Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Numerical stability”

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 685 records · Page 38
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Ideal internal kink stability in presence of plasma flow and neoclassical toroidal viscosity due to energetic particles

Abstract The influence of energetic particles (EPs) on the ideal internal kink mode, in rotating tokamak plasmas, is numerically investigated by simultaneously solving MHD-kinetic hybrid equations together with a toroidal momentum balance equation utilizing the MARS-Q code (Liu et al 2013 Phys. Plasmas 20 042503). The neoclassical toroidal viscous (NTV) torque, induced by precessional drift resonances of trapped energetic particles, acts as the momentum sink term to damp the plasma flow. Quasi-linear initial value simulations show local reduction of the flow amplitude and enhancement of the flow shear near the q = 1 rational surface ( q is the safety factor) due to EP induced NTV. Both effects in turn destabilize the internal kink mode. These numerical findings are robust against the initial linear stability of internal kink, the initial plasma flow profile, as well as the equilibrium distribution model for EPs.

Physics↗
NASA NTRS2021

Wake Instability Behind Isolated Trip Near the Leading Edge of the BOLT-II Configuration

The BOLT-II (Holden Mission) configuration is an extended version of the BOLT flight article and depicts hypersonic boundary-layer transition in the presence of multiple and potentially interacting instability mechanisms. Several numerical studies of the boundary-layer instabilities over these configurations have been reported in the recent literature, including our previous studies of the modal instability characteristics of boundary-layer streaks adjacent to the minor-axis symmetry plane of the BOLT configuration and the wake instabilities behind a diamond planform (“pizza-box”) trip along the symmetry plane on the secondary side of the BOLT-II configuration. The present work extends the latter study to a scaled version of the same trip that is located in the region of nonzero crossflow in the vicinity of the leading edge at X/L = 0.5. Collectively, the trips along the symmetry plane and near the leading edge are the focus of the NASA roughness experiment on the secondary side of the BOLT-II configuration. The laminar basic state computation at the nominal flight design condition of Re ∞ = 5.44 x 10 6 /m and Re ∞ = 2.5 x 10 6 /m shows that the leading-edge trip with k/δ ≈ 0.70 and planform-side-length-to-height ratio of b/k = 3.0 induces multiple asymmetric, longitudinal streaks within the trip wake. The most prominent streak among these resembles a finite amplitude crossflow vortex, and it supports the amplification of multiple families of unstable modes. The application of multi-dimensional instability analysis to the wake flow reveals that the most amplified unstable mode can achieve a peak N-factor of up to 20 by X/L = 0.80, indicating that the onset of transition is more than likely to occur within eighty percent of the model length. To the best of our knowledge, the present study represents the first analysis including nonparallel and curvature effects on hypersonic tripwake instabilities in the presence of boundary-layer crossflow over a three-dimensional configuration.

Boundary layer transition↗
NASA NTRS1980

On the dynamics of large orbiting flexible beams and platforms oriented along the local horizontal

The dynamics and stability of large orbiting flexible beams and platforms oriented along the local horizontal are treated both analytically and numerically. It is assumed that such structures could be gravitationally stabilized by attaching a rigid lightweight dumbbell at the center of mass by a spring loaded hinge which also could provide viscous damping. For the beam it is seen that the small amplitude inplane pitch motion, dumbbell librational motion, and the anti-symmetric elastic modes are all coupled. The three dimensional equations of motion for a circular flat plate in orbit with a two-degree-of-freedom gimballed dumbbell are also developed and show that only those elastic modes described by a single nodal diameter line are influenced by the dumbbell motion. Stability criteria are developed for both examples and a parametric study of the least damped mode characteristics together with numerically simulated transient responses are carried out.

Bainum, P. M.↗
NASA NTRS1978

Investigation of ODE integrators using interactive graphics

Two FORTRAN programs using an interactive graphic terminal to generate accuracy and stability plots for given multistep ordinary differential equation (ODE) integrators are described. The first treats the fixed stepsize linear case with complex variable solutions, and generates plots to show accuracy and error response to step driving function of a numerical solution, as well as the linear stability region. The second generates an analog to the stability region for classes of non-linear ODE's as well as accuracy plots. Both systems can compute method coefficients from a simple specification of the method. Example plots are given.

Brown, R. L.↗
NASA NTRS1992

Investigation of advanced counterrotation blade configuration concepts for high speed turboprop systems. Task 4: Advanced fan section aerodynamic analysis

The purpose of this study is the development of a three-dimensional Euler/Navier-Stokes flow analysis for fan section/engine geometries containing multiple blade rows and multiple spanwise flow splitters. An existing procedure developed by Dr. J. J. Adamczyk and associates and the NASA Lewis Research Center was modified to accept multiple spanwise splitter geometries and simulate engine core conditions. The procedure was also modified to allow coarse parallelization of the solution algorithm. This document is a final report outlining the development and techniques used in the procedure. The numerical solution is based upon a finite volume technique with a four stage Runge-Kutta time marching procedure. Numerical dissipation is used to gain solution stability but is reduced in viscous dominated flow regions. Local time stepping and implicit residual smoothing are used to increase the rate of convergence. Multiple blade row solutions are based upon the average-passage system of equations. The numerical solutions are performed on an H-type grid system, with meshes being generated by the system (TIGG3D) developed earlier under this contract. The grid generation scheme meets the average-passage requirement of maintaining a common axisymmetric mesh for each blade row grid. The analysis was run on several geometry configurations ranging from one to five blade rows and from one to four radial flow splitters. Pure internal flow solutions were obtained as well as solutions with flow about the cowl/nacelle and various engine core flow conditions. The efficiency of the solution procedure was shown to be the same as the original analysis.

Crook, Andrew J.↗
NASA NTRS1978

Investigation of ODE integrators using interactive graphics

In the present paper, two FORTRAN programs are described which use an interactive graphic terminal to generate accuracy and stability plots for a given multistep integrator of ordinary differential equations (ODE). One program treats the fixed-stepsize linear case with complex variable solutions, and generates plots to show accuracy and error response to step driving function of a numerical solution. It also generates the linear stability region. The other program generates an analog with an accuracy plot. Both systems are capable of computing method coefficients from a simple specification of the method. Example plots are given.

Brown, R. L.↗
DOE OSTI2024

Pressure-stabilized fixed-stress iterative solutions of compositional poromechanics

We consider the numerical behavior of the fixed-stress splitting method for coupled poromechanics as undrained regimes are approached. We explain that pressure stability is related to the splitting error of the scheme, not the fact that the discrete saddle point matrix never appears in the fixed-stress approach. This observation reconciles previous results regarding the pressure stability of the splitting method. Using examples of compositional poromechanics with application to geological CO sequestration, we see that solutions obtained using the fixed-stress scheme with a low order finite element-finite volume discretization which is not inherently inf-sup stable can exhibit the same pressure oscillations obtained with the corresponding fully implicit scheme. Moreover, pressure jump stabilization can effectively remove these spurious oscillations in the fixed-stress setting, while also improving the efficiency of the scheme in terms of the number of iterations required at every time step to reach convergence.

42 ENGINEERING↗
DOE OSTI2021

Meshless discretization of the discrete-ordinates transport equation with integration based on Voronoi cells

The time-dependent, gray, linear radiation transport equation is discretized using the meshless local Petrov-Galerkin method with reproducing kernels. The integration is performed using a Voronoi tessellation, which creates a partition of unity that only depends on the position and extent of the kernels. The resolution of the integration automatically follows the particles and requires no manual adjustment. The discretization includes streamline-upwind Petrov-Galerkin stabilization to prevent oscillations and improve numerical conditioning. The angular quadrature is selectively refineable to increase angular resolution in chosen directions. The time discretization is done using backward Euler. The transport solve for each direction and the solve for the scattering source are both done using Krylov iterative methods. The results indicate first-order convergence in time and second-order convergence in space for linear reproducing kernels.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Catalytic production of tetrahydropyran (THP): a biomass-derived, economically competitive solvent with demonstrated use in plastic dissolution

Tetrahydropyran (THP) is a five-carbon heterocyclic ether that is non-carcinogenic, non-peroxide forming, biodegradable, and economically competitive with tetrahydrofuran (THF) as a solvent. In this work, THP has been synthesized from renewable biomass at >99.8% selectivity and 98% yield via hydrogenation of furfural-derived 3,4-dihydropyran (DHP) over Ni/SiO 2 in a continuous flow reactor at 150–200 °C. The apparent activation energy of THP formation is 31 kJ mol -1 , and the reaction orders with respect to the partial pressures of H 2 , DHP, and THP are: 2, 1, and -0.3. The kinetic data has been fitted to a Hougen–Watson model where the rate limiting step is the hydrogenation of adsorbed DHP. Ni/SiO 2 is shown to have a low deactivation rate constant of 0.012 h -1 over 100 h time on stream and can be regenerated in situ. As a performance advantage, THP is shown to be resistant to ring opening polymerization under strongly acidic conditions that THF is not, revealing it to be a superior solvent. Further, the minimum selling price of THP is competitive with the market price of THF ($$900 – 1400 per ton ) at a DHP feedstock cost of $1000 per ton. Conductor-like Screening Model for Real Solvents (COSMO-RS) and molecular dynamics (MD) simulations with 1008 solvents and 8 common plastics have demonstrated that THP can serve as an alternative solvent to THF, 2-methyltetrahydrofuran (MeTHF), and cyclopentyl methyl ether (CPME) for plastic dissolution, especially low-density polyethylene (LDPE), polypropylene (PP), polystyrene (PS) and polyvinyl chloride (PVC). This work establishes THP as a green solvent with excellent thermal, chemical and peroxidative stability that can be used for numerous applications, including waste plastic recycling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

High order explicit local time stepping methods for hyperbolic conservation laws

In this paper we present and analyze a general framework for constructing high order explicit local time stepping (LTS) methods for hyperbolic conservation laws. In particular, we consider the model problem discretized by Runge-Kutta discontinuous Galerkin (RK-DG) methods and design LTS algorithms based on the strong stability preserving Runge-Kutta (SSP-RK) schemes, that allow spatially variable time step sizes to be used for time integration in different regions of the computational domain. The proposed algorithms are of predictor-corrector type, in which the interface information along the time direction is first predicted based on the SSP-RK approximations and Taylor expansions, and then the fluxes over the region of the interface are corrected to conserve mass exactly at each time step. Following the proposed framework, we detail the corresponding LTS schemes with accuracy up to the fourth order, and prove their conservation property and nonlinear stability for the scalar conservation laws. Numerical experiments are also presented to demonstrate excellent performance of the proposed LTS algorithms.

58 GEOSCIENCES↗
DOE OSTI2020

Impact of Vibrational Nonequilibrium on the Supersonic Mode in Hypersonic Boundary Layers

The supersonic mode in hypersonic boundary layers has recently been shown to achieve a larger peak growth rate than the traditional second mode in particular circumstances relevant to free flight. In this environment, high levels of aerodynamic heating are encountered such that incorporation of chemical and vibrational nonequilibrium effects can become critical. The impact of thermal nonequilibrium (TNE) on the supersonic mode in particular has not been thoroughly and systematically investigated. This work uses thermochemical nonequilibrium (TCNE) direct numerical simulation (DNS) and TCNE linear stability theory (LST) to obtain a more complete investigation of the supersonic mode using both nonequilibrium and frozen gas models. The simulation is Mach 5 flow over a 1-mm-nose-radius axisymmetric cone 1 m in length, representative of experimental conditions in ground test facilities. Both LST and DNS results indicate that TNE effects are destabilizing compared with frozen flow and can lead to an N-factor difference of approximately +1 at the end of the cone. LST results also indicate that TNE effects are stabilizing to the second and supersonic modes in comparison with thermal equilibrium. The supersonic mode appeared to be slightly more affected by TNE than the second mode. In conclusion, collectively, the findings in this work suggest that even in ground test facilities where TCNE effects are relatively small compared with free flight, incorporating nonequilibrium models in both the mean flow and stability solvers can have a practical effect on hypersonic boundary-layer transition prediction analyses.

42 ENGINEERING↗
NASA NTRS1978

Modification of the Douglas Neumann program to improve the efficiency of predicting component interference and high lift characteristics

The Douglas Neumann method for low-speed potential flow on arbitrary three-dimensional lifting bodies was modified by substituting the combined source and doublet surface paneling based on Green's identity for the original source panels. Numerical studies show improved accuracy and stability for thin lifting surfaces, permitting reduced panel number for high-lift devices and supercritical airfoil sections. The accuracy of flow in concave corners is improved. A method of airfoil section design for a given pressure distribution, based on Green's identity, was demonstrated. The program uses panels on the body surface with constant source strength and parabolic distribution of doublet strength, and a doublet sheet on the wake. The program is written for the CDC CYBER 175 computer. Results of calculations are presented for isolated bodies, wings, wing-body combinations, and internal flow.

Bristow, D. R.↗
NASA NTRS1981

Weighted-mean scheme for solving incompressible viscous flow

The problem of how a boundary layer responds to the motion of a convexed vortex on a porous wall was investigated. The wall velocity is approximately given by Darcy's law. The vorticity-stream function approach was adopted for solving Navier-Stokes equations of two dimensional incompressible viscous flows. The weighted-mean scheme was used for constructing finite difference approximations of spatial derivatives. Several test problems were solved and numerical results demonstrate clearly the accuracy, stability, and efficiency of the scheme. The weighted mean scheme then can be applied to the vortical flow problem.

Huynh, Q. Q.↗
NASA NTRS1982

On the instability of shock waves attached to wedges and cones

A numerical study is made of the stability of weak and strong shocks attached to wedges and cones. The stability is shown to depend on the boundary conditions imposed, in good agreement with the experimental observations and the principle of minimum entropy. The behavior of the solutions is explained by quasi-static considerations.

Salas, M. D.↗
NASA NTRS1983

Classical linear-control analysis applied to business-cycle dynamics and stability

Linear control analysis is applied as an aid in understanding the fluctuations of business cycles in the past, and to examine monetary policies that might improve stabilization. The analysis shows how different policies change the frequency and damping of the economic system dynamics, and how they modify the amplitude of the fluctuations that are caused by random disturbances. Examples are used to show how policy feedbacks and policy lags can be incorporated, and how different monetary strategies for stabilization can be analytically compared. Representative numerical results are used to illustrate the main points.

Wingrove, R. C.↗
NASA NTRS1986

A shock capturing technique for hypersonic, chemically relaxing flows

A fully coupled, shock capturing technique is presented for chemically reacting flows at high Mach numbers. The technique makes use of a total variation diminishing (TVD) dissipation operator which results in sharp, crisp shocks. The eigenvalues and eigenvectors of the fully coupled system, which includes species conversion equations in addition to the gas dynamics equations, are analytically derived for a general reacting gas. Species production terms for a model dissociating gas are introduced and are included in the algorithm. The convective terms are solved using a first-order TVD scheme while the source terms are solved using a fourth-order Runge-Kutta scheme to enhance stability. Results from one-dimensional numerical experiments are shown for a two species and a three species gas.

Eberhardt, S.↗