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Thermal hydraulic investigations with different fuel diameters of pebble bed water cooled reactor in CFD simulation
Annals of Nuclear Energy 42 (2012) 135–147
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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Thermal hydraulic investigations with different fuel diameters of pebble bed water cooled reactor in CFD simulation Hua Li, Suizheng Qiu ⇑, Youjia Zhang, Guanghui Su, Wenxi Tian Department of Nuclear Science and Technology, State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, 710049 Xi’an, China
a r t i c l e
i n f o
Article history: Received 25 July 2011 Received in revised form 11 November 2011 Accepted 15 November 2011 Available online 2 January 2012 Keywords: Pebble bed water cooled reactor Thermal hydraulics CFD
a b s t r a c t The thermal hydraulic characteristics of the pebble bed water cooled reactor (PBWR) have been studied by computational fluid dynamics (CFD). The ‘‘near-miss’’ model is applied considering the problem on the mesh quality. The standard j–e model is used as the turbulence model. The velocity and temperature fields of the coolant are obtained and analyzed in different fuel diameters (such as 3 and 6 mm). The effects of the diameters on the thermal hydraulic characteristics are also discussed. The distributions of the temperature, velocity, pressure and Nusselt number (Nu) of the coolant on the surface of the pellet are obtained and analyzed. This study can conduct the experimental and mechanism research of PBWR. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction In recent years, the development of clean and efficient energy has become more and more important with the growing severity of environment problem and energy crisis. Since the inherent characteristic of nuclear energy, the proportion of nuclear power in the whole energy structure of China has increased continually that promotes the technological innovation of new nuclear reactors at the aspects of safety, economical efficiency and nonproliferation, etc. Nowadays, safety, clean, effective and low energy consumption are the main melody in the worldwide nuclear power market. The concept of the PBWR has been put forward under this background condition. It (PBWR) is presented by Sefidvash (1985) firstly. This concept reactor is a small modular fluidized bed light water nuclear reactor (Sefidvash, 1996) which used UO2 as the fuel. In Sefidvash’s model, the fuel pellets are movable. In order to reduce the collisions and frictions among the spheres, Sefidvash (2004) presented the concept of fixed bed nuclear reactor on the basis of the previous model. In the field of nuclear power, the pebble bed reactor (PBR) is mainly used for the conceptual design of the high-temperature gas-cooled reactor (HTGR) and supercritical water-cooled reactor (SCWR), meanwhile, the PBWR (with the pebble diameters range between 2 and 10 mm) has the characteristics of both the high temperature gas-cooled pebble bed reactor and the traditional light water reactor. Therefore, pebble bed reactor has attracted wide attention by virtue of its outstanding advantages in the inherent safety performance, high conversion
⇑ Corresponding author. Tel./fax: +86 29 82665607. E-mail address: [email protected] (S.Z. Qiu). 0306-4549/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.anucene.2011.11.010
efficiency and low power density design. In the organization of International Atomic Energy Agency (IAEA), a research group was established which mainly by the component members of American, Russian, Brazilian and Japanese, respectively. After many years of research, four concept reactors were proposed separately, represented by AFPR (Atoms for Pearce Reactor), BWR-PB (Particle-Bedded Boiling Water Reactor), FBNR (Fixed Bed Suspended Core Nuclear Reactor/Fluidized Bed Nuclear Reactor) and PFPWR (PWR with Coated Particle Fuel). In the last few years, the concept of PBWR is expanded to the SCWR by the American and Japanese researchers. In the above four concept reactors, the structures of spherical fuel elements are similar to the coated fuel particles in the fuel element of gas cooled reactor. But the diameter sizes are different in these four reactors. For these concept reactors, the diameter sizes are in the magnitude between 2 and 10 mm. The fixed bed is composed of plentiful fuel elements which are packed randomly. The coolant flows among the pore space between the fuel elements. After exchange heat with fuel elements, the coolant is heated to overheat state. The volume thermal power of pebble fuel can reach the value between 100 and 300 MW/m3. For the PBWR thermodynamic system, the coolant in the core will undergo multiple thermodynamic processes. The fluid in the porous channel has internal heat source and the heat flux is high. So the thermal hydraulic characteristics of PBWR have the features of complex phase state distribution, various coupling mechanism of heat transfer, and so on. Therefore, it is necessary to take some research on the thermal hydraulic characteristics of PBWR. As the complexity and limitations of experimental research, a growing number of investigators adopt the numerical methods to simulate and calculate all kinds of complicated problems. In the
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H. Li et al. / Annals of Nuclear Energy 42 (2012) 135–147 Table 1 Design parameters of the PBWR. Parameter
Value
System pressure (MPa) Surface heat flux (W/m2) Inlet temperature (K) Inlet speed (m/s) Porosity Coolant
10 1.32 105 523 0.06 0.37 Water
Fig. 1. Schematic diagram of PBWR.
5
Fig. 4. Simple cubic (SC).
4
3
4
3
2 Fig. 5. Body-centered cubic (BCC).
1
Fig. 2. Fuel assembly.
Fig. 6. Face-centered cubic (FCC).
Fig. 3. Longitudinal distribution of the fuel element.
Fig. 7. ‘‘Near-miss’’ model.
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(a) 0.5×0.2 mm2 Fig. 8. Geometric model.
(b) 0.5×0.24 mm2 Fig. 9. Solid domain.
(c) 0.5×0.26 mm2
Fig. 10. Fluid domain.
(d) 0.5×0.3 mm2 Fig. 12. Temperature distribution of different mesh sizes (3 mm).
Fig. 11. Position of the plane.
chemical engineering field, some scholars and researchers carried out some experiments and theoretical research. Nijemeisland and Dixon (2001) compared the results between CFD simulation and experimental study on the convective heat transfer in a gas–solid
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(a) 0.5×0.2 mm2
estimation of five different turbulence models in a fixed bed and obtained the pressure drop, velocity and temperature profiles within the model. Over the past nearly 20 years, numerous researchers conducted theoretical research on the PBR by CFD as it has proven to be a reliable tool for the design of fixed bed reactor. Hassan (2008) used the large eddy simulation (LES) method to study the simulation of turbulent transport for the coolant in the HTGR. The complex flow structure of coolant within the gaps between the fuel pebbles was obtained. Eddies between the pebbles were investigated. Lee et al. (2005) conducted some theoretical research on the assessment of turbulence models in CFD. He simulated the heat transfers in the PBR. Other researchers (such as In et al. (2005) and Lee et al. (2007)) obtained the temperature distribution of the fuel and the flow characteristics of the coolant in the HTGR. Helium is used as the coolant among all of the studies demonstrated above, and the liquid water is rarely considered as the coolant in the PBR. In the present study, water is regarded as the coolant and the thermal hydraulic characteristics of PBWR have been investigated. This work can conduct the experimental and theoretical mechanism research of PBWR. For the conceptual design of PBWR, the present study is practical and significant. 2. Model analysis 2.1. General description
(b) 0.5×0.24 mm2
(c) 0.5×0.26 mm2
The schematic diagram of PBWR is shown in Fig. 1. When the reactor is in the normal operation, the water as the coolant is injected into the core by pump from the inferior vena room. The water flows upward through the core and is heated by the pebble fuel elements. After heated, it goes through liquid region to water– steam two-phase region and becomes superheated steam at the outlet. Then, the steam enters into the turbine directly and works. Fig. 2 shows the fuel assembly structure in the core. The fuel pellets are placed in the fire-resistant composite pipe and the axial position of the pellets are limited by the orifice plate and filter screen. The fuel pellets are distributed randomly in the fuel assembly, as shown in Fig. 3. The upper portion of the assembly is divided into three parts by two concentric cylinders, for the purpose of preventing the steam gathering in the center of the tube. The density of the UO2 fuel pellets in ex-cylinder is different from that in internal-cylinder. Table 1 reveals the design parameters of the core used in the present research.
(d) 0.5×0.3 mm2 Fig. 14. Meshes of the model.
Fig. 13. Temperature distribution of different mesh sizes (6 mm).
fixed bed. They presented a ‘‘near-miss’’ model for the CFD simulation. The velocity vector profiles and temperature contours had been obtained. Guardo et al. (2005, 2006) analyzed the particleto-fluid heat transfer in fixed beds by CFD. They proposed a comparison between the performance in flow and heat transfer
Table 2 Statistics of the mesh numbers. Diameter (mm)
3
6
Total elements Total nodes
15,63,685 281,548
16,43,444 293,182
H. Li et al. / Annals of Nuclear Energy 42 (2012) 135–147
(a) Diameter of 3 mm
(b) Diameter of 6 mm
(c) Partial enlarged view of the vector Fig. 15. Velocity vector distributions on a vertical plane.
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(a) Position of the planes
(b) Plane A (3 mm diameter)
(c) Plane B (3 mm diameter)
(d) Plane A (6 mm diameter)
(e) Plane B (6 mm diameter)
(f) Partial enlarged view of the vector Fig. 16. Velocity vector distributions on horizontal planes.
H. Li et al. / Annals of Nuclear Energy 42 (2012) 135–147
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(1) Simple cubic (SC): Eight pellets are placed at the eight cube vertices (as shown in Fig. 4). (2) Body-centered cubic (BCC): Eight pellets are placed at the eight cube vertices and one pellet is seated in the center. The body-centered pellet is contacted with each vertex pellet (as shown in Fig. 5). (3) Face-centered cubic (FCC): Pellets are placed at the eight cube vertices and the centers of the six faces (as shown in Fig. 6). In order to choose the most suitable calculation model, the concept of porosity is defined as follows:
u¼ (a) Diameter of 3 mm
(b) Diameter of 6 mm Fig. 17. Streamline distribution on the surface of the pellets.
2.2. System model Supposing the pellet is inflexible and the pebble bed is packed randomly, the possible distributions of pellets are shown as follows:
(a) Diameter of 3 mm
Vk V
ð1Þ
where Vk and V are the volume of the pore and the total volume in the model, respectively. For the porous media, which is stacked up by the pellets with some constant diameter, the value of u is independent of the pellet diameter. But it is related to the packing modes, the plasticity and surface roughness of the pellets. The porosities of these three distribution modes are 0.476, 0.32 and 0.259, separately. When the pellets are stacked randomly and closely, the porosities are varied between 0.36 and 0.41, and the porosity of the given model is 0.37. Therefore, in this study, a geometrical model of the BCC type is assumed as the structure of the PBWR. In order to investigate the effect of diameter on the thermal–hydraulic characteristics of the coolant in the core, two kinds of diameters (3 and 6 mm) are selected. The fluid water which flows from the entrance to export in the BCC geometrical model is used as the coolant of the PBWR at the inlet pressure of 10 MPa. In the present model, the pellets touch each other and there are numerous contact points, so the mesh size around these points is difficult to generate by CFD, since these regions are discontinuous. To solve this problem, many researchers have adopted various methods. Nijemeisland (2000) and Nijemeisland and Dixon (2001) left small gaps between surfaces (‘‘near-miss’’ model) and assumed zero velocity in the gap. In their studies, several versions of test model with a limited number of pellets were created. The results demonstrated that when the gaps were larger (the 95% and 97% real pellet sizes), the velocity tended to be higher. Both the 99.5% and 99% real size of pellet models were shown in good agreement with the velocity distribution of the touching model. Taylor et al. (2002) introduced an artificial spacing between adja-
(b) Diameter of 6 mm
Fig. 18. Temperature distribution of the horizontal plane.
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cent pebbles and considered the effect of the pebble spacing in a unit cell of the pebble bed structure. Guardo et al. (2006) presented a model that included the real contact points, and the pellets were modeled overlapping by 0.5% of their diameters with the adjacent surfaces. In this study, the ‘‘near-miss’’ model is adopted and the pellet diameter in the BCC geometrical model is 99% of the original size, as shown in Fig. 7. The lyons blue pellet represents the original one and the cyan pellet is the ‘‘near-miss’’ one. The distance between these two pellets is 1% of the original diameter. The geometric models of these two kinds of diameters (3 and 6 mm) are similarity, taking the case of 6 mm for example. The geometric model is shown in Fig. 8. It is composed of the solid and fluid domains. The solid domain is shown in Fig. 9. It contains nine full pellets, six 1/2-pellets, twelve 1/4-pellets and eight 1/8-pellets. The fluid domain is shown in Fig. 10. 2.3. Selection of turbulent models Based on the description above, the CFX-11 is used to simulate the thermal hydraulics characteristics of the coolant. The computation environment is single-phase convective heat transfer at the condition of turbulence. If the 3-D flow heat transfer is in steady state, incompressible, with constant physical properties and without internal heat source, the three basic differential equations can be written as follows: Mass conservation equation:
@u @ v @w þ ¼0 þ @x @y @z
ð2Þ
Momentum conservation equation:
@U @U @U @U þv þw q þu @s @x @y @z @p @2U @2U @2U ¼ Fz þg þ þ 2 @z @x2 @y2 @z
To close these equations, the widely used standard j–e model is adopted. It is the most mature model to describe this kind of issues. In this model, j and e are given by their transport equations, respectively. The explanation of the momentum equation of the standard j–e model in the CFX 11.0 (2006) as follows:
@ qU þ r ðU UÞ r ðleff rUÞ ¼ rp0 þ r ðleff rUÞT þ B @t
ð5Þ
where leff is the effective viscosity accounting for turbulence; p0 is the modified pressure; B is the sum of body forces. The j–e model, like the zero equation model, is based on the eddy viscosity concept, so that:
leff ¼ l þ lf
ð6Þ
where lt is the turbulence viscosity. The j–e model assumes that the turbulence viscosity is linked to the turbulence kinetic energy and dissipation via the relation: 2
lt ¼ qC l
k
ð7Þ
e
where Cl is a constant, having values of 0.09.
2 p0 ¼ p þ qj 3 kinlet ¼
ð8Þ
1 2 IU 2
ð9Þ
where I is the turbulence intensity. The values of k and e coming from the differential transport equations directly for the turbulence kinetic energy and turbulence dissipation rate can be written as follows:
! ð3Þ
Energy conservation equation:
@T @T @T @T k @2T @2T @2T þv þw ¼ þu þ þ @s @x @y @z qcp @x2 @y2 @z2
! ð4Þ
where m is coefficient of kinematic viscosity; U is internal energy; T is temperature; Cp is specific heat capacity at constant pressure; q is density.
(a) Diameter of 3 mm
@ðqkÞ þ r ðqUkÞ ¼ r @t @ðqÞ þ r ðqU Þ ¼ r @t
lþ
lþ
lt rk þ P k qe rk
ð10Þ
lt r þ ðC 1 Pk C 2 qÞ r j
ð11Þ
where rk, re, C e1 and C e2 are all constants having values of 1.0, 1.3, 1.44 and 1.92, respectively. Pk is the turbulence production due to the viscous and buoyancy forces.
(b) Diameter of 6 mm
Fig. 19. Pressure distribution of the horizontal plane.
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3. Numerical simulations 3.1. Computational grids As the geometrical model is complex, it is unable to generate the structured grids. Thus, in the present study, the tetrahedral mesh is adopted. To investigate the effect of the different mesh sizes on the calculated results, the fuel pellet model with the diameter of 3 mm is divided into four kinds of meshes, and the maximum mesh sizes for each case are 0.5 0.3 mm2, 0.5 0.26 mm2, 0.5 0.24 mm2 and 0.5 0.2 mm2, respectively. Using the uniform boundary conditions, the temperature distributions of a horizontal cross-section of the calculations domains in each case of mesh are calculated. The position of the cross-section is shown in Fig. 11. The similar temperatures are found in the three cases (a–c) except in the case of (d), as shown in Fig. 12. The cases of size (a), size (b) and size (c) meet the demand of the calculation. When the diameter is 6 mm, compared with these four kinds of mesh size, the calculation results are that small of a difference (as shown in Fig. 13). Hence, the mesh size of 0.5 0.24 mm2 which not only meets the grid independent qualification but also satisfies the requirement of the computer hardware is adopted to realize the numerical calculation. Fig. 14 shows the detailed mesh generated by ICEM which can generated the geometric mesh. It can be see that the prism mesh is used near the wall, it makes the mesh is highly refined. Considering the complexity of structure, the tetrahedral mesh is adopted. The local grid refinement is applied around the surfaces of the pellets which can simulate the thermal hydraulic characteristics more accurately near the solid surfaces. The specific mesh numbers of each case are shown in Table 2.
(a) +Y axis
3.2. Boundary conditions The boundary conditions of this study are chosen based on the design parameters of the PBWR in China. The inlet temperature (523 K) is given; the normal speed of the coolant is 0.06 m/s with a turbulence intensity of 5%. The outlet boundary adopts the opening boundary conditions and the relative pressure is 0 MPa. The outlet temperature adopts the average temperature of the outlet. All the surfaces of the pellets use the wall boundary conditions, selecting the smooth surface of no-slip. The surface heat flux is 1.32 105 W/m2. Symmetric conditions are used for the side boundaries (except for the inlet and outlet boundaries) of this model.
(b) +Z axis
4. Results and discussion The velocity vectors of the coolant (the diameters of pellet are 3 and 6 mm, respectively) on a vertical plane are shown in Fig. 15. The color index represents the magnitude of the velocity. Compared with these two figures (Fig. 15a and b), the maximum velocity in Fig. 15a is 0.1575 m/s, while in Fig. 15b it is 0.1685 m/s. It can conclude that with the increase of the pellets’ diameter, the velocity of the coolant is increased. Since the gap size is proportional to the diameter. Thus, when the diameter is increased, the region of the gap will become bigger and the flow resistance will be decreased. It is beneficial to the fluid flow. Fig. 16 demonstrates the velocity vectors distribution on the horizontal plane. The specific locations of the plane-A (red1 plane) and plane-B (blue plane) are shown in Fig. 16a. The flow behaviors in each diameter (3 and 6 mm) are similar, as shown in Fig. 16b–e. 1
For interpretation of color in Figs. 2, 4–8, 10–22, 25, and 26, the reader is referred to the web version of this article.
(c) -Z axis Fig. 20. Temperature distribution of the central pellet.
By comparing the results shown in Figs. 15 and 16, it is clear that the velocity of coolant at the vertical direction is bigger than that at the horizontal direction in the central region among the surround-
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ing four pellets, since the flow direction of the coolant is from bottom to top. The stagnation points and secondary flow are observed at the narrow gap region which between two pellets on the vertical plane (at the region a shown in Fig. 15), while they are appeared at the central region among the surrounding fours pellets on the horizontal plane (at the region b shown in Fig. 16b–e). The stagnation points and secondary flow lead to the vortices appear (as shown in Figs. 15c and 16f). The streamline distributions on the surface of the pellets with different diameters are shown in Fig. 17. As shown in these two figures, when the diameter is 6 mm, the flow disturbance is stronger than that in the case of 3 mm. It can be conclude that the flow disturbance is strengthened with the increase of diameter. Since the ratio of the gap size to the pellet’s diameter is inversely proportional to the diameter of the pellet. The ratio will become smaller with the increase of the pellet’s diameter. This will cause the disturbance enhanced. Fig. 18 indicates the temperature distributions of the coolant for different pellet’s diameters (3 and 6 mm) on the vertical plane. It reveals that the high-temperature region (region a) will be reduced with the increase of the pellet’s diameter. By comparing with these
two figures (Fig. 18a and b), the temperature distributions (for 3 and 6 mm) on the vertical plane are similar. The temperature increases along the flow direction. There is also a local high temperature region (region b) in the narrow gap. Similar to Fig. 18, the pressure distributions of the vertical plane with different diameters are shown in Fig. 19. Apparently, the pressure reduces gradually from the entrance to exit, and the pressure drop decreases with the increase of pellet’s diameter. Based on the results achieved from the simulations above, as the calculation results are similar in the cases of different diameters, taking the central pellet in the case of 6 mm for example, the temperature, velocity and pressure distributions of the coolant on the surface of this pellet are analyzed. Fig. 20 illustrates the temperature distributions of coolant on the central pellet in different directions. It is evident that the maximum temperature emerges at the narrow gap region while the minimum temperature occurs at the pore region. Because the minimal gap goes against the fluid flow, this causes the formation of the local high temperature point. Fig. 21 is the velocity distributions of the coolant on the pellet’s surface. This figure illustrates that the maximum velocity of the pellet appears in the neutral position of the four narrow gap regions (as shown in
(a) +Y axis
(c) -Z axis
(b) +Z axis
(d) Maximum velocity of the central pellet Fig. 21. Velocity distribution of the central pellet.
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Z
Y
X
(a) +Y axis
Fig. 23. Definition of / and h (used in Figs. 21–23).
(b) +Z axis Fig. 24. Calculated pressure distributions of the central pellet (/ = 90°).
capacity of heat transfer is the worst at this region. Fig. 22 shows the pressure distribution of the coolant on the surface of the pellet. In this figure, the local low pressure points are generated at the upper narrow gap region of the pellet, as the water flows along the pellet surface and then separates at this region. According to the conclusions above, the temperature and pressure of the coolant on the surface of the central pellet are obtained. Meanwhile, the Nusselt number (Nu) on the surface of the central pellet is acquired. The Nu is defined as follows (in accordance with the original definition):
Nu ¼
hd k
ð12Þ
where h is the wall heat transfer coefficient defined by
h¼
(c) -Z axis Fig. 22. Pressure distribution of the central pellet.
Fig. 21d). The minimum velocity of the coolant emerged at the tail end of the pellet. The negative value of flow velocity represents the existence of backflow which is caused by the vortex. Therefore, the
q00 T w T nw
ð13Þ
d is the pellet diameter, k is the thermal conductivity of the coolant, q00 is the wall heat flux, Tw is the wall temperature of the ith cell and Tnw is the wall-adjacent temperature. Figs. 23–27 reveal the distributions of the temperature, pressure and Nu of the coolant on the central pellet in this model, respectively. The X-axis of each graph indicates the zenith angle (/) from the inlet (/ = 0°) to outlet (/ = 180°) of the central pellet,
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(a) Circle of
φ ( φ = 90°)
Fig. 27. Calculated Nusselt number on the surface of central pellet.
and 145° to 152°. These two regions always emerged at the narrow gap regions. The distribution of Nu is shown in Fig. 27. There are two minimum values which are located at the same azimuthal angle of the two temperature peaks. The two maximum Nu appear at the angles range from 15° to 25°and 155° to 170°. 5. Conclusions
(b) Temperature distributions Fig. 25. Temperature distributions of the central pellet (/ = 90°).
Fig. 26. Calculated temperature on the surface of central pellet.
as shown in Fig. 23, and h is the azimuth angle. Fig. 24 reveals the pressure distribution of the coolant on the surface of central pellet. The local high pressure points are generated when / is about 20°. In this region, the fluid which flows through the channel contacts with the pellet and impacts it. The negative velocity gradient is generated in this region which leads to the pressure increased. The temperature distributions of the coolant (/ = 90°) is shown in Fig. 25. It can be seen that the shape is a circle when / = 90° (Fig. 25a), the temperatures of this circle are shown in Fig. 25b. It is observed that the temperature distribution along h is periodic. Fig. 26 shows the two temperature peaks occur when the angle / range from 42° to 46°
In present study, the thermal hydraulic characteristics of PBWR have been investigated. Liquid water is used as the coolant. The ‘‘near-miss’’ model is adopted for the simulation. The standard j–e model is applied as the turbulence model. The thermal hydraulic characteristics of PBWR with different pellet sizes are analyzed. Some conclusions obtained are as follows: (1) The thermal hydraulic characteristics of PBWR using the BCC structure are numerically investigated. The distributions of the temperature, velocity, pressure and Nu of the coolant are obtained. It is observed that the maximum temperature of the coolant on the surface of pellet appear at the narrow gap region; the minimum temperature and maximum velocity of the coolant are located at the neutral position of the four narrow gap regions which are neighboring it; the minimum velocity occurs at the tail end of the pellet. (2) By comparing with the calculation results of two diameters (3 and 6 mm), it can be concluded that with the increase of diameter, the high-temperature region and pressure drop of the coolant decreased, meanwhile, the flow disturbance increased. Generally speaking, smaller flow disturbance and pressure drop of the coolant are beneficial to the safe operation of the reactor. Therefore, it is important to choose a right and reasonable diameter for the conceptual design and the safe operation of PBWR.
Acknowledgements The authors would like to acknowledge the project supported by Nuclear Power Institute of China (NPIC). References ANSYS CFX 11.0: Help Manual, 2006. Ansys Inc.Canada. Guardo, A., Coussirat, M., Larrayoz, M.A., et al., 2005. Influence of the turbulence model in CFD modeling of wall-to-fluid heat transfer in packed beds. Chemical Engineering Science 60 (6), 1733–1742.
H. Li et al. / Annals of Nuclear Energy 42 (2012) 135–147 Guardo, A., Coussirat, M., Recasens, F., et al., 2006. CFD study on particle-to-fluid heat transfer in fixed bed reactors: Convective heat transfer at low and high pressure. Chemical Engineering Science 61 (13), 4341–4353. Hassan, Y.A., 2008. Large eddy simulation in pebble bed gas cooled core reactors. Nuclear Engineering and Design 238 (3), 530–537. In, W.K., Chun, T.H., Lee, W.J., et al., 2005. CFD analysis of the fuel temperature in high temperature gas-cooled reactors. In: Transactions of the Korean Nuclear Society Autumn Meeting, October, Busan, Korea. Lee, J.J., Kang, S.K., Yoon, S.J., et al., 2005. Assessment of turbulence models in CFD code and its application to pebble bed reactor. In: Proceedings of the Fourth International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, September, Cairo, Egypt. Lee, J.J., Park, G.C., Kim, K.Y., et al., 2007. Numerical treatment of pebble contact in the flow and heat transfer analysis of a pebble bed reactor core. Nuclear Engineering and Design 237 (22), 2183–2196.
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Nijemeisland, M., 2000. Verification studies of computational fluid dynamics in fixed bed heat transfer. M.Sc. Thesis. Worcester Polytechnic Institute. Worcester, MA, USA. Nijemeisland, M., Dixon, A.G., 2001. Comparison of CFD simulations to experiment for convective heat transfer in a gas-solid fixed bed. Chemical Engineering Journal 82 (1–3), 231–246. Sefidvash, F., 1985. A fluidized bed nuclear reactor concept. Nuclear Technology 71, 527–534. Sefidvash, F., 1996. Status of the small modular fluidized bed light water nuclear reactor concept. Nuclear Engineering and Design 167 (2), 203–214. Sefidvash, F., 2004. Preliminary evaluation of the fixed and fluidized bed nuclear reactor concept using IAEA-INPRO methodology, Kerntechnik. Taylor, J.B., Yavuzkurt, S., Baratta, A., 2002. Modeling of the fluid and heat transfer in a pebble bed modular reactor core with a computational fluid dynamics code. In: Proceedings of the 10th International Conference on Nuclear Engineering, vol. 2, pp. 649–658.
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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Thermal hydraulic investigations with different fuel diameters of pebble bed water cooled reactor in CFD simulation Hua Li, Suizheng Qiu ⇑, Youjia Zhang, Guanghui Su, Wenxi Tian Department of Nuclear Science and Technology, State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, 710049 Xi’an, China
a r t i c l e
i n f o
Article history: Received 25 July 2011 Received in revised form 11 November 2011 Accepted 15 November 2011 Available online 2 January 2012 Keywords: Pebble bed water cooled reactor Thermal hydraulics CFD
a b s t r a c t The thermal hydraulic characteristics of the pebble bed water cooled reactor (PBWR) have been studied by computational fluid dynamics (CFD). The ‘‘near-miss’’ model is applied considering the problem on the mesh quality. The standard j–e model is used as the turbulence model. The velocity and temperature fields of the coolant are obtained and analyzed in different fuel diameters (such as 3 and 6 mm). The effects of the diameters on the thermal hydraulic characteristics are also discussed. The distributions of the temperature, velocity, pressure and Nusselt number (Nu) of the coolant on the surface of the pellet are obtained and analyzed. This study can conduct the experimental and mechanism research of PBWR. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction In recent years, the development of clean and efficient energy has become more and more important with the growing severity of environment problem and energy crisis. Since the inherent characteristic of nuclear energy, the proportion of nuclear power in the whole energy structure of China has increased continually that promotes the technological innovation of new nuclear reactors at the aspects of safety, economical efficiency and nonproliferation, etc. Nowadays, safety, clean, effective and low energy consumption are the main melody in the worldwide nuclear power market. The concept of the PBWR has been put forward under this background condition. It (PBWR) is presented by Sefidvash (1985) firstly. This concept reactor is a small modular fluidized bed light water nuclear reactor (Sefidvash, 1996) which used UO2 as the fuel. In Sefidvash’s model, the fuel pellets are movable. In order to reduce the collisions and frictions among the spheres, Sefidvash (2004) presented the concept of fixed bed nuclear reactor on the basis of the previous model. In the field of nuclear power, the pebble bed reactor (PBR) is mainly used for the conceptual design of the high-temperature gas-cooled reactor (HTGR) and supercritical water-cooled reactor (SCWR), meanwhile, the PBWR (with the pebble diameters range between 2 and 10 mm) has the characteristics of both the high temperature gas-cooled pebble bed reactor and the traditional light water reactor. Therefore, pebble bed reactor has attracted wide attention by virtue of its outstanding advantages in the inherent safety performance, high conversion
⇑ Corresponding author. Tel./fax: +86 29 82665607. E-mail address: [email protected] (S.Z. Qiu). 0306-4549/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.anucene.2011.11.010
efficiency and low power density design. In the organization of International Atomic Energy Agency (IAEA), a research group was established which mainly by the component members of American, Russian, Brazilian and Japanese, respectively. After many years of research, four concept reactors were proposed separately, represented by AFPR (Atoms for Pearce Reactor), BWR-PB (Particle-Bedded Boiling Water Reactor), FBNR (Fixed Bed Suspended Core Nuclear Reactor/Fluidized Bed Nuclear Reactor) and PFPWR (PWR with Coated Particle Fuel). In the last few years, the concept of PBWR is expanded to the SCWR by the American and Japanese researchers. In the above four concept reactors, the structures of spherical fuel elements are similar to the coated fuel particles in the fuel element of gas cooled reactor. But the diameter sizes are different in these four reactors. For these concept reactors, the diameter sizes are in the magnitude between 2 and 10 mm. The fixed bed is composed of plentiful fuel elements which are packed randomly. The coolant flows among the pore space between the fuel elements. After exchange heat with fuel elements, the coolant is heated to overheat state. The volume thermal power of pebble fuel can reach the value between 100 and 300 MW/m3. For the PBWR thermodynamic system, the coolant in the core will undergo multiple thermodynamic processes. The fluid in the porous channel has internal heat source and the heat flux is high. So the thermal hydraulic characteristics of PBWR have the features of complex phase state distribution, various coupling mechanism of heat transfer, and so on. Therefore, it is necessary to take some research on the thermal hydraulic characteristics of PBWR. As the complexity and limitations of experimental research, a growing number of investigators adopt the numerical methods to simulate and calculate all kinds of complicated problems. In the
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H. Li et al. / Annals of Nuclear Energy 42 (2012) 135–147 Table 1 Design parameters of the PBWR. Parameter
Value
System pressure (MPa) Surface heat flux (W/m2) Inlet temperature (K) Inlet speed (m/s) Porosity Coolant
10 1.32 105 523 0.06 0.37 Water
Fig. 1. Schematic diagram of PBWR.
5
Fig. 4. Simple cubic (SC).
4
3
4
3
2 Fig. 5. Body-centered cubic (BCC).
1
Fig. 2. Fuel assembly.
Fig. 6. Face-centered cubic (FCC).
Fig. 3. Longitudinal distribution of the fuel element.
Fig. 7. ‘‘Near-miss’’ model.
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(a) 0.5×0.2 mm2 Fig. 8. Geometric model.
(b) 0.5×0.24 mm2 Fig. 9. Solid domain.
(c) 0.5×0.26 mm2
Fig. 10. Fluid domain.
(d) 0.5×0.3 mm2 Fig. 12. Temperature distribution of different mesh sizes (3 mm).
Fig. 11. Position of the plane.
chemical engineering field, some scholars and researchers carried out some experiments and theoretical research. Nijemeisland and Dixon (2001) compared the results between CFD simulation and experimental study on the convective heat transfer in a gas–solid
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(a) 0.5×0.2 mm2
estimation of five different turbulence models in a fixed bed and obtained the pressure drop, velocity and temperature profiles within the model. Over the past nearly 20 years, numerous researchers conducted theoretical research on the PBR by CFD as it has proven to be a reliable tool for the design of fixed bed reactor. Hassan (2008) used the large eddy simulation (LES) method to study the simulation of turbulent transport for the coolant in the HTGR. The complex flow structure of coolant within the gaps between the fuel pebbles was obtained. Eddies between the pebbles were investigated. Lee et al. (2005) conducted some theoretical research on the assessment of turbulence models in CFD. He simulated the heat transfers in the PBR. Other researchers (such as In et al. (2005) and Lee et al. (2007)) obtained the temperature distribution of the fuel and the flow characteristics of the coolant in the HTGR. Helium is used as the coolant among all of the studies demonstrated above, and the liquid water is rarely considered as the coolant in the PBR. In the present study, water is regarded as the coolant and the thermal hydraulic characteristics of PBWR have been investigated. This work can conduct the experimental and theoretical mechanism research of PBWR. For the conceptual design of PBWR, the present study is practical and significant. 2. Model analysis 2.1. General description
(b) 0.5×0.24 mm2
(c) 0.5×0.26 mm2
The schematic diagram of PBWR is shown in Fig. 1. When the reactor is in the normal operation, the water as the coolant is injected into the core by pump from the inferior vena room. The water flows upward through the core and is heated by the pebble fuel elements. After heated, it goes through liquid region to water– steam two-phase region and becomes superheated steam at the outlet. Then, the steam enters into the turbine directly and works. Fig. 2 shows the fuel assembly structure in the core. The fuel pellets are placed in the fire-resistant composite pipe and the axial position of the pellets are limited by the orifice plate and filter screen. The fuel pellets are distributed randomly in the fuel assembly, as shown in Fig. 3. The upper portion of the assembly is divided into three parts by two concentric cylinders, for the purpose of preventing the steam gathering in the center of the tube. The density of the UO2 fuel pellets in ex-cylinder is different from that in internal-cylinder. Table 1 reveals the design parameters of the core used in the present research.
(d) 0.5×0.3 mm2 Fig. 14. Meshes of the model.
Fig. 13. Temperature distribution of different mesh sizes (6 mm).
fixed bed. They presented a ‘‘near-miss’’ model for the CFD simulation. The velocity vector profiles and temperature contours had been obtained. Guardo et al. (2005, 2006) analyzed the particleto-fluid heat transfer in fixed beds by CFD. They proposed a comparison between the performance in flow and heat transfer
Table 2 Statistics of the mesh numbers. Diameter (mm)
3
6
Total elements Total nodes
15,63,685 281,548
16,43,444 293,182
H. Li et al. / Annals of Nuclear Energy 42 (2012) 135–147
(a) Diameter of 3 mm
(b) Diameter of 6 mm
(c) Partial enlarged view of the vector Fig. 15. Velocity vector distributions on a vertical plane.
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(a) Position of the planes
(b) Plane A (3 mm diameter)
(c) Plane B (3 mm diameter)
(d) Plane A (6 mm diameter)
(e) Plane B (6 mm diameter)
(f) Partial enlarged view of the vector Fig. 16. Velocity vector distributions on horizontal planes.
H. Li et al. / Annals of Nuclear Energy 42 (2012) 135–147
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(1) Simple cubic (SC): Eight pellets are placed at the eight cube vertices (as shown in Fig. 4). (2) Body-centered cubic (BCC): Eight pellets are placed at the eight cube vertices and one pellet is seated in the center. The body-centered pellet is contacted with each vertex pellet (as shown in Fig. 5). (3) Face-centered cubic (FCC): Pellets are placed at the eight cube vertices and the centers of the six faces (as shown in Fig. 6). In order to choose the most suitable calculation model, the concept of porosity is defined as follows:
u¼ (a) Diameter of 3 mm
(b) Diameter of 6 mm Fig. 17. Streamline distribution on the surface of the pellets.
2.2. System model Supposing the pellet is inflexible and the pebble bed is packed randomly, the possible distributions of pellets are shown as follows:
(a) Diameter of 3 mm
Vk V
ð1Þ
where Vk and V are the volume of the pore and the total volume in the model, respectively. For the porous media, which is stacked up by the pellets with some constant diameter, the value of u is independent of the pellet diameter. But it is related to the packing modes, the plasticity and surface roughness of the pellets. The porosities of these three distribution modes are 0.476, 0.32 and 0.259, separately. When the pellets are stacked randomly and closely, the porosities are varied between 0.36 and 0.41, and the porosity of the given model is 0.37. Therefore, in this study, a geometrical model of the BCC type is assumed as the structure of the PBWR. In order to investigate the effect of diameter on the thermal–hydraulic characteristics of the coolant in the core, two kinds of diameters (3 and 6 mm) are selected. The fluid water which flows from the entrance to export in the BCC geometrical model is used as the coolant of the PBWR at the inlet pressure of 10 MPa. In the present model, the pellets touch each other and there are numerous contact points, so the mesh size around these points is difficult to generate by CFD, since these regions are discontinuous. To solve this problem, many researchers have adopted various methods. Nijemeisland (2000) and Nijemeisland and Dixon (2001) left small gaps between surfaces (‘‘near-miss’’ model) and assumed zero velocity in the gap. In their studies, several versions of test model with a limited number of pellets were created. The results demonstrated that when the gaps were larger (the 95% and 97% real pellet sizes), the velocity tended to be higher. Both the 99.5% and 99% real size of pellet models were shown in good agreement with the velocity distribution of the touching model. Taylor et al. (2002) introduced an artificial spacing between adja-
(b) Diameter of 6 mm
Fig. 18. Temperature distribution of the horizontal plane.
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cent pebbles and considered the effect of the pebble spacing in a unit cell of the pebble bed structure. Guardo et al. (2006) presented a model that included the real contact points, and the pellets were modeled overlapping by 0.5% of their diameters with the adjacent surfaces. In this study, the ‘‘near-miss’’ model is adopted and the pellet diameter in the BCC geometrical model is 99% of the original size, as shown in Fig. 7. The lyons blue pellet represents the original one and the cyan pellet is the ‘‘near-miss’’ one. The distance between these two pellets is 1% of the original diameter. The geometric models of these two kinds of diameters (3 and 6 mm) are similarity, taking the case of 6 mm for example. The geometric model is shown in Fig. 8. It is composed of the solid and fluid domains. The solid domain is shown in Fig. 9. It contains nine full pellets, six 1/2-pellets, twelve 1/4-pellets and eight 1/8-pellets. The fluid domain is shown in Fig. 10. 2.3. Selection of turbulent models Based on the description above, the CFX-11 is used to simulate the thermal hydraulics characteristics of the coolant. The computation environment is single-phase convective heat transfer at the condition of turbulence. If the 3-D flow heat transfer is in steady state, incompressible, with constant physical properties and without internal heat source, the three basic differential equations can be written as follows: Mass conservation equation:
@u @ v @w þ ¼0 þ @x @y @z
ð2Þ
Momentum conservation equation:
@U @U @U @U þv þw q þu @s @x @y @z @p @2U @2U @2U ¼ Fz þg þ þ 2 @z @x2 @y2 @z
To close these equations, the widely used standard j–e model is adopted. It is the most mature model to describe this kind of issues. In this model, j and e are given by their transport equations, respectively. The explanation of the momentum equation of the standard j–e model in the CFX 11.0 (2006) as follows:
@ qU þ r ðU UÞ r ðleff rUÞ ¼ rp0 þ r ðleff rUÞT þ B @t
ð5Þ
where leff is the effective viscosity accounting for turbulence; p0 is the modified pressure; B is the sum of body forces. The j–e model, like the zero equation model, is based on the eddy viscosity concept, so that:
leff ¼ l þ lf
ð6Þ
where lt is the turbulence viscosity. The j–e model assumes that the turbulence viscosity is linked to the turbulence kinetic energy and dissipation via the relation: 2
lt ¼ qC l
k
ð7Þ
e
where Cl is a constant, having values of 0.09.
2 p0 ¼ p þ qj 3 kinlet ¼
ð8Þ
1 2 IU 2
ð9Þ
where I is the turbulence intensity. The values of k and e coming from the differential transport equations directly for the turbulence kinetic energy and turbulence dissipation rate can be written as follows:
! ð3Þ
Energy conservation equation:
@T @T @T @T k @2T @2T @2T þv þw ¼ þu þ þ @s @x @y @z qcp @x2 @y2 @z2
! ð4Þ
where m is coefficient of kinematic viscosity; U is internal energy; T is temperature; Cp is specific heat capacity at constant pressure; q is density.
(a) Diameter of 3 mm
@ðqkÞ þ r ðqUkÞ ¼ r @t @ðqÞ þ r ðqU Þ ¼ r @t
lþ
lþ
lt rk þ P k qe rk
ð10Þ
lt r þ ðC 1 Pk C 2 qÞ r j
ð11Þ
where rk, re, C e1 and C e2 are all constants having values of 1.0, 1.3, 1.44 and 1.92, respectively. Pk is the turbulence production due to the viscous and buoyancy forces.
(b) Diameter of 6 mm
Fig. 19. Pressure distribution of the horizontal plane.
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3. Numerical simulations 3.1. Computational grids As the geometrical model is complex, it is unable to generate the structured grids. Thus, in the present study, the tetrahedral mesh is adopted. To investigate the effect of the different mesh sizes on the calculated results, the fuel pellet model with the diameter of 3 mm is divided into four kinds of meshes, and the maximum mesh sizes for each case are 0.5 0.3 mm2, 0.5 0.26 mm2, 0.5 0.24 mm2 and 0.5 0.2 mm2, respectively. Using the uniform boundary conditions, the temperature distributions of a horizontal cross-section of the calculations domains in each case of mesh are calculated. The position of the cross-section is shown in Fig. 11. The similar temperatures are found in the three cases (a–c) except in the case of (d), as shown in Fig. 12. The cases of size (a), size (b) and size (c) meet the demand of the calculation. When the diameter is 6 mm, compared with these four kinds of mesh size, the calculation results are that small of a difference (as shown in Fig. 13). Hence, the mesh size of 0.5 0.24 mm2 which not only meets the grid independent qualification but also satisfies the requirement of the computer hardware is adopted to realize the numerical calculation. Fig. 14 shows the detailed mesh generated by ICEM which can generated the geometric mesh. It can be see that the prism mesh is used near the wall, it makes the mesh is highly refined. Considering the complexity of structure, the tetrahedral mesh is adopted. The local grid refinement is applied around the surfaces of the pellets which can simulate the thermal hydraulic characteristics more accurately near the solid surfaces. The specific mesh numbers of each case are shown in Table 2.
(a) +Y axis
3.2. Boundary conditions The boundary conditions of this study are chosen based on the design parameters of the PBWR in China. The inlet temperature (523 K) is given; the normal speed of the coolant is 0.06 m/s with a turbulence intensity of 5%. The outlet boundary adopts the opening boundary conditions and the relative pressure is 0 MPa. The outlet temperature adopts the average temperature of the outlet. All the surfaces of the pellets use the wall boundary conditions, selecting the smooth surface of no-slip. The surface heat flux is 1.32 105 W/m2. Symmetric conditions are used for the side boundaries (except for the inlet and outlet boundaries) of this model.
(b) +Z axis
4. Results and discussion The velocity vectors of the coolant (the diameters of pellet are 3 and 6 mm, respectively) on a vertical plane are shown in Fig. 15. The color index represents the magnitude of the velocity. Compared with these two figures (Fig. 15a and b), the maximum velocity in Fig. 15a is 0.1575 m/s, while in Fig. 15b it is 0.1685 m/s. It can conclude that with the increase of the pellets’ diameter, the velocity of the coolant is increased. Since the gap size is proportional to the diameter. Thus, when the diameter is increased, the region of the gap will become bigger and the flow resistance will be decreased. It is beneficial to the fluid flow. Fig. 16 demonstrates the velocity vectors distribution on the horizontal plane. The specific locations of the plane-A (red1 plane) and plane-B (blue plane) are shown in Fig. 16a. The flow behaviors in each diameter (3 and 6 mm) are similar, as shown in Fig. 16b–e. 1
For interpretation of color in Figs. 2, 4–8, 10–22, 25, and 26, the reader is referred to the web version of this article.
(c) -Z axis Fig. 20. Temperature distribution of the central pellet.
By comparing the results shown in Figs. 15 and 16, it is clear that the velocity of coolant at the vertical direction is bigger than that at the horizontal direction in the central region among the surround-
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ing four pellets, since the flow direction of the coolant is from bottom to top. The stagnation points and secondary flow are observed at the narrow gap region which between two pellets on the vertical plane (at the region a shown in Fig. 15), while they are appeared at the central region among the surrounding fours pellets on the horizontal plane (at the region b shown in Fig. 16b–e). The stagnation points and secondary flow lead to the vortices appear (as shown in Figs. 15c and 16f). The streamline distributions on the surface of the pellets with different diameters are shown in Fig. 17. As shown in these two figures, when the diameter is 6 mm, the flow disturbance is stronger than that in the case of 3 mm. It can be conclude that the flow disturbance is strengthened with the increase of diameter. Since the ratio of the gap size to the pellet’s diameter is inversely proportional to the diameter of the pellet. The ratio will become smaller with the increase of the pellet’s diameter. This will cause the disturbance enhanced. Fig. 18 indicates the temperature distributions of the coolant for different pellet’s diameters (3 and 6 mm) on the vertical plane. It reveals that the high-temperature region (region a) will be reduced with the increase of the pellet’s diameter. By comparing with these
two figures (Fig. 18a and b), the temperature distributions (for 3 and 6 mm) on the vertical plane are similar. The temperature increases along the flow direction. There is also a local high temperature region (region b) in the narrow gap. Similar to Fig. 18, the pressure distributions of the vertical plane with different diameters are shown in Fig. 19. Apparently, the pressure reduces gradually from the entrance to exit, and the pressure drop decreases with the increase of pellet’s diameter. Based on the results achieved from the simulations above, as the calculation results are similar in the cases of different diameters, taking the central pellet in the case of 6 mm for example, the temperature, velocity and pressure distributions of the coolant on the surface of this pellet are analyzed. Fig. 20 illustrates the temperature distributions of coolant on the central pellet in different directions. It is evident that the maximum temperature emerges at the narrow gap region while the minimum temperature occurs at the pore region. Because the minimal gap goes against the fluid flow, this causes the formation of the local high temperature point. Fig. 21 is the velocity distributions of the coolant on the pellet’s surface. This figure illustrates that the maximum velocity of the pellet appears in the neutral position of the four narrow gap regions (as shown in
(a) +Y axis
(c) -Z axis
(b) +Z axis
(d) Maximum velocity of the central pellet Fig. 21. Velocity distribution of the central pellet.
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Z
Y
X
(a) +Y axis
Fig. 23. Definition of / and h (used in Figs. 21–23).
(b) +Z axis Fig. 24. Calculated pressure distributions of the central pellet (/ = 90°).
capacity of heat transfer is the worst at this region. Fig. 22 shows the pressure distribution of the coolant on the surface of the pellet. In this figure, the local low pressure points are generated at the upper narrow gap region of the pellet, as the water flows along the pellet surface and then separates at this region. According to the conclusions above, the temperature and pressure of the coolant on the surface of the central pellet are obtained. Meanwhile, the Nusselt number (Nu) on the surface of the central pellet is acquired. The Nu is defined as follows (in accordance with the original definition):
Nu ¼
hd k
ð12Þ
where h is the wall heat transfer coefficient defined by
h¼
(c) -Z axis Fig. 22. Pressure distribution of the central pellet.
Fig. 21d). The minimum velocity of the coolant emerged at the tail end of the pellet. The negative value of flow velocity represents the existence of backflow which is caused by the vortex. Therefore, the
q00 T w T nw
ð13Þ
d is the pellet diameter, k is the thermal conductivity of the coolant, q00 is the wall heat flux, Tw is the wall temperature of the ith cell and Tnw is the wall-adjacent temperature. Figs. 23–27 reveal the distributions of the temperature, pressure and Nu of the coolant on the central pellet in this model, respectively. The X-axis of each graph indicates the zenith angle (/) from the inlet (/ = 0°) to outlet (/ = 180°) of the central pellet,
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(a) Circle of
φ ( φ = 90°)
Fig. 27. Calculated Nusselt number on the surface of central pellet.
and 145° to 152°. These two regions always emerged at the narrow gap regions. The distribution of Nu is shown in Fig. 27. There are two minimum values which are located at the same azimuthal angle of the two temperature peaks. The two maximum Nu appear at the angles range from 15° to 25°and 155° to 170°. 5. Conclusions
(b) Temperature distributions Fig. 25. Temperature distributions of the central pellet (/ = 90°).
Fig. 26. Calculated temperature on the surface of central pellet.
as shown in Fig. 23, and h is the azimuth angle. Fig. 24 reveals the pressure distribution of the coolant on the surface of central pellet. The local high pressure points are generated when / is about 20°. In this region, the fluid which flows through the channel contacts with the pellet and impacts it. The negative velocity gradient is generated in this region which leads to the pressure increased. The temperature distributions of the coolant (/ = 90°) is shown in Fig. 25. It can be seen that the shape is a circle when / = 90° (Fig. 25a), the temperatures of this circle are shown in Fig. 25b. It is observed that the temperature distribution along h is periodic. Fig. 26 shows the two temperature peaks occur when the angle / range from 42° to 46°
In present study, the thermal hydraulic characteristics of PBWR have been investigated. Liquid water is used as the coolant. The ‘‘near-miss’’ model is adopted for the simulation. The standard j–e model is applied as the turbulence model. The thermal hydraulic characteristics of PBWR with different pellet sizes are analyzed. Some conclusions obtained are as follows: (1) The thermal hydraulic characteristics of PBWR using the BCC structure are numerically investigated. The distributions of the temperature, velocity, pressure and Nu of the coolant are obtained. It is observed that the maximum temperature of the coolant on the surface of pellet appear at the narrow gap region; the minimum temperature and maximum velocity of the coolant are located at the neutral position of the four narrow gap regions which are neighboring it; the minimum velocity occurs at the tail end of the pellet. (2) By comparing with the calculation results of two diameters (3 and 6 mm), it can be concluded that with the increase of diameter, the high-temperature region and pressure drop of the coolant decreased, meanwhile, the flow disturbance increased. Generally speaking, smaller flow disturbance and pressure drop of the coolant are beneficial to the safe operation of the reactor. Therefore, it is important to choose a right and reasonable diameter for the conceptual design and the safe operation of PBWR.
Acknowledgements The authors would like to acknowledge the project supported by Nuclear Power Institute of China (NPIC). References ANSYS CFX 11.0: Help Manual, 2006. Ansys Inc.Canada. Guardo, A., Coussirat, M., Larrayoz, M.A., et al., 2005. Influence of the turbulence model in CFD modeling of wall-to-fluid heat transfer in packed beds. Chemical Engineering Science 60 (6), 1733–1742.
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