Theoretical Analysis and Numerical Simulation of Spectral Radiative Properties of Combustion Gases in Oxy/Air-Fired Combustion Systems

Energy efficiency is one of the major objectives which should be achieved in order to implement the limited energy resources of the world in a sustainable way. Since radiative heat transfer is the dominant heat transfer mechanism in most of fossil fuel combustion systems, more accurate insight and models may cause improvement in the energy efficiency of the new designed combustion systems. The radiative properties of combustion gases are highly wavelength dependent. Better models for calculating the radiative properties of combustion gases are highly required in the modeling of large scale industrial combustion systems. With detailed knowledge of spectral radiative properties of gases, the modeling of combustion processes in the different applications can be more accurate. In order to propose a new method for effective non gray modeling of radiative heat transfer in combustion systems, different models for the spectral properties of gases including SNBM, EWBM, and WSGGM have been studied in this research. Using this detailed analysis of different approaches, the thesis presents new methods for gray and non gray radiative heat transfer modeling in homogeneous and inhomogeneous H2O–CO2 mixtures at atmospheric pressure. The proposed method is able to support the modeling of a wide range of combustion systems including the oxy-fired combustion scenario. The new methods are based on implementing some pre-obtained correlations for the total emissivity and band absorption coefficient of H2O–CO2 mixtures in different temperatures, gas compositions, and optical path lengths. They can be easily used within any commercial CFD software for radiative heat transfer modeling resulting in more accurate, simple, and fast calculations. The new methods were successfully used in CFD modeling by applying them to industrial scale backpass channel under oxy-fired conditions. The developed approaches are more accurate compared with other methods; moreover, they can provide complete explanation and detailed analysis of the radiation heat transfer in different systems under different combustion conditions. The methods were verified by applying them to some benchmarks, and they showed a good level of accuracy and computational speed compared to other methods. Furthermore, the implementation of the suggested banded approach in CFD software is very easy and straightforward.

A temperature predicting model for manufacturing processes requiring coiling

A model for predicting temperature evolution for automatic controling systems in manufacturing processes requiring the coiling of bars in the transfer table is presented. Although the method is of a general nature, the presentation in this work refers to the manufacturing of steel plates in hot rolling mills. The predicting strategy is based on a mathematical model of the evolution of temperature in a coiling and uncoiling bar and is presented in the form of a parabolic partial differential equation for a shape changing domain. The mathematical model is solved numerically by a space discretization via geometrically adaptive finite elements which accomodate the change in shape of the domain, using a computationally novel treatment of the resulting thermal contact problem due to coiling. Time is discretized according to a Crank-Nicolson scheme. Since the actual physical process takes less time than the time required by the process controlling computer to solve the full mathematical model, a special predictive device was developed, in the form of a set of least squares polynomials, based on the off-line numerical solution of the mathematical model.

Dynamics of coherent vortices in mixing layers using direct numerical and large-eddy simulations

Coherent vortices in turbulent mixing layers are investigated by means of Direct Numerical Simulation (DNS) and Large-Eddy Simulation (LES). Subgrid-scale models defined in spectral and physical spaces are reviewed. The new "spectral-dynamic viscosity model", that allows to account for non-developed turbulence in the subgrid-scales, is discussed. Pseudo-spectral methods, combined with sixth-order compact finite differences schemes (when periodic boundary conditions cannot be established), are used to solve the Navier- Stokes equations. Simulations in temporal and spatial mixing layers show two types of pairing of primary Kelvin-Helmholtz (KH) vortices depending on initial conditions (or upstream conditions): quasi-2D and helical pairings. In both cases, secondary streamwise vortices are stretched in between the KH vortices at an angle of 45° with the horizontal plane. These streamwise vortices are not only identified in the early transitional stage of the mixing layer but also in self-similar turbulence conditions. The Re dependence of the "diameter" of these vortices is analyzed. Results obtained in spatial growing mixing layers show some evidences of pairing of secondary vortices; after a pairing of the primary Kelvin-Helmholtz (KH) vortices, the streamwise vortices are less numerous and their diameter has increased than before the pairing of KH vortices.

An experimental/numerical study of the turbulent boundary layer development along a surface with a sudden change in roughness

A theory for the description of turbulent boundary layer flows over surfaces with a sudden change in roughness is considered. The theory resorts to the concept of displacement in origin to specify a wall function boundary condition for a kappa-epsilon model. An approximate algebraic expression for the displacement in origin is obtained from the experimental data by using the chart method of Perry and Joubert(J.F.M., vol. 17, pp. 193-122, 1963). This expression is subsequently included in the near wall logarithmic velocity profile, which is then adopted as a boundary condition for a kappa-epsilon modelling of the external flow. The results are compared with the lower atmospheric observations made by Bradley(Q. J. Roy. Meteo. Soc., vol. 94, pp. 361-379, 1968) as well as with velocity profiles extracted from a set of wind tunnel experiments carried out by Avelino et al.( 7th ENCIT, 1998). The measurements are found to be in good agreement with the theoretical computations. The skin-friction coefficient was calculated according to the chart method of Perry and Joubert(J.F.M., vol. 17, pp. 193-122, 1963) and to a balance of the integral momentum equation. In particular, the growth of the internal boundary layer thickness obtained from the numerical simulation is compared with predictions of the experimental data calculated by two methods, the "knee" point method and the "merge" point method.

Application of a non isotropic turbulence model to stable atmospheric flows and dispersion over 3D topography

A non isotropic turbulence model is extended and applied to three dimensional stably stratified flows and dispersion calculations. The model is derived from the algebraic stress model (including wall proximity effects), but it retains the simplicity of the "eddy viscosity" concept of first order models. The "modified k-epsilon" is implemented in a three dimensional numerical code. Once the flow is resolved, the predicted velocity and turbulence fields are interpolated into a second grid and used to solve the concentration equation. To evaluate the model, various steady state numerical solutions are compared with small scale dispersion experiments which were conducted at the wind tunnel of Mitsubishi Heavy Industries, in Japan. Stably stratified flows and plume dispersion over three distinct idealized complex topographies (flat and hilly terrain) are studied. Vertical profiles of velocity and pollutant concentration are shown and discussed. Also, comparisons are made against the results obtained with the standard k-epsilon model.

On the numerical simulation of machining processes

Numerical simulation of machining processes can be traced back to the early seventies when finite element models for continuous chip formation were proposed. The advent of fast computers and development of new techniques to model large plastic deformations have favoured machining simulation. Relevant aspects of finite element simulation of machining processes are discussed in this paper, such as solution methods, material models, thermo-mechanical coupling, friction models, chip separation and breakage strategies and meshing/re-meshing strategies.

On the numerical integration of rigid body nonlinear dynamics in presence of parameters singularities

One of the main complexities in the simulation of the nonlinear dynamics of rigid bodies consists in describing properly the finite rotations that they may undergo. It is well known that, to avoid singularities in the representation of the SO(3) rotation group, at least four parameters must be used. However, it is computationally expensive to use a four-parameters representation since, as only three of the parameters are independent, one needs to introduce constraint equations in the model, leading to differential-algebraic equations instead of ordinary differential ones. Three-parameter representations are numerically more efficient. Therefore, the objective of this paper is to evaluate numerically the influence of the parametrization and its singularities on the simulation of the dynamics of a rigid body. This is done through the analysis of a heavy top with a fixed point, using two three-parameter systems, Euler's angles and rotation vector. Theoretical results were used to guide the numerical simulation and to assure that all possible cases were analyzed. The two parametrizations were compared using several integrators. The results show that Euler's angles lead to faster integration compared to the rotation vector. An Euler's angles singular case, where representation approaches a theoretical singular point, was analyzed in detail. It is shown that on the contrary of what may be expected, 1) the numerical integration is very efficient, even more than for any other case, and 2) in spite of the uncertainty on the Euler's angles themselves, the body motion is well represented.

Gas-solid two-phase flow in the riser of circulating fluidized beds: mathematical modelling and numerical simulation

A mathematical model is developed for gas-solids flows in circulating fluidized beds. An Eulerian formulation is followed based on the two-fluids model approach where both the fluid and the particulate phases are treated as a continuum. The physical modelling is discussed, including the formulation of boundary conditions and the description of the numerical methodology. Results of numerical simulation are presented and discussed. The model is validated through comparison to experiment, and simulation is performed to investigate the effects on the flow hydrodynamics of the solids viscosity.

Numerical Simulation of Stochastic Di erential Equations

Stochastic differential equation (SDE) is a differential equation in which some of the terms and its solution are stochastic processes. SDEs play a central role in modeling physical systems like finance, Biology, Engineering, to mention some. In modeling process, the computation of the trajectories (sample paths) of solutions to SDEs is very important. However, the exact solution to a SDE is generally difficult to obtain due to non-differentiability character of realizations of the Brownian motion. There exist approximation methods of solutions of SDE. The solutions will be continuous stochastic processes that represent diffusive dynamics, a common modeling assumption for financial, Biology, physical, environmental systems. This Masters' thesis is an introduction and survey of numerical solution methods for stochastic differential equations. Standard numerical methods, local linearization methods and filtering methods are well described. We compute the root mean square errors for each method from which we propose a better numerical scheme. Stochastic differential equations can be formulated from a given ordinary differential equations. In this thesis, we describe two kind of formulations: parametric and non-parametric techniques. The formulation is based on epidemiological SEIR model. This methods have a tendency of increasing parameters in the constructed SDEs, hence, it requires more data. We compare the two techniques numerically.

Particle model for simulating limestone reactions in novel fluidised bed energy applications

The development of carbon capture and storage (CCS) has raised interest towards novel fluidised bed (FB) energy applications. In these applications, limestone can be utilized for S02 and/or CO2 capture. The conditions in the new applications differ from the traditional atmospheric and pressurised circulating fluidised bed (CFB) combustion conditions in which the limestone is successfully used for SO2 capture. In this work, a detailed physical single particle model with a description of the mass and energy transfer inside the particle for limestone was developed. The novelty of this model was to take into account the simultaneous reactions, changing conditions, and the effect of advection. Especially, the capability to study the cyclic behaviour of limestone on both sides of the calcination-carbonation equilibrium curve is important in the novel conditions. The significances of including advection or assuming diffusion control were studied in calcination. Especially, the effect of advection in calcination reaction in the novel combustion atmosphere was shown. The model was tested against experimental data; sulphur capture was studied in a laboratory reactor in different fluidised bed conditions. Different Conversion levels and sulphation patterns were examined in different atmospheres for one limestone type. The Conversion curves were well predicted with the model, and the mechanisms leading to the Conversion patterns were explained with the model simulations. In this work, it was also evaluated whether the transient environment has an effect on the limestone behaviour compared to the averaged conditions and in which conditions the effect is the largest. The difference between the averaged and transient conditions was notable only in the conditions which were close to the calcination-carbonation equilibrium curve. The results of this study suggest that the development of a simplified particle model requires a proper understanding of physical and chemical processes taking place in the particle during the reactions. The results of the study will be required when analysing complex limestone reaction phenomena or when developing the description of limestone behaviour in comprehensive 3D process models. In order to transfer the experimental observations to furnace conditions, the relevant mechanisms that take place need to be understood before the important ones can be selected for 3D process model. This study revealed the sulphur capture behaviour under transient oxy-fuel conditions, which is important when the oxy-fuel CFB process and process model are developed.

Modal testing and numerical modeling of the dynamic properties of layered sheet-steel structure

Recently, due to the increasing total construction and transportation cost and difficulties associated with handling massive structural components or assemblies, there has been increasing financial pressure to reduce structural weight. Furthermore, advances in material technology coupled with continuing advances in design tools and techniques have encouraged engineers to vary and combine materials, offering new opportunities to reduce the weight of mechanical structures. These new lower mass systems, however, are more susceptible to inherent imbalances, a weakness that can result in higher shock and harmonic resonances which leads to poor structural dynamic performances. The objective of this thesis is the modeling of layered sheet steel elements, to accurately predict dynamic performance. During the development of the layered sheet steel model, the numerical modeling approach, the Finite Element Analysis and the Experimental Modal Analysis are applied in building a modal model of the layered sheet steel elements. Furthermore, in view of getting a better understanding of the dynamic behavior of layered sheet steel, several binding methods have been studied to understand and demonstrate how a binding method affects the dynamic behavior of layered sheet steel elements when compared to single homogeneous steel plate. Based on the developed layered sheet steel model, the dynamic behavior of a lightweight wheel structure to be used as the structure for the stator of an outer rotor Direct-Drive Permanent Magnet Synchronous Generator designed for high-power wind turbines is studied.

Dynamic Analysis Model of Spherical Roller Bearings with Defects

Rolling element bearings are essential components of rotating machinery. The spherical roller bearing (SRB) is one variant seeing increasing use, because it is self-aligning and can support high loads. It is becoming increasingly important to understand how the SRB responds dynamically under a variety of conditions. This doctoral dissertation introduces a computationally efficient, three-degree-of-freedom, SRB model that was developed to predict the transient dynamic behaviors of a rotor-SRB system. In the model, bearing forces and deflections were calculated as a function of contact deformation and bearing geometry parameters according to nonlinear Hertzian contact theory. The results reveal how some of the more important parameters; such as diametral clearance, the number of rollers, and osculation number; influence ultimate bearing performance. Distributed defects, such as the waviness of the inner and outer ring, and localized defects, such as inner and outer ring defects, are taken into consideration in the proposed model. Simulation results were verified with results obtained by applying the formula for the spherical roller bearing radial deflection and the commercial bearing analysis software. Following model verification, a numerical simulation was carried out successfully for a full rotor-bearing system to demonstrate the application of this newly developed SRB model in a typical real world analysis. Accuracy of the model was verified by comparing measured to predicted behaviors for equivalent systems.

Application and development of numerical methods for the modelling of innovative gas cooled fission reactors

Innovative gas cooled reactors, such as the pebble bed reactor (PBR) and the gas cooled fast reactor (GFR) offer higher efficiency and new application areas for nuclear energy. Numerical methods were applied and developed to analyse the specific features of these reactor types with fully three dimensional calculation models. In the first part of this thesis, discrete element method (DEM) was used for a physically realistic modelling of the packing of fuel pebbles in PBR geometries and methods were developed for utilising the DEM results in subsequent reactor physics and thermal-hydraulics calculations. In the second part, the flow and heat transfer for a single gas cooled fuel rod of a GFR were investigated with computational fluid dynamics (CFD) methods. An in-house DEM implementation was validated and used for packing simulations, in which the effect of several parameters on the resulting average packing density was investigated. The restitution coefficient was found out to have the most significant effect. The results can be utilised in further work to obtain a pebble bed with a specific packing density. The packing structures of selected pebble beds were also analysed in detail and local variations in the packing density were observed, which should be taken into account especially in the reactor core thermal-hydraulic analyses. Two open source DEM codes were used to produce stochastic pebble bed configurations to add realism and improve the accuracy of criticality calculations performed with the Monte Carlo reactor physics code Serpent. Russian ASTRA criticality experiments were calculated. Pebble beds corresponding to the experimental specifications within measurement uncertainties were produced in DEM simulations and successfully exported into the subsequent reactor physics analysis. With the developed approach, two typical issues in Monte Carlo reactor physics calculations of pebble bed geometries were avoided. A novel method was developed and implemented as a MATLAB code to calculate porosities in the cells of a CFD calculation mesh constructed over a pebble bed obtained from DEM simulations. The code was further developed to distribute power and temperature data accurately between discrete based reactor physics and continuum based thermal-hydraulics models to enable coupled reactor core calculations. The developed method was also found useful for analysing sphere packings in general. CFD calculations were performed to investigate the pressure losses and heat transfer in three dimensional air cooled smooth and rib roughened rod geometries, housed inside a hexagonal flow channel representing a sub-channel of a single fuel rod of a GFR. The CFD geometry represented the test section of the L-STAR experimental facility at Karlsruhe Institute of Technology and the calculation results were compared to the corresponding experimental results. Knowledge was gained of the adequacy of various turbulence models and of the modelling requirements and issues related to the specific application. The obtained pressure loss results were in a relatively good agreement with the experimental data. Heat transfer in the smooth rod geometry was somewhat under predicted, which can partly be explained by unaccounted heat losses and uncertainties. In the rib roughened geometry heat transfer was severely under predicted by the used realisable k − epsilon turbulence model. An additional calculation with a v2 − f turbulence model showed significant improvement in the heat transfer results, which is most likely due to the better performance of the model in separated flow problems. Further investigations are suggested before using CFD to make conclusions of the heat transfer performance of rib roughened GFR fuel rod geometries. It is suggested that the viewpoints of numerical modelling are included in the planning of experiments to ease the challenging model construction and simulations and to avoid introducing additional sources of uncertainties. To facilitate the use of advanced calculation approaches, multi-physical aspects in experiments should also be considered and documented in a reasonable detail.

Numerical Studies of Dark Energy Models and Observations

The cosmological standard view is based on the assumptions of homogeneity, isotropy and general relativistic gravitational interaction. These alone are not sufficient for describing the current cosmological observations of accelerated expansion of space. Although general relativity is extremely accurately tested to describe the local gravitational phenomena, there is a strong demand for modifying either the energy content of the universe or the gravitational interaction itself to account for the accelerated expansion. By adding a non-luminous matter component and a constant energy component with negative pressure, the observations can be explained with general relativity. Gravitation, cosmological models and their observational phenomenology are discussed in this thesis. Several classes of dark energy models that are motivated by theories outside the standard formulation of physics were studied with emphasis on the observational interpretation. All the cosmological models that seek to explain the cosmological observations, must also conform to the local phenomena. This poses stringent conditions for the physically viable cosmological models. Predictions from a supergravity quintessence model was compared to Supernova 1a data and several metric gravity models were studied with local experimental results. Polytropic stellar configurations of solar, white dwarf and neutron stars were numerically studied with modified gravity models. The main interest was to study the spacetime around the stars. The results shed light on the viability of the studied cosmological models.

Implementation of Quantitative Reaction-based Model Refinement

Building a computational model for complex biological systems is an iterative process. It starts from an abstraction of the process and then incorporates more details regarding the specific biochemical reactions which results in the change of the model fit. Meanwhile, the model’s numerical properties such as its numerical fit and validation should be preserved. However, refitting the model after each refinement iteration is computationally expensive resource-wise. There is an alternative approach which ensures the model fit preservation without the need to refit the model after each refinement iteration. And this approach is known as quantitative model refinement. The aim of this thesis is to develop and implement a tool called ModelRef which does the quantitative model refinement automatically. It is both implemented as a stand-alone Java application and as one of Anduril framework components. ModelRef performs data refinement of a model and generates the results in two different well known formats (SBML and CPS formats). The development of this tool successfully reduces the time and resource needed and the errors generated as well by traditional reiteration of the whole model to perform the fitting procedure.