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At least 73 records · Page 4
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NASA NTRS1988

Application of unsteady aerodynamic methods for transonic aeroelastic analysis

Aerodynamic methods for aeroelastic analysis are applied to various flow problems. These methods include those that solve the three dimensional transonic small disturbance (TSD) potential equation, the two dimensional (2-D) full potential (FP) equation, and the 2-D thin layer Navier-Stokes equations. Flutter analysis performed using TSD aerodynamics show that such methods can be used to analyze some aeroelastic phenomena. For thicker bodies and larger amplitude motions, a nonisentropic FP method is presented. The unsteady FP equation is modified to model the entropy jumps across shock waves. The conservative form of the modified equation is solved in generalized coordinates using an implicit, approximate factorization method. Pressures calculated on the NLR 7301 and NACA 64A010A airfoils using the nonisentropic FP method are presented. It is shown that modeling shock generated entropy extends the range of validity of the FP method. A Navier-Stokes code is correlated with pressures measured on a supercritical airfoil at transonic speeds. When corrections are made for wind tunnel wall effects, the calculations correlate well with the measured data.

Whitlow, Woodrow, Jr.↗
NASA NTRS1988

Application of a nonisentropic full potential method to AGARD standard airfoils

An entropy-correction method for the unsteady full potential equation is presented. The unsteady potential equation is modified to model the entropy jumps across shock waves. The conservative form of the modified equation is solved in generalized coordinates using an implicit, approximate factorization method. A flux-biasing differencing method, which generates the proper amounts of artificial viscosity in supersonic regions, is used to discretize the flow equations in space. Calculated results are presented for the NLR 7301, NACA 0012, and NACA 64A010A airfoils. Comparisons of the present method and solutions of the Euler equations are presented for the NLR 7301 airfoil, and comparisons of the present method and experimental data are presented for all three airfoils. The comparisons show that the present method more accurately models solutions of the Euler equations and experiment than does the isentropic potential formulation. In addition, it is shown that modeling shock-generated entropy extends the range of validity of the full potential method.

Whitlow, Woodrow, Jr.↗
NASA NTRS1994

Two-dimensional hydrodynamical simulations of wind-compressed disks around rapidly rotating B stars

We use a two-dimensional piecewise parabolic method (PPM) code to simulate numerically the hydrodynamics of a radiation-driven stellar wind from a rapidly rotating Be star. The results generally confirm predictions of the semianalytic 'wind-compressed disk' model recently proposed by Bjorkman and Cassinelli to explain the circumstellar disks inferred observationally to exist around such rapidly rotating stars. However, this numerical simulation is able to incorporate several important effects not accounted for in the simple model, including a dynamical treatment of the outward radiative driving and gas pressure, as well as a rotationally distorted, oblate stellar surface. This enables us to model quantitatively the compressed wind and shock that forms the equatorial disk. The simulation results thus do differ in several important details from the simple method, showing, for example, an inner disk inflow not possible in the heuristic approach of assuming a fixed outward velocity law. There is also no evidence for the predicted detachment of the disk that arises in the fixed outflow picture. The peak equatorward velocity in the dynamical models is furthermore about a factor of 2 smaller than the lytically predicted value of approximately 50% of the stellar equatorial rotation speed. As a result, the dynamical disks are somewhat weaker than predicted, with a wider opening angle, lower disk/pole density ratio, and smaller shock velocity jump. The principal cause of these latter differences appears to be an artificially strong equatorward drift of the subsonic outflow in the original analytic model. Much better agreement with the dynamical results can be obtained, however, from a slightly modified, analytic wind-compression model with a more detailed specification of the fixed wind outflow and a lower boundary set to the sonic radius along a rotationally oblate stellar surface. Hence, despite these detailed differences, the general predicted effect of disk formation by wind compression toward the equator is substantially confirmed.

Owocki, Stanley P.↗
NASA NTRS1995

Computer Simulation of Motion of Heliospheric Termination Shock

A time-dependent computer model is used to study a non-equilibrium structure of the heliosphere, resulting from the interaction between the solar wind and the interstellar plasma. An interaction of the heliospheric termination shock with various disturbances such as density or velocity jumps or interplanetary shocks in upstream solar wind as well as pressure jumps in local interstellar medium is investigated. Consequences of latitudinal variation in dynamic pressure are also discussed. The initial boundary conditions of unsteady calculations are given by the solar wind parameters as functions of time and/or latitude on an inner boundary, and/or by the local interstellar pressure as a function of time (roughly simulating the effect of the local interstellar medium) on an outer boundary.

Ratkiewicz, R. E.↗
NASA NTRS1973

A correlative study of SSC's, interplanetary shocks, and solar activity

A total of 93 SSC's were examined during the four year period from 1968 to 1971 at and near the peak of the solar activity cycle. Of the 93 SSC's 81 could be associated with solar activity, such as solar flares and radio bursts of Type II and Type IV. The mean propagation speeds of these flare-associated events ranged from 400 to 1000 km/sec with an average speed of 600-700 km/sec. Disturbances associated with 48 of the SSC's have been studied in detail using the corresponding interplanetary (IP) magnetic field, and plasma data when they were available. It was found that 41 of the 48 disturbances corresponded to IP shock waves, and the remaining seven events were tangential discontinuities. Thirty percent of the IP shocks had thick structure (i.e. the magnetic field jump across the shock occurred over a distance much greater than 50 proton Larmor radii). Also given is a statistical study of the gross geometry of a typical or average shock surface based on multiple spacecraft sightings and their relative orientation with respect to the solar flare. It is suggested that a typical shock front propagating out from the sun at l AU has a radius of curvature on the order of l AU. Also given are some general properties of oblique IP flare-shocks.

Chao, J. K.↗
NASA NTRS1974

A correlative study of ssc's, interplanetary shocks, and solar activity

Ninety-three ssc's during the 4-year period from 1968 to 1971 at and near the peak of the solar activity cycle were examined. Of the 93 ssc's, 81 could be associated with solar activity such as solar flares and type 2 and type 4 radio bursts. Disturbances associated with 48 of the ssc's have been studied in detail by using the corresponding interplanetary (IP) magnetic field and plasma data when they were available. It was found that 41 of the 48 disturbances corresponded to IP shock waves, and the remaining 7 events were tangential discontinuities. Thirty per cent of the IP shocks had thick structure (i.e., the magnetic field jump across the shock occurred over a distance much greater than 50 proton Larmor radii). By considering the orientations of 22 well-determined shock normals in relation to the positions of the parent flares on the solar disk, it is suggested that a typical shock front propagating out from the sun at 1 AU has a radius of curvature of the order of 1 AU.

Chao, J. K.↗
NASA NTRS1984

Infrared spectroscopy of interstellar shocks

Infrared emission lines from interstellar shocks provide valuable diagnostics for violent events in the interstellar medium, such as supernova remnants and mass outflow from young stellar objects. There are two types of interstellar shocks: in J shocks, gas properties 'jump' from their preshock to their postshock values in a shock front with a thickness equal to or less than one mean free path; radiation is emitted behind the shock front, primarily in the visible and ultraviolet, but with a few strong infrared lines, such as OI(63 microns). Such shocks occur in ionized or neutral atomic gas, or at high velocities (equal to or greater than 50 km/s) in molecular gas. In C shocks, gas is accelerated and heated by collisions between charged particles, which have a low concentration and are coupled to the magnetic field, and neutral particles; radiation is generated throughout the shock and is emitted almost entirely in infrared emission lines. Such shocks occur in weakly ionized molecular gas for shock velocities below about 50 km/s.

Mckee, C. F.↗
NASA NTRS1977

Application of the wavenumber jump condition to the normal and oblique interaction of a plane acoustic wave and a plane shock

The kinematics of normal and oblique interactions between a plane acoustic wave and a plane shock wave are investigated separately using an approach whereby the shock is considered as a sharp discontinuity surface separating two half-spaces, so that the dispersion relation on either side of the shock and the wavenumber jump condition across a discontinuity surface completely specify the kinematics of the problem in the whole space independently of the acoustic-field dynamics. The normal interaction is analyzed for a stationary shock, and the spectral change of the incident wave is investigated. The normal interaction is then examined for the case of a shock wave traveling into an ambient region where an acoustic disturbance is propagating in the opposite direction. Detailed attention is given to the consequences of the existence of a critical shock speed above which the frequency of the transmitted wave becomes negative. Finally, the oblique interaction with a fixed shock is considered, and the existence and nature of the transmitted wave is investigated, particularly as a function of the angle of incidence.

Kleinstein, G. G.↗
NASA NTRS1974

Variation of the ratio of specific heats across a detached bow shock

Equations are derived which allow the ratio of specific heats behind the earth's bow shock to be evaluated if several pre-shock parameters (the specific-heat ratio, the Alfvenic Mach number, the sonic Mach number, and the angle between the shock normal at the stagnation point and the magnetic field) and the density jump across the shock are known. Numerical examples show that the dependence of the post-shock ratio on the pre-shock ratio is weak.

Chao, J. K.↗
NASA NTRS1992

A model for the radio brightness of the supernova remnant 1987A

The recently observed rise in radio flux from SN1987A is earlier than predicted in models of the interaction with the observed line-emitting gas. The observed size of the radio source is roughly consistent with the expected position of the SN shock wave and the position of the termination shock of the blue supergiant progenitor wind. The radio increase is attributed to the interaction of the SN shock with this density jump. The required efficiency of electron acceleration and magnetic field amplification is larger than usually occurs in SNe and SNR. Possible reasons for the enhanced radio emission are particle acceleration by the weak reflected shock that travels through the interaction region, and the action of the Richtmyer-Meshkov instability near the initial termination-shock density jump. The action of these mechanisms is time-limited; the prediction of this model is that the radio flux should begin to decline within the next year.

Chevalier, Roger A.↗
NASA NTRS1973

Analysis of embedded shock waves calculated by relaxation methods.

The requirements for uniqueness of the calculated jump conditions across embedded shock waves are investigated for type-dependent difference systems used in transonic flow studies. A mathematical analysis shows that sufficient conditions are (1) the equations should be differenced in conservative form and (2) a special difference operator should be used when switching from a hyperbolic to an elliptic operator. The latter results in a consistency condition on the integral equations, rather than the differential, at these points. Calculated jump conditions for several embedded and detached shock waves are analyzed in the physical and hodograph planes. Comparisons are made with previous results, a time-dependent calculation, and data.

Murman, E. M.↗
NASA NTRS1982

Particle drift, diffusion, and acceleration at shocks

The gradient and curvature drifts implicit in change of the ambient magnetic field at a hydromagnetic shock wave are incorporated into the diffusive theory of shock acceleration of charged particles. The conventional jump condition at the shock is modified by a term incorporating the large drift along the shock plane. This term vanished identically for one-dimensional systems, but must be included in general for shocks which are finite in transverse extent or which have transverse structure. It is found that the effect of the drift is such that the transverse drift rate is proportional to the acceleration rate, and for perpendicular shocks is exactly equal to the rate of change of energy in the V x B electric field observed in the shock frame. This establishes a connection with the 'shock drift' models which neglect diffusion.

Jokipii, J. R.↗
NASA NTRS1982

An analysis of shock wave disturbances observed at 1 AU from 1971 through 1978

IMP 6, 7, and 8 data from 104 shock wave disturbances were employed to document the occurrence frequency and properties of the solar wind shock which produce He ion abundance enhancements. The shocks were identified over the 1971-1978 time period and were characterized by a preshock flow with lower than usual average bulk density, a shocked gas layer 12 hr thick, and a postshocked gas layer 1.5 days thick with a high He abundance. A high-temperature peak was found to occur in the first 12 hrs after a He-enriched shock and was not seen when He-enhancement was absent. The total pressure was also three times higher with He-shocks, and speed jumps were greater than 50 km/sec in 56% of the He events. It is concluded that all shock waves in the solar wind at 1 AU originate in coronal mass ejection events, and the presence of He-enrichment is attributable to the geometry of the area that produced the event.

Borrini, G.↗
NASA NTRS1987

On the noncoplanarity of the magnetic field within a fast collisionless shock

Within the magnetic ramp of fast collisionless plasma shocks observed with spacecraft instruments and simulated numerically, the magnetic field undergoes an excursion out of the plane of coplanarity. This rotation is consistently in the direction such that the electrostatic potential jump across the shock, as measured in the de Hoffman-Teller frame of the reference (HTF), is about 2-6 times smaller than the electrostatic potential jump measured in the normal incidence frame. The preferred direction is consistent with a basic whistler mode transition between the upstream and downstream orientations. The potential jump in the HTF is considerably smaller than the change in bulk flow energy across the shock, confirming the recent suggestion that magnetic forces contribute importantly to the slowing of the plasma in that frame. A further consequence is that suprathermal particles leaking back into the upstream region across the shock do not gain much energy from the cross-shock electric field.

Thomsen, M. F.↗
NASA NTRS1981

An analytic treatment of the structure of the bow shock and magnetosheath

A theoretical examination of the jump conditions of the bow shock is used to investigate the influence of the solar wind magnetic fields on the structure of the parameters behind the bow shock. Through the assumption that the average values of the parameters along the radial direction in the magnetosheath are equal to their values just behind the bow shock, the influence of the direction of the solar wind magnetic fields on the average structure of the magnetosheath is determined. From this assumption, a zero-order formula for the thickness of the magnetosheath is deduced which satisfies the boundary conditions and conservation laws of mass and momentum flux. The theoretical estimate of the thickness is compared with satellite observations to check the assumption and select the optimum value of the polytropic exponent of the plasma gas.

Zhuang, H. C.↗
NASA NTRS1972

Comparison of characteristics and shock capturing methods with application to the space shuttle vehicle.

A critical appraisal is presented of a method-of-characteristics (MOC) and a shock-capturing technique (SCT) for calculating three-dimensional supersonic flow. Detailed comparisons are made for pointed and blunt-nosed bodies with a thick delta wing at angles of attack from 5 to 15 deg. The results show excellent agreement between the methods and with experiment. It is established that the SCT code yields accurate shock locations and jump conditions. The SCT code typically requires about three times as many mesh points as the MOC code in order to resolve the bow shock, but the total computation time is about the same. On a point for point basis, the SCT code is about four times faster than the MOC code.

Rakich, J. V.↗
NASA NTRS1973

Distant Bow Shock Observations by Explorer 33

Locations, orientations and magnetic field changes are given for 135 bow shock crossings at distances downstream from earth between 84 and 117 earth radii. The shock locations are dependent on the spacecraft trajectory and agree with locations calculated for the hypersonic analogue for a Mach number of 3.8. The shock normal vectors have been calculated using magnetic coplanarity. The average normal vectors have a greater inclination by approximately 17 + or - 5 deg from the symmetry axis than the Dryer and Heckman shock orientations for a 3.8 Mach number. Over a range of downstream distances from 60 to 115 earth radii, the median magnetic field magnitude jump across the shock changes from 1.90 to 1.70 times.

Mihalov, J. D.↗