Two dimensional Lattice Boltzmann simulation of fluid flow through an idealized micro-structure of disordered media

This technical report discusses the application of Lattice Boltzmann Method (LBM) in the fluid flow simulation through porous filter-wall of disordered media. The diesel particulate filter (DPF) is an example of disordered media. DPF is developed as a cutting edge technology to reduce harmful particulate matter in the engine exhaust. Porous filter-wall of DPF traps these soot particles in the after-treatment of the exhaust gas. To examine the phenomena inside the DPF, researchers are looking forward to use the Lattice Boltzmann Method as a promising alternative simulation tool. The lattice Boltzmann method is comparatively a newer numerical scheme and can be used to simulate fluid flow for single-component single-phase, single-component multi-phase. It is also an excellent method for modelling flow through disordered media. The current work focuses on a single-phase fluid flow simulation inside the porous micro-structure using LBM. Firstly, the theory concerning the development of LBM is discussed. LBM evolution is always related to Lattice gas Cellular Automata (LGCA), but it is also shown that this method is a special discretized form of the continuous Boltzmann equation. Since all the simulations are conducted in two-dimensions, the equations developed are in reference with D2Q9 (two-dimensional 9-velocity) model. The artificially created porous micro-structure is used in this study. The flow simulations are conducted by considering air and CO2 gas as fluids. The numerical model used in this study is explained with a flowchart and the coding steps. The numerical code is constructed in MATLAB. Different types of boundary conditions and their importance is discussed separately. Also the equations specific to boundary conditions are derived. The pressure and velocity contours over the porous domain are studied and recorded. The results are compared with the published work. The permeability values obtained in this study can be fitted to the relation proposed by Nabovati [8], and the results are in excellent agreement within porosity range of 0.4 to 0.8.

Filtration and oxidation characteristics of a diesel oxidation catalyst and a catalyzed particulate filter : development of a 1-D 2-layer model

The emissions, filtration and oxidation characteristics of a diesel oxidation catalyst (DOC) and a catalyzed particulate filter (CPF) in a Johnson Matthey catalyzed continuously regenerating trap (CCRT ®) were studied by using computational models. Experimental data needed to calibrate the models were obtained by characterization experiments with raw exhaust sampling from a Cummins ISM 2002 engine with variable geometry turbocharging (VGT) and programmed exhaust gas recirculation (EGR). The experiments were performed at 20, 40, 60 and 75% of full load (1120 Nm) at rated speed (2100 rpm), with and without the DOC upstream of the CPF. This was done to study the effect of temperature and CPF-inlet NO2 concentrations on particulate matter oxidation in the CCRT ®. A previously developed computational model was used to determine the kinetic parameters describing the oxidation characteristics of HCs, CO and NO in the DOC and the pressure drop across it. The model was calibrated at five temperatures in the range of 280 – 465° C, and exhaust volumetric flow rates of 0.447 – 0.843 act-m3/sec. The downstream HCs, CO and NO concentrations were predicted by the DOC model to within ±3 ppm. The HCs and CO oxidation kinetics in the temperature range of 280 - 465°C and an exhaust volumetric flow rate of 0.447 - 0.843 act-m3/sec can be represented by one ’apparent’ activation energy and pre-exponential factor. The NO oxidation kinetics in the same temperature and exhaust flow rate range can be represented by ’apparent’ activation energies and pre-exponential factors in two regimes. The DOC pressure drop was always predicted within 0.5 kPa by the model. The MTU 1-D 2-layer CPF model was enhanced in several ways to better model the performance of the CCRT ®. A model to simulate the oxidation of particulate inside the filter wall was developed. A particulate cake layer filtration model which describes particle filtration in terms of more fundamental parameters was developed and coupled to the wall oxidation model. To better model the particulate oxidation kinetics, a model to take into account the NO2 produced in the washcoat of the CPF was developed. The overall 1-D 2-layer model can be used to predict the pressure drop of the exhaust gas across the filter, the evolution of particulate mass inside the filter, the particulate mass oxidized, the filtration efficiency and the particle number distribution downstream of the CPF. The model was used to better understand the internal performance of the CCRT®, by determining the components of the total pressure drop across the filter, by classifying the total particulate matter in layer I, layer II, the filter wall, and by the means of oxidation i.e. by O2, NO2 entering the filter and by NO2 being produced in the filter. The CPF model was calibrated at four temperatures in the range of 280 – 465 °C, and exhaust volumetric flow rates of 0.447 – 0.843 act-m3/sec, in CPF-only and CCRT ® (DOC+CPF) configurations. The clean filter wall permeability was determined to be 2.00E-13 m2, which is in agreement with values in the literature for cordierite filters. The particulate packing density in the filter wall had values between 2.92 kg/m3 - 3.95 kg/m3 for all the loads. The mean pore size of the catalyst loaded filter wall was found to be 11.0 µm. The particulate cake packing densities and permeabilities, ranged from 131 kg/m3 - 134 kg/m3, and 0.42E-14 m2 and 2.00E-14 m2 respectively, and are in agreement with the Peclet number correlations in the literature. Particulate cake layer porosities determined from the particulate cake layer filtration model ranged between 0.841 and 0.814 and decreased with load, which is about 0.1 lower than experimental and more complex discrete particle simulations in the literature. The thickness of layer I was kept constant at 20 µm. The model kinetics in the CPF-only and CCRT ® configurations, showed that no ’catalyst effect’ with O2 was present. The kinetic parameters for the NO2-assisted oxidation of particulate in the CPF were determined from the simulation of transient temperature programmed oxidation data in the literature. It was determined that the thermal and NO2 kinetic parameters do not change with temperature, exhaust flow rate or NO2 concentrations. However, different kinetic parameters are used for particulate oxidation in the wall and on the wall. Model results showed that oxidation of particulate in the pores of the filter wall can cause disproportionate decreases in the filter pressure drop with respect to particulate mass. The wall oxidation model along with the particulate cake filtration model were developed to model the sudden and rapid decreases in pressure drop across the CPF. The particulate cake and wall filtration models result in higher particulate filtration efficiencies than with just the wall filtration model, with overall filtration efficiencies of 98-99% being predicted by the model. The pre-exponential factors for oxidation by NO2 did not change with temperature or NO2 concentrations because of the NO2 wall production model. In both CPF-only and CCRT ® configurations, the model showed NO2 and layer I to be the dominant means and dominant physical location of particulate oxidation respectively. However, at temperatures of 280 °C, NO2 is not a significant oxidizer of particulate matter, which is in agreement with studies in the literature. The model showed that 8.6 and 81.6% of the CPF-inlet particulate matter was oxidized after 5 hours at 20 and 75% load in CCRT® configuration. In CPF-only configuration at the same loads, the model showed that after 5 hours, 4.4 and 64.8% of the inlet particulate matter was oxidized. The increase in NO2 concentrations across the DOC contributes significantly to the oxidation of particulate in the CPF and is supplemented by the oxidation of NO to NO2 by the catalyst in the CPF, which increases the particulate oxidation rates. From the model, it was determined that the catalyst in the CPF modeslty increases the particulate oxidation rates in the range of 4.5 – 8.3% in the CCRT® configuration. Hence, the catalyst loading in the CPF of the CCRT® could possibly be reduced without significantly decreasing particulate oxidation rates leading to catalyst cost savings and better engine performance due to lower exhaust backpressures.

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.

Seismic observations of regional gas blowdown at Teal South

A re-examination of seismic time-lapse data from the Teal South field provides support for a previously proposed model of regional pressure decline and the associated liberation of gas from nearby reservoirs due to the production from the only reservoir among them that is under production. The use of a specific attribute, instantaneous amplitude, and a series of time slices, however, provides increased detail in understanding fluid migration into or out of the reservoirs, and the path taken by pressure changes across faults. The regional decrease of pressure due to production in one reservoir has dramatic effects in nearby untapped reservoirs, one of which appears to exhibit evidence for the escape, and possible re-trapping nearby, of hydrocarbons from a spill point. The influx of water into the producing reservoir is also evidenced by a decrease in amplitude at one end of the oil-water contact.

IS THE U.S. SHALE GAS BOOM HAVING AN EFFECT ON THE EUROPEAN GAS MARKET?

This thesis focuses on the impact of the American shale gas boom on the European natural gas market. The study presents different tests in order to analyze the dynamics of natural gas prices in the U.S., U.K. and German natural gas market. The question of cointegration between these different markets are analyzed using several tests. More specifically, the ADF tests for the presence of a unit root. The error correction model test and the Johansen cointegration procedure are applied in order to accept or reject the hypothesis of an integrated market. The results suggest no evidence of cointegration between these markets. There currently is no evidence of an impact of the U.S. shale gas boom on the European market.

DESIGN AND FABRICATION OF RESONANT GAS SENSOR FOR HIGH SENSITIVITY IN THE PRESENCE OF AIR DAMPING

Gas sensors have been used widely in different important area including industrial control, environmental monitoring, counter-terrorism and chemical production. Micro-fabrication offers a promising way to achieve sensitive and inexpensive gas sensors. Over the years, various MEMS gas sensors have been investigated and fabricated. One significant type of MEMS gas sensors is based on mass change detection and the integration with specific polymer. This dissertation aims to make contributions to the design and fabrication of MEMS resonant mass sensors with capacitance actuation and sensing that lead to improved sensitivity. To accomplish this goal, the research has several objectives: (1) Define an effective measure for evaluating the sensitivity of resonant mass devices; (2) Model the effects of air damping on microcantilevers and validate models using laser measurement system (3) Develop design guidelines for improving sensitivity in the presence of air damping; (4) Characterize the degree of uncertainty in performance arising from fabrication variation for one or more process sequences, and establish design guidelines for improved robustness. Work has been completed toward these objectives. An evaluation measure has been developed and compared to an RMS based measure. Analytic models of air damping for parallel plate that include holes are compared with a COMSOL model. The models have been used to identify cantilever design parameters that maximize sensitivity. Additional designs have been modeled with COMSOL and the development of an analytical model for Fixed-free cantilever geometries with holes has been developed. Two process flows have been implemented and compared. A number of cantilever designs have been fabricated and the uncertainty in process has been investigated. Variability from processing have been evaluated and characterized.

LATTICE BOLTZMANN METHOD AND CELLULAR AUTOMATA SIMULATION OF PARTICLE MOTION AND DEPOSITION IN 2-D CASE

This technical report discusses the application of the Lattice Boltzmann Method (LBM) and Cellular Automata (CA) simulation in fluid flow and particle deposition. The current work focuses on incompressible flow simulation passing cylinders, in which we incorporate the LBM D2Q9 and CA techniques to simulate the fluid flow and particle loading respectively. For the LBM part, the theories of boundary conditions are studied and verified using the Poiseuille flow test. For the CA part, several models regarding simulation of particles are explained. And a new Digital Differential Analyzer (DDA) algorithm is introduced to simulate particle motion in the Boolean model. The numerical results are compared with a previous probability velocity model by Masselot [Masselot 2000], which shows a satisfactory result.

Assessments and Computational Simulations in Support of a Time-Varying Mass Flow Rate Measurement Technique for Pulsatile Gas Flow

This thesis covers the correction, and verification, development, and implementation of a computational fluid dynamics (CFD) model for an orifice plate meter. Past results were corrected and further expanded on with compressibility effects of acoustic waves being taken into account. One dynamic pressure difference transducer measures the time-varying differential pressure across the orifice meter. A dynamic absolute pressure measurement is also taken at the inlet of the orifice meter, along with a suitable temperature measurement of the mean flow gas. Together these three measurements allow for an incompressible CFD simulation (using a well-tested and robust model) for the cross-section independent time-varying mass flow rate through the orifice meter. The mean value of this incompressible mass flow rate is then corrected to match the mean of the measured flow rate( obtained from a Coriolis meter located up stream of the orifice meter). Even with the mean and compressibility corrections, significant differences in the measured mass flow rates at two orifice meters in a common flow stream were observed. This means that the compressibility effects associated with pulsatile gas flows is significant in the measurement of the time-varying mass flow rate. Future work (with the approach and initial runs covered here) will provide an indirect verification of the reported mass flow rate measurements.

MODELING DYNAMICS OF OZONE AND NITROGEN OXIDES AT SUMMIT, GREENLAND WITH A 1-D PROCESS-SCALE MODEL

This work presents a 1-D process scale model used to investigate the chemical dynamics and temporal variability of nitrogen oxides (NOx) and ozone (O3) within and above snowpack at Summit, Greenland for March-May 2009 and estimates surface exchange of NOx between the snowpack and surface layer in April-May 2009. The model assumes the surface of snowflakes have a Liquid Like Layer (LLL) where aqueous chemistry occurs and interacts with the interstitial air of the snowpack. Model parameters and initialization are physically and chemically representative of snowpack at Summit, Greenland and model results are compared to measurements of NOx and O3 collected by our group at Summit, Greenland from 2008-2010. The model paired with measurements confirmed the main hypothesis in literature that photolysis of nitrate on the surface of snowflakes is responsible for nitrogen dioxide (NO2) production in the top ~50 cm of the snowpack at solar noon for March – May time periods in 2009. Nighttime peaks of NO2 in the snowpack for April and May were reproduced with aqueous formation of peroxynitric acid (HNO4) in the top ~50 cm of the snowpack with subsequent mass transfer to the gas phase, decomposition to form NO2 at nighttime, and transportation of the NO2 to depths of 2 meters. Modeled production of HNO4 was hindered in March 2009 due to the low production of its precursor, hydroperoxy radical, resulting in underestimation of nighttime NO2 in the snowpack for March 2009. The aqueous reaction of O3 with formic acid was the major sync of O3 in the snowpack for March-May, 2009. Nitrogen monoxide (NO) production in the top ~50 cm of the snowpack is related to the photolysis of NO2, which underrepresents NO in May of 2009. Modeled surface exchange of NOx in April and May are on the order of 1011 molecules m-2 s-1. Removal of measured downward fluxes of NO and NO2 in measured fluxes resulted in agreement between measured NOx fluxes and modeled surface exchange in April and an order of magnitude deviation in May. Modeled transport of NOx above the snowpack in May shows an order of magnitude increase of NOx fluxes in the first 50 cm of the snowpack and is attributed to the production of NO2 during the day from the thermal decomposition and photolysis of peroxynitric acid with minor contributions of NO from HONO photolysis in the early morning.

DEVELOPMENT OF CONFOCAL IMAGING TECHNIQUES FOR PROBING INTERFACIAL DYNAMICS IN MICROSCALE, GAS-LIQUID, TWO-PHASE FLOW

Micro-scale, two-phase flow is found in a variety of devices such as Lab-on-a-chip, bio-chips, micro-heat exchangers, and fuel cells. Knowledge of the fluid behavior near the dynamic gas-liquid interface is required for developing accurate predictive models. Light is distorted near a curved gas-liquid interface preventing accurate measurement of interfacial shape and internal liquid velocities. This research focused on the development of experimental methods designed to isolate and probe dynamic liquid films and measure velocity fields near a moving gas-liquid interface. A high-speed, reflectance, swept-field confocal (RSFC) imaging system was developed for imaging near curved surfaces. Experimental studies of dynamic gas-liquid interface of micro-scale, two-phase flow were conducted in three phases. Dynamic liquid film thicknesses of segmented, two-phase flow were measured using the RSFC and compared to a classic film thickness deposition model. Flow fields near a steadily moving meniscus were measured using RSFC and particle tracking velocimetry. The RSFC provided high speed imaging near the menisci without distortion caused the gas-liquid interface. Finally, interfacial morphology for internal two-phase flow and droplet evaporation were measured using interferograms produced by the RSFC imaging technique. Each technique can be used independently or simultaneously when.

Development of a 1-D Catalyzed Diesel Particulate Filter Model for Simulation of the Performance and the Oxidation of Particulate Matter and Nitrogen Oxides Using Passive Oxidation and Active Regeneration Engine Experimental Data

Back-pressure on a diesel engine equipped with an aftertreatment system is a function of the pressure drop across the individual components of the aftertreatment system, typically, a diesel oxidation catalyst (DOC), catalyzed particulate filter (CPF) and selective catalytic reduction (SCR) catalyst. Pressure drop across the CPF is a function of the mass flow rate and the temperature of the exhaust flowing through it as well as the mass of particulate matter (PM) retained in the substrate wall and the cake layer that forms on the substrate wall. Therefore, in order to control the back-pressure on the engine at low levels and to minimize the fuel consumption, it is important to control the PM mass retained in the CPF. Chemical reactions involving the oxidation of PM under passive oxidation and active regeneration conditions can be utilized with computer numerical models in the engine control unit (ECU) to control the pressure drop across the CPF. Hence, understanding and predicting the filtration and oxidation of PM in the CPF and the effect of these processes on the pressure drop across the CPF are necessary for developing control strategies for the aftertreatment system to reduce back-pressure on the engine and in turn fuel consumption particularly from active regeneration. Numerical modeling of CPF's has been proven to reduce development time and the cost of aftertreatment systems used in production as well as to facilitate understanding of the internal processes occurring during different operating conditions that the particulate filter is subjected to. A numerical model of the CPF was developed in this research work which was calibrated to data from passive oxidation and active regeneration experiments in order to determine the kinetic parameters for oxidation of PM and nitrogen oxides along with the model filtration parameters. The research results include the comparison between the model and the experimental data for pressure drop, PM mass retained, filtration efficiencies, CPF outlet gas temperatures and species (NO2) concentrations out of the CPF. Comparisons of PM oxidation reaction rates obtained from the model calibration to the data from the experiments for ULSD, 10 and 20% biodiesel-blended fuels are presented.