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At least 181 records · Page 10

A class of high resolution explicit and implicit shock-capturing methods

An attempt is made to give a unified and generalized formulation of a class of high resolution, explicit and implicit shock capturing methods, and to illustrate their versatility in various steady and unsteady complex shock wave computations. Included is a systematic review of the basic design principle of the various related numerical methods. Special emphasis is on the construction of the basis nonlinear, spatially second and third order schemes for nonlinear scalar hyperbolic conservation laws and the methods of extending these nonlinear scalar schemes to nonlinear systems via the approximate Riemann solvers and the flux vector splitting approaches. Generalization of these methods to efficiently include equilibrium real gases and large systems of nonequilibrium flows are discussed. Some issues concerning the applicability of these methods that were designed for homogeneous hyperbolic conservation laws to problems containing stiff source terms and shock waves are also included. The performance of some of these schemes is illustrated by numerical examples for 1-, 2- and 3-dimensional gas dynamics problems.

Yee, H. C.↗

An upwind parabolized Navier-Stokes code for chemically reacting flows

A new upwind, parabolized Navier-Stokes (PNS) code has been developed to compute the hypersonic, viscous, chemically reacting flow around two-dimensional or axisymmetric bodies. The new code is an extension of the upwind (perfect gas) PNS code of Lawrence et al. (1986). The upwind algorithm is based on Roe's flux-difference splitting scheme which has been modified to account for real gas effects. The algorithm solves the gas dynamic and species continuity equations in a 'loosely' coupled manner. The new code has been validated by computing the laminar flow (at free stream Mach number 25) of chemically reacting air over a wedge and a cone. The results of these computations are compared with the results from a centrally-differenced, fully coupled, nonequilibrium PNS code. The agreement is excellent, except in the vicinity of the shock wave where the present code exhibits superior shock capturing capabilities.

Tannehill, John C.↗

The development of flux-split algorithms for flows with non-equilibrium thermodynamics and chemical reactions

A finite-volume method for the numerical computation of flows with nonequilibrium thermodynamics and chemistry is presented. A thermodynamic model is described which simplifies the coupling between the chemistry and thermodynamics and also results in the retention of the homogeneity property of the Euler equations (including all the species continuity and vibrational energy conservation equations). Flux-splitting procedures are developed for the fully coupled equations involving fluid dynamics, chemical production and thermodynamic relaxation processes. New forms of flux-vector split and flux-difference split algorithms are embodied in a fully coupled, implicit, large-block structure, including all the species conservation and energy production equations. Several numerical examples are presented, including high-temperature shock tube and nozzle flows. The methodology is compared to other existing techniques, including spectral and central-differenced procedures, and favorable comparisons are shown regarding accuracy, shock-capturing and convergence rates.

Grossman, B.↗

Data Base for CFD Validation

The flow behind the shock wave formed around objects which fly at hypervelocity behaves differently from that of a perfect gas. Molecules become vibrationally excited, dissociated, and ionized. The hot gas may emit or absorb radiation. When the atoms produced by dissociation reach the wall surface, chemical reactions, including recombination, may occur. The thermochemical phenomena of vibration, dissociation, ionization, surface chemical reaction, and radiation are referred to commonly as high-temperature real-gas phenomena. The phenomena cause changes in the dynamic behavior of the flow and the surface pressure and heat transfer distribution around the object. The character of a real gas is described by the internal degrees of freedom and state of constituent molecules; nitrogen and oxygen for air. The internal energy states, rotation, vibration and electronic, of the molecules are excited and, in the limit, the molecular bonds are exceeded and the gas dissociated into atomic and, possibly, ionic constituents. The process of energy transfer causing excitation, dissociation and recombination is a rate process controlled by particle collisions. Binary, two-body, collisions are sufficient to cause internal excitation, dissociation and ionization while three-body collisions are required to recombine the particles into molecular constituents. If the rates of energy transfer are fast with respect to the local fluid dynamic time scale the gas is in, or nearly in, equilibrium. If the energy transfer rates are very slow the gas can be described as frozen. In all other instances, wherein any of the energy exchange rates are comparable to the local fluid time scale, the gas will be thermally or chemically reacting and out of equilibrium. Real gas thermochemical nonequilibrium processes are important in the determination of aerodynamic heating; both convective (including wall catalytic effects) and radiative heating. To illustrate this we consider the hypervelocity flow over a bluff body typical of an atmospheric entry vehicle or an aerospace transfer vehicle (ASTV). The qualitative aspects of a hypersonic flow field over a bluff body are discussed in two parts, forebody and afterbody, with attention to which particular physical effects must be included in an analysis. This will indicate what type of numerical modeling will be adequate in each region of the flow. A bluff forebody flow field is dominated by the presence of the strong bow shock wave and the consequent heating, and chemical reaction of the gas. At high altitude hypersonic flight conditions the thermal excitation and chemical reaction of the gas occur slowly enough that a significant portion of the flow field is in a state of thermochemical nonequilibrium. A second important effect is the presence of the thick boundary layer along the forebody surface. In this region there are large thermal and chemical species gradients due to the interaction of the gas with the wall. Also at high altitudes the shock wave and the boundary layer may become so thick that they merge; in this case the entire shock layer is dominated by viscous effects.

Deiwert, George S.↗

Vibration dissociation coupling in nonequilibrium flows

The final report on research between North Carolina State University and the NASA Ames Research Center is presented. The research was aimed at using the Schwartz, Slawsky, Herzfeld (SSH) theory to simulate the vibrational relaxation of nitrogen molecules undergoing dissociation or recombination over a wide range of conditions. The results of these simulations were then treated as exact, and they were used to develop a model for the coupled vibration-dissociation process. This new model is simple enough to be used in computational fluid dynamics codes, but still captures the physics of the complex process. The model is used to simulate the flow over typical geometries to test it and to determine how much impact it has on the flow field. The key elements of this research are summarized.

Candler, Graham V.↗

Elements of radiative interactions in gaseous systems

Basic formulations, analyses, and numerical procedures are presented to study radiative interactions in gray as well as nongray gases under different physical and flow conditions. After preliminary fluid-dynamical considerations, essential governing equations for radiative transport are presented that are applicable under local and nonlocal thermodynamic equilibrium conditions. Auxiliary relations for relaxation times and spectral absorption model are also provided. For specific applications, several simple gaseous systems are analyzed. The first system considered consists of a gas bounded by two parallel plates having the same temperature. For this system, both vibrational nonequilibrium effects and radiation conduction interactions are studied. The second system consists of fully developed laminar flow and heat transfer in a parallel plate duct under the boundary condition of a uniform surface heat flux. For this system, effects of gray surface emittance are studied. With the single exception of a circular geometry, the third system is identical to the second system. Here, the influence of nongray walls is also studied, and a correlation between the parallel plates and circular tube results is presented. The particular gases selected are CO, CO2, H2O, CH4, N2O, NH3, OH, and NO. The temperature and pressure range considered are 300 to 2000 K, and 0.1 to 100 atmosphere, respectively. Illustrative results obtained for different cases are discussed and some specific conclusions are provided.

Tiwari, Surendra N.↗

Low-frequency ionization-driven instability of a discrete auroral arc model

The low-frequency (time scales of tens of seconds) dynamics of the auroral ionosphere differs from that of the nonauroral ionosphere by the presence of strong, unstable space- and time-dependent ionospheric ionization produced by precipitating auroral electrons. If recombination is relatively unimportant (as at high ionospheric heights), it is shown that, in general, transport processes cannot remove this ionization as fast as it is created, and no equilibrium is possible. These nonequilibrium phenomena are investigated in the context of a nonlinear adiabatic auroral model, which has previously been studied in static situations. A linearized local perturbation analysis is given of what amounts to a current-driven E x B gradient-drift instability with an ionization source, as well as some exact nonlinear solutions valid in a finite but limited spatial region. These solutions show continuing motion of auroral potential and plasma density, as the aurora tries to shift its ionization problems from one place to another. The analysis gives clues to the possibility of generation of chaos and of fine-scale spatial structure.

Cornwall, John M.↗

How Very Massive Metal-Free Stars Start Cosmological Reionization

The initial conditions and relevant physics for the formation of the earliest galaxies are well specified in the concordance cosmology. Using ab initio cosmological Eulerian adaptive mesh refinement radiation hydrodynamical calculations, we discuss how very massive stars start the process of cosmological reionization. The models include nonequilibrium primordial gas chemistry and cooling processes and accurate radiation transport in the case B approximation using adaptively ray-traced photon packages, retaining the time derivative in the transport equation. Supernova feedback is modeled by thermal explosions triggered at parsec scales. All calculations resolve the local Jeans length by at least 16 grid cells at all times and as such cover a spatial dynamic range of approx.10(exp 6). These first sources of reionization are highly intermittent and anisotropic and first photoionize the small-scale voids surrounding the halos they form in, rather than the dense filaments they are embedded in. As the merging objects form larger, dwarf-sized galaxies, the escape fraction of UV radiation decreases and the H II regions only break out on some sides of the galaxies, making them even more anisotropic. In three cases, SN blast waves induce star formation in overdense regions that were formed earlier from ionization front instabilities. These stars form tens of parsecs away from the center of their parent DM halo. Approximately five ionizing photons are needed per sustained ionization when star formation in 10(exp 6) stellar Mass halos is dominant in the calculation. As the halos become larger than approx.10(exp 7) Stellar Mass, the ionizing photon escape fraction decreases, which in turn increases the number of photons per ionization to 15-50, in calculations with stellar feedback only. Radiative feedback decreases clumping factors by 25% when compared to simulations without star formation and increases the average temperature of ionized gas to values between 3000 and 10,000 K.

Wise, John H.↗

Investigation of real-gas and viscous effects on the aerodynamic characteristics of a 40 deg half-cone with suggested correlations for the shuttle orbiter

Parameters were evaluated that might be used to correlate shuttle orbiter aerodynamic data to be used in extrapolating from wind-tunnel to flight conditions. Preliminary calculations indicate that the lee-side forces will have an insignificant influence on the aerodynamic characteristics of the orbiter for moderate angle-of-attack entries; therefore, this work is focused on phenomena which have an overriding influence on windward forces, namely, real-gas (equilibrium and nonequilibrium) and viscous-interaction effects. Analytically determined flow fields previously obtained on 40 deg blunted cones were used as a data source to evaluate various correlation parameters. Inviscid effects were found to be the dominant contributor to the aerodynamic coefficients in the altitude range of 64 to 76.2 km. The most suitable correlation of the aerodynamic forces on these cones is based on local dynamic pressure and local Mach number.

Hunt, J. L.↗

Chemical Thermodynamics and the Mathematical Integration of Reaction Kinetics

Key advances in the development of numerical methods for non-reacting compressible flows have been enabled by translating physical requirements into concrete numerical guidelines, such as the satisfaction of entropy inequalities for shock-capturing techniques [Lax, Contributions to Nonlinear Functional Analysis (1971) 603-634]. In the present work, we present nonlinear numerical analysis tools that draw from Chemical Thermodynamics , the branch of Nonequilibrium Thermodynamics that deals with chemical reactions. Through Gibbs formalism, chemical thermodynamics provides a well-known theoretical expression for the chemical equilibrium constant of a reaction in terms of reduced chemical potentials. A less-known, yet extremely valuable result, due to [Krambeck, Arch. Ration. Mech. Anal. , 38 (1970) 317], states that when this expression is implemented, mass-action kinetic models are consistent with the dynamical prescriptions of the 2nd law of thermodynamics. For fixed-temperature ordinary differential equations modeling constant-volume reacting gas mixtures, this leads to a decreasing Helmholtz free energy. If the temperature is allowed to vary in accordance with conservation of energy (1st law), this leads to the statement of increasing entropy. These nonlinear prescriptions can, and should be, used to further develop temporal integration techniques for reaction kinetics. We demonstrate that Krambeck's result holds even when the equilibrium constants are approximated from data. We prove this result by constructing the implicit free energy and the implicit entropy inherent to a given approximation. This is first done for a 5-species, 17-reaction model problem for air. With this structure established, elements of discrete entropy-stability theory [Tadmor, Acta Numer. , 12 (2003) 451] are leveraged to examine the consistency of time-integration schemes with these prescriptions. Using chemical potentials, one can compute the respective contributions of the kinetics model and of the temporal scheme to free energy/entropy variations. We introduce a nonlinear-stable version of the Discontinuous-Galerkin (DG) scheme in time which shows robustness improvements over the standard linearly-stable version. Most notably, the maximum timestep that can be resolved with the nonlinearly-stable variant tends to grow with polynomial order, in contrast to the linearly-stable variant. We generalize our constructions to arbitrary systems of reversible chemical reactions, ultimately showing that the compressible reacting Euler system admits the opposite of the implicitly constructed thermodynamic entropy as a mathematical entropy . This lays important theoretical foundations towards robust scheme development [Harten, J. Comput. Phys. 49 (1983) 151-164].

STMD↗

Simulating the Benesov Bolide Flowfield and Spectrum at Altitudes of 47 and 57 km

This paper develops a computational fluid dynamics capability for simulating the radiative emission from a meteor shock-layer and wake to an external observer. The developed capability includes the impact of radiation and ablation on the meteor flowfield, where coupled radiation accounts for the impact of radiation on the flowfield energy equations and coupled ablation accounts for the injection of ablation species from the meteoroid surface into the ow. This capability includes updated flowfield chemistry and nonequilibrium radiation models, which are compiled from the literature. To provide a level of validation for this capability, the Benesov spectral measurements are considered. Although the meteoroid was likely fragmented at the 47 and 57 km altitudes considered, and the measurement uncertainty is roughly ±50%, these measurements represent the best available spectral measurements for a relatively large (meter-class) bolide. To determine the equivalent meteoroid diameter to simulate, the continuum component of the spectrum in the 570 to 610 nm range is considered. This range is dominated by air emission from the high pressure and temperature shock-layer in front of the meteoroid, which is simulated with a relatively small uncertainty (because of the abundance of relevant shock tube measurements) and sensitive to the equivalent meteoroid diameter. This allows an equivalent diameter between 0.62 to 0.9 m to be determined, based on comparisons between measurements and simulations in the 570 to 610 nm range. The range of equivalent diameters is due to the various meteoroid geometries considered, where increasing the bluntness decreases the required diameter. Applying these diameters to simulations at 47 and 57 km results in simulated spectra that compare within 30% of the measured values, considering the wavelength integrated values between 400 and 650 nm. This agreement is well within the estimated measurement uncertainty of ±50%. All major spectral features are captured by the simulations. This agreement provides a level of validation for the developed model that has not been previously available.

Luminous efficiency↗

Towards a generalized computational fluid dynamics technique for all Mach numbers

Currently there exists no single unified approach for efficiently and accurately solving computational fluid dynamics (CFD) problems across the Mach number regime, from truly low speed incompressible flows to hypersonic speeds. There are several CFD codes that have evolved into sophisticated prediction tools with a wide variety of features including multiblock capabilities, generalized chemistry and thermodynamics models among other features. However, as these codes evolve, the demand placed on the end user also increases simply because of the myriad of features that are incorporated into these codes. In order for a user to be able to solve a wide range of problems, several codes may be needed requiring the user to be familiar with the intricacies of each code and their rather complicated input files. Moreover, the cost of training users and maintaining several codes becomes prohibitive. The objective of the current work is to extend the compressible, characteristic-based, thermochemical nonequilibrium Navier-Stokes code GASP to very low speed flows and simultaneously improve convergence at all speeds. Before this work began, the practical speed range of GASP was Mach numbers on the order of 0.1 and higher. In addition, a number of new techniques have been developed for more accurate physical and numerical modeling. The primary focus has been on the development of optimal preconditioning techniques for the Euler and the Navier-Stokes equations with general finite-rate chemistry models and both equilibrium and nonequilibrium thermodynamics models. We began with the work of Van Leer, Lee, and Roe for inviscid, one-dimensional perfect gases and extended their approach to include three-dimensional reacting flows. The basic steps required to accomplish this task were a transformation to stream-aligned coordinates, the formulation of the preconditioning matrix, incorporation into both explicit and implicit temporal integration schemes, and modification of the numerical flux formulae. In addition, we improved the convergence rate of the implicit time integration schemes in GASP through the use of inner iteration strategies and the use of the GMRES (General Minimized Resisual) which belongs to the class of algorithms referred to as Krylov subspace iteration. Finally, we significantly improved the practical utility of GASP through the addition of mesh sequencing, a technique in which computations begin on a coarse grid and get interpolated onto successively finer grids. The fluid dynamic problems of interest to the propulsion community involve complex flow physics spanning different velocity regimes and possibly involving chemical reactions. This class of problems results in widely disparate time scales causing numerical stiffness. Even in the absence of chemical reactions, eigenvalue stiffness manifests itself at transonic and very low speed flows which can be quantified by the large condition number of the system and evidenced by slow convergence rates. This results in the need for thorough numerical analysis and subsequent implementation of sophisticated numerical techniques for these difficult yet practical problems. As a result of this work, we have been able to extend the range of applicability of compressible codes to very low speed inviscid flows (M = .001) and reacting flows.

Walters, R. W.↗

Magnetic Reconfiguration in Explosive Solar Activity

A fundamental property of the Sun's corona i s that it is violently dynamic. The most spectacular and most energetic manifestations of this activity are the giant disruptions that give rise to coronal mass ejections (CME) and eruptive flares. These major events are of critical importance, because they drive the most destructive forms of space weather at Earth and in the solar system, and they provide a unique opportunity to study, in revealing detail, the interaction of magnetic field and matter, in particular, magnetohydrodynamic instability and nonequilibrium -- processes that are at the heart of laboratory and astrophysical plasma physics. Recent observations by a number of NASA space missions have given us new insights into the physical mechanisms that underlie coronal explosions. Furthermore, massively-parallel computation have now allowed us to calculate fully three-dimensional models for solar activity. In this talk I will present some of the latest observations of the Sun, including those from the just-launched Hinode and STEREO mission, and discuss recent advances in the theory and modeling of explosive solar activity.

Antiochos, Spiro K.↗

What is New on the Sun?

A fundamental property of the Sun's corona is that it is violently dynamic. The most spectacular and most energetic manifestations of this activity are the giant magnetic disruptions that give rise to coronal mass ejections (CME) and eruptive flares. These major events are of critical importance, because they drive the most destructive forms of space weather at Earth and in the solar system, and they provide a unique opportunity to study, in revealing detail, the interaction of magnetic field and matter, in particular, magnetohydrodynamic instability and nonequilibrium - processes that are at the heart of laboratory and astrophysical plasma physics. Recent observations by a number of NASA space missions have given us new insights into the physical mechanisms that underlie coronal explosions. Furthermore, massively-parallel computations have now allowed us to calculate fully three-dimensional models for the Sun's activity. In this talk I will review some of the latest observations of the Sun, including those from the just-launched Hinode and STEREO mission, and discuss recent advances in the theory and modeling of explosive solar activity.

Antiochos, Spiro K.↗

Radiative energy transfer in molecular gases

Basic formulations, analyses, and numerical procedures are presented to study radiative interactions in gray as well as nongray gases under different physical and flow conditions. After preliminary fluid-dynamical considerations, essential governing equations for radiative transport are presented that are applicable under local and nonlocal thermodynamic equilibrium conditions. Auxiliary relations for relaxation times and spectral absorption models are also provided. For specific applications, several simple gaseous systems are analyzed. The first system considered consists of a gas bounded by two parallel plates having the same temperature. Within the gas there is a uniform heat source per unit volume. For this system, both vibrational nonequilibrium effects and radiation conduction interactions are studied. The second system consists of fully developed laminar flow and heat transfer in a parallel plate duct under the boundary condition of a uniform surface heat flux. For this system, effects of gray surface emittance are studied. With the single exception of a circular geometry, the third system is considered identical to the second system. Here, the influence of nongray walls is also studied.

Tiwari, Surendra N.↗

Multistage Schemes with Multigrid for Euler and Navier-Strokes Equations: Components and Analysis

A class of explicit multistage time-stepping schemes with centered spatial differencing and multigrids are considered for the compressible Euler and Navier-Stokes equations. These schemes are the basis for a family of computer programs (flow codes with multigrid (FLOMG) series) currently used to solve a wide range of fluid dynamics problems, including internal and external flows. In this paper, the components of these multistage time-stepping schemes are defined, discussed, and in many cases analyzed to provide additional insight into their behavior. Special emphasis is given to numerical dissipation, stability of Runge-Kutta schemes, and the convergence acceleration techniques of multigrid and implicit residual smoothing. Both the Baldwin and Lomax algebraic equilibrium model and the Johnson and King one-half equation nonequilibrium model are used to establish turbulence closure. Implementation of these models is described.

Swanson, R. C.↗

Numerical simulations of non-equilibrium shock layers with efficient implicit schemes

Current and future calculations of nonequilibrium shock layers require the use of a very large number of equations, due to a multiplicity of chemical species, excited states, and internal energy modes. The computational cost associated with the use of standard implicit methods becomes prohibitive; it is therefore desirable to examine the potential of several methods and determine if any can be projected to be more efficient and accurate for large systems of equations. Here, the performance of several implicit schemes on several simple practical examples of reacting flows is examined. The Euler equations are solved by three different implicit methods, and two methods of coupling between the fluid dynamics and the chemistry are studied. Several cases of stiffness are considered and both 1D and 2D examples are computed.

Cambier, Jean-Luc↗

Dynamics of Disorder-Order Transitions in Hard Sphere Colloidal Dispersions in micro-g

We performed a series of experiments on 0.518 millimeter PMMA spheres suspended in an index matching mixture of decalin and tetralin the microgravity environment provided by the Shuttle Columbia on mission STS-73. The samples ranged in concentration from 0.49 to 0.62. volume fraction (phi) of spheres, which covers the range in which liquid, coexistence, solid and glass phases are expected from Earth bound experiments. Light scattering was used to probe the static structure, and the particle dynamics. Digital and 35 mm photos provided information on the morphology of the crystals. In general, the crystallites grew considerably larger (roughly an order of magnitude larger) than the same samples with identical treatment in 1 g. The dynamic light scattering shows the typical short time diffusion and long time caging effects found in 1 g. The surprises that were encountered in microgravity include the preponderance of random hexagonal close packed (RHCP) structures and the complete absence of the expected face centered cubic (FCC) structure, existence of large dendritic crystals floating in the coexistence samples (where liquid and solid phases coexist) and the rapid crystallization of samples which exist only in glass phase under the influence of one g. These results suggest that colloidal crystal growth is profoundly effected by gravity in yet unrecognized ways. We suspect that the RCHP structure is related to the nonequilibrium growth that is evident from the presence of dendrites. An analysis of the dendritic growth instabilities is presented within the framework of the Ackerson-Schatzel equation.

Zhu, J. X.↗