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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.

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NASA NTRS1981

Vibration of a liquid with a free surface in a spinning spherical tank

The problem of forced fluid vibrations in a partially filled spinning spherical tank is solved numerically by using the finite element method. The governing equations include Coriolis acceleration and spatially homogeneous vorticity. An exponential instability is detected in the present simulation for fill ratios below 0.5 and centrifugal acceleration to thrust ratios less than 1.7. This fictitious instability appears in the model as a result of the homogeneous vortex assumption since the free slosh equations are neutrally stable in the Liapunov sense.

El-Raheb, M.↗

NASA NTRS1979

Homogeneous vortex model for liquid slosh in spinning spherical tanks

The problem of forced fluid sloshing in a partially filled spinning spherical tank is solved numerically using the finite element method. The governing equations include Coriolis acceleration, empirical fluid damping and spatially homogeneous vorticity first introduced by Pfeiffer. An exponential instability similar to flutter is detected in the present simulation for fill ratios below 50 percent. This instability appears in the model as a result of the homogeneous vortex assumption since the free slosh equations are neutrally stable in the Liapunov sense.

El-Raheb, M.↗

NASA NTRS1983

New discretization and solution techniques for incompressible viscous flow problems

Several topics arising in the finite element solution of the incompressible Navier-Stokes equations are considered. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. The role of artificial viscosity in viscous flow calculations is studied, emphasizing work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some modifications are mentioned.

Gunzburger, M. D.↗

NASA NTRS2004

Mid-frequency Band Dynamics of Large Space Structures

High and low intensity dynamic environments experienced by a spacecraft during launch and on-orbit operations, respectively, induce structural loads and motions, which are difficult to reliably predict. Structural dynamics in low- and mid-frequency bands are sensitive to component interface uncertainty and non-linearity as evidenced in laboratory testing and flight operations. Analytical tools for prediction of linear system response are not necessarily adequate for reliable prediction of mid-frequency band dynamics and analysis of measured laboratory and flight data. A new MATLAB toolbox, designed to address the key challenges of mid-frequency band dynamics, is introduced in this paper. Finite-element models of major subassemblies are defined following rational frequency-wavelength guidelines. For computational efficiency, these subassemblies are described as linear, component mode models. The complete structural system model is composed of component mode subassemblies and linear or non-linear joint descriptions. Computation and display of structural dynamic responses are accomplished employing well-established, stable numerical methods, modern signal processing procedures and descriptive graphical tools. Parametric sensitivity and Monte-Carlo based system identification tools are used to reconcile models with experimental data and investigate the effects of uncertainties. Models and dynamic responses are exported for employment in applications, such as detailed structural integrity and mechanical-optical-control performance analyses.

dynamics↗

NASA NTRS1983

New discretization and solution techniques for incompressible viscous flow problems

This paper considers several topics arising in the finite element solution of the incompressible Navier-Stokes equations. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. Following this, the role of artificial viscosity in viscous flow calculations is studied, emphasizing recent work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some recent modifications are mentioned.

Gunzburger, M. D.↗

DOE OSTI2024

Sequential formulation of all‐way coupled finite strain thermoporomechanics for largely deformable gas hydrate deposits

We develop a numerically stable sequential formulation of thermoporomechanics for largely deformable gas hydrate deposits, extended from the fixed stress split of infinitesimal transformation. Constitutive equations are based on the total Lagrangian approach for both flow and geomechanics, including dynamic full tensor permeability and thermal conductivity updated from the deformation gradient. For space discretization, we take the cell-centered finite volume and node-based finite element method for flow and geomechanics, respectively. Then, we propose a sequential implicit method for all-way coupled thermoporomechanics, where the nonisothermal multiphase flow problem of gas hydrates is solved implicitly first and then the geomechanics problem is solved implicitly at the next step. During solution of the flow problem, we fix the rate of first Pioal total stress for numerical stability as well as apply porosity correction and entropy correction to account for geomechanical effects. We test numerical examples where flow and geomechanics parameters are based on deep oceanic gas hydrate deposits. When applying depressurization, even though the results between the infinitesimal transformation and finite strain geomechanics are similar in the early stages due to small deformation, we find differences between them in the late times as deformation becomes large. Accordingly, permeability and thermal conductivity tensors become nonisotropic full tensors although they are initially isotropic. Furthermore, we identify numerical stability of the developed sequential method from the test cases that exhibit the highly complex coupled gas hydrate systems with large deformation. Thus, the proposed sequential formulation can be applied in largely deformable gas hydrate systems.

42 ENGINEERING↗

NASA NTRS1990

A finite element solver for 3-D compressible viscous flows

Computation of the flow field inside a space shuttle main engine (SSME) requires the application of state of the art computational fluid dynamic (CFD) technology. Several computer codes are under development to solve 3-D flow through the hot gas manifold. Some algorithms were designed to solve the unsteady compressible Navier-Stokes equations, either by implicit or explicit factorization methods, using several hundred or thousands of time steps to reach a steady state solution. A new iterative algorithm is being developed for the solution of the implicit finite element equations without assembling global matrices. It is an efficient iteration scheme based on a modified nonlinear Gauss-Seidel iteration with symmetric sweeps. The algorithm is analyzed for a model equation and is shown to be unconditionally stable. Results from a series of test problems are presented. The finite element code was tested for couette flow, which is flow under a pressure gradient between two parallel plates in relative motion. Another problem that was solved is viscous laminar flow over a flat plate. The general 3-D finite element code was used to compute the flow in an axisymmetric turnaround duct at low Mach numbers.

Reddy, K. C.↗

NASA NTRS2003

Finite Element Method for Capturing Ultra-relativistic Shocks

While finite element methods are used extensively by researchers solving computational fluid dynamics in fields other than astrophysics, their use in astrophysical fluid simulations has been predominantly overlooked. Current simulations using other methods such as finite difference and finite volume (based on finite difference) have shown remarkable results, but these methods are limited by their fundamental properties in aspects that are important for simulations with complex geometries and widely varying spatial and temporal scale differences. We have explored the use of finite element methods for astrophysical fluids in order to establish the validity of using such methods in astrophysical environments. We present our numerical technique applied to solving ultra-relativistic (Lorentz Factor Gamma >> 1) shocks which are prevalent in astrophysical studies including relativistic jets and gamma-ray burst studies. We show our finite element formulation applied to simulations where the Lorentz factor ranges up to 2236 and demonstrate its stability in solving ultra-relativistic flows. Our numerical method is based on the Flowfield Dependent Variation (FDV) Method, unique in that numerical diffusion is derived from physical parameters rather than traditional artificial viscosity methods. Numerical instabilities account for most of the difficulties when capturing shocks in this regime. Our method results in stable solutions and accurate results as compared with other methods.

Richardson, G. A.↗

DOE OSTI2020

The second-generation Shifted Boundary Method and its numerical analysis

Recently, the Shifted Boundary Method (SBM) was proposed within the class of unfitted (or immersed, or embedded) finite element methods. By reformulating the original boundary value problem over a surrogate (approximate) computational domain, the SBM avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we present enhanced variational SBM formulations for the Poisson and Stokes problems with improved flexibility and robustness. These simplified variational forms allow to relax some of the assumptions required by the mathematical proofs of stability and convergence of earlier implementations. First, we show that these new SBM implementations can be proved asymptotically stable and convergent even without the rather restrictive assumption that the inner product between the normals to the true and surrogate boundaries is positive. Second, we show that it is not necessary to introduce a stabilization term involving the tangential derivatives of the solution at Dirichlet boundaries, therefore avoiding the calibration of an additional stabilization parameter. Finally, we prove enhanced L 2 -estimates without the cumbersome assumption – of earlier proofs – that the surrogate domain is convex. Instead we rely on a conventional assumption that the boundary of the true domain is smooth, which can also be replaced by requiring convexity of the true domain. The aforementioned improvements open the way to a more general and efficient implementation of the Shifted Boundary Method, particularly in complex three-dimensional geometries. We complement these theoretical developments with numerical experiments in two and three dimensions.

42 ENGINEERING↗

NASA NTRS1973

The finite element method in shell stability analysis.

A development of the finite element method for thin shell instability analysis is presented, covering three principal aspects: (1) representation of shell geometry, (2) representation of element behavior, and (3) algorithmic tools for solution of the large-order systems of nonlinear algebraic equations which characterize various phases of shell instability. Two shell elements are described, an arbitrary quadrilateral and a triangle, and numerical results are presented for two widely-employed comparison problems for linear (stable) analysis. Two shell problems which include instability effects are also solved.-

Gallagher, R. H.↗

DOE OSTI2024

Bifurcation of equilibrium positions for ellipsoidal particles in inertial shear flows between two walls

We conducted a systematic numerical investigation of spherical, prolate and oblate particles in an inertial shear flow between two parallel walls, using smoothed particle hydrodynamics (SPH). It was previously shown that above a critical Reynolds number, spherical particles experience a supercritical pitchfork bifurcation of the equilibrium position in shear flow between two parallel walls, namely that the central equilibrium position becomes unstable, leading to the emergence of two new off-centre stable positions (Foxet al.,J. Fluid Mech., vol. 915, 2021). This phenomenon was unexpected given the symmetry of the system. In addition to confirming this finding, we found, surprisingly, that ellipsoidal particles can also return to the centre position from the off-centre positions when the particle Reynolds number is further increased, while spherical particles become unstable under this increased Reynolds number. By utilizing both SPH and the finite element method for flow visualization, we explained the underlining mechanism of this reverse of bifurcation by altered streamwise vorticity and symmetry breaking of pressure. Furthermore, we expanded our investigation to include asymmetric particles, a novel aspect that had not been previously modelled, and we observed similar trends in particle dynamics for both symmetric and asymmetric ellipsoidal particles. While further validation through laboratory experiments is necessary, our research paves the road for development of new focusing and separation methods for shaped particles.

Mechanics↗

DOE OSTI2022

An efficient iterative method for dynamical Ginzburg-Landau equations

Here we propose a new finite element approach to solving the time-dependent Ginzburg-Landau equations for superconductivity under the temporal gauge and design an efficient preconditioner for the Newton iteration of the resulting discrete system. It solves the vector magnetic potential in $H$(curl) space by the lowest order of the second kind N´ed´elec element. This approach offers a simple way to deal with the boundary conditions, leading to a stable and reliable performance for superconductor geomtry with reentrant corners. The bench-marking in numerical simulations verifies the efficiency of the proposed preconditioner, which can be employed to significantly speed up in large-scale computations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1991

A new finite element formulation for computational fluid dynamics. X - The compressible Euler and Navier-Stokes equations

A space-time element method is presented for solving the compressible Euler and Navier-Stokes equations. The proposed formulation includes the variational equation, predictor multi-corrector algorithms and boundary conditions. The variational equation is based on the time-discontinuous Galerkin method, in which the physical entropy variables are employed. A least-squares operator and a discontinuity-capturing operator are added, resulting in a high-order accurate and unconditionally stable method. Implicit/explicit predictor multi-corrector algorithms, applicable to steady as well as unsteady problems, are presented; techniques are developed to enhance their efficiency. Implementation of boundary conditions is addressed; in particular, a technique is introduced to satisfy nonlinear essential boundary conditions, and a consistent method is presented to calculate boundary fluxes. Numerical results are presented to demonstrate the performance of the method.

Shakib, Farzin↗

NASA NTRS1988

Composite interlaminar fracture toughness - Three-dimensional finite-element modeling for mixed mode I, II, and fracture

A computational method/procedure is described which can be used to simulate individual and mixed mode interlaminar fracture progression in fiber composite laminates. Different combinations of Modes 1, 2, and 3 fracture are simulated by varying the crack location through the specimen thickness and by selecting appropriate unsymmetric laminate configurations. The contribution of each fracture mode to strain energy release rate is determined by the local crack closure methods while the mixed mode is determined by global variables. The strain energy release rates are plotted versus extending crack length, where slow crack growth, stable crack growth, and rapid crack growth regions are easily identified. Graphical results are presented to illustrate the effectiveness and versatility of the computational simulation for: (1) evaluating mixed-mode interlaminar fracture, (2) for identifying respective dominant parameters, and (3) for selecting possible simple test methods.

Murthy, Pappu L. N.↗

DOE OSTI2026

Data for Clumping Index Estimation With 30°-tilted Cameras in Row Crops: Evaluation of Methods and Segment Size Effects

The clumping index (CI) quantifies the spatial distribution of foliage elements and is essential for accurately estimating the plant area index (PAI), canopy radiative transfer, and photosynthesis. Traditionally, the finite-length averaging method (LX), the gap size distribution method (CC), and a combined approach of CC and LX (CLX) have been applied to instruments like TRAC and digital hemispherical photography to estimate CI. However, a comprehensive evaluation of these methods in row crops remains limited, especially regarding the influence of segment size on CI. Meanwhile, digital cameras offer a cost-effective and user-friendly solution for canopy measurements in row crops, yet their application in this context remains underexplored. In this study, we employed a new approach using a 30°-tilted digital camera to estimate CI in corn and soybean fields, applying the LX, CC, and CLX methods. We systematically assessed the performance of these three methods by combining field measurements in real-world fields with simulations using the LESS 3D radiative transfer model. Our results showed that CLX applied to the whole image and 45° segment offered accurate estimation of CI (bias within ±0.1, RMSE < 0.2) and PAI (bias within ±0.4, RMSE < 1) in real-world fields and LESS simulations. The accuracy of the LX method was highly sensitive to segment size, with the best performance observed at the 15° segment (PAI bias within ±0.4). In contrast, the CC method remained stable across different segment sizes, and its performance was generally comparable to that of LX, except at the 15° segment. Across view zenith angles, CI derived from CC generally showed a continuous increase, while those from LX and CLX followed a rising trend at small zenith angles but began to decline at 68°, likely due to an increasing proportion of no-gap segments. Seasonally, LX tended to show decreasing CI during early growth stages but increased as the canopy matured, whereas CC and CLX showed gradually increasing CI before plateauing at peak PAI. The 30°-tilted camera effectively captured CI variations across different angles and growth stages, making it a practical and robust instrument for row crop canopy structure analysis. Applying these CI methods to digital cameras offers a low-cost and accessible CI estimation alternative, improving canopy structure monitoring accuracy in row crops.

Modeling↗

NASA NTRS1986

Composite interlaminar fracture toughness: Three-dimensional finite element modeling for mixed mode 1, 2 and 3 fracture

Murthy, P. L. N.↗

DOE OSTI2022

Modeling Isotope Separation in Electrochemical Lithium Deposition

Naturally occurring Li consists of two stable isotopes, 6 Li with an abundance of about 7.5%, and 7 Li making up the remainder with 92.5%. The development of a 6 Li enrichment technique, in terms of technical reliability and environmental safety to reach 6 Li future requirements, represents a key step in the roadmap for nuclear fusion energy supply worldwide. This paper uses finite element analysis-based models to simulate electrochemical Li isotope separation, which is an attractive method in terms of simplicity, safety, and scalability. In the model, we quantitatively analyze how different electrochemical factors including thermodynamics, charge-transfer kinetics, and diffusivities affect the separation process (separation factor), together with cell parameters, such as cell length and current density. The maximum separation factor of 1.128 could be obtained with the cell under the optimal thermodynamic, kinetic, and diffusive conditions, which is among the highest separation factors ever reported. Furthermore, these results will assist in designing the actual isotope separation setup with large separation factor and appropriate timing for sample collection.

07 ISOTOPE AND RADIATION SOURCES↗

NASA NTRS1982

Nonlinear structural and life analyses of a combustor liner

Three dimensional, nonlinear finite element structural analyses were performed for a simulated combustor liner specimen to assess the capability of nonlinear analyses using classical inelastic material models to represent the thermoplastic creep response of the one half scale component. Results indicate continued cyclic hardening and ratcheting while experimental data suggested a stable stress strain response after only a few loading cycles. The computed stress strain history at the critical location was put into two life prediction methods, strainrange partitioning and a Pratt and Whitney combustor life prediction method to evaluate their ability to predict cyclic crack initiation. It is found that the life prediction analyses over predicted the observed cyclic crack initiation life.

Moreno, V.↗