development of a core thermo-fluid analysis … · ta et al., deelopment of a core thermo-fluid...

NUCLEAR ENGINEERING AND TECHNOLOGY, VOL.46 NO.5 OCTOBER 2014 NUCLEAR ENGINEERING AND TECHNOLOGY, VOL.46 NO.5 OCTOBER 2014PB 641

1. INTRODUCTION

A prismatic gas cooled reactor is a candidate design for national research programs such as the next generation nuclear plant (NGNP) project of the U. S. [1], and the nuclear hydrogen production and demonstration (NHDD) project of Korea [2]. For the smooth success of the NHDD project, the Korea Atomic Energy Research Institute (KAERI) has been developing key technologies for the design of a prismatic very high temperature reactor (VHTR) [3]. As one of the crucial technologies for the NHDD project, the development of a core thermo-fluid analysis code, named CORONA (Core Reliable Optimization and thermo-fluid Network Analysis), started in 2009. The CORONA code is targeted for a whole core thermo-fluid analysis of a prismatic gas cooled reactor with fast computation and reasonable accuracy.

Figs. 1 and 2 show the conceptual view of a typical prismatic reactor core and its fuel block respectively [4]. The active part of the prismatic core consists of a large number of vertical stacks of a fuel block. Accurate pre-diction of the fuel temperature is crucial to ensure the barrier against the release of fission products into the primary coolant. However, the complex geometry of a prismatic fuel block hinders accurate evaluations of the temperature distribution without elaborate numerical cal-culations.

Therefore, during the development of existing prismatic gas-cooled reactor designs (e.g., MHTGR of the General Atomics [5] and HTTR of Japan [6]), efficient numerical methods were applied to analyse the thermo-fluid behaviour of prismatic cores. The key idea of these efficient methods is to solve a three-dimensional solid heat conduction equation combined with one-dimensional fluid flow equations. A combined method was adopted in the DEMISE code of General Atomics [7] and the FLOWNET/TRUMP codes of Japan [8]. Recently the existing idea was improved by the present authors [9] and implemented into the CORO-NA code. Moreover, the fluid flow model described in [9] has been further improved through a one-dimensional network model.

The present paper summarizes the motivation and strat-egy, major outcomes, and perspective of the development of the CORONA code.

2. DEVELOPMENT MOTIVATION AND STRATEGY

The recent rapid development of computational fluid dynamics (CFD) technology provides a powerful tool to carry out elaborate numerical calculations with complex geometries for nuclear applications. Some CFD codes such as CFX [10] and STAR-CD [11] are commercially available. Thanks to the commercial CFD codes, the ap-

http://dx.doi.org/10.5516/NET.02.2014.020

DEVELOPMENT OF A CORE THERMO-FLUID ANALYSIS CODE FOR PRISMATIC GAS COOLED REACTORS

NAM-IL TAK*, SUNG NAM LEE, MIN-HWAN KIM, HONG SIK LIM, and JAE MAN NOHKorea Atomic Energy Research InstituteDaedeok-Daero 989-111, Yuseong-gu, Daejeon 305-353, Korea*Corresponding author. E-mail : [email protected]

Received February 25, 2014Accepted for Publication June 16, 2014

A new computer code, named CORONA (Core Reliable Optimization and thermo-fluid Network Analysis), was developed for the core thermo-fluid analysis of a prismatic gas cooled reactor. The CORONA code is targeted for whole-core thermo-fluid analysis of a prismatic gas cooled reactor, with fast computation and reasonable accuracy. In order to achieve this target, the development of CORONA focused on (1) an efficient numerical method, (2) efficient grid generation, and (3) parallel computation. The key idea for the efficient numerical method of CORONA is to solve a three-dimensional solid heat conduction equation combined with one-dimensional fluid flow network equations. The typical difficulties in generating computational grids for a whole core analysis were overcome by using a basic unit cell concept. A fast calculation was finally achieved by a block-wise parallel computation method. The objective of the present paper is to summarize the motivation and strategy, numerical approaches, verification and validation, parallel computation, and perspective of the CORONA code.KEYWORDS : Prismatic Core, Fuel Temperature, Fluid Flow Network, Gas Cooled Reactor, CORONA, VHTR

TAK et al., Development of a Core Thermo-Fluid Analysis Code for Prismatic Gas Cooled Reactors

NUCLEAR ENGINEERING AND TECHNOLOGY, VOL.46 NO.5 OCTOBER 2014 NUCLEAR ENGINEERING AND TECHNOLOGY, VOL.46 NO.5 OCTOBER 2014642 643

plication areas of CFD technology have been growing. Commercial CFD codes are user-friendly and well vali-dated against most industrial problems which have a single phase fluid. In spite of the remarkable development of CFD technology, however, a whole prismatic core CFD analysis with geometric details is still a challenging task. Since fine meshes are required for accurate CFD calcula-tions, most CFD applications are limited to local behaviours (e.g., single fuel column [12,13], and seven fuel columns [14]) in the design of a prismatic reactor. In 2009, Pointer and Thomas [15] published the STAR-CD results for a whole core of a prismatic reactor. It is clear that such a CFD analysis requires tremendous computational efforts. Additional significant efforts have to be devoted to gen-erate computational grids of high quality for a good con-vergence. Such efforts are valuable for a final calculation but are too taxing for a designer who wants a large number of calculations with various design options.

The other available option at KAERI could be the use

of system codes such as MARS-GCR [16] and GAM-MA+ [17]. It should be noted, however, that the system codes are targeted for system transients. Their meshes are too coarse for a detailed thermo-fluid analysis of a prismatic fuel block. The accuracy of the system code calculations is not satisfactory for the core thermal design of a prismatic reactor (e.g., hot spot analysis).

Therefore, a new computer code named CORONA has been developed to overcome the difficulties in the available tools at KAERI, i.e., CFD codes and system codes. The CORONA code is intended for whole-core thermo-fluid analysis of a prismatic gas cooled reactor with fast computation and reasonable accuracy. Fig. 3 summariz-es the thermo-fluid analysis codes and their application areas for the design of prismatic gas-cooled reactors at KAERI. The position of CORONA lies in between CFD and system codes. Its position is similar to that of a sub-channel analysis code such as COBRA [18] used in a light water cooled reactor design.

Fig. 1. Conceptual View of Typical Prismatic Reactor Core

Fig. 2. Standard Fuel Block of Typical Prismatic Reactor



Major applications of the CORONA code are (1) a steady-state hot spot analysis, (2) steady-state analysis for off-design conditions such as a coolant channel blockage accident, (3) some transient scenarios (e.g., rod ejection), (4) a coupled analysis (e.g., with neutronics) for high fidelity, (5) design optimization calculations. The CO-RONA code is written in C++ and can be run on either Windows or Linux operating system.

3. NUMERICAL APPROACHES

3.1 Grid Generation Using Basic Unit CellsThe first step in the numerical calculation of thermo-

fluid phenomena is to set up a grid. The unique feature of the CORONA code is the use of the basic unit cells for the generation of computational grids. The concept of basic unit cells provides an efficient generation of unstructured computational grids to model an entire fuel block. The present authors noticed that the prismatic fuel blocks have regular arrangement of hexagonal or pentagonal unit cells as shown in Fig. 4. Prismatic fuel blocks can be repre-sented by several types of basic unit cells and are shown in Fig. 5. The unstructured computational grids are defined within the basic unit cells. Using the combination of the basic unit cells, unstructured grids can be efficiently gen-erated to simulate the thermo-fluid behavior of the fuel blocks. Fig. 6 is provided in order to improve the under-standing of the relation between the basic unit cells and the computational grids. It shows the assignment of the basic unit cells to generate the computational grids of the standard fuel block. The change in generated grids is also simple and convenient. Fig. 7 illustrates an example of computational grids generated using the basic unit cells.

Fig. 8 shows the modeling procedure from the basic unit cells to a whole prismatic core. Initially, computa-tional grids are defined within each type of basic unit cell.

In order to achieve the target of the CORONA code (i.e., fast computation of whole core thermo-fluid analysis with reasonable accuracy), three fundamental strategies were established and applied to the development of CO-RONA: (1) an efficient numerical method, (2) efficient grid generation, and (3) parallel computation.

○ Efficient Numerical Method: The use of an efficient numerical method is the most

important requirement for a new code to achieve its goal. The CORONA code adopts the existing idea of the efficient numerical method used for the design of MHTGR and HTTR (e.g., DEMISE and FLOWNET/TRAMP). This efficient method solves a three-dimensional heat conduction equation for a solid like a CFD code and one-dimensional conser-vation equations for a fluid flow like a system code. In 2012, Travis and El-Genk [19] verified the ef-ficiency of this combined method using STAR-CD calculations.

○ Efficient Grid Generation: For a whole prismatic core thermo-fluid simulation,

grid generation can also be a time-consuming pro-cess. Therefore, an efficient grid generation method using the concept of basic unit cells was developed by the present authors [9,20]. This concept of the basic unit cells adopted in the CORONA code ena-bles the effective generation of unstructured grids for prismatic fuel blocks without a special mesh generator. The revision of the generated grids is also simple and convenient.

○ Parallel Computation: Reliance on a parallel computing technique is inevi-

table for a whole prismatic core simulation since sig-nificant numbers of meshes (e.g., in the order of ten million) are required. Parallel computation leads not only to a speed up of the calculations but also allows the use of a normal personal computer (PC).

Fig. 3. Thermo-fluid Analysis Codes and Their Areas for the Design of Prismatic Gas-cooled Reactors at KAERI



the CORONA code has a similar level as the CFD analysis. However, it should be noted that the computational expense of a solid heat conduction equation (i.e., Eq. (1)) is much less than that of fluid conservation equations in a whole core CFD analysis of a prismatic core.

3.2 Numerical Model for SolidIn order to simulate the heat conduction through the

Then, using an axial combination of the basic unit cells, a hexagonal (or pentagonal) body called a ‘pin’ is made. Three-dimensional computational grids for a hexagonal fuel (or reflector) block are generated using a two-dimen-sional combination of pins. Modeling of a whole core is finally finished using a combination of hexagonal fuel and reflector blocks.

The number of computational grids for a solid used in

Fig. 4. Typical Unit Cell Arrangements in Prismatic Fuel Blocks

Fig. 5. Basic Unit Cell Types and Examples of Computational Grids

Fig. 6. Basic Unit Cell Assignment to Generate Computational Grids of Standard Fuel Block

Fig. 7. Example of Computational Grids Generated Using the Basic Unit Cells for the Standard Fuel Block



orthogonal. At a fluid boundary, the following equation is governed:

Equations (3) and (6) can be rearranged into matrix form as

Equation (7) can be solved simultaneously for all nodes if the material properties and qs,i

conv are known. The detailed derivation from Eq. (1) to Eq. (7) is not given in this paper since it is lengthy and widely available in a CFD textbook dealing with unstructured meshes (e.g., see Ver-steeg and Malalasekera [21]).

3.3 Numerical Model for Fluid FlowIn contrast to the solid geometry of the fuel blocks, the

fluid in the prismatic fuel blocks flows through simple circular channels. A fraction of the core flow bypasses the fuel block coolant channels and passes through the gaps between the hexagonal columns. Such gaps can also be considered as rectangular channels connected to each other. For the fluid flow within a prismatic core, a one-dimensional approach can therefore be a good approximation. Such an approximation avoids fine meshes near the walls as well as turbulence conservation equations which are one of the major challenges in a CFD analysis. A one-dimensional approximation for the duct flows enables a fast calculation with reasonable accuracy. In addition, there is potential for an exchange of coolant between the bypass gaps and the coolant channels due to cross flow gaps which are small spaces between the horizontal faces of the blocks. Therefore, a one-dimensional network model has been widely used for a fluid flow in a prismatic core [7].

complex geometry of the fuel block, the CORONA code solves the following three-dimensional heat conduction equation:

The CORONA code adopts the finite volume method to solve Eq. (1). The key step of the finite volume method is the integration of Eq. (1) over a control volume to yield a discretised equation:

The obtained discretised equation can be expressed for a general nodal point P as follows:

where the superscript 0 represents the known value at the previous time step and the subscript i indicates the neigh-boring node. In Eq. (5), k ˆs,i and δV ˆi represent the thermal conductivity and the node volume at the node face be-tween the node P and the neighboring node i. Equation (3) is a well-known form for unstructured grids and si

non is the cross-diffusion term resulting from the non-orthog-onality of grids. This term disappears if the grids are fully

Fig. 8. Modeling Procedure from Basic Unit Cell to Whole Prismatic Core

(1)

(3)

(6)

(7)

(4)

(5)

(2)



The first step to solve Eqs. (11) and (12) is to guess the pressures at all nodes. These values are treated as prelimi-nary values and donated by ¯ P. The correction δP is de-fined as the difference between the correct pressure field and the guessed pressure field ¯ P.

Similarly, the volumetric flow rate correction δQ and density correction δρ are defined as:

The density of the gas can be obtained using the ideal gas law.

Where R is the gas constant and zc is the compressibility factor. Substitution of Eqs. (13)~(16) into the momentum equation (i.e., Eq. (12)) and neglecting the terms involving the products of the corrections, yield the following equation for the volumetric flow rate correction.

where

Finally, the substitution of Eqs. (14), (15) and (17) into the continuity equation (i.e., Eq. (11)) yields the following equation for the pressure correction.

A fluid flow network model implemented into the CO-RONA code is based on the pressure correction method [22~24]. One-dimensional conservation equation for a fluid flow can be written as:

Under normal operating conditions, the thermo-fluid behavior in a prismatic gas-cooled reactor core can be described using the simplified forms of Eqs. (8)~(10) based on the steady-state, constant flow area, and neg-ligible buoyance assumptions. Fig. 9 shows the concept of a node and junction to derive the mathematical formu-lation for an arbitrary network of one-dimensional fluid flows. In this paper, the simplified equations which are applicable to normal operating conditions are described in the following derivations since a steady-state hot spot analysis is the most crucial concern of the CORONA cal-culations.

Initially, the steady-state continuity equation is applied at a one-dimensional fluid node (i) having an arbitrary number of initiating junctions (Ii) and terminating junc-tions (Ti ), as shown in Fig. 9(a).

For a junction (j) having upstream fluid node (iuj) and down-stream fluid node (idj) shown in Fig. 9(b), the simplified momentum equation can be applied as

(20)

(9)

(10)

(11)

(13)

(14)

(15)

(16)

(12)

Fig. 9. Concept of Node and Junction for Fluid Network

(18)

(19)

(17)

(8)



where i represents each surface of the solid contacted with the fluid node j and As,i,j is the heat transfer area be-tween the solid surface i and fluid node j.

The overall computational procedure for a steady-state analysis is shown in Fig. 10. When the maximum value of the fluid temperature change during the iteration is less than the user supplied parameter, the convergence is regarded as having been achieved.

4. VERIFICATION AND VALIDATION

4.1 Heat Conduction in Unit CellsIn order to verify the multi-dimensional heat conduc-

tion within unit cells of the prismatic fuel block, two concep-tual problems using unit cells were investigated [20]. The verification study started from a single unit cell problem which is one of the simplest test cases. The single unit cell consists of a fuel compact, helium gap, and graphite region. A uniform heat generation in the fuel compact was assumed

Where aj, dj, cj, and dj are the rearranged coefficients in terms of each δP node respectively and ei is the source term.

With the known field of δPi, δQj can be obtained using Eq. (17). Then, new values for Pi, Qj, and ρf,i are deter-mined using Eqs. (13), (14), and (16). The newly updated values are now considered as the preliminary values for the next iteration and the whole process is repeated a number of times after which the fluid energy conservation equation is solved.

The steady-state one-dimensional form for the energy conservation equation governing the fluid flow network can be derived as

where hi is the enthalpy of the fluid node i and αj is the parameter for the donor property defined as

The central differencing scheme can be used as an alternative option for Eq. (21). In the case of a single pipeline, Eqs. (20) and (21) can be solved using the tri-diagonal matrix algorithm (TDMA), while sparse matrix techniques can be applied in the case of complex flow networks.

3.4 Interfacing of Solid and Fluid Models The coupling between the three-dimensional solid model

and the one-dimensional fluid model uses a typical Nus-selt number correlation such as:

Eq. (23) is the correlation of McEligot et al. [7, 25] which is one of the most popular correlations for a prismatic gas-cooled reactor core under normal operating condi-tions. The entrance effect is neglected due to little inter-est in the entrance region. Eqs. (6) and (21) are combined as follows:

(21)

(22)

(23)

(24)

(25)

(26)

Fig. 10. Overall Computational Procedure for a Steady-State Analysis



4.2 Bypass Flow and Crossflow in Fuel ColumnAn air flow experiment performed by Kaburaki and

Takizuka [26] was selected to validate the one-dimensional fluid flow network model implemented in CORONA [27]. Fig. 14 shows a schematic of their experimental appara-tus. Four graphite blocks were stacked up in a column and surrounded by a steel shroud to simulate the bypass gap (~1.2mm) between fuel columns. The hexagonal fuel block has 12 coolant holes 20 mm in diameter. One arti-ficial cross flow gap (~1 mm) was created in the middle of the column to simulate a crossflow gap between fuel blocks. The air at atmospheric pressure was drawn from the top of the test section and flowed down the channels and the bypass gap. The bottom of the bypass gap was completely sealed and the coolant leakage flow, which entered the bypass gap, was merged into the main coolant channels through the crossflow gap. The mass flow rate

and the temperature of the outmost boundary was fixed. Since it is believed that a commercial CFD code can solve a multi-dimensional heat conduction problem accurately, a commercial CFD code, CFX, is used for the verifica-tion of the CORONA code for the multi-dimensional heat conduction problem. Fig. 11 compares the predicted tem-perature profile by CORONA with that by CFX. It shows that CORONA accurately solves the multi-dimensional heat conduction equation. It is obvious that a finer mesh provides a more accurate result.

The second case considers seven unit cells composed of one coolant cell (designated as ‘C’) surrounded by six fuel cells (designated as ‘F’) as shown in Fig. 12. A uniform heat generation in the fuel compacts was assumed and the temperature at the coolant boundary was fixed. In addi-tion, the adiabatic boundary condition was imposed on the outmost boundary of the unit cells.

Fig. 13 shows the predicted temperature profiles along Line A in Fig. 12. It was observed that when a fine mesh is adopted, the accuracy of CORONA is close to that of CFX.

Fig. 11. Result of Verification of CORONA Using Single Unit Cell Problem

Fig. 12. Layout of Seven Unit Cell Problem and Its Boundary Conditions

Fig. 13. Result of Verification of CORONA Using Seven Unit Cell Problem

Fig. 14. Schematic of Kaburaki and Takizuka Experimental Apparatus for Bypass Flow and Crossflow [25]



and the static pressure distribution in each coolant chan-nel were measured. The measurement uncertainties of the experiment were not published and the sensitivity calcu-lations of CORONA confirmed later that the effect of the entrance and exit form losses was small.

Fig. 15 shows a comparison of the CORONA prediction results with the measured pressures. A good agreement can be seen along all of the stacks. This was achieved by ap-plying the correlation of Kaburaki and Takizuka developed based on their experiment. This means that the described one-dimensional fluid flow model is correctly implemented into the CORONA code and is able to simulate the bypass flow and crossflow phenomena reasonably.

4.3 Conjugate Heat Transfer in Fuel ColumnIn order to verify a conjugate heat transfer in a prismatic

fuel block, two conceptual problems with single fuel columns were investigated [28, 29]. Two types of fuel blocks (i.e., standard and reserved shutdown control (RSC) fuel blocks) were considered. Since it is believed that a commercial CFD code is well verified against a single phase conjugate heat transfer problem, the verification of the CORONA code is made using a comparison with the results of CFX. However, it should be noted that a commercial CFD code also needs a sufficient validation for prismatic core condi-tions (i.e., high temperature helium flow at a high heat flux condition in a prismatic fuel block geometry).

Table 1 shows the major thermo-fluid parameters for the considered single fuel column problems under con-sideration. Fig. 16 shows the CFX meshes used to simu-late the single fuel column problems. Using symmetry, 1/12 and 1/2 sections of the geometries were modeled for CFX calculations of the standard and RSC fuel blocks, respectively.

Fig. 15. Result of Validation of CORONA Using the Kaburaki and Takizuka Experiment

Fig. 16. CFX Meshes to Simulate Single Fuel Column Problems

Parameter Standard Fuel Column

RSC FuelColumn

Column thermal power (MW) 3.118 2.832

Column flow rate (kg/s) 1.207 1.268

Coolant inlet temperature (oC) 490 490

System pressure (MPa) 7 7

Number of stacked fuel blocks 6 6

Active core height (m) 4.758 4.758

Bypass gap size (mm) 2 2

Crossflow gap size (mm) 1 1

Axial power profile Uniform Uniform

Table 1. Thermo-fluid Parameters for Single Fuel Column Problems



fair comparison of the computation time is not feasible due to differing convergence criteria and a differing number of meshes. However, it is obvious that significant reduction in the computation time can be achieved by CORONA and the difference in the computation time would dramatically soar in the case of a whole core analysis.

5. PARALLEL COMPUTATION

5.1 Block-Based Parallel ComputationParallel computing capability is important for the CORONA

code since a whole prismatic core simulation requires a huge com-puting cost and a significant amount of computer memory. For a simple implementation of parallel computing capability, a block-based parallel computation method was developed for the CORONA code [30]. The idea of the block-based parallel computation method is based on the fact that each fuel (or reflector) block is completely enclosed by the fluid boundaries due to the existence of bypass and cross flows as shown in Fig. 20. Therefore, the heat conduction matrix shown in Eq. (7) can be naturally decomposed into much smaller matrixes that represent each fuel (or reflector) block. The decomposed matrix can be solved independently using a parallel computation library.

5.2 Application to Whole Core AnalysisIn order to examine the improved performance by the

parallel computation, an example problem for a whole prismatic core was investigated. PMR600 [2] was selected as a reference core. The major thermo-fluid boundary conditions are shown in Table 2. The reactor power profile obtained by the neutronic analysis [31] was applied. The applied power distribution is shown in Fig. 21. The heat loss to the reactor cavity cooling system (RCCS) was neglected.

Fig. 22 shows the calculation model for the CORONA

Figs. 17 and 18 compare the predicted axial tempera-ture distribution at the center of the hottest fuel compact. They clearly show good agreements. Non-continuing re-gions between fuel blocks are generated due to the non-fuel zones (i.e., graphite plug and seat). A comparison of the coolant velocities at the control hole of the RSC fuel column is shown in Fig. 19. It also shows a good agreement. Figs. 17~19 obviously indicate that the CORONA code can re-liably simulate a conjugate heat transfer in the prismatic fuel blocks.

Although the predicted temperature profiles by CO-RONA are comparable to those of CFX, the used compu-tation time is significantly different. In order to obtain the result in Fig. 18, for example, about 46 hours were spent by CFX using four CPUs whereas about 4 minutes were spent by CORONA using a single CPU of the same computer. A

Fig. 18. Comparison of Predicted Axial Temperature Distributions at the Center of the Hottest Fuel Compact for the

RSC Fuel Column Problem

Fig. 19. Comparison of Predicted Coolant Velocities at the Control Hole for the RSC Fuel Column Problem

Fig. 17. Comparison of Predicted Axial Temperature Distributions at the Center of the Hottest Fuel Compact for the

Standard Fuel Column Problem



reduced with the number of processors. The maximum number of processors per PC was limited to 4 due to the random access memory (RAM) capacity of the PCs.

calculation. The total numbers of solid and fluid nodes used were ~39,000,000 and ~200,000, respectively. The calculations were carried out on two PCs with Microsoft Windows 7 Enterprise K. Table 3 shows the specification of the two PCs used. The communications between the two PCs were made using Gigabit Ethernet connections. Intel ® MPI [32] was used for parallel computation library on the Windows operating system.

Fig. 23 shows the predicted maximum temperature within each fuel and reflector column based on a serial calculation. It shows that the predicted temperatures are reasonable. The same calculations were repeated based on parallel computations. Nine cases were tested to inves-tigate the parallel performance and Fig. 24 summarizes the result for the test problem. It was thoroughly checked whether all the cases produced the same results. Fig. 24 shows that the computing speed is significantly improved by the parallel computation. The computing time was

Parameter Value

Core thermal power (MW) 600

No. of fuel columns 108

No. of fuel blocks per column 9

No. of reflector columns with control rod hole 36

Core flow rate (kg/s) 251.3

Coolant inlet temperature (oC) 490

System pressure (MPa) 7

Active core height (m) 7.929

Bypass gap size (mm) 2

Crossflow gap size (mm) 0

Table 2. Major Thermo-fluid Parameters for PMR600 Benchmark Calculation

Fig. 21. Axial Power Distribution Used for PMR600 Benchmark Calculation

Fig. 22. CORONA Model for 1/6 Core of PMR 600

CPU No. of CPUs RAM

PC 1Intel Xeon X5690,

Six Core,3.47 GHz

2 144 GB

PC 2Intel Xeon X5690,

Six Core, 3.47 GHz

2 96 GB

Table 3. Specification of Two PCs for Parallel Computation Benchmark

Fig. 20. Fuel Blocks Enclosed by Fluid Boundaries



blocks. The usefulness of the CORONA code was proved by the example calculations using a whole prismatic core model.

Further research is on-going to improve the physical models and increase the capability of the CORONA code. The major items are (1) coupling with the DeCART code [33] for a high fidelity calculation, (2) variable bypass (and crossflow) gap size model for consideration of the change in the size with the location as well as the burnup, and (3) transient simulation capability.

It is believed that the CORONA code can be practi-cally used in a whole core thermo-fluid analysis for the design of a prismatic gas cooled reactor. In addition, it is envisaged that the excellence of the CORONA code will also be highlighted in a high fidelity analysis combined with a whole core neutron transport calculation.

NOMENCLATUREai = Influence coefficient at node i, defined in Eq. (5)ai

* = Rearranged influence coefficient of ai, used in Eq. (7)aj = Coefficient for junction j, used in Eq. (20)a0

p = Influence coefficient at node P, defined in Eq. (5)ap

* = Rearranged influence coefficient of ap, used in Eq. (7)As = Solid surface area [m2]bj = Coefficient for junction j, used in Eq. (20)bp = Source term for node P at temperature matrix,

used in Eq. (7)cj = Coefficient for junction j, used in Eq. (20)Cj = Resistance coefficient at fluid node j, defined in

Eq. (18)Cs = Specific heat of solid [J/kg K]dj = Coefficient for junction j, used in Eq. (20)D = Hydraulic diameter [m]ei = Source term for node i at pressure matrix, used in

Eq. (20)f = Friction factor [-]g = Gravitational acceleration constant [m/s2]G = Parameter defined in Eq. (19)h = Fluid enthalpy [J/kg]Ii = Initiating junction of node ikf = Thermal conductivity of fluid [W/m K]ks = Thermal conductivity of solid [W/m K]K = Form loss factor [-]L = Fluid channel length [m]N = Number of meshesNu = Nusselt number [-]P = Pressure [Pa]Pr = Prandtl number [-]qs

‴ = Power density generated in solid [W/m3]qf

conv = Convection heat transfer at fluid [W]qs

conv = Convection heat transfer at solid [W]Q = Volumetric flow rate [m3/s]R = Gas constant of helium [J/kg K]Re = Reynolds number [-]si

non = Cross-diffusion termt = Time [s]Tf = Fluid temperature [K]

6. CONCLUSIONS AND OUTLOOK

The development of the CORONA code was started in KAERI for the establishment of the key technologies for the design of a prismatic VHTR. The CORONA code is targeted for a whole core thermo-fluid analysis of a prismatic gas cooled reactor with fast computation and reasonable accuracy. In order to achieve the target, the development of CORONA focused on (1) an efficient nu-merical method using the combination of a three-dimen-sional heat conduction and one-dimensional fluid flow net-work, (2) efficient grid generation using basic unit cells, and (3) parallel computing capability.

The results of the verification and validation studies show that the CORONA code can provide a reasonably accurate result for the thermo-fluid analysis of prismatic fuel

Fig. 24. Result of Parallel Computation Performance Test Using PMR600 Problem

Fig. 23. Predicted Maximum Temperature within Each Fuel and Reflector Column of PMR 600



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Ti = Terminating junction of node iTs = Solid temperature [K]V = Volume [m3]w = Fluid velocity [m/s]z = One-dimensional coordinatezc = Compressibility factor [-]

Greekα = Parameter defined in Eq. (22) ρ = Density [kg/m3]

ACKNOWLEDGEMENTSThis work was supported by Nuclear R&D Program

of the National Research Foundation of Korea which is grant funded by the Korean government (Grant code: NRF-2012M2A8A2025679).

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NUCLEAR ENGINEERING AND TECHNOLOGY, VOL.46 NO.5 OCTOBER 2014 NUCLEAR ENGINEERING AND TECHNOLOGY, VOL.46 NO.5 OCTOBER 2014654 PB

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development of a core thermo-fluid analysis … · ta et al., deelopment of a core thermo-fluid...

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