On Supernova Hydrodynamics
Rebuttal to Colgate criticism of Arnett investigation of gravitational collapse of nonrotating massive stars, discussing energy transport, equation of state and neutrino effects
Arnett, W. D.↗
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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Motion of a cylinder under the surface of a heavy fluid
General equations are derived for the approximate solution of the flow of a heavy infinite depth about a submerged circular cylinder where the center of the cylinder is submerged 1.5 diameter or greater. Then by replacing the cylinder by a dipole of a certain strength an equation is derived for the wave resistance of a circular cylinder moving in a fluid of finite depth.
HYDRODYNAMIC THEORY↗
Cellular automaton formulation of passive scalar dynamics
Cellular automata modeling of the advection of a passive scalar in a two-dimensional flow is examined in the context of discrete lattice kinetic theory. It is shown that if the passive scalar is represented by tagging or 'coloring' automation particles a passive advection-diffusion equation emerges without use of perturbation expansions. For the specific case of the hydrodynamic lattice gas model of Frisch et al. (1986), the diffusion coefficient is calculated by perturbation.
Chen, Hudong↗
The stability of cosmic-ray-dominated shocks - A secondary instability
Previous studies in one spatial dimension showed that the precursors of cosmic-ray-dominated shocks are unstable against traveling acoustic disturbances. Here we report that a secondary, Rayleigh-Taylor type instability can exist in cosmic-ray-dominated media influenced by the acoustic instability. Using the local WKB approximation, the growth rate of the secondary instability is shown to be comparable to that of the one-dimensional acoustic instability itself in the cases we have considered. The nonlinear development has been followed numerically with a two-dimensional PPM hydrodynamics code that also incorporates the two-fluid cosmic-ray energy equation. We show that the secondary instability may cause the precursor and postshock flows to become highly turbulent.
Ryu, Dongsu↗
Jet Stability and the Generation of Superluminal and Stationary Components
We present a numerical simulation of the response of an expanding relativistic jet to the ejection of a superluminal component. The simulation has been performed with a relativistic time-dependent hydrodynamical code from which simulated radio maps are computed by integrating the transfer equations for synchrotron radiation. The interaction of the superluminal component with the underlying jet results in the formation of multiple conical shocks behind the main perturbation. These trailing components can be easily distinguished because they appear to be released from the primary superluminal component instead of being ejected from the core. Their oblique nature should also result in distinct polarization properties. Those appearing closer to the core show small apparent motions and a very slow secular decrease in brightness and could be identified as stationary components. Those appearing farther downstream are weaker and can reach superluminal apparent motions. The existence of these trailing components indicates that not all observed components necessarily represent major perturbations at the jet inlet; rather, multiple emission components can be generated by a single disturbance in the jet. While the superluminal component associated with the primary perturbation exhibits a rather stable pattern speed, trailing components have velocities that increase with distance from the core but move at less than the jet speed. The trailing components exhibit motion and structure consistent with the triggering of pinch modes by the superluminal component. The increase in velocity of the trailing components is an indirect consequence of the acceleration of the expanding fluid, which is assumed to be relativistically hot; if observed, such accelerations would therefore favor an electron-positron (as opposed to proton rest mass) dominated jet.
Agudo, Ivan↗
A new direction in hydrodynamic stability: Beyond eigenvalues
Fluid flows that are smooth at low speeds become unstable and then turbulent at higher speeds. This phenomenon has traditionally been investigated by linearizing the equations of flow and looking for unstable eigenvalues of the linearized problem, but the results agree poorly in many cases with experiments. Nevertheless, it has become clear in recent years that linear effects play a central role in hydrodynamic instability. A reconciliation of these findings with the traditional analysis can be obtained by considering the 'pseudospectra' of the linearized problem, which reveals that small perturbations to the smooth flow in the form of streamwise vortices may be amplified by factors on the order of 10(exp 5) by a linear mechanism, even though all the eigenmodes are stable. The same principles apply also to other problems in the mathematical sciences that involve non-orthogonal eigenfunctions.
Trefethen, Lloyd N.↗
Boundary Layer Instabilities Over a Cone-Cylinder-Flare Model at Mach 6
Computations are performed to investigate the boundary-layer instabilities over a sharp cone-cylinder-flare model at zero degrees angle of attack. The model geometry and the flow conditions are selected to match the experiments conducted in the Boeing/AFOSR Mach 6 Quiet Tunnel (BAM6QT) at Purdue University. The geometry consists of a nominally sharp 5-degree half-angle cone, followed by a cylindrical segment and then a 10-degree flare. An axisymmetric separation bubble is generated as a result of the laminar shock/boundary-layer interaction in the cylinder-flare region. The comparison of the laminar flow solution and the schlieren images shows a remarkable agreement between the respective locations of both the boundarylayer edge and the reattachment shock. The predicted heat flux distribution is also in agreement with the measured values downstream of the reattachment location. The analysis of convective and global instabilities is performed for flare half angles equal to 8, 10, and 12 degrees and nosetip radii equal to 0.1, 1, and 5 mm. The linear amplification of first and second Mack mode instabilities that begin to amplify in the cone region are computed with a combination of the parabolized stability equations (PSE) and the harmonic linearized Navier-Stokes equations (HLNSE). The predicted frequency spectra of the surface pressure fluctuations associated with both planar and oblique instability waves are compared with the measured spectra at the various locations of the PCB and Kulite sensors. The comparison shows that the computational analysis captures the distinct lobes within the disturbance amplification spectra measured in the experiments, but some differences in amplification characteristics are noted at low frequencies. Overall, the oblique disturbances are found to be more amplified than the planar disturbances. To our knowledge, this represents the first successful comparison between convective instability analysis and measured surface pressure fluctuations for a hypersonic configuration with a separation bubble. Finally, the global instability analysis shows that the laminar flow becomes supercritical for flare half angles larger than 8 degrees. The unstable global mode for the experimental configuration of a 10 degrees flare and a sharp nosetip cone corresponds to a stationary three-dimensional disturbance that is concentrated in the recirculation region and achieves its maximum growth rate for an azimuthal wavenumber of 5.
Boundary layer transition↗
Hierarchical Statistical 3D ' Atomistic' Simulation of Decanano MOSFETs: Drift-Diffusion, Hydrodynamic and Quantum Mechanical Approaches
When MOSFETs are scaled to deep submicron dimensions the discreteness and randomness of the dopant charges in the channel region introduces significant fluctuations in the device characteristics. This effect, predicted 20 year ago, has been confirmed experimentally and in simulation studies. The impact of the fluctuations on the functionality, yield, and reliability of the corresponding systems shifts the paradigm of the numerical device simulation. It becomes insufficient to simulate only one device representing one macroscopical design in a continuous charge approximation. An ensemble of macroscopically identical but microscopically different devices has to be characterized by simulation of statistically significant samples. The aims of the numerical simulations shift from predicting the characteristics of a single device with continuous doping towards estimating the mean values and the standard deviations of basic design parameters such as threshold voltage, subthreshold slope, transconductance, drive current, etc. for the whole ensemble of 'atomistically' different devices in the system. It has to be pointed out that even the mean values obtained from 'atomistic' simulations are not identical to the values obtained from continuous doping simulations. In this paper we present a hierarchical approach to the 'atomistic' simulation of aggressively scaled decanano MOSFETs. A full scale 3D drift-diffusion'atomostic' simulation approach is first described and used for verification of the more economical, but also more restricted, options. To reduce the processor time and memory requirements at high drain voltage we have developed a self-consistent option based on a thin slab solution of the current continuity equation only in the channel region. This is coupled to the Poisson's equation solution in the whole simulation domain in the Gummel iteration cycles. The accuracy of this approach is investigated in comparison with the full self-consistent solution. At low drain voltage only single solution of the nonlinear Poisson equation is sufficient to extract the current with satisfactory accuracy. A pilot version of a hydrodynamic 'atomistic' simulator has been developed in order to study the effect of the nonequilibrium, non local transport in decanano MOSFETs on the random dopant induced current fluctuations. For the first time we have also applied the density gradient approach in 3D to investigate the effect of the quantum confinement on the threshold voltage fluctuations. The developed 'atomistic' simulation techniques have been applied to study various fluctuation resistant MOSFET architectures including epitaxial and delta doped devices.
Asenov, Asen↗
Comparison of Non-Parabolic Hydrodynamic Simulations for Semiconductor Devices
Parabolic drift-diffusion simulators are common engineering level design tools for semiconductor devices. Hydrodynamic simulators, based on the parabolic band approximation, are becoming more prevalent as device dimensions shrink and energy transport effects begin to dominate device characteristic. However, band structure effects present in state-of-the-art devices necessitate relaxing the parabolic band approximation. This paper presents simulations of ballistic diodes, a benchmark device, of Si and GaAs using two different non-parabolic hydrodynamic formulations. The first formulation uses the Kane dispersion relationship in the derivation of the conservation equations. The second model uses a power law dispersion relation {(hk)(exp 2)/2m = xW(exp Y)}. Current-voltage relations show that for the ballistic diodes considered. the non-parabolic formulations predict less current than the parabolic case. Explanations of this will be provided by examination of velocity and energy profiles. At low bias, the simulations based on the Kane formulation predict greater current flow than the power law formulation. As the bias is increased this trend changes and the power law predicts greater current than the Kane formulation. It will be shown that the non-parabolicity and energy range of the hydrodynamic model based on the Kane dispersion relation are limited due to the binomial approximation which was utilized in the derivation.
Smith, A. W.↗
Interplanetary gas dynamics.
Observations of the interplanetary medium are considered together with the structure of the solar atmosphere and the kinetic properties of the interplanetary plasma. Methods of gas kinetics and continuum flows are examined, taking into account microscopic and macroscopic representations, the kinetic flow equations, the formal solution of the Vlasov equation, and the continuum flow equations. The collective particle behavior of that interplanetary gas is discussed along with the hydrodynamic coronal expansion, a wave-pump problem, the free expansion phenomenon, and a generalized free expansion problem.
Liu, V. C.↗
Orbital Maneuvering Engine Feed System Coupled Stability Investigation, Computer User's Manual
An operating manual for the feed system coupled stability model was given, in partial fulfillment of a program designed to develop, verify, and document a digital computer model that can be used to analyze and predict engine/feed system coupled instabilities in pressure-fed storable propellant propulsion systems over a frequency range of 10 to 1,000 Hz. The first section describes the analytical approach to modelling the feed system hydrodynamics, combustion dynamics, chamber dynamics, and overall engineering model structure, and presents the governing equations in each of the technical areas. This is followed by the program user's guide, which is a complete description of the structure and operation of the computerized model. Last, appendices provide an alphabetized FORTRAN symbol table, detailed program logic diagrams, computer code listings, and sample case input and output data listings.
Schuman, M. D.↗
Variations on a spherically symmetrical accretion flow
Spherically symmetrical accretion onto a compact gravitating object is considered from a purely hydrodynamical viewpoint while disregarding heating and cooling processes. The study derives the radial perturbation equation, expresses it in a Eulerian form which is simpler than the Lagrangian form considered, for example, by Balazs (1972), and discusses the relation between the two formulations. This perturbation equation is used for the stability analysis of standing waves as well as for the study of short wavelength traveling waves which are a generalization of Parker's (1966) traveling wave solutions in the sense that they are not restricted to isothermal flows. These traveling waves can cause fluctuations in the mass accretion rate to grow large, but will not drive the unperturbed solution away from its assumed stationary profile. The waves conserve the total energy contained in the perturbation.
Petterson, J. A.↗
Time-dependent numerical modeling of dust halo formation at comets
The evolution of gas and dust distributions following a spatially and temporally localized comet outburst was calculated using a hybrid kinetic-hydrodynamic method. In the inner coma the time-dependent continuity, momentum, and energy equations of the dusty gas flow were solved simultaneously using 12 dust sizes. Beyond 300 km a three-dimensional kinetic model was used to calculate the trajectory of each individual dust grain. It was found that following the onset of the comet outburst a gas-dust blast wave propagates outward in the inner coma. About 15 minutes after the increased gas and dust production was initiated at the nucleus, a new equilibrium was reached in the inner coma. The most important feature of this new steady state was the significant increase of the dust terminal velocities. These higher terminal velocity values resulted in larger apex distances for dust particles emitted during the outburst. The dust particles spend a relatively long time near their apex points; therefore, the outburst generates long-lasting distinct dust envelopes in front of the regular dust coma.
Gombosi, T. I.↗
Core plasma in the magnetosphere
The paper presents a review of new findings related to core plasma (which includes ions and electrons with energies less than 50 eV) identified in studies of magnetosphere during 1983-1986. These findings include the cleft ion fountain; the plasmaspheric heavy ion torus; core molecular ions; high core-plasma densities in the plasma-sheet boundary layer; intense transverse heating of core plasmas in the equatorial regions; the supersonic polar wind (H/+/ and He/+/); toroidal or ring heavy-ion distribution functions in the auroral region; conic-to-field-aligned ion signatures of inverted-V auroral events; and the large-scale electron density structure of the magnetosphere. The progress made on modeling core plasma includes simulation of thermal helium heating at the equator; kinetic models of the plasma transport from localized ionospheric regions; time-dependent hydrodynamic models of the polar wind and plasmasphere-ionosphere coupling; and kinetic models of plasmasphere refilling.
Horwitz, J. L.↗
Physics of heavy ions (1989-1990)
The results from studies on polar wind ion heating due to kinetic ion beam instabilities and the effects of such ion heating on the outflow of O(+) in the polar wind are presented and discussed. First, the linear instabilities associated with an O(+) and H(+) polar wind plasma in the presence of O(+) and H(+) beams for a range of O(+)/H(+) beam densities, T(sub e)/T(sub i), and ion beam speeds were examined. Then, nonlinear heating of the polar wind ions was studied, using numerical simulations. The O(+) and H(+) polar wind ions were modeled by isotropic Maxwellian distributions, and the electrons, O(+) beams, and H(+) beams were modeled by drifting Maxwellian distributions. The effects of the kinetic ion heating on the outflow of the polar wind ions were examined from the ionosphere, using a time-dependent hydrodynamic model. A numerical code to solve the O(+) and H(+) continuity and momentum equations in a flux tube from ionospheric to magnetospheric altitudes were developed. The effects of ion heating were included by allowing for the altitudinal variation of the ion temperatures in the momentum equation. The ion temperature profiles were specified based on the ion heating characteristics found from previous kinetic simulations. It was assumed that heating occurred above 1500 km and increased to a saturated value of temperature that was obtained directly from the kinetic simulation study. The characteristics of the dynamical polar wind without ion heating were studied, and a flux tube on closed field lines that suddenly became open at t = 0 was simulated. Then, the effects of ion heating were included. To gain some physical insight, two limiting cases were considered: preferential H(+) heating and preferential O(+) heating. How O(+) heating can lead to enhanced polar wind O(+) fluxes in the polar magnetosphere is shown.
Ashour-Abdalla, M.↗
Convergence properties of finite-difference hydrodynamics schemes in the presence of shocks
We investigate the asymptotic convergence of finite-difference schemes for the Euler equations when the limiting solution contains shocks. The Lax-Wendroff theorem guarantees that certain conservative schemes converge to correct, physically valid solutions. We focus on two one-dimensional operator-split schemes with explicit artificial-viscosity terms. One, an internal-energy scheme, does not satisfy the assumptions of Lax-Wendroff; the other, a conservative total-energy scheme, does. With viscous lengths chosen proportional to the grid size, we find that both schemes converge to their zero-grid-size limits at the theoretically expected rate, but only the conversative scheme converges toward correct solutions of the inviscid fluid equations. We show that the difference in their behaviors results directly from the presence of shocks in the limiting solution. Empirically, we find that when the viscous lenghts tend toward zero more slowly than the grid size, however the nonconservative scheme also converges toward correct solutions. We characterize the asymptotic behavior of the total-energy scheme in a particular problem in which a shock forms. As the grid is refined, a Cauchy error approaches the expected rate of change slowly. We show that the changes in the artificial viscosity alter the diffusion of small-amplitude waves. The differences associated with such waves make the dominant contribution to the Cauchy error. We formulate an analytic model to relate the rate of approach to the effect of varying diffusion in waves and find quantitative agreement with our numerical results.
Kimoto, Paul A.↗
Stability Analysis of Streaks Induced by Optimized Vortex Generators
Numerical computations are performed to investigate the potential for transition control in an axisymmetric boundary layer via fully realizable, streamwise stationary streaks induced by an azimuthally periodic array of surface mounted vortex generators (VGs). Previous work has shown that suitable streaks of this type can significantly reduce the growth of Mack’s second mode instabilities, but large streak amplitudes can make the flow susceptible to previously absent streak instabilities that can become the leading cause of transition. Here, we use the adjoint capabilities of the SU2 flow solver to optimize the VG shape to maximize the reduction in the growth of second-mode disturbances while also preventing the streak amplitudes from reaching large enough values to precipitate an earlier onset of transition via streak instabilities. The geometry and the freestream flow conditions are selected to match a relevant trajectory lo-cation from the HIFiRE-1 flight experiment. Results show that the optimized VGs can increase the mean streak amplitude by 117% with respect to a manually developed baseline design. The stability of this optimized basic state is analyzed via the plane-marching parabolized stability equations, predicting a fully laminar flow over the entire cone, or equivalently, yielding transition delay of 130% versus the 17% for the baseline VGs.
Boundary layer transition↗
Hydrodynamical constraints on cosmic-ray acceleration in relativistic shocks
A two-fluid hydrodynamical model governing the transport of cosmic rays in a relativistically moving background plasma is developed. The equations are used to discuss the time asymptotic structure of a relativistic, plane-parallel shock wave significantly modified by first-order Fermi acceleration of cosmic rays. The model allows for an anisotropic cosmic-ray pressure tensor with pressure components parallel and perpendicular to the shock normal. It is surmised that the well-known energy threshold problem for diffusive shock acceleration that downstream particles have a large enough velocity to overtake the shock and subsequently scatter in the upstream medium before returning to the downstream medium may be expressed hydrodynamically by the condition V less than V(cr), where V is the fluid velocity relative to the shock and V(cr) is the relativistic cosmic-ray sound speed. Astrophysical implications of the results are briefly discussed.
Webb, G. M.↗