Prediction of Upward Flame Spread over Polymers

In this work, the existing understanding of flame spread dynamics is enhanced through an extensive study of the heat transfer from flames spreading vertically upwards across 5 cm wide, 20 cm tall samples of extruded Poly (Methyl Methacrylate) (PMMA). These experiments have provided highly spatially resolved measurements of flame to surface heat flux and material burning rate at the critical length scale of interest, with a level of accuracy and detail unmatched by previous empirical or computational studies. Using these measurements, a wall flame model was developed that describes a flame’s heat feedback profile (both in the continuous flame region and the thermal plume above) solely as a function of material burning rate. Additional experiments were conducted to measure flame heat flux and sample mass loss rate as flames spread vertically upwards over the surface of seven other commonly used polymers, two of which are glass reinforced composite materials. Using these measurements, our wall flame model has been generalized such that it can predict heat feedback from flames supported by a wide range of materials. For the seven materials tested here – which present a varied range of burning behaviors including dripping, polymer melt flow, sample burnout, and heavy soot formation – model-predicted flame heat flux has been shown to match experimental measurements (taken across the full length of the flame) with an average accuracy of 3.9 kW m-2 (approximately 10 – 15 % of peak measured flame heat flux). This flame model has since been coupled with a powerful solid phase pyrolysis solver, ThermaKin2D, which computes the transient rate of gaseous fuel production of constituents of a pyrolyzing solid in response to an external heat flux, based on fundamental physical and chemical properties. Together, this unified model captures the two fundamental controlling mechanisms of upward flame spread – gas phase flame heat transfer and solid phase material degradation. This has enabled simulations of flame spread dynamics with a reasonable computational cost and accuracy beyond that of current models. This unified model of material degradation provides the framework to quantitatively study material burning behavior in response to a wide range of common fire scenarios.

Harmonization of Life Cycle Climate Performance and Its Improvements for Heat Pump Applications

Life Cycle Climate Performance (LCCP) is an evaluation method by which heating, ventilation, air conditioning and refrigeration systems can be evaluated for their global warming impact over the course of their complete life cycle. LCCP is more inclusive than previous metrics such as Total Equivalent Warming Impact. It is calculated as the sum of direct and indirect emissions generated over the lifetime of the system “from cradle to grave”. Direct emissions include all effects from the release of refrigerants into the atmosphere during the lifetime of the system. This includes annual leakage and losses during the disposal of the unit. The indirect emissions include emissions from the energy consumption during manufacturing process, lifetime operation, and disposal of the system. This thesis proposes a standardized approach to the use of LCCP and traceable data sources for all aspects of the calculation. An equation is proposed that unifies the efforts of previous researchers. Data sources are recommended for average values for all LCCP inputs. A residential heat pump sample problem is presented illustrating the methodology. The heat pump is evaluated at five U.S. locations in different climate zones. An excel tool was developed for residential heat pumps using the proposed method. The primary factor in the LCCP calculation is the energy consumption of the system. The effects of advanced vapor compression cycles are then investigated for heat pump applications. Advanced cycle options attempt to reduce the energy consumption in various ways. There are three categories of advanced cycle options: subcooling cycles, expansion loss recovery cycles and multi-stage cycles. The cycles selected for research are the suction line heat exchanger cycle, the expander cycle, the ejector cycle, and the vapor injection cycle. The cycles are modeled using Engineering Equation Solver and the results are applied to the LCCP methodology. The expander cycle, ejector cycle and vapor injection cycle are effective in reducing LCCP of a residential heat pump by 5.6%, 8.2% and 10.5%, respectively in Phoenix, AZ. The advanced cycles are evaluated with the use of low GWP refrigerants and are capable of reducing the LCCP of a residential heat by 13.7%, 16.3% and 18.6% using a refrigerant with a GWP of 10. To meet the U.S. Department of Energy’s goal of reducing residential energy use by 40% by 2025 with a proportional reduction in all other categories of residential energy consumption, a reduction in the energy consumption of a residential heat pump of 34.8% with a refrigerant GWP of 10 for Phoenix, AZ is necessary. A combination of advanced cycle, control options and low GWP refrigerants are necessary to meet this goal.

Mesh Adaption for Tracking Vortex Structures in OVERTURNS Simulation of the S-76 Rotor in Hover

The constant need to improve helicopter performance requires the optimization of existing and future rotor designs. A crucial indicator of rotor capability is hover performance, which depends on the near-body flow as well as the structure and strength of the tip vortices formed at the trailing edge of the blades. Computational Fluid Dynamics (CFD) solvers must balance computational expenses with preservation of the flow, and to limit computational expenses the mesh is often coarsened in the outer regions of the computational domain. This can lead to degradation of the vortex structures which compose the rotor wake. The current work conducts three-dimensional simulations using OVERTURNS, a three-dimensional structured grid solver that models the flow field using the Reynolds-Averaged Navier-Stokes equations. The S-76 rotor in hover was chosen as the test case for evaluating the OVERTURNS solver, focusing on methods to better preserve the rotor wake. Using the hover condition, various computational domains, spatial schemes, and boundary conditions were tested. Furthermore, a mesh adaption routine was implemented, allowing for the increased refinement of the mesh in areas of turbulent flow without the need to add points to the mesh. The adapted mesh was employed to conduct a sweep of collective pitch angles, comparing the resolved wake and integrated forces to existing computational and experimental results. The integrated thrust values saw very close agreement across all tested pitch angles, while the power was slightly over predicted, resulting in under prediction of the Figure of Merit. Meanwhile, the tip vortices have been preserved for multiple blade passages, indicating an improvement in vortex preservation when compared with previous work. Finally, further results from a single collective pitch case were presented to provide a more complete picture of the solver results.

Motion Planning and Controls with Safety and Temporal Constraints

Motion planning, or trajectory planning, commonly refers to a process of converting high-level task specifications into low-level control commands that can be executed on the system of interest. For different applications, the system will be different. It can be an autonomous vehicle, an Unmanned Aerial Vehicle(UAV), a humanoid robot, or an industrial robotic arm. As human machine interaction is essential in many of these systems, safety is fundamental and crucial. Many of the applications also involve performing a task in an optimal manner within a given time constraint. Therefore, in this thesis, we focus on two aspects of the motion planning problem. One is the verification and synthesis of the safe controls for autonomous ground and air vehicles in collision avoidance scenarios. The other part focuses on the high-level planning for the autonomous vehicles with the timed temporal constraints. In the first aspect of our work, we first propose a verification method to prove the safety and robustness of a path planner and the path following controls based on reachable sets. We demonstrate the method on quadrotor and automobile applications. Secondly, we propose a reachable set based collision avoidance algorithm for UAVs. Instead of the traditional approaches of collision avoidance between trajectories, we propose a collision avoidance scheme based on reachable sets and tubes. We then formulate the problem as a convex optimization problem seeking control set design for the aircraft to avoid collision. We apply our approach to collision avoidance scenarios of quadrotors and fixed-wing aircraft. In the second aspect of our work, we address the high level planning problems with timed temporal logic constraints. Firstly, we present an optimization based method for path planning of a mobile robot subject to timed temporal constraints, in a dynamic environment. Temporal logic (TL) can address very complex task specifications such as safety, coverage, motion sequencing etc. We use metric temporal logic (MTL) to encode the task specifications with timing constraints. We then translate the MTL formulae into mixed integer linear constraints and solve the associated optimization problem using a mixed integer linear program solver. We have applied our approach on several case studies in complex dynamical environments subjected to timed temporal specifications. Secondly, we also present a timed automaton based method for planning under the given timed temporal logic specifications. We use metric interval temporal logic (MITL), a member of the MTL family, to represent the task specification, and provide a constructive way to generate a timed automaton and methods to look for accepting runs on the automaton to find an optimal motion (or path) sequence for the robot to complete the task.

POSITIVE FILTERED P_N METHOD FOR LINEAR TRANSPORT EQUATIONS AND THE ASSOCIATED OPTIMIZATION ALGORITHM

We propose a positive, accurate moment closure for linear kinetic transport equations based on a filtered spherical harmonic (FP_N) expansion in the angular variable. The FP_N moment equations are accurate approximations to linear kinetic equations, but they are known to suffer from the occurrence of unphysical, negative particle concentrations. The new positive filtered P_N (FP_N+) closure is developed to address this issue. The FP_N+ closure approximates the kinetic distribution by a spherical harmonic expansion that is non-negative on a finite, predetermined set of quadrature points. With an appropriate numerical PDE solver, the FP_N+ closure generates particle concentrations that are guaranteed to be non-negative. Under an additional, mild regularity assumption, we prove that as the moment order tends to infinity, the FP_N+ approximation converges, in the L2 sense, at the same rate as the FP_N approximation; numerical tests suggest that this assumption may not be necessary. By numerical experiments on the challenging line source benchmark problem, we confirm that the FP_N+ method indeed produces accurate and non-negative solutions. To apply the FP_N+ closure on problems at large temporal-spatial scales, we develop a positive asymptotic preserving (AP) numerical PDE solver. We prove that the propose AP scheme maintains stability and accuracy with standard mesh sizes at large temporal-spatial scales, while, for generic numerical schemes, excessive refinements on temporal-spatial meshes are required. We also show that the proposed scheme preserves positivity of the particle concentration, under some time step restriction. Numerical results confirm that the proposed AP scheme is capable for solving linear transport equations at large temporal-spatial scales, for which a generic scheme could fail. Constrained optimization problems are involved in the formulation of the FP_N+ closure to enforce non-negativity of the FP_N+ approximation on the set of quadrature points. These optimization problems can be written as strictly convex quadratic programs (CQPs) with a large number of inequality constraints. To efficiently solve the CQPs, we propose a constraint-reduced variant of a Mehrotra-predictor-corrector algorithm, with a novel constraint selection rule. We prove that, under appropriate assumptions, the proposed optimization algorithm converges globally to the solution at a locally q-quadratic rate. We test the algorithm on randomly generated problems, and the numerical results indicate that the combination of the proposed algorithm and the constraint selection rule outperforms other compared constraint-reduced algorithms, especially for problems with many more inequality constraints than variables.