## Publications

70 results found

Georgaka S, Stabile G, Star K,
et al., 2020, A hybrid reduced order method for modelling turbulent heat transfer problems, *Computers and Fluids*, Vol: 208, ISSN: 0045-7930

© 2020 Elsevier Ltd A parametric, hybrid reduced order method based on the Proper Orthogonal Decomposition with both Galerkin projection and interpolation based on Radial Basis Functions method is presented. This method is tested on a case of turbulent non-isothermal mixing in a T-junction pipe, a common flow arrangement found in nuclear reactor cooling systems. The reduced order model is derived from the 3D unsteady, incompressible Navier-Stokes equations weakly coupled with the energy equation. For high Reynolds numbers, the eddy viscosity and eddy diffusivity are incorporated into the Reduced Order Model with a Proper Orthogonal Decomposition (nested and standard) with Interpolation (PODI), where the interpolation is performed using Radial Basis Functions. The reduced order solver, obtained using a k−ω SST Unsteady Reynolds Averaged Navier-Stokes full order model, is tested against the full order solver in a 3D T-junction pipe with parameterised velocity inlet boundary conditions.

Ahn JS, Bluck M, 2020, Isogeometric analysis of the time-dependent incompressible MHD equations, *International Journal of Computational Fluid Dynamics*, Vol: 34, Pages: 226-248, ISSN: 1029-0257

This paper presents an isogeometric (IGA) solver for time-dependent, incompressible magnetohydrodynamics (MHD). In this paper, a combination of inf-sup stable mixed discretisations is considered to discretise the hydrodynamic pair (i.e. velocity and pressure) and magnetic pair (i.e. magnetic field and magnetic pressure). The one step θ-method is used for the temporal discretisation. Manufactured and analytical solutions are considered to assess convergence, accuracy and performance of the IGA solver. Moreover, benchmark problems involving a MHD flow over an obstacle and MHD flow under non-uniform magnetic field are considered to examine the effect of the magnetic field on the flow behaviour.

Georgaka S, Stabile G, Rozza G,
et al., 2020, Parametric POD-Galerkin model order reduction for unsteady-state heat transfer problems, *Communications in Computational Physics*, Vol: 27, Pages: 1-32, ISSN: 1815-2406

A parametric reduced order model based on proper orthogonal decompositionwith Galerkin projection has been developed and applied for the modeling of heattransport in T-junction pipes which are widely found in nuclear power reactor coolingsystems. Thermal mixing of different temperature coolants in T-junction pipes leads totemperature fluctuations and this could potentially cause thermal fatigue in the pipewalls. The novelty of this paper is the development of a parametric ROM consideringthe three dimensional, incompressible, unsteady Navier-Stokes equations coupledwith the heat transport equation in a finite volume regime. Two different parametriccases are presented in this paper: parametrization of the inlet temperatures andparametrization of the kinematic viscosity. Different training spaces are consideredand the results are compared against the full order model. The first test case results toa computational speed-up factor of 374 while the second test case to one of 211.

Duan Y, Cooling C, Ahn JS,
et al., 2019, Using a Gaussian process regression inspired method to measure agreement between the experiment and CFD simulations, *International Journal of Heat and Fluid Flow*, Vol: 80, ISSN: 0142-727X

This paper presents a Gaussian process regression inspired method to measure the agreement between experiment and computational fluid dynamics (CFD) simulation. Because of misalignments between experimental and numerical outputs in spatial or parameter space, experimental data are not always suitable for quantitative assessing the numerical models. In this proposed method, the cross-validated Gaussian process regression (GPR) model, trained based on experimental measurements, is used to mimic the measurements at positions where there are no experimental data. The agreement between an experiment and the simulation is mimicked by the agreement between the simulation and GPR models. The statistically weighted square error is used to provide tangible information for the local agreement. The standardised Euclidean distance is used for assessing the overall agreement.The method is then used to assess the performance of four scale-resolving CFD methods, such as URANS k-ω-SST, SAS-SST, SAS-KE, and IDDES-SST, in simulating a prism bluff-body flow. The local statistically weighted square error together with standardised Euclidean distance provide additional insight, over and above the qualitative graphical comparisons. In this example scenario, the SAS-SST model marginally outperformed the IDDES-SST and better than the other two other, according to the distance to the validated GPR models.

Ahn J, Bluck M, 2019, Isogeometric analysis of the steady-state incompressible mhd equations, *SIAM Journal on Scientific Computing*, Vol: 41, Pages: B396-B424, ISSN: 1064-8275

This paper presents an isogeometric (IGA) solver for steady-state incompressiblemagnetohydrodynamics (MHD). MHD is the study of the behavior of electrically conducting fluidsand can be viewed mathematically as a coupled system: the Navier--Stokes equations (for the fluid)and a reduced form of Maxwell's equations (for the electromagnetic field). A key feature of MHDflow is the potential development of very strong shear, usually in proximity to walls. This resultsin two correlated demands on numerical simulation: the need to represent the geometry and thenear-wall shear accurately. In addition, for both the Navier--Stokes and the Maxwell's equations,appropriate discretizations are required for the problem to be well-posed. IGA analysis is a variant ofthe conventional finite element (FE) method, but utilizing the underlying approximations commonlyused in computer-aided design (CAD) to represent geometry, basis functions, and test functions.As a result, IGA can represent curved shapes such as circles and conic sections exactly using B-splines and nonuniform rational B-splines (NURBS). Furthermore, IGA can obtain much improvedaccuracy in the computed solution, for a given number of degrees of freedom, due to its inherentsmoothness and higher continuity of basis functions when compared with standard FE and finitevolume (FV) methods. To address the issue of well-posedness, a set of stable IGA discretizationsfor the Navier--Stokes and Maxwell's equations is developed and incorporated into the IGA solver.A detailed convergence study is carried out to verify the convergence, accuracy, and performance ofthe IGA scheme for certain benchmark cases.

Bluck M, 2019, Analytical solutions to non-uniform surface heat transfer with volumetric sources in magnetohydrodynamic duct flow, *Journal of Heat Transfer-Transactions of the ASME*, Vol: 141, ISSN: 0022-1481

A detailed understanding of the flow of a liquid metal in a rectangular duct subject to a strong transverse magnetic field is vitalin a number of engineering applications, notably for proposed blanket technologies for fusion reactors. Fusion reactors offer thepotential for clean base-load energy and their development is now entering an engineering phase where the practical means bywhich the energy released can be converted into useful heat must be addressed. To such ends, this article considers the convectiveheat transfer processes for fully developed laminar magnetohydrodynamic (MHD) flows in rectangular ducts of the kind proposedin some blanket designs. Analytical solutions which incorporate the non-uniformity of peripheral temperature and heat flux and theeffect of volumetric heating, are developed as functions of magnetic field strength and duct aspect ratio. A distinct feature of theseMHD problems, not yet addressed in the literature, is that unlike the conventional characterisation of heat transfer by a Nusseltnumber, it is necessary to generalise the concept to vectors and matrices of Nusselt coefficients, due to the extreme anisotropy ofboth the flow and heating. The new analytical results presented here capture more complex heat transfer behaviour than non-MHDflows and in particular chracterize the importance of aspect ratio. The importance of these new results lie not only in the improvedunderstanding of this complex process, but also in the provision of characterisations of convective heat transfer which underpinprogress toward systems scale simulations of fusion blanket technology which will be vital for the realisation of practical fusionreactors.

Duan Y, Jackson C, Eaton M,
et al., 2019, An assessment of eddy viscosity models on predicting performance parameters of valves, *Nuclear Engineering and Design*, Vol: 342, Pages: 60-77, ISSN: 0029-5493

The major objective of the present study is to evaluate the performance of a range of turbulent eddy viscosity models in the prediction of macro-parameters (flow coefficient (CQ) and force coefficient (CF)), for certain types of valve, including the conic valve, the disk valves, and the compensated valve. This has been achieved by comparison of numerical predictions with experimental measurements available in the literature. The examined turbulence models include most of the available turbulent eddy viscosity models in STAR-CCM+ 12.04. They are the standard k-ε model, realizable k-ε model, k-ω-sst model, V2F model, EB k-ε model and the Lag EB k-ε models.The low-Re turbulence models (k-ω-sst, V2F, EB k-ε and Lag EB k-ε) perform worse than the high-Re models (standard k-ε and realizable k-ε). For the conic valve, the performance of different turbulent models varies little; the standard k-ε model shows a marginal advantage over the others. The performance of the turbulence models changed greatly, however, for prediction of CQ and CF of the disk and compensated valves. In general, the realizable k-ε model is demonstrated to be a robust choice for both valve types. Although the EB k-ε may marginally outperform it in the prediction of CF at large disk valve opening.The effects of the unknown entry flow and initialization conditions are also studied. The predictions are more sensitive to the entry flow condition when the valve opening is large. Additionally, the uncertainties caused by unknown entry conditions are comparable to overall modelling errors in some cases. For flow systems with multiple stable flow-states coexisting in the flow domain, the output of the numerical models can also be affected by the initialization conditions.When the streamline curvature and secondary flow is modest like conical valve flow, the nonlinear modification of the standard k-ε mode

Duan Y, Eaton MD, Bluck MJ, et al., 2018, ASSESSMENTS OF DIFFERENT TURBULENCE MODELS IN PREDICTING THE PERFORMANCE OF A BUTTERFLY VALVE, 26th International Conference on Nuclear Engineering (ICONE-26), Publisher: AMER SOC MECHANICAL ENGINEERS

Duan Y, Eaton MD, Bluck MJ, et al., 2018, A VALIDATION OF CFD METHODS ON PREDICTING VALVE PERFORMANCE PARAMETERS, ASME Power Conference 2018 (POWER2018), Publisher: AMER SOC MECHANICAL ENGINEERS

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Ahn JS, Bluck M, Eaton M, et al., 2018, A VALIDATION OF RELAP ON PREDICTING NUCLEAR POWER PLANT PHENOMENA, 26th International Conference on Nuclear Engineering (ICONE-26), Publisher: AMER SOC MECHANICAL ENGINEERS

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Pearson RJ, Bluck MJ, Murphy ST, 2017, A symbiotic approach to compact fission and fusion reactors, 2017 ANS Meeting and Nuclear Technology Expo, Pages: 378-381, ISSN: 0003-018X

Bluck MJ, Wolfendale MJ, 2017, An analytical solution to the heat transfer problem in thick-walled hunt flow, *International Journal of Heat and Fluid Flow*, Vol: 64, Pages: 103-111, ISSN: 0142-727X

The flow of a liquid metal in a rectangular duct, subject to a strong transverse magnetic field is of interest in a number of applications. An important application of such flows is in the context of coolants in fusion reactors, where heat is transferred to a lead-lithium eutectic. It is vital, therefore, that the heat transfer mechanisms are understood. Forced convection heat transfer is strongly dependent on the flow profile. In the hydrodynamic case, Nusselt numbers and the like, have long been well characterised in duct geometries. In the case of liquid metals in strong magnetic fields (magnetohydrodynamics), the flow profiles are very different and one can expect a concomitant effect on convective heat transfer. For fully developed laminar flows, the magnetohydrodynamic problem can be characterised in terms of two coupled partial differential equations. The problem of heat transfer for perfectly electrically insulating boundaries (Shercliff case) has been studied previously (Bluck et al., 2015). In this paper, we demonstrate corresponding analytical solutions for the case of conducting hartmann walls of arbitrary thickness. The flow is very different from the Shercliff case, exhibiting jets near the side walls and core flow suppression which have profound effects on heat transfer.

Palazzi A, Bluck MJ, Lo S, et al., 2016, Coupling RELAP5-3D and STAR-CCM+ for simulations of steady and transient single phase flows, 2016 International Congress on Advances in Nuclear Power Plants (ICAPP 2016), Publisher: Curran Associates, Inc., Pages: 2202-2211

A coupling scheme was developed to couple the CFD software STAR-CCM+ v10.04 and the system code RELAP5-3D v4.2.1. In this paper the structure of the scheme is presented, together with validations for single phase flow in smooth pipes in both transient and steady state cases. Attention was also given to the problem of reconstructing the profile at the inlet of the CFD model under the hypothesis of fully developed flow. This problem arises when flow data has to be passed from the one-dimensional system code to the three-dimensional CFD software.

Wolfendale MJ, Bluck MJ, 2015, A coupled systems code-CFD MHD solver for fusion blanket design, *FUSION ENGINEERING AND DESIGN*, Vol: 98-99, Pages: 1902-1906, ISSN: 0920-3796

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Bluck MJ, Wolfendale MJ, 2015, An analytical solution to electromagnetically coupled duct flow in MHD, *Journal of Fluid Mechanics*, Vol: 771, Pages: 595-623, ISSN: 0022-1120

The flow of an electrically conducting fluid in an array of square ducts, separated by arbitrary thickness conducting walls, subject to an applied magnetic field is studied. The analytical solution presented here is valid for thick walls and is based on the homogeneous solution obtained by Shercliff (Math. Proc. Camb. Phil. Soc., vol. 49 (01), 1953, pp. 136-144). Arrangements of ducts arise in a number of applications, most notably in fusion blankets, where liquid metal is used both as coolant and for tritium generation purposes. Analytical solutions, such as those presented here, provide insight into the physics and important benchmarking and validation data for computational magnetohydrodynamics (MHD), as well as providing approximate flow parameters for 1D systems codes. It is well known that arrays of such ducts with conducting walls exhibit varying degrees of coupling, significantly affecting the flow. An important practical example is the so-called Madarame problem (Madarame et al., Fusion Technol., vol. 8, 1985, pp. 264-269). In this work analytical results are derived for the relevant hydrodynamic and magnetic parameters for a single duct with thick walls analogous to the Hunt II case. These results are then extended to an array of such ducts stacked in the direction of the applied magnetic field. It is seen that there is a significant coupling affect, resulting in modifications to pressure drop and velocity profile. In certain circumstances, counter-current flow can occur as a result of the MHD effects, even to the point where the mean flow is reversed. Such phenomena are likely to have significant detrimental effects on both heat and mass transfer in fusion applications. The dependence of this coupling on parameters such as conductivities, wall thickness and Hartmann number is studied.

Bluck MJ, Wolfendale MJ, Marquis AJ, 2015, An analytical solution to the heat transfer problem in Shercliff flow, *International Journal of Heat and Mass Transfer*, Vol: 86, Pages: 542-549, ISSN: 0017-9310

Cinosi N, Walker SP, Bluck MJ,
et al., 2014, CFD simulation of turbulent flow in a rod bundle with spacer grids (MATIS-H) using STAR-CCM, *NUCLEAR ENGINEERING AND DESIGN*, Vol: 279, Pages: 37-49, ISSN: 0029-5493

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Cinosi N, Walker SP, Bluck M, et al., 2014, CFD ANALYSIS OF THE FLOW IN CRUD-COATED NUCLEAR ROD BUNDLES, 22nd International Conference on Nuclear Engineering (ICONE22), Publisher: AMER SOC MECHANICAL ENGINEERS

Bluck MJ, Cinosi N, Walker SP, 2014, A multilevel hierarchical preconditioner for multiscale EM scattering

Palazzi A, Bluck MJ, Lo S, 2014, A coupled RELAP5-3D/STAR-CCM+ simulation for the calculation of friction factor in pipes, Pages: 1323-1329

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. 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. Modern CFD is able to produce high-quality predictions of flows in complex geometries, but only with the use of large computing resources. It would be impractical to build a CFD model of, for example, the entire primary circuit of a PWR. However, much of the primary circuit may well be able to be modelled with adequate fidelity using a cheaper one-dimensional system code, and it may only be in a limited part of the circuit that full three-dimensional effects are important. In this paper, the coupling tool present in the STAR-CCM+ v8.02 software was used, together with RELAP5-3D v4.0.3, to perform a coupled analysis of single phase flow in a circular pipe in order to evaluate Moody's friction factor. Three different cases were studied, following two different models. The first case consisted in using smooth walls for the pipe, whereas, in the second and the third ones, the roughness of the wall was set to 20 μm and 50 μm respectively. The first model consisted in using RELAP5-3D for the upstream part of the pipe and STAR-CCM+ for the downstream part. In the second model, instead, STAR-CCM+ was used for the upstream part of the pipe and RELAP5-3D for the downstream part. The results obtained with these two models have been compared with each other to check for possible incongruences. Furthermore, all the results have been compared with standalone simulations performed with RELAP5-3D and STAR-CCM+ and with experimental data (Moody's diagram).

Bluck M, Cinosi N, Walker S, 2014, A multilevel hierarchical preconditioning method for multiscale scattering bodies

This paper considers the solution of the electric field integral equation (EFIE). Hierarchical conforming bases are developed which are subsequently used in the construction of a multilevel Schwarz type preconditioner. The effectiveness of this approach is demonstrated by the computation of scattering from sub-wavelength scattering bodies. The resulting schemes are shown to be faster than conventional schemes up to an order of magnitude.

Bluck M, Cinosi N, Walker S, 2013, A multilevel hierarchical preconditioner technique for multiscale and complex em scattering bodies, Pages: 1519-1522

This paper considers the solution of the combined field integral equation (CFIE) for lossy/dielectric problems. Hierarchical conforming bases are developed which are subsequently used in the construction of a multilevel Schwarz type preconditioner. The effectiveness of this approach is demonstrated by the computation of scattering in free space from a range of spheres with different permittivity (non PEC material). The resulting schemes are shown to be faster than conventional schemes. © 2013 IEEE.

Bluck MJ, Cinosi NN, Walker SP, 2013, A p-MUS preconditioner for the EFIE, *IEEE Transactions on Antennas and Propagation*, Vol: n/a, ISSN: 0018-926X

This paper considers the solution of the electric field integral equation (EFIE) in electromagnetics. As with associated finite element methods, their solution relies upon the construction of conforming bases. Whilst lowest order (RWG) spaces are near ubiquitous, their extension to higher order offers, potentially, a number of benefits in terms of accuracy and efficiency, which has been well documented in both finite elements and integral equation formulations. A further evolution of higher order conforming bases is the hierarchical basis. These have demonstrated considerable gains in efficiency in finite element applications. Such bases allow for the development of effective acceleration schemes, for instance, the multilevel Schwarz type preconditioner (p-MUS). An obvious question arises as to the applicability of such hierarchical bases and their associated acceleration schemes to integral equations. It is seen that the conclusions as to their efficacy depend strongly on the scattering regime. In particular, high frequency problems (those where the wavelength is the principal determinant of mesh size) are shown to benefit little from hierarchical functions. On the other hand, for {\lq low frequency\rq} problems (where geometry is the main determinant of mesh size), there are significant improvements in performance over corresponding interpolatory schemes.

Bluck MJ, Cinosi N, Walker SP, 2013, A multilevel hierarchical preconditioner for multiscale EM scattering

Integral equation schemes, both EFIE and MFIE, have become a powerful tool, particularly with the development of accelerated schemes such as the fast multipole method (FMM). Key to most such treatments is the requirement to solve matrix equations iteratively, which at their core involve matrixvector multiplications. Much of the cost of such solutions then depends on the number of iterations and the cost per iteration. The vast majority of integral equations implementations employ the simplest Rao-WiltonGlisson (RWG) basis functions on triangles. High order interpolatory bases have been developed which (in principle) offer improved accuracy for a given cost. Within the current developments, the next natural step beyond high order interpolatory methods is to arrange these bases hierarchically, as already experienced within the finite element community. Of themselves hierarchical bases offer little more than their high order interpolatory counterparts. However, as has been demonstrated in finite elements it is possible to employ this hierarchical structure to great effect in the reduction of the computational cost of the underlying iterative scheme via a multilevel Schwarz type preconditioner. In this paper we attempt to apply such hierarchical bases and their associated acceleration schemes to integral equations. The results suggest that their efficacy depend strongly on the scattering regime. In particular, high frequency problems (those where the wavelength is the principal determinant of mesh size) are shown to benefit little from hierarchical functions. Unlike their finite element counterparts, equivalent p-MUS integral equation schemes appear to offer little gain, if any, over nonhierarchical schemes. On the other hand, for ̀low frequency' problems, such as scattering of objects with sub-wavelength features (where geometry is the main determinant of mesh size), there are significant improvements in performance over corresponding interpolatory schemes. Copyright &

Bluck MJ, 2012, Conforming Hierarchical Basis Functions, *Communications in Computational Physics*, Vol: 12, Pages: 1215-1256, ISSN: 1815-2406

A unified process for the construction of hierarchical conforming bases on a range of element types is proposed based on an ab initio preservation of the under- lying cohomology. This process supports not only the most common simplicial ele- ment types, as are now well known, but is generalized to squares, hexahedra, prisms and importantly pyramids. Whilst these latter cases have received (to varying de- grees) attention in the literature, their foundation is less well developed than for the simplicial case. The generalization discussed in this paper is effected by recourse to basic ideas from algebraic topology (differential forms, homology, cohomology, etc) and as such extends the fundamental theoretical framework established by the work of Hiptmair [16–18] and Arnold et al. [4] for simplices. The process of forming hierar- chical bases involves a recursive orthogonalization and it is shown that the resulting finite element mass, quasi-stiffness and composite matrices exhibit exponential or bet- ter growth in condition number.

Cinosi N, Bluck M, Walker S, 2012, Application of Time-Domain BIE to sub-wavelength Scattering Bodies with Finite Conductivity, International Conference on Electromagnetics in Advanced Applications (ICEAA) / IEEE-APS Topical Conference on Antennas and Propagation in Wireless Communications (IEEE APWC) / URSI Electromagnetic Environment and Interference Symposium (EEIS), Publisher: IEEE, Pages: 1177-1179

Bluck M, Cinosi N, Walker S, 2011, A multilevel hierarchical preconditioner for the electric field integral equation, Pages: 1180-1183

This paper considers the solution of the electric field integral equation (EFIE). Hierarchical conforming bases are developed which are subsequently used in the construction of a multilevel Schwarz type preconditioner. The effectiveness of this approach is demonstrated by the computation of scattering from a range of perfectly conducting objects including spheres, cubes, plates and dihedrals. The resulting schemes are shown to be faster than conventional schemes by approximately an order of magnitude. © 2011 IEEE.

Cinosi N, Walker S, Bluck M, 2011, Time-domain bie analysis of large electromagnetic scattering problems with Impedance Boundary Condition, Pages: 1172-1175

Methods for solving the electromagnetic scattering of computationally large problems in a fast and efficient way are well established. However their application is limited to PEC scattering bodies, whilst when applied to lossy or conducting materials they become inefficient and less desirable. In this paper we extend the capabilities of these fast methods to solve for non-dispersive conductors by using the approximation of the Impedance Boundary Condition. © 2011 IEEE.

Cinosi N, Haq I, Bluck M,
et al., 2011, The effective thermal conductivity of crud and heat transfer from crud-coated PWR fuel, *Nuclear Engineering and Design: an international journal devoted to the thermal, mechanical, materials, and structural aspects of nuclear fission energy*, Vol: 241, Pages: 792-798, ISSN: 0029-5493

Water-filled crud on the surface of PWR fuel could offer resistance to the flow of heat, which might be expected to cause higher clad temperatures, and probably more fuel failures, than are actually observed. However, there is some evidence from post-irradiation inspection that the crud is penetrated by pores large enough to permit vapour formation, and it is believed these provide a mechanism for `wick boiling' to occur, which modifies, and indeed can under some circumstances actually improve, heat transfer. This phenomenon is investigated using a two-dimensional coupled multi-physics model, accounting for the flow of water, heat and dissolved species within the crud. The fuel thermal performance is characterized in terms of an effective crud thermal conductivity derived from the use of this model, and the non-linear dependence this effective thermal conductivity has on parameters such as crud thickness and pore density is determined.

D'Arcy M, Weiss DJ, Bluck M,
et al., 2011, Adsorption kinetics, capacity and mechanism of arsenate and phosphate on a bifunctional TiO2-Fe2O3 bi-composite, *Journal of Colloid and Interface Science*, Vol: 364, Pages: 205-212

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