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Scientific design of a large-scale sodium thermal–hydraulic test facility for KALIMER—Part II: Validation of reactor pool design using CFD analyses
Annals of Nuclear Energy 76 (2015) 439–450
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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Scientific design of a large-scale sodium thermal–hydraulic test facility for KALIMER—Part II: Validation of reactor pool design using CFD analyses Jong-Pil Park a, Ji Hwan Jeong a,⇑, Tae-Ho Lee b a b
School of Mechanical Engineering, Pusan National University, Jangjeon-dong, Geumjeong-gu, Busan, Republic of Korea Fast Reactor Technology Development Division, Korean Atomic Energy Research Institute, 1045 Daedeok-daero, Yuseong, Daejeon 305-353, Republic of Korea
a r t i c l e
i n f o
Article history: Received 28 August 2013 Received in revised form 20 October 2014 Accepted 22 October 2014
Keywords: SFR Thermal hydraulics Scaling analysis Computational fluid dynamics
a b s t r a c t A one-fifth scale test loop for a sodium cooled fast reactor (SFR), KALIMER-600, is designed based on scaling analyses. The coolant flow and temperature distribution inside the prototype reactor pool and 1/5 scale model are numerically analyzed using a CFD package. In order to perform the numerical analyses, numerical models are created for the reactor core and heat exchangers. The analyses results are compared with each other in terms of normalized pressure, velocity magnitude, and temperature distributions. These comparisons demonstrate that the scaling analyses for the reactor pool described in Part I are appropriate and that the one-fifth scale thermal hydraulic test facility provides appropriate simulation of the KALIMER-600 prototype. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction In the early 2000s, the Generation IV International Forum (GIF) selected six innovative reactor types that were to be built by 2030 and to have enhanced safety, economy, and nuclear non-proliferation (US DOE, 2002). A sodium cooled fast reactor (SFR) is one of these innovative reactor types. KALIMER-600 was proposed as the reference reactor for the SFR, whose demonstration reactor should be constructed by 2028 in Korea. The sodium cooled fast reactor is recognized as the most promising next generation nuclear power plant (NPP) among the six reactor types under development. The sodium cooled fast reactor has been actively developed with both its conceptual design and its test facility. Korea Atomic Energy Research Institute (KAERI) has developed the conceptual design for KALIMER-600 and is now designing an appropriate thermal hydraulic test facility (Hahn et al., 2007; Lee et al., 2007). The thermal hydraulic test facility was scaled down to be one-fifth of the size of KALIMER-600. The sizing of the test facility was determined based on a similarity scaling law as described in Part I of this research (Hong et al., 2013). The design features and concepts of KALIMER-600 require validation based on numerical analyses as well as experiments. ⇑ Corresponding author at: School of Mechanical Engineering, Pusan National University, Jangjeon-dong, Geumjeong-gu, Busan 609-735, Republic of Korea. Tel.: +82 51 510 3050; fax: +82 51 512 5236. E-mail address: [email protected] (J.H. Jeong). http://dx.doi.org/10.1016/j.anucene.2014.10.023 0306-4549/Ó 2014 Elsevier Ltd. All rights reserved.
Lumped parameter model-based system analysis codes, such as RELAP5, MARS, and TRACE, have been utilized to verify the design of nuclear power plants (NPPs). These system analysis codes provide information of the overall characteristics of NPPs; however, they do not provide detailed local information such as threedimensional velocity fields and temperature distributions. The capabilities of modern computational fluid dynamics (CFD) packages have improved sufficiently such that they can provide reliable analysis results if there is no phase change in the calculation domain. In this regard, it is reasonable to utilize CFD to verify the capability of the scaled-down sodium test facility designed using the similarity scaling law. The application of CFD to NPP safety analysis and design has been increasing for the past decade. The IAEA and OECD/NEA have published documents that provide guidance on how to use CFD in NPP applications, e.g. incorporation of CFD in system analysis codes. INEEL collaborated with ATES and General Atomics to design a nuclear steam supply system (NSSS) through incorporating FLUENT into RELAP5-3D/ATHENA. They developed a protocol that processes the analysis results of each code and that provides boundary conditions to each code. In this research, FLUENT was used to analyze the coolant flow inside the reactor vessel while RELAP5-3D/ATHENA was used for the system response analyses. Jeong and Han (2008) and Jeong et al. (2008) used a commercial CFD package to analyze the coolant flow inside an OPR1000 reactor vessel with internal structures. Based on the CFD analysis results, they evaluated the
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pressure loss coefficient and k-factor, which is user input for the system analysis codes. Recently, Yoo et al. (2010) used CFD as a scaling analysis element in order to develop a scaled-down thermal hydraulic experimental apparatus for a dry spent fuel storage cask. Except for Yoo et al.’s research, it is rare to find research in the literature where CFD is used to validate a scaling analysis. Considering the recent significant advances in CFD technology, however, it can be advantageous to use a CFD package for the flow field analysis in KALIMER-600 and for validation of the design for the 1/5 scale model. In the present study, a three-dimensional thermal hydraulic analysis was conducted focusing on the thermal hydraulic behavior inside the reactor pools of both KALIMER-600 and the one-fifth scaled-down test facility because the similarities of the multidimensional temperature and flow distributions are important. The goal of this research is to validate the reactor vessel design of the test facility through comparing the thermal hydraulic characteristics of the prototype design and one-fifth scale test facility.
flux were also determined. For this thermal hydraulic analysis, the hydraulic models (porosity and resistance coefficient of porous media, turbulence model, boundary conditions, and numerical scheme) were maintained the same as the models used in the previous analysis. The temperature and flow fields were analyzed for the cases of 100% power and coolant flow rate, and 80% power and coolant flow rate. For the 80% reactor power and coolant flow, the heat sink powers of the IHX and DHX were also set to be 80%. The pressure drops across the reactor core, IHX, and DHX should also be reduced to 64% as mentioned previously. However, the temperature level in the reactor pool should remain at the same level as the 100% design power case because the heat source power, heat sink power, and coolant flow rate were reduced by the same ratio. The numerical modeling for reactor core, IHX, and DHX are described in more detail in Sections 3.1 and 3.2. Lastly, the normalized profiles for the pressure, temperature, and velocity of the KALIMER-600 prototype were compared with those of the one-fifth scale model. In order to ensure similarity, the corresponding profiles of the prototype and model were almost the same.
2. CFD modeling method 2.2. Numerical analyses 2.1. Scaling evaluation method using CFD Inside the reactor vessel of the KALIMER-600, there are four intermediate heat exchangers (IHX), two decay heat exchangers (DHX), and two coolant pumps. The coolant in the cold pool is pumped to the core inlet plenum via two connecting pipes. Then, it flows upward to reach the hot pool through the core. The primary heat transport system (PHTS) of KALIMER-600 consists of a large volume sodium pool, which delays temperature rises in emergencies. It is also incorporated with highly reliable passive engineering safety features (ESFs), such as a passive decay heat removal circuit (PDRC), which keep KALIMER-600 safe without operating active components or operator actions during design based accidents (DBA) (Hahn et al., 2007; Lee et al., 2007). In order to verify the functionality of these design features, a one-fifth scale sodium thermal hydraulic test facility was designed. The design parameters of the test facility were determined using an appropriate scaling method for similarity, and it has been described in the Part I paper (Hong et al., 2013). The present work validates the scaled reactor vessel design from the multi-dimensional temperature and flow distribution perspectives using three-dimensional CFD analyses for both the KALIMER-600 prototype and the one-fifth scale model. The validation was performed as follows. The reactor core and IHX were represented using numerical porous media models for the convenience of CFD modeling because the local thermal hydraulic behaviors have little influence on the multi-dimensional phenomena in the reactor pool. First, a CFD analysis was performed for the KALIMER-600 prototype with a full (100%) design flow rate of coolant. At this stage, it was necessary to confirm that the porous media models for the core and heat exchanger were appropriately set. In order to validate this, CFD calculations were performed again with 80% design flow rate of coolant. The numerical models and boundary conditions remained the same, except for the reduced coolant flow rate in this calculation. The pressure drops across the reactor core model and heat exchanger model should be reduced to 64% compared with the 100% coolant flow case. These repeated CFD analyses were also undertaken for the one-fifth scale model in order to confirm its porous media parameters. After the hydraulic models of the KALIMER-600 prototype and its one-fifth scale model were proven to be appropriate, the energy equations were used with the appropriate thermal models for the relevant components. The reactor core was modeled as a heat source, while the IHX and DHX were modeled as heat sinks. Additional boundary conditions concerning the temperature and heat
In the present research, the steady-state Reynolds Averaged Navier–Stokes (RANS) equations were numerically solved for the coolant flow inside the reactor pool. The three-dimensional continuity and momentum conservation equations are written as follows:
@q @ þ ðqui Þ ¼ 0; @t @xi @ @ @p @ @u @u ðqui Þ þ ðquj ui Þ ¼ þ l i þ j qu0j u0 i ; @xi @xj @xi @xj @xj @xi
ð1Þ ð2Þ
where x, u, q, l, p, and qu0j u0 i represent the Cartesian coordinate, time averaging velocity, density, dynamic viscosity, pressure, and Reynolds stress, respectively. In order to analyze the temperature field, the energy conservation equation must also be solved:
@p @ qH @ þ quj H þ F h;j ui sij ¼ þ sh ; @t @xj @t 1 H ¼ ui ui þ h; 2 @T 0 F h;j k þ qu0j h ; @xj
ð3Þ ð4Þ ð5Þ
where sij and sh represent the stress tensor and energy source, respectively. The above conservation equations are discretized and numerically solved using the finite volume method with STAR-CD V4.06, which is a commercial CFD code. These equations were solved on a staggered grid using the RANS equations with turbulence models. The SIMPLE (semi-implicit method for pressurelinked equations) algorithm was used to ensure coupling between the velocity and pressure. The convection terms in the governing equations were discretized using a second order upwind scheme. A RANS turbulence model was utilized in the present research in order to evaluate the turbulence of the coolant flow. The renormalization group (RNG) k-e model is known to well predict flow characteristics that result from anisotropic turbulence, while the standard k-e model has mathematical limitations in describing the anisotropic turbulence (Tzanos, 2004). The RNG k-e model is used to simulate flows with large streamline curvatures, swirls, and anisotropic turbulences. The ‘‘Numerical Reactor’’ project, which was conducted as a ROK-USA collaborative I-NERI program, also involves the evaluation of the turbulence models implemented in STAR-CD, CFX, and CFD-ACE in terms of their ability to calculate flows for a fuel rod bundle configuration (Sofu et al., 2004). This work investigated various RANS models including the standard k-e model, the quadratic and
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cubic k-e models, the RNG variant, and the Reynolds Stress Model (RSM). The results demonstrate that the nonlinear quadratic k-e model and RSM model provide good agreement with the experimental results. Chun et al. (2004) also reported that the RSM model exhibited excellent performance for complex geometries and the RNG k-e model exhibited comparative performance. The RSM model is known to be superior for situations in which the anisotropy of turbulence has a dominant effect on the mean flow, such as highly swirling flows and stress-driven flows. However, the RSM model requires high computing costs and its convergence is relatively poor. Based on the findings of the aforementioned studies, the RNG k-e model was selected in the present research. The RNG k-e model uses the same turbulence kinetic energy equation as the standard k-e model, but it uses a different turbulence dissipation rate equation. The turbulence kinetic energy and turbulence dissipation rate equation for the RNG k-e model are written as follows:
@ ðqkÞ @ quj k @uj @ l @k ; þ ¼ qsij qe þ lþ t @xj @t @xj @xj rk @xj " # 3 2 @ ðqeÞ @ quj e e @ui e e2 þ C l k ð1 k=k0 Þ q e þ ¼ C e1 qsij C 3 @xj @t k @xj k 1 þ bk @ lt @ e ; þ lþ @xj rs @xj q ffiffiffiffiffiffiffiffiffiffiffiffi k k 2Sij Sji ;
e
ð6Þ
ð7Þ ð8Þ
Fig. 2. Half model of KALIMER-600.
Fig. 1. KALIMER-600 CAD model.
Fig. 3. Mesh near the inlet for the CFD analyses.
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e e2 , Cl, rk, re, b, and k0 are the closure coefficients for the where Ce1, C RNG k-e model (Wilcox, 2006).
5.6 Six million meshes Eight million meshes Twelve million meshes
Velocity magnitude (m/s)
5.4
2.3. Numerical model generation
5.2 5.0 4.8 4.6 4.4 4.2 4.0 -0.50
-0.25
0.00
0.25
0.50
Distance from the IHX center (m) Fig. 4. Effect of the mesh on the velocity magnitude at the IHX outlet.
Slip wall, Heat flux (Negative value)
IHX (Porous media, Heat sink)
DHX (Porous media, Heat sink)
Symmetric plane
Heat flux (Negative value)
Reactor core (Porous media, Heat source)
Outlet
Outlet
Inlet
Fig. 5. Numerical porous models and boundary conditions specified for the CFD analyses.
The three-dimensional CAD model for the prototype is illustrated in Fig. 1, where the reactor vessel (shell) is omitted in order to provide an internal view. The CFD analyses were performed using half of the KALIMER-600; thus, the calculation domain had two IHX, one DHX, and two half pumps. Some components that do not significantly influence the coolant flow were omitted or simplified in the calculation domain. The total height of the core was 4.6 m; it consisted of an inactive region between 0.0 m (core bottom) and 1.1 m, an active core region between 1.1 m and 2.1 m, and another inactive region between 2.1 m and 4.6 m (core top). Three porous media models were used to represent the core and a heat source model was applied to the active core. A porous media model was also used to represent the IHX. However, the inside of the DHX was represented by an empty space because there is negligible flow inside the DHX during normal operation, and there is little pressure drop across the DHX. A three-dimensional CAD model for the symmetric half domain of the KALIMER-600 reactor vessel is illustrated in Fig. 2. A 3D CAD model for the one-fifth scale reactor vessel was also constructed. A computational domain was constructed based on the 3D CAD model. Because the CAD model only considers solid parts, the fluid domain was constructed using a Boolean operation. First, a new volume was constructed in order to envelope all parts. Second, the volumes occupied by the solid parts were subtracted from the enveloping volume. Last, the remaining volume represented the fluid domain. The volumes occupied by the core, two IHX, and one DHX were separated from the whole fluid domain because these require special features such as porous media, heat sources, and heat sinks. Unstructured polyhedral meshes were independently generated in these five fluid domains, and these meshes are attached to each other in order to build a complete calculation domain. Fig. 3 presents the mesh of the calculation domain. The standard wall function was used to calculate the flow characteristics in the near wall region. The mesh generation and preliminary calculations were repeated in order that the y+ value of the near wall mesh was less than 100. Through this process, six million meshes were generated. In addition, adaptive mesh refinement was performed in order to generate fine mesh in the region where the velocity gradient is large. Through this mesh refinement, calcu-
Table 1 Design values and boundary conditions of the numerical model. Scaling factors
Numerical model applied scaling factor
Parameters
Scaling law
Scaling ratio
Length Area
l0,R
1/5 1/25
Volume
l0;R
Velocity
l0;R
Power
l0;R
2
l0;R ða0;R Þ 3
1=2 5=2
Mass flow rate
a0;R l0;R
Pressure (Head) Temperature Heat flux
l0;R T 0;R
Power density
l0;R
1=2
1=2
l0;R
1=2
Boundary condition
Prototype
1/5 model
1/125 pffiffiffi 1/ 5 pffiffiffi 1/25 5 pffiffiffi 1/25 5
Inlet mass flow, kg/s
1932.825
34.576
1/5 1 pffiffiffi 1/ 5
Inlet static pressurea, kPa Inlet temperature, K Heat flux at pool top surface, W/m2
227 663 38,555
126 663 17,350
pffiffiffi 5
Heat flux at cylindrical reactor pool vessel, W/m2 Core heat source power density, MW/m3
11,148 93.027
5,017 208.381
IHX heat sink power density, MW/m3 DHX heat sink power density, MW/m3
25.887 0.981
57.987 2.198
Reference: Hong et al. (2013). a The inlet static pressure is calculated using the sum of the reference pressure (101 kPa) and the static head.
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lation domains with eight million meshes and twelve million meshes were obtained. A comparison among the calculation results with six million, eight million, and twelve million meshes demonstrated that the eight million meshes were sufficiently fine to obtain results that are insensitive to the number of meshes, as seen in Fig. 4. Fig. 4 presents the velocity magnitude near the IHX outlet, which was located 1.5 m downstream from the IHX exit. The present CFD analyses were performed on a workstation with eight CPUs of 2.4 GHz and 42 GB of random access memory. 3. Analysis results and discussion 3.1. CFD analyses of the prototype Fig. 5 depicts the locations where the numerical porous models are used and where the boundary conditions are specified for the thermal hydraulic analyses of the KALIMER-600 reactor pool. The inlet boundaries are located at the entrance of the two pipes that connect the pump and core inlet. A mass flow rate of 1932.825 kg/s was specified for each inlet boundary, which is 50% of the total mass flow rate of the pump. This flow rate was selected because the coolant supplied from the pump was delivered to the core inlet via two connecting pipes. In addition, a static pressure of 227 kPa was specified for the inlet boundaries as the reference pressure. The static pressure was evaluated through the addition of atmospheric pressure at the pool surface to the hydraulic pressure as a result of the sodium depth from the pool surface. The coolant temperature at the inlet was specified as 663 K, which is the normal operating temperature of the cold pool. The outlet boundary conditions were specified at the outlet of the two pipes connecting the cold pool and pump entrance. A symmetric boundary condition was applied to the plane dividing the reactor pool into two halves. The slip wall boundary condition was set to the pool surface where the liquid sodium comes into contact with the Argon gas. The slip wall boundary condition was an approximate approach that assumes a zero-stress lid for the free surface. This methodology was used previously in CFD analyses of water flows on the containment floor by NEI and its appropriateness has been validated (Idelchik et al., 1986; Yoo et al., 2010). KALIMER-600 was designed to allow a thermal loss of 1.5236 MW, which corresponds to 0.1% of the rated core power, through the coolant top surface. A constant heat flux condition of 38,555 W/m2 was set on the coolant top surface, which was obtained from the heat flow divided by the coolant top surface area. The KALIMER-600 design also allows a thermal loss of 3.047 MW through the vessel wall in the radial direction, which corresponds to 0.2% of the rated core power. A constant heat flux condition of 11,148 W/m2 was specified on the cylindrical wall of the pool, which was obtained from the heat flow divided by the cylindrical wall surface area. The orthotropic porous media model was used to represent the reactor core because the coolant flow was predominantly in the axial direction of the reactor core. The porous media assumes
Table 2 Thermodynamic properties of the sodium used for the CFD analyses. Density Molecular viscosity Specific heat Conductivity Molecular weight
858.8 kg/m3 0.0002823 kg/m s 1284.3 J/kg K 73.59 W/m K 23
Fig. 6. KALIMER-600 reactor pool: (a) pressure, (b) velocity magnitude, and (c) temperature.
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distributed resistance within the volume of any complex geometry, and it requires two parameters: porosity (the ratio of the volume of the voids within the total volume) and resistance. The cross sectional area of the reactor core and the system flow rate were 16.384 m2 and 7731.3 kg/s, respectively. The average velocity in the core region should be 0.549 m/s if the core is empty. Considering that the average velocity of the KALIMER-600 reactor core is 3.2 m/s in normal operating conditions, the porosity should be approximately 0.17. The resistance factor was evaluated as follows. First, it was assumed that the pressure drop in the reactor core was dominated by a form loss with little frictional head loss. Then, the head loss can be calculated using Eq. (9):
DP ¼ k
qV 2 2
ð9Þ
The pressure loss coefficient (k) is not correlated with the Reynolds number and roughness, but it is correlated with the shape change of the flow path in a turbulent flow regime (Jeong and
Han, 2008). Substituting the design parameters such as pressure drop (213 kPa), density, and average velocity into Eq. (9), the pressure loss coefficient of the reactor core was estimated to be 48. Second, the CFD calculations were repeated with modifications of the pressure loss coefficient until the pressure drop across the reactor core using the CFD was in agreement with the design value of 213 kPa. Finally, the pressure loss coefficient was evaluated to be 49.3, and this value was adopted in the remaining analyses. The pressure loss coefficient represents the value influenced by the axial pressure drop of the reactor core. Very large lateral pressure loss coefficients were specified in order to restrict the lateral coolant flow. The same process was applied to the porous media model for the IHX. The porosity of the IHX was 0.9. The initial estimation of the pressure loss coefficient for the IHX porous media model was estimated to be 85; it was evaluated to be 85.8 using repeated CFD calculations. The reactor core represented by the porous media model was set to be a uniform heat source, while the IHX and DHX were set
Fig. 7. Velocity vector around the IHX (a) inlet and (b) outlet.
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to be uniform heat sinks. In the transients such as a loss of flow accident (LOFA), the thermal hydraulic behaviors in the reactor were significantly affected by the radial power distribution of the reactor core. However, the effect of the radial power distribution might not be significant during normal operations. Thus, the assumption of a uniform heat sink and source model could be applied in the steady state simulation. The reactor core consisted of an active core part and two inactive core parts. The active core part should generate a thermal power of 1523.6 MW. This thermal power divided by the active core volume gives a volumetric power of 93.027 MW/m3, which is specified as the heat source power density. The IHX transfers the total reactor power subtracting the thermal losses; thus, it was specified as a heat sink of 25.887 MW/m3, which corresponds to the net power divided by the IHX internal volume. The DHX was designed to have a capability of 0.5% total core power rejection; thus, the DHX was modeled as a heat sink whose power was 98.145 kW/m3. This value was obtained from 7.168 MW divided by the DHX core volume. Table 1 presents the scaling factors and boundary conditions used in the present CFD analyses. However, the present CFD analyses do not consider the temperature variations of the thermodynamic properties of sodium; instead, constant values were used. The variations of the sodium temperature based on the designed temperature of the hot and cold pools was approximately 150 K, and the thermodynamic properties varied by less than 10% in this level of temperature variation (Hong et al., 2013). The representative thermodynamic properties of sodium are presented in Table 2. Fig. 6 depicts the distributions of pressure, velocity magnitude, and temperature on the plane passing through the center lines of the reactor core and IHX for the 100% coolant flow case. The pressure drop in the reactor core was approximately eight times larger than that in the IHX; therefore, Fig. 6(a) does not exhibit a pressure contour change across the IHX. However, the pressure change in the IHX is presented and discussed in more detail in Section 3.2. In order to validate the selection of the porous media parameters, CFD analyses were also conducted with 80% coolant flow rate. The pressure drops in the reactor core and IHX for the 80% coolant flow case should be reduced to 64% compared with the case with 100% coolant flow rate, because the pressure drop is proportional to a squared velocity. Theoretically, the pressure drops in the reactor
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core and IHX should be 136.3 kPa and 16.47 kPa, respectively. The CFD analyses results demonstrate that the pressure drops were 135.1 kPa and 16.37 kPa, respectively, which are quite close to the theoretically estimated values. Based on these results, the porous media models for the reactor core and IHX were determined to be represented appropriately. Fig. 6(b) presents the velocity magnitude on the plane. The average velocities in the reactor core and at the IHX exit were estimated to be 3.2 m/s and 6.67 m/s, respectively, which are very close to the design values. The coolant flows out of the pump through the reactor core and moves to the IHX entrance via the hot pool. The velocity vector around the IHX inlet and outlet are depicted in Fig. 7. This figure demonstrates that a recirculation flow develops in the space above the inlet and that the coolant is accelerated at the exit as the flow area reduces and forms a jet, as seen in Fig. 7(b). The velocity vector around the DHX is depicted in Fig. 8, which illustrates that the coolant velocity inside the DHX is very low during normal operation. The coolant temperature distribution in the KALIMER-600 reactor pool is depicted in Fig. 6(c). This plot illustrates that the temperature changes significantly in the active core and IHX, while there is little change in the other regions, e.g. the hot pool and cold pool. This results from the heat losses through the pool surface and vessel wall being very small, which are allowed to be 0.1% and 0.2% of the reactor power. The average temperature of the coolant in the buffer region was the same as the temperature of the hot pool. This is a reasonable result because the buffer region is only connected to the hot pool in the present analysis; thus, there is no heat exchange with other regions. The coolant provided by pumps whose temperature was 663 K flowed through the reactor core and reached an average temperature of 819.6 K at the core exit. The sodium coolant received all thermal energy generated by the 1 m-high active core region, which is represented using a porous media heat source model in the present CFD analysis. The exit temperature was quite close to the temperature of the KALIMER-600 hot pool (818 K) at 100% power; therefore, it verifies that the heat source model is well established in the present CFD analysis. Then, the coolant in the hot pool flowed through the IHX and its temperature reduced to 661 K. The IHX exit temperature was also in good agreement with
Fig. 8. Velocity vector around the DHX.
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the temperature of the cold pool (663 K) at 100% power, which verifies that the heat sink model is well established for the IHX. A CFD analysis with 80% coolant flow rate and 80% reactor core power was also conducted in order to verify the parameters for the heat source and heat sink models. The temperature distribution for this case should be the same as that with 100% coolant flow rate and 100% reactor power. The core exit temperature was 819.4 K, while the inlet and exit temperatures of the IHX were 820.8 K and 661 K, respectively, which are the same level as those for the 100% coolant flow rate and 100% core power. Based on these results, the heat source and heat sink models for the reactor core and IHX of the prototype were verified to be set up appropriately.
3.2. CFD analyses of the 1/5 scale model According to the scaling criteria given in Part I (Hong et al., 2013), the scaling ratios of the one-fifth model pffiffiffi to prototype are 1/5 for pffiffiffi the length, 1/25 for the area, 1 5 for the velocity, 1=ð25 5Þ for the power and pffiffiffiflow rate, 1/5 for the pressure drop, 1 for the temperature, and 5 for the power density (see Table 1). The calculation domain for the CFD analysis was constructed to be one-fifth of the prototype size in accordance with these scaling ratios. The locations where boundary conditions are specified and their types are the same as those for the prototype analysis. The boundary conditions such as the coolant flow rate and heat fluxes were also determined according to the scaling ratios. The inlet coolant flow rate was specified as 34.576 kg/s, which was determined in accordance with the scaling ratio to be 1/55.9 of the prototype coolant flow rate. The absolute pressure of 126 kPa was specified as a reference pressure at the inlet. This was calculated through adding the hydraulic static pressure to the atmospheric pressure at the pool surface. The entrance region was located 3 m below the pool surface because the hydraulic test facility is designed such that its geometric length scale is 1/5 of the prototype, while the depth is 15 m in the full scale KALIMER-600 prototype. The coolant temperature at the inlet was specified as 663 K, which is the same as the prototype inlet conditions. The symmetry, slip-wall, and no-slip wall boundary conditions were applied on the 1/2 cut surface, pool surface, and other walls, respectively, which are the same as the boundary conditions used for the prototype analysis. According to the scaling ratios, constant wall heat fluxes of 17.350 kW/m2 and 5.017 kW/m2 were specified for the pool surface and cylindrical vessel wall, respectively. The porosities of the porous media models representing the reactor core and IHX were specified to be 0.17 and 0.9, respectively, which are the same levels as the porous media models for the prototype, while the resistance factors were assigned to be five times larger than the prototype. Using the scaling criteria, the lengths of the reactor core and IHX were 1/5 of the prototype reactor core and IHX. In addition, the pressure drops in the test facility’s core and IHX should also be 1/5 of the pressure drops in prototype core and IHX. pffiffiffi Because the mean velocity in the reactor vessel is reduced to 1= 5 times smaller, the pressure drop per unit length of the porous media should be five times larger. Therefore, the resistance factors were determined to be five times larger than those for the prototype, which correspond to 246.5 and 429.0 for the reactor core and IHX, respectively. A heat source model was applied to the porous media core model, while a heat sink model was applied to the IHX. The core power density should be 2.24 times larger than that of the prototype; thus, a power density of 208.381 MW/m3 was applied to the core heat source model. Based on the same method, the power density of the IHX and DHX were designed to be 57.987 MW/m3 and 2.198 MW/m3, respectively.
Fig. 9. The (a) pressure, (b) velocity magnitude, and (c) temperature distributions of the 1/5 scale reactor pool (100% flow rate and core power).
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Fig. 10. Normalized pressure in the reactor pool of the prototype (left) and 1/5 scale model (right).
Fig. 11. Normalized pressure in the IHX of the prototype (left) and 1/5 scale model (right).
Fig. 12. Normalized velocity magnitude in the reactor pool of the prototype (left) and 1/5 scale model (right).
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Fig. 9 presents the pressure, velocity magnitude, and temperature contours on the plane passing through the center lines of the reactor core and IHX. The average velocities in the reactor core and IHX exit were 1.43 m/s and 2.94 m/s, respectively. These average velocities are in good agreement with 1.429 m/s and 2.988 m/s, which were theoretically obtained from the velocitiespin ffiffiffi the prototype reactor pool multiplied by the scaling ratio (1= 5). The pressure drop in the reactor core of the 1/5 scale model was estimated to be 41.8 kPa, which is very close to 42.6 kPa and is 1/5 of the pressure drop in the prototype. This proves that the reactor core of the 1/5 scale model is represented using an appropriate numerical porous media model. The CFD analyses evaluated the pressure drop in the IHX to be 5.09 kPa, which is also close to 1/ 5 of the pressure drop in the IHX of the prototype (5.146 kPa). In order to validate the selection of the porous media parameters, additional CFD analyses were conducted using the 80% coolant flow rate. The pressure drops in the reactor core and IHX according
to the CFD analysis with 80% coolant flow rate were estimated to be 27.0 kPa and 3.25 kPa, respectively. These pressure drops agree well with the pressure drops in the prototype (41.8 kPa and 5.09 kPa, respectively) multiplied by 0.82 = 0.64. Based on these results, the numerical porous media models for the reactor core and IHX of the 1/5 scale model were verified to be appropriately represented. The average sodium coolant temperature was calculated to reach 819.7 K as it flowed through the active core of the 1/5 scale model. This temperature estimated using the CFD analysis corresponds to less than 1% discrepancy from the design value because the average temperature of the hot pool in the prototype design was 818 K. Based on this result, it was verified that the numerical heat source model for the reactor core of the 1/5 scale model was appropriately specified. The IHX inlet temperature was estimated to be 820.6 K, which agrees well with the hot pool average temperature (818 K). The IHX inlet and outlet temperatures were esti-
Fig. 13. Normalized velocity magnitude in the IHX of the prototype (left) and 1/5 scale model (right).
Fig. 14. Normalized quantities distribution at horizontal plane in hot pool of the prototype (upper row) and 1/5 scale model (lower row).
J.-P. Park et al. / Annals of Nuclear Energy 76 (2015) 439–450
mated to be 820.6 K and 660.1 K, respectively. These temperatures agree well with the hot pool average temperature (818 K) and cold pool average temperature (663 K) of the prototype design. Using these comparisons, it was verified that the heat sink model for the IHX was also represented using an appropriate numerical model. In order to validate the parameters of the heat source and heat sink models for the thermal hydraulic analysis of the 1/5 scale model, CFD analyses were conducted with 80% coolant flow rate
and 80% core power. The temperature distribution obtained with the reduced boundary conditions should have the same levels as those obtained with the 100% coolant flow rate and full core power. The analysis results from the reduced boundary conditions demonstrated that the core exit temperature was 818.7 K, while the inlet and exit temperatures of the IHX were 820.6 K and 659.7 K, respectively. These temperatures had the same level as the results from the 100% operating conditions. Based on these results, the heat source model for the reactor core and the heat sink model for the IHX were determined to be well established.
3.3. Comparison between the prototype and 1/5 scale model analyses
IHX region
Hot pool region near core exit
449
Vessel wall
Normalized quantities
1.0 0.8 0.6 0.4 0.2
Velocity of prototype Temperature of prototype Velocity of 1/5 scale model Temperature of 1/5 scale model
0.0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
Distance from the reactor center (m) 1.10
Prototype 1/5 scale model
Normalized velocity magnitude
1.05 IHX outlet 1.00
0.95
0.90
0.85
0.80 -0.50
-0.25
0.00
0.25
0.50
Distance from the IHX center (m) Fig. 15. Normalized quantities of the reactor pool (upper) and normalized velocity magnitudes of the IHX outlet (lower) for the prototype and 1/5 scale model.
The CFD analyses results for the prototype reactor pool and its 1/5 scale model were compared in order to validate the design of the 1/5 scale reactor vessel in terms of its three-dimensional thermal hydraulic behavior. The CFD results discussed in this section were obtained under 100% flow rate and 100% reactor power conditions. The comparisons were made in terms of normalized quantities. The physical quantities are normalized such that the maximum and minimum correspond to ‘1’ and ‘0’, respectively. Figs. 10 and 11 present the normalized pressure distributions in the reactor pool and IHX of the prototype and 1/5 scale model, respectively. The pressure appeared to change gradually in the reactor core and IHX. The contour lines in the reactor core and IHX also appear to be pressure contours in a pipe flow because they are represented using porous media models. The contour of the normalized pressure in the 1/5 scale model was almost identical to that in the prototype. Figs. 12 and 13 present the normalized velocity magnitude distribution on the plane passing through the reactor core and DHX, and those on the plane passing through the IHX, respectively. In Fig. 12, it is seen that coolant velocity magnitude contour above the reactor core has a complicated pattern. This appears to result from the interaction of the sodium coolant with the upper internal structures when it flows upward above the core. When the coolant comes out of the core, it forms a jet. This contour plot also illustrates that the jet is slightly slanted toward vessel wall. Figs. 12 and 13 also demonstrate that the normalized velocity magnitudes in the reactor pools for the prototype and 1/5 scale model were almost identical. The normalized velocity, temperature, and pressure distributions of the horizontal plane 2.5 m above the core exit are depicted in Fig. 14. The profiles of the normalized velocity and temperature along the line from the reactor center to the vessel wall including the IHX are plotted in Fig. 15, and the detailed profile of the normalized velocity at the IHX outlet is also plotted in Fig. 15. This plot
Fig. 16. Normalized temperatures in the reactor pool of the prototype (left) and 1/5 scale model (right).
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Fig. 17. Normalized temperature in the IHX of the prototype (left) and 1/5 scale model (right).
demonstrates that the profiles obtained from the prototype analyses are in good agreement with those from the 1/5 scale model. The normalized temperature distributions in the reactor pools of the prototype and 1/5 scale model are compared in Fig. 16. In general, they exhibit almost the same normalized temperature level. A significant temperature change was observed in the reactor core, while slight temperature variations were observed in the hot pool and cold pool. It is believed that the heat losses through the pool surface and vessel wall were sufficiently small that they did not cause significant temperature changes in the pools. Fig. 17 presents the normalized temperature distribution on a vertical cross-section through the IHX. These two normalized temperature contour plots for the prototype and 1/5 scale model appear to be the same in general. In contrast, Fig. 16 can be interpreted as the real temperature distribution because the scaling ratio for the temperature distribution was 1. The normalized distributions of the coolant velocity, pressure, and temperature for the 1/5 scale model are in excellent agreement with their distributions for the KALIMER-600 prototype. Thus, it is expected that 1/5 scale reactor vessel model would preserve the multi-dimensional thermal hydraulic behavior in the reactor pool of the prototype. 4. Conclusion In order to validate the similarity of the multi-dimensional thermal hydraulic behavior inside the reactor vessel of the 1/5 scale model sodium thermal hydraulic test facility that was presented in Part I, three-dimensional analyses were performed using a CFD package. The thermal hydraulic flow fields inside the prototype reactor pool and the 1/5 scale model were numerically analyzed in order to assess the similarities in pressure, velocity, and temperature distributions. In order to perform the numerical analyses, simplified porous media models were used to represent the reactor core and IHX. User-defined function features were also used to specify the heat source model for the heat generation by the reactor core and the heat sink model for the heat removal by the IHX and DHX. The boundary conditions for the 1/5 scale model were determined in accordance with a scaling ratio. The analysis results were compared in terms of normalized pressure, velocity
magnitude, and temperature distributions. This comparison demonstrated that the 1/5 scale reactor vessel model could reproduce the multi-dimensional thermal hydraulic behavior in the reactor pool of KALIMER-600. Furthermore, the developed methodology can be used for transient analyses in future studies. Acknowledgements This research was supported by National Nuclear R&D Program (NRF-2011-0031770) and Basic Science Research Program (NRF2012R1A1A2007320) through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology. References Chun, K.H., Hwang, Y.D., Yoon, H.Y., Kim, H.C., Zee, S.Q., 2004. Assessment of RANS models for 3-D flow analysis of SMART. J. Korean Nucl. Soc. 36, 248–262. Hahn, D.H., Kim, Y.I., Lee, C.B., Kim, S.O., Lee, J.H., Lee, Y.B., Kim, B.H., Jeong, H.Y., 2007. Conceptual design of the sodium cooled fast reactor KALIMER-600. Nucl. Eng. Technol. 39, 193–206. Hong, S.H., Lee, D.H., Eoh, J.H., Lee, T.H., Lee, Y.B., 2013. Scientific design of a largescale sodium thermal-hydraulic test facility for KALIMER-Part I: scientific facility design. Nucl. Eng. Des. 265, 497–513. Idelchik, I.E., Malyavskaya, G.R., Martnenko, O.G., Fried, E., 1986. Handbook of Hydraulic Resistance, second ed. Hemisphere, Washington DC, USA. Jeong, J.H., Han, B.S., 2008. Coolant flow field in a real geometry of PWR downcomer and lower plenum. Ann. Nucl. Energy 35, 610–619. Jeong, J.H., Park, J.P., Han, B.S., 2008. Head loss coefficient evaluation based on CFD analysis for PWR downcomer and lower plenum. Heat Transfer Eng. 29, 677– 684. Lee, J.H., Park, C.G., Kim, J.B., Koo, G.H., 2007. Mechanical structure design features of the KALIMER-600 sodium-cooled fast reactor. In: Proceedings of SMiRT-19, Toronto, Canada. Sofu, T., Chun, T.H., In, W.K., 2004. Evaluation of turbulence models for flow and heat transfer in fuel rod bundle geometries. In: Proceedings of ANS Reactor Physics Topical Meeting, PHYSOR 2004, Chicago, USA. Tzanos, C.P., 2004. Computational fluid dynamics for the analysis of light water reactor flows. Nucl. Technol. 147, 181–190. US DOE, GIF, 2002. A Technology Roadmap for Generation IV Nuclear Energy Systems, GIF-002-00. Wilcox, D.C., 2006. Turbulence Modeling for CFD, third ed. DCW Industries, California, USA. Yoo, S.H., No, H.C., Kim, H.M., Lee, E.H., 2010. CFD-assisted scaling methodology and thermal-hydraulic experiment for a single spent fuel assembly. Nucl. Eng. Des. 240, 4008–4020.
Contents lists available at ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Scientific design of a large-scale sodium thermal–hydraulic test facility for KALIMER—Part II: Validation of reactor pool design using CFD analyses Jong-Pil Park a, Ji Hwan Jeong a,⇑, Tae-Ho Lee b a b
School of Mechanical Engineering, Pusan National University, Jangjeon-dong, Geumjeong-gu, Busan, Republic of Korea Fast Reactor Technology Development Division, Korean Atomic Energy Research Institute, 1045 Daedeok-daero, Yuseong, Daejeon 305-353, Republic of Korea
a r t i c l e
i n f o
Article history: Received 28 August 2013 Received in revised form 20 October 2014 Accepted 22 October 2014
Keywords: SFR Thermal hydraulics Scaling analysis Computational fluid dynamics
a b s t r a c t A one-fifth scale test loop for a sodium cooled fast reactor (SFR), KALIMER-600, is designed based on scaling analyses. The coolant flow and temperature distribution inside the prototype reactor pool and 1/5 scale model are numerically analyzed using a CFD package. In order to perform the numerical analyses, numerical models are created for the reactor core and heat exchangers. The analyses results are compared with each other in terms of normalized pressure, velocity magnitude, and temperature distributions. These comparisons demonstrate that the scaling analyses for the reactor pool described in Part I are appropriate and that the one-fifth scale thermal hydraulic test facility provides appropriate simulation of the KALIMER-600 prototype. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction In the early 2000s, the Generation IV International Forum (GIF) selected six innovative reactor types that were to be built by 2030 and to have enhanced safety, economy, and nuclear non-proliferation (US DOE, 2002). A sodium cooled fast reactor (SFR) is one of these innovative reactor types. KALIMER-600 was proposed as the reference reactor for the SFR, whose demonstration reactor should be constructed by 2028 in Korea. The sodium cooled fast reactor is recognized as the most promising next generation nuclear power plant (NPP) among the six reactor types under development. The sodium cooled fast reactor has been actively developed with both its conceptual design and its test facility. Korea Atomic Energy Research Institute (KAERI) has developed the conceptual design for KALIMER-600 and is now designing an appropriate thermal hydraulic test facility (Hahn et al., 2007; Lee et al., 2007). The thermal hydraulic test facility was scaled down to be one-fifth of the size of KALIMER-600. The sizing of the test facility was determined based on a similarity scaling law as described in Part I of this research (Hong et al., 2013). The design features and concepts of KALIMER-600 require validation based on numerical analyses as well as experiments. ⇑ Corresponding author at: School of Mechanical Engineering, Pusan National University, Jangjeon-dong, Geumjeong-gu, Busan 609-735, Republic of Korea. Tel.: +82 51 510 3050; fax: +82 51 512 5236. E-mail address: [email protected] (J.H. Jeong). http://dx.doi.org/10.1016/j.anucene.2014.10.023 0306-4549/Ó 2014 Elsevier Ltd. All rights reserved.
Lumped parameter model-based system analysis codes, such as RELAP5, MARS, and TRACE, have been utilized to verify the design of nuclear power plants (NPPs). These system analysis codes provide information of the overall characteristics of NPPs; however, they do not provide detailed local information such as threedimensional velocity fields and temperature distributions. The capabilities of modern computational fluid dynamics (CFD) packages have improved sufficiently such that they can provide reliable analysis results if there is no phase change in the calculation domain. In this regard, it is reasonable to utilize CFD to verify the capability of the scaled-down sodium test facility designed using the similarity scaling law. The application of CFD to NPP safety analysis and design has been increasing for the past decade. The IAEA and OECD/NEA have published documents that provide guidance on how to use CFD in NPP applications, e.g. incorporation of CFD in system analysis codes. INEEL collaborated with ATES and General Atomics to design a nuclear steam supply system (NSSS) through incorporating FLUENT into RELAP5-3D/ATHENA. They developed a protocol that processes the analysis results of each code and that provides boundary conditions to each code. In this research, FLUENT was used to analyze the coolant flow inside the reactor vessel while RELAP5-3D/ATHENA was used for the system response analyses. Jeong and Han (2008) and Jeong et al. (2008) used a commercial CFD package to analyze the coolant flow inside an OPR1000 reactor vessel with internal structures. Based on the CFD analysis results, they evaluated the
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pressure loss coefficient and k-factor, which is user input for the system analysis codes. Recently, Yoo et al. (2010) used CFD as a scaling analysis element in order to develop a scaled-down thermal hydraulic experimental apparatus for a dry spent fuel storage cask. Except for Yoo et al.’s research, it is rare to find research in the literature where CFD is used to validate a scaling analysis. Considering the recent significant advances in CFD technology, however, it can be advantageous to use a CFD package for the flow field analysis in KALIMER-600 and for validation of the design for the 1/5 scale model. In the present study, a three-dimensional thermal hydraulic analysis was conducted focusing on the thermal hydraulic behavior inside the reactor pools of both KALIMER-600 and the one-fifth scaled-down test facility because the similarities of the multidimensional temperature and flow distributions are important. The goal of this research is to validate the reactor vessel design of the test facility through comparing the thermal hydraulic characteristics of the prototype design and one-fifth scale test facility.
flux were also determined. For this thermal hydraulic analysis, the hydraulic models (porosity and resistance coefficient of porous media, turbulence model, boundary conditions, and numerical scheme) were maintained the same as the models used in the previous analysis. The temperature and flow fields were analyzed for the cases of 100% power and coolant flow rate, and 80% power and coolant flow rate. For the 80% reactor power and coolant flow, the heat sink powers of the IHX and DHX were also set to be 80%. The pressure drops across the reactor core, IHX, and DHX should also be reduced to 64% as mentioned previously. However, the temperature level in the reactor pool should remain at the same level as the 100% design power case because the heat source power, heat sink power, and coolant flow rate were reduced by the same ratio. The numerical modeling for reactor core, IHX, and DHX are described in more detail in Sections 3.1 and 3.2. Lastly, the normalized profiles for the pressure, temperature, and velocity of the KALIMER-600 prototype were compared with those of the one-fifth scale model. In order to ensure similarity, the corresponding profiles of the prototype and model were almost the same.
2. CFD modeling method 2.2. Numerical analyses 2.1. Scaling evaluation method using CFD Inside the reactor vessel of the KALIMER-600, there are four intermediate heat exchangers (IHX), two decay heat exchangers (DHX), and two coolant pumps. The coolant in the cold pool is pumped to the core inlet plenum via two connecting pipes. Then, it flows upward to reach the hot pool through the core. The primary heat transport system (PHTS) of KALIMER-600 consists of a large volume sodium pool, which delays temperature rises in emergencies. It is also incorporated with highly reliable passive engineering safety features (ESFs), such as a passive decay heat removal circuit (PDRC), which keep KALIMER-600 safe without operating active components or operator actions during design based accidents (DBA) (Hahn et al., 2007; Lee et al., 2007). In order to verify the functionality of these design features, a one-fifth scale sodium thermal hydraulic test facility was designed. The design parameters of the test facility were determined using an appropriate scaling method for similarity, and it has been described in the Part I paper (Hong et al., 2013). The present work validates the scaled reactor vessel design from the multi-dimensional temperature and flow distribution perspectives using three-dimensional CFD analyses for both the KALIMER-600 prototype and the one-fifth scale model. The validation was performed as follows. The reactor core and IHX were represented using numerical porous media models for the convenience of CFD modeling because the local thermal hydraulic behaviors have little influence on the multi-dimensional phenomena in the reactor pool. First, a CFD analysis was performed for the KALIMER-600 prototype with a full (100%) design flow rate of coolant. At this stage, it was necessary to confirm that the porous media models for the core and heat exchanger were appropriately set. In order to validate this, CFD calculations were performed again with 80% design flow rate of coolant. The numerical models and boundary conditions remained the same, except for the reduced coolant flow rate in this calculation. The pressure drops across the reactor core model and heat exchanger model should be reduced to 64% compared with the 100% coolant flow case. These repeated CFD analyses were also undertaken for the one-fifth scale model in order to confirm its porous media parameters. After the hydraulic models of the KALIMER-600 prototype and its one-fifth scale model were proven to be appropriate, the energy equations were used with the appropriate thermal models for the relevant components. The reactor core was modeled as a heat source, while the IHX and DHX were modeled as heat sinks. Additional boundary conditions concerning the temperature and heat
In the present research, the steady-state Reynolds Averaged Navier–Stokes (RANS) equations were numerically solved for the coolant flow inside the reactor pool. The three-dimensional continuity and momentum conservation equations are written as follows:
@q @ þ ðqui Þ ¼ 0; @t @xi @ @ @p @ @u @u ðqui Þ þ ðquj ui Þ ¼ þ l i þ j qu0j u0 i ; @xi @xj @xi @xj @xj @xi
ð1Þ ð2Þ
where x, u, q, l, p, and qu0j u0 i represent the Cartesian coordinate, time averaging velocity, density, dynamic viscosity, pressure, and Reynolds stress, respectively. In order to analyze the temperature field, the energy conservation equation must also be solved:
@p @ qH @ þ quj H þ F h;j ui sij ¼ þ sh ; @t @xj @t 1 H ¼ ui ui þ h; 2 @T 0 F h;j k þ qu0j h ; @xj
ð3Þ ð4Þ ð5Þ
where sij and sh represent the stress tensor and energy source, respectively. The above conservation equations are discretized and numerically solved using the finite volume method with STAR-CD V4.06, which is a commercial CFD code. These equations were solved on a staggered grid using the RANS equations with turbulence models. The SIMPLE (semi-implicit method for pressurelinked equations) algorithm was used to ensure coupling between the velocity and pressure. The convection terms in the governing equations were discretized using a second order upwind scheme. A RANS turbulence model was utilized in the present research in order to evaluate the turbulence of the coolant flow. The renormalization group (RNG) k-e model is known to well predict flow characteristics that result from anisotropic turbulence, while the standard k-e model has mathematical limitations in describing the anisotropic turbulence (Tzanos, 2004). The RNG k-e model is used to simulate flows with large streamline curvatures, swirls, and anisotropic turbulences. The ‘‘Numerical Reactor’’ project, which was conducted as a ROK-USA collaborative I-NERI program, also involves the evaluation of the turbulence models implemented in STAR-CD, CFX, and CFD-ACE in terms of their ability to calculate flows for a fuel rod bundle configuration (Sofu et al., 2004). This work investigated various RANS models including the standard k-e model, the quadratic and
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cubic k-e models, the RNG variant, and the Reynolds Stress Model (RSM). The results demonstrate that the nonlinear quadratic k-e model and RSM model provide good agreement with the experimental results. Chun et al. (2004) also reported that the RSM model exhibited excellent performance for complex geometries and the RNG k-e model exhibited comparative performance. The RSM model is known to be superior for situations in which the anisotropy of turbulence has a dominant effect on the mean flow, such as highly swirling flows and stress-driven flows. However, the RSM model requires high computing costs and its convergence is relatively poor. Based on the findings of the aforementioned studies, the RNG k-e model was selected in the present research. The RNG k-e model uses the same turbulence kinetic energy equation as the standard k-e model, but it uses a different turbulence dissipation rate equation. The turbulence kinetic energy and turbulence dissipation rate equation for the RNG k-e model are written as follows:
@ ðqkÞ @ quj k @uj @ l @k ; þ ¼ qsij qe þ lþ t @xj @t @xj @xj rk @xj " # 3 2 @ ðqeÞ @ quj e e @ui e e2 þ C l k ð1 k=k0 Þ q e þ ¼ C e1 qsij C 3 @xj @t k @xj k 1 þ bk @ lt @ e ; þ lþ @xj rs @xj q ffiffiffiffiffiffiffiffiffiffiffiffi k k 2Sij Sji ;
e
ð6Þ
ð7Þ ð8Þ
Fig. 2. Half model of KALIMER-600.
Fig. 1. KALIMER-600 CAD model.
Fig. 3. Mesh near the inlet for the CFD analyses.
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e e2 , Cl, rk, re, b, and k0 are the closure coefficients for the where Ce1, C RNG k-e model (Wilcox, 2006).
5.6 Six million meshes Eight million meshes Twelve million meshes
Velocity magnitude (m/s)
5.4
2.3. Numerical model generation
5.2 5.0 4.8 4.6 4.4 4.2 4.0 -0.50
-0.25
0.00
0.25
0.50
Distance from the IHX center (m) Fig. 4. Effect of the mesh on the velocity magnitude at the IHX outlet.
Slip wall, Heat flux (Negative value)
IHX (Porous media, Heat sink)
DHX (Porous media, Heat sink)
Symmetric plane
Heat flux (Negative value)
Reactor core (Porous media, Heat source)
Outlet
Outlet
Inlet
Fig. 5. Numerical porous models and boundary conditions specified for the CFD analyses.
The three-dimensional CAD model for the prototype is illustrated in Fig. 1, where the reactor vessel (shell) is omitted in order to provide an internal view. The CFD analyses were performed using half of the KALIMER-600; thus, the calculation domain had two IHX, one DHX, and two half pumps. Some components that do not significantly influence the coolant flow were omitted or simplified in the calculation domain. The total height of the core was 4.6 m; it consisted of an inactive region between 0.0 m (core bottom) and 1.1 m, an active core region between 1.1 m and 2.1 m, and another inactive region between 2.1 m and 4.6 m (core top). Three porous media models were used to represent the core and a heat source model was applied to the active core. A porous media model was also used to represent the IHX. However, the inside of the DHX was represented by an empty space because there is negligible flow inside the DHX during normal operation, and there is little pressure drop across the DHX. A three-dimensional CAD model for the symmetric half domain of the KALIMER-600 reactor vessel is illustrated in Fig. 2. A 3D CAD model for the one-fifth scale reactor vessel was also constructed. A computational domain was constructed based on the 3D CAD model. Because the CAD model only considers solid parts, the fluid domain was constructed using a Boolean operation. First, a new volume was constructed in order to envelope all parts. Second, the volumes occupied by the solid parts were subtracted from the enveloping volume. Last, the remaining volume represented the fluid domain. The volumes occupied by the core, two IHX, and one DHX were separated from the whole fluid domain because these require special features such as porous media, heat sources, and heat sinks. Unstructured polyhedral meshes were independently generated in these five fluid domains, and these meshes are attached to each other in order to build a complete calculation domain. Fig. 3 presents the mesh of the calculation domain. The standard wall function was used to calculate the flow characteristics in the near wall region. The mesh generation and preliminary calculations were repeated in order that the y+ value of the near wall mesh was less than 100. Through this process, six million meshes were generated. In addition, adaptive mesh refinement was performed in order to generate fine mesh in the region where the velocity gradient is large. Through this mesh refinement, calcu-
Table 1 Design values and boundary conditions of the numerical model. Scaling factors
Numerical model applied scaling factor
Parameters
Scaling law
Scaling ratio
Length Area
l0,R
1/5 1/25
Volume
l0;R
Velocity
l0;R
Power
l0;R
2
l0;R ða0;R Þ 3
1=2 5=2
Mass flow rate
a0;R l0;R
Pressure (Head) Temperature Heat flux
l0;R T 0;R
Power density
l0;R
1=2
1=2
l0;R
1=2
Boundary condition
Prototype
1/5 model
1/125 pffiffiffi 1/ 5 pffiffiffi 1/25 5 pffiffiffi 1/25 5
Inlet mass flow, kg/s
1932.825
34.576
1/5 1 pffiffiffi 1/ 5
Inlet static pressurea, kPa Inlet temperature, K Heat flux at pool top surface, W/m2
227 663 38,555
126 663 17,350
pffiffiffi 5
Heat flux at cylindrical reactor pool vessel, W/m2 Core heat source power density, MW/m3
11,148 93.027
5,017 208.381
IHX heat sink power density, MW/m3 DHX heat sink power density, MW/m3
25.887 0.981
57.987 2.198
Reference: Hong et al. (2013). a The inlet static pressure is calculated using the sum of the reference pressure (101 kPa) and the static head.
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lation domains with eight million meshes and twelve million meshes were obtained. A comparison among the calculation results with six million, eight million, and twelve million meshes demonstrated that the eight million meshes were sufficiently fine to obtain results that are insensitive to the number of meshes, as seen in Fig. 4. Fig. 4 presents the velocity magnitude near the IHX outlet, which was located 1.5 m downstream from the IHX exit. The present CFD analyses were performed on a workstation with eight CPUs of 2.4 GHz and 42 GB of random access memory. 3. Analysis results and discussion 3.1. CFD analyses of the prototype Fig. 5 depicts the locations where the numerical porous models are used and where the boundary conditions are specified for the thermal hydraulic analyses of the KALIMER-600 reactor pool. The inlet boundaries are located at the entrance of the two pipes that connect the pump and core inlet. A mass flow rate of 1932.825 kg/s was specified for each inlet boundary, which is 50% of the total mass flow rate of the pump. This flow rate was selected because the coolant supplied from the pump was delivered to the core inlet via two connecting pipes. In addition, a static pressure of 227 kPa was specified for the inlet boundaries as the reference pressure. The static pressure was evaluated through the addition of atmospheric pressure at the pool surface to the hydraulic pressure as a result of the sodium depth from the pool surface. The coolant temperature at the inlet was specified as 663 K, which is the normal operating temperature of the cold pool. The outlet boundary conditions were specified at the outlet of the two pipes connecting the cold pool and pump entrance. A symmetric boundary condition was applied to the plane dividing the reactor pool into two halves. The slip wall boundary condition was set to the pool surface where the liquid sodium comes into contact with the Argon gas. The slip wall boundary condition was an approximate approach that assumes a zero-stress lid for the free surface. This methodology was used previously in CFD analyses of water flows on the containment floor by NEI and its appropriateness has been validated (Idelchik et al., 1986; Yoo et al., 2010). KALIMER-600 was designed to allow a thermal loss of 1.5236 MW, which corresponds to 0.1% of the rated core power, through the coolant top surface. A constant heat flux condition of 38,555 W/m2 was set on the coolant top surface, which was obtained from the heat flow divided by the coolant top surface area. The KALIMER-600 design also allows a thermal loss of 3.047 MW through the vessel wall in the radial direction, which corresponds to 0.2% of the rated core power. A constant heat flux condition of 11,148 W/m2 was specified on the cylindrical wall of the pool, which was obtained from the heat flow divided by the cylindrical wall surface area. The orthotropic porous media model was used to represent the reactor core because the coolant flow was predominantly in the axial direction of the reactor core. The porous media assumes
Table 2 Thermodynamic properties of the sodium used for the CFD analyses. Density Molecular viscosity Specific heat Conductivity Molecular weight
858.8 kg/m3 0.0002823 kg/m s 1284.3 J/kg K 73.59 W/m K 23
Fig. 6. KALIMER-600 reactor pool: (a) pressure, (b) velocity magnitude, and (c) temperature.
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distributed resistance within the volume of any complex geometry, and it requires two parameters: porosity (the ratio of the volume of the voids within the total volume) and resistance. The cross sectional area of the reactor core and the system flow rate were 16.384 m2 and 7731.3 kg/s, respectively. The average velocity in the core region should be 0.549 m/s if the core is empty. Considering that the average velocity of the KALIMER-600 reactor core is 3.2 m/s in normal operating conditions, the porosity should be approximately 0.17. The resistance factor was evaluated as follows. First, it was assumed that the pressure drop in the reactor core was dominated by a form loss with little frictional head loss. Then, the head loss can be calculated using Eq. (9):
DP ¼ k
qV 2 2
ð9Þ
The pressure loss coefficient (k) is not correlated with the Reynolds number and roughness, but it is correlated with the shape change of the flow path in a turbulent flow regime (Jeong and
Han, 2008). Substituting the design parameters such as pressure drop (213 kPa), density, and average velocity into Eq. (9), the pressure loss coefficient of the reactor core was estimated to be 48. Second, the CFD calculations were repeated with modifications of the pressure loss coefficient until the pressure drop across the reactor core using the CFD was in agreement with the design value of 213 kPa. Finally, the pressure loss coefficient was evaluated to be 49.3, and this value was adopted in the remaining analyses. The pressure loss coefficient represents the value influenced by the axial pressure drop of the reactor core. Very large lateral pressure loss coefficients were specified in order to restrict the lateral coolant flow. The same process was applied to the porous media model for the IHX. The porosity of the IHX was 0.9. The initial estimation of the pressure loss coefficient for the IHX porous media model was estimated to be 85; it was evaluated to be 85.8 using repeated CFD calculations. The reactor core represented by the porous media model was set to be a uniform heat source, while the IHX and DHX were set
Fig. 7. Velocity vector around the IHX (a) inlet and (b) outlet.
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to be uniform heat sinks. In the transients such as a loss of flow accident (LOFA), the thermal hydraulic behaviors in the reactor were significantly affected by the radial power distribution of the reactor core. However, the effect of the radial power distribution might not be significant during normal operations. Thus, the assumption of a uniform heat sink and source model could be applied in the steady state simulation. The reactor core consisted of an active core part and two inactive core parts. The active core part should generate a thermal power of 1523.6 MW. This thermal power divided by the active core volume gives a volumetric power of 93.027 MW/m3, which is specified as the heat source power density. The IHX transfers the total reactor power subtracting the thermal losses; thus, it was specified as a heat sink of 25.887 MW/m3, which corresponds to the net power divided by the IHX internal volume. The DHX was designed to have a capability of 0.5% total core power rejection; thus, the DHX was modeled as a heat sink whose power was 98.145 kW/m3. This value was obtained from 7.168 MW divided by the DHX core volume. Table 1 presents the scaling factors and boundary conditions used in the present CFD analyses. However, the present CFD analyses do not consider the temperature variations of the thermodynamic properties of sodium; instead, constant values were used. The variations of the sodium temperature based on the designed temperature of the hot and cold pools was approximately 150 K, and the thermodynamic properties varied by less than 10% in this level of temperature variation (Hong et al., 2013). The representative thermodynamic properties of sodium are presented in Table 2. Fig. 6 depicts the distributions of pressure, velocity magnitude, and temperature on the plane passing through the center lines of the reactor core and IHX for the 100% coolant flow case. The pressure drop in the reactor core was approximately eight times larger than that in the IHX; therefore, Fig. 6(a) does not exhibit a pressure contour change across the IHX. However, the pressure change in the IHX is presented and discussed in more detail in Section 3.2. In order to validate the selection of the porous media parameters, CFD analyses were also conducted with 80% coolant flow rate. The pressure drops in the reactor core and IHX for the 80% coolant flow case should be reduced to 64% compared with the case with 100% coolant flow rate, because the pressure drop is proportional to a squared velocity. Theoretically, the pressure drops in the reactor
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core and IHX should be 136.3 kPa and 16.47 kPa, respectively. The CFD analyses results demonstrate that the pressure drops were 135.1 kPa and 16.37 kPa, respectively, which are quite close to the theoretically estimated values. Based on these results, the porous media models for the reactor core and IHX were determined to be represented appropriately. Fig. 6(b) presents the velocity magnitude on the plane. The average velocities in the reactor core and at the IHX exit were estimated to be 3.2 m/s and 6.67 m/s, respectively, which are very close to the design values. The coolant flows out of the pump through the reactor core and moves to the IHX entrance via the hot pool. The velocity vector around the IHX inlet and outlet are depicted in Fig. 7. This figure demonstrates that a recirculation flow develops in the space above the inlet and that the coolant is accelerated at the exit as the flow area reduces and forms a jet, as seen in Fig. 7(b). The velocity vector around the DHX is depicted in Fig. 8, which illustrates that the coolant velocity inside the DHX is very low during normal operation. The coolant temperature distribution in the KALIMER-600 reactor pool is depicted in Fig. 6(c). This plot illustrates that the temperature changes significantly in the active core and IHX, while there is little change in the other regions, e.g. the hot pool and cold pool. This results from the heat losses through the pool surface and vessel wall being very small, which are allowed to be 0.1% and 0.2% of the reactor power. The average temperature of the coolant in the buffer region was the same as the temperature of the hot pool. This is a reasonable result because the buffer region is only connected to the hot pool in the present analysis; thus, there is no heat exchange with other regions. The coolant provided by pumps whose temperature was 663 K flowed through the reactor core and reached an average temperature of 819.6 K at the core exit. The sodium coolant received all thermal energy generated by the 1 m-high active core region, which is represented using a porous media heat source model in the present CFD analysis. The exit temperature was quite close to the temperature of the KALIMER-600 hot pool (818 K) at 100% power; therefore, it verifies that the heat source model is well established in the present CFD analysis. Then, the coolant in the hot pool flowed through the IHX and its temperature reduced to 661 K. The IHX exit temperature was also in good agreement with
Fig. 8. Velocity vector around the DHX.
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the temperature of the cold pool (663 K) at 100% power, which verifies that the heat sink model is well established for the IHX. A CFD analysis with 80% coolant flow rate and 80% reactor core power was also conducted in order to verify the parameters for the heat source and heat sink models. The temperature distribution for this case should be the same as that with 100% coolant flow rate and 100% reactor power. The core exit temperature was 819.4 K, while the inlet and exit temperatures of the IHX were 820.8 K and 661 K, respectively, which are the same level as those for the 100% coolant flow rate and 100% core power. Based on these results, the heat source and heat sink models for the reactor core and IHX of the prototype were verified to be set up appropriately.
3.2. CFD analyses of the 1/5 scale model According to the scaling criteria given in Part I (Hong et al., 2013), the scaling ratios of the one-fifth model pffiffiffi to prototype are 1/5 for pffiffiffi the length, 1/25 for the area, 1 5 for the velocity, 1=ð25 5Þ for the power and pffiffiffiflow rate, 1/5 for the pressure drop, 1 for the temperature, and 5 for the power density (see Table 1). The calculation domain for the CFD analysis was constructed to be one-fifth of the prototype size in accordance with these scaling ratios. The locations where boundary conditions are specified and their types are the same as those for the prototype analysis. The boundary conditions such as the coolant flow rate and heat fluxes were also determined according to the scaling ratios. The inlet coolant flow rate was specified as 34.576 kg/s, which was determined in accordance with the scaling ratio to be 1/55.9 of the prototype coolant flow rate. The absolute pressure of 126 kPa was specified as a reference pressure at the inlet. This was calculated through adding the hydraulic static pressure to the atmospheric pressure at the pool surface. The entrance region was located 3 m below the pool surface because the hydraulic test facility is designed such that its geometric length scale is 1/5 of the prototype, while the depth is 15 m in the full scale KALIMER-600 prototype. The coolant temperature at the inlet was specified as 663 K, which is the same as the prototype inlet conditions. The symmetry, slip-wall, and no-slip wall boundary conditions were applied on the 1/2 cut surface, pool surface, and other walls, respectively, which are the same as the boundary conditions used for the prototype analysis. According to the scaling ratios, constant wall heat fluxes of 17.350 kW/m2 and 5.017 kW/m2 were specified for the pool surface and cylindrical vessel wall, respectively. The porosities of the porous media models representing the reactor core and IHX were specified to be 0.17 and 0.9, respectively, which are the same levels as the porous media models for the prototype, while the resistance factors were assigned to be five times larger than the prototype. Using the scaling criteria, the lengths of the reactor core and IHX were 1/5 of the prototype reactor core and IHX. In addition, the pressure drops in the test facility’s core and IHX should also be 1/5 of the pressure drops in prototype core and IHX. pffiffiffi Because the mean velocity in the reactor vessel is reduced to 1= 5 times smaller, the pressure drop per unit length of the porous media should be five times larger. Therefore, the resistance factors were determined to be five times larger than those for the prototype, which correspond to 246.5 and 429.0 for the reactor core and IHX, respectively. A heat source model was applied to the porous media core model, while a heat sink model was applied to the IHX. The core power density should be 2.24 times larger than that of the prototype; thus, a power density of 208.381 MW/m3 was applied to the core heat source model. Based on the same method, the power density of the IHX and DHX were designed to be 57.987 MW/m3 and 2.198 MW/m3, respectively.
Fig. 9. The (a) pressure, (b) velocity magnitude, and (c) temperature distributions of the 1/5 scale reactor pool (100% flow rate and core power).
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Fig. 10. Normalized pressure in the reactor pool of the prototype (left) and 1/5 scale model (right).
Fig. 11. Normalized pressure in the IHX of the prototype (left) and 1/5 scale model (right).
Fig. 12. Normalized velocity magnitude in the reactor pool of the prototype (left) and 1/5 scale model (right).
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Fig. 9 presents the pressure, velocity magnitude, and temperature contours on the plane passing through the center lines of the reactor core and IHX. The average velocities in the reactor core and IHX exit were 1.43 m/s and 2.94 m/s, respectively. These average velocities are in good agreement with 1.429 m/s and 2.988 m/s, which were theoretically obtained from the velocitiespin ffiffiffi the prototype reactor pool multiplied by the scaling ratio (1= 5). The pressure drop in the reactor core of the 1/5 scale model was estimated to be 41.8 kPa, which is very close to 42.6 kPa and is 1/5 of the pressure drop in the prototype. This proves that the reactor core of the 1/5 scale model is represented using an appropriate numerical porous media model. The CFD analyses evaluated the pressure drop in the IHX to be 5.09 kPa, which is also close to 1/ 5 of the pressure drop in the IHX of the prototype (5.146 kPa). In order to validate the selection of the porous media parameters, additional CFD analyses were conducted using the 80% coolant flow rate. The pressure drops in the reactor core and IHX according
to the CFD analysis with 80% coolant flow rate were estimated to be 27.0 kPa and 3.25 kPa, respectively. These pressure drops agree well with the pressure drops in the prototype (41.8 kPa and 5.09 kPa, respectively) multiplied by 0.82 = 0.64. Based on these results, the numerical porous media models for the reactor core and IHX of the 1/5 scale model were verified to be appropriately represented. The average sodium coolant temperature was calculated to reach 819.7 K as it flowed through the active core of the 1/5 scale model. This temperature estimated using the CFD analysis corresponds to less than 1% discrepancy from the design value because the average temperature of the hot pool in the prototype design was 818 K. Based on this result, it was verified that the numerical heat source model for the reactor core of the 1/5 scale model was appropriately specified. The IHX inlet temperature was estimated to be 820.6 K, which agrees well with the hot pool average temperature (818 K). The IHX inlet and outlet temperatures were esti-
Fig. 13. Normalized velocity magnitude in the IHX of the prototype (left) and 1/5 scale model (right).
Fig. 14. Normalized quantities distribution at horizontal plane in hot pool of the prototype (upper row) and 1/5 scale model (lower row).
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mated to be 820.6 K and 660.1 K, respectively. These temperatures agree well with the hot pool average temperature (818 K) and cold pool average temperature (663 K) of the prototype design. Using these comparisons, it was verified that the heat sink model for the IHX was also represented using an appropriate numerical model. In order to validate the parameters of the heat source and heat sink models for the thermal hydraulic analysis of the 1/5 scale model, CFD analyses were conducted with 80% coolant flow rate
and 80% core power. The temperature distribution obtained with the reduced boundary conditions should have the same levels as those obtained with the 100% coolant flow rate and full core power. The analysis results from the reduced boundary conditions demonstrated that the core exit temperature was 818.7 K, while the inlet and exit temperatures of the IHX were 820.6 K and 659.7 K, respectively. These temperatures had the same level as the results from the 100% operating conditions. Based on these results, the heat source model for the reactor core and the heat sink model for the IHX were determined to be well established.
3.3. Comparison between the prototype and 1/5 scale model analyses
IHX region
Hot pool region near core exit
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Vessel wall
Normalized quantities
1.0 0.8 0.6 0.4 0.2
Velocity of prototype Temperature of prototype Velocity of 1/5 scale model Temperature of 1/5 scale model
0.0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
Distance from the reactor center (m) 1.10
Prototype 1/5 scale model
Normalized velocity magnitude
1.05 IHX outlet 1.00
0.95
0.90
0.85
0.80 -0.50
-0.25
0.00
0.25
0.50
Distance from the IHX center (m) Fig. 15. Normalized quantities of the reactor pool (upper) and normalized velocity magnitudes of the IHX outlet (lower) for the prototype and 1/5 scale model.
The CFD analyses results for the prototype reactor pool and its 1/5 scale model were compared in order to validate the design of the 1/5 scale reactor vessel in terms of its three-dimensional thermal hydraulic behavior. The CFD results discussed in this section were obtained under 100% flow rate and 100% reactor power conditions. The comparisons were made in terms of normalized quantities. The physical quantities are normalized such that the maximum and minimum correspond to ‘1’ and ‘0’, respectively. Figs. 10 and 11 present the normalized pressure distributions in the reactor pool and IHX of the prototype and 1/5 scale model, respectively. The pressure appeared to change gradually in the reactor core and IHX. The contour lines in the reactor core and IHX also appear to be pressure contours in a pipe flow because they are represented using porous media models. The contour of the normalized pressure in the 1/5 scale model was almost identical to that in the prototype. Figs. 12 and 13 present the normalized velocity magnitude distribution on the plane passing through the reactor core and DHX, and those on the plane passing through the IHX, respectively. In Fig. 12, it is seen that coolant velocity magnitude contour above the reactor core has a complicated pattern. This appears to result from the interaction of the sodium coolant with the upper internal structures when it flows upward above the core. When the coolant comes out of the core, it forms a jet. This contour plot also illustrates that the jet is slightly slanted toward vessel wall. Figs. 12 and 13 also demonstrate that the normalized velocity magnitudes in the reactor pools for the prototype and 1/5 scale model were almost identical. The normalized velocity, temperature, and pressure distributions of the horizontal plane 2.5 m above the core exit are depicted in Fig. 14. The profiles of the normalized velocity and temperature along the line from the reactor center to the vessel wall including the IHX are plotted in Fig. 15, and the detailed profile of the normalized velocity at the IHX outlet is also plotted in Fig. 15. This plot
Fig. 16. Normalized temperatures in the reactor pool of the prototype (left) and 1/5 scale model (right).
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Fig. 17. Normalized temperature in the IHX of the prototype (left) and 1/5 scale model (right).
demonstrates that the profiles obtained from the prototype analyses are in good agreement with those from the 1/5 scale model. The normalized temperature distributions in the reactor pools of the prototype and 1/5 scale model are compared in Fig. 16. In general, they exhibit almost the same normalized temperature level. A significant temperature change was observed in the reactor core, while slight temperature variations were observed in the hot pool and cold pool. It is believed that the heat losses through the pool surface and vessel wall were sufficiently small that they did not cause significant temperature changes in the pools. Fig. 17 presents the normalized temperature distribution on a vertical cross-section through the IHX. These two normalized temperature contour plots for the prototype and 1/5 scale model appear to be the same in general. In contrast, Fig. 16 can be interpreted as the real temperature distribution because the scaling ratio for the temperature distribution was 1. The normalized distributions of the coolant velocity, pressure, and temperature for the 1/5 scale model are in excellent agreement with their distributions for the KALIMER-600 prototype. Thus, it is expected that 1/5 scale reactor vessel model would preserve the multi-dimensional thermal hydraulic behavior in the reactor pool of the prototype. 4. Conclusion In order to validate the similarity of the multi-dimensional thermal hydraulic behavior inside the reactor vessel of the 1/5 scale model sodium thermal hydraulic test facility that was presented in Part I, three-dimensional analyses were performed using a CFD package. The thermal hydraulic flow fields inside the prototype reactor pool and the 1/5 scale model were numerically analyzed in order to assess the similarities in pressure, velocity, and temperature distributions. In order to perform the numerical analyses, simplified porous media models were used to represent the reactor core and IHX. User-defined function features were also used to specify the heat source model for the heat generation by the reactor core and the heat sink model for the heat removal by the IHX and DHX. The boundary conditions for the 1/5 scale model were determined in accordance with a scaling ratio. The analysis results were compared in terms of normalized pressure, velocity
magnitude, and temperature distributions. This comparison demonstrated that the 1/5 scale reactor vessel model could reproduce the multi-dimensional thermal hydraulic behavior in the reactor pool of KALIMER-600. Furthermore, the developed methodology can be used for transient analyses in future studies. Acknowledgements This research was supported by National Nuclear R&D Program (NRF-2011-0031770) and Basic Science Research Program (NRF2012R1A1A2007320) through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology. References Chun, K.H., Hwang, Y.D., Yoon, H.Y., Kim, H.C., Zee, S.Q., 2004. Assessment of RANS models for 3-D flow analysis of SMART. J. Korean Nucl. Soc. 36, 248–262. Hahn, D.H., Kim, Y.I., Lee, C.B., Kim, S.O., Lee, J.H., Lee, Y.B., Kim, B.H., Jeong, H.Y., 2007. Conceptual design of the sodium cooled fast reactor KALIMER-600. Nucl. Eng. Technol. 39, 193–206. Hong, S.H., Lee, D.H., Eoh, J.H., Lee, T.H., Lee, Y.B., 2013. Scientific design of a largescale sodium thermal-hydraulic test facility for KALIMER-Part I: scientific facility design. Nucl. Eng. Des. 265, 497–513. Idelchik, I.E., Malyavskaya, G.R., Martnenko, O.G., Fried, E., 1986. Handbook of Hydraulic Resistance, second ed. Hemisphere, Washington DC, USA. Jeong, J.H., Han, B.S., 2008. Coolant flow field in a real geometry of PWR downcomer and lower plenum. Ann. Nucl. Energy 35, 610–619. Jeong, J.H., Park, J.P., Han, B.S., 2008. Head loss coefficient evaluation based on CFD analysis for PWR downcomer and lower plenum. Heat Transfer Eng. 29, 677– 684. Lee, J.H., Park, C.G., Kim, J.B., Koo, G.H., 2007. Mechanical structure design features of the KALIMER-600 sodium-cooled fast reactor. In: Proceedings of SMiRT-19, Toronto, Canada. Sofu, T., Chun, T.H., In, W.K., 2004. Evaluation of turbulence models for flow and heat transfer in fuel rod bundle geometries. In: Proceedings of ANS Reactor Physics Topical Meeting, PHYSOR 2004, Chicago, USA. Tzanos, C.P., 2004. Computational fluid dynamics for the analysis of light water reactor flows. Nucl. Technol. 147, 181–190. US DOE, GIF, 2002. A Technology Roadmap for Generation IV Nuclear Energy Systems, GIF-002-00. Wilcox, D.C., 2006. Turbulence Modeling for CFD, third ed. DCW Industries, California, USA. Yoo, S.H., No, H.C., Kim, H.M., Lee, E.H., 2010. CFD-assisted scaling methodology and thermal-hydraulic experiment for a single spent fuel assembly. Nucl. Eng. Des. 240, 4008–4020.