were conducted for the upper plenum. A symmetrical half of the upper plenum was modeled including 27 riser holes and a core as shown in Fig. 8. For a simple modeling, an isothermal flow was assumed, in which the core was modeled to be a porous media with a pressure drop of 50 kPa (Reza et al., 2006). Inlet condition at each riser hole was obtained from the result of the inlet plenum analysis. Other boundary conditions were treated in the same manner as those for the inlet plenum. The height of the upper plenum was selected as a design parameter for a sensitivity study. The considered ratios of the plenum height to riser diameter (Hplenum /Driser ) are 1.0, 2.0, 3.0 and 4.0. Fig. 9 shows the velocity vectors at the mid-plane of the upper plenum in the cases of the height ratios of 1.0 and 3.0. A complex flow mixing
Fig. 7. Mass flow distribution at each riser hole.
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Fig. 8. Upper plenum geometry and boundary conditions.
Fig. 10. Static pressure distributions at the core inlet. (a) Hplenum /Driser = 0.1 and (b) Hplenum /Driser = 0.3.
the maximum pressure decreases the static pressure distribution becomes more uniform with an increase of the height. The effect of a height change is represented well in Fig. 11. It reveals pressure drops in the upper plenum and a normalized velocity variation at the core exit. Both the pressure drop and the velocity variation reduce and converge at a certain value as the plenum height increases. These results imply that a plenum height taller than three times the diameter of a riser hole is sufficient enough to obtain a minimized pressure drop and velocity variation in the present configuration.
Fig. 9. Velocity vector profiles at the upper plenum. (a) Hplenum /Driser = 0.1 and (b) Hplenum /Driser = 0.3.
Fig. 11. Pressure drop at the upper plenum and the velocity deviation at the core exit.
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Table 3 Physical properties of helium Properties Density (kg/m3 ) Conductivity (W/(m K)) Viscosity (N s/m2 )
Fig. 12. Meshes and boundary conditions for the RPV temperature analysis during a normal operation.
4. Analysis of vessel cooling effects 4.1. Normal operation The CFD code was employed to investigate the effect of a forced vessel cooling on the RPV temperature during a normal operation condition. Fig. 12 shows a computational domain selected for the RPV temperature analysis in a steady state, which is a 1/54 model of the entire domain consisting of a permanent side reflector (PSR), a riser, a core barrel, a gap between the RPV and the barrel, and the RPV. The inner and outer radii of the PSR are 2.415 and 3.425 m. The thickness of the core barrel, the gap, and the RPV are 75, 113, and 216 mm, respectively. The diameter of the riser is 200 mm. Three radial locations of the riser from the center axis of the core are used. The reference location is 3.223 m and the others are moved from it by ±60 mm. The height of the domain is 10.305 m which corresponds to 1 lower reflector block, 10 core blocks, and 2 upper reflector blocks. Uniform inlet velocity and constant static pressure conditions are used at the inlet and exit of the riser and the gap. The inlet mass flow rate at the riser is 5.925 kg/s at 590 ◦ C. The cooling flow rate of the cold helium to the gap is selected as a variable while its temperature and pressure conditions are fixed at 140 ◦ C and 7 MPa, respectively. Periodic conditions are applied in the circumferential direction. The heat transfer between the solid and fluid domains is treated by a so-called conjugate heat transfer method which solves the equations for a heat transfer in solid regions with no flow, so the heat flux at a wall is not provided by using a boundary condition but is computed implicitly from a numerical solution. General grid interface (GGI) connections in the ANSYS CFX (ANSYS, 2005) are used for the fluid–solid and solid–solid interfaces. K– turbulence model is selected for a turbulence closure with a scalable wall func-
Polynomial Expressions 39.881 − 0.18041T + 4.04423 × 10−4 T 2 −4.90968 × 10−7 T 3 + 3.27067 × 10−10 T 4 −1.1211410−13 T 5 + 1.5425710−17 T 6 0.05027 + 3.515110−4 T − 3.00999 × 10−8 T 2 5.42994 × 10−6 + 5.44595 × 10−8 T − 1.63587 × 10−11 T 2 + 2.8945210−15 T 3
tion method of the ANSYS CFX (ANSYS, 2005). The values of y+, the dimensionless wall distance, for the first mesh from the wall are set to be less than 50 for both the gap and riser regions. The discrete transfer model of the CFX code is used to consider a radiation heat transfer. Temperature distribution from the GAMMA system analysis code (Lim and No, 2006) is fixed for the inner wall of the PSR. In the thermal analysis, the physical properties of not only the helium but also the barrel, the PSR and the RPV are changed and dependent on the temperature. Tables 3 and 4 present the properties of the helium and solid materials used in the thermal analysis. There is a parasitic heat loss through the RPV during a normal operation due to a passive operation of the air-cooled reactor cavity cooling system (RCCS), which is designed to remove the residual heat during an accident. In order to model the parasitic heat loss to the RCCS, the CFD calculation was iterated with the GAMMA calculation. From the CFD calculation, the core barrel temperature was obtained by using an assumed heat loss, then, the GAMMA model as shown in Fig. 13 was used to calculate the heat loss from the barrel to the RCCS using the CFD results. This procedure was repeated three or four times to obtain a converged heat loss to the RCCS. Figs. 14 and 15 show the computed temperature contours at the middle plane and the temperature distribution along the centerline of the middle plane for the reference riser location. Both cases of with and without a vessel cooling flow were compared. It is shown that the RPV temperature can be reduced to the desired temperature by adjusting the vessel cooling flow conditions. It should be noted that there is a large amount of radiation heat transfer through the gap, which results in the RPV temperature being higher than the gap fluid temperature. To examine the effects of a convection and radiation on the heat transfer from the core to the RPV, the heat balance in the gap region for the cases with and without a vessel cooling are summarized in Table 5. When there is no vessel cooling, all of the heat coming from the barrel wall is fully transferred to the RPV wall. With a vessel cooling, however, the heat transfer from the barrel is increased by the heat removal of the cold helium flow but the heat transfer to the RPV is decreased when compared to the case of no vessel cooling. The radiation effect on the heat transfer to the RPV is very large, with amounts to 82.2% of the total heat flux in the case of
Table 4 Conductivity of the solid materials Alloy 800H (core barrel)
H451 (PSR)
SA-508 (RPV)
Temperature (K)
Conductivity (W/(m K))
Temperature (K)
Conductivity (W/(m K))
Temperature (K)
Conductivity (W/(m K))
294.3 366.5 477.6 588.7 699.8 810.9 922 1033.1 1144.3 1255.4
11.6 12.8 14.9 16.6 18.4 20.1 22.0 24.0 26.1 30.9
811.1 950.0 1088.9 1227.8 1366.7 1505.6
28.97 32.28 34.58 36.89 39.19 41.5
294 366 477 589 700 873
37.7 38.7 38.6 37.2 35.3 32.3
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Fig. 13. GAMMA model from the core barrel to the RCCS.
Fig. 15. Temperature distribution along the centerline of the middle plane. Fig. 14. Temperature contours at the middle plane.
Table 5 Heat balance in the gap region for the cases with and without a forced cooling Cooling
Location
Total
Convection
Radiation
No
Barrel wall RPV wall
−29.2 kWa (100%) 29.2 kW (100%)
−5.2 kW (17.8%) 5.2 kW (17.8%)
−24.0 kW (82.2%) 24.0 kW (82.2%)
6.4 kg/s
Barrel wall RPV wall
−65.4 kW (100%) 11.5 kW (39.0%)
−35.4 kW (54.1%) −18.0 kW (61.0%)
−30.0 kW (45.9%) 29.5 kW (100%)
a
The “−” sign means heat flux removed from the wall while no sign means that transferred to the wall.
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Fig. 16. Maximum temperatures of the RPV according to a change of the cooling mass flow and riser location.
no cooling. Although there is no vessel cooling, a natural convection flux occurs, which transfers 17.8% of the total heat. For the case of a vessel cooling, the amount of radiation heat transfer increases due to the increased temperature difference between the walls as shown in Fig. 15 but its proportion decreases to 45.9% due to the increased amount of convective heat transfer. The effects of not only the cooling flow rate but also the riser location were investigated. Figs. 16 and 17 show the maximum temperatures of the RPV and the heat losses to the RCCS according to a change of the cooling flow rate and the riser location. The result for the case without a vessel cooling flow indicates the effect of changing the inlet flow configuration in the proposed cooledvessel concept. The maximum vessel temperature for the case with the original GT-MHR design was estimated to be about 577 ◦ C by the GAMMA code. By changing the coolant flow path direction into the graphite structure, that is, by precluding a direct contact of the coolant with the vessel wall, the RPV temperatures are reduced by 100–120 ◦ C and the consequent heat losses are also reduced. However, this reduction is not enough to maintain the temperature below the limit of SA-508/533 steel which is 371 ◦ C (ASME, 2001). When introducing a small amount of a vessel cooling flow, 3.2 kg/s, the temperature is reduced by 100 ◦ C. To ensure a temperature below 371 ◦ C, more than 4 kg/s of a vessel cooling flow is required. Moving the riser location closer to the core also reduces the resultant RPV temperature and heat losses. However, the shape
Fig. 17. Heat losses to the RCCS according to a change of the cooling mass flow and riser location.
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Fig. 18. Grid system of the 1/2 model for the thermal-fluid analysis of the cooled vessel.
of the original temperature variation due to a change of the vessel cooling flow is preserved. The validity of the 1/54 model used in this paper should be verified because the flow distribution at the riser is not uniform as revealed by the inlet plenum analysis of Section 3.1, which might result in a different convective heat transfer through the riser. So, a half domain model, a 1/2 model, was constructed as shown in Fig. 18. The model has 27 riser holes and their inlet condition was fixed as the mass flow distribution in Fig. 7. The other boundary conditions are the same as the 1/2 model except for the symmetric condition at the surface cutting the domain in a half. Fig. 19 shows the temperature contours at three arbitrary horizontal planes of the computational domain. Although a different inlet mass flow passes through each riser, the flow variation at the inlet plenum does not reveal a perceivable effect on the heat transfer from the core to the RPV. The maximum RPV temperatures between the 1/54 and the 1/2 models are compared in the Fig. 20.
Fig. 19. Temperature contours at the arbitrary planes of the computational domain.
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Fig. 20. Comparison of the maximum vessel temperature between the 1/54 and the 1/2 models.
Fig. 22. Maximum fuel temperature variation during the HPCC accident.
When the vessel cooling flow is zero, the two results present nearly the same results. As the cooling flow is introduced, the 1/2 model results in slightly higher values but the difference is not much more than 0.7%. The above results indicate that the flow distribution at the riser has little influence on the RPV temperature so that the 1/54 model is suitable for the thermo-fluid assessment of the proposed cooled vessel. 4.2. Accidents In this section, safety aspect of the cooled-vessel concept is investigated to examine if the integrity of the RPV is maintained during accident conditions. Two of the most limiting events are analyzed using the GAMMA code: the high-pressure conduction cooling (HPCC) and the low-pressure conduction cooling (LPCC) events. The HPCC event is initiated by a complete loss of a forced convection in a reactor coolant loop and a simultaneous failure of a shutdown cooling system. It is assumed that the initial vessel cooling flow at 3 kg/s and 140 ◦ C is lost with the occurrence of an event. Fig. 21 shows the maximum RPV temperature variation during the HPCC accident. It shows that the RPV temperature reaches its maximum of 463 ◦ C within 70 h and decreases to below the creep limit of 371 ◦ C in 186 h after reaching a peak temperature. According to
the ASME Section III Subsection NB with Code Case N-499-2, the SA-508/533 steel can be used for a temperature up to 538 ◦ C with a 1000 h limit. The exposure duration of the RPV above a temperature of 371 ◦ C during the HPCC event is 250 h, which is less than
Fig. 21. Maximum RPV temperature variation during the HPCC accident.
Fig. 24. Maximum fuel temperature variation during the LPCC accident.
Fig. 23. Maximum RPV temperature variation during the LPCC accident.
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the 1000 h limit; however, it should be noted that the 1000 h limit accounts for a total exposure time during the lifetime of a reactor. The fuel temperature during the HPCC event is maintained below its limit of 1600 ◦ C with a sufficient margin, as shown in Fig. 22. Figs. 23 and 24 show the maximum RPV and fuel temperature variations during the LPCC accident. The RPV temperature increases to 517 ◦ C at 82 h and decreases to below 371 ◦ C at 488 h. The peak temperature is still below 538 ◦ C but the duration above 371 ◦ C is increased to 488 h when compared to the HPCC event. The peak fuel temperature during the LPCC event is 1516 ◦ C, which is still below its safety limit of 1600 ◦ C. 5. Conclusions A cooled-vessel concept has been assessed in view of its steady state operational performance and safety during accidents. In the proposed cooled-vessel concept, the riser flow path is directed through the permanent side reflector and then collected in the upper plenum which is also inside the upper part of the graphite core structure. Additional vessel cooling system is provided between the core barrel and the reactor vessel wall. The assessment of a conceptual design of the cooled vessel for a VHTR, which uses proven LWR steels as a material for the reactor vessel, was performed by computational methods. From the steady state CFD analysis, the flow distributions at the inlet and upper plenums and the thermal analysis for the effectiveness of a vessel cooling flow were performed. From the results, it was found that the flow distribution to the riser holes from the inlet plenum had a deviation of about ±20%, however, the flow distribution to the core became more uniform, that is, 3–7% of a deviation due to a mixing effect in the upper plenum. The recommended plenum height is about three times that of the riser diameter. The pressure drop through the inlet and upper plenums was estimated to be from 13 to 25 kPa with a height change. Analysis of the vessel cooling flow reveals that the modified inlet configuration, routing the coolant flow paths inside the permanent side reflector, can effectively reduce the RPV temperature; however, an additional vessel cooling system is required to reduce the RPV temperature further to meet the material limit of the SA508/533 conventional steel vessel. A vessel cooling flow of more than 4 kg/s at 140 ◦ C is sufficient enough to maintain the RPV temperature within the required limit during a normal operation. Moving the riser location inside the core also contributes to a reduction in the RPV temperature.
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For the safety assessment of the proposed cooled-vessel concept, the HPCC and LPCC events were analyzed. It was found that in both events the peak RPV temperatures were below the required limit, 538 ◦ C, and their durations above 371 ◦ C were 250 and 480 h, which are still below the required limit, 1000 h. The peak fuel temperature was also below the safety limit in both events, 1600 ◦ C. In conclusion, the proposed cooled-vessel concept is a feasible option for VHTR applications. However, further and more detailed studies are required to realize this concept, which are how to manufacture the required graphite blocks and pile them up to create the desired configuration, how to reduce or prevent a direct leakage flow from the riser to the core through the vertical gaps between the permanent side reflector blocks, and how to examine the influence of the proposed cooled-vessel concept on a plant’s safety and economy. Acknowledgement The authors gratefully acknowledge the financial support of The Korean Ministry of Science and Technology. References Ahmad, I., Kim, K.Y., Lee, W.J., and Park, G.C., 2007. Numerical study on flow field in inlet plenum of a pebble-bed modular reactor. Nucl. Eng. Deg. 237, 565–574. ANSYS Inc., 2005. CFX, release 10.0, reference manual. ASME, 2001. Use of SA-533 grade B, class 1 plate and SA-508 class 3 forgings and their weldments for limited elevated temperature service, Section III, Division 1, Case N-499-2. Chang, J., Kim, Y.W., Lee, K.Y., Lee, Y.W., Lee, J.L., Noh, J.M., Kim, M.H., Lim, H.S., Shin, Y.J., Bae, K.K., Jung, K.D., 2007. A study of a nuclear hydrogen production demonstration plant. Nucl. Eng. Technol. 39 (2), 111–122. Gougar, H.D., Davis, C.B., Hayner, G., Weaver, K., 2006. Reactor pressure vessel temperature analysis of candidate very high temperature reactor designs. In: Proceedings of the Third International Topical Meeting on High Temperature Reactor Technology, Johannesburg, South Africa, October 1–4. Hoffelner, W., 2004. High temperature materials—the challenge for future advanced gas cooled reactors. In: Proceedings of the International Congress on Advanced in Nuclear Power Plants (ICAPP), Pittsburgh, PA, USA, June 13–17. Kim, M.H., Lee, W.J., Chang, J., 2006. A computational study on an inlet plenum flow for a NHDD Plant. In: Proceedings of the International Congress on Advances in Nuclear Power Plants, Reno, NV, USA, June 4–8. Lim, H.S., No, H.C., 2006. GAMMA multi-dimensional multi-component mixture analysis to predict air ingress phenomena in an HTGR. Nucl. Sci. Eng. 152, 87–97. Matzner, D., 2004. PBMR project status and the way ahead. In: Second International Topical Meeting on High Temperature Reactor Technology, Beijing, China, September 20–24. Reza, S.M., Harvego, E.A., Richards, M., Shenoy, A., Peddicord, K.L., 2006. Design of an alternative coolant inlet flow configuration for the modular helium reactor. In: Proceedings of the International Congress on Advances in Nuclear Power Plants, Reno, NV, USA, June 4–8. Vieser, W., Esch T., Menter, F., 2002. Heat transfer predictions using advanced twoequation turbulence models. CFX technical memorandum, CFX-VAL10/0602.