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Design parameters in an annular, prismatic HTGR for passive decay heat removal
Annals of Nuclear Energy 111 (2018) 441–448
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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Technical note
Design parameters in an annular, prismatic HTGR for passive decay heat removal Odmaa Sambuu a,b,⇑, Jamyansuren Terbish b, Toru Obara c, Norov Nanzad a,b, Munkhbat Byambajav a,b a Department of Chemical and Biological Engineering, School of Engineering and Applied Sciences, National University of Mongolia, Ikh surguuliin gudamj 3, Sukhbaatar District, Ulaanbaatar 14201, Mongolia b Nuclear Research Center, National University of Mongolia, Peace Avenue 122, Bayanzurkh District, Ulaanbaatar 14201, Mongolia c Laboratory for Advanced Nuclear Energy, Institute of Innovative Research, Tokyo Institute of Technology, 2-12-1-N1-19, Ookayama, Meguro-ku, Tokyo 152-8550, Japan
a r t i c l e
i n f o
Article history: Received 22 March 2017 Received in revised form 10 August 2017 Accepted 17 September 2017
Keywords: Passive decay-heat removal Prismatic HTGR Uniform power density Economy
a b s t r a c t We studied the capability of an annular, prismatic HTGR to remove decay heat passively. The purpose of the study was to obtain the design parameters relationship of the annular, prismatic HTGR with passive decay heat removal depending on power density profile and to compare them with those for solid cylinder one. The results showed that the safety feature of the annular reactor is improved a lot compared with that of cylinder one. The safety margin could be increased further by flattening the power density profile. Then fundamental neutronic analysis was performed for the annular reactor whose design parameters are obtained from the condition. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction Reactor design idea which does not rely on the active safety system for reactor safety condition is growing up. This idea or reactor design idea with passive safety system is one of the main features for new generation IV reactor concepts. High-temperature gascooled reactors (HTGRs) as base of the very high temperature reactor (VHTR) concept have several inherent safety features such as high-integrity of coated fuel particles (CFPs) up to 1873 K, highheat-capacity graphite core and support structures and inert helium coolant. Furthermore it is said that the integrity of the CFPs are highly dependent on the following safety functions to be assured: core heat removal, control of heat generation and limitation of chemical corrosion. Among those functions the most important one is successful removal of core heat after reactor shutdown (Hicks et al., 2011; Kroeger, 1990; Hayashi et al., 1989). In our previous papers, we studied the dependence of design parameters of solid cylinder HTGRs which can remove decay heat by passive ways (Odmaa and Obara, 2014, 2015a,b, 2016). This relationship was restrained by design limits of the fuel and structural temperatures and the capability of the reactor to remove ⇑ Corresponding author at: Department of Chemical and Biological Engineering, School of Engineering and Applied Sciences, National University of Mongolia, Ikh surguuliin gudamj 3, Sukhbaatar District, Ulaanbaatar 14201, Mongolia. E-mail addresses: [email protected], [email protected] (O. Sambuu). https://doi.org/10.1016/j.anucene.2017.09.034 0306-4549/Ó 2017 Elsevier Ltd. All rights reserved.
decay heat was limited only by the passive ways considering three main mechanisms as thermal conduction, radiation and convection. The severest condition was assumed for the previous papers in which all cooling systems including active and passive ones were completely lost their performance due to natural disaster. In this paper, we extended the research by choosing the annular cylinder, prismatic HTGRs in which the fuel blocks at the core center region are replaced by graphite blocks. Since there is no heat source in inner reflector for annular cylinder core and graphite has high heat capacity, some amount of heat in core could be transferred into the inner graphite reflector during operation and after shutdown. Therefore, it is expected that the safety feature of the annular HTGRs would be improved due to the maximum fuel temperature of the core is reduced. Then, by taking into account the above advantage of the annular core, it is possible to enhance the reactor power. So, in the present work we have studied the capability of an above-ground, annular, prismatic HTGR to remove decay heat passively by obtaining quantitative relationship between reactor design parameters. The power density profile throughout reactor core is considered as flattened or unflattened. The purpose of the present study is to reveal the impact of inner reflector on the annular cylinder reactor safety feature by confirming the reduction of the maximum fuel temperature of annular cylinder core, to obtain the design parameters relationship of an above-ground, annular, prismatic HTGR with passive decay heat removal depending on power density profiles and to compare them with those for solid cylinder, prismatic HTGR. Therefore, fundamental neutronic
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analysis for the annular reactor whose design parameters are obtained from the condition was performed to confirm its longterm operation without refueling and its higher fuel burnup.
2. Design concept We studied the design of solid cylinder HTGR with passive decay heat removal in our previous works (Odmaa and Obara, 2014, 2015a,b, 2016). The reactor core designs in previous and present works are based on the Japanese prismatic HTTR as a reference (Saito et al., 1991, 1994; Shiozowa et al., 2004; Evaluation of HTGR Performance, 2003). The general layouts of the both solid and annular reactor designs are illustrated in Fig. 1a and b respectively. Here other compartments of the design except core with reflector are the same with these for the solid cylinder reactor. In solid cylinder reactor, the core has only outer reflector as shown in Fig. 1a while annular core has both inner and outer reflectors as in Fig. 1b. Compartments in both reactor are the same as those being in HTTR. As illustrated in Fig. 1, the decay heat transfers through the solid structural domains by heat conduction mechanism and through air domains by thermal radiation. Finally, the heat is dissipated through the air on the reactor building wall by both outside natural convection and thermal radiation. Table 1 compares the dimensions of the HTTR with thermal power of 30 MWt (Saito et al., 1991, 1994; Shiozowa and et al., 2004; Evaluation of HTGR Performance, 2003) and both the reference designs of solid cylinder and annular reactor with thermal power of 200 MWt and average power density of 0.82 W/cm3. The reference design for solid cylinder reactor shown in Table 1 was chosen for our previous paper (Odmaa and Obara, 2016) and in this work, we have chosen the annular cylinder reactor with the same thermal power and average power density for comparison of results to be obtained in this work. In our previous works (Odmaa and Obara, 2014; Odmaa and Obara, 2016) the decay heat transfer analyses were performed for both types of prismatic and pebble bed HTGRs to choose the optimal ratio of core radius and height by comparing the obtained the peak core temperatures after shutdown for the same power reactors with different ratio and without changing the core volume. The ratio of radius to height corresponded to the highest peak core temperature is considered as the worst one which was between 0.46 and 0.55 depending on reactor power and core
temperature at shutdown. So, for barrel type of solid cylindrical prismatic and pebble bed HTGRs, the optimal ratio of core radius and height was chosen as 0.4 and kept this ratio for the future analyses for parametric conditions in order to reduce the number of considerable parameters on comparison of similarity or difference between the conditions for annular and solid cylindrical reactors. So, the same ratio of core radius and height as 0.4, the same materials for the corresponding domains, and the same physical characteristics of region materials applied in previous works (Odmaa and Obara, 2014, 2015a,b, 2016) are used in the decay heat transfer calculations in the present work.
3. Methodology As mentioned in introduction section, it is expected that the safety feature of annular cylinder reactor would be improved because of existence of inner reflector since graphite has high heat capacity. In order to study the impact of the inner reflector on passive decay heat removal feature of the annular cylinder reactor, we conducted the reactor design analyses in which the methodology for decay heat transfer was analogous to those performed in previous works (Odmaa and Obara, 2014, 2015a,b, 2016). The heat transfer analyses was based on fundamental heat transfer phenomena using the natural laws of physics and all calculations were performed using the heat transfer module of COMSOL multiphysics software (COMSOL AB, 2015). Previously, the several studies on core heat transfer analyses for MTHGR (Seker et al., 2012) and Pebble bed Reactor (Peter, 2013) as well as hot channel thermohydraulic analyses for prismatic and pebble bed type of HTGR (Irwanto and Obara, 2013; Triniruk and Obara, 2014) were performed using Comsol multiphysics software. As illustrated in Fig. 1, the residual decay heat in the core after reactor shutdown is transferred from the core through solid structural walls by heat conduction mechanism as #3. Between solid domains, the regions are occupied by the air and the heat transfers through those gaseous domains by thermal radiation as #2 in Fig. 1. So, the surface-to-surface radiation boundary condition between structural walls was used. Finally, the heat was considered to be removed by external natural convection as #1 in Fig. 1 and thermal radiation from the reactor building wall for an above-ground reactor. From the reactor building bottom, the heat transfers through the soil by the conduction #3 in Fig. 1. From
Fig. 1. Basic compartments of a reactor with decay heat transfer mechanisms. a) Solid cylinder core, b) Annular cylinder core.
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O. Sambuu et al. / Annals of Nuclear Energy 111 (2018) 441–448 Table 1 Comparison of dimensions. Reactor region
HTTR, 30 MWt (Saito and et al., 1991, 1994; Shiozowa et al., 2004; Evaluation of HTGR Performance, 2003)
Reference design for solid cylinder reactor, 200 MWt, 0.82 W/cm3 (Odmaa and Obara, 2014, 2015a,b)
Reference design for annular cylinder reactor, 200 MWt, 0.82 W/cm3
Inner reflector (radius height, m) Core (radius height, m) Core with reflector (radius height, m) RPV_inside (radius height, m) Thickness of RPV wall RCV_inside (radius height, m) Thickness of RCV wall RB (inside) Thickness of RB wall
0
0
0.36 7.89
1.15 2.9 2.125 5.25
3.14 7.84 3.5 9.0
3.16 7.89 3.52 9.05
2.75 13.2
5.5 19.0
5.52 19.05
12.2–16 cm 9.25 30.3
26 cm 14.76 39.52
26 cm 14.78 39.57
3 cm 48 50 55 (width lengthheight, m) NA
6 cm 39.82 89.64 (radius height, m) 25 cm
6 cm 39.84 89.7 (radius height, m) 25 cm
Fig. 2. Radial temperature distributions after shutdown for two different power density profiles.
the result obtained in work (Kunitomi et al., 1996), the natural convection of He coolant inside the core was a negligible contribution compared to that by graphite conduction in the HTTR core for DLOFC accident. Therefore, the natural convection of helium coolant inside the core was also neglected in present work since the core components in our work was the same with those in HTTR. In addition, the heat transfer by thermal radiation is much dominant so that natural convection is usually neglected between structural walls in HTGR LOCA accident (IAEA-TECDOC-1163, 2000). We have considered the most severe situation for the annular reactor in this work and therefore to satisfy this situation, the natural convection of the air between the structural walls was not considered in the present analyses. In our previous works for solid finite cylinder reactor, the power density profile of the Bessel function in the radial direction and the cosine function in the vertical direction in a core was used as follows (Odmaa and Obara, 2014, 2015a,b, 2016):
r pz cos Pðr; zÞ ¼ P max J 0 2:4046 Rcore Hcore
ð1Þ
where P max is the maximum power density [W/cm3], Hcore is the core height [cm], Rcore is the core radius [cm]. In the present work, we considered two different power density profiles throughout the annular core. As the first one, the power density profile throughout the annular core was approximated the assumption of the Bessel function in the radial direction and the cosine function in the vertical direction, as follows:
r r inref pz cos Pðr; zÞ ¼ Pmax J 0 2:4046 Hcore Rcore rinref
ð2Þ
where r inref is the inner reflector radius [cm]. As shown in the above equation, the maximum power inside core is generated nearby the inner reflector. It was the simplified approximation because it is hardly to obtain the exact power density profile for annular core. If there is no inner reflector, the typical power density profile for solid finite cylinder reactor core as shown in Eq. (1) can be obtained from Eq. (2) with r inref ¼ 0. In order to operate reactor in safe condition, it is needed to flatten the power peaking factor (PPF) by introducing burnable poisons and/or control rods into the core. By satisfying this condition, we
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can assume that the power density is now uniformly distributed throughout the core before reactor shutdown, as follows:
P ¼ Pav e V core ¼ P av e pðR2core r 2inref Þ Hcore
ð3Þ
where P av e is the average power density [W/cm3], and V core is the core volume [cm3]. Now in both cases the volumetric heat distribution in the core is found from the above power density distributions, as follows:
r rinref Q 000 ðr; z; tÞ ¼ 5 103 Htab ðtÞ Pmax J 0 2:4046 Rcore r inref pz cos Hcore Q 000 ðtÞ ¼ 5 103 Htab ðtÞ Pav e pðR2core r2inref Þ Hcore
ð4Þ ð5Þ
where Htab ðtÞ is the tabular data for decay heat at the time after the shutdown [MeV/fission], and 5 103 is the conversion coefficient from MeV/fission to W. The tabular data (Decay heat tables. Nuclear Data Center, 2014) for decay heat power for thermal fission of 235U and for infinite (1013 s) irradiation recommended by Atomic Energy Society of Japan were used. In COMSOL, the domains of annular reactors were created using 2D axial symmetric space dimension. Heat transfer analyses were performed in 3D geometry, although the power density profile is 2D. In order to carry out the heat transfer analyses it is required to use some nodalisation for calculation domains. In Comsol, there is an option as physics-controlled mesh to nodalise and build a mesh. In this option Comsol multiphysics creates a mesh that is adapted to the current physics settings in the model. In this physics-controlled mesh, the user can change the element size from extremely coarse to extremely fine. Minimum element quality was varied insignificantly by changing element size from fine to extremely fine, and the calculation time was longer in the case using smaller mesh. Then, the domains in our calculations were nodalised using the physics-controlled mesh and the overall element size of the physics-induced mesh of our calculation geometry were set as finer triangular meshes in 2D or revolved into finer prism meshes in 3D (COMSOL AB, 2015). 4. Results and discussion 4.1. Influence of the existence of inner reflector on the peak core temperature after shutdown At first, the preliminary analyses for decay heat transfer for the reference annular reactor with power of 200 MWt and the average power density of 0.82 W/cm3 were conducted to check the influence of the existence of the inner reflector on the peak core temperature. Dimensions of the reactor structures are listed in Table 1. Here, two different power density profiles throughout the core were considered for the discussion about their impact on the peak core temperature. The uniform temperature profile through each domain of reactor at shutdown is assumed as simple assumption for the annular reactor. The temperature of each domain at shutdown listed in Table 2. It is assumed that the temperatures of fuel, graphite matrix and coolant at shutdown are the same, and these are represented by the core temperature at shutdown. The same assumption on the temperature at shutdown was assumed for the solid cylinder HTGR in the previous works (Odmaa and Obara, 2014, 2015a,b, 2016) and the results obtained there showed that the uniform temperature profile at shutdown could be a representative one by keeping the certain temperature margin for the general discussion. Practically, the temperature of inner
reflector at shutdown is somewhat lower than that of the core, however it was assumed the same for both regions for conservative analyses. Table 2 shows the calculation results for annular cylinder reactor compared with those for solid cylinder one. In the previous work the influence of the power density profile throughout the solid cylinder core were studied and described well and the uniform power density profile improves the safety feature (Odmaa and Obara, 2016). This result has also appeared for the annular cylinder reactor. The peak core temperature of the annular cylinder reactor with inner reflector with radius of 0.36 m was 462 K lower than that of the solid cylinder reactor with unflattened power density profile while it was 50 K lower in case of uniform one. In other words, the peak core temperature was reduced by existence of inner reflector in the center of the core. The reduction amount depends on the power density profile throughout the core before reactor shutdown. The inner reflector is made of graphite which has high heat capacity as core however, there is no heat generation. Since the some amount of decay heat generated in core can be transferred from the core to the inner reflector and accumulated there, the maximum core temperature could be decreased from that in case of without inner reflector. Therefore, the annular core design dramatically shortens the radial heat conduction path from the inner edge of the annular core to the interface between the outer edge of the core and the outer radial reflector and the additional graphite moderator in the inner reflector region increases the thermal inertia of the system, resulting smaller temperature drop, yielding a lower peak temperature. This means that the safety characteristics of the reactor can be improved by utilizing inner reflector. With annular core configuration, it is possible to remove the decay heat using passive cooling on the external surface of the reactor vessel, to spread the power more evenly across the reactor core and to limit the temperature rise in the event of depressurization and loss of coolant as well as loss-of-forced-flow accidents (Ingersoll, 2015; Hassan and Chaplin, 2010; Oka, 2014). Fig. 2 shows the radial temperature distributions for annular reactors with different power density profiles at the moment of reactor shutdown (t = 0 s) and at some time periods (15 h, 4.04 days, and 10 days) after reactor shutdown. Here, solid lines with various marks represent the radial temperature distributions for uniform power density profiles at different time steps after reactor shutdown while the dashed ones with different marks correspond to these for Bessel and cosine functions. The general behavior in both cases is that the heat production rate dominates the transfer rate for some period after reactor shutdown. This continuously takes place until the core temperature reaches a maximum value which is about 4 days for annular reactor with both power density profiles of unflattened and uniform throughout the core as shown in Table 2. After the core temperature reaches its maximum, the opposite phenomena would occur. Therefore, there is almost no difference between the two radial temperature profiles at each time step except at the core and inner reflector regions. The temperatures in both cases are lower in the air region between RPV and RCV during the earlier period as at 15 h after the shutdown. For air regions, only radiation heat transfer mechanism is considered due to its dominance than natural convection as mentioned in Introduction section. The radiation heat is proportional to the difference in the fourth powers of the temperatures of these walls and surrounding air space. This difference in the earlier period was large, however it was reduced by heating up all regions as time goes on. Due to existence of the inner reflector where no heat produces and its high heat capacity, the much amount of heat from the core is transferred and accumulated as time goes on. So, it indicates that the peak core temperature can be reduced significantly by the influence of inner reflector. Because
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O. Sambuu et al. / Annals of Nuclear Energy 111 (2018) 441–448 Table 2 Influence of existence of inner reflector on the peak core temperature after reactor shutdown. Reactor type
Solid cylinder (Odmaa and Obara, 2016)
Power profile
Unflattened
Inner reflector thickness, Rinref, m Core thickness, tcore, m Core radius, Rcore = Rinref + tcore, m Core height, Rcore/Hcore = 0.4, m Active core volume, m3 Average power density of core, W/cm3 Reactor thermal power, MW
0 3.137 3.137 7.843 243.9 0.82 200
Region’s temperature at shutdown, K: Core/ Inner reflector/Outer reflector Air between outer reflector and RPV/ RPV Air between RPV and RCV/ RCV Air between RCV and RB/ RB Soil
1200 400 300 295 280
Peak core temperature after shutdown, K Time to reach the peak core temperature, d
2189 5.2
of greater decay heat accumulation in the central core, the peak temperature is rapidly increased in the case of Bessel and cosine functions. When time elapses, a rather large amount of heat is continuously generated even though the decay heat transfers from central core to the peripheral core by thermal conduction throughout the core. However, the peak core temperature increases more slowly for the uniform power density profile due to the smaller temperature gradient in any region of the core.
Uniform
Annular cylinder Unflattened
Uniform
0.36 2.797 3.157 7.893
1546 4.5
1727 4.04
1496 4.04
From those two curves, it is simple to understand the conditions for reactor design satisfying the safety limit of fuel temperature. Fig. 3b displays the analogous conditions for annular reactors with similar power density profile by Bessel function in radial direction and cosine function in axial direction expressed by Eq. (1) which are obtained from the present analyses. All markers and lines at the Fig. 3b have the same meaning with these at Fig. 3a.
4.2. Parameter conditions for reactor design for passive decay heat removal To perform the decay heat removal analysis, a calculation methodology and procedure analogous to those in previous works (Odmaa and Obara, 2014, 2015a,b) were used to obtain new parametric conditions for annular reactor with two different power density profiles: unflattened and uniform. By following this procedure, first, the maximum core temperature was calculated in various combinations of reactor power (from 50 MWt to 1200 MWt), average power density (from 0.82 W/cm3 to 6.6 W/cm3) and core temperature at shutdown (from 600 K to 1200 K). In each combination, the core size was determined from the power and average power density, keeping the core radius-to-height ratio of R/H = 0.4. The temperatures of other regions are not changed as shown in Table 2. The power density ranges from 0.82 W/cm3 to 6.6 W/ cm3 for the uniform power density case. However, the maximum power density varies from 3 W/cm3 to 12 W/cm3 in case of the unflattened power density case. The core size and thermal power of the reactor with the uniform power density of 0.82 W/cm3 or 6.6 W/cm3 equals those of reactors with the maximum power density of 3 W/cm3 or 12 W/cm3 in the Bessel and cosine distributions, respectively. Then by limiting the maximum core temperature at less than the design limit of fuel temperature (1873 K Kroeger, 1990), the allowable maximum power of the reactor was estimated in each combination of core temperature at shutdown and average power density. The peak temperatures of the other structural regions were always less than their design limits. Fig. 3a shows the parametric conditions obtained in our previous works (Odmaa and Obara, 2014, 2015a,b) for cylinder reactors satisfying the safety limit for fuel and other regions temperature in which the power is distributed by Bessel and cosine functions throughout the core expressed by Eq. (5). Here, the dashed curves illustrate the relationship between the allowable power and reactor core size for various core temperatures at shutdown. However, the solid curves represent the relationship between the allowable power and reactor core size for different average power densities.
Fig. 3. Relationship between allowable power and reactor core size at various core temperatures at shutdown and maximum power densities when power density is distributed by the Bessel and cosine functions. a) solid cylinder, prismatic HTGRs (Odmaa and Obara, 2014, 2015a,b), b) annular cylinder, prismatic HTGRs.
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As shown in previous preliminary analyses for influence of existence of inner reflector, the safety feature of the annular reactor with the same design parameters improves drastically than that of the cylinder one. In other words, the allowable maximum power of annular reactor with the same core size and average power density and core temperature at shutdown can be larger than that of cylinder reactor. It means we can design either higher power reactor or smaller sized reactor without changing other parameters and without degrading safety feature by placing inner reflector into core. The parametric relationships for reactor with uniform power density were illustrated in Fig. 4. The results for cylinder reactor taken from previous work (Odmaa and Obara, 2016) shows in Fig. 4a while the corresponding results for annular reactor obtained from the present work are in Fig. 4b. As comparing the results in Fig. 4a and b, the allowable maximum power of annular reactor when core size and temperature at shutdown, and power density are chosen is larger than that of cylinder one with the exactly same parameters. Then the possibility to design higher power reactor without worsening safety feature can be achieved by influence of inner reflector and it does not depend on power density profile throughout the core. Generally, the relationship between parameters in Fig. 4 is similar to those in Fig. 3. However, it is clearly seen from Fig. 4 that a reactor with same design characteristics as those in Fig. 3 has a better safety margin or can be achieved on a smaller size. In other words, higher power or power density is safely allowed in the design of a reactor with uniform power density distribution. This means that the prismatic HTGR safety features can be improved and/or allowable power can be increased by flattening the power density profile. It can be inferred that the safety feature of the annular, prismatic HTGR with uniform power density profile is improved a lot compared with that for cylinder ones. The similar parametric condition for annular reactor with inner reflector radius of 0.18 m and unflattened power density profile was also obtained since the pitch of block constituting the HTTR core equals to 0.36 m (Saito et al., 1991, 1994; Shiozowa et al., 2004; Evaluation of HTGR Performance, 2003) and is shown in Fig. 5. By comparing results in Fig. 3b with these in Fig. 5, the allowable maximum power of annular reactor is lower for reactor with smaller inner reflector. Since the inner reflector radius reduces twice, the amount of accumulated heat in the inner reflector decreases by 6 times. It causes the increase in the peak core temperature compared to that of the reactor with thicker inner reflector so that the allowable power reduces as well.
Fig. 4. Relationship between allowable power and reactor core size at various core temperatures at shutdown and maximum power densities when power density is flat. a) solid cylinder, prismatic HTGRs (Odmaa and Obara, 2016), b) annular, prismatic HTGRs.
4.3. Criticality and burnup analyses Dimensions of annular reactor core with passive decay heat removal feature can be decided from obtained parametric conditions shown in Figs. 3b or 4b or 5. Then, criticality and burnup analyses for the reactor with 100 MWt of thermal power and the core temperature of 1123 K were performed to confirm the possibility of designing a long-life annular core for the given combinations of core size and reactor power which met the condition of removing decay heat successfully. The core consists of prismatic hexagonal blocks, and these blocks are piled up cylindrically to form the core. The fuel cell configuration is the same as that of the HTTR core, and each assembly has 33 fuel rods (Saito et al., 1991, 1994; Shiozowa et al., 2004; Evaluation of HTGR Performance, 2003). A horizontal cross section of the core is displayed in Fig. 6. Since the reactor core is composed of fixed-size prismatic hexagonal blocks of Japanese HTTR (pitch, 36 cm; height, 58 cm) (Saito et al., 1991, 1994; Shiozowa et al., 2004; Evaluation of HTGR Performance, 2003), the real dimensions of the core from piling up these blocks were chosen to be as close to the estimated ones from heat transfer calculations in the previ-
Fig. 5. Relationship between allowable power and reactor core size at various core temperatures at shutdown and maximum power densities for annular reactor when power density is distributed by the Bessel and cosine functions. Rin_ref = 0.18 m.
ous section. Hence, the equivalent radius and the effective height of the active core are little different from the evaluated values from the heat transfer analyses. The dimensions including other main specifications of the core are shown in Table 3.
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Fig. 6. Horizontal cross sectional view of the annular cylinder reactor core.
Table 3 Main specifications of core. Thermal power, MWt Core temperature, K Inner reflector radius/pitch, m Core outer radius obtained from heat transfer analyses, m Core height (R/H = 0.4), m Equivalent outer radius of an active core, m Effective height of an active core, m Average power density (W/cm3) Fuel Fuel enrichment (wt%) Coolant material Top/side/bottom reflector thickness, m Number of fuel assemblies Number of layers Number of control rod blocks in core/in reflector Number of inner/outer reflector blocks
100 1123 0.18/0.36 2.5 6.25 2.47 6.38 0.82 UO2 20% Helium gas 0.58/0.87/0.58 1452 11 396/264 11/264
Fundamental analyses of the reactor for criticality and burn-up with 20% enrichment of uranium were performed using the continuous energy Monte Carlo code MVP 2.0 (Nagaya et al., 2005) and MVP-Burn code (Okumura et al., 2005) with the nuclear data library of JENDL 3.3 (Shibata et al., 2002). All calculations were performed for whole-core, and the control rods were completely withdrawn from the core and replaced by helium. We chose a packing factor of 0.3 for the coated fuel particles in the graphite matrix. The most probable value of neutron multiplication factor (keff) was evaluated based on track length, collision, and analog estimators with the method of maximum likelihood. The number of histories per batch was 50,000 for all cases. The number of batches was 100. The first 20 batches were neglected for the statistical treatments. The fundamental neutronic analyses results for both cores are compared and shown in Fig. 7. The effective neutron multiplication factor in the beginning of the cycle (BOL) is 1.4934 ± 0.1029, and core life cycle is about 34 years and its burnup at the ending of life is about 144,000 MWd/t. To suppress the excess reactivity in the beginning of cycle, it will be used the burnable poisons as rod and/or particle form and the optimizations for core burnup with burnable poisons will be performed in the further work. The fundamental neutronic analyses for cylinder, prismatic HTGR with 100 MWt of thermal power and the core temperature of 1123 K were
Fig. 7. Change in effective neutron multiplication factor as time and fuel burnup.
performed in our previous works (Odmaa and Obara, 2014, 2015c). The results showed that the effective multiplication factor in BOL of this cylinder reactor with 20 wt% of uranium enrichment was 1.4862 ± 0.0205 and it could be critical for about 25 years without introducing burnable poisons. So by comparing these preliminary neutronic analyses results, the annular prismatic reactor operates for longer period than the cylinder one. 5. Conclusions In this work, it has been shown that the existence of inner reflector decreases the peak core temperature. Therefore, the power density profile of annular, prismatic HTGR gives the same effect on passive decay heat removal with that for cylinder one. The present work confirms that there is possibility to enhance the safety performance of prismatic HTGRs by applying inner reflector and by flattening the power density profile throughout the core. Flattening the power density profile can be achieved by inserting control rods and/or introducing burnable poison and optimizing fuel enrichment.
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Therefore, this analysis showed that a reactor whose core geometry is decided by the possibility of passive decay heat removal can be a critical and possible to operate for long period without fuel reloading. Acknowledgements This work has been done within the framework of the project named ‘‘Study on an advanced, small nuclear power reactor” supported by the Asia Research Center, Mongolia and Korea Foundation for Advanced Studies, South Korea. References COMSOL AB, 2015. COMSOL-5.0. Multiphysics modeling, finite element analysis, and engineering simulation software, [Cited 2015 November] Available from: http://www.comsol.com/. Decay heat tables. Nuclear Data Center, 2014. JAEA: http://wwwndc.jaea.go.jp/ DHTable/Table_11.html [Cited 2014 May]. Evaluation of HTGR Performance, 2003. Benchmark Analysis Related to Initial Testing of the HTTR and HTR-10, IAEA-TECDOC 1382. IAEA, Vienna. Hassan, Yassin A., Chaplin, Robin A (Eds.), 2010. Nuclear Energy Materials and Reactors. Encyclopedia of Life Support Systems, Vol II. Oxford, United Kingdom. Hayashi, K. et al., 1989. Assessment of Fuel Integrity of HTTR and its Permissible Design Limit. JAERI-M-89-162. JAERI, Japan. Hicks, T.E. et al., 2011. Modular HTGR Safety Basis and Approach. INL/EXT-1122708. Idaho National Laboratory, USA. Heat transport and afterheat removal for gas cooled reactors under accident conditions, 2000. IAEA-TECDOC-1163. IAEA: Vienna. Ingersoll, Daniel T., 2015. Small Modular Reactors: Nuclear Power Fad or Future. Elsevier Science and Technology. Irwanto, Dwi, Obara, Toru, 2013. Decay heat removal without forced cooling on a small simplified PBR with an accumulative fuel loading scheme. Ann. Nucl. Energy 60, 383–395.
Kroeger, P.G., 1990. Safety evaluations of accident scenarios in HTGRs. Nucl. Eng. Des. 122, 443–452. Kunitomi, K. et al., 1996. Passive heat removal by vessel cooling system of HTTR during no forced cooling accidents. Nucl. Eng. Des. 166, 179–190. Nagaya, Y. et al., 2005. MVP/GMVP II: General Purpose Monte Carlo Code for Neutron and Photon Transport Calculations Based on Continuous Energy and Multigroup Methods. JAERI-1348. Japan Atomic Energy Research Institute, Japan. Odmaa, S., Obara, T., 2014. Possible design in long-life small prismatic HTGR for passive decay heat removal. J. Nucl. Sci. Eng. 177, 97–109. Odmaa, S., Obara, T., 2015a. Neutronic and thermo-hydraulic analyses of a small, long-life HTGR for passive decay-heat removal. J. Nucl. Sci. Technol. 52 (12), 1519–1529. Odmaa, S., Obara, T., 2015a. Above-ground HTGR design for passive decay heat removal. J. Nucl. Sci. Technol. 52 (6), 857–871. Odmaa, S., Obara, T., 2015b. Comparative study on HTGR design for passive decay heat removal. Prog. Nucl. Energy 82, 37–45. Odmaa, S., Obara, T., 2016. Impact of power density profile on passive heat removal in prismatic HTGR. Ann. Nucl. Energy 87, 23–29. Oka, Yoshiaki (Ed.), 2014. Nuclear Reactor Design. An Advanced Course in Nuclear Engineering. Springer. Okumura, K. et al., 2005. MVP-BURN User’s Manual. Atomic Energy Agency, Japan. Peter, Geoffrey J., 2013. Numerical Simulation of Accident Scenario in HTGR (Pebble Bed Reactor) Using COMSOL Code. 2013; ICONE21-16535, pp. V004T09A098; 6 pages, doi:10.1115/ICONE21-16535. Saito, S. et al., 1991. Design and safety consideration in the HTTR. Energy 16 (1/2), 449–458. Saito, S., 1994. Design of HTTR. JAERI-1332. Japan Atomic Energy Research Institute, Japan. Seker, V., et al., 2012. Modeling prismatic HTGRs with U.S. N.R.C advanced gas reactor evaluator (AGREE). International Conference on the Physics of Reactors 2012 (PHYSOR 2012): Advances in Reactor Physics 2012; vol. 3: 1966–1981. Shibata, K. et al., 2002. Japanese evaluated nuclear data library-JENDL-3.3. J. Nucl. Sci. Technol. 39 (11), 1125–1136. Shiozowa, S. et al., 2004. Overview of HTTR design features. Nucl. Eng. Des. 233, 11– 21. Triniruk, Piyatida, Obara, Toru, 2014. Concept of prismatic high temperature gascooled reactor with SiC coating on graphite structures. Ann. Nucl. Energy 63, 437–445.
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Technical note
Design parameters in an annular, prismatic HTGR for passive decay heat removal Odmaa Sambuu a,b,⇑, Jamyansuren Terbish b, Toru Obara c, Norov Nanzad a,b, Munkhbat Byambajav a,b a Department of Chemical and Biological Engineering, School of Engineering and Applied Sciences, National University of Mongolia, Ikh surguuliin gudamj 3, Sukhbaatar District, Ulaanbaatar 14201, Mongolia b Nuclear Research Center, National University of Mongolia, Peace Avenue 122, Bayanzurkh District, Ulaanbaatar 14201, Mongolia c Laboratory for Advanced Nuclear Energy, Institute of Innovative Research, Tokyo Institute of Technology, 2-12-1-N1-19, Ookayama, Meguro-ku, Tokyo 152-8550, Japan
a r t i c l e
i n f o
Article history: Received 22 March 2017 Received in revised form 10 August 2017 Accepted 17 September 2017
Keywords: Passive decay-heat removal Prismatic HTGR Uniform power density Economy
a b s t r a c t We studied the capability of an annular, prismatic HTGR to remove decay heat passively. The purpose of the study was to obtain the design parameters relationship of the annular, prismatic HTGR with passive decay heat removal depending on power density profile and to compare them with those for solid cylinder one. The results showed that the safety feature of the annular reactor is improved a lot compared with that of cylinder one. The safety margin could be increased further by flattening the power density profile. Then fundamental neutronic analysis was performed for the annular reactor whose design parameters are obtained from the condition. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction Reactor design idea which does not rely on the active safety system for reactor safety condition is growing up. This idea or reactor design idea with passive safety system is one of the main features for new generation IV reactor concepts. High-temperature gascooled reactors (HTGRs) as base of the very high temperature reactor (VHTR) concept have several inherent safety features such as high-integrity of coated fuel particles (CFPs) up to 1873 K, highheat-capacity graphite core and support structures and inert helium coolant. Furthermore it is said that the integrity of the CFPs are highly dependent on the following safety functions to be assured: core heat removal, control of heat generation and limitation of chemical corrosion. Among those functions the most important one is successful removal of core heat after reactor shutdown (Hicks et al., 2011; Kroeger, 1990; Hayashi et al., 1989). In our previous papers, we studied the dependence of design parameters of solid cylinder HTGRs which can remove decay heat by passive ways (Odmaa and Obara, 2014, 2015a,b, 2016). This relationship was restrained by design limits of the fuel and structural temperatures and the capability of the reactor to remove ⇑ Corresponding author at: Department of Chemical and Biological Engineering, School of Engineering and Applied Sciences, National University of Mongolia, Ikh surguuliin gudamj 3, Sukhbaatar District, Ulaanbaatar 14201, Mongolia. E-mail addresses: [email protected], [email protected] (O. Sambuu). https://doi.org/10.1016/j.anucene.2017.09.034 0306-4549/Ó 2017 Elsevier Ltd. All rights reserved.
decay heat was limited only by the passive ways considering three main mechanisms as thermal conduction, radiation and convection. The severest condition was assumed for the previous papers in which all cooling systems including active and passive ones were completely lost their performance due to natural disaster. In this paper, we extended the research by choosing the annular cylinder, prismatic HTGRs in which the fuel blocks at the core center region are replaced by graphite blocks. Since there is no heat source in inner reflector for annular cylinder core and graphite has high heat capacity, some amount of heat in core could be transferred into the inner graphite reflector during operation and after shutdown. Therefore, it is expected that the safety feature of the annular HTGRs would be improved due to the maximum fuel temperature of the core is reduced. Then, by taking into account the above advantage of the annular core, it is possible to enhance the reactor power. So, in the present work we have studied the capability of an above-ground, annular, prismatic HTGR to remove decay heat passively by obtaining quantitative relationship between reactor design parameters. The power density profile throughout reactor core is considered as flattened or unflattened. The purpose of the present study is to reveal the impact of inner reflector on the annular cylinder reactor safety feature by confirming the reduction of the maximum fuel temperature of annular cylinder core, to obtain the design parameters relationship of an above-ground, annular, prismatic HTGR with passive decay heat removal depending on power density profiles and to compare them with those for solid cylinder, prismatic HTGR. Therefore, fundamental neutronic
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analysis for the annular reactor whose design parameters are obtained from the condition was performed to confirm its longterm operation without refueling and its higher fuel burnup.
2. Design concept We studied the design of solid cylinder HTGR with passive decay heat removal in our previous works (Odmaa and Obara, 2014, 2015a,b, 2016). The reactor core designs in previous and present works are based on the Japanese prismatic HTTR as a reference (Saito et al., 1991, 1994; Shiozowa et al., 2004; Evaluation of HTGR Performance, 2003). The general layouts of the both solid and annular reactor designs are illustrated in Fig. 1a and b respectively. Here other compartments of the design except core with reflector are the same with these for the solid cylinder reactor. In solid cylinder reactor, the core has only outer reflector as shown in Fig. 1a while annular core has both inner and outer reflectors as in Fig. 1b. Compartments in both reactor are the same as those being in HTTR. As illustrated in Fig. 1, the decay heat transfers through the solid structural domains by heat conduction mechanism and through air domains by thermal radiation. Finally, the heat is dissipated through the air on the reactor building wall by both outside natural convection and thermal radiation. Table 1 compares the dimensions of the HTTR with thermal power of 30 MWt (Saito et al., 1991, 1994; Shiozowa and et al., 2004; Evaluation of HTGR Performance, 2003) and both the reference designs of solid cylinder and annular reactor with thermal power of 200 MWt and average power density of 0.82 W/cm3. The reference design for solid cylinder reactor shown in Table 1 was chosen for our previous paper (Odmaa and Obara, 2016) and in this work, we have chosen the annular cylinder reactor with the same thermal power and average power density for comparison of results to be obtained in this work. In our previous works (Odmaa and Obara, 2014; Odmaa and Obara, 2016) the decay heat transfer analyses were performed for both types of prismatic and pebble bed HTGRs to choose the optimal ratio of core radius and height by comparing the obtained the peak core temperatures after shutdown for the same power reactors with different ratio and without changing the core volume. The ratio of radius to height corresponded to the highest peak core temperature is considered as the worst one which was between 0.46 and 0.55 depending on reactor power and core
temperature at shutdown. So, for barrel type of solid cylindrical prismatic and pebble bed HTGRs, the optimal ratio of core radius and height was chosen as 0.4 and kept this ratio for the future analyses for parametric conditions in order to reduce the number of considerable parameters on comparison of similarity or difference between the conditions for annular and solid cylindrical reactors. So, the same ratio of core radius and height as 0.4, the same materials for the corresponding domains, and the same physical characteristics of region materials applied in previous works (Odmaa and Obara, 2014, 2015a,b, 2016) are used in the decay heat transfer calculations in the present work.
3. Methodology As mentioned in introduction section, it is expected that the safety feature of annular cylinder reactor would be improved because of existence of inner reflector since graphite has high heat capacity. In order to study the impact of the inner reflector on passive decay heat removal feature of the annular cylinder reactor, we conducted the reactor design analyses in which the methodology for decay heat transfer was analogous to those performed in previous works (Odmaa and Obara, 2014, 2015a,b, 2016). The heat transfer analyses was based on fundamental heat transfer phenomena using the natural laws of physics and all calculations were performed using the heat transfer module of COMSOL multiphysics software (COMSOL AB, 2015). Previously, the several studies on core heat transfer analyses for MTHGR (Seker et al., 2012) and Pebble bed Reactor (Peter, 2013) as well as hot channel thermohydraulic analyses for prismatic and pebble bed type of HTGR (Irwanto and Obara, 2013; Triniruk and Obara, 2014) were performed using Comsol multiphysics software. As illustrated in Fig. 1, the residual decay heat in the core after reactor shutdown is transferred from the core through solid structural walls by heat conduction mechanism as #3. Between solid domains, the regions are occupied by the air and the heat transfers through those gaseous domains by thermal radiation as #2 in Fig. 1. So, the surface-to-surface radiation boundary condition between structural walls was used. Finally, the heat was considered to be removed by external natural convection as #1 in Fig. 1 and thermal radiation from the reactor building wall for an above-ground reactor. From the reactor building bottom, the heat transfers through the soil by the conduction #3 in Fig. 1. From
Fig. 1. Basic compartments of a reactor with decay heat transfer mechanisms. a) Solid cylinder core, b) Annular cylinder core.
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O. Sambuu et al. / Annals of Nuclear Energy 111 (2018) 441–448 Table 1 Comparison of dimensions. Reactor region
HTTR, 30 MWt (Saito and et al., 1991, 1994; Shiozowa et al., 2004; Evaluation of HTGR Performance, 2003)
Reference design for solid cylinder reactor, 200 MWt, 0.82 W/cm3 (Odmaa and Obara, 2014, 2015a,b)
Reference design for annular cylinder reactor, 200 MWt, 0.82 W/cm3
Inner reflector (radius height, m) Core (radius height, m) Core with reflector (radius height, m) RPV_inside (radius height, m) Thickness of RPV wall RCV_inside (radius height, m) Thickness of RCV wall RB (inside) Thickness of RB wall
0
0
0.36 7.89
1.15 2.9 2.125 5.25
3.14 7.84 3.5 9.0
3.16 7.89 3.52 9.05
2.75 13.2
5.5 19.0
5.52 19.05
12.2–16 cm 9.25 30.3
26 cm 14.76 39.52
26 cm 14.78 39.57
3 cm 48 50 55 (width lengthheight, m) NA
6 cm 39.82 89.64 (radius height, m) 25 cm
6 cm 39.84 89.7 (radius height, m) 25 cm
Fig. 2. Radial temperature distributions after shutdown for two different power density profiles.
the result obtained in work (Kunitomi et al., 1996), the natural convection of He coolant inside the core was a negligible contribution compared to that by graphite conduction in the HTTR core for DLOFC accident. Therefore, the natural convection of helium coolant inside the core was also neglected in present work since the core components in our work was the same with those in HTTR. In addition, the heat transfer by thermal radiation is much dominant so that natural convection is usually neglected between structural walls in HTGR LOCA accident (IAEA-TECDOC-1163, 2000). We have considered the most severe situation for the annular reactor in this work and therefore to satisfy this situation, the natural convection of the air between the structural walls was not considered in the present analyses. In our previous works for solid finite cylinder reactor, the power density profile of the Bessel function in the radial direction and the cosine function in the vertical direction in a core was used as follows (Odmaa and Obara, 2014, 2015a,b, 2016):
r pz cos Pðr; zÞ ¼ P max J 0 2:4046 Rcore Hcore
ð1Þ
where P max is the maximum power density [W/cm3], Hcore is the core height [cm], Rcore is the core radius [cm]. In the present work, we considered two different power density profiles throughout the annular core. As the first one, the power density profile throughout the annular core was approximated the assumption of the Bessel function in the radial direction and the cosine function in the vertical direction, as follows:
r r inref pz cos Pðr; zÞ ¼ Pmax J 0 2:4046 Hcore Rcore rinref
ð2Þ
where r inref is the inner reflector radius [cm]. As shown in the above equation, the maximum power inside core is generated nearby the inner reflector. It was the simplified approximation because it is hardly to obtain the exact power density profile for annular core. If there is no inner reflector, the typical power density profile for solid finite cylinder reactor core as shown in Eq. (1) can be obtained from Eq. (2) with r inref ¼ 0. In order to operate reactor in safe condition, it is needed to flatten the power peaking factor (PPF) by introducing burnable poisons and/or control rods into the core. By satisfying this condition, we
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can assume that the power density is now uniformly distributed throughout the core before reactor shutdown, as follows:
P ¼ Pav e V core ¼ P av e pðR2core r 2inref Þ Hcore
ð3Þ
where P av e is the average power density [W/cm3], and V core is the core volume [cm3]. Now in both cases the volumetric heat distribution in the core is found from the above power density distributions, as follows:
r rinref Q 000 ðr; z; tÞ ¼ 5 103 Htab ðtÞ Pmax J 0 2:4046 Rcore r inref pz cos Hcore Q 000 ðtÞ ¼ 5 103 Htab ðtÞ Pav e pðR2core r2inref Þ Hcore
ð4Þ ð5Þ
where Htab ðtÞ is the tabular data for decay heat at the time after the shutdown [MeV/fission], and 5 103 is the conversion coefficient from MeV/fission to W. The tabular data (Decay heat tables. Nuclear Data Center, 2014) for decay heat power for thermal fission of 235U and for infinite (1013 s) irradiation recommended by Atomic Energy Society of Japan were used. In COMSOL, the domains of annular reactors were created using 2D axial symmetric space dimension. Heat transfer analyses were performed in 3D geometry, although the power density profile is 2D. In order to carry out the heat transfer analyses it is required to use some nodalisation for calculation domains. In Comsol, there is an option as physics-controlled mesh to nodalise and build a mesh. In this option Comsol multiphysics creates a mesh that is adapted to the current physics settings in the model. In this physics-controlled mesh, the user can change the element size from extremely coarse to extremely fine. Minimum element quality was varied insignificantly by changing element size from fine to extremely fine, and the calculation time was longer in the case using smaller mesh. Then, the domains in our calculations were nodalised using the physics-controlled mesh and the overall element size of the physics-induced mesh of our calculation geometry were set as finer triangular meshes in 2D or revolved into finer prism meshes in 3D (COMSOL AB, 2015). 4. Results and discussion 4.1. Influence of the existence of inner reflector on the peak core temperature after shutdown At first, the preliminary analyses for decay heat transfer for the reference annular reactor with power of 200 MWt and the average power density of 0.82 W/cm3 were conducted to check the influence of the existence of the inner reflector on the peak core temperature. Dimensions of the reactor structures are listed in Table 1. Here, two different power density profiles throughout the core were considered for the discussion about their impact on the peak core temperature. The uniform temperature profile through each domain of reactor at shutdown is assumed as simple assumption for the annular reactor. The temperature of each domain at shutdown listed in Table 2. It is assumed that the temperatures of fuel, graphite matrix and coolant at shutdown are the same, and these are represented by the core temperature at shutdown. The same assumption on the temperature at shutdown was assumed for the solid cylinder HTGR in the previous works (Odmaa and Obara, 2014, 2015a,b, 2016) and the results obtained there showed that the uniform temperature profile at shutdown could be a representative one by keeping the certain temperature margin for the general discussion. Practically, the temperature of inner
reflector at shutdown is somewhat lower than that of the core, however it was assumed the same for both regions for conservative analyses. Table 2 shows the calculation results for annular cylinder reactor compared with those for solid cylinder one. In the previous work the influence of the power density profile throughout the solid cylinder core were studied and described well and the uniform power density profile improves the safety feature (Odmaa and Obara, 2016). This result has also appeared for the annular cylinder reactor. The peak core temperature of the annular cylinder reactor with inner reflector with radius of 0.36 m was 462 K lower than that of the solid cylinder reactor with unflattened power density profile while it was 50 K lower in case of uniform one. In other words, the peak core temperature was reduced by existence of inner reflector in the center of the core. The reduction amount depends on the power density profile throughout the core before reactor shutdown. The inner reflector is made of graphite which has high heat capacity as core however, there is no heat generation. Since the some amount of decay heat generated in core can be transferred from the core to the inner reflector and accumulated there, the maximum core temperature could be decreased from that in case of without inner reflector. Therefore, the annular core design dramatically shortens the radial heat conduction path from the inner edge of the annular core to the interface between the outer edge of the core and the outer radial reflector and the additional graphite moderator in the inner reflector region increases the thermal inertia of the system, resulting smaller temperature drop, yielding a lower peak temperature. This means that the safety characteristics of the reactor can be improved by utilizing inner reflector. With annular core configuration, it is possible to remove the decay heat using passive cooling on the external surface of the reactor vessel, to spread the power more evenly across the reactor core and to limit the temperature rise in the event of depressurization and loss of coolant as well as loss-of-forced-flow accidents (Ingersoll, 2015; Hassan and Chaplin, 2010; Oka, 2014). Fig. 2 shows the radial temperature distributions for annular reactors with different power density profiles at the moment of reactor shutdown (t = 0 s) and at some time periods (15 h, 4.04 days, and 10 days) after reactor shutdown. Here, solid lines with various marks represent the radial temperature distributions for uniform power density profiles at different time steps after reactor shutdown while the dashed ones with different marks correspond to these for Bessel and cosine functions. The general behavior in both cases is that the heat production rate dominates the transfer rate for some period after reactor shutdown. This continuously takes place until the core temperature reaches a maximum value which is about 4 days for annular reactor with both power density profiles of unflattened and uniform throughout the core as shown in Table 2. After the core temperature reaches its maximum, the opposite phenomena would occur. Therefore, there is almost no difference between the two radial temperature profiles at each time step except at the core and inner reflector regions. The temperatures in both cases are lower in the air region between RPV and RCV during the earlier period as at 15 h after the shutdown. For air regions, only radiation heat transfer mechanism is considered due to its dominance than natural convection as mentioned in Introduction section. The radiation heat is proportional to the difference in the fourth powers of the temperatures of these walls and surrounding air space. This difference in the earlier period was large, however it was reduced by heating up all regions as time goes on. Due to existence of the inner reflector where no heat produces and its high heat capacity, the much amount of heat from the core is transferred and accumulated as time goes on. So, it indicates that the peak core temperature can be reduced significantly by the influence of inner reflector. Because
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O. Sambuu et al. / Annals of Nuclear Energy 111 (2018) 441–448 Table 2 Influence of existence of inner reflector on the peak core temperature after reactor shutdown. Reactor type
Solid cylinder (Odmaa and Obara, 2016)
Power profile
Unflattened
Inner reflector thickness, Rinref, m Core thickness, tcore, m Core radius, Rcore = Rinref + tcore, m Core height, Rcore/Hcore = 0.4, m Active core volume, m3 Average power density of core, W/cm3 Reactor thermal power, MW
0 3.137 3.137 7.843 243.9 0.82 200
Region’s temperature at shutdown, K: Core/ Inner reflector/Outer reflector Air between outer reflector and RPV/ RPV Air between RPV and RCV/ RCV Air between RCV and RB/ RB Soil
1200 400 300 295 280
Peak core temperature after shutdown, K Time to reach the peak core temperature, d
2189 5.2
of greater decay heat accumulation in the central core, the peak temperature is rapidly increased in the case of Bessel and cosine functions. When time elapses, a rather large amount of heat is continuously generated even though the decay heat transfers from central core to the peripheral core by thermal conduction throughout the core. However, the peak core temperature increases more slowly for the uniform power density profile due to the smaller temperature gradient in any region of the core.
Uniform
Annular cylinder Unflattened
Uniform
0.36 2.797 3.157 7.893
1546 4.5
1727 4.04
1496 4.04
From those two curves, it is simple to understand the conditions for reactor design satisfying the safety limit of fuel temperature. Fig. 3b displays the analogous conditions for annular reactors with similar power density profile by Bessel function in radial direction and cosine function in axial direction expressed by Eq. (1) which are obtained from the present analyses. All markers and lines at the Fig. 3b have the same meaning with these at Fig. 3a.
4.2. Parameter conditions for reactor design for passive decay heat removal To perform the decay heat removal analysis, a calculation methodology and procedure analogous to those in previous works (Odmaa and Obara, 2014, 2015a,b) were used to obtain new parametric conditions for annular reactor with two different power density profiles: unflattened and uniform. By following this procedure, first, the maximum core temperature was calculated in various combinations of reactor power (from 50 MWt to 1200 MWt), average power density (from 0.82 W/cm3 to 6.6 W/cm3) and core temperature at shutdown (from 600 K to 1200 K). In each combination, the core size was determined from the power and average power density, keeping the core radius-to-height ratio of R/H = 0.4. The temperatures of other regions are not changed as shown in Table 2. The power density ranges from 0.82 W/cm3 to 6.6 W/ cm3 for the uniform power density case. However, the maximum power density varies from 3 W/cm3 to 12 W/cm3 in case of the unflattened power density case. The core size and thermal power of the reactor with the uniform power density of 0.82 W/cm3 or 6.6 W/cm3 equals those of reactors with the maximum power density of 3 W/cm3 or 12 W/cm3 in the Bessel and cosine distributions, respectively. Then by limiting the maximum core temperature at less than the design limit of fuel temperature (1873 K Kroeger, 1990), the allowable maximum power of the reactor was estimated in each combination of core temperature at shutdown and average power density. The peak temperatures of the other structural regions were always less than their design limits. Fig. 3a shows the parametric conditions obtained in our previous works (Odmaa and Obara, 2014, 2015a,b) for cylinder reactors satisfying the safety limit for fuel and other regions temperature in which the power is distributed by Bessel and cosine functions throughout the core expressed by Eq. (5). Here, the dashed curves illustrate the relationship between the allowable power and reactor core size for various core temperatures at shutdown. However, the solid curves represent the relationship between the allowable power and reactor core size for different average power densities.
Fig. 3. Relationship between allowable power and reactor core size at various core temperatures at shutdown and maximum power densities when power density is distributed by the Bessel and cosine functions. a) solid cylinder, prismatic HTGRs (Odmaa and Obara, 2014, 2015a,b), b) annular cylinder, prismatic HTGRs.
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As shown in previous preliminary analyses for influence of existence of inner reflector, the safety feature of the annular reactor with the same design parameters improves drastically than that of the cylinder one. In other words, the allowable maximum power of annular reactor with the same core size and average power density and core temperature at shutdown can be larger than that of cylinder reactor. It means we can design either higher power reactor or smaller sized reactor without changing other parameters and without degrading safety feature by placing inner reflector into core. The parametric relationships for reactor with uniform power density were illustrated in Fig. 4. The results for cylinder reactor taken from previous work (Odmaa and Obara, 2016) shows in Fig. 4a while the corresponding results for annular reactor obtained from the present work are in Fig. 4b. As comparing the results in Fig. 4a and b, the allowable maximum power of annular reactor when core size and temperature at shutdown, and power density are chosen is larger than that of cylinder one with the exactly same parameters. Then the possibility to design higher power reactor without worsening safety feature can be achieved by influence of inner reflector and it does not depend on power density profile throughout the core. Generally, the relationship between parameters in Fig. 4 is similar to those in Fig. 3. However, it is clearly seen from Fig. 4 that a reactor with same design characteristics as those in Fig. 3 has a better safety margin or can be achieved on a smaller size. In other words, higher power or power density is safely allowed in the design of a reactor with uniform power density distribution. This means that the prismatic HTGR safety features can be improved and/or allowable power can be increased by flattening the power density profile. It can be inferred that the safety feature of the annular, prismatic HTGR with uniform power density profile is improved a lot compared with that for cylinder ones. The similar parametric condition for annular reactor with inner reflector radius of 0.18 m and unflattened power density profile was also obtained since the pitch of block constituting the HTTR core equals to 0.36 m (Saito et al., 1991, 1994; Shiozowa et al., 2004; Evaluation of HTGR Performance, 2003) and is shown in Fig. 5. By comparing results in Fig. 3b with these in Fig. 5, the allowable maximum power of annular reactor is lower for reactor with smaller inner reflector. Since the inner reflector radius reduces twice, the amount of accumulated heat in the inner reflector decreases by 6 times. It causes the increase in the peak core temperature compared to that of the reactor with thicker inner reflector so that the allowable power reduces as well.
Fig. 4. Relationship between allowable power and reactor core size at various core temperatures at shutdown and maximum power densities when power density is flat. a) solid cylinder, prismatic HTGRs (Odmaa and Obara, 2016), b) annular, prismatic HTGRs.
4.3. Criticality and burnup analyses Dimensions of annular reactor core with passive decay heat removal feature can be decided from obtained parametric conditions shown in Figs. 3b or 4b or 5. Then, criticality and burnup analyses for the reactor with 100 MWt of thermal power and the core temperature of 1123 K were performed to confirm the possibility of designing a long-life annular core for the given combinations of core size and reactor power which met the condition of removing decay heat successfully. The core consists of prismatic hexagonal blocks, and these blocks are piled up cylindrically to form the core. The fuel cell configuration is the same as that of the HTTR core, and each assembly has 33 fuel rods (Saito et al., 1991, 1994; Shiozowa et al., 2004; Evaluation of HTGR Performance, 2003). A horizontal cross section of the core is displayed in Fig. 6. Since the reactor core is composed of fixed-size prismatic hexagonal blocks of Japanese HTTR (pitch, 36 cm; height, 58 cm) (Saito et al., 1991, 1994; Shiozowa et al., 2004; Evaluation of HTGR Performance, 2003), the real dimensions of the core from piling up these blocks were chosen to be as close to the estimated ones from heat transfer calculations in the previ-
Fig. 5. Relationship between allowable power and reactor core size at various core temperatures at shutdown and maximum power densities for annular reactor when power density is distributed by the Bessel and cosine functions. Rin_ref = 0.18 m.
ous section. Hence, the equivalent radius and the effective height of the active core are little different from the evaluated values from the heat transfer analyses. The dimensions including other main specifications of the core are shown in Table 3.
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Fig. 6. Horizontal cross sectional view of the annular cylinder reactor core.
Table 3 Main specifications of core. Thermal power, MWt Core temperature, K Inner reflector radius/pitch, m Core outer radius obtained from heat transfer analyses, m Core height (R/H = 0.4), m Equivalent outer radius of an active core, m Effective height of an active core, m Average power density (W/cm3) Fuel Fuel enrichment (wt%) Coolant material Top/side/bottom reflector thickness, m Number of fuel assemblies Number of layers Number of control rod blocks in core/in reflector Number of inner/outer reflector blocks
100 1123 0.18/0.36 2.5 6.25 2.47 6.38 0.82 UO2 20% Helium gas 0.58/0.87/0.58 1452 11 396/264 11/264
Fundamental analyses of the reactor for criticality and burn-up with 20% enrichment of uranium were performed using the continuous energy Monte Carlo code MVP 2.0 (Nagaya et al., 2005) and MVP-Burn code (Okumura et al., 2005) with the nuclear data library of JENDL 3.3 (Shibata et al., 2002). All calculations were performed for whole-core, and the control rods were completely withdrawn from the core and replaced by helium. We chose a packing factor of 0.3 for the coated fuel particles in the graphite matrix. The most probable value of neutron multiplication factor (keff) was evaluated based on track length, collision, and analog estimators with the method of maximum likelihood. The number of histories per batch was 50,000 for all cases. The number of batches was 100. The first 20 batches were neglected for the statistical treatments. The fundamental neutronic analyses results for both cores are compared and shown in Fig. 7. The effective neutron multiplication factor in the beginning of the cycle (BOL) is 1.4934 ± 0.1029, and core life cycle is about 34 years and its burnup at the ending of life is about 144,000 MWd/t. To suppress the excess reactivity in the beginning of cycle, it will be used the burnable poisons as rod and/or particle form and the optimizations for core burnup with burnable poisons will be performed in the further work. The fundamental neutronic analyses for cylinder, prismatic HTGR with 100 MWt of thermal power and the core temperature of 1123 K were
Fig. 7. Change in effective neutron multiplication factor as time and fuel burnup.
performed in our previous works (Odmaa and Obara, 2014, 2015c). The results showed that the effective multiplication factor in BOL of this cylinder reactor with 20 wt% of uranium enrichment was 1.4862 ± 0.0205 and it could be critical for about 25 years without introducing burnable poisons. So by comparing these preliminary neutronic analyses results, the annular prismatic reactor operates for longer period than the cylinder one. 5. Conclusions In this work, it has been shown that the existence of inner reflector decreases the peak core temperature. Therefore, the power density profile of annular, prismatic HTGR gives the same effect on passive decay heat removal with that for cylinder one. The present work confirms that there is possibility to enhance the safety performance of prismatic HTGRs by applying inner reflector and by flattening the power density profile throughout the core. Flattening the power density profile can be achieved by inserting control rods and/or introducing burnable poison and optimizing fuel enrichment.
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