Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Formulation”

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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS2007

Comparing Consider-Covariance Analysis with Sigma-Point Consider Filter and Linear-Theory Consider Filter Formulations

Recent literature in applied estimation theory reflects growing interest in the sigma-point (also called unscented ) formulation for optimal sequential state estimation, often describing performance comparisons with extended Kalman filters as applied to specific dynamical problems [c.f. 1, 2, 3]. Favorable attributes of sigma-point filters are described as including a lower expected error for nonlinear even non-differentiable dynamical systems, and a straightforward formulation not requiring derivation or implementation of any partial derivative Jacobian matrices. These attributes are particularly attractive, e.g. in terms of enabling simplified code architecture and streamlined testing, in the formulation of estimators for nonlinear spaceflight mechanics systems, such as filter software onboard deep-space robotic spacecraft. As presented in [4], the Sigma-Point Consider Filter (SPCF) algorithm extends the sigma-point filter algorithm to the problem of consider covariance analysis. Considering parameters in a dynamical system, while estimating its state, provides an upper bound on the estimated state covariance, which is viewed as a conservative approach to designing estimators for problems of general guidance, navigation and control. This is because, whether a parameter in the system model is observable or not, error in the knowledge of the value of a non-estimated parameter will increase the actual uncertainty of the estimated state of the system beyond the level formally indicated by the covariance of an estimator that neglects errors or uncertainty in that parameter. The equations for SPCF covariance evolution are obtained in a fashion similar to the derivation approach taken with standard (i.e. linearized or extended) consider parameterized Kalman filters (c.f. [5]). While in [4] the SPCF and linear-theory consider filter (LTCF) were applied to an illustrative linear dynamics/linear measurement problem, in the present work examines the SPCF as applied to nonlinear sequential consider covariance analysis, i.e. in the presence of nonlinear dynamics and nonlinear measurements. A simple SPCF for orbit determination, exemplifying an algorithm hosted in the guidance, navigation and control (GN&C) computer processor of a hypothetical robotic spacecraft, was implemented, and compared with an identically-parameterized (standard) extended, consider-parameterized Kalman filter. The onboard filtering scenario examined is a hypothetical spacecraft orbit about a small natural body with imperfectly-known mass. The formulations, relative complexities, and performances of the filters are compared and discussed.

Lisano, Michael E.↗
NASA NTRS2008

Stability of Formulations Contained in the Pharmaceutical Payload Aboard Space Missions

Efficacious pharmaceuticals with adequate shelf life are essential for successful space medical operations in support of space exploration missions. Physical and environmental factors unique to space missions such as vibration, G forces and ionizing radiation may adversely affect stability of pharmaceuticals intended for standard care of astronauts aboard space missions. Stable pharmaceuticals, therefore, are of paramount importance for assuring health and wellness of astronauts in space. Preliminary examination of stability of formulations from Shuttle and International Space Station (ISS) medical kits revealed that some of these medications showed physical and chemical degradation after flight raising concern of reduced therapeutic effectiveness with these medications in space. A research payload experiment was conducted with a select set of formulations stowed aboard a shuttle flight and on ISS. The payload consisted of four identical pharmaceutical kits containing 31 medications in different dosage forms that were transported to the International Space Station (ISS) aboard the Space Shuttle, STS 121. One of the four kits was stored on the shuttle and the other three were stored on the ISS for return to Earth at six months intervals on a pre-designated Shuttle flight for each kit; the shuttle kit was returned to Earth on the same flight. Standard stability indicating physical and chemical parameters were measured for all pharmaceuticals returned from the shuttle and from the first ISS increment payload along with ground-based matching controls. Results were compared between shuttle, ISS and ground controls. Evaluation of data from the three paradigms indicates that some of the formulations exhibited significant degradation in space compared to respective ground controls; a few formulations were unstable both on the ground and in space. An increase in the number of pharmaceuticals from ISS failing USP standards was noticed compared to those from the shuttle flight. A comprehensive evaluation of results is in progress.

Putcha, Lakshmi↗
NASA NTRS2000

3D Higher Order Modeling in the BEM/FEM Hybrid Formulation

Higher order divergence- and curl-conforming bases have been shown to provide significant benefits, in both convergence rate and accuracy, in the 2D hybrid finite element/boundary element formulation (P. Fink and D. Wilton, National Radio Science Meeting, Boulder, CO, Jan. 2000). A critical issue in achieving the potential for accuracy of the approach is the accurate evaluation of all matrix elements. These involve products of high order polynomials and, in some instances, singular Green's functions. In the 2D formulation, the use of a generalized Gaussian quadrature method was found to greatly facilitate the computation and to improve the accuracy of the boundary integral equation self-terms. In this paper, a 3D, hybrid electric field formulation employing higher order bases and higher order elements is presented. The improvements in convergence rate and accuracy, compared to those resulting from lower order modeling, are established. Techniques developed to facilitate the computation of the boundary integral self-terms are also shown to improve the accuracy of these terms. Finally, simple preconditioning techniques are used in conjunction with iterative solution procedures to solve the resulting linear system efficiently. In order to handle the boundary integral singularities in the 3D formulation, the parent element- either a triangle or rectangle-is subdivided into a set of sub-triangles with a common vertex at the singularity. The contribution to the integral from each of the sub-triangles is computed using the Duffy transformation to remove the singularity. This method is shown to greatly facilitate t'pe self-term computation when the bases are of higher order. In addition, the sub-triangles can be further divided to achieve near arbitrary accuracy in the self-term computation. An efficient method for subdividing the parent element is presented. The accuracy obtained using higher order bases is compared to that obtained using lower order bases when the number of unknowns is approximately equal. Also, convergence rates obtained using higher order bases are compared to those obtained with lower order bases for selected sample

Fink, P. W.↗
NASA NTRS2013

High Temperature Boost (HTB) Power Processing Unit (PPU) Formulation Study

This technical memorandum is to summarize the Formulation Study conducted during fiscal year 2012 on the High Temperature Boost (HTB) Power Processing Unit (PPU). The effort is authorized and supported by the Game Changing Technology Division, NASA Office of the Chief Technologist. NASA center participation during the formulation includes LaRC, KSC and JPL. The Formulation Study continues into fiscal year 2013. The formulation study has focused on the power processing unit. The team has proposed a modular, power scalable, and new technology enabled High Temperature Boost (HTB) PPU, which has 5-10X improvement in PPU specific power/mass and over 30% in-space solar electric system mass saving.

Chen, Yuan↗
NASA NTRS2013

High-Order Entropy Stable Formulations for Computational Fluid Dynamics

A systematic approach is presented for developing entropy stable (SS) formulations of any order for the Navier-Stokes equations. These SS formulations discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality. They are valid for smooth as well as discontinuous flows provided sufficient dissipation is added at shocks and discontinuities. Entropy stable formulations exist for all diagonal norm, summation-by-parts (SBP) operators, including all centered finite-difference operators, Legendre collocation finite-element operators, and certain finite-volume operators. Examples are presented using various entropy stable formulations that demonstrate the current state-of-the-art of these schemes.

Carpenter, Mark H.↗
NASA NTRS2017

Implicit Formulation of Muscle Dynamics in OpenSim

Astronauts lose bone and muscle mass during spaceflight. Exercise countermeasure is the primary method for counteracting bone and muscle mass loss in space. New spacecraft exercise device concepts are currently being developed for the NASAs new crew exploration vehicle. The NASA Digital Astronaut Project (DAP) uses computational modeling to help determine if the new exercise devices will be effective as countermeasures. The NASA Digital Astronaut Project is developing the ability to utilize predictive simulation to provide insight into the change in kinematics and kinetics with a change in device and gravitational environment (1-g versus 0-g). For example, in space exercise the subject's body weight is applied in addition to the loads prescribed for musculoskeletal maintenance. How and where these loads are applied obviously directly impacts bone and tissue loads. Additionally, due to space vehicle structural requirements, exercise devices are often placed on vibration isolation systems. This changes the apparent impedance or stiffness of the device as seen by the user. Data collection under these conditions is often impractical and limited. Predictive modeling provides a means to have a virtual subject to test hypotheses. Predictive simulation provides a virtual subject for which we are able to perform studies such as sensitivity to device loading and vibration isolation without the need for laboratory kinematic or kinetic test data.Direct Collocation optimization provides an efficient means to perform task based optimization and predictive modeling. It is relatively straight forward to structure a physical exercise task in a Direct Collocation mathematical formulation: perform a motion such that you start at an initial pose, achieve a given amount of deflection i.e a squat, return to the initial pose, and minimize muscle activation cost. Direct Collocation is advantageous in that it does not require numerical integration to evaluate the objective function. Instead, the system dynamics are transformed to discrete time and the optimizer is constrained such that the solution is not considered to be a valid unless the dynamic equations are satisfied at all time points. The simulation and optimization are effectively done simultaneously. Due to the implicit integration, time steps can be more coarse than in a differential equation solver. In a gait scenario this means that that the model constraints and cost function are evaluated at 100 nodes in the gait cycle versus 10,000 integration steps in a variable-step forward dynamic simulation. Furthermore, no time is wasted on accurate simulations of movements that are far from the optimum. Constrained optimization algorithms require a Jacobian matrix that contains the partial derivatives of each of the dynamic constraints with respect to of each of the state and control variables at all time points. This is a large but sparse matrix. An implicit dynamics formulation requires computation of the dynamic residuals f as a function of the states x and their derivatives, and controls u:f(x, dxdt, u) 0If the dynamics of musculoskeletal system are formulated implicitly, the Jacobian elements are often available analytically, eliminating the need for numerical differentiation; this is obviously computationally advantageous. Additionally, implicit formulation of musculoskeletal dynamics do not suffer from singularities from low mass bodies, zero muscle activation, or other stiff system or

physical exercise↗
NASA NTRSDate not supplied

Edge Based Viscous Method for Node-Centered Formulations

This paper presents a novel, efficient, conservative, edge-based method for evaluation of mean flow viscous fluxes and turbulence-model diffusion terms of the Reynolds-averaged Navier-Stokes equations on tetrahedral grids. The new method is implemented in a practical, node-centered, finite-volume computational fluid dynamics solver. The baseline finite-volume scheme that is equivalent to a second-order accurate finite-element Galerkin approximation of viscous stresses is reformulated. The order of operations to compute the cell-based Green-Gauss gradients is changed to combine the operations by edge, which leads to an equivalent formulation on tetrahedral grids, improves efficiency, and preserves the compact discretization stencil based on the nearest neighbors. The computational results presented in this paper verify the implementation of this edge-based method by comparing its accuracy and iterative convergence with those of the well verified and validated baseline formulation. Efficiency gains for residual and Jacobian evaluations result in significant reduction of time to solution. This novel edge-based formulation on tetrahedra can be seamlessly combined with the baseline formulation on cells of other types for computing solutions on mixed-element grids.

Edge Based↗
NASA NTRS2020

Broadening JPL’s Mission Formulation Paradigm with Human Centered Design

Within NASA’s highly competitive environment for funding, Human Centered Design (HCD) and cybernetics could provide advantages to proposers during the mission formulation phase. Opportunities are limited when it comes to funding new science missions. Proposers are challenged to make a compelling case about the scientific desirability, technical feasibility, and resource viability of their concepts. Organizations follow established processes for proposal development using teams that typically include scientists, engineers, and managers. These team members are highly experienced subject matter experts (SME) in their own disciplines, and can respond to requirements from the solicitation. However, they are typically not trained as designers and communicators. Their approach is rooted within NASA’s science and technology paradigm. How can we improve the proposal development process, refine workflow between team members, and deliver clear and appealing offerings to the stakeholders and evaluators? These questions have been addressed by today’s most innovative companies (e.g., Apple, Google, 3M, Dyson), where the design process is not limited simply to engineering and management, but involves an all-encompassing approach drawing from fields such as social sciences, design, and the arts. Like these commercial enterprises, NASA currently employs systems thinking and integrated design, but can benefit further by moving beyond its current practices, which are mostly driven by rigid engineering, technology, science, and project management considerations. At JPL’s Innovation Foundry and through the Solar System Mission Formulation Office, we broadened this paradigm by including HCD in the mission formulation workflow. Our goal was to create a proposal with improved clarity and appeal, thus helping our team to communicate its message and aid evaluators with their work. In this paper we provide examples and lessons learned from our recent proposal development effort using HCD. We discuss touch points where we infused non-linear designerly approaches and cybernetic circularity into the workflow. Implemented design topics include operational design for team building; process design throughout distinct phases of the proposal development and writing process; communication design for streamlined exchange of information within the team and to stakeholders; interaction design; graphic design; and creating boundary objects. While these approaches may feel new or foreign to SMEs and managers in the aerospace community, they produced significant benefits in this mission formulation effort. We will describe how such approaches can be used to broaden NASA’s technology-driven paradigm through design, thus creating an environment which fosters innovation, improved communication, and strategic advantage for proposers and their organizations.

Turner, Neal↗
NASA NTRSDate not supplied

Jet Noise Modeling Using an Acoustic Analogy: From Theoretical Formulation to Practical Noise Predictions

In this presentation an overview of the development of an acoustic analogy formulation, and its implementation into a reduced-order prediction method for turbulent jet mixing noise, will be given. The definition and rationale of an acoustic analogy approach to the prediction of flow-generated noise will be provided. A high-level description of the mathematical processes involved will be outlined in the context of a particular formulation developed at NASA Glenn Research Center. The modelling approximations needed to implement the general theoretical formulation into a practical noise prediction tool will be discussed. Sample results obtained using a noise prediction code based on the NASA Glenn formulation, and comparisons with experimental data, will be presented for a series of turbulent jet test cases. A view on the prospects for continued use of acoustic analogy-based methods for the prediction of flow-generated noise and the assessment of noise-reduction technologies will conclude the presentation.

Jet noise↗
DOE OSTI2024

A simplified all-frequency stable formulation with an implicit Coulomb gauge

A potential-based finite element formulation has been developed in the past to circumvent the low-frequency breakdown issues commonly encountered in electromagnetic (EM) simulations of low-frequency and multiscale problems. In this formulation, the magnetic vector and electric scalar potentials have been employed to express the electric field and magnetic flux, leading to a set of two equations that represents all four Maxwell’s equations and the current continuity equation. To enforce the Coulomb gauge, an auxiliary potential has been introduced, which results in a total of three equations to be solved simultaneously. To reduce the number of equations and unknowns needed in a simulation, a simplified formulation is proposed in this paper to enforce the Coulomb gauge implicitly without the need for the auxiliary potential. A numerical example is given to demonstrate the accuracy of the proposed formulation.

Mekonnen, Minyechil↗
DOE OSTI2023

Shear and combustion characterization of printable ammonium perchlorate composite propellant formulations

Seven formulations of ammonium perchlorate composite propellant (APCP) are developed and their properties relevant for successful additive manufacture are characterized. Extrusion in a custom-built 3D printing system and spindle viscometry are used to collect viscosity measurements of curing primary and non-curing secondary versions of the formulations. The formulations that behave similarly to a Bingham plastic, with apparent viscosities between 4 and 8 thousand Pa*s at 30 minutes post-mix, are determined to be most suitable for printing applications. Measurements of one material show a yield stress of 1 kPa. Ambient pressure burn rates of 2.0–2.9 mm/s were measured for the compositions tested. All measured burn rates were comparable to the lower end of typical burn rates for APCP. In conclusion, the results of the characterization demonstrate a propellant suitable for use in a 3D printing system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Note on two formulations of Crank-Nicolson method for Navier-Stokes equations

Here, we consider two formulations of the Crank-Nicolson (CN) method for the Navier-Stokes equations (NSE). The “natural” way of implementing CN for NSE is formally second order accurate in time for both velocity and pressure, whereas another formulation approximates pressure with only first order accuracy in time. Both versions of the method are applied to the benchmark problem of computing drag and lift in the flow around a cylinder. We show that the presumably more accurate version of the CN can create a solution with nonphysical oscillations and give incorrect predictions for the maximal drag coefficient, whereas the other formulation of the method predicts the drag and lift coefficients more accurately and does not introduce nonphysical oscillations. We locate the source of the issue and suggest several remedies.

Crank-Nicolson↗
DOE OSTI2026

Excipient screening by lyophilization provides insights into spray drying formulations for nanoparticle vaccines

Nanoparticles have shown great promise as delivery platforms in the development of tunable and safe vaccines. Nanolipoprotein particles (NLPs), also known as nanodiscs, are discoidal nanoparticles composed of a lipid bilayer stabilized at their periphery by apolipoproteins. Under the right conditions, the NLP self-assembly process is highly customizable in terms of lipids and apolipoprotein constituents, allowing for tunable physical and chemical characteristics. This flexibility allows a wide range of vaccine antigens and adjuvants to be incorporated onto the NLP platform for tailored vaccine design. The stability of NLPs during long term storage is a very important factor in developing a vaccine delivery platform suitable for widespread global use. When stored in a solution for extended periods of time, NLPs dissociate into their corresponding lipids and protein constituents, leading to particle degradation. Proper stabilization of NLPs can often be achieved by lyophilization (i.e. freeze-drying), a method widely used for various applications including pharmaceuticals. This process, however, can be damaging to particles without the presence of lyoprotectants or excipients that help maintain particle stability during lyophilization. Another method used to stabilize vaccines and pharmaceuticals is spray drying, a process that converts liquid formulations into dry powders through controlled heating and airflow. While spray drying is rapid, scalable, and cost-effective, lyophilization is typically a gentler process that better retains biomolecule structure and function. Both processes use excipients for particle stabilization, so lyophilization can be used as a surrogate to test stability of NLPs, to down-select formulations that may withstand the harsher conditions of spray drying. To screen different formulations, NLPs were synthesized and purified to homogeneity by size exclusion chromatography (SEC) and samples were prepared with a wide range of lyoprotectants and/or excipients. To assess the protective effects of excipients on NLPs upon spray drying, both pre- and post-lyophilized samples were analyzed by SEC. To assess the protective effects upon heating (encountered during the spray drying process), NLP samples were incubated at elevated temperatures prior to SEC analysis. The lyoprotectants and excipients evaluated in this study had different efficiencies in protecting NLPs during lyophilization and heating tests. Trehalose, for example, exhibits stabilization on NLPs both upon lyophilization and heating whereas leucine accelerated NLP dissociation. Although some lyoprotectants are effective by themselves, different combinations can decrease the stabilization of NLPs. Shelf-stable vaccines that do not require cold-chain storage are essential for global accessibility and our findings provide fundamental insight into how to advance NLP-based vaccines for these applications.

Serrano, Litzay J [Lawrence Livermore National Lab↗
DOE OSTI2026

Formulation and Performance Evaluation of Epoxy Sealant Systems for Double-Shell Tank Bottom Refurbishment

The performance of epoxy sealants used in the refurbishment of double-shell tank (DST) systems requires balancing processability, thermomechanical stability, and adhesion to cementitious substrates. This study incorporates Heloxy 8 as a reactive diluent into Westlake 862 epoxy to tailor workability and cured-state properties. Rheological time-sweep analysis demonstrates that increasing the diluent content significantly reduces complex viscosity and extends workability, thereby improving pumpability and flow for large-area applications. However, the targeted 2-hour processing window is not fully achieved. Differential scanning calorimetry (DSC) confirms that all formulations cure at room temperature to glass transition temperatures ( T g ) at least 20 °C above the maximum DST operating temperature (27 °C), thereby ensuring service in the glassy regime. Dynamic mechanical analysis (DMA) reveals formulation-dependent reductions in tan delta and increases in storage modulus, indicating increasingly elastic and mechanically stable networks with diluent incorporation. Pull-off adhesion testing shows that modified formulations (70–90% Westlake epoxy) exhibit significantly higher adhesion strengths than the unmodified system. Grout cohesive failure indicates that interfacial bonding exceeds substrate strength. Collectively, these results demonstrate that controlled reactive diluent incorporation enables optimization of processing behavior, interfacial adhesion, and thermomechanical performance, supporting the suitability of the modified epoxy systems as durable sealant layers for cementitious barrier applications in hazardous waste containment infrastructure.

Differential scanning calorimetry↗
DOE OSTI2024

Feasibility of Formulating Ecosystem Biogeochemical Models From Established Physical Rules

Abstract To improve the predictive capability of ecosystem biogeochemical models (EBMs), we discuss the feasibility of formulating biogeochemical processes using physical rules that have underpinned the many successes in computational physics and chemistry. We argue that the currently popular empirically based approaches, such as multiplicative empirical response functions and the law of the minimum, will not lead to EBM formulations that can be continuously refined to incorporate improved mechanistic understanding and empirical observations of biogeochemical processes. Instead, we propose that EBM parameterizations, as a lossy data compression problem, can be better formulated using established physical rules widely used in computational physics and chemistry, and different biogeochemical processes can be more robustly integrated within a reactive‐transport framework. Through several examples, we demonstrate how mathematical representations derived from physical rules can improve understanding of relevant biogeochemical processes and enable more effective communication between modelers, observationalists, and experimentalists regarding essential questions, such as what measurements are needed to meaningfully inform models and how can models generate new process‐level hypotheses to test in empirical studies. Finally, while empirical models with more parameters are often less robust, physical rules‐based models can be more robust and show lower predictive equifinality, stemming from their enhanced consistency in representations of processes, interactions and spatial scaling.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Phase field dislocation dynamics formulation coupled with Fourier based micromechanics solver and its application to grain boundary–dislocation interactions

A new phase field dislocation dynamics (PFDD) formulation for homogeneous and heterogeneous materials is presented, which couples micromechanical solvers and the time-dependent Ginzburg–Landau equation. The strain fields are obtained from the micromechanical solver by solving the Lippmann–Schwinger equation and then used to define energy terms to model the evolution of the dislocations. Grain boundary (GB)–dislocation interactions are studied using the coupled PFDD formulation and by describing GBs as inclusions. GB energy and stiffness tensors are computed from molecular statics simulations, and a newly proposed lattice energy term that is dependent on the GB energy is considered in the calculations. Interaction of a screw dislocation with minimum energy and metastable states of low and high angle ⟨110⟩ symmetric tilt grain boundaries are studied. We show good agreement between predictions from our PFDD formulation and molecular dynamics simulations of grain boundary–dislocation interactions.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Galerkin formulation of path integrals in lattice field theory

We present a mathematical framework for Galerkin formulations of path integrals in lattice field theory. The framework is based on using the degrees of freedom (DOFs) associated to a Galerkin discretization as the fundamental lattice variables. We formulate standard concepts in lattice field theory, such as the partition function and correlation functions, in terms of the DOFs. For example, using continuous finite element spaces, we show that the two-point spatial correlation function can be defined between any two points on the domain (as opposed to at just lattice sites) and furthermore, this two-point function satisfies a weak propagator (or Green’s function) identity, in analogy to the continuum case, as well as a convergence estimate obtained from the standard finite element techniques. Furthermore, this framework leads naturally to higher-order formulations of lattice field theories by considering higher-order finite element spaces for the Galerkin discretization. We consider analytical and numerical examples of scalar field theory to investigate how increasing the order of piecewise polynomial finite element spaces affect the approximation of lattice observables. Finally, we sketch an outline of this Galerkin framework in the context of gauge field theories.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Pseudospectral particle-in-cell formulation with arbitrary charge and current-density time dependencies for the modeling of relativistic plasmas

This paper introduces a formulation of the particle-in-cell (PIC) method for the modeling of relativistic plasmas, that leverages the ability of the pseudospectral analytical time-domain solver (PSATD) to handle arbitrary time dependencies of the charge and current densities during one PIC cycle (applied to second-order polynomial dependencies here). Here, the formulation is applied to a modified set of Maxwell's equations that was proposed earlier in the context of divergence cleaning, and to recently proposed extensions of the PSATD-PIC algorithm. Detailed analysis and testings revealed that, under some condition, the formulation can expand the range of numerical parameters under which PIC simulations are stable and accurate when modeling relativistic plasmas such as, e.g., plasma-based particle accelerators.

43 PARTICLE ACCELERATORS↗