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All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

On the Importance of the Dynamics of Discretizations

It has been realized recently that the discrete maps resulting from numerical discretizations of differential equations can possess asymptotic dynamical behavior quite different from that of the original systems. This is the case not only for systems of Ordinary Differential Equations (ODEs) but in a more complicated manner for Partial Differential Equations (PDEs) used to model complex physics. The impact of the modified dynamics may be mild and even not observed for some numerical methods. For other classes of discretizations the impact may be pronounced, but not always obvious depending on the nonlinear model equations, the time steps, the grid spacings and the initial conditions. Non-convergence or convergence to periodic solutions might be easily recognizable but convergence to incorrect but plausible solutions may not be so obvious - even for discretized parameters within the linearized stability constraint. Based on our past four years of research, we will illustrate some of the pathology of the dynamics of discretizations, its possible impact and the usage of these schemes for model nonlinear ODEs, convection-diffusion equations and grid adaptations.

Sweby, Peter K.↗
NASA NTRS2002

Computational Study of Near-limit Propagation of Detonation in Hydrogen-air Mixtures

A computational investigation of the near-limit propagation of detonation in lean and rich hydrogen-air mixtures is presented. The calculations were carried out over an equivalence ratio range of 0.4 to 5.0, pressures ranging from 0.2 bar to 1.0 bar and ambient initial temperature. The computations involved solution of the one-dimensional Euler equations with detailed finite-rate chemistry. The numerical method is based on a second-order spatially accurate total-variation-diminishing (TVD) scheme, and a point implicit, first-order-accurate, time marching algorithm. The hydrogen-air combustion was modeled with a 9-species, 19-step reaction mechanism. A multi-level, dynamically adaptive grid was utilized in order to resolve the structure of the detonation. The results of the computations indicate that when hydrogen concentrations are reduced below certain levels, the detonation wave switches from a high-frequency, low amplitude oscillation mode to a low frequency mode exhibiting large fluctuations in the detonation wave speed; that is, a 'galloping' propagation mode is established.

Yungster, S.↗
NASA NTRS2003

An Exact Dual Adjoint Solution Method for Turbulent Flows on Unstructured Grids

An algorithm for solving the discrete adjoint system based on an unstructured-grid discretization of the Navier-Stokes equations is presented. The method is constructed such that an adjoint solution exactly dual to a direct differentiation approach is recovered at each time step, yielding a convergence rate which is asymptotically equivalent to that of the primal system. The new approach is implemented within a three-dimensional unstructured-grid framework and results are presented for inviscid, laminar, and turbulent flows. Improvements to the baseline solution algorithm, such as line-implicit relaxation and a tight coupling of the turbulence model, are also presented. By storing nearest-neighbor terms in the residual computation, the dual scheme is computationally efficient, while requiring twice the memory of the flow solution. The scheme is expected to have a broad impact on computational problems related to design optimization as well as error estimation and grid adaptation efforts.

Nielsen, Eric J.↗
NASA NTRS2003

Defect, Kinetics and Heat Transfer of CDTE Bridgman Growth without Wall Contact

A detached growth mechanism has been proposed, which is similar to that proposed by Duffar et al. and used to study the current detached growth system. From numerical results, we can conclude that detached growth will more likely appear if the growth and wetting angles are large and meniscus is flat. Detached thickness is dependent on growth angle, wetting angle, and gap width and shape of the fins. The model can also explain why the detached growth will not happen for metals in which the growth angle is almost zero. Since the growth angle of CdZnTe cannot be changed, to promote detached growth, the number density of the fins should be low and the wetting angle should be high. Also, a much smaller gap width of the fins should be used in the ground experiment and the detached gap width is much smaller. The shape of the fins has minor influence on detached growth. An integrated numerical model for detached solidification has been developed combining a global heat transfer sub-model and a wall contact sub-model. The global heat transfer sub-model accounts for heat and mass transfer in the multiphase system, convection in the melt, macro-segregation, and interface dynamics. The location and dynamics of the solidification interface are accurately tracked by a multizone adaptive grid generation scheme. The wall contact sub-model accounts for the meniscus dynamics at the three-phase boundary. Simulations have been performed for crystal growth in a conventional ampoule and a designed ampoule to understand the benefits of detached solidification and its impacts on crystalline structural quality, e.g., stoichiometry, macro-segregation, and stress. From simulation results, both the Grashof and Marangoni numbers will have significant effects on the shape of growth front, Zn concentration distribution, and radial segregation. The integrated model can be used in designing apparatus and determining the optimal geometry for detached solidification in space and on the ground.

Larson, D. J., Jr.↗
NASA NTRS2002

The Aeronautics Education, Research, and Industry Alliance (AERIAL) 2002 Report

The NASA Nebraska Space Grant Consortium (NSGC) & EPSCoR programs at the University of Nebraska at Omaha are involved in a variety of innovative research activities. Such research is supported through the Aeronautics Education, Research, and Industry Alliance (AERIAL) and collaborative seed funds. AERIAL is a comprehensive, multi-faceted, five year NASA EPSCoR initiative that contributes substantially to the strategic research and technology priorities of NASA while intensifying Nebraska s rapidly growing aeronautics research and development endeavors. AERIAL includes three major collaborative research teams (CRTs) whose nexus is a common focus in aeronautics research. Each CRT - Small Aircraft Transportation System (SATS), Airborne Remote Sensing for Agricultural Research and Commercialization Applications (ARS), and Numerical Simulation of the Combustion of Fuel Droplets: Finite Rate Kinetics and Flame Zone Grid Adaptation (CEFD) -has a distinct research agenda. This program provides the template for funding of new and innovative research that emphasizes aerospace technology.

Bowen, Brent D.↗
NASA NTRS2003

Structure and Stability of One-Dimensional Detonations in Ethylene-Air Mixtures

The propagation of one-dimensional detonations in ethylene-air mixtures is investigated numerically by solving the one-dimensional Euler equations with detailed finite-rate chemistry. The numerical method is based on a second-order spatially accurate total-variation-diminishing scheme and a point implicit, first-order-accurate, time marching algorithm. The ethylene-air combustion is modeled with a 20-species, 36-step reaction mechanism. A multi-level, dynamically adaptive grid is utilized, in order to resolve the structure of the detonation. Parametric studies over an equivalence ratio range of 0.5 less than phi less than 3 for different initial pressures and degrees of detonation overdrive demonstrate that the detonation is unstable for low degrees of overdrive, but the dynamics of wave propagation varies with fuel-air equivalence ratio. For equivalence ratios less than approximately 1.2 the detonation exhibits a short-period oscillatory mode, characterized by high-frequency, low-amplitude waves. Richer mixtures (phi greater than 1.2) exhibit a low-frequency mode that includes large fluctuations in the detonation wave speed; that is, a galloping propagation mode is established. At high degrees of overdrive, stable detonation wave propagation is obtained. A modified McVey-Toong short-period wave-interaction theory is in excellent agreement with the numerical simulations.

Yungster, S.↗
NASA NTRS2003

Transport Equation Based Wall Distance Computations Aimed at Flows With Time-Dependent Geometry

Eikonal, Hamilton-Jacobi and Poisson equations can be used for economical nearest wall distance computation and modification. Economical computations may be especially useful for aeroelastic and adaptive grid problems for which the grid deforms, and the nearest wall distance needs to be repeatedly computed. Modifications are directed at remedying turbulence model defects. For complex grid structures, implementation of the Eikonal and Hamilton-Jacobi approaches is not straightforward. This prohibits their use in industrial CFD solvers. However, both the Eikonal and Hamilton-Jacobi equations can be written in advection and advection-diffusion forms, respectively. These, like the Poisson s Laplacian, are commonly occurring industrial CFD solver elements. Use of the NASA CFL3D code to solve the Eikonal and Hamilton-Jacobi equations in advective-based forms is explored. The advection-based distance equations are found to have robust convergence. Geometries studied include single and two element airfoils, wing body and double delta configurations along with a complex electronics system. It is shown that for Eikonal accuracy, upwind metric differences are required. The Poisson approach is found effective and, since it does not require offset metric evaluations, easiest to implement. The sensitivity of flow solutions to wall distance assumptions is explored. Generally, results are not greatly affected by wall distance traits.

Tucker, Paul G.↗
NASA NTRS2003

Transport Equation Based Wall Distance Computations Aimed at Flows With Time-Dependent Geometry

Eikonal, Hamilton-Jacobi and Poisson equations can be used for economical nearest wall distance computation and modification. Economical computations may be especially useful for aeroelastic and adaptive grid problems for which the grid deforms, and the nearest wall distance needs to be repeatedly computed. Modifications are directed at remedying turbulence model defects. For complex grid structures, implementation of the Eikonal and Hamilton-Jacobi approaches is not straightforward. This prohibits their use in industrial CFD solvers. However, both the Eikonal and Hamilton-Jacobi equations can be written in advection and advection-diffusion forms, respectively. These, like the Poisson's Laplacian, are commonly occurring industrial CFD solver elements. Use of the NASA CFL3D code to solve the Eikonal and Hamilton-Jacobi equations in advective-based forms is explored. The advection-based distance equations are found to have robust convergence. Geometries studied include single and two element airfoils, wing body and double delta configurations along with a complex electronics system. It is shown that for Eikonal accuracy, upwind metric differences are required. The Poisson approach is found effective and, since it does not require offset metric evaluations, easiest to implement. The sensitivity of flow solutions to wall distance assumptions is explored. Generally, results are not greatly affected by wall distance traits.

Tucker, Paul G.↗
NASA NTRS2004

High-Order Simulation of Non-Linear Oscillations and Shocks in the Solar Atmosphere

The solar atmosphere presents a rich source of highly non-linear magneto-hydrodynamic phenomena: strong gradients and forcing terms result in both large shocks and oscillations. The additional requirements of energy balance and initialization in hydrostatic equilibrium compound the challenge of this problem. A wealth of observational data allows us to check the results of our simulations. The problem of simulating the solar atmosphere provides, in addition to an interesting system in its own right, a challenging testbed for high-order shock-capturing methods. We discuss the challenge of simulating solar atmospheric phenomena, concentrating on various high-order central methods ranging from second to fourth order. Our method is based on the central-upwind scheme of Kurganov, Noelle and Petrova, which we extend to high order via various interpolants. We investigate various initial data for our simulations, corresponding to observed conditions in different regions of the solar surface: the normal quiet sun and sunspots. When non-oscillatory using second- and third-order methods, we are able to reproduce non-trivial observational results. In particular we find a correlation between initial data and both the shock speeds and particle oscillation spectra that match observations in the corresponding regions. When using fourth-order WENO interpolants, we find that while the individual shock profiles at any given time appear non-oscillatory, spurious oscillations appear in the fields after long time integrations. The issue of initialization in hydrostatic equilibrium raises difficult issues. Careful treatment of the gravitational source term can reduce violations of hydrostatic equilibrium, but difficulties remain, primarily due to discontinuities in the piecewise-polynomial reconstructions. In the case of the Euler equations in gravity, the use of high-order methods reduces the violation of hydrostatic equilibrium to a sufficiently low level for the above described results to be obtained. Including various energy flux terms in the equations, however, leads to severe instability when hydrostatic balance is violated. We discuss various strategies to address this problem, including adaptive grid methods.

Bryson, S.↗
NASA NTRS2004

Application of CFD to Abrupt Wing Stall Using RANS and DES

For DES, RANS is responsible for predicting boundary layer growth and separation. LES is responsible for predicting the geometry dependent turbulent flow features. Grid adaptation done using NASA Langley s RefineMesh program. Adaptation on time average of vorticity

Forsythe, Jim↗
NASA NTRS1997

Complex Volume Grid Generation Through the Use of Grid Reusability

This paper presents a set of surface and volume grid generation techniques which reuse existing surface and volume grids. These methods use combinations of data manipulations to reduce grid generation time, improve grid characteristics, and increase the capabilities of existing domain discretization software. The manipulation techniques utilize physical and computational domains to produce basis function on which to operate and modify grid character and smooth grids using Trans-Finite Interpolation, a vector interpolation method and parametric re-mapping technique. With these new techniques, inviscid grids can be converted to viscous grids, multiple zone grid adaption can be performed to improve CFD solver efficiency, and topological changes to improve modeling of flow fields can be done simply and quickly. Examples of these capabilities are illustrated as applied to various configurations.

Alter, Stephen J.↗
NASA NTRS2005

Verification and Validation of the RAGE Hydrocode in Preparation for Investigation of Impacts into a Volatile-rich Target

Before a hydrocode is used to investigate a question of scientific interest, it should be tested against analogous laboratory experiments and problems with analytical solutions. The Radiation Adaptive Grid Eulerian (RAGE) hydrocode[1], developed by Los Alamos National Laboratory (LANL) and Science Applications International Corporation (SAIC)[2,3] has been subjected to many tests during its development.[4,5] We extend and review this work, emphasizing tests relevant to impact cratering into volatile-rich targets.

Plesko, C. S.↗
NASA NTRS2007

A Review of Hypersonics Aerodynamics, Aerothermodynamics and Plasmadynamics Activities within NASA's Fundamental Aeronautics Program

The research program of the aerodynamics, aerothermodynamics and plasmadynamics discipline of NASA's Hypersonic Project is reviewed. Details are provided for each of its three components: 1) development of physics-based models of non-equilibrium chemistry, surface catalytic effects, turbulence, transition and radiation; 2) development of advanced simulation tools to enable increased spatial and time accuracy, increased geometrical complexity, grid adaptation, increased physical-processes complexity, uncertainty quantification and error control; and 3) establishment of experimental databases from ground and flight experiments to develop better understanding of high-speed flows and to provide data to validate and guide the development of simulation tools.

Salas, Manuel D.↗
NASA NTRS2008

Magnetotail Current Sheet Thinning and Magnetic Reconnection Dynamics in Global Modeling of Substorms

Magnetotail current sheet thinning and magnetic reconnection are key elements of magnetospheric substorms. We utilized the global MHD model BATS-R-US with Adaptive Mesh Refinement developed at the University of Michigan to investigate the formation and dynamic evolution of the magnetotail thin current sheet. The BATSRUS adaptive grid structure allows resolving magnetotail regions with increased current density up to ion kinetic scales. We investigated dynamics of magnetotail current sheet thinning in response to southwards IMF turning. Gradual slow current sheet thinning during the early growth phase become exponentially fast during the last few minutes prior to nightside reconnection onset. The later stage of current sheet thinning is accompanied by earthward flows and rapid suppression of normal magnetic field component $B-z$. Current sheet thinning set the stage for near-earth magnetic reconnection. In collisionless magnetospheric plasma, the primary mechanism controlling the dissipation in the vicinity of the reconnection site is non-gyrotropic effects with spatial scales comparable with the particle Larmor radius. One of the major challenges in global MHD modeling of the magnetotail magnetic reconnection is to reproduce fast reconnection rates typically observed in smallscale kinetic simulations. Bursts of fast reconnection cause fast magnetic field reconfiguration typical for magnetospheric substorms. To incorporate nongyritropic effects in diffusion regions we developed an algorithm to search for magnetotail reconnection sites, specifically where the magnetic field components perpendicular to the local current direction approaches zero and form an X-type configuration. Spatial scales of the diffusion region and magnitude of the reconnection electric field are calculated self-consistently using MHD plasma and field parameters in the vicinity of the reconnection site. The location of the reconnection sites and spatial scales of the diffusion region are updated during the simulations. Such an approach allows quantifying the interaction between large-scale global magnetospheric dynamics and microphysical processes in diffusion regions localized near reconnection sites. To clarify the role of smallscale non-MHD effects in diffusion region on the global magnetospheric dynamic and to test different models of dissipation we perform simulations with steady southward IMF driving of the magnetosphere.

Kuznetsova, M. M.↗
NASA NTRS2010

Comparison of DAC and MONACO DSMC Codes with Flat Plate Simulation

Various implementations of the direct simulation Monte Carlo (DSMC) method exist in academia, government and industry. By comparing implementations, deficiencies and merits of each can be discovered. This document reports comparisons between DSMC Analysis Code (DAC) and MONACO. DAC is NASA's standard DSMC production code and MONACO is a research DSMC code developed in academia. These codes have various differences; in particular, they employ distinct computational grid definitions. In this study, DAC and MONACO are compared by having each simulate a blunted flat plate wind tunnel test, using an identical volume mesh. Simulation expense and DSMC metrics are compared. In addition, flow results are compared with available laboratory data. Overall, this study revealed that both codes, excluding grid adaptation, performed similarly. For parallel processing, DAC was generally more efficient. As expected, code accuracy was mainly dependent on physical models employed.

Padilla, Jose F.↗
NASA NTRS2010

Base Flow and Heat Transfer Characteristics of a Four-Nozzle Clustered Rocket Engine: Effect of Nozzle Pressure Ratio

The base pressure and heating characteristics of a four-nozzle clustered rocket configuration is studied numerically with the aid of OVERFLOW Navier-Stokes code. A pressure ratio (chamber pressure to freestream static pressure) range of 990 to 5,920 and a freestream Mach number range of 2.5 to 3.5 are studied. The qualitative trends of decreasing base pressure with increasing pressure ratio and increasing base heat flux with increasing pressure ratio are correctly predicted. However, the predictions for base pressure and base heat flux show deviations from the wind tunnel data. The differences in absolute values between the computation and the data are attributed to factors such as perfect gas (thermally and calorically perfect) assumption, turbulence model inaccuracies in the simulation, and lack of grid adaptation.

Nallasamy, R.↗
NASA NTRS2014

FUN3D Manual: 12.4

This manual describes the installation and execution of FUN3D version 12.4, including optional dependent packages. FUN3D is a suite of computational fluid dynamics simulation and design tools that uses mixedelement unstructured grids in a large number of formats, including structured multiblock and overset grid systems. A discretely-exact adjoint solver enables efficient gradient-based design and grid adaptation to reduce estimated discretization error. FUN3D is available with and without a reacting, real-gas capability. This generic gas option is available only for those persons that qualify for its beta release status.

Biedron, Robert T.↗
NASA NTRS2014

Summary and Statistical Analysis of the First AIAA Sonic Boom Prediction Workshop

A summary is provided for the First AIAA Sonic Boom Workshop held 11 January 2014 in conjunction with AIAA SciTech 2014. Near-field pressure signatures extracted from computational fluid dynamics solutions are gathered from nineteen participants representing three countries for the two required cases, an axisymmetric body and simple delta wing body. Structured multiblock, unstructured mixed-element, unstructured tetrahedral, overset, and Cartesian cut-cell methods are used by the participants. Participants provided signatures computed on participant generated and solution adapted grids. Signatures are also provided for a series of uniformly refined workshop provided grids. These submissions are propagated to the ground and loudness measures are computed. This allows the grid convergence of a loudness measure and a validation metric (dfference norm between computed and wind tunnel measured near-field signatures) to be studied for the first time. Statistical analysis is also presented for these measures. An optional configuration includes fuselage, wing, tail, flow-through nacelles, and blade sting. This full configuration exhibits more variation in eleven submissions than the sixty submissions provided for each required case. Recommendations are provided for potential improvements to the analysis methods and a possible subsequent workshop.

Park, Michael A.↗