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All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

High-Order Shock-Capturing Methods for Modeling Dynamics of the Solar Atmosphere

We use one-dimensional high-order central shock capturing numerical methods to study the response of various model solar atmospheres to forcing at the solar surface. The dynamics of the atmosphere is modeled with the Euler equations in a variable-sized flux tube in the presence of gravity. We study dynamics of the atmosphere suggestive of spicule formation and coronal oscillations. These studies are performed on observationally-derived model atmospheres above the quiet sun and above sunspots. To perform these simulations, we provide a new extension of existing second- and third- order shock-capturing methods to irregular grids. We also solve the problem of numerically maintaining initial hydrostatic balance via the introduction of new variables in the model equations and a careful initialization mechanism. We find several striking results: all model atmospheres respond to a single impulsive perturbation with several strong shock waves consistent with the rebound-shock model. These shock waves lift material and the transition region well into the initial corona, and the sensitivity of this lift to the initial impulse depends non-linearly on the details of the atmosphere model. We also reproduce an observed 3-minute coronal oscillation above sunspots compared to 5-minute oscillations above the quiet sun.

Bryson, Steve↗
NASA NTRS1989

Adaptive numerical solutions of the Euler equations in 3D using finite elements

The development of an adaptive mesh solution for a flow involving shock interaction on a swept cylinder and an initial solution for a flow past a complex fighter configuration is reported. The finite element solution algorithm, the mesh generation, and the adaptivity of the solution are described. Sample results for the flow past an F-18 configuration at Mach 0.9 and alpha of 3 deg and for shock interaction on a swept cylinder at Mach 8.04 are summarized.

Peraire, J.↗
NASA NTRS1993

Cosmic-ray acceleration during the impact of shocks on dense clouds

In order to elucidate the properties of diffusive shock acceleration in nonuniform environments, an extensive set of simulations of the dynamical interactions between plane nonradiative shocks and dense gas clouds was carried out initially in static equilibrium with their environments. These time-dependent calculations are based on the two-fluid model for diffusive cosmic ray transport, and include the dynamically active energetic proton component of the cosmic rays as well as passive electron and magnetic field components. Except when the incident shock is itself already dominated by cosmic ray pressure, it is found that the presence of the cloud adds little to the net acceleration efficiency of the original shock and can, in fact, reduce slightly the net amount of energy transferred to cosmic rays after a given time. It is found that, in 2D cloud simulations, the always-weak bow shock and the shock inside the cloud are less important to acceleration during the interaction than the tail shock.

Jones, T. W.↗
NASA NTRS1973

The transonic aerofoil problem with embedded shocks.

The integral equation approach to the mixed flow problem of infinite wings at high subsonic speeds is adopted for non-circulatory and circulatory (lifting) flows. The solutions are determined from a system of non-linear algebraic equations and, to ensure always unique solutions, the method of differentiation with respect to a parameter has been applied. The resulting Cauchy problem is then solved with the linearised flow solution as the initial value vector. For the case of embedded shocks in the flow field, the method of steepest descent has been added to the calculation scheme. Results for subcritical and supercritical flows past aerofoils are given and compared with solutions obtained by finite-difference techniques.

Norstrud, H.↗
NASA NTRS1976

Table and charts of equilibrium normal-shock properties for hydrogen-helium mixtures with velocities to 70 km/sec. Volume 1: 0.95 H2-0.05 He (by volume)

Equilibrium thermodynamic and flow properties are presented in tabulated and graphical form for moving, standing, and reflected normal shock waves into hydrogen-helium mixtures representative of postulated outer planet atmospheres. These results are presented in four volumes and the volmetric compositions of the mixtures are 0.95H2-0.05He in Volume 1, 0.90H2-0.10He in Volume 2, 0.85H2-0.15He in Volume 3, and 0.75H2-0.25He in Volume 4. Properties include pressure, temperature, density, enthalpy, speed of sound, entropy, molecular-weight ratio, isentropic exponent, velocity, and species mole fractions. Incident (moving) shock velocities are varied from 4 to 70 km/sec for a range of initial pressure of 5 N/sq m to 100 kN/sq m. Results are applicable to shock-tube flows and for determining flow conditions behind the normal portion of the bow shock about a blunt body at high velocities in postulated outer planet atmospheres. The document is a revised version of the original edition of NASA SP-3085 published in 1974.

Miller, C. G., III↗
NASA NTRS1976

Numerical analysis of a two-dimensional nonsteady detonations

In the present work a system of two-dimensional nonsteady hydrodynamic and chemical kinetic equations was numerically integrated for an exothermic system. Assumed two-step reaction model simulates practically an oxyhydrogen mixture. The calculation starts from a plane Chapman-Jouguet detonation as an initial condition. Two-dimensional disturbances are generated by artificially placing nonuniformities ahead of the detonation front. Regardless of the difference of the given initial disturbances, a fixed number of triple shock waves were produced for a fixed combination of mixture model and geometry when the transition period was over. This shows that for a given detonation tube geometry any exothermic system has its own characteristic multidimensional structure. The obtained number of triple shock waves contained in the detonation front was in agreement with existing experimental observations under the same condition.

Taki, S.↗
NASA NTRS1981

Holographic interferometry technique for rotary wing aerodynamics and noise

The concepts of holography and holographic interferometry, as applied to the visualization and measurement of the three dimensional flow field near a rotor tip, are previewed, and initial experimental results of investigations of local shock structures and tip vortices behind the blade are presented. An additional method to visualize the flow in a three dimensional manner is demonstrated, and finally, a method to quantitatively measure the three dimensional flow, which will provide the necessary information to help improve helicopter performance and reduce noise, is introduced.

Kittleson, J. K.↗
NASA NTRS1985

An MHD model of the earth's magnetosphere

It is pointed out that the earth's magnetosphere arises from the interaction of the solar wind with the earth's geomagnetic field. A global magnetohydrodynamics (MHD) model of the earth's magnetosphere has drawn much attention in recent years. In this model, MHD equations are used to describe the solar wind interaction with the magnetosphere. In the present paper, some numerical aspects of the model are considered. Attention is given to the ideal MHD equations, an equation of state for the plasma, the model as an initial- and boundary-value problem, the shock capturing technique, computational requirements and techniques for global MHD modeling, a three-dimensional mesh system employed in the global MHD model, and some computational results.

Wu, C. C.↗
NASA NTRS1987

Simulation of amplitude-modulated circularly polarized Alfven waves for beta less than one

The nonlinear properties of the amplitude-modulated circularly polarized Alfven wave are studied for beta less than one. The temporal behavior of the wave packet of the electromagnetic hybrid simulation is compared with a numerical solution of the derivative nonlinear Schroedinger (DNLS) equation. It is shown that the left-hand-polarized mode evolves into a shocklike structure due to the modulational instability. However, both cyclotron damping and a snowplow effect near the steepened wave packet suppress its further steepening, contrary to the predictions of the DNLS equation. For the right-hand mode, formation of the shock does not take place, and the initial time development is well described by the DNLS equation. The daughter Alfven wave and ion acoustic waves are excited due to the decay instability at a later time. Heating or acceleration of the particles takes place for both left- and right-hand waves. Energy transfer from the wave to the particles occurs effectively when substantial modulation in the wave amplitude is present.

Machida, S.↗
NASA NTRS1989

Thin-film sensors for reusable space propulsion systems

Thin-film thermocouples (TFTCs) were developed for aircraft gas turbine engines and are in use for temperature measurement on turbine blades up to 1800 F. Established aircraft engine gas turbine technology is currently being adapted to turbine engine blade materials and the environment encountered in the Space Shuttle Main Engine (SSME)-severe thermal shock from cryogenic fuel to combustion temperatures. Initial results with coupons of MAR M-246 (+Hf) and PWA 1480 were followed by fabrication of TFTC on SSME turbine blades. Current efforts are focused on preparation for testing in the Turbine Blade Tester at NASA Marshall Space Flight Center.

Hepp, Aloysius F.↗
NASA NTRS1989

Thin-film sensors for space propulsion technology: Fabrication and preparation for testing

The goal of this work is to develop and test thin-film thermocouples for Space Shuttle Main Engine (SSME) components. Thin-film thermocouples have been developed for aircraft gas turbine engines and are in use for temperature measurement on turbine blades up to 1800 F. Established aircraft engine gas turbine technology is currently being adapted to turbine engine blade materials and the environment encountered in the SSME, especially severe thermal shock from cryogenic fuel to combustion temperatures. Initial results using coupons of MAR M-246 (+Hf) and PWA 1480 have been followed by fabrication of thin-film thermocouples on SSME turbine blades. Current efforts are focused on preparing for testing in the Turbine Blade Tester at the NASA Marshall Space Flight Center (MSFC). Future work will include testing of thin-film thermocouples on SSME blades of single crystal PWA 1480 at MSFC.

Kim, Walter S.↗
NASA NTRS1992

A review of transport theory

Ways in which energy change terms arise in the transport equation and how the various terms relate to the modes of energy exchange between the particles and plasma are shown. It is argued that the transport equation cannot be used to describe the initial acceleration of thermal particles by plasma shocks or relativistic shocks where the energetic particle speeds are never much greater than the flow speeds. In most other situations, it describes almost any acceleration process that can be caused by a moving plasma. It describes shock acceleration for both parallel shocks and oblique ones, and stochastic acceleration by the turbulent motion of the scatterers as well as by their motion across the magnetic field.

Jones, Frank C.↗
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 NTRS2004

Global Dayside Ionospheric Uplift and Enhancement Associated with Interplanetary Electric Fields

The interplanetary shock/electric field event of 5-6 November 2001 is analyzed using ACE interplanetary data. The consequential ionospheric effects are studied using GPS receiver data from the CHAMP and SAC-C satellites and altimeter data from the TOPEX/ Poseidon satellite. Data from ~100 ground-based GPS receivers as well as Brazilian Digisonde and Pacific sector magnetometer data are also used. The dawn-to-dusk interplanetary electric field was initially ~33 mV/m just after the forward shock (IMF BZ = -48 nT) and later reached a peak value of ~54 mV/m 1 hour and 40 min later (BZ = -78 nT). The electric field was ~45 mV/m (BZ = -65 nT) 2 hours after the shock. This electric field generated a magnetic storm of intensity DST = -275 nT. The dayside satellite GPS receiver data plus ground-based GPS data indicate that the entire equatorial and midlatitude (up to +/-50(deg) magnetic latitude (MLAT)) dayside ionosphere was uplifted, significantly increasing the electron content (and densities) at altitudes greater than 430 km (CHAMP orbital altitude). This uplift peaked ~2 1/2 hours after the shock passage. The effect of the uplift on the ionospheric total electron content (TEC) lasted for 4 to 5 hours. Our hypothesis is that the interplanetary electric field ''promptly penetrated'' to the ionosphere, and the dayside plasma was convected (by E x B) to higher altitudes. Plasma upward transport/convergence led to a ~55-60% increase in equatorial ionospheric TEC to values above ~430 km (at 1930 LT). This transport/convergence plus photoionization of atmospheric neutrals at lower altitudes caused a 21% TEC increase in equatorial ionospheric TEC at ~1400 LT (from ground-based measurements). During the intense electric field interval, there was a sharp plasma ''shoulder'' detected at midlatitudes by the GPS receiver and altimeter satellites. This shoulder moves equatorward from -54(deg) to -37(deg) MLAT during the development of the main phase of the magnetic storm. We presume this to be an ionospheric signature of the plasmapause and its motion. The total TEC increase of this shoulder is ~80%. Part of this increase may be due to a "superfountain effect." The dayside ionospheric TEC above ~430 km decreased to values ~45% lower than quiet day values 7 to 9 hours after the beginning of the electric field event. The total equatorial ionospheric TEC decrease was ~16%. This decrease occurred both at midlatitudes and at the equator. We presume that thermospheric winds and neutral composition changes produced by the storm-time Joule heating, disturbance dynamo electric fields, and electric fields at auroral and subauroral latitudes are responsible for these decreases.

ionosphere↗
NASA NTRS1985

Hybrid simulation techniques applied to the earth's bow shock

The application of a hybrid simulation model, in which the ions are treated as discrete particles and the electrons as a massless charge-neutralizing fluid, to the study of the earth's bow shock is discussed. The essentials of the numerical methods are described in detail; movement of the ions, solution of the electromagnetic fields and electron fluid equations, and imposition of appropriate boundary and initial conditions. Examples of results of calculations for perpendicular shocks are presented which demonstrate the need for a kinetic treatment of the ions to reproduce the correct ion dynamics and the corresponding shock structure. Results for oblique shocks are also presented to show how the magnetic field and ion motion differ from the perpendicular case.

Winske, D.↗
NASA NTRS1976

Table and charts of equilibrium normal-shock and shock-tube properties for pure carbon dioxide with velocities from 1 to 16 km/sec

Equilibrium thermodynamic and flow properties are presented in tabulated and graphical form for moving, standing, and reflected normal shock waves in pure CO2. Properties include pressure, temperature, density, enthalpy, speed of sound, entropy, molecular weight ratio, isentropic exponent, velocity, and species mole fractions. Incident (moving) shock velocities are varied from 1 to 16 km/sec for a range of initial pressure of 5 N/sq m to 500 kN/sq m. The present results are applicable to shock tube flows and to freeflight conditions for a blunt body at high velocities. Working charts illustrating idealized shock tube performance with CO2 test gas and heated helium and hydrogen driver gases are also presented.

Miller, C. G., III↗
NASA NTRS1998

Numerical Study of Interaction of a Vortical Density Inhomogeneity with Shock and Expansion Waves

We studied the interaction of a vortical density inhomogeneity (VDI) with shock and expansion waves. We call the VDI the region of concentrated vorticity (vortex) with a density different from that of ambiance. Non-parallel directions of the density gradient normal to the VDI surface and the pressure gradient across a shock wave results in an additional vorticity. The roll-up of the initial round VDI towards a non-symmetrical shape is studied numerically. Numerical modeling of this interaction is performed by a 2-D Euler code. The use of an adaptive unstructured numerical grid makes it possible to obtain high accuracy and capture regions of induced vorticity with a moderate overall number of mesh points. For the validation of the code, the computational results are compared with available experimental results and good agreement is obtained. The interaction of the VDI with a propagating shock wave is studied for a range of initial and induced circulations and obtained flow patterns are presented. The splitting of the VDI develops into the formation of a non-symmetrical vortex pair and not in a set of vortices. A method for the analytical computation of an overall induced circulation Gamma(sub 1) as a result of the interaction of a moving VDI with a number of waves is proposed. Simplified, approximated, expressions for Gamma(sub 1) are derived and their accuracy is discussed. The splitting of the VDI passing through the Prandtl-Meyer expansion wave is studied numerically. The obtained VDI patterns are compared to those for the interaction of the VDI with a propagating shock wave for the same values of initial and induced circulations. These patterns have similar shapes for corresponding time moments.

Povitsky, A.↗