Three dimensional finite element simulation of polymer melting and flow in a single-screw extruder : optimization of screw channel geometry

Single-screw extrusion is one of the widely used processing methods in plastics industry, which was the third largest manufacturing industry in the United States in 2007 [5]. In order to optimize the single-screw extrusion process, tremendous efforts have been devoted for development of accurate models in the last fifty years, especially for polymer melting in screw extruders. This has led to a good qualitative understanding of the melting process; however, quantitative predictions of melting from various models often have a large error in comparison to the experimental data. Thus, even nowadays, process parameters and the geometry of the extruder channel for the single-screw extrusion are determined by trial and error. Since new polymers are developed frequently, finding the optimum parameters to extrude these polymers by trial and error is costly and time consuming. In order to reduce the time and experimental work required for optimizing the process parameters and the geometry of the extruder channel for a given polymer, the main goal of this research was to perform a coordinated experimental and numerical investigation of melting in screw extrusion. In this work, a full three-dimensional finite element simulation of the two-phase flow in the melting and metering zones of a single-screw extruder was performed by solving the conservation equations for mass, momentum, and energy. The only attempt for such a three-dimensional simulation of melting in screw extruder was more than twenty years back. However, that work had only a limited success because of the capability of computers and mathematical algorithms available at that time. The dramatic improvement of computational power and mathematical knowledge now make it possible to run full 3-D simulations of two-phase flow in single-screw extruders on a desktop PC. In order to verify the numerical predictions from the full 3-D simulations of two-phase flow in single-screw extruders, a detailed experimental study was performed. This experimental study included Maddock screw-freezing experiments, Screw Simulator experiments and material characterization experiments. Maddock screw-freezing experiments were performed in order to visualize the melting profile along the single-screw extruder channel with different screw geometry configurations. These melting profiles were compared with the simulation results. Screw Simulator experiments were performed to collect the shear stress and melting flux data for various polymers. Cone and plate viscometer experiments were performed to obtain the shear viscosity data which is needed in the simulations. An optimization code was developed to optimize two screw geometry parameters, namely, screw lead (pitch) and depth in the metering section of a single-screw extruder, such that the output rate of the extruder was maximized without exceeding the maximum temperature value specified at the exit of the extruder. This optimization code used a mesh partitioning technique in order to obtain the flow domain. The simulations in this flow domain was performed using the code developed to simulate the two-phase flow in single-screw extruders.

Development of an optimization model for biofuel facility size and location and a simulation model for design of a biofuel supply chain

To mitigate greenhouse gas (GHG) emissions and reduce U.S. dependence on imported oil, the United States (U.S.) is pursuing several options to create biofuels from renewable woody biomass (hereafter referred to as “biomass”). Because of the distributed nature of biomass feedstock, the cost and complexity of biomass recovery operations has significant challenges that hinder increased biomass utilization for energy production. To facilitate the exploration of a wide variety of conditions that promise profitable biomass utilization and tapping unused forest residues, it is proposed to develop biofuel supply chain models based on optimization and simulation approaches. The biofuel supply chain is structured around four components: biofuel facility locations and sizes, biomass harvesting/forwarding, transportation, and storage. A Geographic Information System (GIS) based approach is proposed as a first step for selecting potential facility locations for biofuel production from forest biomass based on a set of evaluation criteria, such as accessibility to biomass, railway/road transportation network, water body and workforce. The development of optimization and simulation models is also proposed. The results of the models will be used to determine (1) the number, location, and size of the biofuel facilities, and (2) the amounts of biomass to be transported between the harvesting areas and the biofuel facilities over a 20-year timeframe. The multi-criteria objective is to minimize the weighted sum of the delivered feedstock cost, energy consumption, and GHG emissions simultaneously. Finally, a series of sensitivity analyses will be conducted to identify the sensitivity of the decisions, such as the optimal site selected for the biofuel facility, to changes in influential parameters, such as biomass availability and transportation fuel price. Intellectual Merit The proposed research will facilitate the exploration of a wide variety of conditions that promise profitable biomass utilization in the renewable biofuel industry. The GIS-based facility location analysis considers a series of factors which have not been considered simultaneously in previous research. Location analysis is critical to the financial success of producing biofuel. The modeling of woody biomass supply chains using both optimization and simulation, combing with the GIS-based approach as a precursor, have not been done to date. The optimization and simulation models can help to ensure the economic and environmental viability and sustainability of the entire biofuel supply chain at both the strategic design level and the operational planning level. Broader Impacts The proposed models for biorefineries can be applied to other types of manufacturing or processing operations using biomass. This is because the biomass feedstock supply chain is similar, if not the same, for biorefineries, biomass fired or co-fired power plants, or torrefaction/pelletization operations. Additionally, the research results of this research will continue to be disseminated internationally through publications in journals, such as Biomass and Bioenergy, and Renewable Energy, and presentations at conferences, such as the 2011 Industrial Engineering Research Conference. For example, part of the research work related to biofuel facility identification has been published: Zhang, Johnson and Sutherland [2011] (see Appendix A). There will also be opportunities for the Michigan Tech campus community to learn about the research through the Sustainable Future Institute.

DEVELOPMENT OF AN OPTIMIZATION MODEL FOR BIOFUEL FACILITY SIZE AND LOCATION AND A SIMULATION MODEL FOR DESIGN OF A BIOFUEL SUPPLY CHAIN

A range of societal issues have been caused by fossil fuel consumption in the transportation sector in the United States (U.S.), including health related air pollution, climate change, the dependence on imported oil, and other oil related national security concerns. Biofuels production from various lignocellulosic biomass types such as wood, forest residues, and agriculture residues have the potential to replace a substantial portion of the total fossil fuel consumption. This research focuses on locating biofuel facilities and designing the biofuel supply chain to minimize the overall cost. For this purpose an integrated methodology was proposed by combining the GIS technology with simulation and optimization modeling methods. The GIS based methodology was used as a precursor for selecting biofuel facility locations by employing a series of decision factors. The resulted candidate sites for biofuel production served as inputs for simulation and optimization modeling. As a precursor to simulation or optimization modeling, the GIS-based methodology was used to preselect potential biofuel facility locations for biofuel production from forest biomass. Candidate locations were selected based on a set of evaluation criteria, including: county boundaries, a railroad transportation network, a state/federal road transportation network, water body (rivers, lakes, etc.) dispersion, city and village dispersion, a population census, biomass production, and no co-location with co-fired power plants. The simulation and optimization models were built around key supply activities including biomass harvesting/forwarding, transportation and storage. The built onsite storage served for spring breakup period where road restrictions were in place and truck transportation on certain roads was limited. Both models were evaluated using multiple performance indicators, including cost (consisting of the delivered feedstock cost, and inventory holding cost), energy consumption, and GHG emissions. The impact of energy consumption and GHG emissions were expressed in monetary terms to keep consistent with cost. Compared with the optimization model, the simulation model represents a more dynamic look at a 20-year operation by considering the impacts associated with building inventory at the biorefinery to address the limited availability of biomass feedstock during the spring breakup period. The number of trucks required per day was estimated and the inventory level all year around was tracked. Through the exchange of information across different procedures (harvesting, transportation, and biomass feedstock processing procedures), a smooth flow of biomass from harvesting areas to a biofuel facility was implemented. The optimization model was developed to address issues related to locating multiple biofuel facilities simultaneously. The size of the potential biofuel facility is set up with an upper bound of 50 MGY and a lower bound of 30 MGY. The optimization model is a static, Mathematical Programming Language (MPL)-based application which allows for sensitivity analysis by changing inputs to evaluate different scenarios. It was found that annual biofuel demand and biomass availability impacts the optimal results of biofuel facility locations and sizes.

Optimization of Monte Carlo code for clinical simulation of electron beams

The aim of this work is to optimize a Monte Carlo (MC) kernel for electron radiation therapy (IOERT) compatible with intraoperative usage and to integrate it within an existing IOERT dedicated treatment planning system (TPS)

Optimization of chemical plant simulation using double collocation

A method has been constructed for the solution of a wide range of chemical plant simulation models including differential equations and optimization. Double orthogonal collocation on finite elements is applied to convert the model into an NLP problem that is solved either by the VF 13AD package based on successive quadratic programming, or by the GRG2 package, based on the generalized reduced gradient method. This approach is termed simultaneous optimization and solution strategy. The objective functional can contain integral terms. The state and control variables can have time delays. Equalities and inequalities containing state and control variables can be included into the model as well as algebraic equations and inequalities. The maximum number of independent variables is 2. Problems containing 3 independent variables can be transformed into problems having 2 independent variables using finite differencing. The maximum number of NLP variables and constraints is 1500. The method is also suitable for solving ordinary and partial differential equations. The state functions are approximated by a linear combination of Lagrange interpolation polynomials. The control function can either be approximated by a linear combination of Lagrange interpolation polynomials or by a piecewise constant function over finite elements. The number of internal collocation points can vary by finite elements. The residual error is evaluated at arbitrarily chosen equidistant grid-points, thus enabling the user to check the accuracy of the solution between collocation points, where the solution is exact. The solution functions can be tabulated. There is an option to use control vector parameterization to solve optimization problems containing initial value ordinary differential equations. When there are many differential equations or the upper integration limit should be selected optimally then this approach should be used. The portability of the package has been addressed converting the package from V AX FORTRAN 77 into IBM PC FORTRAN 77 and into SUN SPARC 2000 FORTRAN 77. Computer runs have shown that the method can reproduce optimization problems published in the literature. The GRG2 and the VF I 3AD packages, integrated into the optimization package, proved to be robust and reliable. The package contains an executive module, a module performing control vector parameterization and 2 nonlinear problem solver modules, GRG2 and VF I 3AD. There is a stand-alone module that converts the differential-algebraic optimization problem into a nonlinear programming problem.

Evaluating the effectiveness of signal timing optimization based on microscopic simulation evaluation

The optimization of the timing parameters of traffic signals provides for efficient operation of traffic along a signalized transportation system. Optimization tools with macroscopic simulation models have been used to determine optimal timing plans. These plans have been, in some cases, evaluated and fine tuned using microscopic simulation tools. A number of studies show inconsistencies between optimization tool results based on macroscopic simulation and the results obtained from microscopic simulation. No attempts have been made to determine the reason behind these inconsistencies. This research investigates whether adjusting the parameters of macroscopic simulation models to correspond to the calibrated microscopic simulation model parameters can reduce said inconsistencies. The adjusted parameters include platoon dispersion model parameters, saturation flow rates, and cruise speeds. The results from this work show that adjusting cruise speeds and saturation flow rates can have significant impacts on improving the optimization/macroscopic simulation results as assessed by microscopic simulation models.

Model optimization and techniques for the simulation of multiphase chemical reactors

Otto-von-Guericke-Universität Magdeburg, Fakultät für Verfahrens- und Systemtechnik, Dissertation, 2016

Development of numerical tools for the simulation, design and optimization of a Helicon Plasma Thruster

This work thesis focuses on the Helicon Plasma Thruster (HPT) as a candidate for generating thrust for small satellites and CubeSats. Two main topics are addressed: the development of a Global Model (GM) and a 3D self-consistent numerical tool. The GM is suitable for preliminary analysis of HPTs with noble gases such as argon, neon, krypton, and xenon, and alternative propellants such as air and iodine. A lumping methodology is developed to reduce the computational cost when modelling the excited species in the plasma chemistry. A 3D self-consistent numerical tool is also developed that can treat discharges with a generic 3D geometry and model the actual plasma-antenna coupling. The tool consists of two main modules, an EM module and a FLUID module, which run iteratively until a steady state solution is converged. A third module is available for solving the plume with a simplified semi-analytical approach, a PIC code, or directly by integration of the fluid equations. Results obtained from both the numerical tools are benchmarked against experimental measures of HPTs or Helicon reactors, obtaining very good qualitative agreement with the experimental trend for what concerns the GM, and an excellent agreement of the physical trends predicted against the measured data for the 3D numerical strategy.

Simulation of sugarcane residue decomposition and aboveground growth

Due to the worldwide increase in demand for biofuels, the area cultivated with sugarcane is expected to increase. For environmental and economic reasons, an increasing proportion of the areas are being harvested without burning, leaving the residues on the soil surface. This periodical input of residues affects soil physical, chemical and biological properties, as well as plant growth and nutrition. Modeling can be a useful tool in the study of the complex interactions between the climate, residue quality, and the biological factors controlling plant growth and residue decomposition. The approach taken in this work was to parameterize the CENTURY model for the sugarcane crop, to simulate the temporal dynamics of aboveground phytomass and litter decomposition, and to validate the model through field experiment data. When studying aboveground growth, burned and unburned harvest systems were compared, as well as the effect of mineral fertilizer and organic residue applications. The simulations were performed with data from experiments with different durations, from 12 months to 60 years, in Goiana, TimbaA(0)ba and Pradpolis, Brazil; Harwood, Mackay and Tully, Australia; and Mount Edgecombe, South Africa. The differentiation of two pools in the litter, with different decomposition rates, was found to be a relevant factor in the simulations made. Originally, the model had a basically unlimited layer of mulch directly available for decomposition, 5,000 g m(-2). Through a parameter optimization process, the thickness of the mulch layer closer to the soil, more vulnerable to decomposition, was set as 110 g m(-2). By changing the layer of mulch at any given time available for decomposition, the sugarcane residues decomposition simulations where close to measured values (R (2) = 0.93), contributing to making the CENTURY model a tool for the study of sugarcane litter decomposition patterns. The CENTURY model accurately simulated aboveground carbon stalk values (R (2) = 0.76), considering burned and unburned harvest systems, plots with and without nitrogen fertilizer and organic amendment applications, in different climates and soil conditions.

A simulation-based evolutionary multiobjective approach to manufacturing cell formation

The purpose of this paper is to propose a multiobjective optimization approach for solving the manufacturing cell formation problem, explicitly considering the performance of this said manufacturing system. Cells are formed so as to simultaneously minimize three conflicting objectives, namely, the level of the work-in-process, the intercell moves and the total machinery investment. A genetic algorithm performs a search in the design space, in order to approximate to the Pareto optimal set. The values of the objectives for each candidate solution in a population are assigned by running a discrete-event simulation, in which the model is automatically generated according to the number of machines and their distribution among cells implied by a particular solution. The potential of this approach is evaluated via its application to an illustrative example, and a case from the relevant literature. The obtained results are analyzed and reviewed. Therefore, it is concluded that this approach is capable of generating a set of alternative manufacturing cell configurations considering the optimization of multiple performance measures, greatly improving the decision making process involved in planning and designing cellular systems. (C) 2010 Elsevier Ltd. All rights reserved.

Acoustic Simulation of a Special Switched Reluctance Drive by Means of Field-Circuit Coupling and Multiphysics Simulation

The approach presented in this paper consists of an energy-based field-circuit coupling in combination with multi-physics simulation of the acoustic radiation of electrical machines. The proposed method is applied to a special switched reluctance motor with asymmetric pole geometry to improve the start-up torque. The pole shape has been optimized, subject to low torque ripple, in a previous study. The proposed approach here is used to analyze the impact of the optimization on the overall acoustic behavior. The field-circuit coupling is based on a temporary lumped-parameter model of the magnetic part incorporated into a circuit simulation based on the modified nodal analysis. The harmonic force excitation is calculated by means of stress tensor computation, and it is transformed to a mechanical mesh by mapping techniques. The structural dynamic problem is solved in the frequency domain using a finite-element modal analysis and superposition. The radiation characteristic is obtained from boundary element acoustic simulation. Simulation results of both rotor types are compared, and measurements of the drive are presented.

Robust integration of real time optimization with linear model predictive control

Here, we study the stable integration of real time optimization (RTO) with model predictive control (MPC) in a three layer structure. The intermediate layer is a quadratic programming whose objective is to compute reachable targets to the MPC layer that lie at the minimum distance to the optimum set points that are produced by the RTO layer. The lower layer is an infinite horizon MPC with guaranteed stability with additional constraints that force the feasibility and convergence of the target calculation layer. It is also considered the case in which there is polytopic uncertainty in the steady state model considered in the target calculation. The dynamic part of the MPC model is also considered unknown but it is assumed to be represented by one of the models of a discrete set of models. The efficiency of the methods presented here is illustrated with the simulation of a low order system. (C) 2010 Elsevier Ltd. All rights reserved.

Real time optimization (RTO) with model predictive control (MPC)

This paper studies a simplified methodology to integrate the real time optimization (RTO) of a continuous system into the model predictive controller in the one layer strategy. The gradient of the economic objective function is included in the cost function of the controller. Optimal conditions of the process at steady state are searched through the use of a rigorous non-linear process model, while the trajectory to be followed is predicted with the use of a linear dynamic model, obtained through a plant step test. The main advantage of the proposed strategy is that the resulting control/optimization problem can still be solved with a quadratic programming routine at each sampling step. Simulation results show that the approach proposed may be comparable to the strategy that solves the full economic optimization problem inside the MPC controller where the resulting control problem becomes a non-linear programming problem with a much higher computer load. (C) 2010 Elsevier Ltd. All rights reserved.

Simulation of irrigated Thanzania grass growth based on photothermal units, nitrogen fertilization and water availability

Simulation of irrigated Thanzania grass growth based on photothermal units, nitrogen fertilization and water availability. The mathematical model to predict the forage yield using photothennal units was utilized with success in Elephant grass, Thanzania and Brachiaria niziziensis in the absence of water stress and nitrogen stress. The aim of this study was to propose models to estimate the forage yield of Thanzania grass under different irrigation (25, 50,75, 100 e 125% of ETc) and nitrogen level in various regions of Brazil. As such, models were developed to estimate the dry matter production of Panicum maximum Jacq. frass cv Thanzania in different irrigation and nitrogen levels, using photothermal units. The models were adjusted to doses of 0, 30, 60, 110 and 270 kg of N ha(-1), doses were divided in applications after each evaluation, with a rest cycle of 35 days. The adjusted model presented good performance in predicting dry matter production of Thanzania grass, with r(2) = 0.9999. The results made it possible to verify that the proposed model can be used to predict forage production in different regions of Brazil. It can be estimated, with good precision. The production of Thanzania grass dry matter can be accurately estimated in specific places (in function of latitude and time of year), with the maximum and minimum temperature values.