Coolant flow field in a real geometry of PWR downcomer and lower plenum

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1 Available online at annals of NUCLEAR ENERGY Annals of Nuclear Energy 35 (2008) Coolant flow field in a real geometry of PWR downcomer and lower plenum Ji Hwan Jeong a, *, Byoung-Sub Han b a School of Mechanical Engineering, Pusan National University, Busan , Republic of Korea b Enesys, Jangdae-dong, Yusong-gu, Daejeon , Republic of Korea Received 7 February 2007; received in revised form 12 August 2007; accepted 13 August 2007 Available online 1 October 2007 Abstract Nuclear vendors and utilities perform numerous simulations and analyses in order to ensure the safe operation of nuclear power plants (NPPs). In general, the simulations are carried out using vendor-specific design codes and best-estimate system analysis codes, most of which were developed based on one-dimensional lumped parameter models. During the past decade, however, computers, parallel computation methods, and three-dimensional computational fluid dynamics (CFD) codes have been dramatically enhanced. The use of advanced commercial CFD codes is considered beneficial in the safety analysis and design of NPPs. The present work analyzes the flow distribution in the downcomer and lower plenum of Korean standard nuclear power plants (KSNPs) using STAR-CD. The lower plenum geometry of a PWR is very complicated since there are so many reactor internals, which hinders in CFD analysis for real reactor geometry up to now. The present work takes advantage of 3D CAD model so that real geometry of a PWR is used. The results give a clear figure about flow fields in the downcomer and lower plenum of a PWR, which is one of major safety concerns. Ó 2007 Elsevier Ltd. All rights reserved. 1. Introduction During the design period and commercial operation of nuclear power plants (NPP), numerous safety analyses are performed, in part because nuclear regulatory bodies require the vendor and utility to report a wealth of simulation results in order to ensure the safe operation of the NPP. In general, simulations are carried out using vendor-specific design codes and best-estimate system analysis codes. Currently, CATHARE (Bestion, 1990), MARS (KAERI, 2004), RELAP (The RELAP5 code development team, 1995), and TRAC (Liles, 1986) are used as best-estimate system analysis codes. These thermal-hydraulic system codes have powerful features such as multi-phase flow and phase-change models and event programming. However, these codes still have weaknesses: They are not mechanistic but use lumped-parameter models. Even * Corresponding author. Tel.: ; fax: address: jihwan@pusan.ac.kr (J.H. Jeong). though some codes recently have incorporated threedimensional (3D) capability, all have been developed based on a one-dimensional (1D) lumped parameter model. This is because development of these codes commenced in the 1970s and 80s. At this time, computing resources were so expensive that reducing computing time was important. During the past decade, however, computing power has been dramatically enhanced in terms of speed, capability, and expenses. Meanwhile, mechanistic computational fluid dynamics (CFD) codes also made considerable progress during this period. Currently, commercial CFD codes are applied to very large and complex systems design such as an indoor auto racing complex (Zhai et al., 2002) and chemical plant buildings (Baker et al., 2002). In spite of the recent progress in computing hardware and software, the nuclear industry still uses conventional system codes based on a lumped parameter model. The use of advanced commercial CFD codes is considered beneficial in the safety analysis and design of NPPs. During the past decade, commercial CFD codes have been applied to NPP real geometry with the aim of exam /$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi: /j.anucene

2 J.H. Jeong, B.-S. Han / Annals of Nuclear Energy 35 (2008) ining local thermo-hydraulic phenomena such as the safety injection flow in the downcomer (Kwon et al., 2003), turbulence due to the incorporation of a mixing vane (In et al., 2001), and sub-channel analysis (Weber et al., 2000). Among the most frequently examined regions where CFD analysis is applied are the downcomer and lower plenum of the PWR (Kwon et al., 2003; Gango, 1997; Wang, 2005). Their design has considerable influence on the flow behaviour in the reactor core and raise safety issues and costs for NPP vendors and utilities. For this reason, the downcomer and lower plenum are of interest regarding CFD applications. In spite of various efforts to apply commercial CFD codes to NPP safety issues with the classical k e model, advanced numerical methods such as LES and DNS have not yet been applied to nuclear reactor systems. The current status and needs in commercial CFD codes usage for NPPs safety analyses are well addressed by Yadigaroglu et al. (Yadigaroglu et al., 2003). The aforementioned applications of commercial CFD codes to NPP safety analyses have been made with relatively simple or simplified calculation geometry. To the best of the authors knowledge, there has been no CFD analysis for the flow in the lower plenum and upper plenum without geometric simplification. The present work analyzes the flow distribution in the downcomer and lower plenum of Korean standard nuclear power plants (KSNPs). The real geometry is used in the analysis. The results provide a clear figure about the flow distribution in the reactor vessel, which is a major safety concern. The STAR-CD, a widely used commercial CFD code, is employed in the present work. 2. Numerical model As the lower plenum governs the coolant supply to each fuel assembly in the reactor core, it is very important to have a clear picture of flow behaviour inside it with minimum uncertainty. This can be achieved by CFD analyses with non-simplified real geometry. Fig. 1 shows a 3D CAD drawing of the PWR lower plenum. Its geometry is very complicated because there are so many reactor internals including the flow skirt, lower support structure, flow plate, in-core-instrument (ICI) nozzles, and ICI nozzle support plate. These complicated reactor internals make it almost impossible to build the geometry of calculation domain and generate a mesh. The present work utilizes the 3D CAD model for a PWR in order to make it possible. In this work, a quarter of the KSNP reactor vessel and internals from the cold-leg inlet nozzle to lower support structure are taken into account. Neither the upper plenum nor the fuel assembly is considered. An empty space is assumed to be placed above the top-end of the lower support structure to model empty reactor core space Geometry and mesh The geometry of the calculation space is built as follows. First, all solid parts of the reactor vessel and internals are modeled using the 3D CAD package. Second, a volume enveloping all solid parts is created. Third, the calculation space is obtained by Boolean subtracting of all solid parts from the volume generated in the second step. Fourth, CAD clean-up and geometry correction are performed to produce the final calculation geometry. The geometry data of the calculation domain is then imported into a mesh generation tool. The average size of cells is about 1 in. and a minimum of 16 edges are made around each circle. These criteria generated more than 3.3 million unstructured cells. During the CFD analysis, adaptive cell refinement is performed based on a gradient of variables. This process increased the cell number to around 5 million cells. The resultant unstructured mesh after adaptive refinement is illustrated in Fig. 2. Numerous cylindrical pillars, which represent holes perforated in the flow plate, appear to interconnect the upper and lower fluid spaces. Fine meshes are generated in the vicinity of walls including holes perforated in the flow plate and flow skirt. Both Figs. 1 and 2 show only the lower plenum, but the calculation domain includes the annular downcomer, cold-leg, and hot-leg nozzles Turbulence model Fig. 1. CAD drawing of lower plenum. Commercial CFD codes usually solve the Reynolds averaged Navier Stoke s equations (RANS models) for a turbulence simulation and they provide users with various turbulence models ranging from the 0-equation model to the large eddy simulation model (LES). Even though the standard high Reynolds (Re) number k e model is used widely in engineering applications, no single turbulence model can predict a sufficiently wide range of flows with accuracy adequate for engineering needs (Tzanos, 2004). Therefore, it is recommended to assess turbulence models for a specific engineering application. Some works for this

3 612 J.H. Jeong, B.-S. Han / Annals of Nuclear Energy 35 (2008) Fig. 2. Unstructured mesh for the lower plenum. purpose have been presented and thus are only briefly summarized here. Tzanos (2004) evaluated a number of k e models including the standard high Re number model, the low Re number model, the RNG model, and a twolayer model. They reported that the discrepancy between flow velocity predictions and measurements was large near components that cause significant flow deflections. They claimed these discrepancies can be attributed to shortcomings of the k e turbulence models. The ROK-US collaborative I-NERI project known as the Numerical Reactor also involves the evaluation of turbulence models implemented in STAR-CD, CFX, and CFD-ACE in terms of their ability to calculate the flow for a fuel rod bundle configuration (Sofu et al., 2004). This work focused on RANS models including the standard k e model, quadratic and cubic k e models, the renormalization-group (RNG) variant, and RSM model. The results show that the nonlinear quadratic k e model is superior to the standard k e model; however, the RSM model provides the best agreement with the experimental results. Chun et al. (2004) also reported that the RSM model showed excellent performance for complex geometries in spite of very large computing costs. Based on the findings of the aforementioned studies, the RSM model was selected in the present simulation. 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 cases include highly swirling flows and stress-driven flows. The RSM involves calculation of the individual Reynolds stresses, u 0 iu 0 j, using differential transport equations. The individual Reynolds stresses are then used to close the Reynolds-averaged momentum equation. The transport equations for the Reynolds stresses are written as follows: o ot ðqu0 iu 0 jþþ o ðqu k u 0 ox iu 0 jþ¼ o ½qu 0 k ox iu 0 ju 0 k þ pðd kju 0 i þ d ik u 0 jþš k þ o l o ðu 0 ox k ox iu 0 jþ k ou q u 0 iu 0 j ou k þ u 0 ox ju 0 i k k ox k qbðg i u 0 jh þ g j u 0 ihþ þ p ou0 i þ ou0 j 2l ou0 i ou 0 j ox j ox i ox k ox k 2qX k ðu 0 ju 0 m e ikm þ u 0 iu 0 m e jkmþ þ S user-defined

4 J.H. Jeong, B.-S. Han / Annals of Nuclear Energy 35 (2008) In order to close the above equation, modeling assumptions for several right-hand-side terms are required because some of the RHS terms are unknown. These include the first (turbulent diffusion), fourth (buoyancy production), fifth (pressure strain), and sixth (dissipation) terms, which have been modeled by many investigators. It is known that the pressure strain term is of great importance in Reynolds stress closure and its modeling is crucial to the success of the RSM model. In this work, the Craft model (Craft and Launder, 1991) was selected for the term since there are impinging flows against reactor internals. Default values were used for various coefficients for the RSM model and the standard wall function was used to treat the wall boundary layer. Based on interim simulation results such as velocity gradient and y+ distribution, cells were refined. Consequently, y+ values were maintained at less than Upward (y-direction) Velocity Component (m/s) M cells 4.2 M cells 5.0 M cells Distance from symmetrical plane (in) (a) Velocity profile just above the flow plate 20 Upward Velocity Component (m/s) M cells 4.2 M cells 5.0 M cells Distance from center of a hole (in) (b) Velocity profile of a hole perforated in the flow plate Fig. 3. Mesh sensitivity.

5 614 J.H. Jeong, B.-S. Han / Annals of Nuclear Energy 35 (2008) Numerical simulation In the present work, a commercial CFD code STAR- CD Version 3.22 was used. This is a 3D multi-physics code based on an unstructured mesh. A second-order upwind differencing scheme for the convection terms is used. Analyses were performed with SIMPLE algorithm and steady state assumption. Inlet boundary condition was applied to the cold-leg inlet nozzle. The velocity at this location was set based on cold stand-by test condition; mass flow rate of 82,500 gpm. The static pressure at this location of Pa was used as a reference value. Outlet boundary condition was applied to an imaginary exit that was extruded vertically upward from the top-end of the lower support structure. Both sides of the calculation domain that confine the quarter volume of the reactor are assigned a symmetric boundary condition. It should be noted, however, that in reality a quarter scale of calculation domain for the KSNP plant may not show the flow symmetry due to the loop characteristics of four cold-legs and two hot-legs. The energy equation is not solved so that single-phase flow only is simulated and no buoyancy effect is considered in this simulation. The convergence criterion for any calculation was such that the scaled residuals decrease to for velocity components and turbulence quantities. In this work, however, the convergence was judged not only by examining residual levels, but also by monitoring its behavior. For some quantities such as turbulence, the residuals start to build up at first, decrease later, and eventually the change slows down. The simulations were performed on a Linux cluster. This cluster computer consists of one master node and two slave nodes. The master node has two 64-bit Opteron processors and 6 Gbit RAM and each slave node has one 64-bit Athlon processor and 3 Gbit RAM. The master node communicates with the slave nodes via a Giga-bit switch. around an obstacle with abruptly changing cross-sectional area like the perforated holes of the lower support structure. Furthermore, in some cases of inappropriate setting of the outlet boundary conditions, the parabolic distribution of flow velocities may not be formed. In order to clarify these concerns, some holes were selected and the velocity profiles of them were examined. One of them is plotted in Fig. 3b and this plot shows parabolic velocity distribution and non-sensitivity of meshing very near the flow holes Flow distribution The flow field and pressure distributions in the downcomer and lower plenum have been analyzed. A contour plot for the velocity magnitude in the downcomer and the lower plenum is illustrated in Fig. 4. Supplied coolant through the cold-leg nozzle impinges onto the inner end of the calculation domain (core support barrel). A stagnant point appears as a white circular area in Fig. 4, and is parallel to the cold-leg inlet nozzle. A dark colored high velocity region encircles this stagnant point, indicating that the coolant flows in radial directions even though it is not uniform. The coolant flow in the downcomer near the cold-leg should be influenced by the existence of hot- 3. Analysis results Before considering the analysis results, the mesh sensitivity needs to be assessed. Fig. 3a shows the velocity magnitude profiles along a horizontal line passing between the lower support structure and flow plate. Since the line proceeds along with a line of holes perforated in the flow plate, the velocity magnitude profile shows cyclic behaviour: velocity is very high above the perforation while low above the plate. This plot compares simulations carried out using 3.3 M cells, 4.2 M cells, and 5.0 M cells. We can see there is slight difference between the results from the 3.3 M cells and 4.2 M cells. This difference appears to be negligible in the cases of 4.2 M cells and 5.0 M cells. Another thing to be addressed is concerned with flow field around perforated holes. Even in case of unstructured mesh using the adaptive refinement based on a gradient of velocity, it is expected to have a variety of predicted flow fields, depending on the shapes and the number of meshes, especially Fig. 4. Velocity magnitude contour in downcomer and lower plenum.

6 J.H. Jeong, B.-S. Han / Annals of Nuclear Energy 35 (2008) Downward Velocity Component (m/s) cold leg hot leg CL of cold leg 4-20 in -40 in -100 in in -220 in Angle (degree) Fig. 5. Downward velocity of coolant in downcomer. leg pipe which passes through downcomer. This contour plot also shows a non-uniform downward coolant flow in the downcomer. A low flow rate region develops below the cold-leg inlet nozzle. A considerable portion of coolant appears to flow away from this region. Fig. 5 shows the downward velocity component at various levels along the azimuthal axis of the cylindrical downcomer. The values of this plot represent the average downward velocity at the middle of the flow path. The CL of cold-leg in the legend (solid rectangular points) represents a horizontal line passing through the center of the cold-leg inlet nozzle. This line is a reference level. The other symbols represent distances from the reference level. The top of the flow skirt would be located at around 240 in. This plot shows that non-uniformity of the flow distribution in the downcomer is significant. A parabolic downward velocity profile implies that the coolant mass flow rate through the flow skirt varies significantly depending on its angular location. This non-uniform flow distribution may influence or be influenced by the downstream, that is, the coolant-flow in the lower plenum. A reduction in downward velocity at a specific location also implies that the coolant flow may have a strong azimuthal-direction component in the downcomer. A velocity vector plot in a symmetric end surface of the calculation domain is shown in Fig. 6. The length and number density of the arrow are proportional to the coolant velocity and number density of the mesh, respectively. This plot shows that the coolant descending through the downcomer flows fast through perforations in the flow skirt and proceeds upward through holes perforated in the flow plate located just below the lower support beams. This plot also shows that a high velocity flow field develops around the in-core-instrument (ICI) guide tubes as well. Fig. 6 also shows that each flow channel divided by crossed lower support beams exchanges coolant flow with the adjacent channels. Contours of velocity magnitude at various levels are plotted in Fig. 7. Each horizontal cross-section corresponds to numbering in Fig. 6. Fig. 7a shows the coolant exiting the downcomer travels to the bottom of the lower head but it is nearly stagnant at the bottom. The ICI nozzle support plate has little effect on coolant flow behaviour, as can be seen in Fig. 7b. Fig. 7c and d shows the coolant jetted toward the center through the flow skirt holes is influenced by instrument guide tubes and mixed as it flows upward. Furthermore, jet lengths of the flows through perforations in the flow skirt are different from each other Fig. 6. Velocity vector plot in lower plenum. h (-220in) g (-235in) f (-240in) e (-250in) d (-260in) c (-270in) b (-275in) a (-290in)

7 616 J.H. Jeong, B.-S. Han / Annals of Nuclear Energy 35 (2008) Fig. 7. Velocity magnitude contour in lower plenum at various level. depending on the perforation size. The flow skirt of the KSNP has three banks of perforations, as shown in Fig. 1. The upper bank and the middle bank consist of single and three rows of perforations of the same diameter. The lower bank has three rows of perforations whose diameter is larger than the others. Fig. 7c and d correspond to levels where the lower bank and middle bank of perforations are situated. These two plots show that the coolant flowing through the lower bank of perforations flows farther into the central region than the flows through the upper and middle banks. The coolant is accelerated when it flows upward through flow plate (e) and it mixes as it

8 J.H. Jeong, B.-S. Han / Annals of Nuclear Energy 35 (2008) flows upward (f h), even though the coolant flows at higher velocity around the ICI guide tubes. Above the lower support structure, the coolant gets further mixed as it proceeds downstream. However, it should be noted that this space is in reality occupied by a fuel assembly but was assumed to be empty in this calculation. Coolant mass flow distribution at the bottom end of the reactor core is of importance because it directly affects the critical heat flux (CHF) and hot channel factor and, consequently, the operating limit of the NPP (Jeong et al., 2005). In a conventional nuclear safety analysis a penalty factor is applied, for instance 20% less than the average mass flow rate, for the hot channel factor calculation. If the exact coolant mass flow rate through each fuel assembly is obtained, we can assess whether the penalty factor is appropriate. Therefore, mass flux through each compartment of LSS was evaluated, as shown in Fig. 8. The cross-section on which the mass flux is evaluated is located between g and h in Fig. 6. The mass flux was calculated by the mass flow rate in each compartment divided by the corresponding compartment area. Fig. 8 shows that the coolant flow rate varies with LSS compartments and the deviation from the average value is within ±20% except for at some points. However, this does not mean that the mass flow rate of each channel varies to this extent, because cross flow among adjacent fuel assemblies is allowed; thus, a b mass flux average mass flux 6000 mass flux (kg/m 2 s) % - 20% cell number Fig. 8. Mass flux at each compartment of lower support structure.

9 618 J.H. Jeong, B.-S. Han / Annals of Nuclear Energy 35 (2008) the mass flow rate difference would be reduced in the reactor core Pressure drop The total pressure, i.e., the static pressure plus dynamic pressure, at the surface of the calculation domain is plotted in Fig. 9. This plot shows that the total pressure of the coolant decreases as it travels downstream. Furthermore, the pressure drop across the flow skirt and flow plate just below the support beams appears to be significant. This agrees with the observed physical phenomenon that a large pressure drop occurs when fluid flows across a region of sudden contraction expansion. In order to extract useful information from this result, average piezometric pressure over cross-sections at several levels was calculated. The pressure drops between two successive stations are summarized in Table 1. This table shows that a large pressure drop occurs across the lower support structure. This work evaluates the total pressure drop between the cold-leg nozzle throat and the top of the lower support structure as 19.5 psi. The pressure drop across the same station was estimated as 18 psi in engineering calculation notes. This discrepancy results from the geometric difference between a real NPP and the model in this work. The KSNP allows a bypass of 3% of total coolant flow through the outlet nozzle clearance, in-core instrument guide tubes, core support barrel alignment keyways, and Table 1 Pressure drop (piezometric) through RV Station DP (psi) Reference design value: 82,500 gpm/cold-leg at nominal full power. core shroud annulus. In this work, however, no bypass was modeled and thus 100% of the coolant should flow through the lower support structure. This effect need to be considered in the pressure drop estimation in order to compare the pressure drop by the current CFD analysis with the KSNP design data. Regarding the pressure drop to be proportional to squared velocity, the pressure drop by the CFD analysis should be evaluated as 94% (= ) of 19.5 psi, 18.3 psi. This value is quite close to the design value. 4. Concluding remarks The understanding of coolant behaviour inside the lower plenum and downcomer is very important in NPP safety analyses as well as with respect to operational performance. However, there has been no CFD analysis for the flow in a nuclear reactor s lower plenum and upper plenum with real NPP geometries, as these geometries are too complicated for CFD engineers to model. The present work utilizes a 3D CAD model for the PWR in order to build the geometry of the calculation domain for the lower plenum and downcomer of a PWR. The real geometry of the KSNP was used in the analysis. A commercial CFD code, STAR-CD, was used to analyze the flow and pressure distribution of single phase coolant in the reactor vessel at normal operating conditions. The results provide a clear figure about flow fields in the downcomer and lower plenum of a PWR reactor. The evaluated pressure drop across the downcomer and lower plenum showed good agreement with the values in engineering calculation data. The coolant flow in the downcomer appeared to be non-uniform with a low velocity region below the cold-leg inlet nozzle. The downward velocity profile developed into a parabolic shape as it flows downstream in the downcomer. The mass flux distribution at the lower support structure was also estimated. The mass flux of coolant at each compartment of the lower support structure varied within a deviation of around ±20% from the average. Acknowledgements Fig. 9. Total pressure contour in downcomer and lower plenum. This research was performed under a program run by the Basic Atomic Energy Research Institute (BAERI), one of the Nuclear R&D Programs funded by the Ministry of Science & Technology (MOST) of Korea.

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