Search NASA⌕ Search

SEARCH · Search NASA

Results for “Integral Equations Finite Element”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

74 records · Page 5

An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS

Here, we present an adaptive space-time phase field formulation for dynamic fracture of brittle shells. Their deformation is characterized by the Kirchhoff–Love thin shell theory using a curvilinear surface description. All kinematical objects are defined on the shell’s mid-plane. The evolution equation for the phase field is determined by the minimization of an energy functional based on Griffith’s theory of brittle fracture. Membrane and bending contributions to the fracture process are modeled separately and a thickness integration is established for the latter. The coupled system consists of two nonlinear fourth-order PDEs and all quantities are defined on an evolving two-dimensional manifold. Since the weak form requires C 1 -continuity, isogeometric shape functions are used. The mesh is adaptively refined based on the phase field using Locally Refinable (LR) NURBS. Time is discretized based on a generalized-α method using adaptive time-stepping, and the discretized coupled system is solved with a monolithic Newton–Raphson scheme. Finally, the interaction between surface deformation and crack evolution is demonstrated by several numerical examples showing dynamic crack propagation and branching.

42 ENGINEERING↗

Sodium Ion Expansion Power Block for Distributed CSP

The Sodium Ion Expansion Power Block for Distributed CSP was a three-plus-one-year effort under the Concentrating Solar Power: Advanced Projects Offering Low LCOE Opportunities (CSP: APOLLO) funding program within the U.S. Department of Energy Solar Energy Technologies Office. The primary objective of this project is to develop a dual-stage modular sodium thermal electrochemical converter (Na-TEC) heat engine power block, which can be potentially integrated with either a small-scale dish solar or large-scale heliostats and parabolic trough CSP. Na-TEC is a heat engine that generates electricity through the isothermal expansion of sodium ions. The Na-TEC is a closed system that can theoretically achieve conversion efficiencies above 45% when operating between thermal reservoirs at 1150 K and 550 K. However, thermal designs have confined previous single-stage devices to thermal efficiencies below 20%. To mitigate some of these limitations, we consider dividing the isothermal expansion into two stages; one at the evaporator temperature (1150 K) and another at an intermediate temperature (650 K –1050 K). This dual-stage Na-TEC takes advantage of regeneration and reheating, and could be amenable to better thermal management. In light of this, we first designed and developed a thermo-electrochemical model, and thermodynamically demonstrated how the dual-stage device can improve the efficiency by up to 8% points over the best performing single-stage device. We also established an application regime map for the single- and dual-stage Na-TEC in terms of the power density and the total thermal parasitic loss. Moreover, a thermal design of an axisymmetric dual-stage Na-TEC is developed to guide the scale-up and fabrication of sub-components of prototype module. A reduced-order finite-element model is used in conjunction with a Na-TEC thermodynamic model that was developed to determine the total parasitic heat loss of this dual-stage design. A number of simplifications are applied in the reduced-order model to decrease the computational time while maintaining acceptable accuracy. According to this analysis, a maximum efficiency of 29% and a maximum power output of 125 W can be achieved. Ultimately, we were able to demonstrate thermal efficiency improvements of the Na-TEC heat engine from 19% up to 40.3%, in a dual-stage (non-optimized) prototype module that we designed, fabricated, and tested with high temperature stage at 923 K. Furthermore, a cost-performance analysis for this improved dual-stage design was carried out for distributed-CSP systems. A high-level techno-economic analysis (TEA) explores four scenarios where a Na-TEC is used as the heat engine for a distributed-CSP system. Overnight capital cost and levelized cost of electricity (LCOE) are estimated for a system lifetime of 30 years, revealing that overnight capital costs in a range from $3.57 to $17.71 per We are feasible, which equate to LCOEs from 6.9 to 17.2 cents/kWh e -1 . This analysis makes a significant contribution by concurrently quantifying the efficiency and unit costs for a range of multistage configurations, and demonstrating that a Na-TEC may be a promising alternative to Stirling engines for distributed-CSP systems at residential scale of 1–5 kW e .

14 SOLAR ENERGY↗