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NASA NTRS1985

A parameterization technique for nonlinear spectral models

An objective parameterization technique is developed for general nonlinear hydrodynamical systems. The typical structure of hydrodynamical systems, regardless of their complexity, is one in which the rates of change of the dependent variables depend on homogeneous quadratic and linear forms, as well as on inhomogeneous forcing terms. As a prototype of the generic problem containing this typical structure, the parameterization technique is applied to various three component subsets of a five component nonlinear spectral model of forced, dissipative quasi-geostrophic flow in a channel. The results obtained lead to specification of the necessary data coverage requirements for applying the technique in general.

Gelaro, R.↗
NASA NTRS1986

A parameterization technique for nonlinear spectral models

An objective parameterization technique is developed for general nonlinear hydrodynamical systems. The typical structure of hydrodynamical systems, regardless of their complexity, is one in which the rates of change of the dependent variables depend on homogeneous quadratic and linear forms, as well as on inhomogeneous forcing terms. As a prototype of the generic problem containing this typical structure, the parameterization technique is applied to various three component subsets of a five component nonlinear spectral model of forced, dissipative quasi-geostrophic flow in a channel. The results obtained lead to specification of the necessary data coverage requirements for applying the technique in general.

Gelaro, R.↗
NASA NTRS1987

A new hydrodynamic analysis of double layers

A genuine two-fluid model of plasmas with collisions permits the calculation of dynamic (not necessarily static) electric fields and double layers inside of plasmas including oscillations and damping. For the first time a macroscopic model for coupling of electromagnetic and Langmuir waves was achieved with realistic damping. Starting points were laser-produced plasmas showing very high dynamic electric fields in nonlinear force-produced cavitous and inverted double layers in agreement with experiments. Applications for any inhomogeneous plasma as in laboratory or in astrophysical plasmas can then be followed up by a transparent hydrodynamic description. Results are the rotation of plasmas in magnetic fields and a new second harmonic resonance, explanation of the measured inverted double layers, explanation of the observed density-independent, second harmonics emission from laser-produced plasmas, and a laser acceleration scheme by the very high fields of the double layers.

Hora, Heinrich↗
NASA NTRS1989

Direct numerical simulations of turbulent convection with a variable gravity and Keplerian rotation

Thermal convection was proposed as a possible mechanism for generation and maintenance of turbulence in the inner accretion disk regime of the primordial solar nebula. It is of fundamental interest to design experiments with the basic physical features of the solar nebula conditions cannot be produced in the laboratory, numerical simulations of hydrodynamic flows, which have been very successful in describing aerodynamic flows, can be suitable modified to provide experimental data for solar nebula modelling. The goals are to modify an extant, proven hydrodynamics code with the most important features of the solar nebula and other thin accretion disks: bouyancy terms to generate convection, internal heating representing the release of gravitational potential energy, a variable gravity linearly proportional the the distance from the vertical midplane due to centrifugal balance, rapid rotation with axis aligned with gravity, and Keplerian rotational shear; to determine the effect that these features have on the turbulent convection by introducing them individually and to determine the cumulative nature of the turbulent convection for accretion disk conditions; and to model the convection and the turbulence. In this manner, prior solar nebula models can be tested and their deficiencies rectified.

Cabot, William H.↗
NASA NTRS1990

Theory of multicolor lattice gas - A cellular automaton Poisson solver

The present class of models for cellular automata involving a quiescent hydrodynamic lattice gas with multiple-valued passive labels termed 'colors', the lattice collisions change individual particle colors while preserving net color. The rigorous proofs of the multicolor lattice gases' essential features are rendered more tractable by an equivalent subparticle representation in which the color is represented by underlying two-state 'spins'. Schemes for the introduction of Dirichlet and Neumann boundary conditions are described, and two illustrative numerical test cases are used to verify the theory. The lattice gas model is equivalent to a Poisson equation solution.

Chen, H.↗
NASA NTRS1994

Analysis of the early spectra and light curve of SN 1987A

Numerical modeling of supernova spectra, light curves, and hydrodynamics requires physical inputs, numerical techniques, approximations, and assumptions which must be thoroughly understood in order to study the details of supernova explosions. Here, we discuss some of these in the context of the early evolution of supernova 1987A. Gray radiation-hydrodynamics is used to calculate the bolometric light curve and the hydrodynamic evolution of the supernova. Synthetic spectra are then obtained for the resulting density and velocity structure. The spectrum calculations are performed using a special-relativistic treatment of the radiative transfer equation in the comoving frame, line blanketing by about 10(exp 5) spectral lines, and departures from local thermodynamic equilibrium (LTE) for H I, He I, Mg II, and Ca II. We find that we are able to simultaneously fit the early light curve and spectra reasonably well, using a progenitor model from Arnett (1991a), without fine-tuning the free parameters. Temperature structures and radiative equilibrium, non-LTE effects, homologous expansion, and mean opacities are discussed.

Hauschildt, Peter H.↗
NASA NTRS1994

A hydrodynamic approach to cosmology: The mixed dark matter cosmological scenario

We compute the evolution of spatially flat, mixed cold and hot dark matter models containing both baryonic matter and two kinds of dark matter. Hydrodynamics is treated with a highly developed Eulerian hydrodynamic code (see Cen 1992). A standard particle-mesh (PM) code is also used in parallel to calculate the motion of the dark matter components. We adopt the following parameters: h equivalent to (sub 0)/100 km/s Mpc(exp -1) = 0.5, OMEGA(sub C) = 0.3, and OMEGA(sub B) = 0.06, with amplitude of the perturbation spectrum fixed by the Cosmic Background Explorer Satellite (COBE) Dark Matter Radiation (DMR) measurements (Smoot et al. 1992) being sigma (sub 8) = 0.67. Four different boxes are simulated with box sizes of L = (64, 16, 4, 1) h(exp -1) Mpc, respectively, the two small boxes providing good resolution but little valid information due to absence of large-scale power. We use 128(exp 3) approximate 10(exp 6.3) baryonic cells, 128(exp .3) cold dark matter particles, and 2 x 128(exp 3) hot dark matter particles. In addition to the dark matter we follow separately six baryonic species (H, H(+), He, He(+), He(++), e(-)) with allowance for both (nonequilibrium) collisional and radiative ionization in every cell. The background radiation field is also followed in detail with allowance made for both continuum and line processes, to allow nonequilibrium heating and cooling processes to be followed in detail. The mean final Zeldovich-Sunyaev y parameter is estimated to be y Bar = (5.4 + or - 2.7) x 10(exp -7) below currently attainable observations, with a rms fluctuation of approximately delta bar y = (0.6 + or - 3.0) x 10(exp -7) on arcminute scales. The rate of galaxy formation peaks at an even later epoch (z approximate 0.3) than in the standard (OMEGA = 1, sigma sub 8 = 0.67) cold dark matter (CDM) model (z approximate 0.5) and, at a redshift of z = 4, is nearly a factor of 100 lower than for the CDM model with the same value of sigma sub 8. With regard to mass function, the smallest objects are stabilized against collapse by thermal energy: the mass-weighted mass spectrum has a broad peak in the vicinity of M(sub B) = 10(exp 9.5) solar mass with a reasonable fit to the Schechter luminosity function if the ratio of baryon mass to blue light is approximately 4. In addition, one very large PM simulation was made in a box with size (320 h(exp - 1) Mpc) containing 3 x 200(exp 3) = 10(exp 7.4) particles. Utilizing this simulation we find that the model yields a cluster mass function which is about a factor of 4 higher than observed, but a cluster-cluster correlation length marginally lower than observed, but that both are closer to observations than in the (COBE) normalized CDM model. The one-dimensional pairwise velocity dispersion is 605 + or - 8 km/s at 1/h separation, lower than that of the DCM model normalized to COBE, but still significant higher than observations (Davis & Peebles 1983). A plausible velocity bias b(sub v) = 0.8 + or - 0.1 on this scale will reduce but not remove the discrepancy. The velocity auto-correlat ion function has a coherence length of 40/h Mpc, which is somewhat lower than the observed counterpart. In all these respects the model would be improved by decreasing the cold fraction of the dark OMEGA(sub CDM)/ (OMEGA(sub CDM) + OMEGA(sub HDB). But formation of galaxies and clusters of galaxies is much later in this model than in COBE-normalized CDM, perhaps too late. To improve on these constraints a larger ratio of OMEGA(sub CDM)/ (OMEGA(sub CDM) + OMEGA(sub HDM)) is required than the value of 0.67 adopted here. It does not seem possible to find a value for this ratio which would satisfy all tests. Overall, the model is similar both on large and intermediate scales to the standard CDM model normalized to the same value of sigma(sub B), but the problem with regard to late formation of galaxies is more severe in this model than in that CDM model. Adding hot dark matter, significantly improves the ability of the COBE-normalized CDM scenario to fit existing observations, but the model is in fact not as good as the CDM model with the same sigma(sub 8) and is still probably unsatisfactory with regard to several critical tests.

Cen, Renyue↗
NASA NTRS1993

Extended hot-gas halos around starburst galaxies

A reanalysis of Einstein Imaging Proportional Counter (IPC) data and new observations from the Ginga Large Area (Proportional) counters (LAC) indicate the presence of extended X-ray emission (10-50 kpc) around the starburst galaxy M82. Here, we discuss our model of this emission, which was obtained by performing numerical hydrodynamic simulations of the starburst event to much later times and larger scales than were previously considered. For our models, we adopted a supernova rate of 0.1/yr, and an extended low-density static halo that is bound to the galaxy. There are three stages to the evolution of the wind-blown bubble and the propagation of the shock front: the bubble expands in an almost uniform density disk gas, with a deceleration of the shock front (t is less than or approximately 3.6 Myr); breakout from the disk and the upward acceleration of the shock front (3.6 Myr is less than or approximately t is less than or approximately 18 Myr); propagation into the halo, leading to a more spherical system and shock deceleration (18 Myr is less than or approximately t). For a halo density of 10(exp -3)/cu cm, the outflow reaches a distance of 40-50 kpc from the center of the starburst galaxy in 50 Myr. We calculated the time evolution of the X-ray luminosity and found that the extended starburst emits 3 x 10(exp 39) erg/s to 10(exp 40) in the Ginga LAC band and approximately 10(exp 41) erg/s in the Einstein band. The degree of the ionization equilibrium in the outflow and its effect on the iron K alpha line emission are discussed.

Tomisaka, Kohji↗
NASA NTRS1987

The acceleration of winds by MHD waves in open magnetic structures

It has become increasingly clear in recent years that the available models describing the acceleration of high speed streams in solar coronal holes are inadequate. Thermal models do not result in winds with the proper thermal speed and density. In addition models which assume acceleration by Alfven waves, though promising, are not self-consistent when applied low in coronal holes where the acceleration of the wind takes place. An Alfven wave in the corona with a period of a few hundred seconds will have a wavelength of the order of 10 cm. This is of the order of the diameter of a coronal hole in the low corona, and therefore it is expected that the MHD waves are guided in some sense by the coronal hole in which they propagate. This basic idea led to the development of a leaky waveguide theory to describe MHD wave propagation in coronal holes. Recent efforts were concentrated in two areas: the development of numerical codes to properly describe the hydrodynamics of the flow, and more realistic models of the coronal hole properties such as density gradients and spherical divergence of the flux tube. Some of the important aspects of the theory are discussed, including the effect of density inhomogeneities and smooth transverse density gradients. In addition it is hoped that some early results from the numerical models will be presented. The acceleration of cool winds is a problem of interest in cool supergiants also. Some work was done on the development of wind models for these stars as well.

Davila, Joseph M.↗
NASA NTRS1993

Large eddy simulation and direct numerical simulation of high speed turbulent reacting flows

The objective of this research is to make use of Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) for the computational analyses of high speed reacting flows. Our efforts in the first phase of this research conducted within the past three years have been directed in several issues pertaining to intricate physics of turbulent reacting flows. In our previous 5 semi-annual reports submitted to NASA LaRC, as well as several technical papers in archival journals, the results of our investigations have been fully described. In this progress report which is different in format as compared to our previous documents, we focus only on the issue of LES. The reason for doing so is that LES is the primary issue of interest to our Technical Monitor and that our other findings were needed to support the activities conducted under this prime issue. The outcomes of our related investigations, nevertheless, are included in the appendices accompanying this report. The relevance of the materials in these appendices are, therefore, discussed only briefly within the body of the report. Here, results are presented of a priori and a posterior analyses for validity assessments of assumed Probability Density Function (PDF) methods as potential subgrid scale (SGS) closures for LES of turbulent reacting flows. Simple non-premixed reacting systems involving an isothermal reaction of the type A + B yields Products under both chemical equilibrium and non-equilibrium conditions are considered. A priori analyses are conducted of a homogeneous box flow, and a spatially developing planar mixing layer to investigate the performance of the Pearson Family of PDF's as SGS models. A posteriori analyses are conducted of the mixing layer using a hybrid one-equation Smagorinsky/PDF SGS closure. The Smagorinsky closure augmented by the solution of the subgrid turbulent kinetic energy (TKE) equation is employed to account for hydrodynamic fluctuations, and the PDF is employed for modeling the effects of scalar fluctuations. The implementation of the model requires the knowledge of the local values of the first two SGS moments. These are provided by additional modeled transport equations. In both a priori and a posteriori analyses, the predicted results are appraised by comparison with subgrid averaged results generated by DNS. Based on these results, the paths to be followed in future investigations are identified.

Adumitroaie, V.↗
NASA NTRS1998

On Pulsating and Cellular Forms of Hydrodynamic Instability in Liquid-Propellant Combustion

An extended Landau-Levich model of liquid-propellant combustion, one that allows for a local dependence of the burning rate on the (gas) pressure at the liquid-gas interface, exhibits not only the classical hydrodynamic cellular instability attributed to Landau but also a pulsating hydrodynamic instability associated with sufficiently negative pressure sensitivities. Exploiting the realistic limit of small values of the gas-to-liquid density ratio p, analytical formulas for both neutral stability boundaries may be obtained by expanding all quantities in appropriate powers of p in each of three distinguished wave-number regimes. In particular, composite analytical expressions are derived for the neutral stability boundaries A(sub p)(k), where A, is the pressure sensitivity of the burning rate and k is the wave number of the disturbance. For the cellular boundary, the results demonstrate explicitly the stabilizing effect of gravity on long-wave disturbances, the stabilizing effect of viscosity (both liquid and gas) and surface tension on short-wave perturbations, and the instability associated with intermediate wave numbers for negative values of A(sub p), which is characteristic of many hydroxylammonium nitrate-based liquid propellants over certain pressure ranges. In contrast, the pulsating hydrodynamic stability boundary is insensitive to gravitational and surface-tension effects but is more sensitive to the effects of liquid viscosity because, for typical nonzero values of the latter, the pulsating boundary decreases to larger negative values of A(sub p) as k increases through O(l) values. Thus, liquid-propellant combustion is predicted to be stable (that is, steady and planar) only for a range of negative pressure sensitivities that lie below the cellular boundary that exists for sufficiently small negative values of A(sub p) and above the pulsating boundary that exists for larger negative values of this parameter.

Margolis, Stephen B.↗
NASA NTRS1990

Direct numerical simulations of stably-stratified sheared turbulence: Implications for oceanic mixing

Direct numerical simulations of the time evolution of homogeneous stably stratified turbulent shear flows have been performed for several Richardson numbers Ri and Reynolds numbers R(sub lambda) in earlier works. The results show excellent agreement with length scale models developed from laboratory experiments to characterize oceanic turbulence. When the Richardson number Ri is less than the stationary value Ri(sub s), the turbulence intensity grows at all scales, and the growth rate appears to be a function of Ri. The size of the vertical density inversions also increases. On the other hand, when Ri is greater than or equal to Ri(sub s) the largest turbulent eddies become vertically constrained by buoyancy when the Ellison (turbulence) scale L(sub E) and the Ozmidov (buoyancy) scale L(sub O) are equal. At this point, the mixing efficiency is maximal and corresponds to a flux Richardson number R(sub f) = 0.20. The vertical mass flux becomes counter-gradient when epsilon = 19(nu)N(exp 2) and vertical density overturns are suppressed in less than half a Brunt-Vaisala period. The results of the simulations were also recast in terms of the Hydrodynamic Phase Diagram introduced in fossil turbulence models. The so-called point of fossilization occurs when epsilon = 4DCN(exp 2); Gibson proposed 13DCN(exp 2). This value is in agreement with indirect laboratory observations and field observations. Finally, the validity of the steady-state models to estimate vertical eddy diffusivities in the oceanic thermocline is discussed.

Itsweire, E. C.↗
NASA NTRS1957

Rough-water Impact-load Investigation of a Chine-immersed V-bottom Model Having a Dead-rise Angle of 10 Degrees

A hydrodynamic rough-water impact-loads investigation of a fixed-trim V-bottom float with a beam-loading coefficient of 5.78 and dead-rise angle of 10 degrees was made at the Langley impact basin. The size of the waves varied from approximately 10 to 60 feet in length and 1 to 2 feet in height. Time histories were obtained showing the position of the model relative to the wave throughout the impact and typical examples are presented. The load coefficient was found to vary primarily with the slope of the impacting wave.

HYDRODYNAMIC CONFIGURATIONS - GENERAL STUDIES↗
NASA NTRS1989

Shock-generated X-ray emission in radiatively driven winds - A model for Tau Scorpii

A one-dimensional radiation-hydrodynamics code is used to numerically investigate the structure and evolution of shocks in the winds of hot stars. Results are presented for the specific case of Tau Sco, a well-studied main-sequence B star for which there are X-ray data from the Einstien satellite's Solid State Spectrometer. A phenomenological radiative acceleration term and a mass-loss rate consistent with UV observations, are used to determine the time dependence of the temperatures within and X-ray emission from an isolated shock region. The driving acceleration leads to the formation of a two-component shock zone with 'forward' and 'reverse' shocks, each with their own characteristic temperature. A denser cold region forms between the two shocks, which could potentially account for the presence of narrow absorption features that are observed in the UV P Cygni profiles of many hot stars. The X-ray emission spectra from the shocks in the calculations are in good general agreement with two-temperature model fits to Einstein X-ray observations.

Macfarlane, Joseph J.↗
NASA NTRS2013

Prediction of Ablation Rates from Solid Surfaces Exposed to High Temperature Gas Flow

A mathematical model and a solution algorithm is developed to study the physics of high temperature heat transfer and material ablation and identify the problems associated with the flow of hydrogen gas at very high temperatures and velocities through pipes and various components of Nuclear Thermal Rocket (NTR) motors. Ablation and melting can be experienced when the inner solid surface of the cooling channels and the diverging-converging nozzle of a Nuclear Thermal Rocket (NTR) motor is exposed to hydrogen gas flow at temperatures around 2500 degrees Kelvin and pressures around 3.4 MPa. In the experiments conducted on typical NTR motors developed in 1960s, degradation of the cooling channel material (cracking in the nuclear fuel element cladding) and in some instances melting of the core was observed. This paper presents the results of a preliminary study based on two types of physics based mathematical models that were developed to simulate the thermal-hydrodynamic conditions that lead to ablation of the solid surface of a stainless steel pipe exposed to high temperature hydrogen gas near sonic velocities. One of the proposed models is one-dimensional and assumes the gas flow to be unsteady, compressible and viscous. An in-house computer code was developed to solve the conservations equations of this model using a second-order accurate finite-difference technique. The second model assumes the flow to be three-dimensional, unsteady, compressible and viscous. A commercial CFD code (Fluent) was used to solve the later model equations. Both models assume the thermodynamic and transport properties of the hydrogen gas to be temperature dependent. In the solution algorithm developed for this study, the unsteady temperature of the pipe is determined from the heat equation for the solid. The solid-gas interface temperature is determined from an energy balance at the interface which includes heat transfer from or to the interface by conduction, convection, radiation, and ablation. Two different ablation models are proposed to determine the heat loss from the solid surface due to the ablation of the solid material. Both of them are physics based. Various numerical simulations were carried out using both models to predict the temperature distribution in the solid and in the gas flow, and then predict the ablation rates at a typical NTR motor hydrogen gas temperature and pressure. Solid mass loss rate per foot of a pipe was also calculated from these predictions. The results are presented for fully developed turbulent flow conditions in a sample SS pipe with a 6 inch diameter.

Akyuzlu, Kazim M.↗
NASA NTRS1971

Collisionless solar wind protons: A comparison of kinetic and hydrodynamic descriptions

Kinetic and hydrodynamic descriptions of a collisionless solar wind proton gas are compared. Heat conduction and viscosity are neglected in the hydrodynamic formulation but automatically included in the kinetic formulation. The results of the two models are very nearly the same, indicating that heat conduction and viscosity are not important in the solar wind proton gas beyond about 0.1 AU. It is concluded that the hydrodynamic equations provide a valid description of the collisionless solar wind protons, and hence that future models of the quiet solar wind should be based on a hydrodynamic formulation.

Leer, E.↗
NASA NTRS1969

Dynamical models of novae.

Nova outburst dynamics investigation by time dependent hydrodynamics computer program including energy transport by radiation and convection

Sparks, W. M.↗