The research undertaken for this Ph.D. thesis concerns the dispersion of solutes in sinuous open channel flows. The aim of the work is to address the void in knowledge and understanding of mixing and transport processes in natural watercourses. The influences of plan form curvature and non-uniform cross sectional shape on transverse and longitudinal mixing are specifically addressed. Experimental work was undertaken on the Flood Channel Facility at HR Wallingford Ltd. This involved creating a pseudo natural sand channel within the concrete meander plan form of the facility, and then stabilising the form. Tracer studies using instantaneous injection to investigate longitudinal mixing and continuous point source release to study transverse mixing were performed. Fluorescent tracer was used. Measurement was by six Turner Design Field Fluorometers in pump through mode and these were digitally logged. Detailed hydrodynamic measurements were made using a two-dimensional Laser Doppler Anemometer (LDA) fitted with a 14mm fibre-flow probe. The resulting data has undergone robust analysis and detailed interpretation. The conclusions are that the dominant processes in mixing, in the natural channel form studied, are shear effects. Simple equations for the prediction of flow fields have been investigated and validated against LDA measurements. It has been possible to make accurate predictions of the transverse and longitudinal mixing coefficients from the predicted flow fields. These predictions have been shown valid for the variations in mixing coefficients over the meander cycle and with discharge.

The project was aimed at describing the mixing phenomena relevant for both safety analysis, particularly in steam line break and boron dilution scenarios, and mixing phenomena of interest for economical operation and the structural integrity. Measurement data from a set of mixing experiments, gained by using advanced measurement techniques with enhanced resolution in time and space help to improve the basic understanding of turbulent mixing and to provide data for Computational Fluid Dynamics (CFD) code validation. Slug mixing tests simulating the start-up of the first main circulation pump are performed with two 1:5 scaled facilities: The Rossendorf coolant mixing model ROCOM and the VATTENFALL test facility, modelling a German Konvoi type and a Westinghouse type three-loop PWR, respectively. Additional data on slug mixing in a VVER-1000 type reactor gained at a 1:5 scaled metal mock-up at EDO Gidropress are provided. Experimental results on mixing of fluids with density differences obtained at ROCOM and the FORTUM PTS test facility are made available. Concerning mixing phenomena of interest for operational issues and thermal fatigue, flow distribution data available from commissioning tests (Sizewell-B for PWRs, Loviisa and Paks for VVERs) are used together with the data from the ROCOM facility as a basis for the flow distribution studies. The test matrix on flow distribution and steady state mixing performed at ROCOM comprises experiments with various combinations of running pumps and various mass flow rates in the working loops. Computational fluid dynamics calculations are accomplished for selected experiments with two different CFD codes (CFX-5, FLUENT). Best practice guidelines (BPG) are applied in all CFD work when choosing computational grid, time step, turbulence models, modelling of internal geometry, boundary conditions, numerical schemes and convergence criteria. The BPG contain a set of systematic procedures for quantifying and reducing numerical errors. The knowledge of these numerical errors is a prerequisite for the proper judgement of model errors. The strategy of code validation based on the BPG and a matrix of CFD code validation calculations have been elaborated. Besides of the benchmark cases, additional experiments were calculated by new partners and observers, joining the project later. Based on the "best practice solutions", conclusions on the applicability of CFD for turbulent mixing problems in PWR were drawn and recommendations on CFD modelling were given. The high importance of proper grid generation was outlined. In general, second order discretization schemes should be used to minimise numerical diffusion. First order schemes can provide physically wrong results. With optimised "production meshes" reasonable results were obtained, but due to the complex geometry of the flow domains, no fully grid independent solutions were achieved. Therefore, with respect to turbulence models, no final conclusions can be given. However, first order turbulence models like K-e or SST K-w are suitable for momentum driven slug mixing. For buoyancy driven mixing (PTS scenarios), Reynolds stress models provide better results.

The flow distribution in the primary circuit of the pressurized water reactor was studied with experiments and Computational Fluid Dynamics (CFD) simulations. The main focus was on the flow field and mixing in the downcomer of the pressure vessel: how the different factors like the orientation of operating loops, the total loop flow rate and the asymmetry of the loop flow rates affect the outcome. In addition to the flow field studies the overall applicability of CFD methods for primary circuit thermal-hydraulic analysis was evaluated based on the CFD simulations of the mixing experiments of the ROCOM (Rossendorf Coolant Mixing Model) test facility and the mixing experiments of the Paks NPP. The experimental part of the work in work package 3 included series of steady state mixing experiments with the ROCOM test facility and the publication of results of Paks VVER-440 NPP thermal mixing experiments. The ROCOM test facility models a 4-loop KONVOI type reactor. In the steady-state mixing experiments the velocity field in the downcomer was measured using laser Doppler anemometry and the concentration of the tracer solution fed from one loop was measured at the downcomer and at the core inlet plane. The varied parameters were the number and orientation of the operating loops, the total flow rate and the (asymmetric) flow rate of individual loops. The Paks NPP thermal mixing experiments took place during commissioning tests of replaced steam generator safety valves in 1987-1989. It was assumed that in the reactor vessels of Paks VVER-440 NPP equipped with six loops the mixing of the coolant is not ideal. For the realistic determination of the active core inlet temperature field for the transients and accidents associated with different level temperature asymmetry a set of mixing factors were determined. Based on data from the online core monitoring system and a separate mathematical model the mixing factors for loop flows at the core inlet were determined. In the numerical simulation part of the work package 3 the detailed measurements of ROCOM tests were used for the validation of CFD methods for primary circuit studies. The selected steady state mixing experiments were simulated with CFD codes CFX-4, CFX-5 and FLUENT. The velocity field in the downcomer and the mixing of the scalar were compared between CFD simulations and experiments. The CFD simulations of full scale PWR included the simulation of Paks VVER-440 mixing experiment and the simulation of Loviisa VVER-440 downcomer flow field. In the simulations of Paks experiments the experimental and simulated concentration field at the core inlet were compared and conclusions made concerning the results overall and the VVER-440 specific geometry modelling aspects like how to model the perforated elliptic bottom plate and what is the effect of the cold leg bends to the flow field entering to the downcomer. With Loviisa simulations the qualitative comparison was made against the original commissioning experiments but the emphasis was on the CFD method validation and testing. The overall conclusion concerning the CFD modelling of the flow field and mixing in the PWR primary circuit could be that the current computation capacity and physical models also in commercial codes is beginning to be sufficient for simulations giving reliable and useful results for many real primary circuit applications. However the misuse of CFD methods is easy, and the general as well as the nuclear power specific modelling guidelines should be followed when the CFD simulations are made.

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Fundação de Amparo a Pesquisa do Estado de Minas Gerais / Esta dissertação é parte de um amplo projeto de pesquisa, que visa ao desenvolvimento de uma plataforma computacional de dinâmica dos fluidos (CFD) capaz de simular a física de escoamentos que envolvem mistura de várias espécies químicas, com reação e combustão, utilizando um método hibrido Simulação de Grandes Escalas (LES) / Função Densidade Filtrada (FDF) Lagrangiana em malha adaptativa, bloco-estruturada. Uma vez que escoamentos com mistura proporcionam fenômenos que podem ser correlacionados com a combustão em escoamentos turbulentos, uma visão global da fenomenologia de mistura foi apresentada e escoamentos fechados, laminar e turbulento, que envolvem mistura de duas espécies químicas inicialmente segregadas foram simulados utilizando o código de desenvolvimento interno AMR3D e o código recentemente desenvolvido FDF Lagrangiana de composição. A primeira etapa deste trabalho consistiu na criação de um modelo computacional de partículas estocásticas em ambiente de processamento distribuído. Isto foi alcançado com a construção de um mapa Lagrangiano paralelo, que pode gerenciar diferentes tipos de elementos lagrangianos, incluindo partículas estocásticas, particulados, sensores e nós computacionais intrínsecos dos métodos Fronteira Imersa e Acompanhamento de Interface. O mapa conecta informações Lagrangianas com a plataforma Euleriana do código AMR3D, no qual equações de trans- porte são resolvidas. O método FDF Lagrangiana de composição realiza cálculos algébricos sobre partículas estocásticas e provê campos de composição estatisticamente equivalentes aos obtidos quando se utiliza o método de Diferenças Finitas para solução de equações diferenciais parciais; a técnica de Monte Carlo foi utilizada para resolver um sistema derivado de equações diferenciais estocásticas (SDE). Os resultados concordaram com os benchmarks, que são simulações baseadas em plataforma de Diferenças Finitas para solução de uma equação de transporte de composição filtrada. / This master thesis is part of a wide research project, which aims at developing a com- putational fluid dynamics (CFD) framework able to simulate the physics of multiple-species mixing flows, with chemical reaction and combustion, using a hybrid Large Eddy Simulation (LES) / Lagrangian Filtered Density Function (FDF) method on adaptive, block-structured mesh. Since mixing flows provide phenomena that may be correlated with combustion in turbulent flows, we expose an overview of mixing phenomenology and simulated enclosed, ini- tially segregated two-species mixing flows, at laminar and turbulent states, using the in-house built AMR3D and the developed Lagrangian composition FDF codes. The first step towards this objective consisted of building a computational model of notional particles transport on distributed processing environment. We achieved it constructing a parallel Lagrangian map, which can hold different types of Lagrangian elements, including notional particles, particu- lates, sensors and computational nodes intrinsic to Immersed Boundary and Front Tracking methods. The map connects Lagrangian information with the Eulerian framework of the AMR3D code, in which transport equations are solved. The Lagrangian composition FDF method performs algebraic calculations over an ensemble of notional particles and provides composition fields statistically equivalent to those obtained by Finite Differences numerical solution of partially differential equations (PDE); we applied the Monte Carlo technique to solve a derived system of stochastic differential equations (SDE). The results agreed with the benchmarks, which are simulations based on Finite Differences framework to solve a filtered composition transport equation. / Mestre em Engenharia Mecânica