Verification and validation of numerical models of the transport of insulation debris

Damage to insulation materials located near to a primary circuit coolant leak may compromise the operation of the emergency core cooling system (ECCS). Insulation material in the form of mineral wool fiber agglomerates (MWFA) maybe transported to the containment sump strainers, where they may block or penetrate the strainers. Though the impact of MWFA on the pressure drop across the strainers is minimal, corrosion products formed over time may also accumulate in the fiber cakes on the strainers, which can lead to a significant increase in the strainer pressure drop and result in cavitation in the ECCS. An experimental and theoretical study performed by the Helmholtz-Zentrum Dresden-Rossendorf and the Hochschule Zittau/Görlitz is investigating the phenomena that maybe observed in the containment vessel during a primary circuit coolant leak. The study entails the generation of fiber agglomerates, the determination of their transport properties in single and multi-effect experiments and the long-term effect that corrosion and erosion of the containment internals by the coolant has on the strainer pressure drop. The focus of this paper is on the verification and validation of numerical models that can predict the transport of MWFA. A number of pseudo-continuous dispersed phases of spherical wetted agglomerates represent the MWFA. The size, density, the relative viscosity of the fluid-fiber agglomerate mixture and the turbulent dispersion all affect how the fiber agglomerates are transported. In the cases described here, the size is kept constant while the density is modified. This definition affects both the terminal velocity and volume fraction of the dispersed phases. Note that the relative viscosity is only significant at high concentrations. Three single effect experiments were used to provide validation data on the transport of the fiber agglomerates under conditions of sedimentation in quiescent fluid, sedimentation in a horizontal flow and suspension in a horizontal flow. The experiments were performed in a rectangular column for the quiescent fluid and a racetrack type channel that provided a near uniform horizontal flow. The numerical models of sedimentation in the column and the racetrack channel found that the sedimentation characteristics are consistent with the experiments. For channel suspension, the heavier fibers tend to accumulate at the channel base even at high velocities, while lighter phases are more likely to be transported around the channel.

Numerical models used for the modelling of the transport of fibrous insulation debris

Mineral wool insulation material applied to the primary cooling circuit of a nuclear reactor maybe damaged in the course of a loss of coolant accident (LOCA). The insulation material released by the leak may compromise the operation of the emergency core cooling system (ECCS), as it maybe transported together with the coolant in the form of mineral wool fiber agglomerates (MWFA) suspensions to the containment sump strainers, which are mounted at the inlet of the ECCS to keep any debris away from the emergency cooling pumps. In the further course of the LOCA, the MWFA may block or penetrate the strainers. In addition to the impact of MWFA on the pressure drop across the strainers, corrosion products formed over time may also accumulate in the fiber cakes on the strainers, which can lead to a significant increase in the strainer pressure drop and result in cavitation in the ECCS. Therefore, it is essential to understand the transport characteristics of the insulation materials in order to determine the long-term operability of nuclear reactors, which undergo LOCA. An experimental and theoretical study performed by the Helmholtz-Zentrum Dresden-Rossendorf and the Hochschule Zittau/Görlitz1 is investigating the phenomena that maybe observed in the containment vessel during a primary circuit coolant leak. The study entails the generation of fiber agglomerates, the determination of their transport properties in single and multi-effect experiments and the long-term effects that particles formed due to corrosion of metallic containment internals by the coolant medium have on the strainer pressure drop. The focus of this presentation is on the numerical models that are used to predict the transport of MWFA by CFD simulations. A number of pseudo-continuous dispersed phases of spherical wetted agglomerates can represent the MWFA. The size, density, the relative viscosity of the fluid-fiber agglomerate mixture and the turbulent dispersion all affect how the fiber agglomerates are transported. In the cases described here, the size is kept constant while the density is modified. This definition affects both the terminal velocity and volume fraction of the dispersed phases. Only one of the single effect experimental scenarios is described here that are used in validation of the numerical models. The scenario examines the suspension and horizontal transport of the fiber agglomerates in a racetrack type channel. The corresponding experiments will be described in an accompanying presentation (see abstract of Seeliger et al.).

Numerical and experimental investigations for insulation particle transport phenomena in water flow

The investigation of insulation debris generation, transport and sedimentation becomes more important with regard to reactor safety research for pressurized and boiling water reactors, when considering the long-term behaviour of emergency core coolant systems during all types of loss of coolant accidents (LOCA). The insulation debris released near the break during a LOCA incident consists of a mixture of a disparate particle population that varies with size, shape, consistency and other properties. Some fractions of the released insulation debris can be transported into the reactor sump, where it may perturb or impinge on the emergency core cooling systems. Open questions of generic interest are for example the particle load on strainers and corresponding pressure-drop, the sedimentation of the insulation debris in a water pool, its possible re-suspension and transport in the sump water flow. A joint research project on such questions is being performed in cooperation with the University of Applied Science Zittau/Görlitz and the Forschungszentrum Dresden-Rossendorf. The project deals with the experimental investigation and the development of computational fluid dynamic (CFD) models for the description of particle transport phenomena in coolant flow. While the experiments are performed at the University Zittau/Görlitz, the theoretical work is concentrated at Forschungszentrum Dresden-Rossendorf. In the present paper, the basic concepts for computational fluid dynamic (CFD) modelling are described and experimental results are presented. Further experiments are designed and feasibility studies were performed.

Verification and validation of numerical models of the transport of insulation debris

A combination of the two-fluid and drift flux models have been used to model the transport of fibrous debris. This debris is generated during loss of coolant accidents in the primary circuit of pressurized or boiling water nuclear reactors, as high pressure steam or water jets can damage adjacent insulation materials including mineral wool blankets. Fibre agglomerates released from the mineral wools may reach the containment sump strainers, where they can accumulate and compromise the long-term operation of the emergency core cooling system. Single-effect experiments of sedimentation in a quiescent rectangular column and sedimentation in a horizontal flow are used to verify and validate this particular application of the multiphase numerical models. The utilization of both modeling approaches allows a number of pseudocontinuous dispersed phases of spherical wetted agglomerates to be modeled simultaneously. Key effects on the transport of the fibre agglomerates are particle size, density and turbulent dispersion, as well as the relative viscosity of the fluid-fibre mixture.

Comparison between Numerical and Simulation Methods for Age-dependent Branching Models with Immigration

2000 Mathematics Subject Classification: primary: 60J80, 60J85, secondary: 62M09, 92D40

Mechanisms governing the eyewall replacement cycle in numerical simulations of tropical cyclones

Eyewall replacement cycle (ERC) is frequently observed during the evolution of intensifying Tropical Cyclones (TCs). Although intensely studied in recent years, the underlying mechanisms of ERC are still poorly understood, and the forecast of ERC remains a great challenge. To advance our understanding of ERC and provide insights in improvement of numerical forecast of ERC, a series of numerical simulations is performed to investigate ERCs in TC-like vortices on a f-plane. The simulated ERCs possess key features similar to those observed in real TCs including the formation of a secondary tangential wind maximum associated with the outer eyewall. The Sawyer-Eliassen equation and tangential momentum budget analyses are performed to diagnose the mechanisms underlying the secondary eyewall formation (SEF) and ERC. Our diagnoses reveal crucial roles of outer rainband heating in governing the formation and development of the secondary tangential wind maximum and demonstrate that the outer rainband convection must reach a critical strength relative to the eyewall before SEF and the subsequent ERC can occur. A positive feedback among low-level convection, acceleration of tangential winds in the boundary layer, and surface evaporation that leads to the development of ERC and a mechanism for the demise of inner eyewall that involves interaction between the transverse circulations induced by eyewall and outer rainband convection are proposed. The tangential momentum budget indicates that the net tendency of tangential wind is a small residual resultant from a large cancellation between tendencies induced by the resolved and sub-grid scale (SGS) processes. The large SGS contribution to the tangential wind budget explains different characteristics of ERC shown in previous numerical studies and poses a great challenge for a timely correct forecast of ERC. The sensitivity experiments show that ERCs are strongly subjected to model physics, vortex radial structure and background wind. The impact of model physics on ERC can be well understood with the interaction among eyewall/outer rainband heating, radilal inflow in the boundary layer, surface layer turbulent processes, and shallow convection in the moat. However, further investigations are needed to fully understand the exhibited sensitivities of ERC to vortex radial structure and background wind.

Application of Numerical Methods to Study Arrangement and Fracture of Lithium-Ion Microstructure

The focus of this work is to develop and employ numerical methods that provide characterization of granular microstructures, dynamic fragmentation of brittle materials, and dynamic fracture of three-dimensional bodies.

We first propose the fabric tensor formalism to describe the structure and evolution of lithium-ion electrode microstructure during the calendaring process. Fabric tensors are directional measures of particulate assemblies based on inter-particle connectivity, relating to the structural and transport properties of the electrode. Applying this technique to X-ray computed tomography of cathode microstructure, we show that fabric tensors capture the evolution of the inter-particle contact distribution and are therefore good measures for the internal state of and electronic transport within the electrode.

We then shift focus to the development and analysis of fracture models within finite element simulations. A difficult problem to characterize in the realm of fracture modeling is that of fragmentation, wherein brittle materials subjected to a uniform tensile loading break apart into a large number of smaller pieces. We explore the effect of numerical precision in the results of dynamic fragmentation simulations using the cohesive element approach on a one-dimensional domain. By introducing random and non-random field variations, we discern that round-off error plays a significant role in establishing a mesh-convergent solution for uniform fragmentation problems. Further, by using differing magnitudes of randomized material properties and mesh discretizations, we find that employing randomness can improve convergence behavior and provide a computational savings.

The Thick Level-Set model is implemented to describe brittle media undergoing dynamic fragmentation as an alternative to the cohesive element approach. This non-local damage model features a level-set function that defines the extent and severity of degradation and uses a length scale to limit the damage gradient. In terms of energy dissipated by fracture and mean fragment size, we find that the proposed model reproduces the rate-dependent observations of analytical approaches, cohesive element simulations, and experimental studies.

Lastly, the Thick Level-Set model is implemented in three dimensions to describe the dynamic failure of brittle media, such as the active material particles in the battery cathode during manufacturing. The proposed model matches expected behavior from physical experiments, analytical approaches, and numerical models, and mesh convergence is established. We find that the use of an asymmetrical damage model to represent tensile damage is important to producing the expected results for brittle fracture problems.

The impact of this work is that designers of lithium-ion battery components can employ the numerical methods presented herein to analyze the evolving electrode microstructure during manufacturing, operational, and extraordinary loadings. This allows for enhanced designs and manufacturing methods that advance the state of battery technology. Further, these numerical tools have applicability in a broad range of fields, from geotechnical analysis to ice-sheet modeling to armor design to hydraulic fracturing.

Mechanisms Governing the Eyewall Replacement Cycle in Numerical Simulations of Tropical Cyclones

Eyewall replacement cycle (ERC) is frequently observed during the evolution of intensifying Tropical Cyclones (TCs). Although intensely studied in recent years, the underlying mechanisms of ERC are still poorly understood, and the forecast of ERC remains a great challenge. To advance our understanding of ERC and provide insights in improvement of numerical forecast of ERC, a series of numerical simulations is performed to investigate ERCs in TC-like vortices on a f-plane. The simulated ERCs possess key features similar to those observed in real TCs including the formation of a secondary tangential wind maximum associated with the outer eyewall. The Sawyer-Eliassen equation and tangential momentum budget analyses are performed to diagnose the mechanisms underlying the secondary eyewall formation (SEF) and ERC. Our diagnoses reveal crucial roles of outer rainband heating in governing the formation and development of the secondary tangential wind maximum and demonstrate that the outer rainband convection must reach a critical strength relative to the eyewall before SEF and the subsequent ERC can occur. A positive feedback among low-level convection, acceleration of tangential winds in the boundary layer, and surface evaporation that leads to the development of ERC and a mechanism for the demise of inner eyewall that involves interaction between the transverse circulations induced by eyewall and outer rainband convection are proposed. The tangential momentum budget indicates that the net tendency of tangential wind is a small residual resultant from a large cancellation between tendencies induced by the resolved and sub-grid scale (SGS) processes. The large SGS contribution to the tangential wind budget explains different characteristics of ERC shown in previous numerical studies and poses a great challenge for a timely correct forecast of ERC. The sensitivity experiments show that ERCs are strongly subjected to model physics, vortex radial structure and background wind. The impact of model physics on ERC can be well understood with the interaction among eyewall/outer rainband heating, radilal inflow in the boundary layer, surface layer turbulent processes, and shallow convection in the moat. However, further investigations are needed to fully understand the exhibited sensitivities of ERC to vortex radial structure and background wind.

Results of Closed-Flow Column Experiments (zip-archive 2.3 MB)

The identification of transport parameters by inverse modeling often suffers from equifinality or parameter correlation when models are fitted to observations of the solute breakthrough in column outflow experiments. This parameters uncertainty can be approached by the application of multiple experimental designs such as column experiments in open-flow mode and the recently proposed closed-flow mode. Latter are characterized by the recirculation of the column effluent into the solution supply vessel that feeds the inflow. Depending on the experimental conditions, the solute concentration in the solution supply vessel and the effluent follows a damped sinusoidal oscillation. As a result, the closed-flow experiment provides additional observables in the breakthrough curve. The evaluation of these emergent features allows intrinsic control over boundary conditions and impacts the uncertainty of parameters in inverse modeling. We present a comprehensive sensitivity analysis to illustrate the potential application of closed-flow experiments. We show that the sensitivity with respect to the apparent dispersion can be controlled by the experimenter leading to a decrease in parameter uncertainty as compared to classical experiments by an order of magnitude for optimal settings. With these finding we are also able to reduce the equifinality found for situations, where rate-limited interactions impede a proper determination of the apparent dispersion and rate coefficients. Furthermore, we show the expected breakthrough curve for equilibrium and kinetic sorption, the latter showing strong similarities to the behavior found for completely mixed batch reactor experiments. This renders the closed-flow mode a useful complementary approach to classical column experiments.

Study of the development and evolution of seasonal thermocline and turbulent processes in the northern parts of Persian Gulf using numerical modeling

The Persian Gulf (PG) is a semi-enclosed shallow sea which is connected to open ocean through the Strait of Hormuz. Thermocline as a suddenly decrease of temperature in subsurface layer in water column leading to stratification happens in the PG seasonally. The forcing comprise tide, river inflow, solar radiation, evaporation, northwesterly wind and water exchange with the Oman Sea that influence on this process. In this research, analysis of the field data and a numerical (Princeton Ocean Model, POM) study on the summer thermocline development in the PG are presented. The Mt. Mitchell cruise 1992 salinity and temperature observations show that the thermocline is effectively removed due to strong wind mixing and lower solar radiation in winter but is gradually formed and developed during spring and summer; in fact as a result of an increase in vertical convection through the water in winter, vertical gradient of temperature is decreased and thermocline is effectively removed. Thermocline development that evolves from east to west is studied using numerical simulation and some existing observations. Results show that as the northwesterly wind in winter, at summer transition period, weakens the fresher inflow from Oman Sea, solar radiation increases in this time interval; such these factors have been caused the thermocline to be formed and developed from winter to summer even over the northwestern part of the PG. The model results show that for the more realistic monthly averaged wind experiments the thermocline develops as is indicated by summer observations. The formation of thermocline also seems to decrease the dissolved oxygen in water column due to lack of mixing as a result of induced stratification. Over most of PG the temperature difference between surface and subsurface increases exponentially from March until May. Similar variations for salinity differences are also predicted, although with smaller values than observed. Indeed thermocline development happens more rapidly in the Persian Gulf from spring to summer. Vertical difference of temperature increases to 9 centigrade degrees in some parts of the case study zone from surface to bottom in summer. Correlation coefficients of temperature and salinity between the model results and measurements have been obtained 0.85 and 0.8 respectively. The rate of thermcline development was found to be between 0.1 to 0.2 meter per day in the Persian Gulf during the 6 months from winter to early summer. Also it is resulted from the used model that turbulence kinetic energy increases in the northwestern part of the PG from winter to early summer that could be due to increase in internal waves activities and stability intensified through water column during this time.

Removal of paracetamol on biomass-derived activated carbon: Modeling the fixed bed breakthrough curves using batch adsorption experiments

The remediation of paracetamol (PA), an emerging contaminant frequently found in wastewater treatment plants, has been studied in the low concentration range (0.3–10 mg L−1) using as adsorbent a biomass-derived activated carbon. PA uptake of up to 100 mg g−1 over the activated carbon has been obtained, with the adsorption isotherms being fairly explained by the Langmuir model. The application of Reichemberg and the Vermeulen equations to the batch kinetics experiments allowed estimating homogeneous and heterogeneous diffusion coefficients, reflecting the dependence of diffusion with the surface coverage of PA. A series of rapid small-scale column tests were carried out to determine the breakthrough curves under different operational conditions (temperature, PA concentration, flow rate, bed length). The suitability of the proposed adsorbent for the remediation of PA in fixed-bed adsorption was proven by the high PA adsorption capacity along with the fast adsorption and the reduced height of the mass transfer zone of the columns. We have demonstrated that, thanks to the use of the heterogeneous diffusion coefficient, the proposed mathematical approach for the numerical solution to the mass balance of the column provides a reliable description of the breakthrough profiles and the design parameters, being much more accurate than models based in the classical linear driving force.

Flow around a hemisphere-cylinder at high angle of attack and low Reynolds number. Part I: Experimental and numerical investigation

Three-dimensional Direct Numerical Simulations combined with Particle Image Velocimetry experiments have been performed on a hemisphere-cylinder at Reynolds number 1000 and angle of attack 20◦. At these flow conditions, a pair of vortices, so-called “horn” vortices, are found to be associated with flow separation. In order to understand the highly complex phenomena associated with this fully threedimensional massively separated flow, different structural analysis techniques have been employed: Proper Orthogonal and Dynamic Mode Decompositions, POD and DMD, respectively, as well as criticalpoint theory. A single dominant frequency associated with the von Karman vortex shedding has been identified in both the experimental and the numerical results. POD and DMD modes associated with this frequency were recovered in the analysis. Flow separation was also found to be intrinsically linked to the observed modes. On the other hand, critical-point theory has been applied in order to highlight possible links of the topology patterns over the surface of the body with the computed modes. Critical points and separation lines on the body surface show in detail the presence of different flow patterns in the base flow: a three-dimensional separation bubble and two pairs of unsteady vortices systems, the horn vortices, mentioned before, and the so-called “leeward” vortices. The horn vortices emerge perpendicularly from the body surface at the separation region. On the other hand, the leeward vortices are originated downstream of the separation bubble, as a result of the boundary layer separation. The frequencies associated with these vortical structures have been quantified.

Numerical modelling and structural optimization of multifunctional maritime structures aimed to protect harbours and produce energy

The main objective of this PhD thesis is to optimize a specific multifunctional maritime structure for harbour protection and energy production, named Overtopping Breakwater for Energy Conversion (OBREC), developed by the team of the University of Campania. This device is provided with a sloping plate followed by a unique reservoir, which is linked with the machine room (where the energy conversion occurs) by means of a pipe passing through the crown wall, provided with a parapet on top of it. Therefore, the potential energy of the overtopping waves, collected inside the reservoir located above the still water level, is then converted by means of low – head turbines. In order to improve the understanding of the wave – structure interactions with OBREC, several methodologies have been used and combined together: i. analysis of recent experimental campaigns on wave overtopping discharges and pressures at the crown wall on small – scale OBREC cross sections, carried out in other laboratories by the team of the University of Campania; ii. new experiments on cross sections similar to the OBREC device, planned and carried out in the hydraulic lab at the University of Bologna in the framework of this PhD work; iii. numerical modelling with a 1 – phase incompressible fluid model IH – 2VOF, developed by the University of Cantabria, and with a 2 – phase incompressible fluid model OpenFOAM, both available from the literature; iv. numerical modelling with a new 2 – phase compressible fluid model developed in the OpenFOAM environment within this PhD work; v. analysis of the data gained from the monitoring of the OBREC prototype installation.

Physical modeling and numerical simulations of degradation mechanisms in devices and insulators for power applications

In this thesis, a TCAD approach for the investigation of charge transport in amorphous silicon dioxide is presented for the first time. The proposed approach is used to investigate high-voltage silicon oxide thick TEOS capacitors embedded in the back-end inter-level dielectric layers for galvanic insulation applications. In the first part of this thesis, a detailed review of the main physical and chemical properties of silicon dioxide and the main physical models for the description of charge transport in insulators are presented. In the second part, the characterization of high-voltage MIM structures at different high-field stress conditions up to the breakdown is presented. The main physical mechanisms responsible of the observed results are then discussed in details. The third part is dedicated to the implementation of a TCAD approach capable of describing charge transport in silicon dioxide layers in order to gain insight into the microscopic physical mechanisms responsible of the leakage current in MIM structures. In particular, I investigated and modeled the role of charge injection at contacts and charge build-up due to trapping and de-trapping mechanisms in the oxide layer to the purpose of understanding its behavior under DC and AC stress conditions. In addition, oxide breakdown due to impact-ionization of carriers has been taken into account in order to have a complete representation of the oxide behavior at very high fields. Numerical simulations have been compared against experiments to quantitatively validate the proposed approach. In the last part of the thesis, the proposed approach has been applied to simulate the breakdown in realistic structures under different stress conditions. The TCAD tool has been used to carry out a detailed analysis of the most relevant physical quantities, in order to gain a detailed understanding on the main mechanisms responsible for breakdown and guide design optimization.

Numerical and physical modelling of axially loaded piles for offshore wind turbines

The scope of the thesis is to broaden the knowledge about axially loaded pipe piles, that can play as foundations for offshore wind turbines based on jacket structures. The goal of the work was pursued by interpreting experimental data on large-scale model piles and by developing numerical tools for the prediction of their monotonic response to tensile and compressive loads to failure. The availability of experimental results on large scale model piles produced in two different campaigns at Fraunhofer IWES (Hannover, Germany) represented the reference for the whole work. Data from CPTs, blow counts during installation and load-displacement curves allowed to develop considerations on the experimental results and comparison with empirical methods from literature, such as CPT-based methods and Load Transfer methods. The understanding of soil-structure interaction mechanisms has been involved in the study in order to better assess the mechanical response of the sand with the scope to help in developing predictive tools of the experiments. A lack of information on the response of Rohsand 3152 when in contact with steel was highlighted, so the necessity of better assessing its response was fulfilled with a comprehensive campaign of interface shear test. It was found how the response of the sand to ultimate conditions evolve with the roughness of the steel, which is a precious information to take account of when attempting the prediction of a pile capacity. Parallel to this topic, the work has developed a numerical modelling procedure that was validated on the available large-scale model piles at IWES. The modelling strategy is intended to build a FE model whose mechanical properties of the sand come from an interpretation of commonly available geotechnical tests. The results of the FE model were compared with other predictive tools currently used in the engineering practice.