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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Symmetry Determining Equations of the Rankine-Hugoniot Equations for Variable Velocity Shock Waves

The “constant velocity piston” problem (Fig. 1), also known as the “piston problem,” is a standard model for a one dimensional, in our case linear, symmetric shock wave moving through an inviscid, perfect gas. The model can be divided into two regions - a perturbed section on the left and an unperturbed section on the right - by a moving shock wave moving left to right. Both the perturbed and unperturbed sections, i.e. the shocked and unshocked regions, respectively, obey the Eulerian conservation equations; however, at the exact location of the shock, there is a mathematical discontinuity not satisfied by the Euler equations. To ensure continuity and conservation of certain quantities when crossing between the unshocked and shocked regions, we evoke a series of equations derived from the Eulerian conservation equations, called the Rankine-Hugoniot equations, or “jump” equations as it is often referred to in the literature on the topic. The classical constant-velocity piston problem assumes the piston features a constant driving velocity (among many other willing suspensions of belief required in the pursuit of a first principles equation model); consequent to this assumption is a constant-velocity shock and a constant-velocity shocked flow state. However, using Lie Group Theory (LGT), also known as symmetry analysis, we can attempt to reinterpret the model with a shock wave of variable velocity in time and space. An extension of the model in this way opens up the possibility for obtaining new analytical solutions to the piston problem for certain shock velocity models. In this report, we use LGT to derive the symmetry determining equations (SDEs), whose solutions are Lie groups, which permit analytical solutions. In the future, we can then use the SDEs to define constraint equations on the shock velocity model and what the successive solutions to the Euler equations might be based off such constraints. This report is structured as follows: Section 2 provides a brief derivation of the Rankine-Hugoniot (“jump”) equations; Section 3 gives an overview of Lie group theory; Section 4 derives the SDEs of the jump equations; Section 5 derives the Euler conservation equations for fluids; and Section 6 presents concluding remarks and opportunities for future studies.

42 ENGINEERING↗
NASA NTRS1975

Incident shock-wave characteristics in air, argon, carbon dioxide, and helium in a shock tube with unheated helium driver

Incident shock-wave velocities were measured in the Langley 6-inch expansion tube, operated as a shock tube, with air, argon, carbon dioxide, and helium as test gases. Unheated helium was used as the driver gas and most data were obtained at pressures of approximately 34 and 54 MN/sq m. A range of pressure ratio across the diaphragm was obtained by varying the quiescent test-gas pressure, for a given driver pressure, from 0.0276 to 34.5 kN/sq m. Single- and double-diaphragm modes of operation were employed and diaphragms of various materials tested. Shock velocity was determined from microwave interferometer measurements, response of pressure transducers positioned along interferometer measurements, response of pressure transducers positioned along the driven section (time-of-arrival gages), and to a lesser extent, measured tube-wall pressure. Velocities obtained from these methods are compared and limitations of the methods discussed. The present results are compared with theory and the effects of diaphragm mode (single or double diaphragm), diaphragm material, heating of the driver gas upon pressurization of the driver section, diaphragm opening time, interface mixing, and two-dimensional (nonplanar) flow are discussed.

Miller, C. G., III↗
NASA NTRS1982

Measurements on a shock wave generated by a solar flare

Shock waves generated by intense solar flares may be driven by a large amount of ejected mass, about 5 x 10 to the 16th g, and the total energy involved may be of the order of 10 to the 32nd erg. The shocks may have initial velocities of the order of 2,000 km/s and, in their exodus through the corona, may be accompanied by fast-moving optical transients, the emission of highly characteristic radio signatures and the acceleration of particles to quasi-relativistic velocities. Here, a review is presented of data on a high-velocity shock generated by a flare on 18 August 1979, 1400 UT, and comments are provided on some previously deduced velocities for the shock. Attention is given to a model, based on current computer programs to account for the overall characteristics of the shock as it propagated through the corona and the interplanetary plasma.

Maxwell, A.↗
NASA NTRS2004

The Collisions of Chondrules Behind Shock Waves

One of the reasons that the mechanism(s) responsible for the formation of chondrules has remained so elusive is that each proposed mechanism must be able to explain a large number of features observed in chondrules. Most models of chondrule formation focus on matching the expected thermal histories of chondrules: rapid heating followed by cooling during crystallization at rates between approx. 10-1000 K/hr [1], and references therein]. Thus far, only models for large shock waves in the solar nebula have quantitatively shown that the thermal evolution of millimeter-sized particles in the nebula can match these inferred thermal histories [2-4]. While this is a positive step for the shock wave model, further testing is needed to see if other properties of chondrules can be explained in the context of this model. One area of interest is understanding the collisional evolution of chondrules after they encounter a shock wave. These collisions could lead to sticking, destruction, or bouncing. Here we focus on understanding what conditions are needed for these different outcomes to occur and try to reconcile the seemingly contradictory conclusions reached by studies of compound chondrule formation and chondrule destruction by collisions behind a shock wave.

Ciesla, F. J.↗
NASA NTRS1985

Computation of three-dimensional shock wave and boundary-layer interactions

Computations of the impingement of an oblique shock wave on a cylinder and a supersonic flow past a blunt fin mounted on a plate are used to study three dimensional shock wave and boundary layer interaction. In the impingement case, the problem of imposing a planar impinging shock as an outer boundary condition is discussed and the details of particle traces in windward and leeward symmetry planes and near the body surface are presented. In the blunt fin case, differences between two dimensional and three dimensional separation are discussed, and the existence of an unique high speed, low pressure region under the separated spiral vortex core is demonstrated. The accessibility of three dimensional separation is discussed.

Hung, C. M.↗
NASA NTRS1974

Interplanetary shock waves associated with solar flares

The interaction of the earth's magnetic field with the solar wind is discussed with emphasis on the influence of solar flares. The geomagnetic storms are considerered to be the result of the arrival of shock wave generated by solar flares in interplanetary space. Basic processes in the solar atmosphere and interplanetary space, and hydromagnetic disturbances associated with the solar flares are discussed along with observational and theoretical problems of interplanetary shock waves. The origin of interplanetary shock waves is also discussed.

Chao, J. K.↗
NASA NTRSDate not supplied

Implicit Large-Eddy Simulation of Axisymmetric and Asymmetric Turbulent Shock Wave Boundary Layer Interaction at Mach 2.5

High-speed inlet flows feature turbulent shock wave boundary layer interactions at supersonic Mach numbers. A canonical Mach 2.5 shock wave boundary layer interaction experiment at the NASA Glenn Research Center was designed for axisymmetric and asymmetric interactions depending on the placement of the shock generator. Four different wall-resolved implicit large-eddy simulations of the experiment were carried out at one-tenth of the Reynolds number of the experiment: (1) Two axisymmetric interactions with shock generator radii of 9.2% and 14.7% of the test section diameter and (2) two asymmetric interactions with 14.7% shock generator radius and shock generator centerline offsets of one-third and one-fourth of the test section radius. For the two axisymmetric interactions, various sub-domains upstream of the interaction, within the interaction, and downstream of the interaction were analyzed with the proper orthogonal decomposition. For all three regions, the dominant modes are streamwise coherent structures with Strouhal numbers based on separation length of 0.15 and below. Fourier spectra of the wall-pressure coefficient for the interaction region have peaks at Strouhal numbers based on separation length of 0.15 and 0.04. For the two asymmetric interactions, the streamwise extent of the separation varies considerably in the azimuthal direction. For both shock generator offsets, the interaction is strongest for the azimuthal location that is closest to the shock generator. Compared to the axisymmetric interaction, the streamwise extent of the separated flow region is noticeably reduced and a substantial crossflow is observed. Fourier analyses of the unsteady flow indicate low-frequency content f or the upstream part of the interaction which is more two-dimensional. Away from the upstream region, with increasing sweep angle and crossflow, the low-frequency content is diminished.

Computational Fluid Dynamics↗
NASA NTRS2002

Energetic Particle Abundances as Probes of an Interplanetary Shock Wave

We examine the unique abundance variations of Fe/O and He/H in solar energetic particles from a W09 event of 2001 April 10, that have leaked through the flank of an interplanetary shock launched from W04 on April 9. Shock waves from both events reach the Wind spacecraft on April 11. During the second event, both Fe/O and He/H begin at low values and rise to maxima near the time of passage of the shock waves, indicating greater scattering for the species with the highest rigidity at a given velocity. Strong modulation of Fe/O suggests preferential scattering and trapping of Fe by the wave spectrum near and behind the intermediate shock. A significant factor may be the residual proton-generated waves from the very hard proton spectrum accelerated by the early shock wave prior to the onset of the second event. Thus, ion abundances from the later event probe the residual wave spectrum at the earlier shock.

Reames, D. V.↗