Search NASA⌕ Search

SEARCH · Search NASA

Results for “Rarefactions”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2

Ion-acoustic solitary waves in a magnetized plasma with arbitrary electron equation of state

The oblique propagation of fully nonlinear, slow ion-acoustic solitary waves in a collisionless, low-beta, magnetized plasma is examined. The analysis includes the effects of a finite ion pressure, electron trapping, and multicomponent particle populations. The existence of both compressive and rarefactive modes propagating obliquely to the magnetic field in a plasma with two distinct Boltzmann electron populations and cold ions is demonstrated. It is shown that paired electrostatic shocks observed over the earth's auroral zone may be closely related to the rarefactive modes. As a measure of the collisionless dissipation encountered by the solitary waves, the linear response of the plasma to slow ion-acoustic waves is also examined.

Witt, E.↗

A geometric approach to high resolution TVD schemes

A geometric approach, similar to Van Leer's MUSCL schemes, is used to construct a second-order accurate generalization of Godunov's method for solving scalar conservation laws. By making suitable approximations, a scheme is obtained which is easy to implement and total variation diminishing. The entropy condition is also investigated from the standpoint of the spreading of rarefaction waves. Quantitative information is obtained for Godunov's method on the rate of spreading which explain the kinks in rarefaction waves often observed at the sonic point.

Goodman, J. B.↗

Oxygen acoustic solitary waves in a magnetized plasma

Ion-acoustic solitary waves in a magnetized plasma containing an arbitrary mixture of H(+) and O(+) ions are studied. A nonlinear wave equation has been derived from the Poisson-Vlasov equations, including a uniform magnetic field and dissipation due to reflected electrons. When dissipation is ignored, the equation has soliton solutions associated with both oxygen and hydrogen acoustic modes, which can be either rarefactive or compressive depending on the ion concentrations and the electron/ion temperature ratio and, more weakly, on the bulk drifts of the species. If electron reflection is included, the solitary wave can be intensified. Under somewhat restrictive conditions the oxygen solitary wave is rarefactive and propagates with a velocity comparable to that observed by the Viking satellite. The three-dimensional solitons obey a relation of scales parallel to the magnetic field and in the transverse direction. Computer simulations of one-dimensional versions of the nonlinear wave equation are presented.

Qian, S.↗

Models of the Cartwheel ring galaxy: Spokes and starbursts

Recent observations of this famous ring galaxy, including optical and near-infrared CCD surface photometry, and VLA radio continuum and 21 cm line mapping (Higdon 1992b, in prep.), have inspired a renewed modeling effort. Toomre's (1978, in The Large-scale Structure of the Universe, eds. Longair and Einasto) series of restricted three-body simulations demonstrated how the multiple rings could be produced in a nearly head-on galaxy collision. New models with a halo-dominated potential based on the 21 cm rotation curve are able to reproduce such details as the spacing between rings, ring widths, offset of the nucleus, and several kinematical features, thus providing strong support for the collisional theory. The new observations have shown there are little or no old stars in Cartwheel; it may consist almost entirely of gas and stars produced as a result of compression in the ring wave. To model this process Smooth Particle Hydrodynamics (SPH) simulations of the Cartwheel disk have been performed. Fixed gravitational potentials were used to represent the Cartwheel and a roughly 30 percent mass collision partner. The interaction dynamics was treated as in the usual restricted three-body approximation, and the effects of local self-gravity between disk particles were calculated. We are particularly interested in testing the theory that enhanced star formation in waves is the result of gravitational instability in the compressed region (see e.g. Kennicutt 1989, ApJ 344, 685). The gas surface density in a number of simulations was initialized to a value slightly below the threshold for local gravitational instability throughout most of the disk. The first ring wave produces relatively modest compressions (a factor of order a few), triggering instability in a narrow range of wavelengths. Self-gravity in the disk is calculated over a comparable range of scales. Simulations were run with isothermal, adiabatic, and adiabatic with radiative cooling characterized by a relatively short timescale. The isothermal approximation is good except in the vicinity of the strong second (inner) ring, and several snapshots from one case are shown in the figure below. Flocculent spiral segments are present before the collision, and these are compressed into dense knots in the ring wave. These knots are likely to be sites of vigorous star formation. In the strong rarefaction behind the outer ring most of the knots are radially stretched and sheared, giving rise to spoke-like features. A few dense knots are evidently very tightly bound, because they retain their coherence and are stretched relatively little through the rarefaction. This is in accord with evidence for continuing star formation in some spokes (Marcum, Appleton and Higdon 1992). The number and spacing of spokes is a direct function of the scale of the gravitational instability in the disk. Thus, the gravitational instability theory, together with the hypothesis that massive stars are only formed in dense knots of gas, can account for most of the distinct morphology of the Cartwheel.

Struck-Marcell, Curtis↗

Hypersonic blunt body wake computations using DSMC and Navier-Stokes solvers

Numerical results obtained with direct simulation Monte Carlo (DSMC) and Navier-Stokes methods are presented for Mach 20 nitrogen flow about a 70-deg blunted cone. The flow conditions simulated are those that can be obtained in existing low-density hypersonic wind tunnels. Three sets of flow conditions are considered with freestream Knudsen numbers ranging from 0.03 to 0.001. The focus is on the wake structure: how does the wake structure change as a function of rarefaction, what are the afterbody levels of heating, and to what limits are continuum models realistic as rarefaction in the wake is progressively increased. Calculations are made with and without an afterbody sting. Results for the afterbody sting are emphasized in anticipation of an experimental study for the current flow conditions and model configuration. The Navier-Stokes calculations were made with and without slip boundary conditions. Comparisons of the results obtained with the two simulation methodologies are made for both flowfield structure and surface quantities.

Moss, James N.↗

The hydrodynamic theory of detonation

This report derives equations containing only directly measurable constants for the quantities involved in the hydrodynamic theory of detonation. The stable detonation speed, D, is revealed as having the lowest possible value in the case of positive material velocity, by finding the minimum of the Du curve (u denotes the speed of the gases of combustion). A study of the conditions of energy and impulse in freely suspended detonating systems leads to the disclosure of a rarefaction front traveling at a lower speed behind the detonation front; its velocity is computed. The latent energy of the explosive passes into the steadily growing detonation zone - the region between the detonation front and the rarefaction front. The conclusions lead to a new definition of the concept of shattering power. The calculations are based on the behavior of trinitrotoluene.

Langweiler, Heinz↗

Fourth order difference methods for hyperbolic IBVP's

Fourth order difference approximations of initial-boundary value problems for hyperbolic partial differential equations are considered. We use the method of lines approach with both explicit and compact implicit difference operators in space. The explicit operator satisfies an energy estimate leading to strict stability. For the implicit operator we develop boundary conditions and give a complete proof of strong stability using the Laplace transform technique. We also present numerical experiments for the linear advection equation and Burgers' equation with discontinuities in the solution or in its derivative. The first equation is used for modeling contact discontinuities in fluid dynamics, the second one for modeling shocks and rarefaction waves. The time discretization is done with a third order Runge-Kutta TVD method. For solutions with discontinuities in the solution itself we add a filter based on second order viscosity. In case of the non-linear Burger's equation we use a flux splitting technique that results in an energy estimate for certain different approximations, in which case also an entropy condition is fulfilled. In particular we shall demonstrate that the unsplit conservative form produces a non-physical shock instead of the physically correct rarefaction wave. In the numerical experiments we compare our fourth order methods with a standard second order one and with a third order TVD-method. The results show that the fourth order methods are the only ones that give good results for all the considered test problems.

Gustafsson, Bertil↗

Magnetospheric response to solar wind dynamic pressure variations: Interaction of interplanetary tangential discontinuities with the bow shock

Some magnetic impulse events observed in the polar region are related to vortices associated with plasma convection in the ionosphere. Recent analyses of satellite and ground data suggest that the interaction of solar wind dynamic pressure pulses and the magnetosphere may lead to the formation of velocity vortices in the magnetopause boundary layer region. This can in turn lead to the presence of vortices in the polar ionosphere. However, before reaching the Earth's magnetopause, these interplanetary pressure pulses must interact with and pass through the bow shock. A variation of the solar wind dynamic pressure may be associated with shocks, magnetic holes, or tangential discontinuities (TDs) in the interplanetary medium. We study the interaction of interplanetary TDs with the Earth's bow shock (BS) using both theoretical analysis and MHD computer simulations. It is found that as a result of the collision between a TD and the BS, the jump in the solar wind dynamic pressure associated with the TD is significantly modified, the bow shock moves, and a new fast shock or fast rarefaction wave, which propagates in the downstream direction, is excited. Our theoretical analysis shows that the change in the plasma density across the interplanetary TD plays the most important role in the collision process. In the case with an enhanced dynamic pressure behind the interplanetary TD, the bow shock is intensified in strength and moves in the earthward direction. The dynamic pressure jump associated with the transmitted TD is generally reduced from the value before the interaction. A fast compressional shock is excited ahead of the transmitted TD and propagates toward the Earth's magnetosphere. For the case in which the dynamic pressure is reduced behind the interplanetary TD, the pressure jump across the transmitted TD is substantially weakened, the bow shock moves in the sunward direction, and a rarefaction wave which propagates downstream is excited. We also simulate and discuss the interaction of a pair of tangential discontinuities, which may correspond to a magnetic hole, with the BS.

Wu, Bor-Han↗

Numerical magetohydrodynamics in astronphysics: Algorithm and tests for one-dimensional flow`

We describe a numerical code to solve the equations for ideal magnetohydrodynamics (MHD). It is based on an explicit finite difference scheme on an Eulerian grid, called the total variation diminishing (TVD) scheme, which is a second-order-accurate extension of the Roe-type upwind scheme. We also describe a non-linear Riemann solver for ideal MHD, which includes rarefractions as well as shocks. The numerical code and the Riemann solver have been used to test each other. Extensive tests encompassing all the possible ideal MHD structures with planar symmetries (i.e., one-dimensional flows) are presented. These include those for which the field structure is two dimensional (i.e., those flows often called '1 + 1/2 dimensional') as well as those for which the magnetic field plane rotates (i.e., those flows often called '1 + 1/2 + 1/2 dimensional'). Results indicate that the code can resolve strong fast, slow, and magnetosonic shocks within two to four cells, but more cells are required if shocks become weak. With proper steepening, we could resolve rotational discontinuities within three to five cells. However, without successful implementation of steepening, contact discontinuities are resolved with approximately 10 cells and tangential discountinuities are resolved with approximately 15 cells. Out tests confirm that slow compound structures with tow-dimensional magnetic fields are composed of intermediate shocks (so-called 2-4 intermediate shocks) followed by slow rarefaction waves. Finally, tests demostrate that in two-dimensional magnetohydrodynamics, fast compound structures, which are composed of intermediate shocks (so-called 1-3 intermediate shocks) preceeded by fast rarefaction waves, are also possible.

Ryu, Dongsu↗

Direct simulation Monte Carlo and Navier-Stokes simulations of blunt body wake flows

Numerical results obtained with direct simulation Monte Carlo and Navier-Stokes methods are presented for a Mach-20 nitrogen flow about a 70-deg blunted cone. The flow conditions simuulated are those that can be obtained in existing low-density hypersonic wind tunnels. Three sets of flow conditions are considered with freestream Knudsen numbers ranging from 0.03 to 0.001. The focus is on the wake structure: how the wake structure changes as a function of rarefaction, what the afterbody levels of heating are, and to what limits the continuum models are realistic as rarefaction in the wake is progressively increased. Calculations are made with and without an afterbody sting. Results for the after body sting are emphasizes in anticipation of an experimental study for the current flow conditions and model configuration. The Navier-Stokes calculations were made with and without slip boundary conditions. Comparisons of the results obtained with the two simulation methodologies are made for both flowfield structure and surface quantities.

Moss, James N.↗

Motion of the heliospheric termination shock 3: Incident interplanetary shocks

In this paper the response of the heliospheric termination shock to an incident interplanetary shock is examined. This paper is an extension of a recent study by Barnes (1993), which treated the analogous problem for an incident contact discontinuity. The termination shock is treated as a strong gas-dynamic shock. The post-interaction configuration consists of a moving termination shock, a postshock contact discontinuity, and either a shock or rarefaction wave propagating the disturbance signal into the downstream medium. For a decrease in dynamic pressure a rarefaction wave propagates downstream, and the new termination shock propagates inward, while, for an enhancement of dynamic pressure, the termination shock moves outwards and a weak outer shock propagates into the downstream medium; speeds of motion of the termination shock are typically of the order of approximately 100 km/s. The results are similar to those presented by Barnes (1993) indicating that the results of that paper are robust within the gas-dynamic model, in the sense of being independent of the details of the initial disturbance.

Naidu, Kamcilla↗

Review of blunt body wake flows at hypersonic low density conditions

Recent results of experimental and computational studies concerning hypersonic flows about blunted cones including their near wake are reviewed. Attention is focused on conditions where rarefaction effects are present, particularly in the wake. The experiments have been performed for a common model configuration (70 deg spherically-blunted cone) in five hypersonic facilities that encompass a significant range of rarefaction and nonequilibrium effects. Computational studies using direct simulation Monte Carlo (DSMC) and Navier-Stokes solvers have been applied to selected experiments performed in each of the facilities. In addition, computations have been made for typical flight conditions in both Earth and Mars atmospheres, hence more energetic flows than produced in the ground-based tests. Also, comparisons of DSMC calculations and forebody measurements made for the Japanese Orbital Reentry Experiment (OREX) vehicle (a 50 deg spherically-blunted cone) are presented to bridge the spectrum of ground to flight conditions.

Moss, J. N.↗

Rarefied Flows of Planetary Entry Capsules

The impact of rarefaction on entry capsules and spacecraft aerothermodynamics is emphasized for various aeroassist missions. The capability of the direct simulation Monte Carlo (DSMC) method to simulate such flows is demonstrated through examples of validation studies and applications. Several space flight projects and ground-based experiments are reviewed for which rarefaction effects have significant effect on spacecraft performance or experimental measurements. This review clearly demonstrates the significant role that the DSMC method plays in characterizing such flows.

James N Moss↗

Rarefied Flow

Rarefaction effects are important for hypersonic applications for a wide spectrum of conditions ranging from low-density (high altitude) situations to relatively high-density flows where the characteristic dimension is small. The present chapter concentrates on two hypersonic flow problems at flow conditions that produce a significant range of rarefaction effects: corner flow with jet interaction and blunt body flow with special emphasis on the near wake, These problems were chosen because they involve complex flow interactions that have significant implications for both spacecraft and re-entry vehicles. In an effort to clarify issues associated with these two general flow problems and to enhance their respective databases, both experimental and computational contributions were executed by an international group of researchers. In some cases, multiple data sources for both experimental and computational contributions are achieved.

James N. Moss↗

DSMC Simulations of Ballute Aerothermodynamics Under Hypersonic Rarefied Conditions

This paper presents computational results obtained with the direct simulation Monte Carlo (DSMC) method for towed ballute applications. A ballute is an inflatable drag device that can be used to create a large amount of drag at high altitudes. Consequently, ballutes provide a potential technology for achieving aerocapture when the primary spacecraft velocity reduction (ΔV) is achieved at much higher altitudes than with the conventional rigid aeroshell. Since the ΔV is achieved at relatively high altitudes, rarefaction can be significant and is the motivation for the current study with the DSMC method. Computed surface and flow-field results are presented for a toroidal ballute, isolated tethers when exposed to free-stream flow conditions, and the flow interactions resulting from a toroidal ballute when towed by a six meter diameter Mars Pathfinder shaped (without tethers) spacecraft. All results presented are for Earth entry at velocities of 14 to 7 km/s (primary focus is at 8.55 km/s, same as some previous Titan aerocapture studies) and altitudes of 200 to 100 km. Variations of drag and heating coefficients as a function of rarefaction are presented. A description of the flow structure is provided and also an explanation of how it is affected by shock interactions produced solely by the ballute and those resulting from the two body combination of towed ballute and spacecraft is also given.

James N Moss↗

Orion Aerodynamics for Hypersonic Free Molecular to Continuum Conditions

Numerical simulations are performed for the Orion Crew Module, previously known as the Crew Exploration Vehicle (CEV) Command Module, to characterize its aerodynamics during the high altitude portion of its reentry into the Earth's atmosphere, that is, from free molecular to continuum hypersonic conditions. The focus is on flow conditions similar to those that the Orion Crew Module would experience during a return from the International Space Station. The bulk of the calculations are performed with two direct simulation Monte Carlo (DSMC) codes, and these data are anchored with results from both free molecular and Navier-Stokes calculations. Results for aerodynamic forces and moments are presented that demonstrate their sensitivity to rarefaction, that is, for free molecular to continuum conditions (Knudsen numbers of 111 to 0.0003). Also included are aerodynamic data as a function of angle of attack for different levels of rarefaction and results that demonstrate the aerodynamic sensitivity of the Orion CM to a range of reentry velocities (7.6 to 15 km/s).

Moss, James N.↗

Magnetohydrodynamic Effects in Propagating Relativistic Ejecta: Reverse Shock and Magnetic Acceleration

We solve the Riemann problem for the deceleration of arbitrarily magnetized relativistic ejecta injected into a static unmagnetized medium. We find that for the same initial Lorentz factor, the reverse shock becomes progressively weaker with increasing magnetization s (the Poynting-to-kinetic energy flux ratio), and the shock becomes a rarefaction wave when s exceeds a critical value, sc, defined by the balance between the magnetic pressure in the ejecta and the thermal pressure in the forward shock. In the rarefaction wave regime, we find that the rarefied region is accelerated to a Lorentz factor that is significantly larger than the initial value. This acceleration mechanism is due to the strong magnetic pressure in the ejecta.

Mizuno, Y.↗