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At least 1,081 records · Page 60

Greening the Grid: Pathways to Integrate 175 Gigawatts of Renewable Energy into India's Electric Grid, Vol. I -- National Study

The use of renewable energy (RE) sources, primarily wind and solar generation, is poised to grow significantly within the Indian power system. The Government of India has established a target of 175 gigawatts (GW) of installed RE capacity by 2022, including 60 GW of wind and 100 GW of solar, up from 29 GW wind and 9 GW solar at the beginning of 2017. Thanks to advanced weather and power system modeling made for this project, the study team is able to explore operational impacts of meeting India's RE targets and identify actions that may be favorable for integration. Our primary tool is a detailed production cost model, which simulates optimal scheduling and dispatch of available generation in a future year (2022) by minimizing total production costs subject to physical, operational, and market constraints. Our team comprises a core group from the Power System Operation Corporation, Ltd. (POSOCO), which is the national grid operator (with representation from the National, Southern, and Western Regional Load Dispatch Centers) under Ministry of Power, National Renewable Energy Laboratory (NREL), and Lawrence Berkeley National Laboratory (LBNL), and a broader modeling team that includes Central Electricity Authority (CEA), POWERGRID (the central transmission utility, CTU), and State Load Dispatch Centers in Maharashtra, Gujarat, Tamil Nadu, Karnataka, Rajasthan, and Andhra Pradesh. Our model includes high-resolution wind and solar data (forecasts and actuals), unique properties for each generator, CEA/CTU's anticipated buildout of the power system, and enforced state-to-state transmission flows. Assuming the fulfillment of current efforts to provide better access to the physical flexibility of the power system, we find that power system balancing with 100 GW of solar and 60 GW of wind is achievable at 15-minute operational timescales with minimal RE curtailment. This RE capacity meets 22% of total projected 2022 electricity consumption in India with annual RE curtailment of 1.4%, in line with experiences in other countries with significant RE penetrations (Bird et al. 2016). Changes to operational practice can further reduce the cost of operating the power system and reduce RE curtailment. Coordinating scheduling and dispatch over a broader area is the largest driver to reduce costs, saving INR 6300 crore (USD $920 million) annually when optimized regionally. Lowering minimum operating levels of coal plants (from 70% to 40%) is the biggest driver to reduce RE curtailment - from 3.5% down to 0.76%. In fact, this operating property is more influential than faster thermal generation ramp rates in lowering the projected levels of curtailment. While this study does not answer every question relevant to planning for India's 2022 RE targets, it is an important step toward analyzing operational challenges and cost saving opportunities using state-of-the-art power system planning tools. Further analysis can build upon this basis to explore optimal renewable resource and intrastate transmission siting, system stability during contingencies, and the influence of total power system investment costs on customer tariffs.

24 POWER TRANSMISSION AND DISTRIBUTION↗

MOOSE IPL Extensions (Control Logic)

In FY-2015, the development of MOOSE was driven by the needs of the NEAMS MOOSE-based applications, BISON, MARMOT, and RELAP-7. An emphasis was placed on the continued upkeep and improvement MOOSE in support of the product line integration goals. New unified documentation tools have been developed, several improvements to regression testing have been enforced and overall better software quality practices have been implemented. In addition the Multiapps and Transfers systems have seen significant refactoring and robustness improvements, as has the “Restart and Recover” system in support of Multiapp simulations. Finally, a completely new “Control Logic” system has been engineered to replace the prototype system currently in use in the RELAP-7 code. The development of this system continues and is expected to handle existing needs as well as support future enhancements.

97 MATHEMATICS AND COMPUTING↗

Greening the Grid: Pathways to Integrate 175 Gigawatts of Renewable Energy into India’s Electric Grid, Vol. 1. National Study

The use of renewable energy (RE) sources, primarily wind and solar generation, is poised to grow significantly within the Indian power system. The Government of India has established a target of 175 gigawatts (GW) of installed RE capacity by 2022, including 60 GW of wind and 100 GW of solar, up from 29 GW wind and 9 GW solar at the beginning of 2017. Using advanced weather and power system modeling made for this project, the study team is able to explore operational impacts of meeting India’s RE targets and identify actions that may be favorable for integration. Our primary tool is a detailed production cost model, which simulates optimal scheduling and dispatch of available generation in a future year (2022) by minimizing total production costs subject to physical, operational, and market constraints. Our team comprises a core group from the Power System Operation Corporation, Ltd. (POSOCO), which is the national grid operator (with representation from the National, Southern, and Western Regional Load Dispatch Centers) under Ministry of Power, National Renewable Energy Laboratory (NREL), and Lawrence Berkeley National Laboratory (Berkeley Lab), and a broader modeling team that includes Central Electricity Authority (CEA), POWERGRID (the central transmission utility, CTU), and State Load Dispatch Centers in Maharashtra, Gujarat, Tamil Nadu, Karnataka, Rajasthan, and Andhra Pradesh. Our model includes high-resolution wind and solar data (forecasts and actuals), unique properties for each generator, CEA/CTU’s anticipated buildout of the power system, and enforced state-to-state transmission flows. Assuming the fulfillment of current efforts to provide better access to the physical flexibility of the power system, we find that power system balancing with 100 GW of solar and 60 GW of wind is achievable at 15-minute operational timescales with minimal RE curtailment. This RE capacity meets 22% of total projected 2022 electricity consumption in India with annual RE curtailment of 1.4%, in line with experiences in other countries with significant RE penetrations (Bird et al. 2016). Changes to operational practice can further reduce the cost of operating the power system and reduce RE curtailment. Coordinating scheduling and dispatch over a broader area is the largest driver to reduce costs, saving INR 6300 crore (USD 980 million) annually when optimized regionally. Lowering minimum operating levels of coal plants (from 70% to 40%) is the biggest driver to reduce RE curtailment—from 3.5% down to 0.76%. In fact, this operating property is more influential than faster thermal generation ramp rates in lowering the projected levels of curtailment. While this study does not answer every question relevant to planning for India’s 2022 RE targets, it is an important step toward analyzing operational challenges and cost saving opportunities using state-of-the-art power system planning tools. Further analysis can build upon this basis to explore optimal renewable resource and intrastate transmission siting, system stability during contingencies, and the influence of total power system investment costs on customer tariffs.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Predicting Baseline for Analysis of Electricity Pricing

To understand the impact of new pricing structure on residential electricity demands, we need a baseline model that captures every factor other than the new price. The standard baseline is a randomized control group, however, a good control group is hard to design. This motivates us to devlop data-driven approaches. We explored many techniques and designed a strategy, named LTAP, that could predict the hourly usage years ahead. The key challenge in this process is that the daily cycle of electricity demand peaks a few hours after the temperature reaching its peak. Existing methods rely on the lagged variables of recent past usages to enforce this daily cycle. These methods have trouble making predictions years ahead. LTAP avoids this trouble by assuming the daily usage profile is determined by temperature and other factors. In a comparison against a well-designed control group, LTAP is found to produce accurate predictions.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Energy Efficiency Roadmap for Uganda, Making Energy Efficiency Count. Executive Summary

Like many countries in Sub-Saharan Africa, Uganda has focused its energy sector investments largely on increasing energy access by increasing energy supply. The links between energy efficiency and energy access, the importance of energy efficiency in new energy supply, and the multiple benefits of energy efficiency for the level and quality of energy available, have been largely overlooked. Implementing energy efficiency in parallel with expanding both the electricity grid and new clean energy generation reduces electricity demand and helps optimize the power supply so that it can serve more customers reliably at minimum cost. Ensuring efficient appliances are incorporated into energy access efforts provides improved energy services to customers. Energy efficiency is an important contributor to access to modern energy. This Energy Efficiency Roadmap for Uganda (Roadmap) is a response to the important role that electrical energy efficiency can play in meeting Uganda’s energy goals. Power Africa and the United Nations Sustainable Energy for All (SEforALL) initiatives collaborated with more than 24 stakeholders in Uganda to develop this document. The document estimates that if the most efficient technologies on the market were adopted, 2,224 gigawatt hours could be saved in 2030 across all sectors, representing 31% of the projected load. This translates into 341 megawatts of peak demand reductions, energy access to an additional 6 million rural customers and reduction of carbon dioxide emissions by 10.6 million tonnes in 2030. The Roadmap also finds that 91% of this technical potential is cost-effective, and 47% is achievable under conservative assumptions. The Roadmap prioritizes recommendations for implementing energy efficiency and maximizing benefits to meet the goals and priorities established in Uganda’s 2015 SEforALL Action Agenda. One important step is to create and increase demand for efficiency through long-term enabling policies and financial incentives combined with development of technical expertise in the labor force to allow for the promotion of new business models, such as energy service companies. A combination of enabling policies, financial schemes, regulations, enforcement, and skill development are needed to open the energy efficiency market.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Insights Gained from Forensic Analysis with MELCOR of the Fukushima-Daiichi Accidents.

Since the accidents at Fukushima-Daiichi, Sandia National Laboratories has been modeling these accident scenarios using the severe accident analysis code, MELCOR. MELCOR is a widely used computer code developed at Sandia National Laboratories since ~1982 for the U.S. Nuclear Regulatory Commission. Insights from the modeling of these accidents is being used to better inform future code development and potentially improved accident management. To date, our necessity to better capture in-vessel thermal-hydraulic and ex-vessel melt coolability and concrete interactions has led to the implementation of new models. The most recent analyses, presented in this paper, have been in support of the of the Organization for Economic Cooperation and Development Nuclear Energy Agency’s (OECD/NEA) Benchmark Study of the Accident at the Fukushima Daiichi Nuclear Power Station (BSAF) Project. The goal of this project is to accurately capture the source term from all three releases and then model the atmospheric dispersion. In order to do this, a forensic approach is being used in which available plant data and release timings is being used to inform the modeled MELCOR accident scenario. For example, containment failures, core slumping events and lower head failure timings are all enforced parameters in these analyses. This approach is fundamentally different from a blind code assessment analysis often used in standard problem exercises. The timings of these events are informed by representative spikes or decreases in plant data. The combination of improvements to the MELCOR source code resulting from analysis previous accident analysis and this forensic approach has allowed Sandia to generate representative and plausible source terms for all three accidents at Fukushima Daiichi out to three weeks after the accident to capture both early and late releases. In particular, using the source terms developed by MELCOR, the MACCS software code, which models atmospheric dispersion and deposition, we are able to reasonably capture the deposition of radionuclides to the northwest of the reactor site.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Energy Savings Analysis of the Proposed Revision of the Washington D.C. Non-Residential Energy Code

This report presents the results of an assessment of savings for the proposed Washington D.C. energy code relative to ASHRAE Standard 90.1-2010. It includes annual and life cycle savings for site energy, source energy, energy cost, and carbon dioxide emissions that would result from adoption and enforcement of the proposed code for newly constructed buildings in Washington D.C. over a five year period.

Commercial Energy Code↗

Evaluation of Preventative Radiological/Nuclear Detector Archetypes to Validate Repurpose to the Consequence Management Mission

In the event of a radiological or nuclear emergency involving a large-scale release of radioactive material, local responders would be the primary means to perform radiation measurements to assess impacts and issue protective action recommendations for the responders and the public. Over the first 24-36 hours, Federal responders and resources will deploy to augment the local efforts, and if necessary, provide extensive radiation monitoring and assessment capabilities coordinated by the Department of Energy-led Federal Radiological Monitoring and Assessment Center and Federal Emergency Management Agency-led Multiagency Coordination Group. Unless Federal resources happen to be deployed at the moment an incident occurs, such as a preventative radiological/nuclear detection mission for a scheduled special event, the local response to an incident will commence and persist for many hours with no on-scene Federal support. For a catastrophic incident, such as a nuclear detonation or severe reactor accident, the local jurisdictions may not have a full range of adequate supplies of health physics instruments and personnel dosimetry. Therefore early in a crisis, the local responders will inevitably conduct their operations with the radiation detection and dosimetry capabilities that they have available until additional resources and support are requested and arrive. Most of the radiation detection instruments currently fielded at the local level are carried by law enforcement personnel and are designed for interdiction missions - referred to here as preventative radiological/nuclear detection (PRND) instruments. This study investigated how this PRND equipment can be repurposed in consequence management (CM) missions.

61 RADIATION PROTECTION AND DOSIMETRY↗

Negotiating Terms and Conditions: An Overview of the Federal Energy Regulatory Commission Hydropower Settlement Agreement Process

The process for obtaining, transferring, or surrendering a Federal Energy Regulatory Commission (FERC) hydropower license or exemption from licensing can be a series of complex negotiations. In many instances, the process may include stakeholders with different and/or competing perspectives or objectives related to the original license, new license (i.e., relicense), transfer of a license, or surrender of a license. Divergent perspectives and objectives can lead to disputes among project participants, which may impact the development of FERC license terms and conditions. One mechanism to resolve disputes between project participants involving a FERC authorization is informal and formal settlement agreement conferences, which often result in settlement agreements addressing the disputed issues. This report provides hydropower stakeholders with a better understanding of the FERC settlement agreement process, including information on: How to initiate a settlement agreement. The procedural steps associated with the settlement agreement process. The legal standards the Commission must adhere to when determining whether settlement agreement provisions can become lawful and enforceable terms or conditions of a FERC authorization. Examples of settlement agreement provisions included as license terms and conditions or in off-license agreements from a collection of settlement agreements and Commission orders.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Guidance on How to Report Testing of BOP Shear Rams

The Bureau of Safety and Environmental Enforcement (BSEE) Well Control Rule (Subpart G)1 was published on April 29, 2016, and became effective on July 28, 2016. This rule is part of BSEE regulations pertaining to well control equipment used for oil and gas operations on the U.S. Outer Continental Shelf (OCS).

58 GEOSCIENCES↗

Improved Fracture Models for Relocation Modeling

The BISON fuel performance code is being developed to provide a modern tool that has the flexibility to analyze a wide variety of fuel forms and to model conditions and phenomena that could not be represented in legacy tools. There are a number of motivations for this, including providing support for development of advanced fuel with improved accident tolerance for existing light water (LWR) reactors, improved understanding of mechanisms in fuel designs in current use in a wider variety of conditions, and facilitating the development of fuel for advanced reactor designs. To accomplish these goals, it is clear that BISON must rely on models of fuel behavior that are based on fundamental physical behavior, rather than on empirical correlations that represent that behavior in a simplified fashion. BISON still does employ many empirical models that were originally developed for other fuel performance codes, but efforts are underway to replace these with models that are more physically based. Radial relocation in LWR fuel is an example of a phenomenon that is currently represented by an empirical model, but which is ripe for replacement by physically based models. During normal operation, ceramic LWR fuel experiences significant fracturing that is driven by spatially nonuniform volumetric expansion. This occurs due to the significant thermal gradients within the fuel that occur in fresh and irradiated fuel, as well as nonuniform swelling due to fission products that occurs over longer-term irradiation. Fracture and fragmentation of fuel allows the outer radius of the fuel pellet to expand due to the loss of mechanical constraint and outward radial migration of fragments. This radial expansion has a significant effect on the fuel system response because it decreases the size of the gap between the fuel and cladding. This decreases the thermal resistance across that gap, which leads to decreased fuel centerline temperatures. This report documents recent work to improve the ability of BISON to model radial relocation using the extended finite element method (XFEM). These enhancements include the ability to include cohesive zone models, improved code architecture for propagating cracks based on fracture integrals, and improved handling of fuel and cladding interfaces with XFEM. These capabilities are demonstrated on a simulation of radial relocation including a surface interaction model that enforces residual opening.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

MOOSE IPL Extensions (Documentation)

In FY-2015, The development of MOOSE was driven by the needs of the NEAMS MOOSE-based applications, BISON, MARMOT, and RELAP-7. An emphasis was placed on the continued upkeep and improvement MOOSE in support of the product line integration goals. New unified documentation tools have been developed, several improvements to regression testing have been enforced and overall better software quality practices have been implemented. In addition the Multiapps and Transfers systems have seen significant refactoring and robustness improvements, as has the “Restart and Recover” system in support of Multiapp simulations. Finally, a completely new “Control Logic” system has been engineered to replace the prototype system currently in use in the RELAP-7 code. The development of this system continues and is expected to handle existing needs as well as support future enhancements.

99 GENERAL AND MISCELLANEOUS↗

Progress toward a new implementation of the mortar finite element method in MOOSE

The mortar finite element method has been used for many years in a variety of applications, including the enforcement of continuity conditions across decomposed domains, the implementation of Dirichlet boundary conditions, obtaining improved estimates of surface fluxes, and for solving large deformation contact mechanics problems. There is a currently great deal of interest in developing more robust mechanical and thermal contact solution strategies in the MOOSE framework and physics modules, and schemes based on the mortar finite element approach appear to be a promising avenue of development. There are a number of challenges associated with the development of a robust Lagrange multiplier based formulation of the mortar finite element method which can be tackled using the relatively simple framework of thermal contact problems, before tackling more complicated applications such as thermomechanical contact. In this report, we describe several aspects of our mortar finite element method implementation for solving thermal contact problems. The approach and notation used are based primarily based on the work of Bin Yang et al. ("Two dimensional mortar contact methods for large deformation frictional sliding," International Journal for Numerical Methods in Engineering 62(9), 2005).

97 MATHEMATICS AND COMPUTING↗

AGR-1 Irradiation Test Final As-Run Report

This document presents the as-run analysis of the AGR-1 irradiation experiment. AGR-1 is the first of eight planned irradiations for the Advanced Gas Reactor (AGR) Fuel Development and Qualification Program. Funding for this program is provided by the US Department of Energy (DOE) as part of the Next-Generation Nuclear Plant (NGNP) project. The objectives of the AGR-1 experiment are: 1. To gain experience with multi-capsule test train design, fabrication, and operation with the intent to reduce the probability of capsule or test train failure in subsequent irradiation tests. 2. To irradiate fuel produced in conjunction with the AGR fuel process development effort. 3. To provide data that will support the development of an understanding of the relationship between fuel fabrication processes, fuel product properties, and irradiation performance. In order to achieve the test objectives, the AGR-1 experiment was irradiated in the B-10 position of the Advanced Test Reactor (ATR) at the Idaho National Laboratory (INL) for a total duration of 620 effective full power days of irradiation. Irradiation began on December 24, 2006 and ended on November 6, 2009 spanning 13 ATR cycles and approximately three calendar years. The test contained six independently controlled and monitored capsules. Each capsule contained 12 compacts of a single type, or variant, of the AGR coated fuel. No fuel particles failed during the AGR-1 irradiation. Final burnup values on a per compact basis ranged from 11.5 to 19.6 %FIMA, while fast fluence values ranged from 2.21 to 4.39 x 10 25 n/m 2 (E >0.18 MeV). We’ll say something here about temperatures once thermal recalc is done. Thermocouples performed well, failing at a lower rate than expected. At the end of the irradiation, nine of the originally-planned 19 TCs were considered functional. Fission product release-to-birth (R/B) ratios were quite low. In most capsules, R/B values at the end of the irradiation were at or below 10 -7 with only one capsule significantly exceeding this value. A maximum R/B of around 2 x 10 -7 was reached at the end of the irradiation in Capsule 5. Several shakedown issues were encountered and resolved during the first three cycles. These include the repair of minor gas line leaks; repair of faulty gas line valves; the need to position moisture monitors in regions of low radiation fields for proper functioning; the enforcement of proper on-line data storage and backup, the need to monitor thermocouple performance, correcting for detector spectral gain shift, and a change in the mass flow rate range of the neon flow controllers.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Pilot Scale Operation and Testing of Syngas Chemical Looping For Hydrogen Production

The Syngas Chemical looping (SCL) process provides efficient and economic means to utilize the abundant fossil reserve of coal. The main problem associated with coal utilization is the CO 2 emissions resulting from its combustion. Even though CO 2 regulation or carbon tax is currently not in place, its enforcement is expected in the near future. Such a greenhouse gas emission control, if adopted in current power plant systems, will drive the efficiency down and increase the cost of electricity, due to the energy and capital-intensive nature of current CO 2 separation techniques. This highlights the need to develop technologies that present a solution to the rising cost of electricity in the future. The integrated gasification combined cycle (IGCC) presents an improvement to the above predicament, but it is capital intensive due to the extensive unit operations involved. The efficiency for a CO 2 capture incorporated IGCC system is around ~32%, resulting in approximately 45% increase in cost of electricity. This is definitely a better path to traverse than the conventional pulverized coal (PC) power plants as it has improved economics and efficiencies accompanied by product flexibility. The SCL process advances the benefits even further when integrated with the IGCC process. The SCL process removes the expensive WGS system and CO 2 separation columns, thereby saving on capital and operational expenses. This integration results in a 12 – 21% increase in efficiency accompanied by a reduction in cost of electricity by 15 – 28%, over conventional IGCC systems. Therefore, SCL process provides the best route to harness the energy from coal. The overall project objective was to construct and operate a syngas chemical looping pilot scale test unit at the NCCC. The project scope of work was divided into 3 phases. In Phase I, cold flow model studies using a 1:1 scale acrylic test unit constructed at Particulate Solids Research, Inc. (PSRI) was successfully completed confirming robust solid flow control is achievable in the non-mechanical system design. In Phase II, the high pressure, high temperature, chemical looping reactor was successfully designed with all necessary equipment and safety instrumentation/controls specified to allow for fabrication, site construction, and assembly to commence in Phase III. In Phase III, the SCL pilot plant was successfully assembled and all necessary functional checks and pre-startup safety reviews completed. During unit commission over the course of 200 hours of testing, operational issues were observed with premix burner used for system startup. With the grants awarded by the National Energy Laboratory (NETL) and the Ohio Development Services Agency (ODSA) under awards DE-FE0023915 and D-14-18, the SCL pilot unit underwent three auxiliary equipment modifications to resolve all of the startup operational issues encountered. The unit was successfully demonstrated with 300+hr continuous operation. Key results obtained include high syngas conversion of 97.95% with 16.03% oxygen carrier conversion in the moving bed reducer and >99% purity H 2 produced from the moving bed oxidizer.

01 COAL, LIGNITE, AND PEAT↗

High-Order, Stable, and Conservative Boundary Schemes for Central and Compact Finite Differences

Stable and conservative numerical boundary schemes are constructed such that they do not diminish the overall accuracy of the method for interior schemes of orders 4, 6, and 8 using both explicit (central) and compact finite differences. Previous attempts to develop stable numerical boundary schemes for non-linear problems have resulted in schemes which significantly reduced the global accuracy and/or required some form of artificial dissipation. Thus, the schemes developed are the first to not require this tradeoff, while also ensuring discrete conservation and allowing for direct boundary condition enforcement. After outlining a general procedure for the construction of conservative boundary schemes of any order, a simple, yet novel, optimization strategy which focuses directly on the compressible Euler equations is applied. The result of this non-linear optimization process is a set of high-order, stable, and conservative numerical boundary schemes which demonstrate excellent stability and convergence properties on an array of linear and non-linear hyperbolic problems.

97 MATHEMATICS AND COMPUTING↗

Development of high-fidelity models for liquid fuel spray atomization and mixing processes in transportation and energy systems

Significant inadequacies of current models for multiphase flows present a major barrier to rapid development of advanced high-efficiency low-emissions combustion devices. Liquid spray atomization processes largely determine fuel-air mixture formation, which subsequently govern combustion and controls performance, emissions, and durability of a device. The current study presents a fundamentally-consistent framework to model the effects of breakup processes, liquid drop deformations, and internal flow dynamics on mass, momentum, and energy exchange functions. This framework builds on the Taylor Analogy Breakup (TAB) model which naturally quantifies local drop deformation dynamics. Real-fluid multicomponent thermodynamic property modeling and Gradient Theory simulations facilitate accurate calculations of molecular two-phase interface exchange functions, surface tensions forces, drop oscillations, and breakup processes. The analysis establishes that these drop dynamics, along with finite liquid viscosity effects, significantly alter gas-liquid exchange functions. The study quantifies these effects for the resulting drag coefficients of liquid drops and demonstrates significant deviations from the classic dynamic drag model, which is widely applied in modern simulations performed in academia and industry. This work also quantifies effects, which originate from gas-liquid coupling dynamics, on evaporation and heating rates. The analysis establishes that the consideration of these coupling dynamics modify mass and energy transfer rates even more significantly than the corresponding drag forces from momentum exchange. This physical complexity, however, is largely neglected in modern studies from academia and industry. A new set of equations is presented to improve the modeling of drop breakup processes to address the current shortcomings in the prediction of resulting drops proper- ties over the full range of relevant breakup conditions. The framework is based on a refined energy balance equation which explicitly enforces drop momentum conservation during the breakup process. The introduced modeling framework is entirely derived from conservation equations for mass, momentum, and energy and does not, as a consequence, introduce new modeling constants. The significance of the developed modeling advances to fuel injection processes is demonstrated using Large Eddy Simulation (LES) with a Lagrangian-Eulerian modeling approach.

42 ENGINEERING↗

Quantum Representation of Classical Dynamics

A constructive proof is given to show that there is an exact embedding of a classical system of N ordinary differential equations (ODEs) within a quantum mechanical system corresponding to a classical phase space of dimension 2N. Doubling the classical phase space allows one to express any set of ODEs through a classical Hamiltonian that is a sum over a set of constraints. The Lagrange multipliers that enforce the constraints are canonically conjugate to the dependent variables of the original ODE and satisfy equations that ensure that the evolution of the system is symplectic. For the quantized system on extended phase space, Heisenberg’s uncertainty principle is satisfied by each variable and its canonically conjugate momentum, the Lagrange multiplier. However, there is no uncertainty in a simultaneous measurement for any of the variables of the original ODE. Hence,there is complete fidelity for the quantum representation of the classical system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗