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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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At least 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Numerical calculation of transonic flow past a swept wing by a finite volume method

The utility of numerical methods for predicting transonic flows over wings and bodies is well established. The computer program FLO22, based on a method presented earlier, has actually been widely used to calculate the aerodynamic performance of wings of transport aircraft. Provided that a correction is made for the displacement effect of the viscous boundary layer, this code has been found to give predictions which are accurate enough to serve as a useful design guide. The main disadvantages of the scheme used in FLO22 are the use of nonconservative difference formulas, which result in a failure to satisfy conservation of mass across shock waves, and the difficulty of finding suitable transformations of coordinates to permit the treatment of more complex geometric configurations. The method described here is an attempt to overcome these shortcomings, while retaining the successful features of the previous method. The basic idea is to use a discrete approximation which directly represents a balance of the mass flow through small volume elements. This leads to a relatively simple treatment of the potential flow equation in conservation form.

Jameson, A.↗
DOE OSTI2021

Second-order invariant domain preserving approximation of the compressible Navier–Stokes equations

Here, we present a fully discrete approximation technique for the compressible Navier–Stokes equations that is second-order accurate in time and space, semi-implicit, and guaranteed to be invariant domain preserving. The restriction on the time step is the standard hyperbolic CFL condition, i.e. τ ≲ O ( h ) / V where V is some reference velocity scale and h the typical meshsize.

42 ENGINEERING↗
DOE OSTI2020

Discontinuous Galerkin sparse grids methods for time domain Maxwell’s equations

In this paper, we present a time-explicit sparse grid discontinuous Galerkin method for solving the three-dimensional time-domain Maxwell equations. The conservation properties and convergence rates are established for different choices of numerical fluxes. The convergence rates are proved theoretically and then verified by several numerical examples. Even though our scheme does not preserve the divergence, but by implying the higher order polynomial, one can observe the same convergence rate as numerical solution. Several numerical tests are presented to validate these conclusions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1989

An Entropy-Based Approach to Nonlinear Stability

Many numerical methods used in computational fluid dynamics (CFD) incorporate an artificial dissipation term to suppress spurious oscillations and control nonlinear instabilities. The same effect can be accomplished by using upwind techniques, sometimes augmented with limiters to form Total Variation Diminishing (TVD) schemes. An analysis based on numerical satisfaction of the second law of thermodynamics allows many such methods to be compared and improved upon. A nonlinear stability proof is given for discrete scalar equations arising from a conservation law. Solutions to such equations are bounded in the L sub 2 norm if the second law of thermodynamics is satisfied in a global sense over a periodic domain. It is conjectured that an analogous statement is true for discrete equations arising from systems of conservation laws. Analysis and numerical experiments suggest that a more restrictive condition, a positive entropy production rate in each cell, is sufficient to exclude unphysical phenomena such as oscillations and expansion shocks. Construction of schemes which satisfy this condition is demonstrated for linear and nonlinear wave equations and for the one-dimensional Euler equations.

Merriam, Marshal L.↗
NASA NTRSDate not supplied

Explicit Discontinuous Galerkin Methods for Conservation Laws

The two explicit DG methods in this study are based on a ‘predictor-corrector’ formulation, the first introduced by Lörcher, Gassner, and Munz (2007, 2008) called space–time expansion discontinuous Galerkin or STE-DG scheme, and the second, introduced independently by the author (Huynh 2006, 2013) called the upwind moment scheme. The predictor step of the two methods is essentially identical using a Cauchy-Kovalevsky (CK) procedure, which involves no interaction of the data among neighboring cells. The corrector step also shares the same space-time integration formulation and is where interaction of the data among neighboring cells takes place; the difference, however, is in how the resulting space-time volume integral is estimated. As a consequence of the different estimates, for the case of advection in one spatial dimension (1D), the moment scheme has a CFL (Courant-Friedrichs-Lewy) condition of 1 for all p and is accurate to order 2p+1, i.e., it possesses the super accuracy property, whereas the STE-DG method has a more restrictive CFL condition and is accurate to the expected order of p+1. For 1D advection, compared with the CFL conditions of 1/(2p+1) of standard RK-DG (Runge-Kutta) scheme where space and time discretization are of the same order, the moment scheme allows a significantly larger time step size. It also turns out that the scheme yields a result identical to Van Leer’s scheme III (1977), which amounts to shifting the data a distance of advection corresponding to the time step and projecting the result onto the space of polynomial solutions. Contrary to Van Leer’s approach, however, the space-time ‘predictor-corrector’ formulation facilitates extensions to the case of systems of equations. Concerning 2D extensions, in the case of advection, when the flow is along the diagonal direction, the CFL conditions for the moment schemes become restrictive as will be shown by Fourier (Von Neumann) stability and accuracy analyses. Since the moment scheme employs the right Radau points as collocation points in time, the method is closely related to the implicit Radau IIA scheme, which is stable for any time step size. The role of Radau IIA in relieving stability restriction for these explicit DG schemes remains to be explored

Discontinuous Galerkin↗
DOE OSTI2024

Feasibility and performance of the staged Z-pinch: A one-dimensional study with FLASH and MACH2

Z-pinch platforms constitute a promising pathway to fusion energy research. Here, we present a one-dimensional numerical study of the staged Z-pinch (SZP) concept using the FLASH and MACH2 codes. We discuss the verification of the codes using two analytical benchmarks that include Z-pinch-relevant physics, building confidence on the codes' ability to model such experiments. Then, FLASH is used to simulate two different SZP configurations: a xenon gas-puff liner (SZP1*) and a silver solid liner (SZP2). The SZP2 results are compared against previously published MACH2 results, and a new code-to-code comparison on SZP1* is presented. Using an ideal equation of state and analytical transport coefficients, FLASH yields a fuel convergence ratio (CR) of approximately 39 and a mass-averaged fuel ion temperature slightly below 1 keV for the SZP2 scheme, significantly lower than the full-physics MACH2 prediction. For the new SZP1* configuration, full-physics FLASH simulations furnish large and inherently unstable CRs (>300) but achieve fuel ion temperatures of many kilo-electron volts. While MACH2 also predicts high temperatures, the fuel stagnates at a smaller CR. The integrated code-to-code comparison reveals how magnetic insulation, heat conduction, and radiation transport affect platform performance and the feasibility of the SZP concept.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Assessing physics of ion temperature gradient turbulence via hierarchical reduced-model representations

In this work, the saturation physics of ion temperature gradient (ITG) turbulence is probed by studying how amplitudes and scalings with key parameters vary across a hierarchy of reduced models. The models derive from nonlinear fluid equations for toroidal ITG turbulence under approximations to the mode coupling interactions in wavenumber space and the representation of turbulent decorrelation. Mode coupling approximations include local-in-wavenumber treatments like the spectral density of flux in quasilinear theory, a truncation to three nonlinearly interacting waves, and the interactions in a cascade to high radial wavenumber mediated by a single zonal flow. Turbulent decorrelation treatments are based on the triplet correlation time with and without eddy damping. Model fidelity is assessed by the scalings and magnitudes of the squared amplitudes of unstable mode, stable mode, and zonal flow with respect to the flow-damping rate and temperature gradient. It is shown that all models reproduce fundamental scalings, provided they incorporate the coupling of unstable mode, stable mode, and zonal flow. Accurate amplitude prediction requires eddy damping in the triplet correlation time and proper representation of the zonal-flow drive by interactions associated with the radial wavenumber cascade.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1986

Numerical modeling of rotor flows with a conservative form of the full-potential equations

A computer program has been developed to solve a three-dimensional conservative formulation of the full-potential equation. Its ability to solve transonic, unsteady rotor flows is demonstrated by comparison to forward flight non-lifting pressure data at low to moderate advance ratios. A 'split potential' formulation has been added to the code which incorporates known vorticity fields into the full-potential calculation. Using this methodology, rotor wake contributions have been incorporated into the computer code. Pressure results are presented for lifting rotors in hover. These results are compared to experimental data as well as to other predictions.

Strawn, R. C.↗
DOE OSTI2026

Validating corrosion models: Influence of physical properties

In chloride containing environments, two metals in physical contact can undergo galvanic corrosion limiting the lifetime of components. Being able to accurately predict galvanic corrosion damage distributions over time has not been widely presented in literature. Therefore, Finite Element Method (FEM) corrosion models were experimentally validated for two galvanic couples as a function of governing equations, environment, anode material, anode:cathode ratio, and time. Carbon steel/stainless steel (CS/SS) and zinc/stainless steel (Zn/SS) galvanic couples were exposed to NaCl solutions at room temperatures for up to 14 days. For the galvanic couples and environments, the Laplace equation with variable conductivity and reactions was sufficient to model the experimental corrosion damage. Increasing the chloride concentration for the CS/SS galvanic couple, regardless of the anode:cathode ratio, decreased the observed and modeled corrosion damage. Decreasing the anode:cathode ratio (i.e., increasing the cathode length), increased the experimentally observed and modeled corrosion damage. For small anode:cathode ratios, the governing equations deviate over long time periods with the Nernst-Plank equation being conservative. For the Zn/SS galvanic couple, the cathode length controls the dominant cathodic reduction reaction. For small cathode lengths, the hydrogen evolution reaction is dominant. For larger cathode lengths, the oxygen reduction reaction is dominant. The results are discussed with regard to the influence of solution chemistry, ohmic drop, and governing reactions. Overall, validated FEM models were presented, and the resultant models, physics, and mechanisms can be applied to other corrosion scenarios with confidence.

Carbon steel↗
DOE OSTI2020

A general metriplectic framework with application to dissipative extended magnetohydrodynamics

General equations for conservative yet dissipative (entropy producing) extended magnetohydrodynamics are derived from two-fluid theory. Keeping all terms generates unusual cross-effects, such as thermophoresis and a current viscosity that mixes with the usual velocity viscosity. While the Poisson bracket of the ideal version of this model has already been discovered, we determine its metriplectic counterpart that describes the dissipation. This is done using a new and general thermodynamic point of view to derive dissipative brackets, a means of derivation that is natural for understanding and creating dissipative dynamics without appealing to underlying kinetic theory orderings. Finally, the formalism is used to study dissipation in the Lagrangian variable picture where, in the context of extended magnetohydrodynamics, non-local dissipative brackets naturally emerge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Theory of ignition and burn propagation in inertial fusion implosions

A detailed analytic model is presented here to investigate the physics of burn propagation in inertially confined plasmas. The onset of ignition and burn propagation occurs when alpha heating of the hot spot causes rapid ablation of shell mass into the hot spot. This allows large energy gains to be achieved since most of the fuel mass is located in the shell. Here, we first present a comprehensive review of previous analytic models that have been used to describe the physics of hot-spot evolution and ignition; we then show that a proper description of a propagating burn wave requires a comprehensive model of hot spot and shell evolution that includes proper mass conservation in the shell, fusion reactivity, and fuel depletion. The analytic theory is in good agreement with detailed radiation-hydrodynamic simulations that predict the onset of burn propagation as occurring when the yield enhancement caused by alpha heating is between 15- and 25-fold, $f_α$ ~ 1.4, where $f_α$ = alpha energy deposited/hot-spot energy at bang time, and the hot-spot burnup fraction is approximately 2%. We show that the definition of ignition is not sensitive to the alpha-particle stopping power nor asymmetries provided that the absorbed fraction of alpha particles $θ_α$ is correctly accounted for. Finally, we use the results of 2-D simulations to show that even when $θ_α$ is small and unknown (as is true in hot spots with mid modes that have significant leakage of alpha particles into the surrounding cold bubbles), one can still relate the experimentally measureable parameter $\chi^{53}_α$ to the yield amplification and the burning-plasma parameter $Q^{\text{hs}}_α$ = alpha energy deposited/total input work delivered to the hot spot

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Extending the Heat Index

The Heat Index is a widely used measure of apparent temperature that accounts for the effects of humidity using Steadman’s model of human thermoregulation. Steadman’s model, however, gives unphysical results when the air is too hot and humid or too cold and dry, leading to an undefined Heat Index. For example, at a relative humidity of 80%, the Heat Index is only defined for temperatures in the range of 288-304 K (59-88 degrees Fahrenheit). Here, Steadman’s thermoregulation model is extended to define the Heat Index for all combinations of temperature and humidity, allowing for an assessment of Earth’s future habitability. The extended Heat Index can be mapped onto physiological responses of an idealized human, such as heat exhaustion, heat stroke, and even heat death, providing an indication of regional health outcomes for different degrees of global warming.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Theoretical Understanding of the Linear Relationship between Convective Updrafts and Cloud-Base Height for Shallow Cumulus Clouds. Part II: Continental Conditions

This is the Part II of a two-part study that seeks a theoretical understanding of an empirical relationship for shallow cumulus clouds: subcloud updraft velocity covaries linearly with the cloud-base height. This work focuses on continental cumulus clouds that are more strongly forced by surface fluxes and more deviated from equilibrium than those over oceans (Part I). We use a simple analytical model for shallow cumulus that is well tested against a high-resolution (25 m in the horizontal) large-eddy simulation model. Consistent with a conventional idea, we find that surface Bowen ratio is the key variable that regulates the covariability of both parameters: under the same solar insolation, a drier surface allows for stronger buoyancy flux, triggering stronger convection that deepens the subcloud layer. We find that the slope of the Bowen-ratio-regulated relationship between the two parameters (defined as λ) is dependent on both the local time and the stability of the lower free atmosphere. The value of λ decreases with time exponentially from sunrise to early afternoon and linearly from early afternoon to sunset. The value of λ is larger in a more stable atmosphere. In addition, continental λ in the early afternoon more than doubles the oceanic λ. Validation of the theoretical results against ground observations over the Southern Great Plains shows a reasonable agreement. Physical mechanisms underlying the findings are explained from the perspective of different time scales at which updrafts and cloud-base height respond to a surface flux forcing.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Generalized Lapse Rate Formulas for Use in Entraining CAPE Calculations

Abstract Common assumptions in temperature lapse rate formulas for lifted air parcels include neglecting mixing, hydrostatic balance, the removal of all condensate once it forms (pseudoadiabatic), and/or the retention of all condensate within the parcel (adiabatic). These formulas are commonly derived from the conservation of entropy, which leads to errors when nonequilibrium mixed-phase condensate is present. To evaluate these assumptions, a new general lapse rate formula is derived from an expression for energy conservation, rather than entropy conservation. This new formula incorporates mixing of the parcel with its surroundings, relaxes the hydrostatic assumption, allows for nonequilibrium mixed-phase condensate, and can be formulated for pseudoadiabatic or adiabatic ascent. The new formula is shown to exactly conserve entropy for reversible ascent. Predictions by the new formula are compared to that of older and less general formulas. The errors in previous formulas arise from the assumption of hydrostatic balance, which results in considerable warm biases due to the neglect of the energy sink from buoyancy. Predictions of ascent with entrainment using the new formula are then compared to parcel properties along trajectories in large eddy simulations. Simulated parcel properties are better predicted by the formula using a diluted analogy to adiabatic ascent, wherein condensate is diluted at the same rate as other parcel properties, than by the diluted analogy to pseudoadiabatic ascent, wherein all condensate is removed. These results suggest that CAPE should be computed with adiabatic, rather than pseudoadiabatic, parcel ascent.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1972

A method for calculating laminar viscous, compressible flows with small pressure gradients

A method is presented for calculating laminar viscous, compressible flows in which pressure gradients are assumed to be neglibible in energy conservation and in developing property relations, but not in momentum conservation. The equations are developed from Navier-Stokes equations in a noninertial reference frame. The method is an extension of an approximate method developed for calculating combined forced and contained natural convection in a rotating tank. The restriction to small density and temperature variations in the previous method is removed. For illustration, a two-dimensional simulation of the rotating tank problem is formulated, and the numerical computation procedure to be used is indicated.

Martin, E. D.↗
NASA NTRS1973

Time-split finite-volume method for three-dimensional blunt-body flow

An efficient numerical method for calculating plane, axisymmetric, and fully three-dimensional blunt-body flow is presented. It is a second-order-accurate, time-dependent finite-volume procedure that solves the Euler equations in integral conservation-law form. These equations are written with respect to a Cartesian coordinate system in which an embedded mesh adjusts in time to the motion of the bow shock that is automatically captured as part of the weak solution. With such an adjusting mesh, oscillations in flow properties near the shock are shown to be virtually eliminated. The scheme uses a time-splitting concept that accelerates the convergence appreciably. Comparisons are made between computed and experimental results.

Rizzi, A. W.↗
NASA NTRS1975

Pressure- and buoyancy-driven thermal convection in a rectangular enclosure

Results are presented for unsteady laminar thermal convection in compressible fluids at various reduced levels of gravity in a rectangular enclosure which is heated on one side and cooled on the opposite side. The results were obtained by solving numerically the equations of conservation for a viscous, compressible, heat-conducting, ideal gas in the presence of a gravitational body force. The formulation differs from the Boussinesq simplification in that the effects of variable density are completely retained. A conservative, explicit, time-dependent, finite-difference technique was used and good agreement was found for the limited cases where direct comparison with previous investigations was possible. The solutions show that the thermally induced motion is acoustic in nature at low levels of gravity and that the unsteady-state rate of heat transfer is thereby greatly enhanced relative to pure conduction. The nonlinear variable density profile skews the streamlines towards the cooler walls but is shown to have little effect on the steady-state isotherms.

Spradley, L. W.↗
NASA NTRS1976

Numerical solution of nonlinear partial differential equations of mixed type

A review is presented of some recently developed numerical methods for the solution of nonlinear equations of mixed type. The methods considered use finite difference approximations to the differential equation. Central difference formulas are employed in the subsonic zone and upwind difference formulas are used in the supersonic zone. The relaxation method for the small disturbance equation is discussed and a description is given of difference schemes for the potential flow equation in quasi-linear form. Attention is also given to difference schemes for the potential flow equation in conservation form, the analysis of relaxation schemes by the time dependent analogy, the accelerated iterative method, and three-dimensional calculations.

Jameson, A.↗