Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Mathematics”

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.

At least 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
NASA NTRS2014

A Mathematical Model of Oxygen Transport in Skeletal Muscle During Hindlimb Unloading

During hindlimb unloading (HU) dramatic fluid shifts occur within minutes of the suspension, leading to a less precise matching of blood flow to O2 demands of skeletal muscle. Vascular resistance directs blood away from certain muscles, such as the soleus (SOL). The muscle volume gradually reduces in these muscles so that eventually the relative blood flow returns to normal. It is generally believed that muscle volume change is not due to O2 depletion, but a consequence of disuse. However, the volume of the unloaded rat muscle declines over the course of weeks, whereas the redistribution of blood flow occurs immediately. Using a Krogh Cylinder Model, the distribution of O2 was predicted in two skeletal muscles: SOL and gastrocnemius (GAS). Effects of the muscle blood flow, volume, capillary density, and O2 uptake, are included to calculate the pO2 at rest and after 10 min and 15 days of unloading. The model predicts that 32 percent of the SOL muscle tissue has a pO2 1.25 mm Hg within 10 min, whereas the GAS maintains normal O2 levels, and that equilibrium is reached only as the SOL muscle cells degenerate. The results provide evidence that there is an inadequate O2 supply to the mitochondria in the SOL muscle after 10 min HU.

Mathematical models↗
NASA NTRS2026

Mathematical Model of a Regenerative Fuel Cell for System Optimization

This thesis developed a system-level optimization model of a regenerative fuel cell (RFC) system for long-duration, off-world energy storage applications. Prior RFC design studies have typically been limited to reduced parameter sets and simplified constraints due to computational limitations relative to the number of relevant degrees of freedom. As a result, important nonlinear interactions between subsystems have not been fully captured. This work began to address that gap by developing a higher-fidelity, nonlinear optimization framework that incorporates a broader set of design variables and coupled constraints, enabling a multidimensional model that captures the coupled behavior of RFC subsystems and demonstrates the feasibility of applying optimization to such systems. An expanded system-level optimization approach was established that captures interactions between electrochemical performance, structural requirements, and storage design. This enabled a more comprehensive evaluation of trade-offs than conventional formulations. The model integrates four coupled subsystems: a fuel cell, an electrolyzer, reactant gas, and high-pressure storage tanks, and was formulated to accommodate a wide range of mission parameters, including operational time and required output power. It incorporates constraints on available solar array power, reactant mass balance between production and consumption, and pressure-dependent storage requirements. To enable reliable convergence, the optimization problem was reformulated to reduce dimensionality and improve numerical stability, with subsystem models organized for efficient evaluation. Problem dimensionality was reduced by consolidating lower-level design variables into higher-level representative quantities, and subsystem behavior was evaluated within the optimization loop. A multi-start initialization strategy was employed to mitigate sensitivity to local minima and improve solution quality, while nonlinear relationships were solved using robust numerical methods. The results showed that convergence was achieved across a range of required output power values. Specific energy reached a maximum at a critical mission power level, where the electrolyzer power matched the available solar input and operated near its voltage and current density limits. Beyond this point, further increases in required power resulted in less mass-efficient operation, increasing total system mass and reducing overall performance. The developed model represents an advancement in RFC system-level optimization by enabling analysis of a broader and more tightly coupled design space than previous considerations. While convergence behavior and computational cost remain challenges, the methods introduced improve solvability and allow inclusion of additional design variables with minimal loss of physical fidelity. However, the numerical results should not be interpreted as definitive design recommendations, as the model includes simplifying assumptions and omits several higher-order effects. Future work should extend this framework by incorporating additional subsystems and loss mechanisms, such as thermal management, parasitic power consumption, and reactant losses, to improve fidelity and ensure more representative design conclusions.

Electrochemistry↗
DOE OSTI2022

Mathematical Tools for the Analysis of Periodic and Aperiodic Grid Signals

Numerous sensing techniques and instrumentation are used in determining the state of the electric grid. Coupled with such measurements are the methods and analysis tools used. The parameters of interest result in both periodic and aperiodic signals. An examination of appropriate analysis tools is presented

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Evaluation of the rheological and electrical percolation of high‐density polyethylene/carbon black composites using mathematical models

Abstract In this work, conductive polymer composites (CPCs) of bio‐based polyethylene (BioPe) containing different concentrations of carbon black (CB) were developed. By using oscillatory rheology analysis, a Newtonian plateau was observed in BioPe, and all BioPe/CB composites had a behavior of a pseudo‐solid and that composites with volume fractions ranging from 0.24 to 0.56 presented higher viscosity, storage, and loss modulus. This suggests the formation of a percolated network and by using the power‐law models, it was observed that the electrical percolation threshold was higher than the rheological percolation threshold. The electrical conductivity was measured using the four‐point probe method and a sigmoid model was used to predict the CPCs' electrical conductivity percolation threshold. The results indicated that the four‐point probe method presented satisfactory results according to the calculated standard deviations and voltage–current characteristics for each round of measurements considering the same ranging as used in rheology analysis. The analytical model used showed a coefficient of determination ( R 2 ) higher than 95%, allowing the prediction of the electrical conductivity of the CPC and the percolation threshold as a function of the volumetric fraction of the CB.

da SiIva, Moacy P.↗
DOE OSTI2021

Mathematical modeling of novel porous transport layer architectures for proton exchange membrane electrolysis cells

Thin foil based porous transport layers (PTLs) that contain highly structured pore arrays have shown promise as anode PTLs in proton exchange membrane electrolysis cells. These novel PTLs, fabricated with advanced manufacturing techniques, produce thin, tunable, multifunctional layers with reduced flow and interfacial resistances and high thermal and electric conductivities. To further optimize their design, it is important to understand their fundamental impact on the transport of protons, electrons, and liquid/vapor mixtures in the electrode. In this work, we develop a two-dimensional multiphysics model to simulate the coupled electrochemistry and multiphase transport in an electrolysis cell operated with the novel PTL architecture. The results show that larger pores improve access of water to the anode catalyst layer, which is beneficial for both the oxygen evolution reaction and membrane hydration. Larger pore sizes also improve oxygen gas transport from the catalyst layer, because generated oxygen gas is forced to travel in-plane through the anode catalyst layer until it reaches a pore opening that is connected to a channel. The discussed results confirm that the proposed thin foil based PTLs are fundamentally different from conventional PTLs, such as felts or layered meshes. The model developed in this work also provides generalizable insight into fundamental PEMEC phenomena, such as the competition between liquid and gas phase transport, membrane hydration and water management, and nonuniform electrochemical reactions, which are processes relevant to all PEMEC designs.

25 ENERGY STORAGE↗