Nuclear thermal hydraulics
Nuclear thermal hydraulic analysis using coupled CFD and nuclear system codes
The thermal hydraulic analysis of nuclear reactors is largely performed by what are known as “System Codes”. These codes predict the flows in the complex network of pipes, pumps, vessels and heat exchangers that together form the thermal hydraulic systems of a nuclear reactor. Codes in this category include the US codes RELAP, TRAC and TRACE and the European codes CATHARE and ASTEC.
They embody necessarily highly simplified models that in essence, solve one-dimensional forms of the conservation equations for mass momentum and energy. They necessarily make heavy reliance on empirical correlations for such things as frictional pressure drops. This use of empirical correlations extends to their treatment of two-phase flows, where quantities such as inter-phase mass momentum and heat transfer are, again of necessity, represented using empirical correlations. These codes have been used for many decades, and are now very well-established, and given this long process of refinement, they are able to produce remarkably accurate predictions of plant behaviour under both steady and transient conditions. The most widely used of these codes, and the worldwide workhorse of nuclear reactor thermal analysis, is the RELAP suite, originating with the US NRC.
However, such codes are fundamentally limited in that they are at heart only one-dimensional. If a part of the plant can reasonably modelled as one-dimensional flow in a pipe, these codes are excellent. However, there are plainly many important phenomena and locations where this one- dimensionality is not a good approximation. An obvious example of this might be flow within the bulky, 3-dimensional reactor vessel itself.
There have been attempts to extend these System Codes to handle multi-dimensional effects. These have had some success, but there is naturally a trade-off between the fidelity of the representation and the computational complexity. It is over-simplified, but one might characterise a "3D System Code" as an array of one dimensional parallel pipes, allowed to interact ‘sideways’ with each other via some ‘crossflow’ coupling. The models so produced can be better than the original one-dimensional ones, but do not represent complex flows well.
The most capable tool available to us for modelling these multi-dimensional effects is computational fluid dynamics (CFD). Modern CFD is able to produce high-quality predictions flows in complex geometries, but only with the use of large computing resources. It would be utterly impractical to build a CFD model of, for example, the entire primary circuit of a PWR.
However, much of the primary circuit may be able to be modelled with adequate fidelity using a cheap one-dimensional systems code, and it may only be in a limited part of the circuit that full 3-dimensional effects are important. The natural response to this is to develop methods where simple one-dimensional models are replied where they are appropriate, but where these are then coupled to full 3-dimensional treatments of those parts of the system which require it.
Single-phase flow in non-circular ducts
The core aim of this project is to help towards understanding heat transfer in non-circular channels of high aspect ratio, with partial blockages perturbing flow. Towards this end, secondary flows must be taken into account in the modelling process.
The first stage of this project is to calculate the flow field in channels of appropriate rectangular geometry using a variety of computational tools. These range from non-linear k-E models, through RST Models to LES. One interesting feature of this approach is a comparison of the various models and an establishment of the level of complexity required to obtain a valuable solution to the problem. Secondly, it is necessary to carry out very detailed measurements of the flow fields in rectangular channels of appropriate size using an appropriate laser-based technique such as PIV.
A detailed comparison of CFD simulations with experimental results will allow validation of the choice of turbulence model.
Additionally, simulations and measurements will be carried out in channels after having introduced small blockages, such as gas bubbles. The previously validated models will again be compared with experimental results to gain further insight.
A possible extension to the project would be gaining an understanding of the mechanisms involved in bubble detachment and their removal by advection.
Modelling of flow boiling and the prediction of the critical heat flux using CFD-based methods
In a nuclear reactor, uncontrolled boiling can lead to the hazardous condition often referred to as the “critical heat flux” (or CHF) which can result in the fuel clad no longer being wetted and the integrity of the fuel being compromised; this condition defines the upper limit for safe reactor operation and therefore there is an essential requirement for the engineering capability to predict the onset of this condition (and hence to accurately predict the behaviour of boiling flows).
Today’s state-of-the-art in boiling modelling in CFD embodies a significant degree of empiricism by way of using correlations to define the overwhelming majority of closure terms in the modelling formulation. In addition to this, the formulation is itself unrepresentative of the many interacting heat transfer mechanisms at work during the boiling process. These factors impose an upper bound on the predictive capability (and range of application) of the CFD code, which limits its usefulness as an engineering tool. Whilst some empiricism will inevitably tend to remain due to the multifaceted nature of the boiling phenomenon, incorporating more mechanistically-based (or semi-constitutive) models to describe these closure terms s well as to describe the various heat transfer mechanisms should permit improvements to today’s CFD capability, and this is an endeavour that has been gaining momentum in the academic community for some time.
The current work involves the identification, implementation and subsequent demonstration of such improvements to the current state-of-the-art in “component-scale” modelling of boiling and CHF prediction in CFD codes with an emphasis on applications in nuclear reactors (under conditions of high-pressure turbulent flow boiling in non-circular geometries).
Fundamental microscopic multi-physics modelling of boiling
Critical Heat Flux Prediction in Nuclear Reactor Sub-Channels
Critical Heat Flux Analysis in non-circular channels
Computer Analysis of Buoyancy Driven Flows
Nuclear reactor physics
Uncertainty Quantification in Neutron Transport
Integration of Design and Analysis for Radiation Transport Problems using Isogeometric Methods
The neutron transport equation frequently needs to be solved on extremely complex geometries, usually incorporating conic sections. These are represented exactly in the Computer Aided Design (CAD) model using Non-Uniform Rational B-Splines (NURBS), but for analysis purposes this exact representation is usually approximated using polygonal or quadric surfaces for techniques such as Finite Element Methods (FEM). This has two major drawbacks: that the exact geometry is not represented and that the mesh is computationally expensive to create.
An alternative approach is Isogeometric Analysis, in which the NURBS basis functions are used to represent both the geometry and the solution, thereby eliminating two of the major drawbacks of FEM. My project is to investigate the use of this technique in application to first order forms of the neutron transport equation in one, two and three dimensional geometries. This will involve employing various stabilisation techniques such as variational multiscal and Galerkin Least Squares (GLS), as numerical approximations to this equation are typically unstable.
Isogeometric Analysis also has analogues to traditional h and p refinement from FEM, as well as k-refinement (which has no analogue). A possible extension could be to investigate the use of simple adaptive schemes in the hpk refinement space.
Parallel, Hierarchical Solution Algorithms for Radiation Shielding Analysis of Naval Pressurized Water Reactors (PWRs)
Uncertainty Quantification/Stochastic processes in time dependent neutron transport
Isogeometic and T-Spline methods for Second-order forms of the Boltzmann Transport Equation
The Boltzmann transport equation is central to the modelling of a wide variety of academically and industrially important areas of engineering and physics including: reactor physics, shielding and criticality, medical imaging, cloud radiation and photon transport in plasmas. However, many challenges are posed in obtaining numerical solutions due to the seven dimensional phase space of solution variables – position, energy, angle and time (x, y, z, E, θ, χ, t). Its application to reactor analysis is also made increasing complex by the multiscale nature of the problem as these geometries range from the fuel pin-cell (cm) to the assembly and the entire reactor core (m). This represents an immensely challenging problem with over 289 fuel pins within an assembly and around 200 fuel assemblies within a whole Pressurized Water Reactor (PWR) nuclear reactor core. The diagram (see insert above) shows an adaptive mesh used in the modelling of a UK Advanced Gas Cooled Reactor (AGR). The AGR is the predominant reactor design used currently in the UK (operated by British Energy/EDF) but will be replaced in the new build programme by PWRs of the AREVA EPR design or the Toshiba-Westinghouse AP1000 design.
Advanced Multiphysics Modelling of a Novel Aqueous Homogeneous Reactor (AHR) for Medical Isotope Production
- Babcock & Wilcox TSG
A new novel reactor is being developed by the Babcock and Wilcox (B&W) company for producing medical isotopes such as Molybdenum-99 (Mo-99). This novel reactor is based upon an aqueous homogeneous reactor (AHR) design and utilises Low Enriched aqueous Uranyl Salts as a liquid fuel (LEU). This project involves the production of a series of point kinetics models of increasing complexity to capture the physics of the reactor core. This involves elements of neutronics and fluid flow processes. The models focus on predicting the response of the reactor to transients caused by changes in reactivity. Polynomial chaos is also applied to one of the models in order to model the effects of uncertainty on the performance of the reactor.
A Stochastic Simulator for the Detection of Weak Radiation Signal: Application to Nuclear Safeguards and Security
Goal Based Coupled Adaptive Mesh Refinement (AMR) and angular adaptivity on Cartesian Meshes for Modelling Neutron Transport in PWR Reactor Cores
The purpose of this project is to develop techniques for the efficient modelling of neutron transport in pressurised water reactor (PWR) cores. The transport of neutrons is governed by the Boltzmann transport equation, a complex function of space, energy, angle and temporal variables. The problem is computationally demanding. The aim is to develop fully automatic adaptive procedures on Cartesian meshes that enable the mesh and angular discretisation to be locally refined if needed. Reliable local error metrics are required to identify where refinement is needed. The error metrics used to drive the automatic refinement strategy will give estimates for the error incurred in discretisation as well as estimates for the error in key quantities such as the K-effective and reaction rates.
The advantages of goal based adaptivity will be investigated. This involves solving the adjoint equation to give an estimate for the importance of an error in any particular cell for a certain functional of the solution.