Conditional moment closure modelling of soot formation in turbulent, non-premixed methane and propane flames

Presented are results obtained from the incorporation of a semi-empirical soot model into a first-order conditional moment closure (CMC) approach to modelling turbulent, non-premixed methane–air and propane–air flames. Soot formation is determined via the solution of two transport equations for soot mass fraction and particle number density, with acetylene and benzene employed as the incipient species responsible for soot nucleation, and the concentrations of these calculated using a detailed gas-phase kinetic scheme involving 70 species. The study focuses on the influence of differential diffusion of soot particles on soot volume fraction predictions. The results of calculations are compared with experimental data for atmospheric and 3 atm methane flames, and propane flames with air preheated to 323 K and 773 K. Overall, the study demonstrates that the model, when used in conjunction with a representation of differential diffusion effects, is capable of accurately predicting soot formation in the turbulent non-premixed flames considered

CO2 pipelines material and safety considerations

This paper presents an overview of some of the most important factors and areas of uncertainty affecting integrity and accurate hazard assessment of CO2 pipelines employed as part of the Carbon Capture and Sequestration (CCS) chain. These include corrosion, hydrate formation, hydrogen embrittlement and propensity to fast running ductile and brittle factures. Special consideration is given to the impact of impurities within the CO2 feed from the various capture technologies on these possible hazards. Knowledge gaps in the modelling of outflow and subsequent dispersion of CO2 following the accidental rupture of pressurised CO2 pipelines, central to their safety assessment, are also presented

CFD Simulation of Single- and Two-Phase Natural Convection in the Context of External Reactor Vessel Cooling

In recent decades, and with renewed importance after the events in Fukushima, the nuclear community has focused on the opportunity to rely on passive safety and, after plant shutdown, to ensure that reactor cooling can be safely guaranteed by natural processes, at least for a sufficient time before any active power intervention is needed. Buoyancy-driven flows and natural convection provide an efficient and potentially highly reliable and inexpensive heat transfer mechanism but, at the same time, these are rather complex flows because of the strong two-way coupling between the velocity and thermal fields, and the interaction between buoyancy and turbulence. In view of this, numerical tools able to predict these flows with accuracy and confidence are necessary to support the informed design and the safety assessment of present and future nuclear power plants. This paper is focused on research ongoing at the University of Leeds on the development of computational fluid dynamic tools to predict buoyancy-driven flows, of particular relevance to external reactor vessel cooling (ERVC). In ERVC, the aim is to retain the melted corium inside the reactor vessel, which is cooled from the outside by natural convection in the flooded reactor cavity where boiling is expected to occur on the outer vessel wall. The work starts by considering single-phase flow in a square buoyant cavity that is used to assess and improve the accuracy of available Reynolds-averaged Navier-Stokes (RANS) models, some of which, through the turbulence models embedded within them, are known to have shortcomings in predicting natural convection. In the same geometry, the superior accuracy of the large eddy simulation technique, the results from which may underpin further development of RANS approaches, is demonstrated. A two-fluid Eulerian-Eulerian model including boiling at the wall, which will be required to predict the whole ERVC phenomena, is also preliminary tested in the final part of the paper. Overall, encouraging results are found and weaknesses of the available modelling techniques and areas for future development are identified

Predicting Two-Phase and Subcooled Boiling Flows with a Two-Fluid CFD Boiling Model Combined with a Population Balance Approach

In recent years, computational fluid dynamics has emerged as one method that is able to improve our ability to predict subcooled and saturated boiling flows. In the nuclear field, accurate modelling of the critical heat flux (CHF), which is perhaps the main threat to the integrity of reactor fuel rods, has stimulated much interest. In predicting the CHF, one short-term objective is to develop models that can be applied with confidence to both bubbly and boiling flows. In this paper, the accuracy of an Eulerian-Eulerian averaged two-fluid model implemented in the STAR-CCM+ code is evaluated against air-water bubbly and subcooled boiling flow data. The model includes a Reynolds stress turbulence model and a population balance-based approach with newly implemented source terms for bubble break-up and coalescence. The boiling model is based on the heat flux partitioning approach and accommodates the heat flux due to single-phase convection, quenching and evaporation. Despite achieving a satisfactory accuracy for air-water bubbly flows, predictions of subcooled boiling are less accurate in areas such as the average bubble diameter and the velocity profile close to the wall. However, the accuracy obtained for void fraction, turbulence levels and temperature encourages future efforts to improve the model described. Further developments to increase accuracy and general applicability, in particular in relation to the boiling and population balance models, are identified

CFD Simulation of Boiling Flows with an Eulerian-Eulerian Two-Fluid Model

In the nuclear field, computational fluid dynamics (CFD) is being applied increasingly often to improve the prediction of the boiling flows that are to some extent experienced in almost all water-cooled reactors. For reactor-scale flows, although the development of advanced CFD methods is progressing at a fast rate, Eulerian-Eulerian averaged two-fluid models still represent the only practicable option. In these models, boiling at the wall is normally incorporated using the heat flux partitioning approach and, overall, a number of sub-models and closure relations are required, some of which still rely mainly upon empirical arguments. In view of this, further progress is needed in our ability to model and predict boiling flows and, eventually, extend the modelling to other areas such as the prediction of the critical heat flux. The present paper discusses the development of an Eulerian-Eulerian two-fluid model, implemented in the STAR-CCM+ CFD code. The model includes a Reynolds stress multiphase turbulence model and the Sγ population balance model with improved breakup and coalescence sources. Turbulence and average bubble diameter predictions are firstly, and independently, validated against air-water bubbly flows. Finally, the whole boiling model is assessed against a large database of subcooled boiling flows that covers an extended range of flow conditions. Validation is extended to some recent experiments and some sensitivity studies are made on the modelling of interfacial forces and condensation in the bulk of the flow. Overall, many areas of the model reach a satisfactory accuracy, but a number of weaknesses still persists and, consequently, areas of further improvement are identified

Digital predictions of complex cylinder packed columns

A digital computational approach has been developed to simulate realistic structures of packed beds. The underlying principle of the method is digitisation of the particles and packing space, enabling the generation of realistic structures. Previous publications [Caulkin, R., Fairweather, M., Jia, X., Gopinathan, N., & Williams, R.A. (2006). An investigation of packed columns using a digital packing algorithm. Computers & Chemical Engineering, 30, 1178–1188; Caulkin, R., Ahmad, A., Fairweather, M., Jia, X., & Williams, R. A. (2007). An investigation of sphere packed shell-side columns using a digital packing algorithm. Computers & Chemical Engineering, 31, 1715–1724] have demonstrated the ability of the code in predicting the packing of spheres. For cylindrical particles, however, the original, random walk-based code proved less effective at predicting bed structure. In response to this, the algorithm has been modified to make use of collisions to guide particle movement in a way which does not sacrifice the advantage of simulation speed. Results of both the original and modified code are presented, with bulk and local voidage values compared with data derived by experimental methods. The results demonstrate that collisions and their impact on packing structure cannot be disregarded if realistic packing structures are to be obtained

Multi-Fluid Computational Fluid Dynamic Predictions of Turbulent Bubbly Flows Using an Elliptic-Blending Reynolds Stress Turbulence Closure

The accurate prediction of bubbly flows is critical to many areas of nuclear reactor thermal hydraulics, mainly, but not only, in relation to the key role bubble behavior plays in boiling flows. Large scale computations of flows with hundreds of thousands of bubbles are possible at a reasonable computational cost using computational fluid dynamic, multi-fluid Eulerian-Eulerian models. The main limitation of these models is the need to entirely model interfacial transfer processes with proper closure relations. Here, the capabilities and advantages provided by a model that includes an elliptic-blending Reynolds stress turbulence closure (EB-RSM), allowing fine resolution of the velocity field in the near-wall region, are tested over a large database. This database includes mostly monodispersed bubbly flows over a wide range of operating conditions and geometrical parameters, including upward and downward pipe flows, large diameter pipes and a square duct. The model shows encouraging accuracy and robustness, with good agreement over most void fraction distributions and accurate prediction of the magnitude and position of the near-wall void fraction peak. The model does not include any wall force, avoiding all the related uncertainties, and the prediction of the void fraction peak relies on the fine resolution of the near-wall pressure gradient induced by the turbulence field. Overall, the EB-RSM allows accurate resolution of the velocity and turbulence field near the wall, and the transition to this and similar turbulence closures is of value in assisting the ongoing quest for thermal hydraulic models that are accurate and of general applicability. Additional modifications to the near-wall modeling approach, which is still based on its single-phase counterpart, may be required to deal with high void fraction conditions and, in the overall model, additional improvements to momentum and, most importantly, bubble-induced turbulence closures are desirable

Coupled Calculations of Bubble Departure Diameter and Frequency from Mechanistic Principles for Nucleate Boiling Applications

Nucleate boiling is trusted as an efficient heat transfer mechanism in a wide range of engineering applications. However, the entire physical process of boiling is extremely difficult to predict with accuracy, and engineers have mostly relied on empirical models and correlations for this purpose. In recent years, however, significant advances in the development of more mechanistic approaches have been made. Developments are driven by the benefits in safety and efficiency that are achievable with a more accurate estimation of boiling heat transfer and a reduced operational safety margin on the critical heat flux. This paper further develops a bubble departure diameter mechanistic model based on the forces that impact bubble growth and departure. The heat transfer model includes contributions from the microlayer beneath the bubble, the superheated liquid layer around the bubble surface and condensation when the bubble cap is surrounded by subcooled liquid. Improvements in the modelling of the contribution of condensation are implemented and successfully tested. The model is validated against a large set of measurements that includes saturated and subcooled flow boiling and a new database for forced convection boiling in cross-flow conditions. This database is used to validate the model for the coupled calculation of bubble departure diameter and bubble departure frequency. Although the model predicts the bubble growth time with accuracy, improvements are still required in the modelling of the waiting time after bubble departure. Models of this kind can be used as a basis for the prediction of boiling beyond nucleate boiling conditions, as well as for implementation in wall boiling routines of computational fluid dynamic multiphase flow models