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NASA NTRS1993

Validation of a Computational Fluid Dynamics (CFD) Code for Supersonic Axisymmetric Base Flow

The ability to accurately and efficiently calculate the flow structure in the base region of bodies of revolution in supersonic flight is a significant step in CFD code validation for applications ranging from base heating for rockets to drag for protectives. The FDNS code is used to compute such a flow and the results are compared to benchmark quality experimental data. Flowfield calculations are presented for a cylindrical afterbody at M = 2.46 and angle of attack a = O. Grid independent solutions are compared to mean velocity profiles in the separated wake area and downstream of the reattachment point. Additionally, quantities such as turbulent kinetic energy and shear layer growth rates are compared to the data. Finally, the computed base pressures are compared to the measured values. An effort is made to elucidate the role of turbulence models in the flowfield predictions. The level of turbulent eddy viscosity, and its origin, are used to contrast the various turbulence models and compare the results to the experimental data.

Tucker, P. Kevin↗

NASA NTRS1994

Three-dimensional hydrodynamic Bondi-Hoyle accretion. 1: Code validation and stationary accretors

We investigate the hydrodynamics of three-dimensional classical Bondi-Hoyle accretion. Totally absorbing stationary spheres of varying sizes (from 10.0 down to 0.02 Bondi radii) accrete matter from a homogeneous and slightly perturbed medium, which is taken to be an ideal gas (gamma = 5/3 or 1.2). To accommodate the long-range gravitational forces, the extent of the computational volume is typically a factor of 100 larger than the radius of the accretor. We compare the numerical mass accretion rates with the theoretical predictions of Bondi, to assess the validity of the code. The hydrodynamics is modeled by the piecewise parabolic method. No energy sources (nuclear burning) or sinks (radiation, conduction) are included. The resolution in the vicinity of the accretor is increased by multiply nesting several (6-8) grids around the stationary sphere, each finer grid being a factor of 2 smaller spatially than the next coarser grid. This allows us to include a coarse model for the surface of the accretor (vacuum sphere) on the finest grid while at the same time evolving the gas on the coarser grids. The accretion rates derived numerically are in in very good agreement (to about 10% over several orders of magnitude) with the values given by Bondi for a stationary accretor within a hydrodynamic medium. However, the equations have to be changed in order to include the finite size of the accretor (in some cases very large compared to the sonic point or even to the Bondi radius).

Ruffert, Maximilian↗

NASA NTRS1994

Three-dimensional hydrodynamic Bondi-Hoyle accretion. 2: Homogeneous medium at Mach 3 with gamma = 5/3

We investigate the hydrodynamics of three-dimensional classical Bondi-Hoyle accretion. Totally absorbing spheres of varying sizes (from 10 down to 0.01 accretion radii) move at Mach 3 relative to a homogeneous and slightly perturbed medium, which is taken to be an ideal gas (gamma = 5/3). To accommodate the long-range gravitational forces, the extent of the computational volume is 32(exp 3) accretion radii. We examine the influence of numerical procedure on physical behavior. The hydrodynamics is modeled by the 'piecewise parabolic method.' No energy sources (nuclear burning) or sinks (radiation, conduction) are included. The resolution in the vicinity of the accretor is increased by multiply nesting several (5-10) grids around the sphere, each finer grid being a factor of 2 smaller in zone dimension that the next coarser grid. The largest dynamic range (ratio of size of the largest grid to size of the finest zone) is 16,384. This allows us to include a coarse model for the surface of the accretor (vacuum sphere) on the finest grid, while at the same time evolving the gas on the coarser grids. Initially (at time t = 0-10), a shock front is set up, a Mach cone develops, and the accretion column is observable. Eventually the flow becomes unstable, destroying axisymmetry. This happens approximately when the mass accretion rate reaches the values (+/- 10%) predicted by the Bondi-Hoyle accretion formula (factor of 2 included). However, our three-dimensional models do not show the highly dynamic flip-flop flow so prominent in two-dimensional calculations performed by other authors. The flow, and thus the accretion rate of all quantities, shows quasi-periodic (P approximately equals 5) cycles between quiescent and active states. The interpolation formula proposed in an accompanying paper is found to follow the collected numerical data to within approximately 30%. The specific angular momentum accreted is of the same order of magnitude as the values previously found for two-dimensional flows.

Ruffert, Maximilian↗

NASA NTRS1997

Coupling of Sph and Finite Element Codes for Multi-Layer Orbital Debris Shield Design

Particle-based hydrodynamics models offer distinct advantages over Eulerian and Lagrangian hydrocodes in particular shock physics applications. Particle models are designed to avoid the mesh distortion and state variable diffusion problems which can hinder the effective use of Lagrangian and Eulerian codes respectively. However conventional particle-in-cell and smooth particle hydrodynamics methods employ particles which are actually moving interpolation points. A new particle-based modeling methodology, termed Hamiltonian particle hydrodynamics, was developed by Fahrenthold and Koo (1997) to provide an alternative, fully Lagrangian, energy-based approach to shock physics simulations. This alternative formulation avoids the tensile and boundary instabilities associated with standard smooth particle hydrodynamics formulations and the diffusive grid- to-particle mapping schemes characteristic of particle-in-cell methods. In the work described herein, the method of Fahrenthold and Koo has been extended, by coupling the aforementioned hydrodynamic particle model to a hexahedral finite element based description of the continuum dynamics. The resulting continuum model retains all of the features (including general contact-impact effects) of Hamiltonian particle hydrodynamics, while in addition accounting for tensile strength, plasticity, and damage effects important in the simulation of hypervelocity impact on orbital debris shielding. A three dimensional, vectorized, and autotasked implementation of the extended particle method described here has been coded for application to orbital debris shielding design. Source code for the pre-processor (PREP), analysis code (EXOS), post-processor (POST), and rezoner (ZONE), have been delivered separately, along with a User's Guide describing installation and application of the software.

Fahrenthold, Eric P.↗

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 NTRS1996

Parallel Simulation of Unsteady Turbulent Flames

Time-accurate simulation of turbulent flames in high Reynolds number flows is a challenging task since both fluid dynamics and combustion must be modeled accurately. To numerically simulate this phenomenon, very large computer resources (both time and memory) are required. Although current vector supercomputers are capable of providing adequate resources for simulations of this nature, the high cost and their limited availability, makes practical use of such machines less than satisfactory. At the same time, the explicit time integration algorithms used in unsteady flow simulations often possess a very high degree of parallelism, making them very amenable to efficient implementation on large-scale parallel computers. Under these circumstances, distributed memory parallel computers offer an excellent near-term solution for greatly increased computational speed and memory, at a cost that may render the unsteady simulations of the type discussed above more feasible and affordable.This paper discusses the study of unsteady turbulent flames using a simulation algorithm that is capable of retaining high parallel efficiency on distributed memory parallel architectures. Numerical studies are carried out using large-eddy simulation (LES). In LES, the scales larger than the grid are computed using a time- and space-accurate scheme, while the unresolved small scales are modeled using eddy viscosity based subgrid models. This is acceptable for the moment/energy closure since the small scales primarily provide a dissipative mechanism for the energy transferred from the large scales. However, for combustion to occur, the species must first undergo mixing at the small scales and then come into molecular contact. Therefore, global models cannot be used. Recently, a new model for turbulent combustion was developed, in which the combustion is modeled, within the subgrid (small-scales) using a methodology that simulates the mixing and the molecular transport and the chemical kinetics within each LES grid cell. Finite-rate kinetics can be included without any closure and this approach actually provides a means to predict the turbulent rates and the turbulent flame speed. The subgrid combustion model requires resolution of the local time scales associated with small-scale mixing, molecular diffusion and chemical kinetics and, therefore, within each grid cell, a significant amount of computations must be carried out before the large-scale (LES resolved) effects are incorporated. Therefore, this approach is uniquely suited for parallel processing and has been implemented on various systems such as: Intel Paragon, IBM SP-2, Cray T3D and SGI Power Challenge (PC) using the system independent Message Passing Interface (MPI) compiler. In this paper, timing data on these machines is reported along with some characteristic results.

Menon, Suresh↗

NASA NTRS2004

Performance of Gas Scintillation Proportional Counter Array for High-Energy X-Ray Observatory

A focal plane array of high-pressure gas scintillation proportional counters (GSPC) for a High Energy X-Ray Observatory (HERO) is developed at the Marshall Space Flight Center. The array is consisted from eight GSPCs and is a part of balloon born payload scheduled to flight in May 2004. These detectors have an active area of approximately 20 square centimeters, and are filled with a high pressure (10(exp 6) Pa) xenon-helium mixture. Imaging is via crossed-grid position-sensitive phototubes sensitive in the UV region. The performance of the GSPC is well matched to that of the telescopes x-ray optics which have response to 75 keV and a focal spot size of approximately 500 microns. The detector's energy resolution, 4% FWHM at 60 keV, is adequate for resolving the broad spectral lines of astrophysical importance and for accurate continuum measurements. Results of the on-earth detector calibration will be presented and in-flight detector performance will be provided, as available.

Gubarev, Mikhail↗

NASA NTRS1986

A Fourier transform telescope for sub-arcsecond imaging of X-rays and gamma rays

This paper describes a Fourier transform telescope designed to image solar flare X-rays and gamma rays at energies up to 1 MeV with arcsec resolution. The imaging technique makes use of a bigrid collimator divided into a number of smaller areas called subcollimators. The grids in each subcollimator consist of a set of linear apertures so configured that each subcollimator provides a measurement of a single Fourier component of the angular distribution of the source. The imaging concept is therefore a mathematical analog to aperture synthesis in radio astronomy. For X-ray and gamma-ray astronomy, this approach has significant advantages in terms of relaxed requirements for astronomy, this approach has significant advantages in terms of relaxed requirements for position sensitivity in the detector and for control of grid alignment in the large scale telescope structure. The concept of the Fourier transform telescope will be illustrated with numerical parameters of a version now under study for the Pinhole/Occulter Facility.

Crannell, C. J.↗

NASA NTRS1989

Analysis of a second-order-accurate finite-volume method for temporally-growing compressible shear layers

A finite-volume method for solving the compressible laminar Navier-Stokes equation in two dimensions is assessed for use in the simulation of transitional flows. The method is second-order-accurate, uses alternating-direction-implicit time integration, and a total-variation-diminishing smoothing operator in the inviscid flux terms. The test problem was a free shear layer with a forced periodicity in x at a specified wavelength and with the parallel mean flow specified as a hyperbolic-tangent profile. A grid refinement investigation verified this method to be second-order-accurate with less than 4 percent error in the growth rate of isolated modes on a 32 by 64 grid. The interaction between modes of similar amplitude was small, less than 1 percent. However, in cases where there was a dominant mode, numerical phase error pumped energy into all other modes. This error results in nonphysical growth rate for modes whose energy content is several orders of magnitude below the dominant mode. In the case when the dominant mode saturates, the pumping action stops and the growth rate of the next largest growing mode regains physical significance.

Atkins, H. L.↗

NASA NTRS2014

A New Cell-Centered Implicit Numerical Scheme for Ions in the 2-D Axisymmetric Code Hall2de

We present a new algorithm in the Hall2De code to simulate the ion hydrodynamics in the acceleration channel and near plume regions of Hall-effect thrusters. This implementation constitutes an upgrade of the capabilities built in the Hall2De code. The equations of mass conservation and momentum for unmagnetized ions are solved using a conservative, finite-volume, cell-centered scheme on a magnetic-field-aligned grid. Major computational savings are achieved by making use of an implicit predictor/multi-corrector algorithm for time evolution. Inaccuracies in the prediction of the motion of low-energy ions in the near plume in hydrodynamics approaches are addressed by implementing a multi-fluid algorithm that tracks ions of different energies separately. A wide range of comparisons with measurements are performed to validate the new ion algorithms. Several numerical experiments with the location and value of the anomalous collision frequency are also presented. Differences in the plasma properties in the near-plume between the single fluid and multi-fluid approaches are discussed. We complete our validation by comparing predicted erosion rates at the channel walls of the thruster with measurements. Erosion rates predicted by the plasma properties obtained from simulations replicate accurately measured rates of erosion within the uncertainty range of the sputtering models employed.

electric propulsion↗

NASA NTRS2017

The Root Cause of the Overheating Problem

Previously we identified the receding flow, where two fluid streams recede from each other, as an open numerical problem, because all well-known numerical fluxes give an anomalous temperature rise, thus called the overheating problem. This phenomenon, although presented in several textbooks, and many previous publications, has scarcely been satisfactorily addressed and the root cause of the overheating problem not well understood. We found that this temperature rise was solely connected to entropy rise and proposed to use the method of characteristics to eradicate the problem. However, the root cause of the entropy production was still unclear. In the present study, we identify the cause of this problem: the entropy rise is rooted in the pressure flux in a finite volume formulation and is implanted at the first time step. It is found theoretically inevitable for all existing numerical flux schemes used in the finite volume setting, as confirmed by numerical tests. This difficulty cannot be eliminated by manipulating time step, grid size, spatial accuracy, etc, although the rate of overheating depends on the flux scheme used. Finally, we incorporate the entropy transport equation, in place of the energy equation, to ensure preservation of entropy, thus correcting this temperature anomaly. Its applicability is demonstrated for some relevant 1D and 2D problems. Thus, the present study validates that the entropy generated ab initio is the genesis of the overheating problem.

Liou, Meng-Sing↗

NASA NTRSDate not supplied

Implicit Thermochemical Nonequilibrium Flow Simulations on Unstructured Grids using GPUs

Thermochemical nonequilibrium flow simulation capabilities have been previously implemented, verified, and validated for central processing unit (CPU) systems in NASA’s unstructured-grid computational fluid dynamics solver FUN3D. Many exascale-class high-performance computing systems will rely on graphics processing unit (GPU) architectures for high throughput and energy efficiency; thus, CPU-based scientific computing software unable to effectively utilize these systems must be updated. In this work, we present a CUDA C++ implementation of FUN3D’s thermochemical nonequilibrium flow simulation capabilities targeting NVIDIA Tesla GPUs. An overview of the porting and optimization strategy is described and performance comparisons with other recent architectures are presented. Scaling to thousands of GPUs is demonstrated, yielding computational performance equivalent to that of several million CPU cores. The implementation enables efficient, high-fidelity, scale-resolving simulations of thermochemical nonequilibrium flows for many applications including atmospheric entry, hypersonics, and combustion.

GPU↗

NASA NTRSDate not supplied

A New Approach for a Wider Class of Entropy Split Methods for Compressible Gas Dynamics and MHD

The high order entropy split methods of Sjögreen & Yee [1, 2] by entropy splitting of the compressible Euler (inviscid) flux derivatives for a thermally-perfect gas are based on Harten’s entropy function [3, 4, 5]. Their derivation takes advantage of the homogeneity property of Euler flux, symmetrizable Euler flux derivatives and energy-norm stability in conjunction with high order classical spatial central, DRP (dispersion relation-preserving) [6, 7, 8] or Padé (compact) spatial discretizations [9] with summation-by-parts (SBP) operators [10]. Our entropy split methods have been proven entropy conserving and stable [1, 11, 12]. Our proofs do not rely on a two-point numerical flux, but rather only a linear difference operator is required to derive these methods. To extend the entropy split method for the MHD, we used the Godunov symmetrizable non-conservative MHD form [12, 13, 14]. These high order entropy split methods not only preserve certain physical properties of the chosen governing equations but are also known to either improve numerical stability, and/or minimize aliasing errors in long time integration of turbulent flow computations without the aid of added numerical dissipation. In our previous published work, extensive error norm comparison with grid refinement was performed to show the high accuracy performance of these methods. These studies also showed how well the entropy split methods conserve the entropy, momentum and mass, and preserve the kinetic energy for long time integration of the various flows [1, 2, 12, 13, 14]. The objective of the present work is to use a new approach to obtain a wider class of entropy split methods consisting of a two-point numerical flux portion and a non-conservative portion in such a way that the homogeneity property of the compressible Euler flux is not required. For high order classical spatial central, DRP (dispersion relation-preserving) or Padé (compact) spatial discretizations, this new approach can be proven to be entropy conservative with conservative spatial dsicretizations while at the same time allowing a wider class of symmetrizable inviscid flux derivatives. We also use this generalization to derive an entropy split scheme that is entropy conserving for the equations of MHD without the homogeneity property using the Godunov symmetrizable ideal MHD formulation [15].

High Order Physical Preserving Methods↗

NASA NTRS1977

Thermal energy storage heat exchanger: Molten salt heat exchanger design for utility power plants

The use of thermal energy storage (TES) in the latent heat of molten salts as a means of conserving fossil fuels and lowering the cost of electric power was evaluated. Public utility systems provided electric power on demand. This demand is generally maximum during late weekday afternoons, with considerably lower overnight and weekend loads. Typically, the average demand is only 60% to 80% of peak load. As peak load increases, the present practice is to purchase power from other grid facilities or to bring older less efficient fossil-fuel plants on line which increase the cost of electric power. The widespread use of oil-fired boilers, gas turbine and diesel equipment to meet peaking loads depletes our oil-based energy resources. Heat exchangers utilizing molten salts can be used to level the energy consumption curve. The study begins with a demand analysis and the consideration of several existing modern fossil-fuel and nuclear power plants for use as models. Salts are evaluated for thermodynamic, economic, corrosive, and safety characteristics. Heat exchanger concepts are explored and heat exchanger designs are conceived. Finally, the economics of TES conversions in existing plants and new construction is analyzed. The study concluded that TES is feasible in electric power generation. Substantial data are presented for TES design, and reference material for further investigation of techniques is included.

Ferarra, A.↗

NASA NTRS1979

WTG Energy Systems' Rotor: Steel at 80 Feet

The design, specifications, and performance of the 80 foot diameter fixed pitch rotor operating on the MP1-200 wind turbine generator installed as part of the Island of Cuttyhunk's electric power utility grid system are described. This synchronous generating system rated 200 kilowatts at 28 mph wind velocity, and produces constant 60 Hz, 480 VAC current at +/- 1 percent accuracy throughout the machine's operating range. Future R & D requirements and suggestions are included with cost data.

Barrows, R. E.↗

NASA NTRS1979

Electromagnetic heating of minor planets in the early solar system

Electromagnetic processes occurring in the primordial solar system are likely to have significantly affected planetary evolution. In particular, electrical coupling of the kinetic energy of a dense T-Tauri-like solar wind into the interior of the smaller planets could have been a major driver of thermal metamorphism. Accordingly a grid of asteroid models of various sizes and solar distances was constructed using dc transverse magnetic induction theory. Plausible parameterizations with no requirement for a high environmental temperature led to complete melting for Vesta with no melting for Pallas and Ceres. High temperatures were reached in the Pallas model, perhaps implying nonmelting thermal metamorphosis as a cause of its anomalous spectrum. A reversal of this temperature sequence seems implausible, suggesting that the Ceres-Pallas-Vesta dichotomy is a natural outcome of the induction mechanism. Highly localized heating is expected to arise due to an instability in the temperature-controlled current distribution. Localized metamorphosis resulting from this effect may be relevant to the production and evolution of pallasites, the large presumed metal component of S object spectra, and the formation of the lunar magma ocean.

Herbert, F.↗

NASA NTRS1987

Numerical modeling of troposphere-induced gravity wave propagation

Sources of internal gravity waves (IGW) in the upper atmosphere are assumed to be meteorological processes in the troposphere. These sources are vertically and horizontally inhomogeneous and time dependent. In order to describe the IGW propagation from such sources, a numerical solution of a system of hydrodynamical equations is required. In addition, it is necessary to take into account the influence of the altitude latitude inhomogeneity of the temperature and wind fields on the IGW propagation as well as the processes of dissipation. An algorithm is proposed for numerical modelling of the IGW propagation over a limited area from tropospheric local sources to the upper atmosphere. The algorithm takes into account all the above features. A spectral grid method is used with the expansion of wave fields into the Fourier series over longitude. The upper limit conditions were obtained from the requirement of a limited energy dissipation rate in an atmospheric column. The no slip (zero velocity) condition was used at the Earth's surface.

Gavrilov, N. M.↗

NASA NTRS1990

Topographic distribution of clear-sky radiation over the Konza Prairie, Kansas

A method for exploring the topographic modulation of clear-sky incoming radiation using a two-stream atmospheric model together with digital elevation data is presented to obtain the temporal and spatial distribution of this energy. Utilizing this methodology for the Konza Prairie, it is observed that the variance and spatial autocorrelation of the simulated radiation data changed with sun angle and elevation grid spacing. An analytical formula that describes the behavior of the variance as a function of optical depth, sun angle, and mean terrain slope can be developed by considering direct solar radiation variability on a constant-slope terrain which has a uniform albedo and a uniform distribution of slopes. The decrease in mean slope and the increase in slope and autocorrelation is attributed to a loss of some of the shorter-wavelength terrain features at coarser grid spacings.

Dubayah, Ralph↗