Computations of Viscous Compressible Flows in h, p, k Finite Element Framework with Variationally Consistent Integral Forms

This thesis presents mathematical models for time dependent and stationary viscous compressible flows based on conservation laws, constitutive equations and equations of state using Eulerian description. In the presence of physical viscosity, conductivity and other transport properties, the mathematical models are well recognized Navier-Stokes equations. Variable transport properties as well as ideal and real gas models are considered for equations of state. The mathematical models are a highly non-linear coupled partial differential equations in space and time. The mathematical and computational infrastructure using finite element method is presented for obtaining numerical solutions of the Boundary Value Problems and Initial Value Problems associated with the mathematical models. This infrastructure is based on h, p, k (h-characteristic length, p-degree of local approximation, k-order of approximation space) as independent computational parameters with an additional requirement that the integral form be variationally consistent in case of Boundary Value Problems and space-time variationally consistent in case of Initial Value Problems. All methods of approximation except Least Squares and Space-Time Least Squares Processes are Variationally Inconsistent. Variational Consistency and Space-Time Variational Consistency of integral forms ensure unconditionally stable computational processes. A variety of numerical studies are presented for Initial Value Problems as well as Boundary Value Problems. 1-D transient viscous form of Burgers equation, 1-D Riemann shock tube with ideal and real gas models and Boundary Value Problems in 2-D compressible flow : Carter's plate with Mach 1, 2, 3 and 5 flows and Mach 1 flow past a circular cylinder are used as model problems. Shock evolution, propagation, interactions and reflection are quantified based on the rate of entropy production using Air as a medium for 1-D Riemann shock tube. It is clearly established that rarefaction shocks are not possible for FC70 for any choice of initial conditions. In all studies evolution of a shock is presented (unlike the published work). Its existence and sustained propagation is established based on Sr, the rate of entropy production per unit volume. In case of transient Burgers equation it is demonstrated that time accurate evolutions can be computed for any finite Reynolds number. Contrary to the common belief, the work presented here shows that solutions of Boundary Value Problems in compressible flows present no special problems. In Summary : (i) the mathematical models for the compressible flow are based on Navier-Stokes equations. (ii) computational infrastructure is based on $hpk$ and unconditionally stable integral forms with higher order global differentiability in space and time. (iii) All numerical studies utilize actual transport properties of the medium. (iv) Up-winding methods such as SUPG, SUPG/DC, SUPG/DC/LS are neither needed nor used. (v) existence of shocks is established through evolution and not using Rankine-Hugoniot relations. (vi) Governing Differential Equations in the mathematical models are neither linearized nor altered in any form during the entire process of formulation and computations. The work presented here clearly demonstrates that the numerical simulations of Boundary Value Problems and Initial Value Problems based on Navier-Stokes equations describing viscous compressible flows can be done in a straight forward manner in $h, p, k$ framework with Variational Consistent and Space-Time Variationally Consistent integral forms. The computational processes always remain unconditionally stable. The mathematical models based on Euler's equations lack physics, computational methods for Euler's equations use problem dependent up-winding methods which lack mathematical basis and rigor and thus in our view are of little merit if at all for numerical simulations of Boundary Value Problems and Initial Value Problems in compressible flows

Integrated Radiation Transport and Nuclear Fuel Performance for Assembly-Level Simulations

The Advanced Multi-Physics (AMP) Nuclear Fuel Performance code (AMPFuel) is focused on predicting the temperature and strain within a nuclear fuel assembly to evaluate the performance and safety of existing and advanced nuclear fuel bundles within existing and advanced nuclear reactors. AMPFuel was extended to include an integrated nuclear fuel assembly capability for (one-way) coupled radiation transport and nuclear fuel assembly thermo-mechanics. This capability is the initial step toward incorporating an improved predictive nuclear fuel assembly modeling capability to accurately account for source-terms and boundary conditions of traditional (single-pin) nuclear fuel performance simulation, such as the neutron flux distribution, coolant conditions, and assembly mechanical stresses. A novel scheme is introduced for transferring the power distribution from the Scale/Denovo (Denovo) radiation transport code (structured, Cartesian mesh with smeared materials within each cell) to AMPFuel (unstructured, hexagonal mesh with a single material within each cell), allowing the use of a relatively coarse spatial mesh (10 million elements) for the radiation transport and a fine spatial mesh (3.3 billion elements) for thermo-mechanics with very little loss of accuracy. In addition, a new nuclear fuel-specific preconditioner was developed to account for the high aspect ratio of each fuel pin (12 feet axially, but 1 4 inches in diameter) with many individual fuel regions (pellets). With this novel capability, AMPFuel was used to model an entire 17 17 pressurized water reactor fuel assembly with many of the features resolved in three dimensions (for thermo-mechanics and/or neutronics), including the fuel, gap, and cladding of each of the 264 fuel pins; the 25 guide tubes; the top and bottom structural regions; and the upper and lower (neutron) reflector regions. The final, full assembly calculation was executed on Jaguar using 40,000 cores in under 10 hours to model over 162 billion degrees of freedom for 10 loading steps. The single radiation transport calculation required about 50% of the time required to solve the thermo-mechanics with a single loading step, which demonstrates that it is feasible to incorporate, in a single code, a high-fidelity radiation transport capability with a high-fidelity nuclear fuel thermo-mechanics capability and anticipate acceptable computational requirements. The results of the full assembly simulation clearly show the axial, radial, and azimuthal variation of the neutron flux, power, temperature, and deformation of the assembly, highlighting behavior that is neglected in traditional axisymmetric fuel performance codes that do not account for assembly features, such as guide tubes and control rods

Adaptive Model Reduction For Parareal In Time Method For Transient Stability Simulations

Real time or faster than real time simulation can enable system operators to foresee the effect of crucial contingencies on the power system dynamics and take timely actions to prevent system instability. Parareal in time method uses concurrent computations on different segments of the time domain of interest to speed up the dynamic simulations. This paper describes the application of an adaptive nonlinear model reduction method in improving computational speed of the Parareal solver. The proposed method adaptively switches between a hybrid system with selective linearization and a completely linear system based on the size of a disturbance. The functions in the hybrid system are linearized based on the electrical distance between specific generators and the area where disturbances originated. The proposed method is tested on the 327-machine 2383-bus Polish system

Groundwater Flow Modeling in Karst Aquifers: Coupling 3D Matrix and 1D Conduit Flow via Control Volume Isogeometric Analysis—Experimental Verification with a 3D Physical Model

A novel numerical model for groundwater flow in karst aquifers is presented. A discrete-continuum (hybrid) approach, in which a three-dimensional matrix flow is coupled with a one-dimensional conduit flow, was used. The laminar flow in the karst matrix is described by a variably saturated flow equation to account for important hydrodynamic effects in both the saturated and unsaturated zones. Turbulent conduit flow for both free surface and pressurized flow conditions was captured via the noninertia wave equation, whereas the coupling of two flow domains was established through an exchange term proportional to head differences. The novel numerical approach based on Fup basis functions and control-volume formulation enabled us to obtain smooth and locally conservative numerical solutions. Due to its similarity to the isogeometric analysis concept (IGA), we labeled it as control-volume isogeometric analysis (CV-IGA). Since realistic verification of the karst flow models is an extremely difficult task, the particular contribution of this work is the construction of a specially designed 3D physical model ( dimensions: 5.66 × 2.95 × 2.00 m) in order to verify the developed numerical model under controlled laboratory conditions. Heterogeneous porous material was used to simulate the karst matrix, and perforated pipes were used as karst conduits. The model was able to capture many flow characteristics, such as the interaction between the matrix and conduit, rainfall infiltration through the unsaturated zone, direct recharge through sinkholes, and both free surface and pressurized flow in conduits. Two different flow experiments are presented, and comparison with numerical results confirmed the validity of the developed karst flow model under complex laboratory conditions

liionpack: a Python package for simulating packs of batteries with PyBaMM

Electrification of transport and other energy intensive activities is of growing importance as it provides an underpinning method to reduce carbon emissions. With an increase in reliance on renewable sources of energy and a reduction in the use of more predictable fossil fuels in both stationary and mobile applications, energy storage will play a pivotal role and batteries are currently the most widely adopted and versatile form. Therefore, understanding how batteries work, how they degrade, and how to optimize and manage their operation at large scales is critical to achieving emission reduction targets. The electric vehicle (EV) industry requires a considerable number of batteries even for a single vehicle, sometimes numbering in the thousands if smaller cells are used, and the dynamics and degradation of these systems, as well as large stationary power systems, is not that well understood. As increases in the efficiency of a single battery become diminishing for standard commercially available chemistries, gains made at the system level become more important and can potentially be realised more quickly compared with developing new chemistries. Mathematical models and simulations provide a way to address these challenging questions and can aid the engineer and designers of batteries and battery management systems to provide longer lasting and more efficient energy storage systems

Integrated Radiation Transport and Nuclear Fuel Performance for Assembly-Level Simulations

The Advanced Multi-Physics (AMP) Nuclear Fuel Performance code (AMPFuel) is focused on predicting the temperature and strain within a nuclear fuel assembly to evaluate the performance and safety of existing and advanced nuclear fuel bundles within existing and advanced nuclear reactors. AMPFuel was extended to include an integrated nuclear fuel assembly capability for (one-way) coupled radiation transport and nuclear fuel assembly thermo-mechanics. This capability is the initial step toward incorporating an improved predictive nuclear fuel assembly modeling capability to accurately account for source-terms and boundary conditions of traditional (single-pin) nuclear fuel performance simulation, such as the neutron flux distribution, coolant conditions, and assembly mechanical stresses. A novel scheme is introduced for transferring the power distribution from the Scale/Denovo (Denovo) radiation transport code (structured, Cartesian mesh with smeared materials within each cell) to AMPFuel (unstructured, hexagonal mesh with a single material within each cell), allowing the use of a relatively coarse spatial mesh (10 million elements) for the radiation transport and a fine spatial mesh (3.3 billion elements) for thermo-mechanics with very little loss of accuracy. In addition, a new nuclear fuel-specific preconditioner was developed to account for the high aspect ratio of each fuel pin (12 feet axially, but 1 4 inches in diameter) with many individual fuel regions (pellets). With this novel capability, AMPFuel was used to model an entire 17 17 pressurized water reactor fuel assembly with many of the features resolved in three dimensions (for thermo-mechanics and/or neutronics), including the fuel, gap, and cladding of each of the 264 fuel pins; the 25 guide tubes; the top and bottom structural regions; and the upper and lower (neutron) reflector regions. The final, full assembly calculation was executed on Jaguar using 40,000 cores in under 10 hours to model over 162 billion degrees of freedom for 10 loading steps. The single radiation transport calculation required about 50% of the time required to solve the thermo-mechanics with a single loading step, which demonstrates that it is feasible to incorporate, in a single code, a high-fidelity radiation transport capability with a high-fidelity nuclear fuel thermo-mechanics capability and anticipate acceptable computational requirements. The results of the full assembly simulation clearly show the axial, radial, and azimuthal variation of the neutron flux, power, temperature, and deformation of the assembly, highlighting behavior that is neglected in traditional axisymmetric fuel performance codes that do not account for assembly features, such as guide tubes and control rods

Anomalous Discharge Product Distribution in Lithium-Air Cathodes

Using neutron tomographic imaging, we report for the first time the three-dimensional spatial distribution of lithium products in electrochemically discharged lithium-air cathodes. Neutron imaging finds a nonuniform lithium product distribution across the electrode thickness, with the lithium species concentration being higher near the edges of the Li-air electrode and relatively uniform in the center of the electrode. The experimental neutron images were analyzed in context of results obtained from 3D modeling that maps the spatiotemporal variation of the lithium product distribution using a kinetically coupled diffusion based transport model. The origin of such anomalous behavior is due to the competition between the transport of lithium and oxygen and the accompanying electrochemical kinetics. Quantitative understanding of these effects is a critical step toward rechargeability of Li-air electrochemical systems

A minimal information set to enable verifiable theoretical battery research

Batteries are an enabling technology for addressing sustainability through the electrification of various forms of transportation (1) and grid storage. (2) Batteries are truly multi-scale, multi-physics devices, and accordingly various theoretical descriptions exist to understand their behavior (3−5) ranging from atomistic details to techno-economic trends. As we explore advanced battery chemistries (6,7) or previously inaccessible aspects of existing ones, (8−10) new theories are required to drive decisions. (11−13) The decisions are influenced by the limitations of the underlying theory. Advanced theories used to understand battery phenomena are complicated and require substantial effort to reproduce. However, such constraints should not limit the insights from these theories. We can strive to make the theoretical research verifiable such that any battery stakeholder can assess the veracity of new theories, sophisticated simulations or elaborate analyses. We distinguish verifiability, which amounts to “Can I trust the results, conclusions and insights and identify the context where they are relevant?”, from reproducibility, which ensures “Would I get the same results if I followed the same steps?” With this motivation, we propose a checklist to guide future reports of theoretical battery research in Table 1. We hereafter discuss our thoughts leading to this and how it helps to consistently document necessary details while allowing complete freedom for creativity of individual researchers. Given the differences between experimental and theoretical studies, the proposed checklist differs from its experimental counterparts. (14,15) This checklist covers all flavors of theoretical battery research, ranging from atomic/molecular calculations (16−19) to mesoscale (20,21) and continuum-scale interactions, (9,22) and techno-economic analysis. (23,24) Also, as more and more experimental studies analyze raw data, (25) we feel this checklist would be broadly relevant