Progress in numerical modeling of non-premixed combustion

Progress is made on the numerical modeling of both laminar and turbulent non-premixed flames. Instead of solving the transport equations for the numerous species involved in the combustion process, the present study proposes reduced-order combustion models based on local flame structures.

For laminar non-premixed flames, curvature and multi-dimensional diffusion effects are found critical for the accurate prediction of sooting tendencies. A new numerical model based on modified flamelet equations is proposed. Sooting tendencies are calculated numerically using the proposed model for a wide range of species. These first numerically-computed sooting tendencies are in good agreement with experimental data. To further quantify curvature and multi-dimensional effects, a general flamelet formulation is derived mathematically. A budget analysis of the general flamelet equations is performed on an axisymmetric laminar diffusion flame. A new chemistry tabulation method based on the general flamelet formulation is proposed. This new tabulation method is applied to the same flame and demonstrates significant improvement compared to previous techniques.

For turbulent non-premixed flames, a new model to account for chemistry-turbulence interactions is proposed. %It is found that these interactions are not important for radicals and small species, but substantial for aromatic species. The validity of various existing flamelet-based chemistry tabulation methods is examined, and a new linear relaxation model is proposed for aromatic species. The proposed relaxation model is validated against full chemistry calculations. To further quantify the importance of aromatic chemistry-turbulence interactions, Large-Eddy Simulations (LES) have been performed on a turbulent sooting jet flame. %The aforementioned relaxation model is used to provide closure for the chemical source terms of transported aromatic species. The effects of turbulent unsteadiness on soot are highlighted by comparing the LES results with a separate LES using fully-tabulated chemistry. It is shown that turbulent unsteady effects are of critical importance for the accurate prediction of not only the inception locations, but also the magnitude and fluctuations of soot.

Combustion rumble prediction with integrated computational-fluid-dynamics/ low-order-model methods

The pressure oscillation within combustion chambers of aeroengines and industrial gas turbines is a major technical challenge to the development of high-performance and low-emission propulsion systems. In this paper, an approach integrating computational fluid dynamics and one-dimensional linear stability analysis is developed to predict the modes of oscillation in a combustor and their frequencies and growth rates. Linear acoustic theory was used to describe the acoustic waves propagating upstream and downstream of the combustion zone, which enables the computational fluid dynamics calculation to be efficiently concentrated on the combustion zone. A combustion oscillation was found to occur with its predicted frequency in agreement with experimental measurements. Furthermore, results from the computational fluid dynamics calculation provide the flame transfer function to describe unsteady heat release rate. Departures from ideal one-dimensional flows are described by shape factors. Combined with this information, low-order models can work out the possible oscillation modes and their initial growth rates. The approach developed here can be used in more general situations for the analysis of combustion oscillations. Copyright © 2012 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Multi-physics modelling for the fabrication, packaging and reliability of micro-systems components

The latest advances in multi-physics modelling both using high fidelity techniques and reduced order and behavioural models will be discussed. Particular focus will be given to the application and validation of these techniques for modelling the fabrication, packaging and subsequent reliability of micro-systems based components. The paper will discuss results from a number of research projects with particular emphasis on the techniques being developed in a major UK Goverment funded project - 3D-MINTEGRATION (www.3d-mintegration.com).

Blind Characterisation of Sensors with Second-Order Dynamic Response

Compensation for the dynamic response of a temperature sensor usually involves the estimation of its input on the basis of the measured output and model parameters. In the case of temperature measurement, the sensor dynamic response is strongly dependent on the measurement environment and fluid velocity. Estimation of time-varying sensor model parameters therefore requires continuous textit{in situ} identification. This can be achieved by employing two sensors with different dynamic properties, and exploiting structural redundancy to deduce the sensor models from the resulting data streams. Most existing approaches to this problem assume first-order sensor dynamics. In practice, however second-order models are more reflective of the dynamics of real temperature sensors, particularly when they are encased in a protective sheath. As such, this paper presents a novel difference equation approach to solving the blind identification problem for sensors with second-order models. The approach is based on estimating an auxiliary ARX model whose parameters are related to the desired sensor model parameters through a set of coupled non-linear algebraic equations. The ARX model can be estimated using conventional system identification techniques and the non-linear equations can be solved analytically to yield estimates of the sensor models. Simulation results are presented to demonstrate the efficiency of the proposed approach under various input and parameter conditions.

Real-time parameter estimation of dynamic temperature and humidity models for greenhouse adaptive climate control

A real-time parameter estimator for the climate discrete-time dynamic models of a greenhouse located at the North of Portugal are presented. The experiments showed that the second order models identified for the air temperature and humidity achieve a close agreement between simulated and experimantal data.

Application of genetic algorithms in the design of an electrical potential of fractional order

Fractional calculus (FC) is currently being applied in many areas of science and technology. In fact, this mathematical concept helps the researches to have a deeper insight about several phenomena that integer order models overlook. Genetic algorithms (GA) are an important tool to solve optimization problems that occur in engineering. This methodology applies the concepts that describe biological evolution to obtain optimal solution in many different applications. In this line of thought, in this work we use the FC and the GA concepts to implement the electrical fractional order potential. The performance of the GA scheme, and the convergence of the resulting approximation, are analyzed. The results are analyzed for different number of charges and several fractional orders.

Fractional order modelling of dynamic backlash

This paper studies the dynamical properties of systems with backlash and impact phenomena. This type of non-linearity can be tackled in the perspective of the fractional calculus theory. Fractional and integer order models are compared and their influence upon the emerging dynamics is analysed. It is demonstrated that fractional models can memorize dynamical effects due to multiple micro-collisions.

Modeling Vegetable Fractals by means of Fractional-order Equations

This paper characterizes four ‘fractal vegetables’: (i) cauliflower (brassica oleracea var. Botrytis); (ii) broccoli (brassica oleracea var. italica); (iii) round cabbage (brassica oleracea var. capitata) and (iv) Brussels sprout (brassica oleracea var. gemmifera), by means of electrical impedance spectroscopy and fractional calculus tools. Experimental data is approximated using fractional-order models and the corresponding parameters are determined with a genetic algorithm. The Havriliak-Negami five-parameter model fits well into the data, demonstrating that classical formulae can constitute simple and reliable models to characterize biological structures.

Modelling, control and supervision for a class of hybrid systems

The aim of this thesis is to narrow the gap between two different control techniques: the continuous control and the discrete event control techniques DES. This gap can be reduced by the study of Hybrid systems, and by interpreting as Hybrid systems the majority of large-scale systems. In particular, when looking deeply into a process, it is often possible to identify interaction between discrete and continuous signals. Hybrid systems are systems that have both continuous, and discrete signals. Continuous signals are generally supposed continuous and differentiable in time, since discrete signals are neither continuous nor differentiable in time due to their abrupt changes in time. Continuous signals often represent the measure of natural physical magnitudes such as temperature, pressure etc. The discrete signals are normally artificial signals, operated by human artefacts as current, voltage, light etc. Typical processes modelled as Hybrid systems are production systems, chemical process, or continuos production when time and continuous measures interacts with the transport, and stock inventory system. Complex systems as manufacturing lines are hybrid in a global sense. They can be decomposed into several subsystems, and their links. Another motivation for the study of Hybrid systems is the tools developed by other research domains. These tools benefit from the use of temporal logic for the analysis of several properties of Hybrid systems model, and use it to design systems and controllers, which satisfies physical or imposed restrictions. This thesis is focused in particular types of systems with discrete and continuous signals in interaction. That can be modelled hard non-linealities, such as hysteresis, jumps in the state, limit cycles, etc. and their possible non-deterministic future behaviour expressed by an interpretable model description. The Hybrid systems treated in this work are systems with several discrete states, always less than thirty states (it can arrive to NP hard problem), and continuous dynamics evolving with expression: with Ki ¡ Rn constant vectors or matrices for X components vector. In several states the continuous evolution can be several of them Ki = 0. In this formulation, the mathematics can express Time invariant linear system. By the use of this expression for a local part, the combination of several local linear models is possible to represent non-linear systems. And with the interaction with discrete events of the system the model can compose non-linear Hybrid systems. Especially multistage processes with high continuous dynamics are well represented by the proposed methodology. Sate vectors with more than two components, as third order models or higher is well approximated by the proposed approximation. Flexible belt transmission, chemical reactions with initial start-up and mobile robots with important friction are several physical systems, which profits from the benefits of proposed methodology (accuracy). The motivation of this thesis is to obtain a solution that can control and drive the Hybrid systems from the origin or starting point to the goal. How to obtain this solution, and which is the best solution in terms of one cost function subject to the physical restrictions and control actions is analysed. Hybrid systems that have several possible states, different ways to drive the system to the goal and different continuous control signals are problems that motivate this research. The requirements of the system on which we work is: a model that can represent the behaviour of the non-linear systems, and that possibilities the prediction of possible future behaviour for the model, in order to apply an supervisor which decides the optimal and secure action to drive the system toward the goal. Specific problems can be determined by the use of this kind of hybrid models are: - The unity of order. - Control the system along a reachable path. - Control the system in a safe path. - Optimise the cost function. - Modularity of control The proposed model solves the specified problems in the switching models problem, the initial condition calculus and the unity of the order models. Continuous and discrete phenomena are represented in Linear hybrid models, defined with defined eighth-tuple parameters to model different types of hybrid phenomena. Applying a transformation over the state vector : for LTI system we obtain from a two-dimensional SS a single parameter, alpha, which still maintains the dynamical information. Combining this parameter with the system output, a complete description of the system is obtained in a form of a graph in polar representation. Using Tagaki-Sugeno type III is a fuzzy model which include linear time invariant LTI models for each local model, the fuzzyfication of different LTI local model gives as a result a non-linear time invariant model. In our case the output and the alpha measure govern the membership function. Hybrid systems control is a huge task, the processes need to be guided from the Starting point to the desired End point, passing a through of different specific states and points in the trajectory. The system can be structured in different levels of abstraction and the control in three layers for the Hybrid systems from planning the process to produce the actions, these are the planning, the process and control layer. In this case the algorithms will be applied to robotics ¡V a domain where improvements are well accepted ¡V it is expected to find a simple repetitive processes for which the extra effort in complexity can be compensated by some cost reductions. It may be also interesting to implement some control optimisation to processes such as fuel injection, DC-DC converters etc. In order to apply the RW theory of discrete event systems on a Hybrid system, we must abstract the continuous signals and to project the events generated for these signals, to obtain new sets of observable and controllable events. Ramadge & Wonham¡¦s theory along with the TCT software give a Controllable Sublanguage of the legal language generated for a Discrete Event System (DES). Continuous abstraction transforms predicates over continuous variables into controllable or uncontrollable events, and modifies the set of uncontrollable, controllable observable and unobservable events. Continuous signals produce into the system virtual events, when this crosses the bound limits. If this event is deterministic, they can be projected. It is necessary to determine the controllability of this event, in order to assign this to the corresponding set, , controllable, uncontrollable, observable and unobservable set of events. Find optimal trajectories in order to minimise some cost function is the goal of the modelling procedure. Mathematical model for the system allows the user to apply mathematical techniques over this expression. These possibilities are, to minimise a specific cost function, to obtain optimal controllers and to approximate a specific trajectory. The combination of the Dynamic Programming with Bellman Principle of optimality, give us the procedure to solve the minimum time trajectory for Hybrid systems. The problem is greater when there exists interaction between adjacent states. In Hybrid systems the problem is to determine the partial set points to be applied at the local models. Optimal controller can be implemented in each local model in order to assure the minimisation of the local costs. The solution of this problem needs to give us the trajectory to follow the system. Trajectory marked by a set of set points to force the system to passing over them. Several ways are possible to drive the system from the Starting point Xi to the End point Xf. Different ways are interesting in: dynamic sense, minimum states, approximation at set points, etc. These ways need to be safe and viable and RchW. And only one of them must to be applied, normally the best, which minimises the proposed cost function. A Reachable Way, this means the controllable way and safe, will be evaluated in order to obtain which one minimises the cost function. Contribution of this work is a complete framework to work with the majority Hybrid systems, the procedures to model, control and supervise are defined and explained and its use is demonstrated. Also explained is the procedure to model the systems to be analysed for automatic verification. Great improvements were obtained by using this methodology in comparison to using other piecewise linear approximations. It is demonstrated in particular cases this methodology can provide best approximation. The most important contribution of this work, is the Alpha approximation for non-linear systems with high dynamics While this kind of process is not typical, but in this case the Alpha approximation is the best linear approximation to use, and give a compact representation.

Fractional order modeling of large three-dimensional RC networks

An incidence matrix analysis is used to model a three-dimensional network consisting of resistive and capacitive elements distributed across several interconnected layers. A systematic methodology for deriving a descriptor representation of the network with random allocation of the resistors and capacitors is proposed. Using a transformation of the descriptor representation into standard state-space form, amplitude and phase admittance responses of three-dimensional random RC networks are obtained. Such networks display an emergent behavior with a characteristic Jonscher-like response over a wide range of frequencies. A model approximation study of these networks is performed to infer the admittance response using integral and fractional order models. It was found that a fractional order model with only seven parameters can accurately describe the responses of networks composed of more than 70 nodes and 200 branches with 100 resistors and 100 capacitors. The proposed analysis can be used to model charge migration in amorphous materials, which may be associated to specific macroscopic or microscopic scale fractal geometrical structures in composites displaying a viscoelastic electromechanical response, as well as to model the collective responses of processes governed by random events described using statistical mechanics.

Time-delay systems : design of delay-free and low-order observers

This note provides a comprehensive treatment on the design of functional observers for linear systems having a time-varying delay in the state variables. The designed observers possess attractive features of being low-order and delay-free and hence they are cost effective and easy to implement. Existence conditions are derived and a design procedure for finding low-order observers is given.

Low-order estimation scheme for large-scale systems with interconnection delays

This paper deals with the practical aspects of reduced-order distributed functional state observers design for interconnected linear systems subject to time delays in the interconnections. Contrary to some estimation strategies which only take the ideal instantaneous output information into account, the proposed scheme incorporates output information that is inevitably encountered with time delays in the course of its transmission from the distanced subsystems. It is proved that such estimator possesses less restrictive existence conditions with the acceptance of measurement data from other interrelated subsystems. Upon the satisfaction of the established existence conditions, it will be demonstrated through a simple design procedure and simulation results that a feasible observer can be realized for a given numerical system.

Decomposition properties of PVA/graphene composites during melting-crystallization

Abstract The thermal decomposition of PVA and PVA composites during the melting-crystallization process is still unclear due to indistinct changes in chemical compositions. Using graphene as a model, the decomposition properties of PVA and PVA-graphene composites were systematically analyzed under multiple melting-crystallization cycles. And a series of isothermal decomposition experiments around the melting-crystallization temperature were carried out to simulate the corresponding decomposition kinetics. Based on multiple cycle melting-crystallization, the weight loss of PVA and PVA/graphene composites was successfully quantified. Further morphology investigation and chemical structure analysis indicated that the decomposition was non-uniformly distributed, rendering the possibility of crystallization for PVA and PVA/graphene composites after multiple heating-cooling cycles. In addition, isothermal decomposition analysis based on reduced time plot approach and model-free iso-conversional method indicated that Avrami-Eroffev model could well match the decomposition process of the neat PVA and PG-0.3 composite, while the Avrami-Eroffev and first order models could precisely forecast the decomposition of PG-0.9 composite. Both analyses during multiple cycle melting-crystallization and isothermal decomposition demonstrated that graphene served as decomposition accelerator in the whole thermal decomposition process, and particularly the decomposition of neat PVA and PVA/graphene composites was highly related to the band area ratios of C-H and O-H vibrations in Fourier transform infrared (FTIR) spectrum.

A fault detection scheme for time-delay systems using minimum-order functional observers

This paper presents a method for designing residual generators using minimum-order functional observers to detect actuator and component faults in time-delay systems. Existence conditions of the residual generators and functional observers are first derived, and then based on a parametric approach to the solution of a generalized Sylvester matrix equation, we develop systematic procedures for designing minimum-order functional observers to detect faults in the system. The advantages of having minimum-order observers are obvious from the economical and practical points of view as cost saving and simplicity can be achieved, particularly when dealing with high-order complex systems. Extensive numerical examples are given to illustrate the proposed fault detection scheme. In all the numerical examples, we design minimum-order residual generators and functional observers to detect faults in the system.

Forecasting accuracy and estimation uncertainty using VAR models with short- and long-term economic restrictions: a Monte-Carlo study

Using vector autoregressive (VAR) models and Monte-Carlo simulation methods we investigate the potential gains for forecasting accuracy and estimation uncertainty of two commonly used restrictions arising from economic relationships. The Örst reduces parameter space by imposing long-term restrictions on the behavior of economic variables as discussed by the literature on cointegration, and the second reduces parameter space by imposing short-term restrictions as discussed by the literature on serial-correlation common features (SCCF). Our simulations cover three important issues on model building, estimation, and forecasting. First, we examine the performance of standard and modiÖed information criteria in choosing lag length for cointegrated VARs with SCCF restrictions. Second, we provide a comparison of forecasting accuracy of Ötted VARs when only cointegration restrictions are imposed and when cointegration and SCCF restrictions are jointly imposed. Third, we propose a new estimation algorithm where short- and long-term restrictions interact to estimate the cointegrating and the cofeature spaces respectively. We have three basic results. First, ignoring SCCF restrictions has a high cost in terms of model selection, because standard information criteria chooses too frequently inconsistent models, with too small a lag length. Criteria selecting lag and rank simultaneously have a superior performance in this case. Second, this translates into a superior forecasting performance of the restricted VECM over the VECM, with important improvements in forecasting accuracy ñreaching more than 100% in extreme cases. Third, the new algorithm proposed here fares very well in terms of parameter estimation, even when we consider the estimation of long-term parameters, opening up the discussion of joint estimation of short- and long-term parameters in VAR models.