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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Full potential integral solution for transonic flows with and without embedded Euler domains

Two methods are presented to solve for the transonic airfoil flow problems. The first method is based on the integral equation solution of the full-potential equation in terms of the velocity field, and a Shock Capturing-Shock Fitting (SCSF) scheme has been developed. The SCSF-scheme consists of a shock-capturing part and a shock-fitting part in which shock panels are introduced at the shock location. The sock panels are fitted and crossed by using the Rankine-Hugoniot relations. The second method is based on coupling the integral equation of the full-potential equation with the pseudo time integration of Euler equations in a small embedded region around the shock. The integral solution provides the initial and boundary conditions for the Euler domain. This scheme is named as the Integral Equation-Embedded Euler (IEEE) scheme. The two methods are applied to NACA 0012 and NACA 64A010A over a wide range of Mach numbers, and the reults are in good agreement with the experimental data and other computational results. The schemes converge within a number of iterations which is one-order of magnitude less than the finite-difference schemes.

Kandil, Osama A.↗
NASA NTRS1987

The Uranian bow shock - Voyager 2 inbound observations of a high Mach number shock

The Voyager 2 magnetometer and plasma detector measured a high Mach number, high beta bow shock on the dayside of the Uranian magnetosphere. Although the average conditions on either side of the shock are consistent with the Rankine-Hugoniot (MHD) relations for a stationary, quasi-perpendicular shock, the data revealed both detailed structure in the transition region as well as considerable variability in the downstream magnetosheath plasma. The bulk plasma parameters and the magnetic field exhibited some of the characteristics of a supercritical shock: an overshoot followed by damped oscillations downstream, consistent with recent theoretical models of high Mach number quasi-perpendicular shocks.

Bagenal, Fran↗
NASA NTRS1987

Interaction of interplanetary shocks with nonuniform ambient solar wind

Three interplanetary shock wave events are selected from the plasma and magnetic field data of Helios 1 and 2, IMP-8, and Voyagers 1 and 2 for study of the interactions of a weak interplantary shock with a nonuniform ambient solar wind. These events occurred during the periods 22-26 November 1977, 1-7 January 1978, and 2-5 April 1979, respectively. It is found that the shock surfaces of these events are highly distorted. In addition, a portion of the shock surface may be degenerated into a disturbance which does not satisfy the Rankine-Hugoniot jump conditions.

Chao, J. K.↗
NASA NTRS1988

Shock analysis - Three useful new relations

The behavior of collisionless hydromagnetic shocks in interplanetary space is considered analytically, with a focus on relations, implicit in the governing Rankine-Hugoniot equations, involving the magnetic field (B) and the plasma velocity (V). A moving reference frame aligned with the shock is employed, and expressions are derived which make it possible (1) to determine the speed of a shock of arbitrary orientation from upstream and downstream measurements of B and V; (2) to characterize the change in flow direction as the plasma crosses the shock in terms of the plasma beta, the Mach number, and the angle between the upstream field and the shock normal; and (3) to infer the third component of the upstream-downstream velocity jump from B and two-dimensional V measurements. These expressions are applied to ISEE-3 data on an interplanetary shock on April 5, 1979, and the results are presented in tables.

Smith, Edward J.↗
NASA NTRS1988

Electron heating in superhigh Mach number shocks

Fluid and MHD models, as well as direct extrapolation of the earth's bow shock measurements in the high Mach number (HMN) range to the superhigh Mach number (SHMN) range predict that the downstream electron pressure is only a negligible fraction of the Rankine-Hugoniot downstream pressure. Following Alfven, plasma physics experimental-theoretical data combined with magnetospheric observations were used to probe the physics of the SHMN shocks. It is shown that inclusion of proper plasma physics considerations in the interaction of the reflected and transmitted ions and the electrons at the 'foot' of the shock leads to the surprising result that electron heating can dominate in the SHNM range. A stationary model of the shock structure is derived and shown to be the result of extrapolation of the high Mach number shock physics wiht incorporation of collective interactions at the foot.

Papadopoulos, K.↗
NASA NTRS1988

Switch-on shocks

It is argued that parallel propagating Alfven waves steepen to second order in the wave amplitude, rather than first order, as is the case for oblique MHD waves. An analytical solution for the structure of weak switch-on shocks is derived. The Rankine-Hugoniot relations for finite amplitude switch-on shocks are obtained in a compact form. The differential equation for resistive switch-on shocks is solved, and the resistive critical Mach number is obtained. The differential equation for resistive switch-on shocks with finite ion inertia is identical to the one obtained in the pure resistive case. It is argued that efficient electron heat conduction can significantly extend the range of upstream parameters for which switch-on shocks are expected.

Kennel, C. F.↗
NASA NTRS1989

Calculation of unsteady flows in turbomachinery using the linearized Euler equations

A method for calculating unsteady flows in cascades is presented. The model, which is based on the linearized unsteady Euler equations, accounts for blade loading shock motion, wake motion, and blade geometry. The mean flow through the cascade is determined by solving the full nonlinear Euler equations. Assuming the unsteadiness in the flow is small, then the Euler equations are linearized about the mean flow to obtain a set of linear variable coefficient equations which describe the small amplitude, harmonic motion of the flow. These equations are discretized on a computational grid via a finite volume operator and solved directly subject to an appropriate set of linearized boundary conditions. The steady flow, which is calculated prior to the unsteady flow, is found via a Newton iteration procedure. An important feature of the analysis is the use of shock fitting to model steady and unsteady shocks. Use of the Euler equations with the unsteady Rankine-Hugoniot shock jump conditions correctly models the generation of steady and unsteady entropy and vorticity at shocks. In particular, the low frequency shock displacement is correctly predicted. Results of this method are presented for a variety of test cases. Predicted unsteady transonic flows in channels are compared to full nonlinear Euler solutions obtained using time-accurate, time-marching methods. The agreement between the two methods is excellent for small to moderate levels of flow unsteadiness. The method is also used to predict unsteady flows in cascades due to blade motion (flutter problem) and incoming disturbances (gust response problem).

Hall, Kenneth C.↗
NASA NTRS1989

Shock temperatures in silica glass - Implications for modes of shock-induced deformation, phase transformation, and melting with pressure

Observations of shock-induced radiative thermal emissions are used to determine the gray body temperatures and emittances of silica glass under shock compression between 10 and 30 GPa. The results suggest that fused quartz deforms heterogeneously in this shock pressure range. It is shown that the 10-16 GPa range coincides with the permanent densification region, while the 16-30 GPa range coincides with the inferred mixed phase region along the silica glass Hugoniot. Low emittances in the mixed phase region are thought to represent the melting temperature of the high-pressure phase, stishovite. Also, consideration is given to the effects of pressure on melting relations for the system SiO2-Mg2SiO4.

Schmitt, Douglas R.↗
NASA NTRS1989

Recurrent solar wind structures in the outer heliosphere

The paper presents recent work on evolution of recurrent solar wind structures in the outer heliosphere. Corotating shocks, corotating interaction regions, and merged interaction regions are studied, and an MHD simulation model in which the jump conditions at all shock crossings satisfy the Rankine-Hugoniot solution is examined. Simulation results which describe the evolution of idealized recurrent solar wind structures between 14 AU and the termination shock are reported which show that merged interaction regions belonging to two to four consecutive solar rotations coalesce with each other between 30 AU and the termination shock to reshape the heliospheric structures. In the outer heliosphere, forward and reverse interplanetary shocks which continuously heat the solar wind plasma are investigated.

Whang, Y. C.↗
NASA NTRS1990

Interaction of minor ions with fast and slow shocks

The coronal slow shock was predicted to exist embedded in large coronal holes at 4 to 10 solar radii. A three-fluid model was used to study the jumps in minor ions propertes across the coronal slow shock. The jump conditions were formulated in the de Hoffmann-Teller frame of reference. The Rankine-Hugoniot solution determines the MHD flow and the magnetic field across the shocks. For each minor ion species, the fluid equations for the conservation of mass, momentum, and energy can be solved to determine the velocity and the temperature of the ions across the shock. A simularity solution was also obtained for heavy ions. The results show that on the downstream side of the coronal slow shock the ion temperatures are nearly proportional to the ion masses for He, O, Si, and Fe in agreement with observed ion temperatures in the inner solar wind. This indicates that the possibly existing coronal slow shock can be responsible for the observed heating of minor ions in the solar wind.

Whang, Y. C.↗
NASA NTRS1988

Calculation of unsteady Euler flows in turbomachinery using the linearized Euler equations

The model used by the present unsteady cascade flow calculation method is based on the linearized unsteady Euler equations and accounts for blade loading and geometry, shock motion, and wake motion. The steady flow that must be determined prior to the unsteady flow is ascertained by means of a Newton iteration procedure. A noteworthy feature of the procedure is the use of shock-fitting to determine steady and unsteady shock positions; the use of the Euler equations in conjunction with the Rankine-Hugoniot shock-jump conditions is found to directly model the generation of entropy and vorticity at shocks. Results are presented for both channel and cascade flows.

Hall, Kenneth C.↗
NASA NTRS1989

Impact jetting of water ice, with application to the accretion of icy planetesimals and Pluto

Jetting can occur during oblique impacts of water-ice bodies at relative velocities as low as 500 m/sec, because of the low Hugoniot elastic limit and high compressibility of ice compared to rock. In jetted ice, incipient melting, complete melting, and incipient vaporization occur, upon release to low pressure, at impact velocities of 1.3, 2.0, and 2.7 km/sec, respectively, much less than the 3.4, 4.4, and 5.3 km/sec, required in head-on collisions. Uncertainties in the shock equation-of-state may allow complete melting during jetting of relative velocities as low as 1.2 km/sec. Because jet speeds exceed impact speeds during the accretion of icy bodies greater than a few 100 km in radius, there may be a significant loss of icy material. Thus, jetting during a Charon-forming collision (and not vaporization) may account for Pluto-Charon's relatively large rock/ice ratio, should the C/O ratio of the solar nebula turn out to be too low to sufficiently raise the rock/ice ratio of outer solar nebula condensates by formation of noncondensable CO.

Mckinnon, William B.↗
NASA NTRS1990

Structure and evolution of small-amplitude intermediate shock waves

A simplified set of equations is derived that approximates the magnetohydrodynamic (MHD) Navier-Stokes equations for weakly nonlinear disturbances whose speeds are close to the MHD intermediate speed. Its shock structure solutions are then examined. The fast and slow shock solutions are uniquely specified by their Rankine-Hugoniot relations. However, the intermediate shock solutions, which are not unique, are characterized by the integral through the shock of the noncoplanar component of the magnetic field. For situations in which this integral is conserved, the Riemann problem is well defined and predicts the evolution of intermediate shocks. This analysis is substantiated by numerical computations.

Kennel, C. F.↗
NASA NTRS1990

Shock-induced temperatures of CaMgSi2O6

Results are presented from experiments on CaMgSi2O6 (diopside) single crystal, an end-member pyroxene relevant to studies of the composition of the earth's mantle. Also, experiments were conducted on diopside glass with a density 86 percent that of the diopside crystal. The shock-induced radiation from diopside is used to constrain the temperature of its shock-compressed (Hugoniot) states. The results are combined with other data to place constraints on the high-pressure phase relations in the CaMgSi2O6 system. These constraints are compared with existing models for the earth's mantle. The results imply that the temperature of the D-double prime region must be less than 3000 K.

Svendsen, Bob↗
NASA NTRS1990

Properties of large scale plasma flow during the early stage of the plasmaspheric refilling

The objective is to better characterize the macroscopic properties of the interhemisphere plasma flow by solving a more complete set of hydrodynamic equations than that solved previously. Specifically, the ion continuity, momentum and energy equations were solved for the plasma flow along the closed magnetic field lines. During the initial stage of the supersonic outflow in the equatorial region, the ions cool substantially. Using the hydrodynamic model for the large-scale plasma flow, the dynamics of shocks was examined which form in the geomagnetic flux tubes during the early stages of refilling. These shocks are more like those forming in neutral gases than the electrostatic shocks driven by microinstabilities involving ion-ion interaction. Therefore, the shocks seen in the hydrodynamic model are termed as hydrodynamic shocks. Such shocks are generally unsteady and therefore the usual shock jump conditions given by Rankine-Hugoniot relations are not strictly applicable to them. The density, flow velocity and temperature structures associated with the shocks are examined for both asymmetrical and symmetrical flows. In the asymmetrical flow the outflow from one of two conjugate ionospheres is dominant. On the other hand, in the symmetrical case outflows from the two ionospheric sources are identical. Both cases are treated by a two-stream model. In the late type of flow, the early-time refilling shows a relaxation type of oscillation, which is driven by the large-scale interactions between the two identical streams. After this early stage, the resulting temperature structure shows some interesting features. In the equatorial region the streams are isothermal, but in the off-equatorial regions the streams have quite different temperatures, and also densities and flow velocities. The dense and slow stream is found to be warmer than the low-density fast stream. In the late stage of refilling, the temperature is found to steadily increase from the conjugate ionospheres towards the equator; the equatorial temperature is found to be as high as about 8000 K compared to the ionospheric temperature of 3600 K.

Singh, Nagendra↗
NASA NTRS1990

Heating of minor ions by the coronal slow shock

The coronal slow shock has been predicted to exist embedded in large coronal holes at 4-10 solar radii. In this paper, a three-fluid model is used to study the jumps in minor ion properties across a slow shock such as the coronal slow shock. The jump conditions are formulated in the de Hoffmann-Teller frame of reference. The Rankine-Hugoniot solution determines the MHD flow and the magnetic field across the shocks. For each minor ion species, the fluid equations for the conservation of mass, momentum, and energy can be solved to determine the velocity and the temperature of the ions across the shock. Also obtained is a similarity solution for heavy ions. The results show that, on the downstream side of the slow shock, the ion temperatures are nearly proportional to the ion masses for He, O, Si, and Fe, in agreement with observed ion temperatures in the inner solar wind. This indicates that the possibly existing coronal slow shock can be responsible for the observed heating of minor ions in the solar wind.

Whang, Y. C.↗
NASA NTRS1990

Simulation of period doubling of recurrent solar wind structures

Based on satellite observations of a recurrent solar wind structure conducted in 1974, an MHD simulation model, and input functions generated from plasma and magnetic field data, the continuing evolution of the solar wind structure outside 5 AU is studied. The model uses the Rankine-Hugoniot relations to describe the jumps in flow properties across the shocks, and it treats shocks as surfaces of discontinuity with zero thickness. Two interaction processes (the collision and the merging of shocks) play important roles in restructuring the solar wind in the outer heliosphere. The simulation result shows that period doubling occurs between 5 and 10 AU. The recurrent solar wind appears to be a persistent new structure between 10 and 20 AU, and it consists of one merged interaction region per solar rotation.

Whang, Y. C.↗
NASA NTRS1991

The high-pressure melting curve of iron - A technical discussion

The melting curve of iron is reliably determined to 105 GPa using the laser-heated diamond cell, in close agreement with independent measurements using piston-cylinder and large-volume presses or shock-wave experiments. In order to obtain reliable melting data from the internally heated diamond cell, whether by laser or Joule heating, temperature gradients across the sample must be quantitatively measured; otherwise, such 'wire heating' experiments can lead to significant underestimates of the melting temperature and its pressure dependence. The best estimate of the high-pressure melting curve of iron, as derived from the laser-heated diamond cell and Hugoniot temperature measurements, yields melting temperatures of 4800 + or - 200 K and 6700 + or - 400 K at 133 GPa and 243 GPa, respectively.

Williams, Quentin↗