### Integrated System CFD Modeling of the Flow Distribution within a Pebble Bed Modular Reactor

The Pebble Bed Modular Reactor (PBMR) is an advanced graphite-moderated High Temperature Gas-cooled Reactor (HTGR), using helium as the coolant. Since helium is lighter than air and the graphite structure is designed to allow block movement due to effects of temperature and irradiation, it is expected that helium will distribute as follows: -main flow: helium carries the energy out of the reactor -engineered cooling flow: portion of helium is intentionally bled for cooling purposes -leakage: unintentional flow of helium within the reactor

The complex hydrodynamic phenomena of a PBMR are partly attributed to the inter-connecting flow paths. Modeling the hydrodynamics phenomena provides insight to the reactor over the range of operating conditions. A detail three-dimensional computational fluid dynamics (CFD) model is one of the modeling options; however, the hydrodynamic complexity of a PBMR would require substantial computing power and considerable modeling effort, thereby rendering CFD modeling an inappropriate tool for prompt feedback in the design-analysis cycle.

An integrated system-CFD approach treats the flow paths as a flow system, or more appropriately, a flow network. Flownex is a one-dimensional thermal fluid simulator which allows complex systems to be analyzed with relative ease. In Flownex, a basic flow path is simulated as flow traversing through a pipe element. The simpler flow paths in a PBMR are modeled using this fundamental approach. The complex flow paths that are more geometrically dependent are characterized using detailed CFD modeling to establish the dimensionless flow-pressure drop relationships. The characterization data are then defined in Flownex to model the flow paths in order to account for the effects of flow geometry and fluid properties.

The method combines the advantage of CFD modeling in simulating the detailed flow interaction to the more robust solver applied in Flownex. Although this approach is inherently geometry-dependent, its application in a large network or complex model has seen a reduction in the simulation time compared to the CFD modeling approach, without compromising the resulting integrity. The approach also improves the design process by providing faster feedback design-analysis cycle. The paper will discuss the theory of such integrated approach, and the modeling of key gaps in a PBMR within the reactor flow distribution model will be used as an example.

### Flownet Nuclear Architecture, Implementation and Verification & Validation

Flownet is a general network analysis code used by PBMR (Pty) Ltd for the thermalfluid design and analysis of the PBMR plant. It is based on an implicit pressure correction method (IPCM) that solves the continuity, momentum and energy equations (including rotating element dynamics) in large arbitrary structured networks for both steady-state and dynamic analysis. In order to facilitate maximum code re-use and maintainability it was re-developed in an object-oriented paradigm, using C++, within a strict quality system. This paper presents the architectural design, model development, implementation, and verification and validation philosophies used during the development of Flownet. Finally it comments on results obtained with this software package.

### Modelling of the HTTR in Flownet

Flownet is a user-friendly software package allowing the dynamic simulation of mass, momentum and energy transfer in thermal-fluid networks integrated with controllers. It is currently used extensively in the modelling and design of the South African Pebble Bed Modular Reactor (PBMR) power plant. The code was recently extended to include a model for the High Temperature engineering Test Reactor (HTTR) that is currently being demonstrated by Japan Atomic Energy Research Institute (JAERI). This paper describes the thermal network and flow path discretization that is used to simulate the physical geometry of the reactor core for the simultaneous solution of the governing equations in the fluid passages and solid structures. The numerical integration and solution scheme for the equations are discussed in an accompanying paper. The current paper also shows results of a preliminary steady-state sample calculation.

### Changing the face of nuclear power via the innovative Pebble Bed Modular Reactor

It is estimated that electricity demand in South Africa could outstrip supply by current power stations between 2005 and 2010. Furthermore, the emphasis on export has lead to more and more large industrial plants being erected near the coast resulting in load growth in coastal areas, away from the traditional Gauteng industrial hart land. This, in turn, increased the burden on the Eskom power transmission network and gave rise to a growing need for smaller, distributed power generation units.

### Dynamic systems CFD simulation code for the modeling of HTGR power plants

In this paper the development of a dynamic systems CFD simulation code for the modeling of HTGR power plants will be discussed. The basic methodology of the numerical method is known as an implicit pressure correction method (IPCM) will be presented. The method is capable of solving the pressure distribution, mass flow rate and temperature through an arbitrarily structured, physically realistic thermal-fluid system. The different component models used in the modeling of a typical HTGR power plant will also be presented. A loss of load incident for a three shaft recuperative Brayton Cycle will be modeled and the results obtained from the simulation will be discussed to demonstrate the utility of the code. The simulation will be used to show both the steady-state and dynamic ability of the method.

### Dynamic modelling of heat, mass and momentum transfer in the pebble bed modular reactor

In this paper the development of a system simulation model that can predict the dynamic behaviour of the Pebble Bed Modular Reactor (PBMR) will be described. The model predicts the transient mass, momentum and energy transfer in all components in a coupled manner. Very important is that the nuclear reactor and heat exchangers are not treated as lumped systems but as 2-D distributed systems. This allows one to take full account of the thermal inertia of the system. Another feature of the model is that it can deal with conduction heat transfer through solid structures. The paper will focus on the overall modelling approach and the simultaneous solution of the mass, momentum and energy equations. A few cases emanating from a benchmark study are presented in this paper. This includes the sudden closure of a valve in a pipeline, transient heat transfer through a reservoir wall and transient heat transfer in the recuperator.

### Validation of a transient thermal fluid systems CFD model for a packed bed HTGR

This paper provides an overview of the theoretical basis for a new thermal-fluid systems CFD simulation model for high temperature gas-cooled reactors, contained in the Flownex software code. Flownex provides for detailed steady state and transient thermal-fluid simulations of the complete power plant, fully integrated with core neutronics and controller algorithms. The reactor model is founded on a fundamental approach for the conservation of mass, momentum and energy for the compressible fluid flowing through a fixed bed, as well as the heat transfer in the pebbles and core structures. The time-wise integration of the resulting differential equations is based on an implicit pressure correction algorithm. This allows for the use of rather large time steps making it very suitable for simulating the slow transients that can be expected to follow incidents like reactor shutdowns. The paper also compares the Flownex results for four transient tests with the measured results from the SANA test facility as well as to the results of simulations with the Thermix/DIREKT code that were done at the Research Centre Jülich. The Flownex results compare well with the Thermix/DIREKT results for all the cases presented here. Good comparison was also obtained between the simulated and measured results, except at two points within the pebble bed near the inner wall. The fact that quick computer simulation times were obtained indicates that the new model indeed achieves a fine balance between accuracy and simplicity. However, the discrepancies obtained at the two points near the inner wall, together with the fact that additional uncertainty was introduced in the original SANA test set-up by not being able to control the temperature of the outer wall, highlight the need for additional systematic tests to be performed in order to better validate the new model.

### A systems CFD model of a packed bed high temperature gas-cooled nuclear reactor

The theoretical basis and conceptual formulation of a comprehensive reactor model to simulate the thermal-fluid phenomena of the PBMR reactor core and core structures is given. Through a rigorous analysis the fundamental equations are recast in a form that is suitable for incorporation in a systems CFD code. The formulation of the equations results in a collection of one-dimensional elements (models) that can be used to construct a comprehensive multi-dimensional network model of the reactor. The elements account for the pressure drop through the reactor; the convective heat transport by the gas; the convection heat transfer between the gas and the solids; the radiative, contact and convection heat transfer between the pebbles and the heat conduction in the pebbles. Results from the numerical model are compared with that of experiments conducted on the SANA facility covering a range of temperatures as well as two different fluids and different heating configurations.

### A thermal hydraulic analysis of pipe breaks in the pebble bed modular reactor main power system

This paper presents the observations from the analyses of small, medium and large pipe breaks that are presumed to occur in the Pebble Bed Modular Reactor’s (PBMR) Main Power System. The PBMR is a multibillion-rand grossly ambitious project that is tasked with the design, commissioning and marketing of a first-of-a-kind pebble-bed, high-temperature and gas-cooled nuclear technology. The main loop of the envisaged PBMR nuclear power plant comprises of a single Brayton thermodynamic cycle which integrates the pebble-packed reactor to a system of heat exchangers, and to a single-shaft turbine-generator-compressor system. The coolant for the reactor is helium which under 9000kPa and exiting the reactor at close to 900 °C, drives the downstream turbine in a direct action setup, thereby supplying roughly 163MW of electricity into the grid. The PBMR’s Main Power System and its support systems have since progressed through to advanced design phases and thermal-hydraulics analysis has played an integral role in providing various design and systems engineering functions with the necessary input data. There are certain critical positions in the Main Power System (MPS) of the PBMR’s Demonstration Power Plant (DPP) that warrant analysis in order to determine the effect of pipe breaks on certain critical components. Twenty-eight positions around the MPS have been identified for the capture of the helium pressures, temperatures and velocities which are then incorporated into the shear ratio calculation. The calculated shear ratios are thereafter employed in estimating possible dust lift-off fractions that could result from the pipe break scenarios and also in the subsequent prediction of nuclear doses that are likely to affect the reactor’s adjacent compartments and the immediate civil environment. This work provides the observations captured from the pipe break analyses and a brief insight into the implications of the evaluated shear ratio values to dust lift off and dust deposition within the main power system.

### A comprehensive reactor model for the integrated network simulation of the PBMR power plant

The theoretical basis and conceptual formulation of a comprehensive reactor model to simulate the thermal-fluid phenomena of the PBMR reactor core and core structures is given. Through a rigorous analysis the fundamental equations are recast in a form that is suitable for incorporation in a network code. This formulation of the equations results in a collection of one-dimensional elements (models) that can be used to construct a comprehensive multi-dimensional network model of the reactor.

### A finite volume-based network method for the predicition of heat, mass and momentum transfer in a pebble bed reactor

In this paper a new control volume based network scheme for the prediction of heat, mass and momentum transfer in a pebble bed reactor is presented. The discretization scheme takes detail effects such as convection, radiation and conduction heat transfer into account and also provides for several types of reactor flow elements. The network representation of the reactor is solved as an integral part of the overall thermal-fluid network for the entire power conversion unit. The new control volume based network scheme facilitates the setting up of the reactor network taking detail effects such as complex radiation and effective pebble bed-solid interface conduction into account. The model is used as a benchmark for the current element-based network scheme and it is also used to investigate the effect of more accurate radiation discretization on the temperature profile in the reactor. Excellent agreement has been found with the current element-based reactor model.

### Comparison of the thermal-fluid analysis code Flownex with experimental data from the pebble bed micro model

In this paper a comparison of the thermal-fluid analysis code Flownex with experimental data from the Pebble Bed Micro Model (PBMM) is presented. From the measured data it became clear that there were substantial heat losses from the turbines and the associated support structure as well as from the pressure vessel to the ambient. The original Flownex model was improved to account for these heat transfers. The new Flownex model was then used to simulate a mass injection transient test done on the PBMM. In order to do proper simulation it is necessary to understand and quantify all the processes taking place in the plant. This is difficult when complex geometries are being modeled and when components are installed in different conditions than the conditions under which they were tested and characterized. Keeping these limitations in mind, good agreement between the experimental and simulation results was obtained.

#### More...

### An integrated systems CFD simulation of a pebble bed reactor

The theoretical basis of a systems CFD model of a pebble bed reactor is discussed. This model is employed to simulate the thermal-fluid phenomena of the reactor core. The formulation of the fundamental equations results in a collection of one-dimensional elements that can be used to construct a network model of the reactor. One preliminary test is discussed to illustrate the application of the model.

### Validation and Verification of Flownex Nuclear

This paper provides a summary of the Software Verification and Validation (V&V), which has been performed on the nuclear safety-relevant elements in Flownex that are currently used in the PBMR. M-Tech and PBMR have embarked on a rigorous V&V process to guarantee the integrity of engineering analyses and to satisfy the statutory requirements regarding the licensing and operating of nuclear plants. Tools used in the verification of Flownex Nuclear include test plans and procedures, code reviews, user testing, automated testing and regression testing; all implemented under an ISO 9001:2000 quality management system at MTech, the code developers. Validation of Flownex Nuclear is performed by comparing the results of the theoretical models with benchmark data obtained from appropriate methods or sources such as analytical data, experimental data, plant data and data obtained form other codes such as Spectra, XNet and Star CD in both separate effect and integrated tests.

### Verification and validation of a thermal hydraulic code used to model the PBMR

Flownex is a general-purpose thermal-fluid network analysis code used as a tool in the design of the Pebble Bed Modular Reactor. The National Nuclear Regulator requires the use of benchmarks to Verify and Validate (V&V) such a design code. This paper covers the verification and validation of selected fundamental components and aspects in Flownex. Attention is also given to the integration of these components to verify and validate their use in arbitrary structured thermal-fluid networks.

### The application of systems CFD to the design and optimization of high-temperature gas-cooled nuclear power plants

The approach with the design of power plants is to first carry out a thermodynamic cycle analysis and then to vary certain cycle parameters such as the overall pressure ratio in order to determine the optimum or design point condition. One would then proceed to design the different components to match the process conditions. However, since component design has an impact on overall system performance, one cannot optimize the design of the components in isolation from the rest of the system. Furthermore, the main task of plant designers is not to do design point analyses but to analyze off-design performance, to do uncertainty analyses, to optimize the design and to characterize the dynamic behavior of the system. An approach that has been used with great success is the systems CFD approach. Systems CFD codes are based on the network approach and allow one to model the performance of large complex systems in an integrated fashion. In this paper the systems CFD approach will be discussed.