Andrei Horvat - Academia.edu (original) (raw)

Journal articles by Andrei Horvat

The ITER Ion Cyclotron Range of Frequencies (ICRF) antenna’s capacity to couple power to plasma i... more The ITER Ion Cyclotron Range of Frequencies (ICRF) antenna’s capacity to couple power to plasma is determined by the plasma Scrape-Off Layer (SOL) profile, shaping of the front strap array, layout of the Port Plug (PP) and detailed design of its RF components. The first two factors are taken into account by the Torino Polytechnic Ion Cyclotron Antenna (TOPICA) calculated strap array Scattering/Impedance24-port (S24 × 24−/Z24 × 24−) matrices, while this paper deals with the optimisation of the PP layout and components. The RF modeling techniques are explained and used to maximize the coupled power under a set of constraints on RF quantities inside the PP. The total PP RF surface conductive and volumetric dielectric losses are calculated. The resulting S-parameters at the rear RF PP flanges are evaluated as input for the design of the pre-match, decoupling and matching network outside the PP. A discussion of the effect of errors on the PP excitation on the coupled power is also included.

The Duct Liner for the International Thermonuclear Experimental Reactors (ITER) Heating Neutral B... more The Duct Liner for the International Thermonuclear Experimental Reactors (ITER) Heating Neutral Beam (HNB) system is a key component in the beam transport system. Power loading on the top and bottom beam scraping panels of the Duct Liner occurs primarily due to direct interception of the HNB and it is highest at the extreme steering angles of the beam. Furthermore, power loading due to direct interception is dependent on the size and orientation of the scraper panels with respect to the neutral beam axis. This paper outlines the design features of the proposed Duct Liner and describes the analysis performed to optimize the compatibility of the top and bottom scraper panels (also known as Duct Liner Modules) with a normal beam operation scenario. Thermo-mechanical analyses have been performed to validate the design of Duct Liner Modules incorporating deep-drilled cooling technology with a peak power density of 1.2 MW/m2 and incident power of 0.27 MW, and also to verify its conformity with ITER structural design criteria. Furthermore, numerical simulations of the transient draining procedure were performed by using a one-dimensional thermo-hydraulic code to demonstrate complete emptying of the proposed parallel-layout cooling circuit without any reliance on conventional gravity draining.

In enclosure fires, density-driven vent flow through an opening to the fire compartment is direct... more In enclosure fires, density-driven vent flow through an opening to the fire compartment is directly dependent on the state of the fire and the evacuation of smoke and hot gases. If a fire is strongly under-ventilated, there may be heavy production of flammable gases. If a sudden opening occurs, e.g. a window breaks or a fireman opens a door to the fire compartment, fresh air enters the compartment and mixes with hot gases, thus creating a flammable mixture that might ignite and create a backdraft. In this article, we consider the critical flow approach to solve the classical hydraulic equations of density-driven flows in order to determine the gravity controlled inflow in a shipping container full of hot unburnt gases. One-third of the container’s height is covered by the horizontal opening. For the initial condition, i.e., just before opening the hatch,
zero velocity is prescribed everywhere. When the hatch is opened, the incoming air flows down to the container floor and the hot gas flows out. The interface in between them (the neutral plane) can move up like a free surface in internal flows, making it possible to use the techniques of open channel hydraulics devised by Pedersen [1].

The phenomenon of backdraft is closely linked to the formation of a flammable region due to the m... more The phenomenon of backdraft is closely linked to the formation of a flammable region due to the mixing process between the unburnt gases accumulated in the compartment and the fresh air entering the compartment through a recently created opening. The flow of incoming fresh air is called the gravity current. Gravity current prior to backdraft has already been studied, Fleischmann (1993, Backdraft phenomena, NIST-GCR-94-646. University of California, Berkeley) and Fleischmann
(1999, Numerical and experimental gravity currents related to backdrafts, Fire Safety Journal); Weng et al. (2002, Exp Fluids 33:398–404), but all simulations and experiments found in the current literature are systematically based on a perfectly regular volume, usually parallelipedic in shape, without any piece of furniture or equipment in the compartment. Yet, various obstacles are normally found in real compartments and
the question is whether they affect the gravity current velocity and the level of mixing between fresh and vitiated gases. In the work reported here, gravity current prior to backdraft in compartment with obstacles is investigated by means of three-dimensional CFD numerical simulations. These simulations use as a reference case the backdraft experiment test carried out by Gojkovic (2000, Initial Backdraft. Department of Fire Safety Engineering, Lunds Tekniska Hoegskola Universitet, Report 3121). The Froude number, the transit time and the ignition time are obtained from the computations and compared to the tests in order to validate the model.

A computational model of flashover is presented that closely follows the experimental setup at CN... more A computational model of flashover is presented that closely follows the experimental setup at CNRS-ENSMA-Poitiers. A propane burner with thermal power of 55 kW is used as a primary source of fire and square beech wood samples (30 mm × 30 mm × 5 mm) as fire spread targets. The computational model describes the wood pyrolysis with a progress variable. Using the conservation of heat fluxes at the solid-gas interface, the thermal diffusion in the wood samples is coupled with the convective and the radiative heat transfer in the ambient gas phase. The incoming heat flux at the upper surface of the wood samples reaches values between 20 and 30 kW/m2. With the ignition and subsequent combustion of the pyrolysis volatiles, the heat flux increases by approx. 12 kW/m2. The results show that the ignition of the wood samples is triggered at an approx. surface temperature of 650 K. Due to large local variations in incident heat flux, significant differences in the ignition times of the wood samples are observed. The comparison of the calculated and the experimentally measured temperature shows a good agreement for the first wood sample and the model predicts the ignition time very well. But for the second and the third wood samples the model overpredicts the temperature, which leads to a premature ignition of these wood samples.

The analysis focuses on the importance of accurate description of walls' thermal behaviour with p... more The analysis focuses on the importance of accurate description of walls' thermal behaviour with particularly relevance to fire safety cases. To accurately predict thermal loads on the walls in a complex fire situation, time dependent phenomena of thermal convection, diffusion, radiation and heat transfer across the wall have to be taken into account. The heat transfer
across the walls is often neglected as it requires fine grid resolution to approximate large temperature gradients. The analysis shows that this can lead to substantial errors and proposes a transient semi-analytical approximation of thermal wall behaviour. Unsteady heat diffusion equation is solved by semi-analytical approximation of a temperature profile in a wall. The temperature profile is approximated in each time step and for each wall grid node separately using the temperature at the wall internal side and Biot number at the external side for
boundary conditions. Wall heat transfer coefficient is calculated as a temperature profile derivative and then used in the coupled numerical model of the fire. The semi-analytical approach does not rely on a discretisation procedure and the accuracy of its solutions is independent of grid spacing. Therefore, such semi-analytical technique is computationally
less expensive and especially attractive for long transient calculations.

A new thermal hydraulic computer code, WAHA, was developed within the WAHALoads project of the Eu... more A new thermal hydraulic computer code, WAHA, was developed within the WAHALoads project of the European Union Fifth Framework Program. The code's aim is simulation of water hammer transients in piping systems and is based on a one-dimensional, two-fluid, six-equation model of the two-phase flow. The WAHA code can describe two-phase flows in long piping systems (1D geometry) with variable cross section. The code contains correlations for heat, mass, and momentum transfer between the phases and for wall friction in dispersed and horizontally stratified flow regimes. The WAHA code physical model takes into account the elasticity of the pipe through Korteweg's equation; it takes into account water properties and the unsteady wall friction, and contains a set of subroutines for calculation of forces on the piping system. Special models in the WAHA code are implemented for abrupt area changes and branches, for constant pressure (tank), for constant velocity (pump), and for valve closure boundary conditions. The physical model and the main correlations and closure laws, which are applied in the present work, are described and verified with several experiments. The code was successfully applied for simulations of two-phase critical flow, several column-separation types of water hammer, and for condensation-induced water hammer experiments.

This paper describes the numerical scheme used in the WAHA code that was developed within the WAH... more This paper describes the numerical scheme used in the WAHA code that was developed within the WAHALoads project for simulations of fast transients in 1D piping systems. Two-fluid model equations described in a companion paper entitled "Two-Fluid Model of the WAHA Code for Simulations of Water Hammer Transients," are solved with an operator splitting procedure: the non-conservative characteristic upwind scheme is used to solve the hyperbolic part of the equations with the non-relaxation source terms, while the relaxation source terms are treated in the second step of the operator splitting procedure. Water properties are calculated with a newly developed set of subroutines that use pretabulated water properties. Special models that were developed for treatment of the abrupt area changes and branches in the piping systems are described. Various test cases, which were used to test the accuracy of the basic numerical scheme and the accompanying numerical models, are described and discussed together with the typical results of simulations.

The article describes full-scale backdraft experiments in a shipping container using methane as a... more The article describes full-scale backdraft experiments in a shipping container using methane as a fuel. Numerical modelling has followed the experimental setup. The numerical
simulations show the initial gravity current, the ignition, the spreading of flame in the enclosure, the external fireball, and the subsequent decay. The Detached Eddy Simulation
(DES) approach has been used to model turbulence. In order to describe the combustion process of the mixture from the local ignition to progressive deflagration, three separate
combustion models have been implemented for laminar, low- and high-intensity turbulence flow regimes. The calculated ignition time is slightly shorter than the average ignition time observed in the experiments. The fire front progresses through the combustible mixture, generating a cloud of hot gases that are accelerated from the container into the external environment. The velocity increases up to 20 m/s. When the fire front reaches the door, combustion continues outside the enclosure as the fuel has been pushed through the door. The comparison between the calculated time history of relative pressure and the pressure sensor record shows that the numerical simulations slightly overpredict the flame front speed, with a stronger pressure pulse and higher temperatures than the observations.

This paper reports preliminary computational fluid dynamics (CFD) simulations of backdraft observ... more This paper reports preliminary computational fluid dynamics (CFD) simulations of backdraft observed in an experimental rig at Lund University. The analysis was performed with the CFX software using the Detached Eddy Simulation (DES) turbulence model, a hybrid of Large Eddy Simulation (LES) and RANS, in combination with the EDM combustion model. The DES model uses a RANS formulation in wall proximity to avoid computationally expensive grid resolution that is necessary for realistic LES predictions in wall layers.

The preliminary results are qualitatively promising. The simulations began at the instant at which the door opens. A stream of fresh and cold air enters the enclosure as a gravity current. In the rig, ignition was triggered by flammable conditions existing at a wire, which was constantly heated. In the CFD model the ignition time is computed automatically when flammability conditions are reached inside the enclosure, at the wire, as part of the analysis. Subsequently, the fire front is formed. The deflagration expels fuel-rich mixture into
environment, and the combustion continues outside the enclosure as a typical ‘secondary’ event. Considering that backdraft is a very complex phenomenon, the outcome is considered by the authors to be encouraging.

Transient numerical simulations of fluid and heat flow were performed for eight heat exchanger se... more Transient numerical simulations of fluid and heat flow were performed for eight heat exchanger segments with cylindrical and wing-shaped tubes in staggered arrangement. Their hydraulic diameters were from 0.5824 to 3.899 cm for the cylindrical tubes, and from 0.5413 to 3.594 cm for the wing-shaped tubes. Based on the recorded time distributions of velocity and temperature, time average Reynolds number Re, drag coefficient Cd, and Stanton number St were calculated. In general, the drag coefficient and the Stanton number are smaller for the wing-shaped tubes than for the cylindrical tubes. However, with an increasing hydraulic diameter, these differences between both forms of tubes diminish. The time average values were further used to construct the drag coefficient and the Stanton number as polynomial functions Cd(
dh,Re) and St(dh,Re).

A solid-gas-phase model for thick wood gasification/combustion is extensively studied, after a re... more A solid-gas-phase model for thick wood gasification/combustion is extensively studied, after a re-examination of the kinetic constants for the char gasification reactions. The solid-phase model, which includes the description of all the relevant heat and mass transfer phenomena and chemical reactions, is coupled with a CFD code for the gas-phase processes. Both the gasification and combustion of single wood logs are simulated (log radius in the range of 0.06-0.1 m, initial moisture content, on a dry basis, 1-81%, inlet gas temperature 1253-1613K, inlet gas velocity 0.5-1.0 m/s, and various compositions of the gaseous mixture). For comparison purposes, a solid-phase model, with global heat and mass transfer coefficients and a constant-property gas phase, is also considered. Although both models predict the mass loss dynamics to be qualitatively similar, the solid-phase model overestimates the total heat flux and underestimates the char combustion rate. Extensive experimental validation of both models is carried out in terms of conversion time and average mass-loss rates. Acceptable
agreement is obtained for the comprehensive model, whereas in the other case, the conversion times are generally
underestimated and the average mass loss rates are overestimated. However, improvements in the predictive
capabilities of the solid-phase model could be achieved through the introduction of corrective factors for the external heat and mass transfer coefficients.

Transient numerical simulations of fluid and heat flow are performed for a number of heat exchang... more Transient numerical simulations of fluid and heat flow are performed for a number of heat exchanger segments with cylindrical and ellipsoidal form of tubes in a staggered arrangement. Based on the recorded time distributions of velocity and temperature, time-average values of Reynolds number, drag coefficient, and Stanton number are calculated. The drag coefficient and the Stanton number are smaller for the ellipsoidal tubes than for the cylindrical tubes. With an increasing hydraulic diameter, the difference between the two forms of tubes diminishes. To validate the selected numerical approach, the calculated time-average values are compared with experimental data. The time-average values are further used to construct the drag coefficient and the Stanton number as polynomial functions of Reynolds number and hydraulic diameter. The polynomial functions obtained are to be used as input correlations for a heat exchanger integral model.

Detailed transient numerical simulations of fluid and heat flow were performed for a number of he... more Detailed transient numerical simulations of fluid and heat flow were performed for a number of heat exchanger segments with cylindrical, ellipsoidal and wing-shaped tubes in a staggered arrangement. The purpose of the analysis was to get an insight of local heat transfer and fluid flow conditions in a heat exchanger and to establish widely applicable drag coefficient and Stanton number correlations for the heat exchanger integral model, based on average flow variables. The simulation results revealed much more complex flow behavior than reported in current literature. For each of the almost 100 analyzed cases, the time distributions of the Reynolds number, the drag coefficient and the Stanton number were recorded, and their average values calculated. Based on these average values, the drag coefficient and the Stanton number correlations were constructed as polynomial functions of the Reynolds number and the hydraulic diameter. The comparison of the collected results also allows more general conclusions on efficiency and stability of the heat transfer process in tube bundles.

A conjugate heat transfer model of fluid flow across a solid heat conducting structure has been b... more A conjugate heat transfer model of fluid flow across a solid heat conducting structure has been built. Two examples are presented: a.) air-stream cooling of the solid structure and b.) flow across rods with volumetric heat generation. To construct
the model, a Volume Average Technique (VAT) has been applied to the momentum and the energy transport equations for a fluid and a solid phase to develop a specific form of porous media flow equations. The model equations have been solved with the semi-analytical Galerkin method. The detailed velocity and temperature fields in the fluid flow and the solid structure have been obtained. Using the solution fields, the whole-section drag coefficient Cd and the whole-section Nusselt number Nu have been also calculated. To validate the developed solution procedure, the results have been compared to the results of the finite volume method and to the experimental data. The comparison demonstrates an excellent agreement.

An alternate approach based on hierarchic modeling is proposed to simulate fluid and heat flow in... more An alternate approach based on hierarchic modeling is proposed to simulate fluid and heat flow in heat exchangers. On the first level, the direct simulations have been performed for the geometry that is similar to a segment of the examined
heat sink. Based on the obtained results, the Reynolds number dependencies of the scaling factors f and St Pr^0.66 have been established. On the second level, the integral model of the whole heat sink has been built using the volume averaging technique (VAT). The averaging of the transport equations leads to a closure problem. The direct model Reynolds number dependencies f and St Pr^0.66 have been used to calculate the local values of the drag coefficient and the heat transfer coefficient, which are needed in the integral model. The example calculations have been performed for 14 different pressure drops across the aluminum heat sink. The whole-section drag coefficient and Nusselt number have been calculated and compared with the experimental data. A good agreement between the modeling results and the experiment data has been reached with same discrepancies in the transitional regime. The constructed computational algorithm offers possibilities for geometry improvements and optimization, to achieve higher thermal effectiveness.

A mathematical model of fluid flow across a rod bundle with volumetric heat generation has been b... more A mathematical model of fluid flow across a rod bundle with volumetric heat generation has been built. The rods are heated with volumetric internal heat generation. To construct the model, a volume average technique (VAT) has been applied to momentum and energy transport equations for a fluid and a solid phase to develop a specific form of porous media flow equations. The model equations have been solved with a semi-analytical Galerkin method. The detailed velocity and temperature fields in the fluid flow and the solid structure have been obtained. Using the solution fields, a whole-section drag coefficient Cd and a whole-section Nusselt number Nu have also been calculated. To validate the developed solution procedure, the results have been compared to the results of a finite volume method. The comparison shows an excellent agreement. The present results demonstrate that the selected Galerkin approach is capable of performing calculations of heat transfer in a cross-flow where thermal conductivity and internal heat generation in a solid structure has to be taken into account. Although the Galerkin method has limited applicability in complex geometries, its highly accurate solutions are an important benchmark on which other numerical results can be tested.

Direct numerical simulation of a passive scalar in fully developed turbulent channel flow is used... more Direct numerical simulation of a passive scalar in fully developed turbulent channel flow is used to show that Nusselt number is not only a function of Reynolds and Prandtl number, but also depends on properties of a heating wall. Variable thickness of the heating wall and variable heater properties, combined in a fluid–solid thermal activity ratio can change the Nusselt number of the turbulent channel flow for up to 1% at the same Reynolds and Prandtl number and at the same wall heat flux.

A fast-running computational algorithm based on the volume averaging technique (VAT) is developed... more A fast-running computational algorithm based on the volume averaging technique (VAT) is developed and solutions are obtained using the Galerkin method (GM). The goal is to extend
applicability of the GM to the area of heat exchangers in order to provide a reliable benchmark for numerical calculations of conjugate heat transfer problems. Using the VAT, the computational algorithm is fast-running, but still able to present a detailed picture of temperature fields in air flow as well as in the solid structure of the heat sink. The calculated whole-section drag coefficient and Nusselt number were compared with finite-volume method (FVM) results and with experimental data to verify the computational model. The comparison shows good agreement. The present results demonstrate that the selected Galerkin approach is capable to perform heat exchanger calculations where the thermal conductivity of the solid structure has to be taken into account.

International Journal of Heat and Mass Transfer, 2003

A fast running computational algorithm based on the volume averaging technique (VAT) is developed... more A fast running computational algorithm based on the volume averaging technique (VAT) is developed to simulate conjugate heat transfer process in an electronic device heat sink. The goal is to improve computational capability in the area of heat exchangers and to help eliminate some of empiricism that leads to overly constrained designs with resulting economic penalties.

International Journal of Heat and Mass Transfer, 2003

Offshore wind farms located in a shallow water environment and in areas prone to hurricanes may e... more Offshore wind farms located in a shallow water environment and in areas prone to hurricanes may experience extreme breaking waves. Although little is known about their characteristics, breaking waves may represent a dominant load that a wind turbine structure is subjected to over its design lifetime. Existing analysis approaches may have limited applicability, especially for large diameter monopiles. The main goal of the research program is to improve methodology for determining the wave loading. Reducing the uncertainty associated with the load spectrum a structure can be subjected to will enable a lower design safety factors, and therefore reduce the cost of offshore wind power generation systems.

The contribution focuses on a CFD study to determine the characteristics of slam loads based on anticipated wave behavior from modeling and physical observation. The model will use a numerical representation of a wave tank with a flap-type wave generator to create virtual breaking waves to analyze slam forces on a monopile foundation. Buoy data from of the North Carolina coast will be used to validate the developed CFD model. The results will be used to assess the applicability of and suggest revisions to the wave load equations for large diameter monopiles.

With the rising cost of nitrogen based fertilisers caused by global energy price increases, and c... more With the rising cost of nitrogen based fertilisers caused by global energy price increases, and concerns surrounding the depletion of global phosphorus resources, efficient use of fertiliser is a major concern for modern Agriculture. Equipment used to apply fertiliser should be accurate and precisely calibrated as variations in the distribution of fertilisers can lead to reductions in crop yield, soil damage and environmental run-off which ultimately lead to loss of income to the farmer.

In a competitive environment, a simulation driven design process can significantly reduce development time of agricultural machinery. This paper looks at the development of a numerical model that was used to improve the design of the Marshall Multispread fertiliser spreader. The model tracks fertiliser particles as they are loaded onto the spinner disc, are captured by the spinner vanes and then subsequently ejected over the field.

Key design parameters such as spinner speed; particle loading position on the disc; the number of spinner vanes and their angle relative to the centre of the disc; particle drag coefficient and breakage thresholds and prevailing wind speed and direction are used as model inputs. Using particle motion and ballistic equations, the model outputs a map of the fertiliser distribution for a given paddock area which can be used as a comparison against industry based performance standards.

A number of techniques were used to validate the model outputs including high speed photography, a bespoke collector device for measurement of angular distribution of particles as they leave the spinner disc and field based spread testing under controlled conditions.

The sensitivity of the spreader’s performance to changes in wind speed and direction, fertiliser consistency and machine setup was analysed. Prototyping and Simulation of different spinner vane and chute designs was undertaken until the optimum machine configuration was achieved.

As a result of this study a spinner design that is tolerant of variations that occur under real life spreading conditions was developed. The new Type D spinner design was placed into production in early 2012, achieving a 25% improvement in spread width over the previous configurations, allowing farmers to spread fertilisers at wider widths in the paddock, reducing labour and fuel costs, whilst maintaining accurate placement of fertilisers.

The successfully completed design improvement demonstrates the value of numerical simulation techniques in the Agricultural Equipment design process.

A fluid-structure analysis of a test case representing a radio antenna that is subjected to wind ... more A fluid-structure analysis of a test case representing a radio antenna that is subjected to wind load is performed. Due to high wind speeds, large deflection of the protective fabric occurs, which may damage the sensitive electronic equipment. Therefore, accurate prediction of maximum fabric deflection under the most severe wind conditions is of vital importance. The analysis is performed for the wind speed of 155 mph.

The maximum deflection of the protective fabric is calculated using four alternative methods, including a 2-way coupled fluid-structure simulation. Issues that the authors encountered performing the numerical simulations are also discussed. The comparison of the results shows that, for the studied case, a difference of approximately 12% exists between the full 2-way coupled solution of the fluid-structure system and a simple estimate of the maximum deflection using algebraic expressions. The level of deviation increases with increasing fabric deflection (e.g. lower elasticity modulus, higher wind speed) and non-symmetrical pressure load (e.g. change of the antenna design).

Turbine efficiency remains a critical component of the overall economic justification for a poten... more Turbine efficiency remains a critical component of the overall economic justification for a potential wind farm. There is therefore a requirement for prediction methodologies that are capable of addressing the in-situ performance of multiple turbine installations within a specific local environment and operating in a range of conditions. The work presented here is the first stage in a programme of work that aims to develop a practical engineering methodology for the CFD-based assessment of multiple turbine installations. In this first stage a CFD benchmarking exercise was performed using the wind turbine design in the Unsteady Aerodynamics Experiment (UAE) conducted by the US National Renewable Energy Laboratory. Initially blade sections were analysed in 2D and the results used to construct and validate a 3D CFD model of the turbine. The 3D results were used to develop
estimates for actuator disk induction factors. Finally these factors were used to modify the classical actuator disk treatment of wind turbines. The results from the modified actuator disk model were in good agreement both with CFD and experiment.

A modelling approach was developed to simulate fire spread from combusting gases to a solid surfa... more A modelling approach was developed to simulate fire spread from combusting gases to a solid surface material. The development work was performed at ANSYS Europe Ltd. as a part of the EC funded Firenet project, which investigated phenomena related to under-ventilated fires.

The motivation to develop a fire spread model and to link it to the ANSYS CFD package was the need to obtain a reliable computational tool for solid material ignition under fire conditions, subsequent pyrolysis and combustion. The objective was to develop a fire spread model that could be linked to the ANSYS CFD package and hence used in fire safety engineering as well as in industrial applications (e.g. for combustion of solid fuels). Alternative approaches to this modelling are also being explored at ANSYS Europe Ltd.

The computational model was validated by using experimental data from CNRS-ENSMAPoitiers. In their case, a propane burner with thermal power of 55 kW was used as a primary source of fire and square beech wood samples (30 mm x 30 mm x 5 mm) as fire spread targets. The comparison of the calculated and the experimentally measured temperatures shows a good agreement for solid material samples closer to the main fire source where the model predicts the ignition time very well. For the samples further away from the main fire source, the differences are larger (the authors believe due to geometrical simplifications),
which are discussed in the paper. In general, the performance of the developed fire spread model is satisfactory although caution is needed in its application due to sensitivity to material properties and geometrical simplifications.

Numerical analysis of natural convection inside a heat generated fluid was performed for four dif... more Numerical analysis of natural convection inside a heat generated fluid was performed for four different spherical geometries that match the experimental vessels used by Asfia et al. [5-7]. The transient calculations were performed with the CFX 5.7 fluid dynamic software. The simulations show that the highest heat flux is just below the rim of the cavity and it can be 50 times higher than at the bottom. Based on the numerical results, the local values of heat transfer coefficient and the distributions of global Nusselt number were calculated. The present, three-dimensional simulation results were compared with the numerical results of Mayinger et al. [3] and Reineke et al. [4], and with the experimental data of Asfia et al. [5-7]. The agreement between the results that is well inside the experimental scatter verifies the selected modeling approach.

Influence of the stiff inter-phase exchange source terms on the propagation velocities of the two... more Influence of the stiff inter-phase exchange source terms on the propagation velocities of the two fluid models is analyzed. If infinitely fast inter-phase exchange is assumed, i.e. instantaneous thermal and mechanical relaxation, the results of the two-fluid models should be similar to the results
homogeneous-equilibrium model, despite different characteristic velocities of both models. Results of the present work show, that the propagation velocities of the two-fluid model with infinitely stiff relaxation terms are indeed equal to the propagation velocities of the homogeneous-equilibrium model - despite large differences in the eigen-structures of the two-fluid models and HEM model. It is known that the speed of sound in two-fluid model is not the same as the HEM speed of sound, however, the propagation speed of the sonic waves of the two-fluid models with infinitely stiff relaxation terms is close to the HEM speed of sound and not the speed of sound of the two-fluid model. For non-stiff relaxation source terms the characteristic velocities of the two-fluid model are approximately equal to the wave propagation velocities.

The performance of two-equation turbulence models for heat transfer predictions in buoyant flows ... more The performance of two-equation turbulence models for heat transfer predictions in buoyant flows is investigated. The study compares the k-epsilon, the RNG k-epsilon, the SST, and the SSG models. For the k-epsilon model, a ‘scaleable’ wall function is used which reduces the sensitivity of the model to the grid near the wall. For the SST model, a near wall model is used, which automatically switches from a low-Reynolds number form to a wall function formulation, based on the grid spacing. Simulations have been carried out for a buoyant plume, a vertical and a horizontal mixed convection jet. The comparison with the experimental correlations of Rouse et al. [9], and Shabbir and George [10] show that the k-epsilon and the SST model correctly predict velocity and specific weight deficiency distributions, whereas the RNG k-epsilon and the SSG models are much less dissipative, overpredicting velocity and specific weight deficiency.

An algorithm for simulation of conjugate heat transfer used to find the most suitable geometry fo... more An algorithm for simulation of conjugate heat transfer used
to find the most suitable geometry for an electronic chip heat
sink is described. Applying Volume Averaging Theory (VAT) to
a system of transport equations, a heat exchanger structure was modeled as a homogeneous porous media. The interaction between the fluid and the structure, the VAT equation closure requirement, was accomplished with drag and heat transfer coefficients, which were taken from the available literature and inserted into a computer code. The example calculations were performed for an aluminum heat sink exposed to force convection airflow. The geometry of the simulation domain and boundary conditions followed the geometry of the experimental test section. The comparison of the whole-section drag coefficient and Nusselt number as functions of Reynolds number shows a good agreement with the experimental data. The calculated temperature fields reveal the local heat flow distribution and enable further improvements of the heat sink geometry.

Volume Averaging Technique (VAT) is employed in order to model the heat exchanger cross-flow as a... more Volume Averaging Technique (VAT) is employed in order to model the heat exchanger cross-flow as a porous media flow. As the averaging of the transport equations lead to a "closure" problem, separate relations are introduced to model interphase momentum and heat transfer between fluid flow and the solid structure. The hierarchic modeling is used to
calculate the local drag coefficient as a function of Reynolds number. For that purpose a separate model of REV is built and DNS of flow through REV is performed. The local values of heat transfer coefficient h are obtained from available literature. The geometry of the simulation domain and boundary conditions follow the geometry of the experimental test section used at U.C.L.A. The calculated temperature fields reveal that the geometry with denser pin-fins arrangement (HX1) heats fluid flow faster. The temperature field in the HX2 exhibits the formation of thermal boundary layer between pin-fins, which has a significant role in overall thermal performance of the heat exchanger. Although presented discrepancies of the whole-section drag coefficient are large, we believe that hierarchic modeling is an appropriate strategy for calculation of complex transport phenomena in heat exchanger geometries.

An algorithm for simulation of conjugate heat transfer in an electronic chip heat sink is describ... more An algorithm for simulation of conjugate heat transfer in an electronic chip heat sink is described. Applying Volume Averaging Theory (VAT) to a system of transport equations, a heat exchanger structure is modeled as a homogeneous porous media. The interaction between the fluid and the structure, the VAT equation closure requirement, is accomplished with drag and heat transfer coefficients taken from the available literature and inserted into a computer code. The system of partial differential equations is solved using the Galerkin method to decompose the temperature field into a series of eigenfunctions.

An example calculation is performed for an aluminum heat sink exposed to force convection airflow. The geometry of the simulation domain and boundary conditions follow the geometry of the experimental test section used in the Morrin-Martinelli-Gier Memorial Heat Transfer Laboratory at University of California, Los Angeles. A comparison of the whole-section drag coefficient and Nusselt number as functions of Reynolds number shows good agreement with finite volume method results as well as with experimental data. The calculated temperature fields reveal the local heat flow distribution and enable optimization of the surface geometry.

Code for analysis of the water hammer in thermal-hydraulic systems is being developed within the ... more Code for analysis of the water hammer in thermal-hydraulic
systems is being developed within the WAHALoads project
founded by the European Commission [1]. Code will be specialized for the simulations of the two-phase water hammer phenomena with the two-fluid model of two-phase flow. The proposed numerical scheme is a two-step second-order accurate scheme with operator splitting; i.e. convection and sources are treated separately. Operator splitting technique is a very simple and “easy-to-use” tool, however, when the source terms are stiff, operator splitting method becomes a source of a specific non-accuracy, which behaves as a numerical diffusion. This type of error is analyzed in the present paper.

Heat exchangers are one of the basic installations in power and process industries. The present g... more Heat exchangers are one of the basic installations in power and process industries. The present guidelines provide an ad-hoc solution to certain design problems. A unified approach based on simultaneous modeling of thermal-hydraulics and structural behavior does not exist. The present paper describes the development of integral numerical code for simulation of heat exchangers. The code is based on Volume Averaging Technique (VAT) for porous media flow modeling. The calculated values of the whole-section drag and heat transfer coefficients show an excellent agreement with already published values. The matching results prove the correctness of the selected approach and verify the developed numerical code used for this calculation.

Prediction of thermal loads on nuclear reactor vessel lower plenum after core melting and relocat... more Prediction of thermal loads on nuclear reactor vessel lower plenum after core melting and relocation during a severe accident requires knowledge about the core melt behavior, especially the circulation pattern. To analyze the heat transfer dynamics on the lower plenum walls, two-dimensional numerical simulations of a fluid flow with internal heat generation were performed for Rayleigh numbers 10^6, 10^7, 10^8, 10^9, 10^11 and 10^13 at Prandtl number 0.8. For subgrid motion modeling, a Large-Eddy Simulation
Smagorinsky model was implemented.

The minimum, time-average and maximum Nusselt numbers on the boundaries were calculated. The dynamics of fluid
structures were analyzed to reveal the instability mechanisms and transition to turbulence. Results disclose Rayleigh-Taylor
instabilities as a dominant mechanism for turbulence appearance, which occurs when the Rayleigh number is increased over 10^8. The structure dependence of fluid motion at high Rayleigh numbers makes the time-average of heat transfer hard to assess. The time-average values should be supplemented with probability distributions of related variables.

Prediction of thermal loads on lower plenum walls after core melting and relocation during severe... more Prediction of thermal loads on lower plenum walls after core melting and relocation during severe accident conditions requires knowledge about the core melt behavior, especially the circulation pattern. To analyze the heat transfer dynamics on the lower plenum walls, two-dimensional numerical simulations of a fluid flow with internal heat generation were performed for Rayleigh numbers 10^6, 10^7, 10^8, 10^9, 10^11 and 10^13 at Prandtl number 0.8. For subgrid motion modeling, the Large Eddy Simulation (LES) Smagorinsky model was implemented. Time and boundary-averaged Nusselt numbers were calculated. Results show that differences between minimum, average and maximum Nusselt number increase in exponential manner when the Rayleigh number is increased beyond 108. Probability densities of Nusselt number were also calculated to realistically assess unsteady thermal loads. The calculated probability density functions indicate that time-average Nusselt numbers usually do not coincide with most probable values. The study also discloses the appearance of multiple Nusselt number probability peaks.

During a hypothetical severe accident, a melt pool may form in the lower plenum of the reactor ve... more During a hypothetical severe accident, a melt pool may form in the lower plenum of the reactor vessel as a consequence of reactor core overheating and melting. High temperatures and further heat generation due to fission products decay may jeopardize the integrity of the reactor vessel. To prevent this the plenum walls would have to be externally cooled. At present, external vessel flooding is one of the possible emergency procedures.

To determine the cooling characteristics of the melt pool, the heat transfer through the lower plenum wall must be known. The natural convection behaviour of the melt pool was studied for this purpose. Although some experimental studies have been carried out in the paste it is not feasible to perform large-scale experiments at realistic reactor conditions. Extensive numerical studies were also carried out regarding the lower plenum cooling problem using one of k-epsilon models to model turbulent motion.

Because of extensive computational requirements of the k-epsilon models, we propose a modified Smagorinsky Large-Eddy Simulation model which is mainly used in forced convection turbulence calculations.

In the early 80's the SMUP computer code was developed at the "Jozef Stefan" Institute for simula... more In the early 80's the SMUP computer code was developed at the "Jozef Stefan" Institute for simulation of two-phase flow in steam generators. It was suitable only for steady-state problems and was unable to simulate transient behaviour. In this paper, efforts are presented to find a suitable numerical method to renew the old SMUP computer code. The obsolete numerical code has to be replaced with a more efficient one that would be able to treat time-dependent problems. It also has to ensure accurate solution during shock propagations. One-dimensional shock propagations in a tube were studied at zero viscosity. To simplify the equation of state the ideal gas was chosen as a working fluid. Stability margins in the form of transport matrix eigenvalues were calculated. Results were found to be close to those already published.

A possible severe accident scenario is a general meltdown and relocation of the reactor core duri... more A possible severe accident scenario is a general meltdown and relocation of the reactor core during which molten core material accumulates in the lower plenum of the reactor vessel. The decay heat generated in a radioactive material would have to be removed through the walls of the lower plenum in order to ensure the integrity of the reactor pressure vessel. Numerical simulations of turbulent natural convection in a geometry representing the lower plenum cavity of a reactor pressure vessel were conducted. A two-dimensional numerical code based on a finite-volume method was developed to simulate turbulent natural convection in a fluid with internal heat generation using large-eddy simulation. Simulations were performed at Rayleigh numbers 1e10 and 2e11 and Prandtl numbers 1.2, 7 and 8, which corresponds to conditions in the numerical investigations made by Nourgaliev et al. (1997) and in the experimental work done by Asfia and Dhir (1996). The results are shown to be in satisfactory agreement.

Melting ultimately requires the heat production rate to exceed the removal rate. In a nuclear rea... more Melting ultimately requires the heat production rate to exceed the removal rate. In a nuclear reactor this situation is initiated by either overpower or under-cooling conditions. The latter is related to reduced cooling through loss of coolant flow or loss of coolant itself and may lead to general meltdown of the reactor core.

Molten material is accumulated in the lower plenum of the reactor pressure vessel. The separation of phases results from different components densities of molten material. High temperature molten UO2 will slowly melt through the wall of RPV lower plenum. To avoid disruption of RPV, an instantaneous heat transfer is needed.

To simulate the situation described above, general multiphase flow equations were developed In order to describe the multiphase flow fully, the continuity, momentum and energy equations were derived using ensemble averaging rather then time or spatial averaging. Because of geometry of the lower plenum a spherical coordinate system was used, to enhance the accuracy of the calculation on the border.

The steam explosion phenomenon is generally divided into four stages: premixing of melt and coola... more The steam explosion phenomenon is generally divided into four stages: premixing of melt and coolant, triggering of explosion, explosion escalation and propagation, expansion and work production. This contribution is assessing the first stage of steam explosion process while taking advantage of alternative approach, namely probabilistic multiphase flow equations.

First, the equations and method of their solution are briefly discussed. Following the experiments "Billet 1000" (Oulmann and Hamon, 1994) the geometry was modelled using finite difference technique. The results for four phase mixture (melt, water, vapor, air) are presented in form of graphs
depicting velocity, pressure, and phase presence probability
fields. At the end, the conclusions and future plans are given
aiming at better steam explosion understanding.

Heat transfer coefficient in the fully developed turbulent channel flow bounded with walls heated... more Heat transfer coefficient in the fully developed turbulent channel flow bounded with walls heated with constant heat flux, is known to be a function of Reynolds and Prandtl number only (if the temperature is assumed to be a passive scalar). The present study, based on the results of the Direct Numerical Simulations reports a small difference of approximately 0.5% that exists in heat transfer rates near the wall of fully developed turbulent channel flow at the same Reynolds and Prandtl numbers, the same heat flux, but with different thermal activity ratios.

Advanced Computational Methods in Heat Transfer VII

The present paper describes construction of an algorithm for conjugate heat transfer calculations... more The present paper describes construction of an algorithm for conjugate heat transfer calculations in order to find the most suitable form for a heat sink. Applying Volume Averaging theory (VAT) to a system of transport equations, a heat exchanger structure was modeled as a homogeneous porous media. The example numerical simulations were performed for test sections with isothermal structure as well as with heat conducting Al pin-fins. The geometry of the simulation domain and boundary conditions followed the geometry of the experimental test section used in the Morrin-Martinelli-Gier Memorial Heat Transfer Laboratory at University of California, Los Angeles. The comparison of the drag coefficient as a function of Reynolds number reveals good agreement with already published data, whereas the comparison of the Nusselt number distributions shows much larger discrepancies. Finite conductivity of a solid phase decreases the heat transfer coefficient and the Nusselt number. The influence of conductivity becomes larger with increasing Reynolds number.

Advanced Computational Methods in Heat Transfer V

Reactor pressure vessel lower plenum retention problem was studied to determine external cooling ... more Reactor pressure vessel lower plenum retention problem was studied to determine external cooling margins of the plenum walls. The accumulated melt was modelled as an incompressible fluid with internal volumetric heat generation in a rectangular cavity. A Smagorinsky type of Large-Eddy Simulation model for buoyancy flows was implemented. Because of uncertainty about the upper wall thermal boundary conditions, isothermal and adiabatic boundary conditions were used to assess heat transfer margins (Nusselt number) at each boundary of the simulation domain. It was found out in both calculated cases that the Nusselt number is the lowest at the bottom of the simulation domain and increases with height. In the future nuclear safety studies, the most severe wall thermal conditions from both simulated cases will have to be considered.

A fast running computational algorithm based on Volume Averaging Technique (VAT) is developed and... more A fast running computational algorithm based on Volume Averaging Technique (VAT) is developed and solutions obtained using the Finite Volume Method (FVM) and the Galerkin Method (GM). The goal is to improve computational capability in the area of heat exchangers and help eliminate some of the empiricism involved in their design that leads to overly constrained designs with resulting economic penalties.

VAT is tested and applied to a simulation of air-flow through an aluminum (Al) chip heat sink. Using VAT, the computational algorithm is fast running, but still able to present a detailed picture of temperature fields in the air-flow as well as in the solid structure of the heat sink. The calculated whole-section drag coefficient, Nusselt number and thermal effectiveness were compared with the experimental data to verify the computational model and validate numerical code. The comparison also shows a good agreement between GM and FVM results although different thermal boundary conditions at the bottom were used.

The constructed computational algorithm enables prediction of cooling capabilities for the selected geometry. It also offers possibility for geometry improvements and optimization, to achieve higher thermal effectiveness.

The worst hypothetical accident scenario in the nuclear power station is the general meltdown. In... more The worst hypothetical accident scenario in the nuclear power station is the general meltdown. In this case the reactor core melts and accumulates in the lower plenum of the reactor vessel. Heat is further generated in a melt pool due to fission products decay. Because of the high temperature melt, the integrity of the lower plenum could be threatened unless a sufficient outside cooling exists. To determine needed intensity of the cooling e.g. heat removal, the prediction of melt thermodynamic processes is the crucial task.

Natural convection as a consequence of the internal heat generation is the most important heat transfer mechanism. Because of high temperatures and melt's material properties, the experimental tracking of the phenomenon is practically impossible. On the other hand, the common problem of all numerical simulations is an intense turbulent behavior of the fluid at high Rayleigh numbers.

Presented work is focused on modeling of turbulent natural convection in a volumetrically heated fluid, where turbulence is captured with the modified large-eddy simulation method. The numerical computer program was developed and used for time dependent simulations of natural convection in a two-dimensional rectangular cavity at the Rayleigh numbers Ra = 1e6-1e11 and the Prandtl number Pr = 0.25.

The simulation results disclose the dynamics and heat transfer in the fluid. It has been established that the fluid flow is laminar for the Rayleigh numbers Ra < 1e8. The flow regime becomes turbulent as a consequence of the Rayleigh-Taylor instabilities at the top wall and the Kelvin-Helmholtz instabilities at the vertical walls. Locally the heat transfer is the highest in the upper corners of the simulation domain, whereas the appearance of vertical cold intrusions (thermals) reduces the heat transfer through the upper boundary. Based on the calculated Nusselt number time distributions, the time of the appearance for the first and the second bifurcation point was determined. The time-spatial averaged values of Nusselt number show, that the Rayleigh-Nusselt number dependence is not monotonically linear in the log10-log10 diagram. Moreover, it reflects the flow regime changes. The average heat transfer is the highest on the top wall of the simulation domain. It was estimated that due to natural convection the 48 percents of the thermal energy load the lower plenum walls, whereas the rest returns back to the reactor vessel.

A failure of reactor core cooling and major safety systems may cause melting of nuclear fuel and ... more A failure of reactor core cooling and major safety systems may cause melting of nuclear fuel and reactor vessel equipment. In the reactor vessel, the melt flows down into the lower plenum, where it is accumulated. In the past, the common opinion was that the melt would break through the reactor vessel and start to desintegrate the reactor concrete base. However, recent investigations revealed that the core melt can be safely retained in the reactor vessel lower plenum if it is properly cooled.

The processes in the reactor core melt in the lower plenum are specific and not yet fully understood. As revealed by a comprehensive overview of the lower plenum cooling problem, natural convection is the most important phenomenon that controls heat transfer from the melt. In the case of natural convection, fluid motion is caused by volumetric forces and density gradients. If these are strong enough, thermal instabilities may result in hydrodynamic instabilities. It was discovered that transition from laminar to turbulent flow occurs at the value of Rayleigh number Ra=5e5 in the case of Rayleigh-Bénard convection and at Ra=1e6 in the case of fluid with internal heat generation.

The main problem of turbulent phenomena modeling is the size of turbulent fluid flow structures, which are in general too small to be described accurately using a discrete numerical mesh. The base of the Smagorinsky model is the assumption that the smallest flow structures, which are separated and modeled as a subgrid term, are isotropic and homogeneous. Therefore, viscous dissipation is equal to the production of turbulent kinetic energy. As the Smagorinsky model is too dissipative in the vicinity of the walls, turbulent viscosity wall functions have to be implemented.

Natural convection in the melt of nuclear reactor core was modelled as natural convection in a fluid with internal heat generation in a rectangular cavity. The value of Rayleigh number was Ra=1e10 and the value of Prandtl number was Pr=1.2. Numerical simulations were restricted to two-dimensional space, due to computer hardware limitations. The finite volume method was used for spatial discretisation and a combination of Adam-Bashford method and projection scheme was used for time integration.

As the calculation of heat transfer in the form of dimensionless Nusselt number revealed, the most severe thermal loads occur on the side walls in the vicinity of the cavity upper boundary. Calculated values of heat transfer can be safely extrapolated to higher values of Rayleigh number.

A vapor explosion is a physical phenomenon in which hot liquid (fuel) rapidly fragments and trans... more A vapor explosion is a physical phenomenon in which hot liquid (fuel) rapidly fragments and transfer its internal energy to a coolant. The coolant vaporizes at high pressure, expands and does work to its surroundings. In case of prolonged and complete failure of normal and emergency coolant system in a nuclear reactor, the fission material decay heat would cause melting of the reactor core. In severe accident safety analyses the occurrence of vapor explosions was considered if molten fuel contacts the residual coolant. Namely, the strength of vapor explosion contributes to reactor failure and containment failure, and consequently to the release of radioactive substances into environment.

WAHA single phase code is designed for simulations of a single phase 1D transients with pressure ... more WAHA single phase code is designed for simulations of a single phase 1D transients with pressure pulses and shocks expanding through a piping system. The code uses second-order accurate numerical scheme and is being used for testing the phenomenology of single phase pressure pulses and modelling of different elements of the piping system for further development of the WAHA two-phase code.

The document gives an overview of the numerical method, which is used in the current version of t... more The document gives an overview of the numerical method, which is used in the current version of the WAHA code and is planned to be used in the final version of the WAHA code. The described numerical scheme can be used with conservative, primitive, or with some other sets of basic variables. The final choice of the basic variables depends on the simulations of the smooth-area change flows that are currently tested.

Another undetermined choice is a number of the basic equations, which depends on the chosen physical model. The most likely choice is the 6-eq. two-fluid model, however, if the assumption of the thermal equilibrium of the vapor phase is adopted, the 5-eq. two-fluid model will be used.

Some minor details that are not clarified in the present version of the document (for example: treatment of very small vapor or liquid volume fractions) will be addressed in the next versions of the document.

Simulation techniques are becoming a tool of choice in risk assessment studies as they allow inve... more Simulation techniques are becoming a tool of choice in risk assessment studies as they allow investigation of diverse accident scenarios in a safe manner with minimum simplification of environmental conditions, and with a non-destructive outcome. This gives them cost-benefit advantage in comparison to equivalent physical testing. Much larger flexibility of the simulation approach often allows assessment of more adventurous designs, which further stimulates engineering progress. Nevertheless, lack of acceptability of the simulation results in the planning and permitting (i.e. regulatory) process may have a negative impact on development and use of such techniques.

Computational Fluid Dynamics (CFD) models solve fundamental equations describing the fluid flow and heat transfer phenomena. For the last two decades, they have been increasingly used for fire dynamics simulations in order to predict smoke and heat distribution behaviour. Beside mathematical models, today's CFD software packages (CFX, FDS, FLACS, Fluent, Star-CD etc) incorporate also different pre- and post-processing tools that vastly simplify simulation work and increase its productivity.

It is challenging for a simulation engineer to select a suitable CFD simulation package; there is a large difference in their capabilities, accuracy and price. What is often underestimated is the impact that software user-friendliness and availability of technical support have on the analyst productivity. The lecture reviews theoretical background of Fire Dynamics Simulator (FDS) and ANSYS CFD packages, and discusses through comparative examples their main strengths and weaknesses. As the most important factor for quality of CFD analysis is the practitioner, basic features of a quality assurance (QA) process and their applicability to fire simulation analyses are presented.

- Introduction - Project and analysis objectives - Input control - Process quality assurance - Cl... more - Introduction
- Project and analysis objectives
- Input control
- Process quality assurance
- Client communication and conclusions

Global energy demands and dwindling fossil fuels are making zero-head wind and water turbines inc... more Global energy demands and dwindling fossil fuels are making zero-head wind and water turbines increasingly important as renewable energy devices.

Device efficiency is a key parameter in the economic viability, recovery of initial capital investment and long term profitability of such devices.

To determine a performance curve of an operational turbine, a range of aspects need to be taken into account. These include complex fluid dynamics, local topology and other environmental conditions, structural loadings and vibrations, transmission loads and generator dynamics.

Furthermore, in most cases, turbines are installed in groups or farms. Flow interaction in a multiple turbine installation reduces the power output and thus has an important influence on economics of whole installations.

yoomi is a rechargeable, BPA-free, self-warming baby bottle that warms baby's feed to the natural... more yoomi is a rechargeable, BPA-free, self-warming baby bottle that warms baby's feed to the natural temperature of breast milk at the touch of a button (www.yoomi.com).

It was a technical challenge to design a warmer to heat the milk from 5 to 32C for the first drop flow rate (200 ml/min) and to maintain steady-flow conditions.

Modelling fluid and heat flow in such device is challenging:
- laminar flow of milk from the bottle to the teat
- air flow is squeezed from the teat and flows in the opposite direction
- solidification process and heat generation
- thermal material properties of solid parts
- heat transfer (convection & conduction) from the warmer to the fluid flow and the solid parts
- flow stability

- The bottle exploits the subcooled nature of sodium acetate mixture, which remains liquid below its solidification temperature.
- The mixture is contained inside a warming unit with channels for the milk flow.
- When the solidification process is triggered, latent heat is released.
- As the milk flows along the channels, it is heated to the correct temperature - above 32C.
- The warmer is recharged by placing it in boiling water or a steam sterilizer.

Overview of fluid dynamics transport equations - transport of mass, momentum, energy and composit... more Overview of fluid dynamics transport equations
- transport of mass, momentum, energy and composition
- influence of convection, diffusion, volumetric (buoyancy) force
- transport equation for thermal radiation

Averaging and simplification of transport equations
- spatial and time averaging
- influence of averaging on zone and field models
- solution methods

CFD modelling
- turbulence models (k-epsilon, k-omega, Reynolds stress, LES)
- combustion models (mixture fraction, eddy dissipation, flamelet)
- thermal radiation models (discrete transfer, Monte Carlo)

Conclusions

Motivation and problem definition Wind turbine modelling methodologies Wind farm simulation Maxim... more Motivation and problem definition
Wind turbine modelling methodologies
Wind farm simulation
Maximizing investment yield
Optimisation of the wind farm layout
Conclusions & further work

Averaging and simplification of transport equations
- spatial averaging
- time averaging
- influence of averaging on zone and field models

Zone models
- basics of zone models (1 and 2 zone models)
- advantages and disadvantages

Field models
- numerical mesh and discretisation of transport equations
- turbulence models (k-epsilon, k-omega, Reynolds stress, LES)
- combustion models (mixture fraction, eddy dissipation, flamelet)
- thermal radiation models (discrete transfer, Monte Carlo)
- examples of use

Conclusions
- software packages

Examples
- diffusion flame
- fire in an enclosure
- fire in a tunnel

Update of MOD3.3 assessment calculations against two real transients at Krško NPP, caused by MSIV... more Update of MOD3.3 assessment calculations against two real transients at Krško NPP, caused by MSIV 1 and MSIV 2 inadvertent closure.

Assessment of RELAP5/MOD3.3 for fast transients (water hammer).