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All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

On the Exit Boundary Condition for One-Dimensional Calculations of Pulsed Detonation Engine Performance

In one-dimensional calculations of pulsed detonation engine (PDE) performance, the exit boundary condition is frequently taken to be a constant static pressure. In reality, for an isolated detonation tube, after the detonation wave arrives at the exit plane, there will be a region of high pressure, which will gradually return to ambient pressure as an almost spherical shock wave expands away from the exit, and weakens. Initially, the flow is supersonic, unaffected by external pressure, but later becomes subsonic. Previous authors have accounted for this situation either by assuming the subsonic pressure decay to be a relaxation phenomenon, or by running a two-dimensional calculation first, including a domain external to the detonation tube, and using the resulting exit pressure temporal distribution as the boundary condition for one-dimensional calculations. These calculations show that the increased pressure does affect the PDE performance. In the present work, a simple model of the exit process is used to estimate the pressure decay time. The planar shock wave emerging from the tube is assumed to transform into a spherical shock wave. The initial strength of the spherical shock wave is determined from comparison with experimental results. Its subsequent propagation, and resulting pressure at the tube exit, is given by a numerical blast wave calculation. The model agrees reasonably well with other, limited, results. Finally, the model was used as the exit boundary condition for a one-dimensional calculation of PDE performance to obtain the thrust wall pressure for a hydrogen-air detonation in tubes of length to diameter ratio (L/D) of 4, and 10, as well as for the original, constant pressure boundary condition. The modified boundary condition had no performance impact for values of L/D > 10, and moderate impact for L/D = 4.

Wilson, Jack↗
NASA NTRS2007

A Shock-Refracted Acoustic Wave Model for Screech Amplitude in Supersonic Jets

A physical model is proposed for the estimation of the screech amplitude in underexpanded supersonic jets. The model is based on the hypothesis that the interaction of a plane acoustic wave with stationary shock waves provides amplification of the transmitted acoustic wave upon traversing the shock. Powell's discrete source model for screech incorporating a stationary array of acoustic monopoles is extended to accommodate variable source strength. The proposed model reveals that the acoustic sources are of increasing strength with downstream distance. It is shown that the screech amplitude increases with the fully expanded jet Mach number. Comparisons of predicted screech amplitude with available test data show satisfactory agreement. The effect of variable source strength on the directivity of the fundamental (first harmonic, lowest frequency mode) and the second harmonic (overtone) is found to be unimportant with regard to the principal lobe (main or major lobe) of considerable relative strength, and is appreciable only in the secondary or minor lobes (of relatively weaker strength).

Kandula, Max↗
NASA NTRS2007

A Shock-Refracted Acoustic Wave Model for the Prediction of Screech Amplitude in Supersonic Jets

A physical model is proposed for the estimation of the screech amplitude in underexpanded supersonic jets. The model is based on the hypothesis that the interaction of a plane acoustic wave with stationary shock waves provides amplification of the transmitted acoustic wave upon traversing the shock. Powell's discrete source model for screech incorporating a stationary array of acoustic monopoles is extended to accommodate variable source strength. The proposed model reveals that the acoustic sources are of increasing strength with downstream distance. It is shown that the screech amplitude increases with the fuiiy expanded jet Mach number. Comparisons of predicted screech amplitude with available test data show satisfactory agreement. The effect of variable source strength on directivity of the fundamental (first harmonic, lowest frequency mode) and the second harmonic (overtone) is found to be unimportant with regard to the principal lobe (main or major lobe) of considerable relative strength, and is appreciable only in the secondary or minor lobes (of relatively weaker strength

Kandula, Max↗
NASA NTRS1974

Determining particle density using known material Hugeniot curves

A method is detailed to determine the density of particles wherein the closing velocity is known between the impacting particles and a plate of known material. Either the shock wave velocity or the material velocity produced in the plate upon impact by an unknown material particle is determined and compared with the corresponding shock wave or material velocity that would by produced by different known material particles having the same closing velocity upon impact with the plate. The unknown material particle density is derived by obtaining a coincidence of the shock wave velocity or material velocity conditions initially produced upon impact between the known material plate and one of the different material particles and from the fact that shock wave velocity and material velocity are ordered on the impacting particle material density alone.

Dibattista, J. D.↗
DOE OSTI2020

A numerical study of particle jetting in a dense particle bed driven by an air-blast

In this work, the particle jetting behavior in a blast-driven dense particle bed is studied at early times. Four-way coupled Euler–Lagrange simulations are performed using a high-order discontinuous Galerkin spectral element solver coupled with a high-order Lagrangian particle solver, wherein the inter-particle collisions are resolved using a discrete element method collision model. Following the experiments of Rodriguez et al. [“Formation of particle jetting in a cylindrical shock tube,” Shock Waves 23(6), 619–634 (2013)] and the simulations of Osnes et al. [“Numerical simulation of particle jet formation induced by shock wave acceleration in a Hele-Shaw cell,” Shock Waves 28(3), 451–461 (2018)], the simulations are performed in a quasi-two-dimensional cylindrical geometry (Hele-Shaw cell). Parametric studies are carried out to assess the impact of the coefficient of restitution and the strength of the incident shock on the particle jetting behavior. The deposition of vorticity through a multiphase (gas–particle) analog of Richtmyer–Meshkov instability is observed to play a crucial role in channeling the particles into well-defined jets at the outer edge of the particle bed. This is confirmed by the presence of vortex pairs around the outer jets. Furthermore, the effect of the relaxation of the relative velocity between the two phases on the vorticity generation is explored by analyzing the correlation between the radial velocity of particles and the radial velocity of the gas at the particle location.

42 ENGINEERING↗
NASA NTRS1991

Direct numerical simulation and analysis of shock turbulence interaction

Two kinds of linear analysis, rapid distortion theory (RDT) and linear interaction analysis (LIA), were used to investigate the effects of a shock wave on turbulence. Direct numerical simulations of two-dimensional isotropic turbulence interaction with a normal shock were also performed. The results from RDT and LIA are in good agreement for weak shock waves, where the effects of shock front curvature and shock front unsteadiness are not significant in producing vorticity. The linear analyses predict wavenumber-dependent amplification of the upstream one-dimensional energy spectrum, leading to turbulence scale length scale decrease through the interaction. Instantaneous vorticity fields show that vortical structures are enhanced while they are compressed in the shock normal direction. Entrophy amplfication through the shock wave compares favorably with the results of linear analyses.

Lee, Sangsan↗
NASA NTRS1953

Equations, tables, and charts for compressible flow

This report, which is a revision and extension of NACA-TN-1428, presents a compilation of equations, tables, and charts useful in the analysis of high-speed flow of a compressible fluid. The equations provide relations for continuous one-dimensional flow, normal and oblique shock waves, and Prandtl-Meyer expansions for both perfect and imperfect gases. The tables present useful dimensionless ratios for continuous one-dimensional flow and for normal shock waves as functions of Mach number for air considered as a perfect gas. One series of charts presents the characteristics of the flow of air (considered a perfect gas) for oblique shock waves and for cones in a supersonic air stream. A second series shows the effects of caloric imperfections on continuous one-dimensional flow and on the flow through normal and oblique shock waves. (author)

Source record↗
NASA NTRS1981

Predicted and experimental steady and unsteady transonic flows about a biconvex airfoil

Results of computer code time dependent solutions of the two dimensional compressible Navier-Stokes equations and the results of independent experiments are compared to verify the Mach number range for instabilities in the transonic flow field about a 14 percent thick biconvex airfoil at an angle of attack of 0 deg and a Reynolds number of 7 million. The experiments were conducted in a transonic, slotted wall wind tunnel. The computer code included an algebraic eddy viscosity turbulence model developed for steady flows, and all computations were made using free flight boundary conditions. All of the features documented experimentally for both steady and unsteady flows were predicted qualitatively; even with the above simplifications, the predictions were, on the whole, in good quantitative agreement with experiment. In particular, predicted time histories of shock wave position, surface pressures, lift, and pitching moment were found to be in very good agreement with experiment for an unsteady flow. Depending upon the free stream Mach number for steady flows, the surface pressure downstream of the shock wave or the shock wave location was not well predicted.

Levy, L. L., Jr.↗
DOE OSTI2023

Symmetry and scaling in one-dimensional compressible two-phase flow

Investigations of shock compression of heterogeneous materials often focus on the shock front width and overall profile. The number of experiments required to fully characterize the dynamic response of a material often belie the structure–property relationships governing these aspects of a shock wave. Recent observations measured a pronounced shock-front width on the order of 10 s of ns in particulate composites. We focus on particulate composites with disparate densities and investigate whether the mechanical interactions between the phases are adequate to describe this emergent behavior. The analysis proceeds with a general Mie–Grüneisen equation of state for the matrix material, a general drag force law with general power-law scaling for the particle-matrix coupling of the phases, and a volume fraction-dependent viscosity. Lie group analysis is applied to one-dimensional hydrodynamic flow equations for the self-consistent interaction of particles embedded in a matrix material. The particle phase is characterized by a particle size and volume fraction. The Lie group analysis results in self-similar solutions reflecting the symmetries of the flow. The symmetries lead to well-defined scaling laws, which may be used to characterize the propagation of shock waves in particle composites. An example of the derived scaling laws for shock attenuation and rise time is shown for experimental data on shock-driven tungsten-loaded polymers. A key result of the Lie analysis is that there is a relationship between the exponents characterizing the form of the drag force and the exponent characterizing the shock velocity and its attenuation in a particulate composite. Comparison to recent experiments results in a single exponent that corresponds to a conventional drag force.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1976

Annular arc accelerator shock tube

An annular arc accelerator shock tube employs a cold gas driver to flow a stream of gas from an expansion section through a high voltage electrode section to a test section, thus driving a shock wave in front of it. A glow discharge detects the shock wave and actuates a trigger generator which in turn fires spark-gap switches to discharge a bank of capacitors across a centered cathode and an annular anode in tandem electrode sections. The initial shock wave passes through the anode section from the cathode section thereby depositing energy into the flow gas without the necessity of any diaphragm opening in the gas flow from the expansion section through the electrode sections.

Leibowitz, L. P.↗
NASA NTRS1990

Evolution of a superbubble blastwave in a magnetized medium

Researchers investigate the effects of interstellar magnetic fields on the evolution and structure of interstellar superbubbles, using both analytic and numerical magnetohydrodynamic (MHD) calculations. These cavities of hot gas, surrounded by shells of cold dense material preceded by a shock wave result from the combined action of stellar winds and supernova explosions in OB associations. If the medium in which a superbubble goes off is homogeneous and unmagnetized, the blast wave expands isotropically. As the interstellar gas flows through the shock, it cools significantly and gets strongly compressed such that thermal pressure remains approximately equal to ram pressure. Hence, the swept up material is confined to a very thin shell. However, if the ambient medium is permeated by a uniform magnetic field B sub o approx. 3 mu G (typical value for the interstellar matter (ISM)), the configuration loses its spherical symmetry, and, due to magnetic pressure, the shell of swept up material does not remain thin. Researchers found the following qualitative differences: (1) Except in the immediate vicinity of the magnetic poles, the shell is supported by magnetic pressure. (2) The refraction of field lines at the shock and the thermal pressure gradient along the shell both contribute to accelerating the gas toward the equator. The resulting mass flux considerably decreases the column density at the magnetic poles. (3) Away from the poles, magnetic tension in the shell causes the field lines (particularly the inner boundary) to elongate in the direction of B sub o. In contrast, the shock wave radius increases with increasing theta. (4) The reduced inertia of a parcel in the polar neighborhood makes it easier to decelerate, and accounts for the dimple which appears at the poles in numerical simulations. This dimple also results from the necessity to call on intermediate shocks in order to insure a smooth transition between a purely thermal shock at the poles and a magnetic shock in the rest of the shell. (5) The shock wave propagates faster than in the absence of magnetic field, except near the poles where the reduced mass of the shell allows it to be more efficiently decelerated.

Ferriere, Katia M.↗
NASA NTRS1993

Some aspects of the aeroacoustics of high-speed jets

Some of the background to contemporary jet aeroacoustics is addressed. Then scaling laws for noise generation by low-Mach-number airflows and by turbulence convected at 'not so low' Mach number is reviewed. These laws take into account the influence of Doppler effects associated with the convection of aeroacoustic sources. Next, a uniformly valid Doppler-effect approximation exhibits the transition, with increasing Mach number of convection, from compact-source radiation at low Mach numbers to a statistical assemblage of conical shock waves radiated by eddies convected at supersonic speed. In jets, for example, supersonic eddy convection is typically found for jet exit speeds exceeding twice the atmospheric speed of sound. The Lecture continues by describing a new dynamical theory of the nonlinear propagation of such statistically random assemblages of conical shock waves. It is shown, both by a general theoretical analysis and by an illustrative computational study, how their propagation is dominated by a characteristic 'bunching' process. That process associated with a tendency for shock waves that have already formed unions with other shock waves to acquire an increased proneness to form further unions - acts so as to enhance the high-frequency part of the spectrum of noise emission from jets at these high exit speeds.

Lighthill, James↗
NASA NTRS1983

An experimental investigation of multiple shock wave/turbulent boundary layer interactions in a circular duct

Detailed pitot, static and wall pressure measurements have been obtained for multiple shock wave/turbulent boundary layer interactions in a circular duct at a free-stream Mach number of 1.49 and at a unit Reynolds number of 4.90 x 10 to the 6th per meter. The details of the flow field show the formation of a series of normal shock waves with successively decreasing strength and with decreasing distance between the successive shock waves. The overall pressure recovery is much lower than the single normal shock pressure recovery at the same free-stream Mach number. A one-dimensional flow model based on the boundary layer displacement buildup is postulated to explain the formation of a series of normal shock waves.

Om, D.↗
NASA NTRS2004

Lunar and Planetary Science XXXV: Chondrules: The Never-Ending Story

The session "Chondrules: The Never-Ending Story" included the following reports:Dust Size Distribution in Solar Nebula Inferred from Shock-Wave Heating Model for Chondrule Formation; Collisional Destruction of Chondrules in Shock Waves and Inferred Dust to Gas Mass Ratio; Evaporation and Accompanying Isotopic Fractionation of Sulfur from Fe-S Melt During Shock Wave Heating ; Evaporation During Chondrule Formation, Recondensation as Fine Particles, and the Condensation of S and Other Volatile Elements; Fe Isotopes and the Formation of Chondrules; Pristine and Processed Metal in CR Chondrites: Condensation in the Solar Nebula and Partial Reequilibration During Chondrule Formation; Variation of the Condensation Path of Supercooled Silicate Melt; Volatile and Moderately Volatile Trace Element Composition of Chondrules and Matrix from CM Chondrites: Implications for Chondrule Formation; Opaque Mineral Assemblages at Chondrule Boundaries in the Vigarano CV Chondrite: Evidence for Gas-Solid Reactions Following Chondrule Formation; Forsterite and Olivine in Sahara-97210 (LL3.2) and Chainpur (LL3.4) Chondrules: Compositional Evolution and the Influence of Melting; The Vaguries of Pyroxene Nucleation and the Resulting Chondrule Textures; Contemporaneous Formation of Chondrules in the Al-26-Mg-26 System for Ordinary and CO Chondrites; and Al-Mg Isotopic Systematics in Ferromagnesian Chondrules from the Unequilibrated Ordinary Chondrite.

Source record↗
NASA NTRS2008

Initial Results from the Variable Intensity Sonic Boom Propagation Database

An extensive sonic boom propagation database with low- to normal-intensity booms (overpressures of 0.08 lbf/sq ft to 2.20 lbf/sq ft) was collected for propagation code validation, and initial results and flight research techniques are presented. Several arrays of microphones were used, including a 10 m tall tower to measure shock wave directionality and the effect of height above ground on acoustic level. A sailplane was employed to measure sonic booms above and within the atmospheric turbulent boundary layer, and the sailplane was positioned to intercept the shock waves between the supersonic airplane and the ground sensors. Sailplane and ground-level sonic boom recordings were used to generate atmospheric turbulence filter functions showing excellent agreement with ground measurements. The sonic boom prediction software PCBoom4 was employed as a preflight planning tool using preflight weather data. The measured data of shock wave directionality, arrival time, and overpressure gave excellent agreement with the PCBoom4-calculated results using the measured aircraft and atmospheric data as inputs. C-weighted acoustic levels generally decreased with increasing height above the ground. A-weighted and perceived levels usually were at a minimum for a height where the elevated microphone pressure rise time history was the straightest, which is a result of incident and ground-reflected shock waves interacting.

Haering, Edward A., Jr.↗
DOE OSTI2020

From Interstellar Cloud to Star to Laboratory: Frontier HEDP Studies of Magnetized Colliding Plasma Flows with Strong Radiative Cooling (Final Report)

High-speed flows of gas are the norm in astrophysics where exploding stars, winds from the regions around black holes and streams of galactic material create “supersonic flows”. As the flows collide, strong shock waves are formed where gas is compressed and heated. The regions behind these shock waves are of great interest to scientists. New stars can form in these shock regions in the context of galaxies. In the context of planets like our Earth, the shocks waves come from the interaction of the solar wind with our planets’ magnetic field causing Aurora and placing astronauts and satellites in jeopardy. Thus, understanding supersonic flows of magnetized plasmas is essential for progress in many fields of astronomy and space physics (relevant to planets and the Earth). Remarkably, we can also create these kinds of flows in the laboratory using Z-pinches and laser driven experiments that include magnetic fields. The exploration of these forms of “High Energy Density Physics” (HEDP) flows is also critical in order to achieve Inertial Confinement Fusion, which is a step towards developing a sustainable source of Fusion energy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Air-coupled tsunamis generated from impacts and airbursts: Our understanding before Hunga-Tonga Hunga-Ha'apai

The effort to prevent or mitigate the effects of an impact on Earth is known as planetary defense. A significant component of planetary defense research involves risk assessment. Much of our understanding of the risk from near-Earth objects comes from the geologic record in the form of impact craters, but not all asteroid impacts are crater-forming events. Small asteroids explode before reaching the surface, generating an airburst, and most impacts into the ocean do not penetrate the water to form a crater in the sea floor. The risk from these non-crater-forming ocean impacts and airbursts is difficult to quantify and represents a significant uncertainty in our assessment of the overall threat. We are currently working to better understand impact scenarios that can generate dangerous tsunamis. One of the suggested mechanisms for the production of asteroid–generated tsunamis is by direct coupling of the pressure wave to the water, analogous to the means by which a moving weather front can generate a meteotsunami. To test this hypothesis, we ran a series of airburst simulations and provided time-resolved pressure and wind profiles to use as source functions for tsunami models. We used the CTH hydrocode to model the various airburst scenarios to compare to the results of other simulations and provide time dependent boundary conditions as input to shallow-water wave propagation codes. The strongest and most destructive meteotsunamis are generated by atmospheric pressure oscillations with amplitudes of only a few hPa1 (mbar), corresponding to changes in sea level of a few cm. The resulting wave is strongest when there is a resonance between the ocean and the atmospheric forcing. A Proudman resonance takes place when the atmospheric disturbance’s translational speed (U) equals the longwave phase speed $\sqrt{gh}$ of shallow water wave. Coupling is strongest when the Froude number (Fr=U/c) is unity. A weather front propagates much slower than the speed of sound, so meteotsunamis are most common and dangerous in shallow bodies of water such as the Mediterranean Sea or Lake Michigan. By contrast, the blast wave from an airburst or crater-forming impact propagates at a speed faster than a tsunami in the deepest ocean, and a Proudman resonance cannot be achieved even though the overpressures are orders of magnitude greater. However, blast wave profiles are N-waves in which a sharp shock wave leading to overpressure is followed by a more gradual rarefaction to a much longer-duration underpressure phase. Even though the blast outruns the water wave it is forcing, the tsunami should continue to be driven by the out-of-resonance gradient associated with the suction phase, which may depend strongly on the details of the airburst or impact scenario. The open question is whether there are any conditions under which such an airburst-driven tsunami can be dangerous enough to contribute to the overall impact risk. We have also identified other potential mechanisms for airburst-generated tsunamis: 1) reaction force at the surface from the plume ejected into space, which carries significant momentum, 2) expanding toroidal vortices at the surface, which travel more slowly than the shock wave and can generate a Proudman resonance in relatively shallow ocean (such as continental shelf), and 3) steam explosion from seawater ablation by a “Type II” (Libyan Desert Glass-type) airburst in which the hot vapor jet descends to the surface. On January 15, 2022, the Hunga-Tonga Hunga-Ha’apai volcano, located approximately 60 km north of Tongatapu, the main island of Tonga, violently erupted with a powerful explosion, culminating the period of volcanic activity that started in December of 2021. This event and resulting tsunamis provided an existence proof for the air pressure wave coupling mechanism we proposed. It also suggests that it can be stronger and more significant over much greater distances than we contemplated, leading to global tsunamis associated with impact events on land as well as in the water. Large atmospheric explosions generate global Lamb waves with larger amplitudes, longer periods, and slower speeds than the local and regional blast waves we modeled prior to that event. This paper reviews our analysis and modeling of airburst-driven tsunamis prior to the 2022 Hunga-Tonga Hunga-Ha’apai tsunami, which was the subject of two presentations at the 2023 Planetary Defense Conference and is the subject of another paper currently in preparation.

54 ENVIRONMENTAL SCIENCES↗